eaeceebdcaeaacedadabcaaceeaeedadebadbdeaeebbbedbecaeddcecbdebcadbbeaabdbcddacbcdbbaebadbccecaedbdebdbdbceaadbabaedaccccdccdaedeedbdacccdababaeacbbbaeabbcdbcbcacaddabeacaaecececbaaecbaedeadcbbacdedabacbdedeaeadcdbabbddbcbedddaedaaaaddeaeeacdaecddcdabbcdbbdcdeebabdedadbdeddabaebabaaebaadeaeeceecbaeecdabaeceacedaabcdcedbecdbdbccbdaedeaacaddcdaaccbaadededcedeabbbabedabbdcbacbaaecadcbeedadcbeadbdceecdcecacedbaabaaeebedbcbeeaceecddacacccbbeedaabedbbdceebdbbbeebaeaabbedabbbbcaddcbecdcaccbcdcabedeabeaeddcccaccebecccdabeecbddaecdbccdcabbebeeceecadeebaaddbebcebdabbcbecbbceeabbddbedbabddeddbbdebadbeceadccacbadcbdcaebdecbdaddaaccceececeaaabcaecceeccdcaedcebbdeabbebdbdcabbceadceceeaddacdbaecebecabddaddbcdddddbaeeecdbdddadaeececbcceeabbeecbcebccacddcacdcdecddacdbeabeecebdcaaddeabbbecedcbdeaadaebddaabbdcaecaddeebeadcdbadddadabddaadedecccbaeeabaeaebcaebcdcaebeebdbceccdaccbabeaabcddbdecadaaadcbcaebebceccdbceaedcaedbaedcdcaebbbeaabcddeeeacbecdeaeeeebccdeebdebcaaeeeceadadcddceaaaeeabdcadededbdeabeeaeaabbacaedadddccbadcdaecabdbbccaaebeccbddeedccbbdcabbcdaebdbeacebaaadbcaebbdbdedcedceccdeccdebdecedebdcaabebcebcddccaeedebeabbaacaaaaecaedddcbabccddaeebaddebaedbbdaeedcebdaeccebdcdabeecadcadedcccdbdeedaadcbedcbabaedccababebdeeeeeabdeceacdaacdbcecbddadabebcbacabeccbebdadcbadeccabbcbebbcacaeabecadcdeddebaeabbbaaeaaceacaddbadeadadbdadaacdcdeaaaeddaadcebaaaceccdebbaacaeeecbbeddaceccaebaccacbbcbabaabbdddbcbcbbdaaecebcadbadcbcddedeebcbbbccbcaceaecaeeeeacebcaebadeecedcdebaacbbedeedbcdddababcecdedcabecdecacdbaceedbeaaeabaeeabacdceabdbbbbcdbbadbaadebbddbaacdabedbcedcbeedaabdeedaecaaeecdcbbbeacbeaaeacecdbeedbcdcadbccdcbebadabeadbdbcbdbdcaeeadbbaededbdabcadddcbcbbdeecdbbbcaebdadaaaceceaebbeadabeeadccaadcbadcdaebaaecadbcabdadbccbeccdeacacadcadaddddcdadacbbcdabaabaababcebadadeebcebcceacedcaadcedecdcbdbaacebdbbbbcdcbeaaeceedaaaeecceddebddbaeaceabeabecddabdbdaddacbabdadddaeccdebbbbedcaaddddccedaecbaebecdaaccadabbaeccadabbcaddddeedabdeeccebcabacecaaccddabceaabcdebeceeaeedbebcdcbdabcaabceaaaccdcdcdcdaaebeeebaaeddeabacabbacbadaaeeeaadecaadacbcbbdedbecbdbbdbdcceaabeaadedddcddcacbbdccebdedbabbcaedbaeaaebaccccdecdabccedbedcaeaaacdabdbabcdcedeccbdeddcbaaacedadddeeeaeedecabcbcbdbebdcccaaecedbadeccbaeabeabcbbdbbeaecdededddabcbddcacbdcaadabaddddbbdbcebecadabbcbbacaeececacccaebbcccdcecebeaccdbcebedcbebdcddbadbbbcbadaebebabdceaedbebbebcdcadebebdbbecbddedabbacaabbcecadbdeeaabbbbaeebacaeeaaacbbeadcedebaaebeedecbecbaabebdadcbeaeaeaeecacacbdcbecaeebdbaeaebabcdcadaaaaecbebadbcaeceeebdacaaebbeabaacaedabdecebbaebeacbbcdddcbddcbbaeababbceeccccddbccddacbccbaaccbeadedcaaeedccadebcebbdebccceeaeecbdabdddaaaccdacdabecabcecbdcabeaecddaaaaccbdadeecebccdadaeeacaddbddaaebebcccdbececbdbdbbcbdcaecbebddaeabbbbacaabeeeeccbbdaccccaacdedaeabeddcecbeaededdaccadedcedeadacdcbcdabcacccbcaeeebbadcadbccecbecaeeceeaacdadcccddebdccbbeaedcaddbbddabadaccedaeaabbedbadecbedbdbdcebcaebcacccedacdcdadcaabedebebaadabeecbddaacbedeaaddcebbecbcdcdddceedbcdcecacebbecebdecaedecdcacdecaccbaeacabaaabcbeccccdcbdeeacedbcaadaeeddcdaebdaebaddeccaceeacdaebdddadaebcbcaebcbeeaedcdebaaeccccddbeebccaabbccaecbadabecebdbcbddceadbcbbdcabebeebdceeaaabaabecbadcedbbeaceaeadbbbbbbedcbbccbccbbaaccdbaeaccbddbacccdedcdabcdbddbeaeedaddaabcbeccbadebacedcdacbbdaceabaaedeabaaabeeacbbedaedcddeeeaaadbaacabbbdceeccccceeebbedbbdcdbaaebbbdbebdbdaabbeaeebacdbaddeadbdcbdacdecbddeeaeadbebddcaceeaedeeaedbdbcbcabebaaaddeddabaebadbbbeeedaedbdbbadebeeaacceadeabbccdcbedacdaaaeeebbcdadedcbccaccaedaecbeeeddbcadbdecebecacdabccdddbbeaecacbbdeebdeecdcdbeebecbddceeeddeebdbdcbebaadadaacbebcabcaccecacceddcdeaeebbcaeeecdcababdeacabddbbceabbeeeddaebbcdccadbeecaedcdbeabdbecedccadccbeeaeaabcaebdcbccbecdbddadabbacbdaccebeecaedbbcaeaadaacacdebeeabeddbdbeebadbceeabeecaecebeebcbeccaeedeaebddeeacbaeecaccedbbeebaaededbddbdadccbeebcddeeaabededbedadecebaeeabebbddccbbbdeadbdbddbccadebbdbededdcaecbebdcbabecdbbeeccdbbcaadaeaceaebdebcdbbedeeddeeecceebdaedaedecccecdcdacecabddaebbbcccccbcbecbdceabedcbbdbbddeddeadbbbbcadccdcdbceeadedabaccddbdaddbcaaeedbecaeabbebadbbabedecabbecaaceceedcacccaddadeadddacdcdaedccecaeeddbcabccdeddcaddedccbdbddbcbaeebdcbbbbadceaecbcdcadbaebcdeecadcecceaeeccbebcbbebcaaebaeadbaddeaecebcdadedcaeaabcabdcabbbdecabcedeaadcbdbacbbadbdccacbdbddecbebcbdadcbbecaeddbbebdedabebccaebcdeecedebabdbbcdbbbcecaeceaddaddcdbdaccccebadbddedccacadebcccaecccbdccebeeaedddeacdaaddaebbabccaabceedebebeceaddecceceaabbbdcaadeadddadaccadeabaeeaadadcadceceaadebececcecdbcccaeacbbebcbedbeeaddedbbbcedaeebeedeababdacebaaedbcdcaebbcecbebdedcedbeadcbddbeacebcedaaecaeacbcbbbacdcbedeaaedcebdeeabadebdbbccdadabacbaeaededbcecdcbdaaeecebaadecaadccdcddccdebddddbbdbceacccceccedddcbdaeeddccaaeedabeeaadaadcedcecdbebadaceadddbcdbbebeaadbababebeabccdccddcabcadeababeaebbbbdebbdcdeacbbbbdadbecaecdccbaaaababbbcbbcaddbadcdeddbdcbabdeccdaddabddedddddeadbedaebeaabdececaeacabdbbceedabcaaabcabebcebdedacdbaddeacbecdbebbecbeddbbebddceeeddebdebcdbccdaaebceaeeecbceddcebadabbeaeabadbcbeacccaadaeeecdcdeeeadecbdbddebbbceedaceddedeaedcdcccaedeceedbdbcedccdabdcabceaeadbdacadbdccbccdccceddcaaaeccbceacacbdedbaeabacbaabceaecbeaeeeabdaaeadaaaebadadaeebabbcdedebccabddbeadecaaeedbaccbbadddaebeaceaaebecdbabadbddedaaaadaecacdeedeaedeacbedebcdebdacaedadebacddbabddceccdacddccccadbaadeeaaedddcdceeddcabcbcbebedbbaeaeeaabadabcaecabbaddebeeeadeacaaacebdcbedbeedadeeeedbbbedaebecbdeccdecdcecebeeececdaaeeaeccdcbddcddadeedddcabbabccccdbabaaccedbabdebbebccedbedcbabeccccdadbcadecdacedadcdcceedccccbdbddeaddeebbcbaddeddeeddbbdcabcbabdeccadeddaeebbbebcdcbddcdabbbcdcccbdeaecedccddcebcdcedceaecddbcebadbdcbccdbbbcdcdccedddeebebcdaececeacddcddcdeebabcadbadabaadecdbccacedcaaecedebedaaeccddaadceccaeaadcbcadaebbeececccacdcebdccccdaaacadcadbdbbedaaabdeedeebebbecaeadbabecbbedecdceeebcddedebdeecaacdaaaeadbeeedbeeebbabbbbdcddecbcebaecebddcdddceecdeeadbdbcbaceccbbabdbdcedcbeedbeabebdbadbccedbdebaecbacdadcaedddabcedbdbbaddecbebdecaabdedaeacedbceaaacdeedbbcacebaeaeeddbdbbabababcacaeeabbcceaecdbbeebacceddecadebedbbaaaeeebccecdacbecbbaaeaaadcddaebbadeecdaeabbaedeaddbcececbcaddbaebdccbdceabebacebcddddbceadddeabbedcbeeaedacddcecedbbadeeacabbcebdcdedbebdecdaabecadbdedeaeababeebaeadacdcbbeedbbeececedadaccaacccdeeddddbabcbddeceadbadaaeeacbbadecacbbdbcaadadadbddbebbbbecceededadbccbedadaacbaacabaaeccbbdaeaaacbabadbbcddeddeebcbeeeacceeeccaecbeabbeccebacbadbdadeadadbcecdaedebbccdecaebaecbdaabdaadccbddeedddcdcbecdeeecbeceedccbdeebbeaaedaeeddaecceadceccbbbdcecebaeebdccbeacbedeebbaaaeddbdebeedcbbdcadcbbcbddadcebbacadeacddacccdcbdbeedebdccacaedbaeaaabdabeedbbcadbdabceeeebdaddbcaaeccabcdcaeccdaddcbbacadbbdcbdeeaebeaecdceacaccbbacbaccbbaabccdbbddabadbabeeebcebbecccbeeaaedebbbdcebadedbdeaeabddcaedbceebebcecbbeddcbcabbdbbeeedccedbeaeebeddddeabebdbebdbebadbbdeebbeaaaceecbeddcdabceccabedccaaeddebddbbcbcabacaeaadadebeabbcaceecebacecbdaadbaabeaccbdabdeededdeaacedadbdbeacdbeccacdbadccecdccbbcdabcdabeabbebbebedbdaebbeabbbbccddcebaeccbadccabaccecbecebbbcacbbcbdddcedecdcaebcbaedbeeadaacdcbecdcaaccdddbbecceccebbaebabcdbdeaeeeebcedbaebbabeadedcdacbbbcebaaceeedcaceadebcdcbeedabeddeddcaadebdbaeaaeadddbbddccdbabdbedacbdaceeaabaaebebcceccedbdcaacccdabdcbdedddbcbcaecaebbaaecddcdadaadeccbacbeebebaecddbceeeecaaeddbbbbdbdcbacadaddaabbdebcbcececedeedbaeceeeccaddceadbdbdbcdbedecdeeebebcbdbcdedadabecdcdceecbbbdccedecbcadbeadadccabbdceeebabdbdcaeccedaddecceadcedaabdcceacdcdeeebabddccdbbeebbaebeadcedeedbcbdcaecadbadbbdacebeaebccdecbaabaccedcacaedddbbebcacdbdeeaecccbddadebdecdeecedccaeeedceeeebcadeebbedaeaedbecdceddabacecbcbeddabbcdcebdbcadeedbceacdcbaddcecebdaeacbeaeeaaacbbdadcccdbaaebaeebbdeadeeabdddaebbdaceaaacebeeecacaabcdacdcdadbbacebddaadeceecbbdceccacdeebabbdbdbdbdabaedabeccbacdbbeaaaddadedcbcbdcdaaccdabedcdeeadbbbdcbcedcbdbbeaebdbeaddcacebcaebaeedaebaadeccadababbbabaeaebbcdbacededdbdebbdccbaadeeabcabdceaeeecbebbaaaadadaeebbeddabeaeebbabadcdbbcceadaccadabceaeedeccdcadcbbbdaeeebabaccdbcbdaadbcbeaaacdcdcaccccaaeaddcacaacbedaeddadaabeeadcdeeadebdcddebdaaddaaaecebaeaecddcdbbdcdceeddaceccdebbabbccbbcecdbaacdceebbcaecedbcaacedacebcedccbdbbcbaddbbabdbccdbeacebbecaececcdccccdddccabeacbacbeaaedececacebceadebcbadceedcdbaaceebceebbbbeddbaaecdaaaededeccddaadbaecbcdbabbddbcbcccdebbdedddeaddccaaedcbcdacaaeddcecbbeacacebaabedeaecdbadeadadbdabccabbcbaacdbdcecbeceebcaaaabeddadcebebaedccbabccadeebcaaeeadadebceccacbdcdccbedeedadcabbedddaecbbdbebbedbaaeaaeddddbeeadeaccebdabdcbacacbedabeababbdecabbcbdcceeadaecdcadaddbbceabbddcdbcdbdcecadcaeaceccdbbebeeacebdeecaceeedcadeceebcaebaedaabcbadadcccbcaaeeaeceeabdabcaedcacdbacbabbeeaaeedcedcadadcadaaadabdecaedaaecabeaccccebececceaebaceaaeabdbaacbaacaececadbccdaaadccebaadadcecdedddadaddaceaadaabadadacdcaebabadeddedaaadacebadcdbdcdcddceedecbcedbbcaacabdaabaaecdcceedeccbccbdbdaabeacaedcbabeadbeddcaabacdbbbcdcaaaceacdddeabbbcdabbbbedbcacdaecdbaeebeacbdebeeecbebccaddebdbcabedbbbaccaccbbbcaabddcadaaebbacdedcdadcbeecbbdaaabbeebbceeadcdcaccbacabdceecabedaabdcebbdedebebedcedcdabcacdcbdedebcaaedadadacceaceebdcebcbedcadaaeebaeeeedabaceceaecebbccbcbbbedbebabeeebabccccdedaccdabcbaebebdadedacdedbbcdeaeaeaaecbbdedcbdaccdaeadaebaeeadbbdaeecadeaaebededabcecadaeccbbedeeddbbcebaeccdbbeadccdeaeeeddbcbcaacbdaedebbbaeeaeaeaeeebddabdeaaedecadccabacbdacaedeceddecbccdbbacdcebcdaccbaacadeadeadbacbebecabababdaededbaedbbcbaedabcbcaedcedacdceeaacaddacebdcedaceeaaeacdbdaeaebaaabdccaebdabdaacdacdeeddeaacccddecddcbcecdacabbbdbaaadcdebabaddeecdecacddabbdeaeaccbbadddaabedcbeedadcdecddbbaadceeeeccdeabeccadceebceccacaeddeddbddddccecebbceaecacbdcabbdaccacecbbbcbcdebbcbcaadcdedaabbeeddaabadaeebebdceedecdedbbadcecdecbbcceaceedaedccdcdaebadbeabeeaebccaeeacbdccddcdeaeeeeaaaabaaccdabceacedaabdacecdbabedacdbcabcaceaaeddabecbedadecdbecdabdabcabbaaaddbdabbbddbeddcbbadaebddacaecaeedbcedbeeecdddabeeecdccdedbaebaeadbddcddbeebacadebeaeddbcebbbeadcbdbccbbaaaabbdabbeeeddeddadcadbabcddeabccbebdeedbaacdeadbdccaabecaccdedcabbbbbeaceccaeaabcbeebebebcdeaaccaaadcbccbbcaccbebebaddeceabbbbdecaecccadaebebddaecacebebdaabaaacebbbcccdcaedecdbddccccedabcdaeaedccaddbcadbcdedbbbedaeceedaceeccaadeacdedddedcbeedaacecdaaeebcccccbccbdbcabbddcddbbaadbdbadcccdacbabcecceacecbedacdcadabdcbbbaaacbcbecebeaadaceceecbecbbaedcbddbcdeddbedeccdddeaacaadadbeedadcdeabacabecababdccdedbacdbdbcabcccdbaccdcebdaadcbceabbebcbbeccdceccedbbdcadbbcabebebbcacdbcdeadcdcdccacddcbddcbebcebaacabbacbbeacaddccdbbccdcbbecebacccecaabbdcdabaadceedbdeddcdddeeadbbcacddaacebddccceddbbbbacbbbddddcebddbbadacbbbdaccbeacedcaedccdadaadeddcebcdddddecacbdedaeeeeabdcaaedadbbbaacebcbeaaddcdbaebdaceecaddadaadacdbebedbdccddceaaecccdbbcbcedddabdbdacebeabbbbbbaeeadabbabbecbacbbeceacebdecbcdceacbbabebbbedccbabecbdecaeaeacacddcddaaaceeeceeeeacdccbeaceedbdbdbaabbabccedeebadbacbddbbceeccdbcbdacbbaebadabdabdeccbbddaddaabdebdccedcbccaccdcaaddeeeedeebadecbababeeeebeccdabbcebddcbeebddbdbbdcdcedbaccdaadcaaaeebaceebbaedbecaecababbbaacdbebedecedacdaebdeccdcccabcbddeaeebbadedccbebbbebdbcbabaaeabcadcebbcaddeeeeecedaadbaebbadebceadcccacbabcdddcbdabeaeebeaceeadabedbaaeccdbdddbadaecbabaecdadebaabecbdbcdcccdeeecadbcbabcdddeaccacbceadeeacbbcabbcceeeccccededceeacbdcaaeddddeadddaedeabcbceebabecedaadcacaaebccdcebedeeaababeaeeadbeddeeebcbeddeeadedddcdcededeebadaabedcacadcbcdcdabceddbdaadebbcacecbcddadadabcbdcddaabbeeedaedcdaaedaabdcacbbeaeeeeccdcdadbcecdcbcebeeaeecdebacdaddcdecaccdbbbcbcadeaeebdeabdcbcbeecddccabceaeabbbdabadceaeeceadbeaebadbcdcaaceeeddacdcccdcdbaeaaabddaaaccceaadbeacbaeabaaabdabccacdbebbbdceeceaddbcdadaceabeddceecaccdceecacecacecdecaeadacacdcbcdbbadadecdbddbcebabebadaedcaaadebecabedabdbbacbdbcecdabbcdeeaeeceacdaeccbeeadebcccbeeecdabcceaabaeecaeebbeebbcecbbbeeebcddadabceeabcddbeedbdbcaedeabcccdcbcecbbdcdbdccdabcadacbbcdddecaeeaededcdcbaecaabbddeecadcabeeccdeeaabcabacbceabbdadcceabbeaabacbaacebecdbdcadbcccdcbbcadeedacecdbbaeedadcddddceeabebeaebcbbbddcaaadeabaacddbabdceebbdadbddaadecbbabbcdaaaededccaecbabcadcaebddecbbaabecdecacabaccdcaccecdbeeaadedbecabedcdadbaecaceabdabdeaeacbdbbebcdbdeecebadabdabacddbcdcdacbbeacebbaebcbcceedacbccddedbedbebbbcbeceacbdddcdeababdaebdacdeddbeccbbcddaaaaddecabccdbdbeebcdacbabceeaebbacccebdddadcdbdecceaadccdddcebaccdddddbdeeabdbeabaddbbdeeabcadbdcbddeeacdeacdabbcecdbaeebcaedcbcbbdcbbdaceacdddddacaccdbbcdededeeedaeadececabccbabeeebcccbeeaeceaaeecccdcdccacbdecaccadcaabdcecccabccdadadcdcbeacaecacbcbeacabdcecdcbdddbacedceccddbcbbaadddbdbedacddedcecdaabcaebcccadbecaaabeedcbeebcebdcbdeedcaddeedaecdcedecaeaddaebbccadabebbcceaadeeaacabaeaccddecdbbcddeabbdeabaccddbeaeebcdcaabdddebdeacbeeaeaedcbeebadbbaabbbbaceeedaeecebbdedbeaecdaabdcaddecacebaebacacadaeeddddaccdcadbdaeddeeacdcacbbbcebcbebaebdddacdeddbeddcdadeeddcdbdecacbcacdcabbadbbaaaadedaaccaecbdacdcacedbadeacededccbeebedadaeddbabbceacedeacbacbbadcbddcdecddcbedcbdebbebbceccbcbadbeaddaddcdcdeceeecbccdcdcabcacdcbedaeadcaebcecedacdbdeeaebbbdecacebeecdceaccdbeaecbcaaedbaedbbabbbcddeddbbdbaecaebeebcbeccedebacdeebcccaeacecedaaeeaeeabdebcaebcecedacddbbeeceedbdaabaeedaeaeeabebbeddbbbecdecbeacaccbacceadcbecadedacacdcacaedcacdbceaecbdcaaccaabacbdabaddbeadddabedcbeddedbeeadcdcabddeadbbbbabdcaeaeeaaccabcaeadacadccdaedabbbdebaeaedebdbdacececdbbcecaecaaeaeeedcaedaccddaaddeabdbcbedbdebcedcbaeeacabbdeecadebbeeeabeecccccbedeeaebcaabeaabebbabaeaddecbcebbeccebccbdcbadbaccbedadaaacebedcdabceaabcbeadacdeaebeebbeecedbcbadacaabaaeebcedbcbceeddcaaddeabbbbddbacccacdbbeddbcacaabcbeecdbeebdcabcbdbaebccbdbcacbbcebdadccdeaabebddeebccbaacdacccbbcaaabddcbaecedaceacbaebadebcebcaddcabcbcaabdeeaceeecddeccaeacccdcaebbcbeadbbcacccacaabcebbebaecebcaaebdacbbdcbaccabdeeaedaababbbbaeebaadeeeaccbaedddadacaddebddaedaacdaecacacbeeeddeeabddedeccccbeadcebdacbdbacdeeeedccabceddbdadcadeabecdddeaddadbaceddebdbdbdeecdcbdeaebedabbcceadbeabacdabbcceabeeaedbceebddbaaaeaeecedcdebddaeddabaedaeeedcbabacabaeabeadbbadedadbdbeedeedaeeeadabadbaedacecaebddbeabeeecddebedaecdebadeecbaaeeddaebecbbabababddaaaebadaaaaaccababadbedbcebabbeeeedecdebaeccddbebeacacbbdbccedbccacacbbaacdacbbbcaaacdcbdbccbbbddceccddedabbcdbaecabddbdcbcaadacaabbbbbadeddedaadbbeebbccaedaeedacbeaaceeeabbedcdcbceaeecceddeaaddadcdadddeecdedcccacdaeabddeaebbdaeabcdeedabaabdaebabcbedeeeddaececddaddeeadcceabacbddbcdedcebbabbacbbedddddbbbedcaeeddbecdceabccbeaadbeabdedcbbaddccaebcecebcbeaaeaabecbadebbcbabbdaaeeceaccaaaecabcadaaadceeccbddebaecbeaecbdebaeddcaadecbeeedcadcbbdedcaaedcccabbbbeeeaeecbddadadadbbcdbcbbbebadcbbbabbeeeddeeacdcbebeceaebcaadcbdbddaeeeeeeadecdadddadbabddeebeddaebbbcabaabbeeebeeaaceacbcedcbcdeaebcbbeeecacbbebaccdbbeeeecedaeadbecbaedaddabdbddcbadbadaaaebababcdbbbbedaceecdbadbdedacdebcaeebccadbaebddcdadadcdedccdbacabdddeeaacbeaebeedeaeedcebbebdabbdcabebbdbdedaabeaeaddbeabaadcdbaaadabccddbaebaadabbabebeeebbaddbedbbdcaadbcbadeeabeddccaccdbabaaccbceaecedbaddcadacaaedbaacdeddaaaddddadebacabdbcdbcbcbbacabaadedcbeaadaddbddddbedeadedaaaeddbdabdcbcbaacacebaeabbabbebccdeceebbdceeeddbbbdddadadecaebddabacbbbcdbaaacabbbbccbabccabeacccadabaaecbcdcecbbceddeeeadaaddacedbecebecbdabecbadceeacdbdacbaeccdcbbdccddebcbbdbacbdabdeaedeacdbcecaaccbbaedeeecdcceabdecaadacdbdabdabaeabeccaacdcabdbdcaccabcbedaeeadabcecdbbdeceeabdeadcbbbecbeeedcdcdaccccbecebeedbcdaaebbcddaaacaccdbeaaaeccebdadaadddddedddeabeeddbcaacdebbabbdaaecbeedebaaacbabcaedbabdabadbacacabcabaecdecbeddcbadaecaeaddcabcbdebacdbbcaaabeadccabceecdebaacbcbaedbedcdbcadcbbeeeccaccedebdbaaaebcceecddedabdcaeedaadebbdbedabcdcdeecbebeadaedabadeeedabbbdaeebcccdcddbcaadeaaaabcdbdbcceeeadeadcdbdcdadbcccdbedcaaaeaaabacdacdaccaddcdbcccaacbadebacdddeaebeedeaeedcacbecaecbbcbbadbecaedaaabbdcebedbcaacedbccceabaadeacdeccabcdaabebebeebaabacabdcbacecaadaaadddcebcccabcbcbaabadbbeedbbbbbbdbedcecccbbebbcdadddeeaebceadacbccadecbcddcaebdddcaaaddbceeeabaeaeadedbbdbaeebbcabecbbadbbdbeeabbcebebaecebeddcbaebdecdebdabbecdeeacdbcebbcdaadaadebdcbaebdccbedbadeddaeeeecaabebcbccaaeebdabdadcadeaecdcdabcaedddcdeebebbebddccdaceedecdeccceedadaddddddaddbbeebbbaaedcdbddaadaccebbdeabdecdaddcaebcacaeabdbcaaeaaaadaaeedbcbecccaccdeccdbdbeccdedcecaaedccdcbdadbceecdedecedbaeebcedebbecdcdeedbedaceeabedbeeecdcbbadddeaeaaaebbcbeaaabccacbdbdecbeccebabaacadaabeaadceabeacceaacaedeeacedccdedadcbdbedeecccedaacbcadedadacbaeedcbbaddeaebbaaccacbdecddcaeddbaaeadecaadccaaccdccbbaacbdcbbabeaeecedddddaeabceabedbbcaedbcdeabebbebeddceaedadccbbbcedcddcbececbedbbccdcacaeaecabedbbabbbdcabdacdaeedbbcdcaaaedcbceddbdedcdeddadacdbbdcbacedbaadaecbabeedebaeaaecbcbdbbddceebedbaebcdbbeecedaeeebeabbebdecedabeacbccaaadebccbcbaeaecacceacbeeebcdebdeabddbabdbbddeddcbccbcdcbdcceceadbcdddcaeaabeabeacaededdbacdccedddeabedbadcbbdedbbaabeeacacdcacbbbddbbcedeacdbdededbdddddebcecbcaedeabeaaecddecbecbcdbcaadccbcdacdabcaeeccdabccbcbaaddacecedbbcdccacccddcceaeaeccbdeaebeadaaabecceabecbcdeeadacddbccbaebeecbbededdebadeeeedebedebcdaaddaebbaadeeadeaacaeeabeacbdbceaabeeaccdccbcebebdccddaeeebbcedaaceadcadcbaddcdbebcecdcdecaabaaceeceaaabaaaebdcbdddbbebebbacbbaecadcbaebdadbdbdbbaceeeecdcdcaedcacbbecaadcecacdddeeedaadaccaebbbaaceaabeaabaaeabaabccbbacccaeaabdccdbbdecabaccbbebbebadddaabeacadadbeebbbdeebdabceebbbbbccdcddddbcbeabdbcaeecbdeddeaccdadbbcccadcceadccddebeeaabaaaedeacdacccaaeabaaabccddaccbbbbddcedaceaaadbecbeddadaccbeeeaaaaeeebacacbbabddebddbdaddcbdbdacbadbbbcdecabbbbdeabdceeaaababacdbcececcceecbbdddcacedbdacddeeeecccaceeadbcdacebabeaddabbdbeeccccebdbbeeeaeebaeceedecacbedddbdddacbbebeecbeedbdbcdbbddbeedbaebcbdbcdecedecaceadbdeccaeaddebcabedaebcdadeabeeabeacdedbeeedaecbecdedeadeaaeaceebeccacedceedcdaabbbabbcaeceabecbcbddebedcbaecdbdddcddceaebbacadcebdabddcdbdacaeecdbabeabcdaececcccbdbbebeaebbcbbcdbdbccbdcaaecaceadabecadadcaddeaddedbbcdcabcaabdeccedcaddbadacaacdeecaceedeaeabccabeaeaeecbdbceeabdebbebacdecabaeeedccaeceaebbebecadedbdbdaceedebedaaedddddcaddedeaaaaecadbccbbbddeadbeeadddcedaccacdbecdcaabeddabbdeebebdcdbbaaebebecedaddededdadecdccdabdabddccbacdaacceaeaeedadebadcdeedbabcbcaaecdebebbcdcccbdaebdeebaeabbbeddaeebeabcdccccdeabaedebdccdabaaedaeeddecdabcbeecdddcdaaedabadcbebcedaccdaaccceeeadcccdceabcaebdaceeedaededcbeaeadbacccecdccbdcdbbadcaceeeaeecacbbcacccadcebbdcdbdabebddbeecabedeaccbdecadabbaaebcccabdcdbeddcddaceedcaabbdbeeaddebbdbaddcdedadeccccaaebceabceddcbadabebbebeacaeadabcbcacaaeaeabbceeaacbaacdbaadaaeddcaccdeebacebcddbcbecbabeedeacaebcdbbabdaaccbccddcabcedacdcdabeedaeaeacbbcbdccacebddcdadcbbdaecdbceaedcceeaddcedddabccddddcbbdadcebdaaadecaaaaeaadaeeebeaeaeaaddceacdcccacdcedcabeacbdbebbbabeceeeeacdcbcbeabaaebbbcadebdddabcbcaeddceacbedadeaebdcbecceeddbaecebbecbecacacdcdbbcddbadaabcaceeeddaddeecbdbbabaaddadaeaaacbdcbbcceeadadececaabdeaeaecbccdcebccecddbeacdbaccbacbbadeebdcaaecceaeeaccbabbccbbcacbabbcceeeaeddbbdccaadaadcbdedabebacbdbecbbaeedeaaadebbaccddcbeabeeddcebadccaccebcddeaebbebcdcabdebcaebbbbcddededcbeaadebcddeaabddccbbdecdabaecccedeccebbacccdaadecceeeacddbcdbcaabedecbbdaebeeeabcdbdcebaecaabadddccbdcaadeccacdbdaccddedebdbdedccccaacabccebbddabccebeabdacecaceeeacaddacaedeacaacedbbddbabcdeccecbedeacbcabcbeaabdbccaaaaabaeddbdddeddbeddbcbacbdcbcdadaccdbcbcabcadddaeceeaaabcdcdaddbdacbddeeaaabeacecebecdcebacabbdecabbdbbaeeedceddcbcedbaedaaceeabdddcdbeeddaccbbbcdbdbccbaaecbecbaabbebdbecbdcdbdeadddaaabaedbcadcdbdcabbcbaabeeebabaeadcbcaccdececccdbdcadbabadaaaeaeedeeadbdadcaddbddebaccaeeccbadcedaadeadceacbaacaccedecaebdbacadaedeaddcdedeadebbbaeadbdeebdadbddcebdddabedaeaeabcadceaedaabddaddeaebcdadebbbbedecdceeedbcbbebdbcecddcbdbaaeeaaeadcebcecccccddadaaaebcadecadbbbacddaecbeedeadceeaaecceceaccaaaaecaeebcacceaabdbecabacbacaeeeabdadabbbacdeabbdebadcecaccddbbbdeccbaaedadcdbdaaaccbbcececdabdbededdaaabbbcddacedeeaebacebaedeccaeebdcdacddbcbbecaaaecebbbcdadcababaadceceaeeeedcedebcbacdedeaaeccccdbbeeebbdaeedbacdbbcdaebeecbddeeeccddedeeadbcabcdeebeedbcacbecbcdacddddddabdacacebbeadeebabddeeabbcadeaddaabbabebcedbcebcdbedaedaedaedbeebdcccbecaceeeacbedbecabdbdededbbcbacddcdeaddbabdacbcabbdccdeccddccacdbbdedbaddededdddbddececdacdebacdccbbdceacdaaddcddeacceadaeaebedeadccadcceaebbceceaaeecdbadeebddcdbbcdccceaaecddededccdddbabceeebeaeddacccdddadaccbbcdecccbdaecacbbeabeedeaccadddcaeabebbedeacacaedaeccadeceddddbcceebdacedcbbcdeebcbaccdcabcbadbdebdbccdaadedccdcaceeabbcbabcecaeebbcdbdbadccbcbdabbaaccedaededeeddbdacaedddecaacdaacaabbeeeeedbbccdebebabbaceddeabdecdadbedcccabcdeedacaeebaddccebcdebcdeddbbecddaebdaaeacaecedbbedaceeeadadddeceebaaddedccaaeedaacbaabcbabceeaddedebceccbaeeccdacbcecdebabcbecdbcaadaaaddcbbabccecbedcadcdebcdccacaaeaedbccbdeadbbaaddcdeebaaddceceeaebdbebddbddddaedecbbdbdeededcdbcddacacbdcbddecbedeadaacaddcbdecaecacdeaedbdebeccbddceddaabddebcccbbdbaeaeecddcadcabdbcaaeaeaaabbadbceebeabdaeecbdeeddeadecabcbcaedceabbadeaddcdbcaedbeebcaddaeeeaddacedceeaaeeeddeeacaeecdceedcbebcacedebebdacdadbeaeddeabcbbecbaedcbcabcdbdededbbaeededdedaeededecaebbcdbceeacdcdeeadbbbdbabdedabbedddeababbaecebbebbebaeabeceecebccecbeccabbecebdeebbddcbeeddbcdadedccbcebdceeddadaeabeddbcaecabcbcbedcabacacdbdbceeedccbbadebbececddedbebceacadaaceaedcbdaaccacccabcebdcbedbcdeceecaceadeccceedddbbaecceddaccccaaadeabbccdbbadedadcecebbacdeadacddcbedabbdcbeccddbdbebaaeacccacaabcbdbbbdbeccaaceeaabbaaadbeaacaaabcdbaaeadacaecbccdedbccbbbaeabbadcebaabcedabbebbceecedaeaceeadaecaceddedccdbccacdbdceabdaceaeaeeceaaadbbabbdeecacadbcabccbeebdddbebbcaaaaaeeceddbcedebcabedcbbbbdcdbaecaaeecbdaaeccabacceaadcddbbbeceacebdeddeaddddddbbabbcecdccacddcccebecebdceaaaebabedbcddceadcabaeecdbbdbcecccabcbadeaecebacedccadaccbbadedbbcaeabaaedbbcedeeadebddeceacadccdabcaaebabbbcddceadbdbccaecdbbecbebddbcecddadcbaaadcacaaaabcaaecbdcabdbbdaaeddaecbdabecbbeedcececdaadcbbbadacacacebcaddebceeddacdbadaeeecaabebaabaecbaeeeccdceeecbcbeeddaabebeaaaebbaedcbaddedaaacaecdeecdaadaabcbbcaccbccbbbcbaedadaebcecdbadebbaeabaeacebdcbdadebdcdebdeeccacdbcdabbedaedadeeccbceedddabbbcedbaabebbaaecbbeceeedacebdccdaaccebeedabeabbabcddcaabcdbadacdeeaeeeeacaeeaebcedcedddbbbdceacebdddabddedabecaebcdbcdeeeeebabbdcacadcbeacbcceeadababbdcceaddbeabddbaabaaadddecddcdaeaaebaaedecabdcceeabcacceddaaeaaedbbecdedbdaacabadedaccbdecdabeeabcabdccceecdeaebabbbccbdbcaabcbaaedecbeeedecaaabceeededacaceccdaebcdecedeadecddcddccbaabcbbbeaccbaeadeaaacaeeccbeaeceaebaaadaadedbbcabecaeececbeabdbccaebbbebcdcbddedabecdcdbedacccaceeaaeecedbebaabcbddadddebbeadabcbbabacecbbebbcddcdeabadcdebeadddeedcadedebbbaabeabbeabedcbcaabddbadeeabebdecabbdedabceeacbbbbabaeaadcdbbabbbdddadaebbddecdedcaaeccebbdcddeebeadaecbaeaeacdebebccdccaacccccacbbdaebaacecbbbbcbdcaecdbaecdcadadaabaaadebcaaaeaebdebadcadaeebcdeceadcbcbbcdaceacbbbebbacdaddccddabcddadaedeedcdedcaeebcdbbaaabdeaeabeabddbeddcaeeceeeddbbdecbddacdacdecbaebebabdcbcdbadedeaaaccdeebccbbcabddcecdcadccbabeeaebdededecabbeacdeecdcdcebedcddcbbaaededbcdcecdbccbcdaedabbcdeaebbcacccbbadbdadddeabedbcabbeaedebcbeadbdceaddadaaaecaeadabdcacaeccaceeacebceeadcdcecbccedadebaadabcdcdaebaaeeeddbcaeddebeeeebaddcaeddacaadbcbccbabedcecaeaacbbcbbaeeacedbeeeebdbdbaceaccddcceddbcaecabecebcdbeaedceedceecbaeaacccbbaacaebabdabcaccdccdeabaaaeaadbbceebdccbeedcedbcebadabbbbdedaecaacbcdedaadcdccebeedcadbebdaeedecdecdcaeaaeddcededccdcaccbbeadbdeaebeecceecddababebacdcbaadcdeaacccedbdcbadbedadbcbdcebbaeeaacbccedbdadccbcdeedcbcccbadcbdddbeaadbdedaaedaeaeabeaacbbdcbaaacbcaedcdecaabacccebadaeaccdbaacdacebaadaddeddbaaabcbbceeacccaeacbeedbcacaccdbdecbeacbdaedcdeaddadacedabecaacbaaebcbbacacebdddaddeedadddbedbdadbabdeacedadccadebeacecbcbecaeacedeceeddeccebdeacaeaeaeeabdabaaadaaccdbaeebabdccaededabaadbddcccebddbdeddacdaecaaaaebdccabdbaaeeabceddbaeedabbbebecebaccecdbcadccdbebadcecdddccccbeecddbabbccedcebdbbddecccbcbbbbbacdabcbdedaedceabecedecbdeedadcdbcbeeddbaeddcacedcaececaabccedaacccaccecebbddccedcaedcbecebbbdaabdeacebdaceaecbeecdeabcccbdcecadebbdaddbebaeedcabdecbecbbcaabeadbbbdeddbceccccedadcbcaeaeccaecdecadcdeeccbceabcacbdccadaabebdcbaaedcaaccedeceecdadbdbcabddcabdedbedbbbabebedddcddcaedacaebadebbdeeeacacbedeaebeddeceeabcbecceacabcbdeeebadcaedcacbbdbbedccddbcbabbdedacaceadecdabceadacabebeccbcbccdbbbeacebebecaabbdcbacaaecdabcccbdabddcbcacdbcbaaaeccebbeeebebaddedcdceaecebecadbdaaacdebdacbbbaccbbdbeccbebbbabdcddbdaececcadabadddadcacecbdeebcdcedcbababcebbbcedccbbabdcbeaaabbbaceebadddacdbdeebceeeecbdaeeceacddaceddcdeddcabacacbdbceaacbbbdebaaeecebabdadeaaeeebaaabedebbbbdeddacbcabcabddbcbeaeddacddcaecdadcbeabeeebadeeacdaaeccccaaecdcccbaebaccecbcabceddcabdeaacbcabaeecadbecdacdaeceedbddddacbddedcbdedcaeacceebbdcbdceaedacbbdeddecdbadeebabaddcbccaadebabcddaddddaaabdaeaaaabaaaadeebebacbbcacecadccaeebaadddcceaedaecbdcbbdcdedebcaeaabeaccbccacedcdacceededababedcbacbebbbddbbeeaeeeeaccaaeebbaddcdddebccabccadccaeeaccddbacbcceeabccdddebccbdddaebacdaccecddccbbebebecacecccdcececaddbebabadadbcebbccdcbbdbbdabcbceadadecbeecbaeaeeadcecddeeccbcceaedeadcddeacddebdaacbccddcdcaeebebbdbcacdebbaaedacdcdcdbceaecbcbddcdccdbaecbceaedbbcdcbdaabeadaabccccbacbedabbecdcdbcbdddaeeebbbcebbdceaddbbabebcbdeebcacbeaedbaebdabdadecedacaecbcadbbaeeedeaaaaecebaeedbebaebaeecdbddcdcdcbbcdeeacdabeaeebeababccabdebcaceddbcbedcdbaabccdbdeddddabedebcbcdaebbbcadbcbbabbdeaedeaddddbaacebacdaacbbedeaeaceaebaeecceebcdcebacbdeaaedbccebbaeabbaedbabddadecaacbcceceeaebacbbcddaabdabbaeacbcbbcdacbaddbebacebcebbddcccdeaddacdedbeacdebbabaabeabdabccbebbdaecbbbacdbbcbabadddeabcdedaaecdbbdcbeaceaddacddabbccebbbddaeadcdccabdbbcdcacabbadaaddcadddcbebcadacbaaecbdabdcdaadeaaecebacdbbcdadcceeadcdcbdbaccbdddbdccbbeeceaabbbcccbbbddbadccaabeddadddbebbaeeaabbbaedbcbaebdcdbcdebeedeebeadbdabcabdebeeadcebacdebededadcacbdcbaebebccbcaebcaacaaeeadaebdbeebdabdcbabbaaceeacebdbdbceccededdcdccaccabaacedadeeeddaacdbdcdbbbceebaedcbaaebeadebdedbbecbedbcbeeeaeaaebaabddbcaeedbbbaceddaecbeddceabbdaecbcaaecdcbdbaeccaadeadaacdccbdacaabebdddabccaddcecbeebcdcdbaebdeaeedadbdadbdbeaaebabbaacbdccccbdecaeaaecbbaedbedaaadadcceaeabddbdeceddccbbdcdabddcebddbdccdedabeceebbbdbbdaccebecbabddeccdbedaedcdeaacdacdeaadbedbdebbadecdbacdceacdeddebcabbedbcdbabbdcecaddadedbcbaabeabecebacedcbcceeedecbabdebcaaeebdaaaddddccceacdaaaeeaaeaaeebcddddbeddabbaaadbcaacadbdbeadadbeadaaccaaceabaaacebdebcbccccbadcccdbebceacaabddecdbaabddbaeaabdeeacdeddeeebbccaddeebebdbdacabbacceebcebaaeeeaddeacbaaddccbecebedcedbcedccdacbbedacdacebddabbbdbcaeeedaeccbaeaeeddaaecdcaeacbdedcadaddcccbeeeeacaaebdeaaeccabeeebadeaaccdedbadcaddebeeacebebaaabdcbebadeecadcacebecbcdaedbbceaceaeeaaaadeecbceedeebdcccebbedccebdbaecacdbdebccdcbdecacacceeeecddbddeadbbebedcadedccadccacdbadadaeccacdaedabddeebacadabedbebaedceadbbcaddbcbbbeaceeababddbacebbaccdabbabacbcabebdadebaccdedbdacaecddbeadaecbcaeacabdebaaeeeabdbcbeaedbbaaebcccbecadcaecaaabeeadedacbebeebedcdecbdddcbccdcbeeadbeebeaaaadeccddedcddcebadaebddaddaadcababcedabcaccceebeecadbbeabcdcdbecaacbebeadaecbedadacecceaeeedadeadabbaabdadcabceededadeebedbcdebebaadbeebbebdcaaceecacabcecdeeccdbecbdeccddbaadecceababbbccaeceedeeccbecccaeedadbaeadadcbaebacbacebecbedcceaababedacccdebaeaecedecbaccbbacbebcacceedebdcdabaddcddbadbcaaeddcaaaedcebdcecdbabdedeebddaeeacbceacaeabddeedbadaabeaeaedaeebdceccacdbdcdaeacabcecaabdbeacbcecceaabbdbabbbdbedebcbecabcccdecacebeeceeddceecacaeedbabeebbcaaccacbdaabaabedbbdebbbaeaebacbadbebaabebabbbecdacacccedcbaddacdbddaaccddaacdccbdadddabcccbaedaccaeeacebaaacceccbbaeaebaddabaeaaeebbdcbeedeacadaeeccddccedabceebeaabdacedaabacdbdeaeaacdddcbccdeccbcedacccccedbdcebcdcbbbdbaeccdccaddcaebcaaeedddaaebbbacbcabcdbbcccbbecaeceadabaabbdeddbccbbabecdcdcbdbcbedccecceeebbedadadbabddeeedcabcebabdaebbebceebeedebddaeeeeaeddaaaabbeedbbcbcbcbaadeabbadacbbdcdddadebeacdedbcebabcccbeabbbaaadacbcbdbacecadadebcdeecaeaeccedeeaeaedbceabdeadeeebbdbceabcadeeaeeecdabdcaeeccbaadabadcedccbcbddcaceedddbecceadeeaabedbbdabdbcdaddebbbcbabdcdaebbabeedcadcaaeeddabdaabaeacdaedecacddaedcaeaecacecaeaeaebacdaecceddaebbaeacacaddbacedbecbbbebccdbedababdccceccceaceaeedddabecacdbbeadebdebdedbabecededaccebcbecaaccaccaaccecaddecebaececbbdecdceccaaadeabcbcedcdacceeebdeadcccabaacdbdbebbebcecbdcddacecbaecdeddbdebcddadbaaccabceeaabeacbcebccbdddaedadaeaccbddadcbbdaabcacecdddadbbadbaccbebebdadaecaeabebdcedbbacacebdbbbdeabeacdedbacadddcdbeeeebcacdadddebbdceeaabbeabadcadcdddcdbecebabeaaaacdaeaeddecbcadeeaacaacbbedbdbdeeaacbadbcdcbecdcdacacbdcaddbbeedbcdaeeaeceeebbadddaaadecebebdcdcbcdeaabcdeeeedaaeadbbbbedbecbbacbceeebdbacecdceadaddccdddcdceeddaadeedcadddccaceaadcbababceccdcbaedbdabbeedadaeccbaeaaacdadbcbddaaeccbeabbcebcccbebcdbaddceeabcbeaccecedaeccacedccaacedbceebeaedadadaaaeebecabdeadddaedbbccaaadcdceacbacadaeaebdeeccecaaabcedededbeebacdccabcebacbcececbedeadacbcaedecacacccdcdaecbbaedaacadbaddcbedebddcdeaccddcbcecbdccbebcddbbbddecdeacccaebcaeebeabbebcecacbcabbbcdecacadaeeaeeaecdbadaeebdaaeedbadeacecbbebbddeaddedcbcdcdcaacaeeabbacdebaeacbeaccdbdaededccbaddbdeabeeccdbebdbaebdbcbeadddaaaebdbbcdaebebbbdabeccccdbeccceeedbacaeddcdddaabacedccdcdbcbcddeebbbcbeabddaadacedebedacbdbcbaacdaeadcdecceacdcbbcbbbcbddabcbcebdeedabacebcbddbbcbeacceaaaeadbedaceecaabaeedaecbeecddecaacebedbcbbcacebebeebeacecdabeaaccdabbeaadccedeaaecaedcbadebbcebaceabbecddcaddbbcbacccceaaeaeaedbaedeaceaebeebcaedcadcdbeaedbdceeaebebbaaaaecaedacaebbdcddcacabbacabcadeadcddaadcbdaaabdbccbbbacedcdccebaabeedbdbcebeaaeeecdaebccaceeadddbcebdccdaadbcaadbbcaaddecaddababadbdcdacdcadcabbeeddbaedceabbaabebccaabebaceaeadabcbbadabebabbcbbeeaaeedaececbbaedbdccbaadcdcddbdbacebddbbdaddcdabaeececeeebaaaedaabadaededacddadbbcccebdaddbbdceaaaccddaacaecaceccebedeeaeccacebcaeecddddecedaaabaddaacdabbbcdbdececdcdbeccacddbdcddaebdaacdbadabbdaaedccceaececbdcedaebcadaeddaeeedbccabbbaabebdddcacdcceeeddbedcbacebcbeabaecdcbcaeaebecdddcecaddebeedbebdcbebbaeaaacdadbaadacbaabceaccdabacaaddebbabebcecdeddeeeddcabdbbecadbbecccebdedabbaecbcecabbacbbbebcacccccbcccbadbadecdcebdeedcddeabdbecdabedadccaecacedaccdabcaabbcceabddcaaabbcbddabaaaacdcaacbabcbdaebeaabdadcbeceedcaeaedbdacdbccecdccccadaebeeaecceacbacecaeccacabeebcadedeceacbaaccbedddbcececedcccecaccaadededabddaaadbbceacddabdaacbecebacbebbbcbbbcbdacdecbadaeadddceaaadaabaeceedcbbedacbaecbbedabdcbceababeebbecedcbdceaebebeebadbededcdadeeaacbebdcbcdeabdaeacbbcdbabbccddceceabcbccadeebbcbeaaebabcccbcaddcbacdacbeceedeebaaacccbbbcedebaacccbbeaeadccbbbbbccbdaddcbaadceaacbeedcbbbbdeaebedebececccbadeaccebabddcedcacaadcdbaedceacebbdeabcceeaaebcddadcaaecdadbaaebaddaebcbbcdceddaababbdcecdebabbdaadbbaaaeecdacbdacddbcdebaebdacbbacbcccbabaadddcecbbbdabadcbeabbcecddaeedbaedeaeeaedebaddcddcccaadbacccbbebecdedeaaedbaabdbdeebcecabaeeacdaaecbaaedecbcbdbeeebbadeacbacdccaedeeabaacecceedaaedaaadcdbeaeaaebcaedabdceadcceacacbddcedaecaaecaddcadcddbaddebcacaccdebeaedbeeddbabceeebabececcccccbcbadcccdecdddedcbababebaeeabebdceccbacbaeebcacbeceaecddbaaacbbbbbabbeebbdadcedcedcbbbeeaeebedeeccacbebacaeedbbcacbabebceceaadaddddbabedddccceadaccbebdebcaceebeadeedabecaedbccabceaaaccdbebcbcdccdeebdaaaddacacabbeeceaeabcbceeadaeeeabccaabbeccddbbacdaeebdbabbadbaaaeacaebdcaacddaecdcaaedcecdadcacdccaaaedceeacebbbaeebdadcecbceeaccaedcebbccdcbbebecaeaeccabcecbebbecdaaeccddbdcaeaadcaccbeebcaccedcacdcbddbcccbcccdeaacedaedbecaceaebbaaebdaaabeddedeaeabcadebcddadeedebedacacbbabecdccdbbdcadbbaccddacedbacbdccdcbabaeececdeecbddcadbbabddbeedecbebcddcabadbddaadbddaadbbdcaddcdddcbeddacbdcccdbbadbedbececeeaabaedbadebdbdeadacadbbaebdcdeaaebbeccbeebbecedcdcdaceaaddeaccbaeaebabeedbabdecdcbcdcacaebacedecbcdbeeadccaaaaddcceceacdeddecaaeedcdadebeeeeaaebcdbaededeadbbcbbcccbadacdeebbaceecebceedaabbacbbbeebbccdccebdaeaeeeccedeadbceabdeedbacbecbaeedcdabdcebcdeebcaeeedcceaeaaabeeddedbaaebdcdccebacbdecbacdeabecdedececcbddaccaaaeaecabbedcdeccdcbcdadddbeeebeabdcabbabddaeeddbaeadbdbbdabbcbeedaedadabcaeaecaeedcddbadcacabeddceabacbbedbdeeeeabcbadecceaeadaeebcbedbadebccdbdbcdcaaeddeadcbcadcbbdbcccadaeacbaaebacaccbeebddeacbcabacdaccbadcbcdbeabcdacddbabdcbdcabccbabdbacbebcdddaceddcaaeeacddebaacaacdeabadddeddcbbbcbeaceccdadadaebcdbeacadaabaecbdadbaacedeebeedcdbeebedcddacdadceaccadcbcdbddadecdaeaedbebcccddbeeebceeedbaacbeecbbdcabbcacbdddadbaeceabbccaecebaedadadbacddabeaadccecadcaebddcbabeaedeaecdebcbcdaeddddbbdcadcadcbadaaddcacaaddacadbcedbcccaabdaaecabcbaeaeccaccdeacdaadeabbdabbdbecadedddddccabbbbdeecaaeebdaecbecaccbcebcaacbeddeccadcdbcdbbaabecbdeebabcdadeddaddbacdbebcacbececebcdeeeabedcddbebcdbbedcaadbedecbbddcebaddcbbaecdceabbabeadccdbdedbecbcabaadcaaddcacbabddcaadaececaeeaceacdceaddbbaddadebaecaaedceabadebdbecbbebddcbcbeaeaaecccaeeecebebceceeeedeaccbeebbadedcababbbddeeebcdccdccaaddbaabeeebdcbdaacbcebdaebdebbcbbbaaecdececdeccdcebcccddccedeededbebbbbbeadeedbdeecbdeeeebdddccbebdacaccbdcbbdaedcdaeddccccbcdeebdbeaceebadbacaebceecbabddabadecbccacbdcbcdacbcaaedaeddecbbbbcdeacebbdbebabbbccbabddcabecdaceaeaeeedddbedeaeabecaacccbdacdbdddaaadeccadcddadddccddedcbaaccdececdddedaaaebaadcdccdbaacbacacaacaceadaabcebbdcbceebddbadbbcdbbeaeebecaccebcbccabdaeacebacddcaeeaecadaaaeedcddcdacdbdcadeeecaddaaacaebaaeeaabecacecccbbecadbedbedacceedcbcdaedddcdcbceabbbddcbdcdaeccacaeaeaaebdecbeabbdabecdabeedbbbeabddbeceeddccdbebaccbbedbeabecaebcbeeeeedacaedecacdbdddeeebcceeeddcdaeabdbaaeaddebccbdbcadecadccdecbbaededaaabeddecabeecaecbbcbbbbcacecaccbedbaaebdecebdccdabeadeeaaeacaaaaedbaabbceeeabaaeeabeccbcebcacedddadabcbcbcbebbdadbabacdbbaecbbebddbdabdcebaebddeeeecbdcbcececcabceeebcebccacaaabbaeabceacdbaecdbebeacdbbcbebbaebaabdccacdedcebadcacddebaedeccacddeadcaddebeaeaaaacaeebbbcbadaaddedebceecdececeecdbdbccededcbbebcaededeaaccbbaacdbcabbaceaaddaaedcacbaedbcdabeabddddcbeaeddcbbdbbbddaadaeacbeaaecdccebbeaddbdebcaadebceeeaccedcbbcdaddadddeeaebdcacbdcdcdcbeaceeceabeaccdabedeeeaeeeedadceaddeeeedeaaaebbeedcdcccdabdccdaabbeeadabdaabbedaebadabccbeceaeaaaedbedeabdbaceadbcaecabebbedceaadbadeeaaeadcebbcedeaaabcaadeaccecbaebbcebbeabbbaabbcddcedcdedddedeeaceaaedbaecddccbdaebbcaedaacbabcbbecdcccaeaeaeadbbaccddbcddddcbedbbceeceaceebbdabedaccdcbdbeabaedbdeeccdeeabccdeabcdadbcedecdeabdaceacbeedadedaecabcdbcadceacecbcbbbaecbceeedddadccdeabdccdacccacebebdbdcecebcbddddebadddedabeddaccbaaceaddacdccddbbbcedeacbbcdecaaeaecdadeceeacecdacaacedadaacddccdeaaebadeccbeabcdaaaacdbadddebbcdadbdeddeaabdeebcaceaadacebacdadcbecbadaedbbbddadcbaaadceabadaaedababceeadeebaebceabdbcbdcadaadeabadaddaedabbacaccacbadbbebccedcbccbbceeebcccacedacecdcceabeeebedcabeababdbccedeeaebbdeeebcdbbbaecebdbbdccceccecbacbdabcecdcadcebeedcdcedcbedecabcbaddbbcdeedddaedbddcebadebbcddbcecbcccdcbdddccbebeeacbdaccdabecbdaebeeaeebedeaadeedeaabebbaeccebbebcbcabeebbdbbcacbededcbaaabdeebbbbcceaaaeaadacbddeaebcbdeababcddcecbdbacbacbcabebbdebeeedeaabdddaabdeecdeedbaabbbbaddaecaccecbdeeecdeacbbbebbabaededeecdacbaeedeccbabdaabdbacdeaedddbaecaeaaccadbaccccacbcbebaacebcbcdabbabcabcdcceecabdedcecaaabccabcddaeacebeccabdccbacedccebecbdaadbbbabdcdacdeddacacbaedaebeeedabbdcdabddbbceeacdedcceadcbaeecabbdeeaaaeacbcecdacccbcbceccababbbcebaadecadccecadedbbdadedddbeceeeacbaceedcbabeccbcaddcecddbacedeececdbdeecbcabdcabaabddeeedadeaecbdddeecebceadcbbdbbacdebbceabaacbacaaaadbabcddeaebbaaabdaecacebcdeaddceccdeeabbccacbabceceddbceeebeeeabddbbddecabecaedadabccceaedabbebbdcdedcdedcedacdceeabedebcbabdbcdeeabedaddcaecbcdccdbedceccebdeceeddbbbddcaeecadacceddcdbdedcaadbcaeeadaecbbdaeedcbaecdacdbedcededcdcaacdbebeedcaceddebcbdbbcedcbceeccbeaeceaeadaedcebddeacadadadeecaeabdedeeaebdaebebadaebabcbeccaecdbdeadcadbdcddbabcdaeeeacaadeaadddaddacbccaedbaeebbaedccdbcbccbdcedaeccecbebceaadeacaeebdbabaaccabadbacddbdabeddebcedeceaedadbebceddaaabcbbebaddbcdadebedadbaddaeaadebbebeeccdbcceeeddbdeceecbdbdebddecebeadaceccdbbccdacccbdaacccebddcadcddeccebcaaccaecbadecaaabaadcecabacceddaaceebdbdabeaaeddbcecddeeadbebbcabbdeacbaeecdbceeaedebacacaabeccbcccdcdceccabaaedadcbccbeadcdedbeabcddeacaecddabbbeeadcaaceadcadbcdbeaaeabeadbbdcdddeadaabdcaaebaddeedadcbbdececdcdbddeddbcdeddcbcedededecebaebdacbbbdeaaabdcaacddcccdbbecdabbdcedeababddeaccdecdaedecaeeeaebecaaaddaebabeacecbaaebeddebbcadcbebcdebbdeaaadaeebdadceaceaeaeceabdbdbbcbacdbddbcacbeeccddcebbbabecaecdddadbabcdbbeccdaaeacbcdbaeabcadbcedaaedacccbdebcdbabcbccaedcbeecabacddbcebdddabdcdeeeedbdaaddcaceaeecbaededddaddebeeaadccededebdadcaeabdecdeadbbddedeacddedddcdeaceeedcdccdceabdcabebbbadaadddaaccbeeaeaddedbcbacdebedcbdddadbbddbecbbeedbababdabdcdcdabdbbadccbcbcceabbbccdbccbeedaedbbcdcccacacdabbbecaceadbacbadcbbdccbaedeaddbdacadbbeeaebbaadededaaacebabdbdbbbaacaeccdedecbedcdacbcabeacabadecbcedcedddcabbdcbbabcdbadebaecbcaeadddeabeebbabbedcddcbdacceadeeeabacdddebdaebecbcdeaebebbbeadbbdcdeeecbceaaddccaeecbadabbaceacbeadcebcbbccebebdbaaecbcbbadeacdeeccecdeeeecacdcdedcbbddcaccbccdbaeacabcebaccccebdabcbbabbeeacababebbeaeabbdaececebeecbeeebdebddaaccbdceaebcaddcdbcbeaacedecdaeaadbcecdeadbbcdbdeabdadbbdabbddbcecdbaedcdbcccdecbcacdddceacdcabaccceeabdcadcbcdedcbbeabddebaadaadccadabeaeabadeeaecdeceadeebdecbddacbeaeadebcdabdceedddbdbaebcecccdbabcbbeccadeebcacaaacebdcaeeacbccdaadaadcebbedbeaebececabdaebadecabcbecbaacecdadcbaebdaadaaadcedcacdccaceacaecdcbabadaeacbbeaccceecdeedaaebaeaccbdcadbbaccbeeedccbdaeeaddecbaadddddceaedacaeabcddbcbebcaddaebbddcceceadbaededcdadcdcbcbbebbbccbadceeaacbedacdbaeecbdddabeedaadeccaceeddcbbecaeeabcddbadbbdbbaaaaaceaedcbeebabbaaebcbeabbdadcaceecbebccdcaceebadaedbdaaadcaacedbdcddecbeeccdedbedcbabeedaeddcdeaeccebbbddbdeaedeacceabadccbcaaecaedbdceeddaeaeecddaabdadadebbcecbcdddbdcdcdaeaaabaabcbaebebebedcdcdedaaaecaaddbbbcdeebbdedbdacbabeebaaabbadadeaccdbdbdddbaaaddccbbeaeededbacbcceceaceaccdcbbdccdacddbbaaeaddadeebbbaadbcededdadbbaaaecebcbdabaacecabbaaadeeaaddebbccecdbaedeebbdaabebbecedabaeedbdcebbedeccbaedbbcceccbabeecbeeedddbcebabeaeaceeeebcaebcdaaebbdddedcbceccceccbecbeebcddcbecbaeaeeceaacbbabababedeacbbbcdeacdaaeedaecadedcacaecbbbcdeeceaecebbdbddaedaecabdaeacaebdadededdadbbbbacdedecdbaeaacdabbadaeeddbdbbabebecbebbcededebbaaabdeadabcabecedbeaacbeaabebaddaabbcacebaacadabaeebcdaadbdbcbdabbbdadbbaaacabcdecedcbabaddacaeaaddbbeeaebebececdcedadcdbabeccccaaccdebddbbecaaaccacecbcbaedaaddbbabdaacbbcbdcdddabdeedcabaddcedaabdcabdcebbceedadccccedddabeebacbdbbeabbbbeaaddcabbeecedbbedeceaeecabadebdeaeebacdbdbdbeacabddaacacbaececbbcaeaaddccbebaeabdcbccdbcabaedbdbbaceecdaebadecdedcdaedcddbdcdbedddcbaddddbecdeccceeadcceecacaeebaedebbcbbacaeacaecbcdcdcdabdddddccbccaadccdaadeceaacadcedbddebccaadcbabceadcaadcbccabcdbeaaaedacddadbadcdbaabeeaaaeccdceaececcebeeabdbacbcceaddddcccbeedccbbcbbdbddcaacaadedbbcbcebbabaaceaaccbcaebcabbaebeaebbeacedacacbedaeadacbabaeaddeececadddddecdeadeccadecdbccaeceacaccecaeaceabbabbbebceaebdcbaccbabbddcecedbacaabcbecadddecadeddbedcdecabededeceedbddadeabdaecaeeddacdbccbbbecddcabaedcebbcdbbcddacdbadbbdcedccbdceeaaaaeaedddabdaaccdaecdeeddeeaabceacdcaebeeabcdcadeecdbcaaaaccabbdccbebbdbccbabdececeedcecbbacddcaabdadadecedcaaeceeaaaaedaacbabeecddbeabecdccbabaaadcdeceaeececdcedebcdcabecacabdadadecaeecbdddaebcaeaebbeccbadcdccaadaebaeeaaeccebadecbeceeddacceebbecbebdcbbddbdebabedaaacdcdcecdecbdebaaceacaacaadbcbdeadbeceeecedabecbeaccbdceceaeaaeabbbbcbabbcdbdedbaededbcbcbcdcecbabccbcaaabbecadabcaeeebdcbeddeccbdadabbaccedecbdcadbcabbabdaeeeeddbdccadcbecdcaaeedcbcbcdbaacbabeaacdabeabcdebbaacdddcccbcedcaeabdacccaeeeabbceebacecbcebaebceeddaebdbbddaebaabddabbdcbbaceccecaadeeccbbdedccbaaacddcecaeccaeddcedbdcbadeebdacbacdadcbeceacedddaeebaeededeecbdecacbdaacdcaabecbabdccdaddcebdcbcacabcbaacaeddaddacedabaadcdedbacebabbbbaeacebbbebbaaddadeeaeccdebddaecaaaddbaecbaaddbedbcddaacacceeaaeabbccacecbacbeeeaacccbdcdcabcaaddadaceaeccedcdcadeaebcdaeeceeacbdcaeddcadeeedabbbacadcdeaedeccbbeadebedcbccdcdebdabceacabaaaaabaeeedcbccedcebccddeedeaaebdcdecbdcaebeaaaceaccbcdcacdbebacbcbaacabbbaababaddadddacdcaaeabbeadbdbebcadaeedbaadeaceabceccadaacdbcdcebeebecdccaceeedddddbecdccdcbdedbbcbccaabaaaaeeaaecdcbabebccadbcdbdbaaadaeccaadaacacbaecbecceccbebeececdbeaacdacaecdcbcbccabeebddebdebacddcbaccdcaeaeaddaeadbcabbccbeacdadabaccdceabceccbcebaaebebeabeabeebacbbdeccbecdadceaedbaaaaaebdaeceadeceeeabaacabaadcceedbbabbbdddaebdebdeeecbdeacceabcaacedeeedaddeaacddecdebcdedccaebdeaeeadedcaaabdeaabcbbceaddeacbbddbedaeeddccbddebbbabdedbeceecbadcedcaabbaeebbecaeacbadadabeacedbaabdbceabbbaaaecdebeeecaaebbcdbeaedbddcecebdaaebcaeebbaeceabecbbdeceadbabadeeacbdbbcdcaaedaabddaaebbcebeaccceeecdddeaacebdebaaaebaeaddbcccccaedaececbbacbcaeecbeedebddbebdaaaaaeeeaaaceaceadbeabdbacdbebcebebedacdebeaeaeeedcdbcceecbcadacddbaaceeceabaaeeadbdddabaebcecadbeacddbcaeeaeeccbeabbbdbcedceadeababeaeccceacecdebbcddcaeabdcaeaeebcdeddcbebbecdddaeaaebeceeeaacebedabbaceacbbdaddcbbeeceaddcdcdeaeaecbaeabcadbaeaebadcbbbdccadeeccdadbedeadcaabecbaecadaeebaaabbbeaaededbdaceaccbceaaadcdaeddeadceedebceeeecaceccbbebeecdedebeccbbedcaadeeeeebbabdeeccabbadecdaccadddadacadecbeeebeaacbdaedeebabcebeadccedcdccbeebdeedeeddebddbbccdbadbdbaecdbdeaaaadbccdbbcabacaaeebcbadddaecebbceaabbddcdeeacabaebdebbdeccebecbebcbaeaeddeaecebdedcebbdaddeacdecaadbdbcbeadabebeaedcdddecebeecdedadedecbcbbedadbbacaceccabccaeacabcecbbbeebcdddecdbcccdbacdacbeeeabaddcbabceededbeaccbadbeddcebedceeebedddebaadbadbebbdbcacdddacdbcdbbbdabdbaaabeacddebaaebdaddaaacdeeddcecbaaeedaaeddcdcaaaccaadbdeebeecddabdeecceddebddeadbadcbdccdacbecbeaeecedddecaacdbcedbdaabbdcabccaacebcacaeedbcdcacbcaeccceadcbeaeceeeedcdebbebcdbcaabedbcbbdbdebddddbacdbaaedcebadbdceeabeedadeaddcebbedcabdbaacbdebbcbcdbeabcedebaedcaabbcbbbbdadcdbecdaccddbddcdebebcacbccdecbccceeedacecbcadcdaebdbecebdeaadeeddbbbedebbbaeddacdecabcaeddecdbdadacbdbbbceacabdadecacdadeecedeacbacaaeebabbabeacaeacdbdacdedbebcdadaecccbaecdecacdbdadabccbdacbceaeebbddbceadbdbdceeaedbdcdeebbabedccabbceaddbbeeedcbdbbbedeaaaaadcbdebeeabeddbebbcbbcedbbdebbbacdebcaadaccaaecceadaccbbcedebeebedcebcbecebacebbaadccabecdbcaeecaceaddaaadcacccbdaddeeedccccaacabbddbbdcabecbecaabcaaceaadcccabcddebdceaebacaabdbebeaebdccedaddbaebbecaecaaeaecedabdaaaebceaecaaaeeecdebbeccaaedaddecdccdebbaaacebdaadaedadcabdacccaebdccaedaeacaccbeadacceededaccceaceedadbeeddccbbaecabebbcbbceeebbbccedbcccdccabcbcddcecbadcabebbeacecedaadaeaaedabbecebadeddcbcdbedcdebbcaeaababaceccceecedbebabebcbeccadcaeddaeeccdcaebbcbecaaceddbbadedcabccabcecbcbeadcbcecdcdaccbaedcacdbabeddecdceabddedbeabbcbabbbbdcecabccdeedbbbcaebcaebabcedbadcdabcbbabcadeaeebeccbabbedceddabaaaccaaebbeecccbcaedbcbbabdbcbaeebbbcdeedecdaecacdccdaccceedecacbccebbcadecededacdccdaeecebbbeabcebeeadbdbecabadabcbacbdecdcededabacdcedababbadbbbbcddcdbeacbdeeddeadcdecebcbbeabbaeddececbeadabbbebcdbcbabeecaeecbdbbaeddcdaabbeabccdeccbebeedcdadaceaaeddabebabcedebaaccedeadeacdbedebeeddddeadebebabddbbdbbedeaedeebceaebeededccebeddaeecbbdbcdbdabadecaecebedabbaddcaaeebbcabaadeebdaeadcebcadebeadbdedccecbbbedbdacdcacccdadcedceddcbeadbadbdedadacbeccdaeaeeeedabaacceaacdebababebaacacdceebbadcebecccedbebdbbcccbcaaeaadbcdceebaddeebdaeaceaececdbcececaceddcaaceddbbcabcbdbbcebdcbcaeecadbdbdacbaabdddaadbebbaeceeebcbdcabaacdcddbdcaddaebdadebaeedadabcebeacbddbdebeddcddbdaacceeabdbebacebbeeedadcdceeacbdbedbadeabdbabeadaaaeabcceadabdaeadeedebbeddcaacadcccebabddbcabeccecbeaaebecddeaceceeedeebecbbcdcacbddbeedbbbcddbdcbeadcedbbcbabbbdbcedddebbaeedeebdbdbbaddbccddadbcdabbdbddcdeeecebcbccaccdececbbaebdbabeecbddadaeebaeddddaccadebccdcbeebdedcecacbaaabcdcceccaedbcbcaddabdcedadcbcdaeeadcecbdaeebebcaceecabdcbbdbbbdcdadbedabaadddedcbddccbaccccecebabdbebbaccaaceabbbdccbbdedebdbbbedeebbccadeadcdbdbedbeccdbdcdddabcceadecdbcbccacecbbadbdbccecaeaddbecdaaedbbceebdeddaddaeeadcdaeebbbbeeaebbedabbdadcabacabdbcedbdbbcebbcdeeeecccabbccccacadedaacaedbbbeaadbbaddcddaddbacbacabebeadabdcbbedbdcabccaabeeeabbeddaeeedccebebccbeccbdaceaddbbaeaacacaecdedbacdecadecbeecababaaabbacecebebbceedceacbdadcaadacdcdcedeccbebadaeccacabcbdcdeadedeccdaadebaeebacccedceabdbbccbcdcebcdcebaeddbaebdebdaceccceeaaddacbeebdabbddababcbdebadddbbdbccabbadaaebbecbacaeedbddccebeadcbdaeacacecaddeabedceaceaebabcaceeccdbeabedbedcacacecbebcdeaabababbdbedceedeebbdeaeebbaacbdabddaccebceaabaecdabeaabebdcedcabaeceaacaedcccbbdacdbcbcededcbedccdcddaecaaccdeeacaacaacedbeaebeaeedabcaaaedeaadeabaccaaecaaaebccbecaeaddccceabcbcdaedddebceeebcbaedbdbeabbaacbbececccebcebaeabcbddddebdcbdccadcaedebcbdccccbbdbcccacadeaacaddddedabeacbcebcecacbdbbebeeecbdacabdcaabcdbeddbdaeccadedecbadddacbbdeddebdbcacebdabdadaaeaedaacbccaeedaabeebbdacdaabcdededcdcecdabdbcdcddbdbcadbcbddacccebcbabdcaaeaabaecaccacabcecbcccbccecceaabedcdeebdbbacbebbaddbeaddabcabdbdbdeedbadeecebedecacdebcdadacabcecbedaccbbcbdeedabddddbbaeaadedecebcbcedcdeeebdaadedaccedecddcedccbababeeecadbccdedbbdbbadbcacdacaabacbeadaedcdecddbcdcbcdecacbbebcccbdbdbeccecddaebaadeaddcdcccdebeccbebeaebbedadeccccbedaaeeadcacebbdcedeebcbbabbaccceccaeddaebcbeeaceadbcadacbcbdbbbdddbaebeddcdaadcccbebcadedacaabadcedbaccbedcbdebacedbdbddbaaaeddeaacbdeeacaccdaaaeecdabeccccacdabdbeaabeabacbcbeeccdbabcbecadbdcccebbcabceaeecceadcadcdccdededceacabbdecabeaccbbcaddbbdcdcbeddabceeecadaabdddaacbddaeeeacdddebbaecdbcbbabcdacbceddeeedbdeaaebaaecebeddaebecabebaabadeacacbbdcbdeadeaceeaeebedbbdecadeeaeeaebeabbddbddcebdaaeceddcbabceededdeeeeadeeccacaedbaeacceddeabdadaebadabebacdebaadaeeebcbeadeaecaccdccaddeacbbeaccbababeccbecdedaceadcbdabcddddceeabbcbdaadeacdeaaeddcbeaaeedcabcaadcbeddcbbdeccbbbadbbbbadccdedecaeececbaedaaccdebbedacbeeaabbeeaedaadcabecdabbcccedccbdcaeeaacbbabaacbcaddccedcececddcddaadaaedddcebbdaccecadccdeeebdaadaccecebaacbbbedbdeabadcabeaddcdaaccbeebebcebdbcbdddcaeaeaaddbbeededddebdaaaeceeadacbdaabdddaabcdbcabcaaddcbbebdcedaccedaecaeceeaebadebdeddbadcdbdeeabeaabcdabadcecdcdceeeacdddbbcebcaedbdbabcedbeaddedeeeceecddccbadaaeedeeacaeecebdcaadeaedcbbebaeeaedbbecdbbdbbbcaddedbdccabdebdeaadbdddccbdbcbabbbadceceeccdbdccceccaedbebdecabdddcbbbcebbdcbbcedcbcccbebaccdddcaaeeaebeecdbaeaacdeaebbbaedebbdebeabeaedbcbecdbeeecccaadcdeceacdccaeaddaaebaedeeaecaaeebacbbbcaaaacabddbdaaeecdbdddebebceaeecceccedbaaacedbcaccabccbacccacdedcedcdacbccdacbcbebbeecaadbbbcddbdcebabddcacdacedbcccbdebcaaacbdeebbcbcdebebceacadcaaecedaacbccedaaaaabdcdccdcbceddabeebaedbbababebbdaadcdbdbddcdecdaaddbbdceecdcecabbabadddbecedbdddcbdaceebccbebcbebccdacedeeeaabaadaadabdcbbabdcccbecadebcdaaccbaedbbdcebbdaadacdacaaebddbaeaacdccbdcdddbedcdeedeeaeccbeeacaaccbaabeccdabeebcecdadacbddedddedaeedeabacbadebadcbaabceacaaeaddedeabeeccdbdbceacedabcaabaacdadabbbddbceaedcacbcbbadccddacddcabeddddccacbccbecbcdabdeddecaddcdbebbddcbeedacbccdedeecabedcbccaadcadbbadedcadeaccabdcdddedeacdaccbdceaaeaaabadebebeddaaaecabcdcccebadabddebcbedcbaedaeabaceabbecbdcbdcbeeacececdeaeddccacaddecdadbecababcaacbcbeeabbabebeecacceedcbdacaadbacbdeebdcceaadcdadcdedceebbedbeccbecdacbbddebbaaaacdcacedcaeaddbbddaccdadbaaadeccabcdcadbcebccabbaabcbccccccdaeaddabedbecceeaabbceedbabedebabddcdccadedccebecbcacbbcaaecabeeceeeeaaecbddecdcbedacbcecdcdeaeeeacebcbedababdddbacbecdebbcddaddbeaddbcabadcacdccceeedcbdaeceebadbaddeedeaecdebbeaebebcaedddedabaaadeaddeacbcbdcdddabeddbeeaeaaebdaabcecbcadedbdbabadaacdeeadeecbabcbdaddceeaacaddcedeeeabaecbcdbeadbdacdeecbaaacedcbbdebbcdababcdddcdadbccabcddceecddaaddcbdcbbabbddceaadecccdccecdebbdcabbacdccbedbecbaeacbacdbbcbbdebdbaceadceeececdceeaaaddecdcbabebddeadceecacaddbeaceddccdadbddadbeedacadaaccedddcddcedbaeecbcbebeacebddccdadbdbedebcaeabbacddbdacbaedaaececcbecccadbeaabbddacdbdccbdacdebcceeeedaacacccdaadceacbedaaabbbdacdbdbabbccbbbcabeabcaabdecdaceebdbaaecaeadddcaaddedddbaeeaebbbddbbaaddccadbbbbeecaaadaabbedbaddbbbdadbcbaddcccdebbcedcaaccdebcacaceccabadedbcabaeebeacbceeaecabeaeeedabbbaabeeebdbdbdbbabcbdadaadebcaaebbadecaebdaadaeecbecadaecbebeaacdcbdcddadeececaebadbadabedabbaabdebababaabddaccaebcbceecbebedaaeddcbbbebbabacccabdeccabbeeacddcadacebbbebddbdcaedcbdaddbeddcececcacbacdceebbacbcaddedabccbdebbceedcebbbcdecebbbadeadaddecceeabdbcdccaeecbcaeeddbacabcedbcacababbcdacaedecebaabccacddbcaeedddbaebadaabbedcbaccaeeedbdbcdaaeebaadedbcacdbcaeebabceaaddbebdcdbcbcacacbdadeeeacceabbddebeadaccbededcaedcccbabceeaaebadcdbadebedaaaabdedabbaeecaabccdbddcebedacbecdcedadbdbecbaaeebbbbadbacaedbcaeeaceddcedccededbceeecaabaaabbeaeccadcebabceddcaccdaacebcbdbcadbdbbeaecbcabeaedabadbeaadcdebeeaccbcbddccdcebeadeccaccabcccbbaaebdbebdcdcdccddababbdacbdaaeceddacecaddbbbaaebdacdcaeedddacedddbaedcecbcdeacbddaccbebceecebacbccbeabeebaedcededaacedbaaeeceecdebcbadcdacbcabacacecbcbcddbcacbaecbdaaaebbdecccddaebdebbdcaebecccbdeaeeceeebeeecadddbcbdcaadcbcedcebebabdccdebcdaabdeeaadcceaccecabbcddbeadceeddbececbbbadacedadebaabecabebecdddbbacaadacebdadaeeddeebeebebbadddbddcecbbdcdeadaececedebbadabdcbbbdcdcdeecbcdebedcedacaacecdeadeebedebbcdaeabeaeebacebcedacdaccaceceedacadcbebaebacdacdaedcbabdddaadedbaabcdacdcddccbdeadebaadbeddcdeddceebadeedecaebeabadccdebdcaabebcbebaaaacbdbbaeacddcedcadbededeabeaabceecacbbbbcbacaeecedeedeeebbccebceaaeededbceeadeeaddcdbabbddabeaecedbdddcbeaecbdaaadbeaeaaabebdcddcccadcbbbbeddcecceddeeabdedebceeeeacabbccebeedeaceaabaddabaebeebcbeaeddabbbadeddedbbcdacaaeecdcebaabeeddcedeabaceaaeecedbacbeecdccebbedeabadccdddccbddeabddaddedcddcaedadbedabbdacccebaecdebcdaedaccaddbcdeeccdeecacdaedbdaedbdbcabeddbaaddeaeedacaddeacccedaddccaccadcdbdeedaaddcbdadbbadceecacccdeacabbcaceccaeedceaebbddddecdeeacdddcaebdacdaabbeacbddedceeabeccdabbddaeaedcaacdaabcacddaccaacbecacabdbeecbbcbbecadeacdddacdbeeeebcebeabeceaaaabcccbaddbeaebaabcbebbaacbcbbbeaaadbebdaaeccbacdeaacbcccabbebebebeabccacedebdbebacdbbecbeaababdccbcccddbcdceedccebacedceedbabceaaabdddcecddbdeeeaaedcbeacaceacdccdebdecaabecbcbbbebadacdabdeadeebecdcaaeebecceeddeacedcbeedacabdeeacacaecdcbbcbaebeaebdeebddbcdddedcbcdebbbddeadacaaeaceecadccaaeebccedcebaadcddeabdbbaaebebbbaaedbaadeacabaeddddbcecaaceddbacccdbedaaacadcbacdbedebaedabccbbdbcaeecbebaaacaeeaecdccbdeacaadbccbbddecaebedaccadecbcdececdaccbdecbdeaeedbdbcbcaedeeeeddbcdebadbbdbbccddeabdedcbdcdeececdeeacdebaebdddaccaddeccdacddbedabeecaeeacbecbaeaddecdcbcabbaaecbaaacdcbbcddaaaedeebcdeadebedabdcebbbdbeedbdbaccbbbccdeceadbebabececbaeecbbdebecbbbeebcabaeecabaadaacdaddeebdadeacbbbdeadbeebdaacadbecbcbaeedcceeaccdceacebdecccebceaebbcccacccbaebeddaeaddbdedbcdcbcdbeedaaaaebbbacaebbddaadbddcbbecadadbedadcabadcaedbecaedccacaadccadbcccedbbeeccaaeecbacaeeabcdeabdeaddddeedcbcacbeeddbbbdbdaccddddcaabecdcecadcabbbeeabdcddbcbdeadbbabceabddecbcbdbcabcebaedaaeaddbeceaaaeccbbdbabbcaceaadccaebcdcebadaaaedceedbcdedbacbedeccecaaeecedacccdbbdeceebbeddadcdcddaabaaaaccabeaaaecdeeedbcaebcbdbecbbbbebeccdeaabddcadccdeabeddeeadaeddcdcccbebcaaebabdbeacebbbceddbabacaedaebaccdcbbadcadcacedceabcbadbaebdddeaebddeddedeedadaacaebebacbeeeabeedcdedcacacaecbadeeaeaeddbbdddbeedbabeeddcedaaeccdaeeddadbbebaebdccdaeacebbcebbcdebceadddedccecbcbaceceeebcdbdebebbdebacbdeeeedebcbaecbbeddbaddeacbcabdebeadccdbcabdededddebcdedbcdbabceadadaeeeccebecbbaccdbcabdcddadacbcaacedaddbacceabdebdbcacbbaaeeccbcdaadbecbbbbadddadbeaabedcbaedcbcbcdcbbeddebdcdecdebadeddcdaccbaadcdeabdabecaabbebccceeeaeaceabcbbaadcabdeceaccaceddbcadcebdedaacbeedcadeedecebdadddaedccdacdabaebbdeadddceadbeecaeadbdbcbcbeeaabcabcadedaceaecdbbddaddceabedbceecbdcedcdaedbedabeebbbbedbadbcbaddecacbceebadedbaceeaddeeaedcddeebdecddebacddbacacaaebcaccbdcbeacdcadbcadebeedbddcadaebcdeedcbdceeababebaccacdedededbbedddabbedcaeaebdebcabdbdccdeaebcdbebbeeeeeeacddaacdaeedbbbccdeebbdebcadedabecabeddaacbeaacdeaaccbcaeacbadaaaaabdbbcdbbbebacbcbaeadbabdddbccbeeaaacebeebbcadeecdeaaacbdceebecdbbadbadacbcebcaddaeababaeccbcbccdeaaebdaacaecebcdabaaabadbbcebedebbdddbabecacacbcebedccdcddbbbdebdbddcdbbacdabecbcbeabadaabaccccbcecbcaecbeccccbdddaeccdaabcaaabadadeeacbccdeacaacabebecabecdcbadadcdebabeabdcdbaebdcddadccaebddaecbddededebbeebceddbbbcbecacdcbdcdbbaedaccecbbbbdbeeecbcbaceeaaddebbcdedddedacadabeccebaadbedbeaeabcdeebcbaaacbaecadabddebbacebebeaddbcccccbbdabdaedeeebabdbcbabaceeceebdddcbbbbabbadcceccbdadbceeddcaedcadadbbeccabacdccdedbedbecaadcbbbcacccbcaabaebbdcdcdcccceaeddececddcccecddcbaceeebdeddbeabbbeedbaaadabeadbdabdcaaabeedabbdcbeabbcbdbcbccdcdeccedbabeadaabcbaaacceecbcaecacbadceaacccaadabacbcdaaecbebadbdcaaacaccecbeabbacaaedaaacadaadcdbdaebaedbaacdcaaceebbadcdcbadcaadccceabbdbbbadcbacecbeecbdbedbbcbaebdbbdbdccbabadcabebbdcdabcdddeeaceaeeecbcaecbbcddddecbceaadaddcaababbbedccaeadccecabeccbceebaceabbeaaacccebbaacebbedddcbebdadccdeddeabbddeacdcbeaecadbdbdaeeaecceacccddbebdeaeddebdbacdccedaeccbcbbcadeaabaeebbedeceaeceebbabcbcbbebadcbaceacadbbbcbceeeeeeecabeccceadabaeeddeeebceacbccbeaeacdccbdccccbaeebabaaeedcbcaedeaadeaadecacbaeddaeeddcadedcaabebdaedbcecbaddabeeaaeeadcadccbbceceecaecbdbceddabeecedcdaeceeeedaebdcbcdabbcaeadccadeeadddbcabebedddbecdbdaccdadabdecdaeeeabcebaedcbedadecbdbccbadecebdcdbbaabbdaceacbbbacedcaacaebaeeaccceccaddeaaeeabbabececbbadecedcbbbabaecaaecddedaebccabdbedaaecadbdbedebdaaaaabddeadebaddcdecdbeaedaedbebbdbaeacbdecdacdcaedadadabedecabbababbcaeebeaabdcebabcabaeeecaaaddbccddeeaeabaeecbebcdebeaaceeddacbbeddcebeecebccedcdbbebdaacceeecaebbccaeccaeaacdcdceacbeabaaaebbacaeeebbcececcaeaecabcbdaacabdbacaaecabbdaebbbbebdaedaebdeacdeedadeeeeadbcebbdaeeddadcddaecdbabbcacbbaaeaeedcceedcdabbecebaacaedcaeebbbaaededadebbdccccadbdcacbbaeebaabcdebbaaccedaadeccedccbceedeadaabaebeebbdaceaddabeadabbddebaceeecdecaedebaeddcccaaeebeeeadcadaddabdcbeebbcabaeeadbcabdbeaeddedeecbddadbeaacadeaacbbbeecededdecadbdebdaadbeaedabbdccacbedeabdeaabaaaecdcbdabeebedcccbbeedbbbbaebccbedabbbdcadcaebcbaeddbaaadbbedacaebedcddcebbdececcbdaddaabcbabcaedaecaceeccaccebeacebbbaaeccdbadcbdceaecaeecddbcaabceceebacbbeedbecbddedcabcecaaeddaebcecdceccaeaddcbcedbdbadadeeeddaaceabbedbebceedaebeaeeabbcabaedebceadcaebedbdccabdbcacbaecbbddadbdeebcecddedcacbbddaceccbbccabcbdacecdaaeeaecccbbabebebaadddcaedcbcaebeaaecbaaeababdedadbebadcdacceacaddcbeeeaeadcacbcdcdccabdddccbabdbaeddebdccacacedbebdeabccbdbbcdedebaeddbaacbceadedaebbdacdabdbcdcbdbabcadebdbdaebbdbcacdbcdecebabbecababcdcebdaeedbeddddcdebdeccdbdeaeedcaeedbdeeceeeadbbadccecaddecebcbedcbacbdbbdbebaccdaeebbdbecadebaabdbbdebbdedceeeaaaaaeddccdbacdccaecdcaccaeaedbaaadddbbddecacabdcbaadedecdeabcddbeeaaabdadaedcdcbdddecccbdaabdebdcecbdeacedaadcbebbdcecbecaeadeaaeacbaabceaddecdebdaaececebceaaebeedccccacbabcbcdcbaaaacaeeddbeaaeeceeaccbaedebcacbbddcacbddeecdeecebcbbaecebbbaeeacbeeddaeaabbceaccedbddbdaddbebecedeccdcdacbcdbeabccbbebacbbcdeaaccacedaecadbeecdbbabddcedbdeeabcbadecdadeabbedeebaadaadbdabaceaedcdbbcdbaccbaecddcebeeebdbecbaecadaaaaebccbabaddaedadeaadaeaddbcbdeebdcdababcbecceedbdaeddaabbadedddddeddccabbecbacebebccadebbdcabceaccebebcaeaadacdedaddddbaeecaacdabadbecdcadeaeeebbdbceadbbaedeccaeadcaaeaacadaedbdcccdababbacdbedbbcaaaecaeeddaeabedadabeabeedbadebddaddeddbcdeaedbdacedadaebdbeebaecbaceaaddbcbaddbccecbecbcbdbddcddabdaaebcbaeceaccceddebbaaeecedeebbbcddbaabdcabbdccaddbcaaacdeaebcaaeddadbbabedebaebaecceeebdaaaedcedcaecaaeeceecdaeaeaeccdeecaeadcddababcceddeceaeaeaeccedbbeacadacbdbebdbbabebdeabedbddebccdcbdceecbabeebedecadeedbdadecdaebacccaccacbdceaacbbedeadcbebdcbdaceaebcabeabdcebaecbdecabbbcbedeeadaedbeeddbdceeabeaeeccdaeaeabaaeabebcdacecbdaedbccabdedcaeedbbbcabeddceccddeeaedbbcecacaeabbbbaeacabbdabcedcabcdcbadcacbebedcdabebacabddbcddacdbeeabbddcdcceedbeabdcdedeaaeeadacaeccccacbcdbbecbbdcebbbeddeaceedadbeecacedeeaecbdaaaeaebdebaddaedecdeaceecbccddccaccaccedecccdcadbaabccccbcdccedcadcbcdbbeedeedbcbdddcdaeeddeeddabecddbecdadcadcebebcbcadcbeeacbdbedeadaabdaceabeedcccddecdaddecbbcccdcddbbbdcbabbbcacacedadbddbbeadeceeeeeaadcdbccedbaddcaaceaabbcabeaaeebbcadbdecadceacebdccaaaeddbacdcaeaecbcebacdcaedbdaadcebaabeddcdecbadbabbdebdbacdaceceddcebcbacbbbcdadceebdbabaddebadecbeaebcccebdbdaacbecabaaddabbeaabcceecbbbdedaecbdbbdeeeadeeadacaadacbaebebbbbccdbcdaedcacdcddcbeeaccabdecdbececbeadebdeadacccbcbabdaedbbbccccdbccebdaccbeebeebaeedeeeccdceccbbbabdbcddededebaddededbcbacbceddaaddeabcaccbddbabbdaaccddbabcdcabcddbaeeebcbbdddbccbbeaaabdcedbbbbabeaacdcedcebdabcbacccdbceabbdcbeeedddcaccecceccadbeacceddababdeaadcecdebeaadceeabaebabaaebddabadabccbaeddebeaaebeddadeedbcbbabddbbececdaaecacbacaabcbdceeddbeccecdecabdababebaaecabeebcebeddeebeaedddbabecbcbadacaadecccaebbdaabededecaeacbaeebadaadaabdeceacebbcbaeddadadaeddccddacdbcadcabdabedbcbccbcbaaddbbcacddddbedadbdbbdbcadebecaabedebbbeadededddcdaaeaadceebabcbcdaaeedeeeebaadabacedbdbaccdebadcaacabdaabedcbbacabbadbdedaddcabceeaedeedbecaeccdeccebbcdddcaaeaabebdceccdeebdcbcacaaabeacdccaecddcbaacbceadbdecbccbcacadabaaaabaedcbeabeecdacdecadbbebdeeeecdabacdcaabcbeeeaceaedbedbbbbcebdcaddceabcdaacbeeceecaadaeaacedcccabdbdeccebbbcacddcbbadcaeccbcdececebcddbcdaabecddacebecaeabbceadababbdeebeedbabaecdbadccbbccbdeacddaccaecddeeceabdaacddbbdcacdabeaadeaabbbbadddeaecccadcecadaceacdbcbadcebcabecaeecaaaecbbdabcdbbdadadddabdbdcaaaababcebebadabdcbedbcedaddbaaedacbaecaddecedcaadbaadaededdeebaabaebbaacdbbbdcaebaacaaeabcadceaaabdbebeccaaacaeacebedcacdabbeeaecebdebcbdaaebbebbacebdbcdeabcbabcdddacbeabbabdaeebbbabbbddaaccdececeeacacbedddcebbedecdebcecbceceaaadbdabbebdcbccdaaaadbedbecdaeaaeecaddcaccdeedbaccadeceedaabddcdbecedceceeabdabdbedaaabeeedbccbaceebaeaaaaabdabdbaeaeeabaeeeeeeaabdcaadbcebbeccadddcaaeeecdceaccccbaedcbcdeeddcebecaacaecaeaeaacecceddbbaeeebbeaceeebdddeecbecceaccbccdbdddcadaccbcaaaddccaaeeeaccabdddbeacecacdeeecddadbadacaededeecdbcbceeeecaaeddceeeebcecceddeaadceeadceedbeacedabdcabbaedceddaadddbabeabeedeeaabacabcdccddeeababdeeedabceaabccacbcaaebaceeeeeeecacddaabbecbbcdbbdccbedeaeddabedecdacbddaabcaacebadebedbecceecebacadacbedecbacbcdbbeeadaededeaeddebaaeebdadcdccdbcccdbbecadaadabdbbdcbddebaecceaecebaeaaebcbcaccedacccbbdccbdaaebabebecbebbabcabadaadcebecdeabcbadcccebccdebeeeeccaaabedccddbebbaaccdccbbeecaecaeeebbbaadbdcacebdbdaeacdabbadebbdbdedddaecadeadbbacabadabaaabacbaeaeaebdabbbcbeaccebddacdbaaabaebeabeeccdbcaccadbedbbbeecaaeeabeaebceebcedbcbbeaaedbaeeeaadbbedbeccccaddbeaebabdabcaceabedbaedbeccaabecdccaedcdaaacbabbcbcedbacbdbcedceeeeadbbbbcbaeaeedbaabadbaebebacaecdcbaccebecbdbaceddcbebbeebdaeaedeeebdceeecdbecaecddeeedaddadaabedeecdedbdedbeadddabcadabebacdcbacabbeacccadbbcbabceccabdeebdbecbddacdedebbcdbedaaceeeebeadaeedabaedaaeaaceddeddceeebaaecabbcdbeeebadccaabacadcaedcadccdacedadcdbaacddbbcaeeecddadcedccabcbcaadebdabddeabaeaadbdbabcdcdebdedbddbbccbaeebcaabdbccbededcbcebcbbeeebaacadecedaaeceddbddddcaccdcaddeddeddedceabebceaddbcccbbcbbbbeaaaeaddeebdeaddebcdbeaccbdcdeeedabbcaababeaaebaaaeeadebdebbaaebbbbacebbddaebbaeecacaabbecaaececcaacdacddeecaedebbecdcbccebdceeaaddaaccddeccdabdacadbcabadebcadeccacedbbeeaedcbacdeaadddabacababcdaccaaedbcbeabedeecceecedcdcddcdaacbebdcaaeddeedabeacabeedeaacdaacdcccbdbdedbcebbceadeaacaeeeabbbeaceeaebdccbadcbdecadcdabccaaebccabecdbdaadebaecabadecebdccdecbacccdcdcccbaabaacedddebcdeacaeacbbbbeeaaacdabdbcdeacbceceededccbedebcaadaeeaacceeccebbbadadcbdeddbdcebccdabdbdbcaddadecdeadabacdccddaeaaaeecccaebbcecbeebbdedbaaebcbebccbaadecaccdceaebceaaddeaecdbccdccdbbcecaaabebebbabdebcbabecbbbbaeaeddbadcbdceceadeeceedbedaaecabeedddbeceedcdabbaccbdedbddaddebbddddaadbabaeedbadbaaaccbbbcddbdededceadebdaccdcbccdebeccbdbbddccaaeaaacdcbeaebbbdeddecaadeccbadaeacbcbbaaaeaddcadaeedadadaaceaaddababacbaeeedcdbaebacbccddeccccbbbedacdeecaeaaacccbeaeaecebabbeeebddbbcbcdeaaeedccadaccaecedbecddecdacacadbedcaabaaabaaeadbecbcdecebceedcdcaabdaacbddeddcceadeedaeabdcbceedaccabacbbccbadadbbbccebcdcecadababeeecabedadebcdbbaacecdcbcedabaabdddeeaeaddabaebdbdebcdeacbecdeecbbbeaecbcadecbcbdbadcdaedaebbdcbdceaabdbdacbbdbdcbedebdabcecdaabccbddbdadedbddbbacbecbbddceebcaaaeeebddcedabebdaecdddebdeccedbaeeaccdceddeaadbebadecbdddedddcabaacacabbddbebdebbaebeedccbbeedaeadbedcacaebcdccbbabdaaccbcceabeadebbddbacdbbacbbcbebcacceeacaeadbacaccadbdcacbbdddacdadaacbbbbeeaebcbebabceabdeecdbcbddabbeaeeeccbedeeccbadabeebbeacaadbdcaebeabadaeebaabebbbcacecbcedccceeacdaadccbeeebeeadaccdbbcedbdeaaebdcbbeedecdeaaddaeeeeecbeaacdbecbbbaccdcaadaebccccedbedceebacdbbaacadabcdadcbbcddeebbaedacbeccdbeeeddcabbaaecadeaccddedbddaecaeadadeacebacddacedbbdbcbcbebadebeeaececebaeeeacaaeadddbbaccddadeebacaaebebcbebaaebeabcccceabcbdbecccbaddbbadaabeeaedcaeacddebaaaaeeddaeaddecdedcdddacaaadbbccbdcedbcecaccbdaecddcdecbceaeaedaaddcbedabecadabdadbceecaaacbbeeeaedaecedcababebabbdacaabaddbaebabbddaadebbcdcaddecbcdcccbccddcdaabadadedeaddcacbbcbbaecbcecaacdacdeeadadabbecddeecadcaceeebaadcaadbcbecdeaaddddebadabeebdcdedeeaedccdeabeaceabedadaeacbdbbdebedccecceccaddaeaccdeacdcebebecabaeaededcaabdbdddabcbeedadaacadaeddacbaaaaeeeceeddebdbbaebddbcccdbcbdaebbcdcccebdcbbaadbcdbaedddadaaadbdcaeacaceaadceadaaceccddacdcbdecedcecacbaddabebabddbbdbedeadcbebdadaecabdcebbbeccadaeebeddbebdcdeeebaeaaaeaaeeeececebaeacebaabdebebccebedeeaceceaeeaacaaeecbcdebcccacdceebcbebbdbaaacccbdabdbbeeadbaaabcbecdccbeebbbaedebddcbeebecdccdccbbbcdebaaacdbecdbbaddccacdaaecbcdbddcbeeecdbdbdbedadcdbbadcbebbedaabcbdeaceacbeabdaeceecddbdceaaedbdcdbaaebdecdcdddddcceabdcabeceebbccceddceadaaeacceddcdebbbbcbddcabcadebacceadabbeadcdbccadecacaebabacdcdbcbaaedddadaeddbadabbbccadccbacccbaedebbccccbcceeeeeeaaacedcaeccbebebbcaaebeeebdedbbccbdaaaddaaaababdcaccedaeaeeaccdabeddcabbcddbedbeadbbadeecccbbbdadceeedbebdcabeadbaddcabeaacaabbdbdcaacbebddedddeceeeadbbbcdecbacbedcadbbddbaeddbeecddadebcabcdbbadedccddccecaceaddaeccaaecedaaacdcdedaceaebebccccbbdcbcebecabbcabdeabecddabcbddbbeaadbdeeeaebabadabacbacedecaaadeadabedcbedabeabcbdaddcecbebededebaacccdbaaedccecabbacedecaedebadddbeabcddebcbeeeceebaaaddedaddcdeccdcdbbaedabccddaacbecdeaaecacabbcacaacdbdebeebbcbaacadcdeeccecabbdaeddbcbebaacbcebdbebaabccbddcebebccddbbadebdaacaddddaabddbdccecdcebeabbdbeebdcbdabaddceeceaaccbcaebbcdddddabaaeddcbadadaedbccabcdebbdcbeeaacdadecdabbabdaabacccacbddeeedccbbaadccbaaaeeaddaddacdedbedceadbeebacceeeeeeecebcccdaaecbbdbdccdebaeeeeaedecebeeabaeeadabeedbeebacdddbbbeeaaeeaceadcaebcebeccbeeabdebebadeadddedcbeeccbddcacebcecdceabecdbeecedcebdeadecdeddebbbeeacaacaabeaacadabccdceabeacbcaecbcbbacebadbebedabadbbeacdbbbdddcbedecedddaadbcaddebbcceacbdbcacabeccbbdabbadbbcbbbccbebadacbebddebabcaeebeebbdeedeecbbbbccbcdcdbabebbbbcdddcbbdbcaabcbcdebbbbeccedaadebdddbcdbbacdedaaeaccbabdadcbbccdeceedbcaeeaeebebbbccccdcebeadedddedcddbdecbaaaabcaaddbeceecddcbeeccbddbcbedbcacbdbebddaebbabccdeaedaceaccabaccaecadeaeaceddebeecedebbecdcabbdcbcccddeccabaaeadeebabdccaacbebecddddcaaadebddacdaaeaeeaeccbeceedeaadcdcacadacaedcadccdceadccacbbcdbbdeeebeaccbdaaebcbbeaeeecbdeccbdbcbeeaabcaceccdaaeccbacceeeeadbcaadedcaeeaacacccaabdebadddedbcbeaeeeadbdedacddcedabbcceaadddedaabdebacacbdcabdaabacacabbdbaabcddcaddbecbdbabceecbaadddcbbdaccedbdcadceedceebdecdcddccdbccccaaaacdbeaaaadbdabcccbeacbdbbcebcdcbadaaaaabddacadbbbcecadbebddcabbcddcbecddededeceecccabdeecbedebecbbcacbedbddddcedbeeeabecebeeddbdebacabbcceaaadcedaaddccbebcbeaccbbdceacbabdcebbaabccedcdddebaedecdecbacdaecbccbbeceadedadeeedecaaedceccccceadadedbcdaeaeadbccbaaddcbcbaabcabbcadaabeaeeeeddaebcbebbbacdaecaebcbccabbdbcbcaeabdbbeddbacdbacdbdcebdeebcdcdbdcceadbddabdbbceedcbcdaecdecabaebadabacceddbaabccdeeaacadeeddcaeeecdbbcbdadeaeabedaeddcbbadeaccdcedeaccdabbbbcdcdcaccccdacccedbaacabcaedcecbdeecabeaeeddabdcebcccccaceeebddecaebbeeedabecadabdecbedcbbbacaeabdbcceadceddccbaeaceaaadadadedebebbcaabcaececaceceadcedbbdadecdaebeccabedacdabcdaeeddbecbdbeebbaeecbbbbedeaaabdaedbccbbbdabdbbebdbcccddbdbdadaaddbecacddceacbcaeacbaabdbadccbacdebdaaacabbacdedcceaababbcaabbbacdebdcbdaacaebabdbbacbbbddeaabbbadccbdcdadecacabadacbbacdeddaedeeaedadcbecbaaebceebdaabbeeaebaebdbbddeddacdbdbebabaeadabbeaeeaaebaddeadacecbdcacbaaaacdddaaddbbbdccdaaaadeaeedceceaabcdadeeadedeaddcaaebaeabcedbbcaedaedbcdbcbeaddcedddeeceecccdcabecdcaecccdbaedcadbddcdcebebcbecddcbedaeedddbbdadeeabdcdcaeedbebcddaaecceeabacbbbbacaadcbdbeadbeecbabebabaadbdecabcccdbdbaddbceeabacdabadccceaeeaaecccedbebadedbbbcaaaaddaaebadeeeddbdcbececebecbcbaacbdecaecbdceebbaeeadaceddeedbcaddccaaeaadcdddadddebdcedacdbcbbecabdecbbbabbcdccbeaebecabbeadddbedeaabbceedbeabccaaaeddbadbbcbecaaeeebaccddedcbbdaceaccbadddbdeebbaadbbdabddadeeddceaeebebbdebcbdcbcdaaabaccdabdebcebdcccbdbabddbbeadaacbeceabaaeaabbdddbeebbeddccababebddddabcdaaecdebaabadbdaedbacccadedbacaddcacecccaacecaeabddddaccdeabaaecdbddcdbbaaacebbabdbaeaeddbaadbebdcccceccbbadecdedaadabdbaaacccdaedaabcbaaedcccddabaeedbbdcacbecdcbaacddbbabcdcdedddaccaecbeebdeacbccdddbccaeadabbaddbdcacdcbeeebeedbeadecdeebbeaeadcddebebebecdcbccdecbddcdeacddccdabcedeedacddbeeaeeacbbcbcdbaedaacabaeadbbbbaeaedaaaacdabadceeadbedacabcecdadbedbbdcdeebcbbaabdbeeaccbcbdebddeadcabecaebaabedcbdcebddbcdebbddeccbbeadbdcbbacbddbabbcdcbebbebeceabebadaeeabbdcaccadaeaadceeeabbcaaaabeabbecddbebdeececdcaadcbececededcbeebdaeaadecaccbbaababcbcebcdeebaddadaaddcebdbecbcdacccbbccbdebeaaadbecbcdceeceebeaacbaeeaecdacebedaaadbeaceacecdebadbbcedeebebdcbbaebcbaabedbcddecabbbbbdcbbcbdedbdbdbccbdcddbccbdaeecbeadcbedadcacbcddaeeddcbeacdaddcceabbbdeadbacbdcaeaebedbcaadbebecddbeccbaabccdddacbeabaddacedbadebcbcdeacddbbcbedebdcbbaabadeecdeebacecebbaacebceadeccadacdaeeaadaddbeecdbbbddeddbeddccbcedddcbbaeaceceabdeeebbcccbdaacbdaeccbadbebaabceedacebbeeeeeebbdaecbcdebadbbbeaaeabccdbacdadedacabbebadabbccbecbcccddcabaaeedecbeedbabeadeaabdaebdaaaaeeebdbbccdaaeaebbdabadccddccdeeabdcbadebbdabeacbdbadddebeabdbcadaaabdeadbdbebcecbbccadccaacdbaccaaecacddcddeccbdcabacccaedcaedcbeabdbdceccabdecddbddecbacddacabdbeddebaccdeeddaddabecbdbbeabcccaceabebaeaabbedddcdedccceddaecdceeabcbcaddaeadccdbbbabdcedaddbbccddeabcdbadcdabebedbedcdecabadaeedababeabcaecabcbdeaabcddbbdeceebbcaccbebecdccbeecebacabbaecabaabebecceecdbdddcbcaecabbaebaaadcabecadeaebdcbcaeceedbdbcacebaadeedbbacccdeddaeaeaacacbcecaddcdcbdebcdcdbcdadbaacceedcddbccceccbbdbebcaaeccdcdaecbdbadaebbdabbbdcaabdccabeedcdbedeabdaddadbbbbddccabbacbeedecaabbbaaacbddbbcdebdcacbeaacddddedacddceceeeeabdbdcabdbeeeeddbedaaceaebcbdbacaecaadbcdeecbabbedabcabbddbecdedbccedaebedbdbaccaceccbeeebecaeedabdceebaabddaeebadeaeaecbeeceededbacddaeebedcacdbbcdeecaacbccdadeabeacdcbdebaebddbcebedbecacbadabecdbbedeabbacecbebbaddbdaaabccabcacbdbcdacdeccaacbcaababbcbaaeabadcaaabadcedcacbbeeeacaecaaeecdecddbbecdbeabbaaeddedebdeeddcbeebacdbacacadbdababdccbcedaacedcddcbdccdcdaedadcbedaaedbabdcdbdbacbddbbceddadbceedecebcbaeadeecddbdabbccebaadeebbdddecdecebbaccbccadbeacbdbbbabdeebbddebcadacbabbecbeccddeadcebccdbadaaecdbaaaaaecaaaaeabbeabccddbbcacacbbeabedeaeebbedccbbaccadbcdeecaacaaebdacdadabaeeadaaaacaddedcaceecdeceaaacebeecbcbdabbaccdaaeddadedecbeeddbbebbcbbcaabaebddedaeacddbcabcbdbdaedecabaedbccddbcacabdbcbecdbbcacecbacbeddccbeedcbdaedbbaaaaededdabbbeebceecbcbdcbbccabcecceceaebcdabacebcacebcddcbdbaedcaabdadeecebcadccebdddbaebedbbacdbcdabcdcceccdddcecadbbbbedddbbadbeeeecdbdbdbcadaecbddbedaabeabdacababecceceeaedeeaaaadcabdecadcbcdcccecbeebcadceaeccabaeaedaabbedaeaadacecbdcdaacceacecbeceeddcbadbbdeccabddcaeaebbdbbbdedbdecdabcecceeeeeeadadcbbeebecdabdaeaececaceeccebeedeeeecacccacdecaaecbaeddbeddbbacdcabacebcadeeabbddbaacdbcccecebebdeadeedcbccccdeedbdeccdaabaacedcabeaadadeeadbbacadcdaeeadbdcbbacdeddcebdaebeacdecbbbcbeaeeedeececccedebcdddebdddeebeababbcdaaaacccbacddaaabaaeeccbcdeaabddabeeeaabdcbddeeacdaabbdeddaaacbaeabddaeddabbeeedecbedeebedcabdacebaabbedeeebccabecbaebeeccdaadaeabbddedeaddecabbacbeabecbbaaaddeddedecbbdebcabbbdacbddedbdaecceaabcbbaadbabeadbaadaeaabcaeaabaceaaabdbdedbcaaeebcadabdbcdecdebaaccedbacaedaeddcdbcbbaadcadbceeabaaaabbceebcbedbaddcdacedcecdbabaadadeeeaeceaecbeeecbcadecbeaeaadbabacedebebbaebdeddeeabcdaddaaebabeaaeebabdbcdaaceaabeebbcaecbacccdaebbbdabaebedaaabaebeaabcbdababededcdbebbebcdadbccebdccdcecbcaadccaaacacededaaddebaadcebeeadabbedaadbadbaeeaadabeadbcbbbdcbddeccbcecbbcbeaadaecbeadbddcbbeddeaabbccbeecaedebdecdccaabcadcbaeebebccdaacebecdbeaeeabdeababcccabbabcdebcddbecdabacaeaaacaaeacebbdecacddebeecbcddebdecaebedebcabaacdeabcaecbdcbdebeaadbadedcedcdcbbdeaabdcedcdadebddacddedebbabdaeaedecceabbaadaabaadaeedcabdecbcdcabcddcabaededcdecbbabbecaeedadcdacaabdcbcbcbdabcbaacdcacaaaadccecdcdcbcaeaeaabcadcdcebeabebccddcaadddadbacaacaeaaacdcacadaddbaeeedaecdedbabdaceadebdbebaeceebdaaeeccaeabbabbedaedceeedcdcacceaabeedbbdbaaadadaedaacbaacadbcacbcdabaccebdddecaaccdecdaaebbdccbbacdacbabdbdccdbbeeaebdadbdaaebdcdddedaeadcdcceadbcbdeadcbddcadaedccbaceabadcddaddbddaeeabcebbaddbeddcbcedcaaedcbacdabdbcdeebdadededaccdaeecadbebcedbdddeecdeceebbeaecaadbadcecabdbcbeddeaedcdebedbebebcadbbeadbebcceddaeebbddeaecbceebaabaaaaaacbecbbdedeecdbeebcddabdcbebbeadadebcaddbcebadddacddbccaecbbbaddacccadbebdbaddbaaabeeadbddbbebdbecbcedaccceeacccddeaeedebbaaeededdadccbbaaeeddabababbebcabbabbcaceddbddcdaeeddbabedcddeedecbcbaccecdebbcbdeccabcdeeddabacbddadcaecbdbbbaeaadeacadadbeeeebdcebbaadbbcadcccccedcbbccaeaeebadbcdeeaeaadcedbcadbcceceabcedcceacaabcabeacabdcbccbcddaaabcaeaecebdcebabceaebabdbebbaabebeccdbdddbbaaccaebeeedebbcabeedecddcadbbbbdebedcdaeceecbbbcbdbcdbbcbcbeeceadbabccdebdeeaeddebbecddeeecabbceedaccaebacbbeabbaaedcdaadbdeadabdcdcebccecadedbabccbbcaecdacadcededcaacdeebebadcacedcdaadeaceeeabbcadbdcdbbcecaabdcbabcddcbcbaedcacdbdabbdadddbbbecddcbaeacdddbbeadcaeeaddaeacdecdbceeddcbdccbdecebdecaabeccdacbebdddeaacadbdbecedddabdecaecdedabccbcebcbcdbaeedcaeaddcabbddcbaabbcbcdbbbcbacaebeedcceeddbebeaebdeeabaaaebecbdaeaccbaaebbbdbabdbeaeececeabbbbeeeaebaddabcccecdbadcaeaeeacaaaecbcddbdacaeacbaeebaedabadddadcedbacecedebebcadcbdbbaddaeeaedcbcaceadeecabdbcebeccdbeededaabcaceebbbcebeabcedcaeaadedecadddbaaadaceddbcadcbdbaddddababaabdbcebcdacbebbbaadaaaecbcebbceedcebddeeecdeaedebdbaaabdbaaaeedbbedebddbaebcabcdaadcccdecaecdecbdcabadccbbcadeacaedbcecedcbceedaabaccaacacaaccdbeaceceaaedabeadbeaabadbdddacbbdedbbbcecaadedaaeaadccbcbcdaaaadbbeacdeecdeeedaceababeddaaccdbbbebaabaadabacdecdaecaadbbabedacbaadceaceecdabbccbebecebcbbdaaadecbbccdeceabdcabeadcdbcadbadcceedecbeaaeddaebacbdaaaccceaddcbbebbcdcdbdbccdeddbabeaaeabaeedabcdadbbdbdeebeebcedbdedcbbcbaceddceeabbedbcbebdcdaecdecaaeceebccacadbebadbaeeddcebdeebcccbbaecaaacdedccddbdbdadbcdbcadeadcadeccaebdacbcbdacabacbbeadcaecbecabeeabaddbaeddabdccbdccdbbcabccdcaaabaedabeedbadbbdeeaddcaeceeeacdaeecbbcdcdceabbceebbcaeacbabedeacbadebeeededbacdddeceedceaddcbcacdaacdbaeeeabaabaccaddbabaaebdebcdeacadbddbeaaeacabbedacddbbdbeddaeaebcddeddddbbeaccedbadbbadabbadbeeceecbabacaecccebddedcbdecdcddaebcecbdadadcdebdaaaeeadbeccdebdaacbdaabdadabccdbcedebebacbcacddcebcdcccceedebeeaeccadcecbdedbeccbcacecebbeebebdceadbecddeccbcedbbeaabccadeeddabeaaaedededdeaadccecccddaaccdacbccaacbedddabdebcbaadacbcaabbcbadaaebdeebebcadddabacedabddbbadedacaacbacacbbbddacadedaeceabcceedcdbcabbeeebeaaaecbdeebeeabadeccaddbbeadcddaebdbbccabaadeabebaadeaaeeccdecddbcdbaeccbabbccbbcdcdadbcbaabdadeaacceddbcdaecaecbadddabdeeedadecdaeacedbdeecececcaceacbadeaecadaaddeadaabcbbbaabbbcececadbeebbdaeaedeaedddadedbaaaadecacdacceacedcbbecabaecabecbaaabcabdebabdcddaebabaceedbcbdedecbdceeacedecdebdbcceabeabedeedbbdccebdbaddaabccdbdbeeaeddebaebcdcdddcdaacbaeabeeccddededddaebaccccedeabeecdedbdcbdddaecbddcaceaaeeeceadaaeeccbbceaacadabaccaebdbdbbbaaedaeedbcceacaeabceabeaebeddbecbddddabceaaaeceadbaacbeaaeaddabdaeadedbdbaddcdeacebeccedcecaacdecbcebdbcbeeadbccbaeedcaadadecbedecaeecaeeecececcadcaaadbbebeababeedeacbdaddcecbcadbadccedbbedeacacbdbceacbadddaecdbdedbdddebceeaeadbaddeebbdbeccbaaaeacecabbdcebedaeebbedcadbadbbbcdeaaddaddbcedebedaaaeadbccccdbaadaaaddaeababdbeaebabedacdcdacbeeebdcbabccabeebaceebcedaeadabacdeccaecbdeceeabccebdecbccbbdaeacbaebaebadcdbdccbcabacecbeaaeeeaeebccddbcbaacccbebbebbbcbcaedaeaeaeeedbcdecddcaececeacdecebeebbcddcbdcdcddeeddeadabebbcccebaaaebdaebbdaaeeeedccaaadbecadaddeabadbebaeccdcdbedeeaacaeeaaebbadbebceeaacdeccecdebccbebbcdacdccecdacacdcbcadaaeeebeeabedbdaebcddedbaadeeddbabadeaaabbeeabcadbbdabbecdeabddadacadcaeeaabebecabeebedcdbeebbdecbbbcbcaecaadcacadbbdbecbcdccecbcedcbcbaddbbceccabeaadceddebcaadbcacddbdbbccbebbdebbbdbbbaaeddeabeecbcecbbaedcdeedcbecebbcdcbebdaeecbbcaaceaeccaaeedcebeabbabaeeccbbbdeabdcacaeeaecebddaeccbeebccecaabedcdbcecddddabecadadcedbabaaabdadabacaebcbcdeddccabeeadbdeddaccddecddddebdaaaabeedebedcccddcadcbecdcdebcccbabaebeebaaadeaddaacceddeebadbecbbacacbbcaaebdbadbedbbbeeebddbdccbcecbcbbcbbdccdaadecbebaacaccadabcdbccbaedadcbaeecabebbaeabacbabadabbcdddbbdaaaeceedaaedcebcebbacaceaeedcecbbaabbaccaacecacadbccdadaecbebebcbbabeacddeccdddbdeeeabcdacabdddcbadeabccdebacdceeaeaaddaacdebbdccbcbbedddadacbaccdadedddaacabccdaaceaacecddbcbeadedeaccbbbebddceacbdaaedbbabebdddadaaabecdebceeedebaeaaddcbbacbdcabcacaebbcbecdcbdcbebdcaddceedadcabbaaedbcddabaabbbcabacdedecabdeadeabeadcbaecadecdaeddbcebddbedabbeebdeddedebdaaccaecbcbceedccadcbccbbeaaabcaabedacbeeeeedcdceeaedeccbcedccceddeecadabdacaeecccaeedbdddcaecbdeabdbcbcaeacadabaeabcbbaadeaeacbaeadbeedbebabcbcaaaceedbbebebccacbcebabdedcdecaaadecebbbeaccaeedbccbacecbdadacdcdacdaedbeadaeccdeeaadbbeeabeadebabbbaeacebdbaccbaaaabeacbbceebdbbedeaacaadbbebdcddceaabecbcceeaaeaeeaebedececebbaccaaaddaddbaceccdcddedcecbeaaeececeeadcdadaeebdacbceccaabdbcecebebcaacaccbcadbaecabeeeadbabdacdcaeeedcacbdbcddbcaeaacdcbccceedcedeeddbcbbbebebebbddddbbdcbceddceeaecdbebcebebcbadadceaddedabaabceedccebdaccdbbebadaabacecedeebbbbaaddcacbdcaeacaedbacddcaccbbbcddaccabbecdbeacecdceacbaabbbbbcdbddcdebdcedcadbdbdeeccacebebdddbdcedaddadddabcdddadeabdeeedbedcaaadededbcaecedccdadcaedeccacdaadbeabecaddbcedacaeebbdcdcebebacadbcdedadeededeadaeddbddcbbdaeeaeedbcacabcbacaacbeeadddaceadddceabdecbcedbcdccaaccaeedbbbabbcabcddaebceababcaccadaebbddddadaaaceaececdabeccdacbebbcecdbadbcccabeabdecebcbecbbddedbddeebeceecbbcddcaceaddedeecebadbeedeccceedadabeeeaeacdeeaaebcbdddedbdceaaaeedbdacbdbdadadabbddcceadbeabeeaeccbccbdbbededecaedeaeeecedadceaaaeedaecdcbbedeabeccedebdeaebebdcdbabbadeebcbebaadbbbddaeedbbbacbaebabbbaeebabcaddedeaedcdccdddadabbdbaacbebbeadabdcdbeebbabaadcbbcdeecaadcdeeccdaaadbcdaeabcbddaedeccdeccebabbddedbebccdcedeecbbaebbbbcccabbdadbeecbbaeceadeeddecccddaddbaaeedcbeedcbbadddddaceaedacbebedddbaeebaccdbccccecdccbdaabadaceedcadabbeabdcabbacdbcebcbebcabdcccacadaccddbbdeaeedaaadedeabdbeaeeceeadddbaaeaaaadaadbaaebbaccadcbedcbeaeddbbbabcecdececbeacabecbbadcbbecacbeedbaccbcdcaecdcbdaaabebeedaddbdcceecccdebbdcebbbadbbeebaedacdcaeabbccaebeaaebdedacbdbbdbebcbababdeabcecbdadcbcceaaeddbdadbabdbbcbecccbebddcbbcbacbeebacbcaeaccdbbabeadccbcadadeabcdceceaecaeaeabdbaaaddacbeaacbdddabcbcecebdddebaadaebdeaeadaeaacacdbcabcdeaaddabbceeaaaceadaadbbdacaeacecacbaacdecbcbcbaecacdaaabeabdbedabdebcddbaebcbdaadedceddcadbeeaacbedeabebcebaebddcecebdebaaeeaeeeccbacecdcdcecdddcddadcdcbaccbbabbbcaccbbdccccebbeecdaeacdcedeecebcddbeeabaacdcdbaaadbeecbaaebcdebaeaebeedacaaaadebeddddadcecdceccadaabcdaeaddcddacdcbabbcecabdacecbdecdecbadcbcbddbcdacdbabaeecdedacbbdeadaedabdbcdeeceecbabeedccabceecadbacdebcabbdadbccabadbeaaccbccbaeecebcaddccacecddcddabacddeadccdbcaedcaabacbdadccccccbcbeaadecadbbeecddddccadaacdcdbebabacaceeddccebebbeccacedabaebddcbeaaabadcaadbaccbcbeccebdcbbcaebbbeeebdcaebcacdbacccedcbcdaaacdedbbbeecaaeceaceeacbeadbaaadcbccceebdabdcbeddccdceebcbcdecbebdcbccbccdcadeedadacbaeabbcbedbadeaaccbaedbdadcebeaebaabebdabbeadcbbdaebcadadbadeacabbaccaabcecdbcedcceacaddbddacdeabbdaddbcaaedcbeabccdbdaadddbeaabadbbebcdbeaeaadeaeaaabdaaaccdcbacceeaeaaececdadbaceeaceceeeceaebaebeaacaebaebebaedbbecaddbaceaceacedbabdadbebcbddceddbececbadedcabedccdbbaadcedcbeeacecdeeeabaecdbcccdabbcecbcebdaabdabcdddebcdaddbeecebbbbedacbabcaabcbecaecaaecebbeaabaccccbcdcdeedeebadcedadaddacecbccdbbcdbccdeaaeaeacdaabeeabbaceeaaecaadbcaebbcccdeeeeddccdaabcbebcdeaebdadccebdeeeedceedaacdedbbeabbddecbecacacbcaabadcbdebaebdeeacbdbbabdcddbeeaeadecdeddbedaeebcecaaaceaccccadabcbabacebbbccaddaadeadcdcabcaaebdabeedaaeaaeabcdbbbcccddaeabaaeeddaddabdcaedebcbcabdcdbbedbdcddbbccebeabbeeadabbeebcdacedaccceceaeebedaceeebedddbdebebaedceeccdecdcdedcebecdadbecadbdddceacebdbdbabebddceeaabadadacbebebdabdadecebbeeedaececccaecbcdeaddedbcbdacbdaccccbccbccdeeaceacdaacbaccbbcbaacddddebddeedadadaedddccdedcdeaaccbeeceddbbecddddacccbdabacdcdbbdedabeeadeddbccbdadddcdaecdaaaceccbcdddebeddacdbcdbacbdaccadaabeccceabaeadbaaccabcddaeeebabdaeecbdaaddbcbebbbeaabacebcabadddeebaedcaecdcddcabbcdabebccdcdebeeccdeddaaeaadaccdcaabdebeeaeabddacdebbacbcaaaeedcdbedaebaadbaecabcabdcabebeccaeeabecbbcadeaacddddabaeccebeeadacdaccdebdeabcdccdecdddaeedeeebabacdeeedceabaeeaeebbeaeeebbadadaeeacadededbdcacaceaddadbacbdcbccdddbabdacdedebaeaaaddeaccaeacdeadacebcdcdabacaaadccbbabddccbcddadbaabbecaabbbedccaceadbebeaeeecbbaeaceecdcebaaedaaebadcaaaacdcaaccdbcacedbaabecabeebbeeebdecacaadecdbecdedbceecbadbbbbdabaadbdeaaceadeececbecddcdaeddbcaedabccacddebbeecbebaededbbeabdabdbddeeccbadecbcdcccebbcbcccadadbaacdedabebaacdabedbaeccbcdbccbabcdbbaadecebecebcdbdcdddebedcaacdeecbaeaaadebdababceaeeccaebdeadeabcbedaceababcebeeeadbeaeeacdcdccbedaeecdaeadadeaabedcededdacebabdbdccdcecdaeadcdcccdacebcabaddbaeaaaebdcddaaddceebdbedaddacbaccdcacbcadbbbeecccedbebcebabcdedbadaaaadbbecbcdecaacabbbbddecaceeebcbebcbcabcaadebadecabecdbdddaeabeaadedeecebebadbdedcbaadbbaddeccbaababbaaeccecbeccacadcbeccbebedaaaccacebedbcaededdbdbcceeeacdeedaaedddababbbcdacedcaaeadbbdaceecbbdecbdddebbcdbeddebaeacddedbaceceaeeeabdcdcedaedabebccdbbccdcedcbedecacaebbabaabebbbbecaeddebdaeaecdddeeaacbacebebddddbdcbccebcbcddedcadebeeebdcbbeedcdbabeecbdaaebaeebaaecebaddeeaedeaddcaadeebabeabcabebcdcabdbbdcabecdcaabadbaddddbaaddcedcacbebcaaadadbbeededcddbadabaebceaaadbdbcbbecadacbacacdbcbeebcebcebddedcebcacebcbadbaadbaaeedaedaedbdbcbabcedaeedaccbdeccbbaccadcedecacbbeccebaadddabcdeccbcddceaebaaeaaddaddaaacdedbbbccdbddbaaeadacbaeeaebbdcaebbecadaeceaeabbbddbadecdaceeaadabcbcccaaceaeccebbccdadbdaebbcdabcbbbedabaddaabcaacebbacbcedcabbcebebdedcdabddabbeddaeabcdddaeccccddcdaedeabceceddddeeeeabbcbcacceeebcbecbaebccaacdeebbcabdbbadacdecbedecdcdadaccdaaccbecebbcebbdabaeeeebadbeacdcdbdbcbdaddbdaddadeedbecdacaccbeaaadccebadaaeadcebbabceacacbccdaacddaebdeddadecebdabdbbdbdddeabacddebddbdeccdbaaeceedcddddddaaddabeeceeaaadedcdeecdaaedeabdbceddccdaaccbdcabaabbedbbdaaddcaeecacddcebcaabddcbbdabcdedbacdbadeeaeadeebeddadececcddccecedeaccdeabcbddacbddbeeccbcabbeededcdeedbaccadbeeeaebbcbcbeccaacbbbcccedeebccaddddbedebecabdaebddecbacdbbaacbcabcabbebacaeaaaedaacecebbeeacaabbebbeaddaddbadedabbdedcceededacdcbabdabaeeeeaebebcadbceecdabbeaabadebeebcdebdbcebabebbcdcbaadcaaadeaccbecbdadadcddcebecbcccedacbeaebadbabaeccbcdbaabeaceaddeeeebecdabdcbccadedabedaecebbcebcbcdacddadbedceaedbdbcdbdcdaaecddecceabeaabdeddbaccdddabdadbacdcbebbecdcaccbaccbacbaabdadbbacceeddbeaebeabcaecaecaedeaccbccdadaeaebcaeadddebddebdcaadabadbcbdcaedebadecdaecbcdebaccdddcacaabbaaeecacdedecbbccddbacaeabcaadaadaaebaddabeeabaaeecddabcdecedbaadceabddeedabadbebebadcadaccbadabedbbebabebbcaebaddeddccbdadbaaabadaeebcbceabaeddcdcdbeacacaecaccbddddcdbddcbdeceabadcbdaddbacabaceccbcedcaebbdbebdceecbadaddeaaecbddcbecccaaabeedaecdddaeacbccaebaddcdbbedeedbccacddecbdbecceddebebcdabcedbeaddadccbeecaeaaaeaceccbeccebbbcdeaccdccdbddcecacdcbedbacaaccdadeccaabbdccccaccaeadbbdbcdebdaaeeaaeeedbdeabeeaeabeccddbbbbbdddbebbdccddeebcbdabeccbeccaceebdeeacecdcbccacbbaeeedeccbbaeeeaddcabaedcddbcabeddcbdccccedebbedceeaaccebdbbaacdadaadedaeeaeddecedbaaecbacbdaacdeeabcadabbeaaccddbceeedabacabaaebcddcedcecabaababeeccbebcddcdbdddaedcabbbcddaeaaddaaebeeceabccaedeabdedaeaaebcccedcecaeabbbdadcdbbaedaeedcabeaeaecebbecdecaedcebcebbbceeadadecbddaeeaeadbcbcadcecabebabdcbeabaebbdabbaeacbacecdbbaeaebeabbebddcbbdbabaaaaddedeaabeeeabdbcddaabdbdcecadbcdedbdcccebccedbdaabcbaebbccbcacbadebdacdcccbbababcbacdcabcebeeccbeeaaaaecedeadbbaeabedcbcdbdeabdcbcebcdadaccdbdbcdbbdeeececeedabebcdbebdebeccccbbcadbcbecaddacdbbebcaaacdeeaaaceaeebadcebaeccbdbebcabbbcbecddbdccbccedeceaccecbcaacceababddbabddbbcbdeaddbcdbcbedbcbdabbaadddacccaabdbbaceeeadaaeaceeaddbdebdcbddaeabbbecdcadcebceececabbbbdcebddbecbdacaeddeedbebcacbbaabeeabeeceeabebbbabdabedccbccedddadacdcdbbbccdcadecbeebcbeebbcddacedbdaebebabdbcaebaceacaaadcdcdbebbbaddaadeaedadaaebabbbcbdebaeacaaccdbecbdbbceabebbbeecdcbbeedadbdbceadcceaeecbdabcadcebdaeadddeededadcddcaeadcebcabacaacacbcccaecaeecedcadabaebeeecadbcedcaedbbdddecbdcaeecaedbaebbbcccecbadbdcadacaaabbbdbcceabbcdcdcebecaccdeeabdaabccececeeeebddbdaebadbcebdebbdcceeeeadabaedeabcacdeecacbccdebceecaedcdedddbbcadddedacaaabaecbeababdaedcbddbecabbcbbadbadbbdaeeacabedabbdccccbdcbecebacaacbaacbbbdbadccedcabcedebbcabeeaedacdcadaadccbbaceebcbcdeeeebaeedbabcdcbbaeaaeadbeeeacabacebdddeddecbcdaadeaeabdbddccdbeabaeeaccccbcacaaaddbaadadedbaceedccaceaadeacdcaeeadaabbddabdbddbabceaebccbdaedeecdaedbcbdeeccaabcecbaeadebdbbacdbcebdeadaebbadbbbcecacceecbbbeeeccaebdcbaaedbcbbeaadbdbeecaabdbceeebaeedcebadaabebcedeedcecbceabcdcedbbbcdbcdadcdbabcbbddeabccabacbadeddabacabeaaabeedcababdcdcddcdbddceebdcebdecebabaddbedadbdddbdcbbcecdabdabaeeedbaabbdaeabbeecddcbdbcebcbceaebebcbbdccaacaaebabbbebeceedadbdccbabcdbbaeaddadcecebddbebeadbcbbcabcdbbbadedeacdebabeabadbdcacdbecddbebacedddecaaddbbdbedeaabdccdddcaebcceeedcbbaadaecaadcccadaebccdaeaecaecebedcebcebcacebccbbaecccadeaabecbabaadddcbdeebccbcbebadbadebeceebedeabacbcebcebbbbdbeececccbdebecdccadbcedbbacddbddccbbdaecdcabdeeeabebeeaedabcddcdedacdcbdebcabdaebadbaabebdbbedddadccaddeaaeaeaeaaddcacbdceecebdabadaecacabebeedeababbcaebeeaaeeeebaebdecdeddddabbcbebedaeecbdacbdacabedabadbaabedaccaecaaebdbcdddcebbdeacbaeabeaaeebabeebeebaacbcdeddbeaaaadddceabeeeecedacbebceabbcdbbeeecdddbdbddacaaebccbcdebdaaaeddbaaeedbaeeaedcedcecbccdecebcabcebaebcedbcddeddcdbbcabaebddabadeabbcdedcdeadddaccdeccbcbaaaabaabccaacedcbbadbadccaddcbccbbececbcebdbeeeeddcaeacceaabdadaadcbbdecdeabebcdceccaeaecbeacedcbebbbcbbdceadbceebbdeaeabecbddeeccddbabcaceeadddcbadaceadbeacaddbcebceeaedaeaddebaabeaaacecbbbadaebecdbcccbdcdbaaecccacdbedcabbceeedbbecbbadedecbadabaedbeaeabcceabbacdacebcceccaaddddaccdcecedbecbeebacabdaeebebcaaacbbbbdcbbddaacaccaebebddcddbaaaaecabaaabcaadedebecceabbdecedabdddcdbedbcdecdeccccbeecabdccdbeaaecbabaadaceaacbcbacaeacacbeceacbeedecceedeaeabeedaebdeceaaedcaeebcdeeadbdadeebdabbdaadcabebbcbedceadadbdaaeebedaddbdabeebdaeadaeecddaedaaaddecdcdaabbbcbbcbaecdeeeeecedebbcdccbacdbaecdedeadaccbbabcbeaecbbccabebdcaadbbeedadbceeeebcbaeeecbceccddbeadaebcdcecaacbdbcdacaeceadedcbbbcadbaeecdbeabecaeedcdecbbcdaccaedecdbdddbcdadceecdbbdecaccacecabbeecccbbadaeaaababaccbdeededecbdbcadeeaeadcdbdecdcdacaebbcbcaccabdaabbbacaeeebdceebeeededeacbadccdcbedbcebebabeedadcaacdccabbcacecaecdeeacecbcaabedeabddbabaaecdeacaeeeacbcaedcacabddbddcbeddedbceebcdebbdbcedbadddaacbceddabadacceadebebaadaeebdcdcbddcacdbcbcdcedbedbadebedaecacacbcedbdeebcbadabbcdbadeddcbcdddeceebecebbcbddddbdeaedbedebdeeaeacedbbbbabcbaebcdbbddedaecdedadcdabdcbdecbbabbbeadaabaadecdbbbdabdedadedebadcdcbaecdbaceecaabbabebecaebeaeaccbacaeaeeaeaeabedceceecababcbbeacebdddaaabedebedeebdacdbaccbaeababbeabeeadedadaacbecebdaceededceddedecdddbdbaabceceaddeebadaaeaacdcedcaebaaddeabaeeeabebaeceebabbddcacededbababaabeeecbdcdadcceaeebeedcdbdcaeeaacbcaadeaeadeccdbdabaadbdabdaceebabadbebaccddbaeacbddcaaeddceeeaacaeedbadacdbedaeeeaabcbbcdcddecbeabceaedadbdcabeddeddbeeeeaecdedcdeeabcccabbbecdaaeaceccabccbdaeaeabeecaecddeeaadbcecddcedccabcccacbdedbaaddcbdedcbaaadccdeabecbdedcebbbbedebdaddcaeacceccccadbeecbcebededdcaccdcdcbeedaeccbcbedacceadbdcbadcedbcdedcaabdbccdccadbbdcccceecbbdcbbccbdeeedcabbaeeeccaaaeceaddabbceebdccbeccbacabbcbbaeabdaebdddbcabcddaecedcacbecacbbaeceedcceeabdbabbacbaaebbeabecdecceacbcdacdaceabebcaebccabaeecdaacbaaeecdddeedddbaaecdbdbbaeddeceabecbcbadadddaeeaccebdbeedecbdaedaecbecedbbccddbbbedbddeeacbecdccdbdeeddeadbadddbcbcaedeaeaddcdbebdacededcdaccecccdcabddcabbbdebaacacdedebdbadbceecdecadddcedaadaedecaeddcaaebebadbbdebdacdadccadaecedccccacbbebebaecdecdebbcabaaadddcdddbbeacacdcdbbbcbceebaadddbccecabbaadecacdacddbbddacaeebbdadbdbaaacceceebcbdbbabaaccbcbaeadaebdcddecadbaabbbcbcbeaeecaeeeddebeeaaedeebcbaecedcdbaeccdaacbbcbdcdbbebbdabcedeceacebaeadcbecbbebabcbbcccaedecddabacbcdedeeddedbebdbacadcaecdabcbebdbaecacadadebadaddcecebbcceaeedabdccebccddedcbeebbbdeddbeaddbabadcabdceeecebbedcccaddacbdecbdccdbdabcaebbccaaabbddadcbbcecadabbcbacbceddcbbeceebcdeedbbdbdcdbcadaceabaeccceaaccdbcebaaabcccdceebbcdbcbaebeebeedecbbebdddaaacbaacceddddbdcebcececaecacedeccbbedddeccddcbcdadccceacdaccecddddaabbdcdccbbdcaebdbbbddbaeecdedbbbaaecabbbeedbdadecbddacdbeddaebdbdaddacbbcddeeecdadbabddbedeeaccaeecedbdadbcbccebebeeaecbbdbacdbcebccebbcabbaceeadacecbaecbccdadcbbcbebaadccabdabeaeaaddecddbddccedecdcbdeaaddaeddcbcaecaddcabbcecacacecdeadcbcbdeecaaaaabecbbecbbababcbadeeacbbabecacbdaedbbcbbddbcbcddddadbedacdacaddbddacaaeaecdcbbaaadeabebdddadbaaaceabdcaadddbceeeccdaebccacdcbcacbcdabcbdabdbcccebceceabccbaabebdcdacbebdbbcebbcedcbecbbdebadcdeedaaecdeadbcbddbeaccbbaddceddeeaececddeabadecdeeebdabdbcaadbddbeededdbaddbcdbcecbdbbabaabceecbabaaabbddaeeecdabdccbacabaeccdceaecbcdadcecadeaabeddcceebeeeaeabbabebdeadcbecacacacaeacbecccccdceecbecadcedcdbbeaeaeacdbbddecbbadebbcbeeadebdbbebbdaaeabdbdcdcebbcbccabbdeedbaadcadedadcacabbedadeabeadadeaadeeabababdbeaeeebadaaeaedcacbcbdabccecdcaddcddcbdacebcecbabcccbaccbbcddcbdaacbedcbdacaadbbeddeabbbadadcedaabbbcaabbbdcbaceecbaaebdbecabdababeadcbccaacdaccecbcdbbeeeedebeecabdbedabaeaadeadacbbedecacedaacddbccbbbbeadcacdaecabcccdbdabbeaeaaeeaceacdabceeddddaaedbcadebeecaabdbceadbcdaaceaabcabdadbccaaabadcdaeedbaadbaaacbaccbcbeccbadabbbbbcdabadccdeecceaecedadeaebebdabbebaabdccddedabcbedebdbbdabdebeecabcdededdbbeaabcbdeddabbbbcaecceddadbeebeacadcdbaebbaaadbcbccadbcdcedcecbaaddbbceccaebabcadeeaeaebddacaeecdaaeaaeabadeaadedaeaabdacabcbebbacbdeeeecebadedaebedaecbbeddcacdcebbeecacdaabcaaeebecbcccedcccaaecbdcacddeebeabdaedbadaaeceddaddcbecaaceabaebadddcbedbcdbacebaaeacbecacceedcabdbebedceccebdacebabcbdaeeaadabcbdccbcaaecabdddaadaecaadeccbebbbcddcddbaddcbedccecddebbacaebecbcbeaabcbadcbcaacccbacbbcdebaabcabeeabcabdcecadbedbbbeeacccdbbbebeabebadccecadacebdeabdceebaaedcabdaeeacabceeadadccedaebadcaddbebdddaceddcdbccbadecdcceaeadcdeaddadeeedbbbccbccedabeebbddcbdbbadcdddecacadedcbedccbacbabbbabdabaabeaedaadacacebccdbedebaabdeabecccdeebbcbedcaebaaaaaecdeceeacadacaecbbbddadedbaedcacddcebacedbeedcceecdabddbadececdddcdebceacbabbadcbbddcddeabadceaeabdabbadadebcbbccacdbbaacdcdbdbcecadeaeaaabeabccaeebabeccdbdbeebabaccecadbdccddbdbdedebeaeecbaadeebcddcbabccdecacbbabadebadecbccceaacebddabdacdcddebacdcdebaceadceeabbcddaacbcdccdddcdebcaecdbcebaccceddadbebeceddbaadeaaaabdcebeacbbcbabddbdebaeadadeeacddedbbeedbbbcdaebabecdadbcecdbebdacbeebdaaeeaabcedeedceaadceddcabedaabaeedecbeaebcceabcdbbdbbcaceedcddeecbceabddaebbaccbdabcbacdaaedcdbdaecaaddbddeeedaccdabceeebaaebacbcdceecdebebbebeaedadcccedcacceabbbeddccebcaddbecddadeaacaaecbedbdcabaccdcaecebdceadbcddbbdeaaccadcacddcedceeacedbeecaabbbeacaaaaebdeabcedebbcdbadadddbebdacbcabdcdcdedaabbdcbdccdeedbadcbddedbbacaeaabedddbcdeaeeeebedddeedaedacdceabecdcbccdbacaaddabecceecedcbebeccdccdeaecbdcbcadeadbabbcaaecdccbedcbbdcbedbbddcceadeedcccedbbbedcbdcdbecaaaceecceaaadabdebbaedddaededebdccabecaedebaabcdaedbcaebdeceaecbcecbbaeebaeeceaecedabadaeadecebdebabcbecdbebaeabbecabacccaecebeccddddcbccaadadeccbcdeaddccceccceaebbceccdaceaccdbebdaaaebbcedccdeecabdbeadeaaccbcbacdcacaaeceaddcdabcaddecaaeedbaebeabeeceebedaebdaaecccbabdabeaecabdbcbaaebbecebdaabcbcabebbbaaabaabeecceabaecbacbdaddcdccababdedccaddbbebabdeaddccbabbdeaeacaebacdaeebdecebaaabecacadedcdedccddbeeccddcddddadceadadcabeabecabeaaeaaedceacbedeabbecadddceddecbdcaecdcbdbcdaeabdedabeeccadeebdceacdaddcdbbebccaececadbdeddeccbddeeadcbdabdeecbddedcdaeceaaaeadbcbcabeabdcaedbaacdeaccaeeacbedeaaccceaebcbbdeddaeeecaeccebdaaaabdacdbeaddacdddbbdaceedeccbbeaeeabeabcaedceeeebbdbccccceebeebbbdcbbecececeeebdeebeaeeadeebbbdcedadbeecdcbcdbcdeddbdebbcceadceaaebbddcbccaeaeaabbbadeeaeeeecdbcdcadbbaadbbaeebbcdcccdcccebcbdcbdbddceedbacceddbbbbdeebddacbabbabbeebbdbdebedbdbaaebcdbdebccbeddeaddcdcaadeaeaecbcbecaaceedbeaeaedbceaebaadebdecaadeaccdabdbcaebbcccedbbbbcdeeabcadcdbaddbcedaedddbacdeebcbcedceadbecbbddbdddebccabadccebbabccacacadbecaadbcacacdbdedbecdbbabaeaccaeadcddcabcdaebdccbceaecacedeedaebddeabeaacdbdeebdecbecaaaccaebcdceebadeebbebcdccbbebbbeeccebdacddbeebebbadbcebecadcecbdadcdbdadcabcedadebaeddcccebddccaacecaaeedabbbedcdaedbdaecaaaabdecbebbbaabeccabdddaaceeeccadabbbcddaddceebedcbeacdceabecdbcccdaaacbeebbbcdabcaeebcceaaaadcdadcaecebbdebbeacbacbedbdbedcaabbebbdaaacedeaaacbccadebddbaceecacebbeadaceaceedddbbbadadbcabaedbeaaddeecacdcecbeabcbbbebddccccabbdeaeabcacbcbaaabcdbedaebeabeccbedbcdacababddcbdbedbcdbecaebeeabebbcebdaaaabaceedceebaeecdebadecbdcdebdbdceadebdcaabedcdcceeebebbbebebeacccdbeaaecabbdceaebdabddcadaaaabacacceacedcbcecdccdcaacdbbcabdcdbdddebbadddceadacedbebeadeeeeabebdbcabaabddecdbcdbbbdaceacceaedbaeacddeddbbaccbadeddaadceecdededcecebaeeccebbabeaacaacddddecbbcddaedeaccebdebaedbacbcccdbecebcadccbdcbdbbdbaeececadcbdeedbdeabadbbadcebdadeabcddadeebadbcaadeaeeceacebaededbeeccbddecbaedababeebaaeeeeeebcedbcecdcdbeeecaaeabdebbeacbabcbedbccbeacedbaedeaaecebeddebadebceeabbdcbaccaabebecaabccaeeeddedbdaabebaebeccaadaeaaedcadbdbdaeacbeedecaeadedbbacacdeabceababaeabbadbbebbbdeedaddedbadcaddcbcedbbbdcacaaedbeaceaaadcbbceabacaccbcabdbbccacbdaaaedcaabedaadaeabbcebbbcddebaabaedebcabbeccdbececbbdbcebcbcdbdddbdddbdabedecabcadccdacebcaaeeacbcbdadadaedebcabccbaecdbbbcdcaeabdcbdccbccdcabbaccbcacddebeebecbdcbaeebeddeeebebabdcdabddeeaededbdeacbcddcacdcccadedaebdeaaedccdeeeaedaecabbddaaecdeeeecdcadeedbdeeddceceedbdaebdbbdeebbecdcdedebbedcbcdbdbcaababbedbaadedcbebddbedceabeecdeaddbedaddedcacbeebddaaababdcebdebaeaebccecceebdccedcbadcaeeaeebdeababaaeabcbdbacbbbcdcadbdebbadcbbeedbbaebccdebbcedaabbcaabeecabcbaabbbdbbedccbecbddcbcbceecaadbccebaaacbacabadceedbeaccaaecdeeeaadcbedaeaacdacbadcaecbebbbdaabbbdddadcecdceacedcecbbdddbedaadaaeacbededcacdbdcacdecdbbaeaabdeceecccccbebdacabcecbedecedaebdcedbdecdebcbedecaccdeceedaecebadeaccbaebabadeeecaaaeaacbeebecbabaddccebbdadbdaeececacebebdceeeabbaeddacbdadbabdeacccceacbadccacdaeabbaeedacaeaeddaddceadaadebabcbeadedecdbaedbbacacdadcaebccebcbcabebeaeeccecdeeeccabcdacabecbdcbaccbcdcdabdbcbcbdcbccaadacdbcaceacaadedadcdccdeabacaabcadddaddaecbcacaedbebbdbcaceccbaeacacacaebacadeccbdadbbbdeecceddacdbcedbddeaceabdbceeedeabbeabeabbbbdbaabceeaaeedbdecacaeababbdddebccecdaeeccccabadccaabacecabecdadebaeebbdeaecbbaaaeeeebbeedecebdadddeebadadbacebedeeeabecccbaacacdccccbbeaacebcbbebcbadeaeddacbbcaebbaababdebbdeebaaabbdaeedbebacabdacedabbaacbbcbbeadbcddddccccceecdcaeaedbaaddacbacaccedeadecbbecbbbebabacdebddddddccceabcabdadadcadbdebcabebeeecadaeaeadaccabbadccdedabbecbeeeceaaecaaecebccccbceacdebcbaabadccaccbabaacbbdcebdcedbebebdaaacdadcacbedceacddcdaaaecebabebbceadbccbeedcaebdebebbecabceeaacccbbccbaacaeadacccaeebacdcdbccdcddececdedacdcddeeacbbaccadbebededcaedceccbbaaeecedacdbaeeacedccbcbcbbeecddddecdebcbbdaeaccdaccecadcbdeddaebdecbadccdedeeaaededbaabbaededcaeedcabcdbaeeceddcadbabacecbcedbaceedddadbdaedeabceadeadcbaaceededabacdeabcbbeaadebbdaeacaeedadbbeebbededecabbbbacacbadeccdebabbcadcbbcdaeabadaeeabddedbeebebebcbedbddabaeeacbdaabecdabbeaacadbdebbabddabdabebdeaddaecdaecdbdecaddeaeeaaddaebbedcceddbccadabeccdbedbeadeebabeeecdbeddacaceccbcbcdbdbbdbabbdeceeaedcdedbadababedadbceadceaaedcbddeeabddaabbcbdadaacccacdcbdcdabdecaebdacdbceacecbcccdceedbaeccccbddacdcaeacbbaedddcdeeceddacdbaeaeadcdebdccecdeeebaadaecaacecabdecacdadcecbedceaceecbaebcceaeceedbcbeaeacbeeaaaeecbdebbdeacdaaeebcdeeadbdeabaacaeabdeadeebdaaddaedeecbeaadadaeebcedddaebdbbdacaaecdededaebaabcaaddbacccdcbadbebabcbbcceadaeceacccbbddeabaabaebeaeeeaebebadcbeeadbeddabbccddaaeeeeecebbeacadcceeceadcbcdbaacaadbaaecddcdebcdcddddabdcdaebbecedbcbaaeddccdcbbddaedabeaaeabedcbaeaddbcadeceebebaecdebabbcedeebcdbabaedaebccbeeebcadabadbeedcaedebddcaedcbbbedbbcedbccdadeaebbeddbddbabedbbdabadbdbbaddcdddbcdbadecdceecccbdceabdeadabcbbebcacdbdaebeebbdaddebdcaeaebbadaadbaebcdedecddedabedbaeecebbbeceadecccdeccaebdadccbdbaadbdcacdddddcaddcedcebadabaeeabcdabcdededbbebcdaaeedeeedbbbbdecacbdcadebcadbddcbdebdeedeacadadadeaaddbacadeeddaeacabaabcdebdabcbcddceaeeeeadbcebadcbbbcbdbeaacbbccbaaebadbcdcbcbcbaaaedbbadabedaedeecddbbeacaeabbbabbadddcbacdbacaebadbdeaaeddbadbeeccceaebcddcedadbbeacedbaebbadbdaeeebbcceeeaddabceacedebecedeaebbaaebaceaaacebaeeaacbbceebbaebeeaabebaeceababbacceaddaebeecabaabccaddcebaacddbeeabacacecabcacdedaecedadecaecaeebdacebdadebbeadaedbaebaecacaeeebcddaeebeacdddcbdbdbdcdeacecbcbdbccbddcdddeccecebcdbddceaccecbbddcabcecdceccecddceabebbcdecbaeceacccabbccedebdddceebacbcadbcccedbddaebcdeddcaeaaeebabaccebaaeeaeedbedebbeeacbeadeccbccaabbcbbdeeaadbadbabedaeacccdeaceaadbcacdbbaaaaeccbedbdeebbaaeeebdedeaadcabcdddceccdeaceacceaedececcaadeadcbcccebabccdddbaebbcdcadaeaabccbaeeecbccabdacedbedcdcebccddabbeecaeaacebcbeccdadaaadcaabcceedbadbedcbbbdbaebacdbceaeadaeeacddbebbeacabdadcbadabcbdcdcdcbeaacccacedeebcadaedcbeaeecdddabeedcaaebadbabaaabdddbadccceaaeeddaadedaeebabeecaabacbbaedaddeaccaebccadcbaadedddcdcdbcdabdccbdbbebcbcabbabbabecddeaeeccabbadbbeebcbecdbaeeddeeddbdebdbcbacccccbeeacbedbdeaaebceedbadadebebaceeadbbbdecbcdeecedaceebceaabadeeabbededecceabeeacbcdeeabeeaecadbbeadeadbcadebdacbacbebebbedaebabedbdbecabceaebbcaecdbedebcbeadccaadccdeaaaacccbedbbddbaeeddddcbbcedbeddaccbcdaeaacaddcecabadeccbebcacdbddddbdddebdddacabebcaabcaeecdbcbcbeaecaacdcadeaaedbeeaddeaacdabddbceabebebedeaeabceeccecdbcbccdbccadbacdebebddbbaabacbdebcbaabeabbcacedcadeabeadecdebddbebbcddcdbaeaaccbaaddaebbbaebbbccabbdeaacbcbdcaadeadacaaacaebabadbbddcedacbddcdebbbeedcdbccbdadcdbcdadbccdaacddbabbcdbbeedbadaabecbdaababeeecabcddccaddabbebaacaaacdbebbddbcaaaeecedddbdaebadcacbdbaacbabbeeeebeeaaabceabcdadbabbbccacccccdeddbddedcbedeaacdbedbccbcccbdceddadcdedeeaedeeeaaaecabccaabbceccbeebdabaceccbedaccecaddeecbaccbdaecaadcbeeeaebaaceddeecdaaaddacbbaacdcedaebadedcacddedacecbddabcbeaebbbeeececeddebcedddbdccadaacddeaebecdaebecddcbeeebadadeedbaceaebabeacbdaeaeccdeccbdddabccdaaadabbbcdbedabaeebaeeaebaaccbeaabaacdddecddaeacbdaecbddaeccdcbeeadcbdababddaeddcdaacdceacaaebceaedbcbacbeebeaabdeccececbdaedbabdbaeddcebbbcdaadedbdabbecabeceadecccdddcdeeddcebbdcdddaadcbcbdadadacbeededbabeababbdbacdbdcaeccabcaeceeeebbecbceccbaaaaebdbbcdcaaabedacaadceccaececeaaeaebdbcaaccdbcabaddabbaddeedeabebacadceacebdaedaeebccceeeccdbcecebddebededaccbdbddcbdbdcbbabdecdbbadbceceabedbdedddceebcbaaaddacabbaecacdbebcdaccedabbeaaedabcaeaeaaabcedeebbaeecaecbabdacbacbacbeaadeebebeadebeeeabdeeccaddaeaaaddcabdcbabecbcaddeaaedbdbcbacbcebdadbedeecdccaaeabcaecbdbdbbbbddaceeacdabacdaaedabeceeccbedddbcadbecdbbddddbdbbdaeaeedebaddeaddddcadcbdcdbdbbeccecdbeaecebdcbabbcbcacbddecebabdddcdbebcdacacedcdaaaaedeedceecbeddbcedcacbbcbebbbbcccadcaeccbeaabbeddacceaadceecabedcdeabdbbdddacdcacdacccadecaddbeaebdcdceeabbacceaeeaacbaeeedbbbbeebbdbcacbdbbcbeaebeeaadebeaedcdbececdaadebbbcddbdcadcdcdceeeebdbeeaacacabaddebaeeedcdaacbdedcdbadccedeaceccdacadbdedbdeeadddcdcddaabdddbadbddebacdabdbaaebaaebaddceaccddebbbacbcbcedebbbdacabcaebeaebedaecbeaaceddcebbcdbddbceecaecdebdeeceeceeeacaaacacedaaecedeaacdbdbdaedbddaacbcbbedceeadebcdebbeddbddebeddcacdabbebacbcabadaeacaecccbadecdddbdbeabeabccbdbcabbdadbbaeccdaaeadccdcdcbddcdbdaccdaaddbacaadddbccdcadeebabcadaabbbadaaadecccadcaedcbbabecabbdbaacbeeecbdebedbaebebecadaaedcbcbeedbdcbbeeeaaedaaeeaebeacaabdeaeeccdaedbbebabccaababecdaebbecaaeceebaaccbadeebdddbcdcbeadecabceeedbcdbddbdaeaaaddbbecccbdeedeadccbecbdbacddbcebcedecaebbcddecadeaeebbbeedaaababdcbabbcccbcdeaebeaadeeddaebbecadbaebdcbdceededceedcebacdbeabdebaeedcbaaadeecaeecdebabaebcdcdbaccedeccdeececaebdbaceddebbdcabccddbaccabbaadadaccdddeceadecdecedaaceabdeacedbbbbdebcdedcddbcaeacdbeaadadbbdadddebbccacceecbeaddedcbaaedeebacadccdedadedacdaddaaeaeeabceaadecbbccbcebcbaadadcedbccacdaabaaacbadbedacddeadddcdabdecabeedddaddedececbaecdceedbebcaaabcbcdeaeebbecbaaccbabdcecbeabaebbbddcbeeabedabdaabdaacbceebbdcabcddeeaadeeeaedddccdeedcaacadddcdecebeacbecbdacceddaebbcdecdccccebcdeccbceadbaebbcaaedcdcabbedbdebeeaebdeadddcbeedbeccdaceecccebedcbbcdacdadaaaeccddcedeeccedccbadaeacebbbbecbceececedbdbeadcabdccdcdceacaddaadeccaccdeddaaadcdebadbdedcbcccacadccaedabebcdedacbdbdbbacbaebaebaacbedbdeacedadedeaeaecbdbceeceeeecaebecdccbdcecdbdcabcceeddadabacbcbbababcedcbdbadcadebbaadddddbdadeecdbbacdbdedcacbbbddddccecbbdeeaceddbedaabdaccedaadbbaadaabbdbeecaccaaabccaaecacccbaaaeaccaabaecebecdbbbabecacaccbabbcacceeecccaaeabdcdeceadeadcaaabdececedbaeddabdccdeeddbdbcceadabaeccdbbadbcebacadaeedabdddcedbabeeaaabcbcdcaeaeecacbeeccebdebebbbecbdbcadbeeaddbaddddcdeebdcedadbeeebeaaddbaadeddacbaededccaadeeeaadaaabbdecbbedaedeeeaeceddccabceedaecadaddcacbeceddbbdcdaebbbbcceaabdcadbccddbecdcbaddbbbbaccaabeaeaebeebcaabbdedbddbbabddcbccaddedccbcbccbceccdcdcdbbdddbbaecdcebedbdedaaceddbccadbabcabaeadeaedaeacddcdadccabaaaeebebbccdcbdcdeeacbccbbedcdaedbbcceeeedaceddeabaeadadebebdeeceeaaeebcbaadedecdaebaeeeceebaabddadeeeeeeecccdaebdbdaebccbaeaaedaebadbdebcadeeebdaceceeaecceaecbacccacecacdebadabeddbdccbcceeebdcadaececcbebedebeccabdbdceaaaddeedccadadbdabecbadddeabceaeaeceadcbdddeeedbcedcbedbeaccdbdbbbcbcabcbebbacebcceebcecbbbbcabddcccaaeddeabcbbdbacbbadabdacccedccbadbecbddeddecbaeabeadbceebddecccdacddecabcdcbbbaaaecebddbdedebbbbecbadbaeebcdaebadbeeaebbcebadadacbccbbbabddbcbdbdcaededdbecdcedcdddcceeecaebabcdaeeccdccddcaaadabeaadcbebdbdcccbcadbdeccaddeeacecccedbabdabbddcadbdddbbabdabcdddaaededbcbeaeeaecbbcebdbbcdabdccacebecbaacbeaecaababebbaecabeaeccedecabdbcbbebecdbbcbdceacdacabadabbddecbdaedccaeeaccbebccdaadebadedcebcabababceacbaacaeeccbcdeccbebbaabcdbdbbedeeeaabcaebeebccababaebaebeccbbdcdaeeddecbbcaadedecdcbebddaaadcbebeaddeeddabadbacbbcbdaedabadccadeaaaeeacaadbddadaabddaedaeceebcccaddcccebacdbddebeededeedcdbcbaabaedeadbdbaabdcdebbceaceadadcdcebbcdbbcaeeeeebecbedccbbaddbdbcaaddeebceaddecdcadcbeececeadbaceadaacdbbdbbbddbbddecdbdaeeeaaaebacdecaeceddcbedccacdbcccacacbcadaeaacabbbdcdaededbeccebbaecdcbaeccbeebcccdbabdceabeaccecbbcdebbdbddebcbcaebddaaecbdedadaecdcaaaaeaaceabeeddacaacaaadeeeccbecaddcbbaedadecbcbbaaabedecbdebedadbdabaddcdbdedeecacecebceebdbeddeeccedaacdaaadcabeacbadeabeccdcccdaadebdaeaedecbbceabbbcaddedcaecdeeecebeebdcadccbdabbcdcbaadbccadebaccdcbccbccaeddecdadedeeedbcdbdcbedddaaabbacdabbbaaddcbcceeddaedadeddaddaeebacbebdcacececadbdeecaabbccaccaebdedbaabacebcbdabacedaaaaacebcdbddcadaacbbbedebdcabccababadebeaeeacceedbbaccbddeaedaeeddeecaaeaccdcdaadaeeeaaebbacdedcdeaddeaedcbddceabbcabdeabeececcdadbecbeaabddbccdacaedadaededebdabbdceceedecbaecedcecbbecbadebdcacccaaebbeacaadacedcaaabaacbcddcbcdebcbecadbbccadebcccbeeaeaacaeebaadecaacaeadccedbedbcdbbdbeaeeecccdecceabcababaceeccbdcdeaaadeeaeedceacdeedcddedacccbdcaaacbbedcadeaecdabebadbdbddbecbcebbabababdecccbeabdbacddedeadedccbaecadcbbaebebbddcdbebebcdcaacabeccdbdacdccdbabddaadeeddeaeaacacacdaddaedceabcaaacccdccadbcacbabdbdbeebaaeeddabbebbacdaacbbbcdabdaddecddaadedeeeacbcbbcceaecdbaddeecebedbdeaeeadddcaeecacacbcbaebcccdadbcdcabdcbebdeaaeeeecebacedcbbdabdadabdbddbdaedacaaeeeaeabaaddbbadbddbeedbddedddcdeecedbaeaedbaebcccbceacbbbddcacecdecaeeaeaacababcddddcbdaeadaceeeeaaddacdadeebaeabeebeddeaebcbdbadedabcaecccdddebcecbdeaacaeadcbaacbcaadbedabebacddcbdbbebcdeeabbaabebccaacbbbbbdcbadbacaccdddcaddcdcaceeaededeaececdddbcebaedeabcaeabceacaceacbcebcdababbdcceddcddaacdbcedebeccdacbebdbbaadaadcbcebbedceeaaabcceeccbadeccaddecbdcddebadabdbdacbceaaadbccdebbebceaebadadddbbcdbdeeceddebdedbaceeeaeebadbadebbecddcdaedeabcabeadbbbcaedaeabdcbbccdcbcdacabdbadecccaaccbcadcacceabdcedbcaddbeeecbcbadaaeeedeebedebadbbeeaeedbdeeddabedabbbccbabecabcedbbaaaebceebceceabcebddeabdbbededbaedeabededacaabadaebecedbebeebeceddeccdcabdadbcdcccdbccecbcabebecaadaeccbdbbdbcdcdecaddddaeddadeadabdcddadcbdaceddadcaeaaeccddaeabccaedebbeccccbbedcbddebbbbbbcbbccebdbcdaebbabcbcecaeaedeecabcdcacbaedaccaedabeaebaebceceeaceedcacaabbaededddadbaaeebbcedadceeccbdabcbcaedaaccaaeddeadbacdbcabadeacdcacadeeaddcaedbecdaccbaaceddcdcaadedebbcecceadbaecaeabcbbdbbacaabcbceaacebeaeedbedbcaeccbbeaedebccaaceecaaecabbbcdabccadbbdbeeadacadbeeedcdacdbbcdaedbceeeedbbdebebeecdcddaddbabbeecddadeabebbdaeaebdebeecbeadcebdeaacbdacdcdadaaccbedbeadcbadbcaedbbbedeaeececdebdeeeaecabcbbdbbebbcbdddabbabdabbbbababebdebdadeecabbabecaebeeeeaacacaecbcaeacbabaddaeabbbbbbddceedcaebaabdcbcaaecbaeeeeeebccedbdaedacbeaeebdbbedeecbddaebdabccdeeeaadceedcbeeebbdaabcadbdabbceddededbedbaaebbdbadcacaaecaaeeabcdabcdbeaaabeabaddcaeccabaedbddcdbbdbcbbbaceeecbcecddbbcddeacebbdaaaeecbcabbacdbecdcbdbaeceabaaaabcaebdcaddabaaddbcadddcdcbeebdecbdcbddeccbebdeacbbbbeaaceedaedeeaebaccaadbbabbbbacdebbaddaebcceaceedcbcbecbdbadcdcaabcebdbeaeeebdbeabaebaaaccaaacccaaaebceecdcceeccabeacaadedeabdbedaeedebddbbbbcaadbedeeccddbddeeaacbcdbcbdadbbecdbacacccdccacaedcedcedcaeecaaceceacababadacdddbacebedacabbbaddcbbaadcaebecccbacdceeeacabdcaacacbbbbececbabcdcececdbbdbadaabddcbcaaeceddcebbdccdeaedeccdebdaecbdcdabbbabcbeabcdceeedecacebdcccabcbebceebcdbaacaadcdbdcbcbcddaccdaecebcccbbdddcdaaceecabecbceedecbaeaaaaddbeebbcdaecedaabcecdaaddebddbbeceedddccdeddbcccbabebaedabecdaaedaecdbedcaaeebcbaadadcdbcaabaebdadeedccdedadebadbbcadceddaabceecadcbebecebddbbeddbcecbecebeaebbeacdaedaaabbadbdeeeabecbdceeececbdabeeedeebaebdddeebcaeacbccbaebcbbbaeaedeacecacbacbadccececdbedbadecadcdddaedddadcecedaddeacadceebeadedcababdccecddaeebbbeabaceeebcdeeceacbbedbdedccdaadcabdccbccdcaebaddbebdddbeeadadaebcbadadebbaeadcdaebbdeadacbcebdadedecdadabebdcbeabaadeacaedbbdceacacadcbcddadbeabaaeeaadccaebbaacecbcaabdbeeabbeceddbdbdcdecdcaebbceececbcaccbbdadbbdacaacdcbddcceeccdebbadbeeedaadbcedcaadcbebeccddbdbdeebcebeaeebaaccdbaecdbbceaaaebdddbecbabebadccdaacdbbeeccaddbeabdaceebabaaebbbdbbbddbeedabeebedededaeaadabedebccabeaeadcabedbdeabedeceeeabbbdebeeaeccadeebaaeeadceebdeaaceccdcecabdeeddeecdeecebebdabcdceedececbbdabcdecdeaceceddecaadcabcebbbadcdbdcbeddceaceaebbededdabeaecebabaceeacaceedeceaddedabbaabeebacdbbddabddaaeeadbbbabdedcdaeacbbdcaacacaceceabbebbdddacdacabbabeecbbccaadbabedbadadedbccdebbbebdcaeddccdeaadbeaeeebccbedcecdeabeaaadaccaabdadcaaedbbddbadcdeeacebdcadcdebddcbcdbedbdccdabccdecedabdddabaaacdbaeeeaacbaccaaddaeebbdacceabcccadbecabddbbbacdeadaecebeddedacbccebaaacdcceecdecddbdbcceacaeecccdbeabedeeeaecadcbcbbaebbbdcbcadebadccceedcdceaaaaaecdecbcbbabdddcecbcbebeddbccaeedaddcbeadeabbddabdddabddbadbccebeaaeacaaeabedbdbbbadddeacbacbadeedaacaccedcebdacbebaacaaeadbbeabaedecedecdcaccedbdecdbbeedeaacedeadbbdcadacbcabccacdccccdaadbaddaecabccdccbacdccbcbadbacdcbddcdadcccedacaeedaeabebdacbbaecebdaeaabcabadebdcdebabceadececaecaeadabdeddcabbccebbebcebccbcccbaaabbccdddeebbdbccbddbcdabcaaedeeaadbbdadbabcceeaceadddceaadacbacdeadceaebdbbccadddeaaaddcebacdbcbeabeeaddbbccceeeecaeecdbdccdeeaddadadcbaadbaedceeeaaecbceeecbcbeeeadaaecabcdeeaaeedddadacaaedacbecccabeeabbbbdeecaaadaeabcdabebeccabcdcadccadbcbdccbababdbdcbabeaabaeeadadccbdcceacbcbdabbdaaecabdaeedceeeabcaecddaddaccdeecdabdcdeaedabebeaddccacdecccdeacbacabedccbbdaddabbcbeaaeadeeadbaeeddcbbecedbcdaaedaedeaaebdbddcabacbeeaaddbddadacdbcdeebaeaadeadbacadbeacdbeaaadabeacadcaebddbaebababeaceaaadcceaaeabdbcbddbbcebbaeaaddabdadacbabadeceebeedaedacdcdbaeadcbbbedaabcadcbceceacadbcdcdbeebaacadeebbaeeccbdaaeaeddbecabbababceebadcabaecdcbdbebdceabaeddecadbbabcdbddabaadcceebcddaaebacabedddeaeedcbdabdebdeaaeeecddaecedcbebccbdeacdedcaccdbedaaeadabddcbbceaddcdcaccabcccaeadeacbaadadaaaeccbccaedbaccadeddaaabeebadcacebbdaebebeebcbdbacdcdeddecaeaeaeacaeebbeadbecdaaaaacbbceecaedbebaabddcbededaeaccbccddccbaaebeacceeadcaccacbcaeecedccacbccdebbcbdbbbddcadeeabdbddaadedccdccbcaaebcceddcabbaebbdabceedcbdeceaacddbabeedccbadecbdadadccecddbacbedabeaeadcceaebeacadacedceecddddcaacabeabbdacbbadeaebdecaccedeaadeddbecdccabdcaccdcbbdbeeedbabcebbccbbbeecdceabdcbceeebbbedcceebeeeeccdbeecdadbbdcdccccddbaacacbcbdeabdbedabcecabdcbbdeaabaeabdaeaabaceabbaddabcbeebbacaddddcebddbdccadcacedcadcccddadccbaadaadbcbbcdacaaddaecbaadceecbdccacecadbabcebbacecaeadedcbdaceccabeaaabdeaecccacaddcdbcecbdabbcaddebbecddcbadeacdbdbedbddedaedcdacbaaccbeeadecabddeecdbbdbaccbceddebbcccbdbaaabecbeecbdbeecdcabcbabbcbbccdbdacdaeabedaecdbeecdbdcbedaebaecdeaeebbcbbbaabeabaeabbdbceddbaeeeceaeaaeaebbdbaecdbbdabccdadaaadcbeaebdbeeaaedcccabcdabbaeadbccacbcdeedbbbccdcababdedebcdbcadbbeabeaddceadbcadddebcadabcddbccbeddebbcbcaaaabdccdabbacccaebabebcddddedaaeeebdadcadbcdeaeacdcaeadebdbeaaacdbaabcebbccbdcdbaaecddaabbaaaaccebadccbcdaacadacdeaeeabdaabbeebabbcdacbdebdeeebbcddcdcabbccaccaddcbbceebdaaaceaebcaeadcaabecedbdadeccdaaabaeddeebebbaeceecabecbedabeeeaeabdbccceaebebceaabacaeadabadccdeeabeceaedcbbccdddacccacecbdbccbebdbbdbdadbdecddceabaeeccdecbdadbceddcedbdaedeccbaebbdbadbceeeecbcbcbdbaddbdecdecdaccecdecacbbbcdbecddcedbaabadcdbeabacbceaebdcebdabbecbeadcbcdaeecdaecdabaccebeebccdbdbbcbbabddeabadeddddededbecdecabeaccdbdcaacabdbaeeeedddeceaaddaaccebacaaadbebbebbceeccebdeabacbdabcebbbcebddbaceeddaaaedcbbccbcceaeeebdcacdaaebbcaebeedeecebdeeccddbcdeabbdcaceedddbdadddbccebceaddeebcdaeaaebadaceebbdedcadddecccaeabcddbddaadceadecdeebbdbcbacdcdcbaacaeccceaccdbeaedccbdaaacaedabeeadbdeccedacbaaacbeedbceaedccdeecebdccabcbecdccdeddceccacacaacedddacddbeebdebcbaadcbcbccabccdaededdbaecdbbbbcdaeaccedcddbdbbbadacccbaccecaddabacacaacabdbcdbadbbdbbbeeeeaecbbdeaabcbcbbdeaaacadcbebebaebdcccdaaeecbcceadebebedbebacccebebbbecdeadebddaaadeedadbeeebcaedbbcaeccccbeebdbddbbcbbcebdaeebccaeadcdeedabbeaaddcdceabdbcaebeaeaeddaeddbaeecdccacceceeddcebabbeaabcadbcdecbaadbdbcececadcceecabbdcccdcedecbacaebdaccbddedddcbbcdcbcadbcdcacabeebccadcbbbbcadaadcebddcdbaaabbaecadebbbdaaaeecbacddaeedcdceeeadbbcaebaddaabbbccdebbeebbdbabadabcdcecbbbddeabeadeaeeabadbbebbeaceeeaacdaeaadcdcebadccebeeaecdeeccdccebbcacadcbedaacdaaccbecacacbdeceaeeeabbdadadeabeeddcbdbcddecdaadddccccebadddadcbcebebeebaceceaaccccccddcddacbecbdcaeedbbddaaddeecdebccebdaeadddaaebdebcdacdbeebedebcdaaddaaadbcededeedbcaacdbdbbeebadecdadbaadaccbdbaaaceacaccdbededbbadbececabbdcceaebebbbadecadaeeeaccdecacebdaccbcdbebdaeaeceacecbdaaacaebbdabcbcaadeccedddaadbbbbbccaacdadaadbbeddeebbaeaceeeebeedcbdbadcccdbdbdbbeadaaddadbdcbeadacddbdebeeaedbbaeaadaeadbbaecdacbebbdbddccebbeeceaeaadceeeacedbebadabcdbcaabadccdcddaeabedceeddabcbcbbcebddadbcadeceddbaebcbedeeedceeadbccebaccebdeeceacabcecaecbddebcadddbebcaadecdaaebccdaccadaddcccddecbccbcbcbaaaceedaecebbdecaadecadabdedbbdbcebdeedaaaceaccdcebaadedaebddecabbdaadddecdaeeebbaeeadaedcbbabbdbbddbdbaeacbbeaebdabbceaacdebeadccacebaebaabeaedbabecacbaceebaaedaeaaaecccbdadbadbacdaedadebdbacdbdbbbccabaceeddcbdcbcadbbeaaeeebebeebbadacbcabacddeadbdadabdaaaabcdcbaebdcddbadcbcebdaeddbdbaadaeaaddbaeddebcaeacaeaadcaaedbaebbebdcdecabdcacaceeeddddaaacbcddecaabcddcbabbaccbbbceeaedcddaacabeaaaeebaabdeadaaceccadababbbbcaeeccdddeeacbcadaedacbcceaacedacdacabdaaedbcbecaaadadadaadcaadbecbcedcadacbeadaebedeecdceebddcbdcadbcebccacbeaabdacbdcbcbbeebaedcaebbdedbbdcebadabdbbcecdadadeeeaeaeeccbaadccddbdccbccecaccceaeabdbaaabeebdebdabbecdccddbebddbaacbeaecdeacdbbbecbbadbaddcaadadddcecccbaaeebaabaadccccacbeaacabcebbcceccebadabeccdeeebaebacadeccbbbdbbcaceccaaceacabcadcbabaabcacdebadbacbbddbdadbddcdaadabbcbbceeeeeedbbebddbacccacadbcdeacabbacabcddbacbcbbabeeeedcbbccbcebbeeeaacdeacdabedaeacecbdbeddebccadacdeaebccdccacbdcaaceabbededbddecbecbbecccebaeddccdaaadaebaecbceccaadeeaedcaeababdcaddddcadeeabcddadbebabaeabcdadddebddacadbcbeabeabcddcbcebbacbadeaadeaabbbbabeaecebabceadddadeecaeebcdebeacdaeaeeabdceecadceaaddedddccbeacbaabebabddbeccadaacdacacdedcbacedaaacadbdaaccedbbceeadedbeeddadbabcbbceadaaebebbeedbdebbdaaecabbcdaabbebebdeedbdebadbddbcbbcdbecbbbcdacadcadcaedacdbceccbdcabcebbadccdebedcbeebbdecdcedeabcaaababeadaecaaececdedceacdaebcaeeadeecaaaddebabdbdaabcbacebcdadebbccecbcbabdaeebabccbbeadcbdbdebbbaeadcdbedeacaaccadcdcacecbdccddecbdebaebabeacddcdbcddaaddbaceeecabadeacbecbedcbebabaabbabedeacdedddceecabeebcbadbbeacdadbddbeebdeaeacaabdcabaaeebeadcddcdeadebcacbdabedacebbeadaaaecbeabbadceacaeedaccedceadebebceeebedceeebadadceddccdacdceeaebcabaddedbaebbbbbebddabddccacaeddcdcaebcccaaaeaeacdeadeecbbbdedaceedbaacaeddeebecdaecbacdeccbedcddebdecacdebacaeebbeaacaaceadbdcbdaaccdceeecbaedbcbeabbdedbbdceddbdbbaeeedddbeebcacccabcdeaeadecbdaadceebbedcaaeabaddbaeabdebecedccbcdacadecaeebbdadbaedaccedaadcedcbaceccabdbebcaadbcdcaddadacabcbdabbebebddadcebceeabebbecddaeeddbedacbcbeccbacaacebaaccaeabaaabebbabeebacadecbceaadbddcddbeaaeedcdeaedbceadaababdbbedaadbbedddedaccecacbbdcabcccaeeceeaccceeaccbbdcedadbaadaddbcbdccaabbbaaaabcbcbaaccadabadebdebcdbaceddadbbadcbdacedccaddcacbabaadeeeeedaacebabbececeeeadbacdedcdaaadecdbeadbedbdbddddeadeeeaaceeecddcdbceddedbbcbdbbdeedcaeaaaabecbbcacbdabcbcaedeeadeddcababadadeeeaecadebbdbaadbebdbdcbabdaacaadcdcaabadbebadbdccdaeacebbbabcbadaaebeebcbcebeaeaebddadecebaabeebccdcdcbebbbcbaeecacdaebcacaaabdeebabceccaeaecaeedcbaedaeeacecbcecbeceedcceadbbdbbcedcbabececbcabbaaeeacecaaddebeedaebccbacbdccadceebbaebcbabdbecbadaaddecbccebdbaeecdbcdbaecadcbabecccbabedadcdccbaaccadcbaaeebccbccecbeddaecebddbcaedacbadeaacaacebbadadbecbdbddaaccdbebaeebbedaecbbbaacdbeeacbbeaebedcdbcecabededaeecccdecbaebabccdaadaddedadbdacdbbdeabbaccccdecedaeabbdcecacccddcaadeccdbbadeceeabcacbdeceeeecbcbcdcaeceeaeedbbdaedeeadcebbbdacbbeabdbbaadeabbbbedabcbccebeedbabcbadbbaeaabbbcbbbeacbdceeccadbcdbdbcbacbcdeaaddadcadbebddceaaabdeedcbaebcdccbceaabcadaaeeabeedaedcacbdadbceaaabaaddebecdebebeccaccbeadbcbbecbbdbcbaeecacbadcedbdedbddbdbeceddeabcebbbadcaabbbaddcbbbcdcedaecdbdbdcabebcaceecbdebebacbeadedcacaeddeaadbbebcebeeaaeecbbaebdbccccaeddacebecacdbdabacbeebdebaaadebbbcbceeebcacceecabaaabcbeecbbbddbbaaacedeeddcaaaaacddeccbeebacccbadceebbdeabaadaeeacbdadacadabccadcecaedebecbbbbceedcabbcaadeebccdaccccaeadcebbdeaebeacdedbaedbedeadbaabccacbbbdebbebbbdaccebceaebdbecdcabeacaebdaaaadbaddedcaeceaeadbeecdeccabcbebaebeabdbddcdadccdcdecbebeceacecbedbbcdccbcdbaeaeeedeabbeccaedbadceeaceeccdeebeeeaaaebdbdacdcebedecacbcdeccedcdcadeccdaedecedbaeeaebeceebadceccacbbdeacbaedcedcbebecbcdaabbaabcadbcabacaebbbbdddadbddaadabaecceaccaedabadebdeabdcddeaacacdbbcbeeeccaedcbcaadceecbaeeeebacebcdbbdbdaebcacedcdcdecaddaaeeacabbdddabaabbbbeadcbacacdeceeeaedbccadbcbedbbebdcdebaacdecbaceecaeddaeacebadcbccdbbebbcadadcbebcbdbdaaddceecdacadccebedabcddcaaecddeedcaeebeabdddbeaceeeebddbabcccdbacabaadabddcbecdcbbaabceddaeceeecdbdeebcbeabdeeacccecbadeeadaadceabaaebdabacebecebccdcabaacaabeaebcbcebedcebbedbbdceceecaeccbbedcebedccabddcedcccababddccdddcaebcceceddcaeebcdeedcdadbaddeceeacbcdebdcbbbdcaacdacbbaaebeeabecdbedcbcebcacebcdabeaaebeecceacceedecbcaecbaabcaeddebadccbdcbbcaedccbaeebaeacbcddbdeeeaaaacdaeecdacbcdeabddbcabcbeabaacdbaeddaecbceeddebecbeebbbdabadeecaaeebbcabbeeeebaadebbceabeddeadaabbdacdbdaabecdaddeedecbccaecdedadbaabededbbbdcdacecdcdadebeeabdcccdddeabaabebbeaaeeddceeeebdacdcbcbaacaedddeabbbdadeacbebcdcbdbaaaedecdeddbeebabeedbecadebaabebecbaaeabecdaeebcbdedeebaeebaacdededebdccbcabeeceeaeebeecedebbdcbbeeacbacbaaeaeadbddccadcccacaedeacbcaddbdddccccddeeddebaaeeabdaeadccecadaaaddadcdbaccccbcdabecbcbdcbebabdaacbeedbecddccecdeebdccadacceacbaaecccecbaeabedbccaedceeeadeacececcdbacccdbedcecceaeaedecdddbecbecdbeeacaceceadccebeecbeaacdaddebbbbdebbcecdbdcdcdcecdecccbdbecbeebdcaaabbadbacebeceabddddcdbceadaaadeecccddcccdcadaaecaddaceaecdccbedbdbaccccbeaaeaccececcdbcaacbbbbcedeecebaddcbcdedbcdddacbaddbbbdddddccbcbeddbadbecddbeeaaacbcdceaeeccdbeecaaacdbcaecabcdcbacebbdeccadcdadacccbbabcdbaadcdaedceacccaecabcbddbbeeeddaabacbabccaabaedcbebeeaaddcbeebccaceaeccecacdebcaeccedbdaaaedccddbeeecdaabdddccceaddbeabbddbabcccebcceebcebacccaebccbbebeecbeacdcdddaaebeedbbeeadadbaedbabacceadaaeedcaeadbeaddaaddddaccedbaacbddabddaddcbcdbbdabcacdaebaeddbebeeeecdbcccacececcdeecbcbcbcbbacaecdbeaedebddbdaaddbecedaeccdececcdddcadbeeaeedbccceacbdeecebcaedbcdbebcccebbcaddabaabbebbabcccaccaeabdbedddbdcdcdbabcceebeaabebbebcecbdabbcaeeacdcbdeeeededbcacdbacbecebbdceedeacbacadaaabbbaeeecebdbcbcbdccbdaadeaccceaaabdbcdbadbeeceadbaaabccaecaddbeccaeaeadaeaecdcbcdeccebabedceabadaaaadeaeaebbeacbcbccdaecaacdcecbecbcecdaddbcdeebbcddaacedecaaccaaeeddeaceccdcaeaacbadbdcdbcededeeabeaebcedadececadaaceeaeaaadeecccbabdcdceccdceaaccaabadedcdcabbaaaaabccdabeceeebcdaccaecacedbeceaedbdacbebaacaecedebedbeccdeacccadadcaedbbdccdcbecbecaedcababbabedaaecbcabcaeddecbbeecdddacaaeeaabdaeacadabcebecbbdbdabbcbccdaaededbccebecbbcaaabbabbebcebdadacbdaeaeabdaaddbcdaecbdbeaccaecaaeeecacebecaaeaabdcebbcdeacdcbdaecdeecdbeeeeeddacbcaaeddbcaabeccbeeebaaaeabdeebdbdbdccbbbacdccddeaacecbaedecccbebccbbaacadaaaceaabebecadebbaabdadedadcdebbcaadccbcedbaaabebeaaceaecaadeccbbaecdedabbdaeebdcadeeabdeebbedaebaadbaeaaedcebccbeecbebeccbbbdbdddbddcebaeaeccaaedbacbceedebcecdbeababcecbeaadcaecedbaceeacbcdaebededbccecdabeadcebbbbbebdcbabbeccdebecbaecdbdaedcbcecdddddaaddadaccacaeadbbcdaeccadcdebdaabddcaddeadbebacddedaedcedcddedacbeaabbcaaeeedcbceadbecbbeadeddebccdecaeebdcebbbecabaadabcccabeedcedbeaedcbaaadadebaaebcbdddbaabecbeadedbddeccaadbcaacdaddddcdbaccecbbdbcececebcbcaaabaddbcbaabccaadcacaeceebecdeaabcbecdeeedbeacaddbcdbeaeedcceeeaeaebccdbededddeccbeacaaacbcaeacdeaaaacdaadaeeeedbbcadbaadaabcddaacebbdaedcedeaecccbeddeededdddeacccacdcebddedadeadeabccbdacabaaacecdaeacacacacddbaaaaceeecabeaeaedacdaacecbdddcadddebbeebeecebaaadadacbbaabddbecdabdaaacedacccccdeacbcdeedbbcdccecaabebbdaedccbdcabccbdeaaecdbadbbceaceacadcadcabceecaebcedbdeddddacdedebbebeccecbecbaebbebddcbccaadbcebcaddecaeadcccadaacededadbabdadcdecccdceacdbaecabbbebbddbacbdebceeaeebeaaceaabadcccbdcbbaadbbccbedacabcebadedaeeddedadecdcacbbaaaeddabaabdbbdcecdabcdeccedeadbadbceedaacdcebcaaacccdabcdddbbcdeeedbcecdaebadebcbddbabdcbeeeebdaceebbbdabebbcaeebaebdcbbbbdabecbccacdeeabcbbbcddeedeaaddededccabdaeedccdeeedbdeedaaddeaaadccabdcacdecaaebdecebccdbebececdcccaccdbdeadecacbacddaecaccadbaeeeaecabadeecacdbaebbdeccbaaaecdcacaacbbcddcccbcaecdbccabdcceedbebdcababcccbaeccdbaacaccedebadecedbbececadabeddeabecbeeccdbddccabbedbababdaeabaecbbabacbcbacdacbeddbbccadddbcbcbbdcbdeaaadbdaecbadddcaccabcccceabecaadbdeaeececdbcabebaccdcaebaadbddcecebdeaaaecbebeabdedceacadecaccedeeabdcbeaececdacbedbbabadcdcaddaeaeaacebdbdbecedadbbceaadabacebaaaddebaedbdbcaaacdeaedeeecadedabecedaeccabbeacaeabaedcadbbcadeabcbbbcebdbaacaadbdaddcdbbbbdecaeaadbaeebbacaddbdccebaaccacadbebbeebeeacdabbaedaebbcabdbbaaccbdcdcbbeaaedcbbaedaeebacebeabedebabeaabeddcacbdedbcaaaeadcbccaababcebbdbbeceebaedbbbdbdabbcaabbbecebcccdbeaaeedadccdcedaecbeaadeeaacabcbcaddeadababcabcacbdadacdcbaeabcebabaaceecebbdcbebcdddebddedbcacabcdcbebbebdbdbdddbbcdaacbaecacacecbbccaeaaeebbceaadcdeebdbcbbddccecbdccaddecceebcdbbccbeebcdaebbadcdaaaaeaecebebacbbabcceacdebaececbcaededeaaceececdaccddcebebcbeeedcdbebbceacbccacbbcbbeacddcdbaceedddbdeeddddbadbeccdabadebeeeaddbcdbaeeddeedbdcedcaeadbebdedeccdbabadbdbaabbdedaacbbbecdaeecedddcacdeedeabddedcbdcbdcbcdaccabdebaebbbbcdbcdeeadaddddadbdeececcdeeaadaaadcddbdebcdbbdaedadabddeeddbdccecdbadaeaceccdbbeceeddcebadeecdcdbecbaeecededabddcdbeadddceccbbdedeabaaaebdbaddadbdbcbadceaccdabadcabbceceaabddadaadeabcabaceebdedededbddebeabebadcebccedcdadaeeaddebddcacdcabeacbcdddaeccaecdbbeeebecbdaebbdbcbadaecaeeceecdddbcdaeaabbdecacddbaaeecadaeeecedbeaddeeadbcbcedebdeeececbabbdebeeebeeacdccbbdbdedacccdbcadacbddccabadbdbabdaeabccdbeeeeaaaeabeabbeebcdddecddabeaabadaeadaaddbeaacbbacecbacaacbdbabadacdadcdcdbbebbdbceeeadbedeaaaaceadbbecbebbbcdbaaccbbbaecbccdabacabaccaabaaeaaecbbeacbcdcaecedbacbadcacbabbdeeadbaededceccdbaddadcdbdaedaccdcbedbcabacdbdacbddccddaccebeebadabecaadeeccddedaabcadccbaadabbbeeabcdcabacbecdcbdaeecbcbaeedcededcbecacacdaaedbccbccddcbdbebeeeaeaadededadeaeddeaebaebeaaecebaddecabcacacdcbcbedbdedcedceabdbbbceadbeebaabcccedddabbeeaecdcaaaeceebbacacecadacaacbdadeddcdadedcddedaccdcabbcdacbacdebdbadaeabeacabdacacdbaabaeccdbdcddbbececbaddbdaeccbabccebeecaeabdaadabddaadebcaddcbcbbcabaedbcaebdaaeddbeedcbaadedeaeeadaccbeaabcebdbeaeecaecdebddbcbebceeddaacededacddcdaadcdbeaccadababcbaddcccccccaedccccbccbbdbeadbaeeaeeaedaecceedadbcebddedaaabbbcaaacedacecddeabbbccebcecccdbedaceccacbbccddacaadbdbdaedadeacbddaeeaddebbdabbeedcbbadddcaceadeeebbceeecaeebeacacebebeacaadddeabdccdbdbbacecebbbbacebdeeadabcacdceaaabdddbabaedbcaadecdddddbdadbcdceddaacaabcaceceadeaccbbdccdeebcddbedcbccaabebaececbddbadeaeeebdbaebeadebddeddaccebdeccbbeececdedaabcdcdccbbceeedbbebcbcecbbbdaeaabcaaccbedabceaddcbaacbaddbeabaaceaecaddbbccdcbeedcacacceebeaaeaacadaedcecaaaacababbaaccebaccaebbddbdaeabbccbaacccbacedccbdabcccbecccccdeccbddcdbabaaabcceddcddcbbeaeeaddabdcaadeddbbadcddaaecdbaadbeddacbabaebaaadbdcacaeddbcdbdbbadeaccbadebdedbaedbcbdbabbdaeeebadecdeacbecebdbeebecccecbceaaeedcaaadceebccdecbcddcbecdbebceeeeabdebadebeaceeacbdceabadbcaddaaeaaabadbdbdbdbbbececbebceaaccaecaeeedaecdaedbbdabaaeeebecaedaabecaeabdebbbdedecdaeaeaacdaaecadedccecbcebeedabedbdaaedbedabbbcdbccdcaccbabcecebeddacebedabaacabebcccbaeeddaadeccbbbaedadbcaddbdaddbdccdbacebcedabdddcdceadceaaeecdeaebdeebceedacbecbaadaacdcaacdddebadccbacdcaedbebcdbeabdbbcbebbdededabbaddcdbaeeebceabebcdebeabcecbdcaabaacbddaeaabaaebaebadccceceabccaadddeacccadeeecaabdbbedadbeeebdcedaadeccbbccbceacabbeeaccbeecadcceedaacedbebeaeebdbcebaaaceabbdcaabeaeaeacbcdccabdabddeeddcbedebacdcdeabbbbdccedacedcdababbbbdaadbcbbbceddeeaedbcabdaeeeaaedcebdccabebdcabbaaaedaaceaecedbcbdbcbbcbbcdbeaccaacbdabeeebbacddeeebacdddbcebeddbeebebdedbeedccbaabcadbaabadeceaeabbbcdbdcaccacccbbcbdebeeecacaedaaadcdccbccbcedbceeadeacbdbeddcecbcdbacbdcebbcccbdacbacbdcaebaecdcebdbacdbaccbaadacaebdbeceabceebdaedbdaadaaabaebdcbbbeaeebddeabcaeecbedeaabaddeaeabdbdaebcbbabaecdcaeabeaabbccbbebeecbcebeaaebccaccbbdecabbddcbaabaceedbdceaecbcebbdbecbceaaeaaddccabeceaedeccddccceedebecaeeacbcaccadcdcdbbdcceddabbbbbecccbdebcedbdbbbedbcbcecceaeecdbaabcbabeadbccabececccacadcaecbeeeadcdbebbbbbbcbcceededdacadbcaedbbcaeeacaddeeceecabaacbeacdadacdadedacbdececaebabbdcbaabcbadabeeeaeeecdaeaddbecbbacdeebacaeadecdaaaabdddaeacbcaeaebedccddeabdcddaeabbbbdcbdeacedeaaabaaedaebbceaeabceadddddbdcedeadbdabaaccbecaadbbbbedbbcccebcbdeeabbbcbccaaacaddcbaaabedbcadcadaeabdcaedacbdabbddcaccaaeeaccbaaacdccbbeebbedaebbddcaababbbacbdddddcbbadebadedbbbdcdcddeddcecabebeedbeacccbcdcbdcaddcabaebbbabdebbecdbacacaabdcdddcbeeeccbaeecbbbbbeabdceedcebecdddebabcdcacdadecddacaabcecbeecbcccdcddbcddccaddaeebdceccceedceceebdbeeaedeedaddaccbedcdebccbedecbeeeedbdbaababaedccbcedaadbacdaaabbceaccbeabccbaeebeabaabcbedabcaabeceddaaddedecdebbabbcedccbdebaccbdacdebddbcaadbbddaceacceacedcbcacddabdceeedbbbddadeedebacbebebdbbcaabcbcceaeeedcccdaebabbbcadaabaeadcdabebddacedeedcebebceceaacbabcbcbbbebcbeaeecdeabcebdbdaceebcbaaccadedbdcebcaddbdaadadbacdeadadeadcdabddbedbbeadbdcadbecdbdabcccbacaaacbeddcadaeaaadbababeabedcaadcbbddbaabbabbcdaeebebbbcbadcdecbacaebbcebeacebcdabdaecabedadbbdbececcededebdccdbebdbbaeddaaababdceaaddabceddabcbebaaedbbcededbbbbdaadabceaadebbecbeeddbcbcadedecaaacbacccecaddddcbdcbeddcaebdcacacbacaeeeabcbcdeaceaebebaaaddadabdaaedeadbabcdeedacdadcdabeedeedebedddaceabeeeaeebcddeabedecedaecdeeedbeabbbcadbbadccbdbeebabeadbcedeaeaaadeedbdedabbadaeaaebebbdaddabccecbadbaacdaecbdadbaacccebcbddccaeedaeeaddbaadbcdabeabacebaedaebbdcbbdcbbcedbcbdddeadceebdcccaabcccabeddaadccaebeddebaaddacadebdddedbcaeddccdbadcecccebedebeebccdcebdebdccaadacaebbeebaeaeccaeacebeccdeceebacadbbdaaaaaacdbecbedaedcbdcdebccecdcbbdadbeaeadcccbdbacdeaedeadbeadaededbacbecdccdaadeabcdaaeeeaddcbeccedccebecbcabeaadeaceadcaddaacbedacbddcecccdcdadacecdaaceadbbeddecbebdceeabceddaeabbcbeaecceeebdeabdbcdeeaacdeaadadcabeebdcbcbdaedaadbdcacdcccaaceddaeecbbbbcceadabacaaabaadaeeceaacbdcabdcaddaadcbcbacdedecbccbeababcbbcebbedcddacdaaccdaecbddeaadebeacdbdcebadebedbdcdeadcaeeceedccabdedadbbacaadaecabdaaadcdabbeeecaceaacaacddeaebcbdddbddaceabbebbacebcabecabcaddcbbaebecdcdeacededeceeecbeabbabacebaceeeaccacdbbacebacbdabddeeabdcdbdbbaecdcbebedcdcbabeebaadbbcceadcbedcacbaadaedddaccbdbaadeeeccebcdbadaeaeecedccdceaeaedcabbbaadabdebaaadcedaecbeebedbccddccebdadedeaedcbabaeadeddcceceabecdacdacdebbceeebbaaecdddcaedbdcccceddbeacccceeecdbabbddbceabeadbabeeccbbbabdaedecbbaaeedeaeabaccbbbccdeeabbbdcccbeccbcbcbdaddceecdbdcacecaeaacaaddeacaeebdceebcabeaecccedbebaaadbcccbbcdceadedddabdedcaccedeeadbaacbdaaaeaebebdadcdbcdeeacdeeedaeebddaacaaeaececedadebccddbdecaaabdebbccbbedbeedddccdaaeeeeacbcaeaeaaacbcbdacbcdbccdeaaecbbcbdaabbacabebacaeabcbccbdbdccceaaaebbbcbeddaccabceedabbceaeaeacdcdaceaadddcdacecbacebbbcbbbbaaebdddaeccebbeabdeacecedcebdacaacdaddbaaabcdaadbbcabadcbdcacdabbbdabeeccaccdbbbbcaaadddeadeadcbdaeedeccbdaabcdaaddaddacdbcdaeebdeeebdbdadbeadbbcabecdedcceddbeecaaeaacadebcbadbdddddcbbbbbddbbcabacbdbdbcbaeaaedcbeacdbcdedecddadecedaeaebaddaabbedecadabedcbddccebacdbaaeaaccecdddabbcecdceaeebcedecbacdeddecadacddbcbedccdddaadbbbcceedabecdbbaaecddddbecedadbaabcdebbedeadabdaeeceeebdcaaddcedcddcaddbdcabedcaacbaceeecdaacceaceadabdcdcddcccdbcaadceebaebedebdeceeadeaedaaceaaccddbaaacbcdddcdbdceeebbcbbecebaeececcedaacaadcebbdcbedbbcecdacaebcdbdebaaaeaabdadabcaeddaeccdcddaadcbcbeeabbaccdbcaeeadaeececebebcaeecceedbbaccbcecdbbddcaaeddaaacabedaeebcbcddedadbeceaacbceeccdabbebbceecccdbabbccedacdebeeaaadeebccabeceadbdcddcccbeeecdecdecabadbdaccecdbbacdcdbabbeaeabddadeedacbadbaeadbadeecbedecdaeabecdcadedeaeeadaeddccabbdebbeadcabcbaadbdeebedbdbdeeeddcbcccddaaebcccdbbedbeccabcddbabbbebcdeeccecccddcccedacbbecaaabbddbbeadcaacdbedeeecbcebeeacbaeebdaabbaebaebeeaeaccbeeeaeedbdbdaebcdbecbcbbeaaceaaeaebdcedeacdbaadcdeeeecdbeabaeaccdcabaacdcacdaeecbbdeecbdeaaeebeebdaebdcedebbbeddcecdecccabedebcececedbcebabbaeadaddccccbabbbceebacceadabbbdbdcaeacedddeaccadacbbbabdadabbdeedcdabeaedbcaeadaaaebbaeedcedebedbcbecaabcdbaaeacdcebabeaecddbbddebdecbcdacdbbadbabddeeeeaadaeeecbedeeacbaadeaedcddceebbddbbecacaeddeaaeabeedceeebeaedacbddabdecddacdeeabedcaceccaabbeecbccbbaaabdeebabbcdeadbacaacaaccabacaeadaeaecadcdecbaedcdbaacdebccaddbaadbcbabcabdeacdcddaebeeddeaeeebeaceebbbcdbddabaaccbcdecaadbaebecabcddbcddaebcdeccabadebbcbaeccbdbeedcccbaaccbcdcadcaceaddaedccedecbaacbecceecbadeaccbbcabbabebedadcdccdeceadbaabebdbbacdeaddaebbbbceeedaadddceeaeeaddecdcccabcbacbaecadeddddaecccbacbedadcedacaebedcababbdbbbcdbbccdabdeaeeecbacbeacbbabcbdacdeaccdacdaccddeeddeaaedeababdabdcdeceeaeeccdbabbbbcebbbdccccabbdcedebbdacbbacaadacdbdbccbbcdcaacedaecddeddccedecbcddcacbcaccbbdbcecabebeadabeacecbeddbcddbeaadcbecdcabcceecebcaeeabbaecdeadbddbacebaebabdddbecaeebebbeaacbbecdadbeeebcdcabcddbaeceaaedaccabaeeebbbeaeadaebdddacdcceebdeadbaecedbaeeaebdcccdbbbdcadceccdbcdabaccccecebbdaedaaedebacbacbeaabdabddebebedecbaaecedcbdabdebabaadbabcdbdeceabbedcedcecdbccddbeaacdbcabdbbcbcbdedbbebddbaaadeedcddabdaadbeeecebedceebaecbdeabeedaabdaaeaaaeddaeebbeeccdbeadaebadedcadcdcaaedcaaaeacccdaccecdbdebcdbdbaaacceacbaccebeedbdabadcdaacceeecbaddacbebbdbabecceecbecbbcccaaabeeddbbcdeabcacbeeaaebabebbedaedccddaacbaabbcabacdadeacbebecbaebacdcbbedaadbbbbadbacddbdacbebabbabeddcbedecadeabbabacabcecbebdaccdacacbaaabaebabbbbcbbbbddadecceebbaccebdeabcabaaebccbbbdcedeaccbabaaadbdcbbedccedbeccaadeccbdedbbbdadbbbbaabecbadeedcccedbeadacdabcceeadcbbcccaebcacbeecaedabeaeccbedbabccbbccdebcecdabccedacaedccaddaabeddabebcccbabdceeaecbcedbcccadaebaeecbcddccdaedeecbeebcecaabceaaeeebdaedabaabaaeaebbcebedcdeabbaccbdbeabcadbbbaacacdbcbdebcbbcdaadbceabadeddedaddccdebeddcbaedecccebabccbccabbbbdaebeddababddbecbeabcaaaaebdebacebadbbdeecbcaecdbabeadecaedabbeaddaaabceadceaecdbabbcedbcdadeeeacbdaecebbcebeaeabbaacabcadbedeeadbdcadaaebddbcadeaebccbcdeebdadbdabbedbdaedabdcbaedddbadbaedcbabcaaadbdaebbccacdebcacadeabbdaedbcbeeddccdcddbaaddbebadebdabaaaecebedaabcaeaaeecbdabeedebdeecdaceaacdcbcdbaaacbdeecabcccaecbacdaeeaebeeadedcaeacedadcdeadbbaecceaededeedbcbcdeecbdbbaedabbbbaceeabbbaeeeebccccedbbaaaaadccadbceddcaddddeaebccbdadebebeebedcbebceceeeaccdebeddaeaadddeddcaabebdcdeeddbcadceaaabbcceddbcbcbeeaebdddbeadaeaddeadecdcdbadcbbebddcaabdeaadabebdcbbdebdabedeaddcbacbaccbbaccccacccdabacadcecbacccdbdcbadacdbceedbdceaeebdeeaeebbaceebebccaeecccecbabaeaebadceebaadebacceaaeedeeedadaebabddbcabecbaeaeecabcbedaaeebebcbecaabdbbbabbbdbaabeecedcbcaaacaeebdbabbeeeedbacceecaaaacadeddbcdacbdaedbabbedeeceedceebcbdbadacdcdecaebaedaaacaaebbaabaaceadbccedebcacbbaeebbccbadbacdeeacacaacdcbaabccaeeebadaededadecbabaecebbddeeedadbedeebbbaccebbbebcdacceddcdaededbccceceaabaeeddabeebdeabbdedaebbdbedaaeeecceebdbabdccbcdadccebebdbcccaadeeadceeacecdadbbccddbbddabcbeedacacbbbddceaaeaacaecbedbcdceadaddedeabacabcdebdcbaceaeeddeebdeeccbdebaddcbedeebdaccaedaacdaddceebcdbacdcabddcdaabaaedccbaaeeaacabdaecbebababaccedaacddbcaabadeebdabcceabebdcbddcbcdacbebeeeeeddecbaadeaabdeecdbedbaebacbcebaaceccddabdcbedabcebccaeccdaddbccbabcdccaedebceaaecddebccecdcadbcadebdcddeebeacbecbceaeeaaaaddaabcaebdebddaecaddbaeaababdbbaaeadabcbedcdabeaccadcceaacaaaaedeeeadbbdeebcdbcccbeacbeedaaadeacbbdabeeddcbdeedbbdebdcbedcebeeccebcecaeccdebadbbcaadeeebbeaecdaceddaabcbecbbadbacaabeddecceabaeeeaeacdbbbdcacadbddebbdbaceebdccebabcbcebecdddbeddeebdadbeaeebdceaccaaacdeeaadbbdbedaecdadbacbcdbbbdbadcddeeacdddcdbdcbacdbdeaebecadacdcacdbbdacbacaeeedcdaebcaadbebcdcaddaadacbadbacadbcaadbcaebbeadcbdaeeaedecaddbaabcbeeecbdcbeddbcbdedecdbebdeeedacceaceececbecdaadbbcaecdddebebbeaacddddabadbbaabdbbdcdceccbaedabdcaaddadcbadcdbeeccdbbebeddbadbccacdbededebbeabddbeaececbabececdceeebaeadeebeddbccbcddccceecceaaacdeaeabacdbeaabadcdccdcdedeedebbbacceddabeacebddcedaedbccbccebadeababcedbbeddbadaaaaebdbeecedbcdeeaadabccdabbdecacddeccbabddadabacbcadcabeddcdceeadbcedebcceedecbadcecabdeeddbadaadaacbcbcdbcbccbabbeddbcadadbbedababaaadabcabbbadacbbaccbacedcccdbbcbdbadedbddcbbbbeebcbadbdecbadbddadaaeeabedceebccddecabacbcaacdbdbbaaaadbadacebcecbccbaacdcbcdaadadecacabcccaeadccbcccdeadebdcbdcaaecadbdceacadeedbdebdaccdacbdaeeedebabedbaeedcceccbdbebbdcbdbbdcbabadbecdadbacdcbcdbdccadaebceabbceccdbceddbbaabdceecbbedcbdeeabedabbdaacdececcdbabbaeeaebbadadbbbacacdabeaebaebdebbbedcccbaddddebcaaaedeacdccbcccbcebacbdddabdcbbdbebddcacccceebcddabcedbcecebabcbbceabeaabccdcaeaeddebabdbaddabedcbeaacbcacacdcaecabdaedaebabdcaedbaacababbdcabedddaececcaddbebccacbccaecebceaaabcddbaceabbbdeecbdaeceadbddbccabcceaebacacbbdabbabdeceedbdbbbdebceccacbaeaceddbbcadacaceeacaeaeddcbdadadcddeceaccbdccedcccbdcdcddebbadbadcaeccababcacbcbbeacbdaecacbdcaceeaadacaeabeccabcabcaaedcecabdddccbcbededcadbaddbbdbbdedaaddcbaceedebebdbbeeabeaedcddebdbacacacdcaeabcdbcadedeedccdbacedadbabeedadceceacdbeaebbbbbabedaeeededceeaaeaacbadeccdcccbaccaceddcbeecaecbacdddccbabbedbbaeaebdebbcddbadddaebaccdeccdcadcbdbeaccdebbcabbabaddacbbcedcbcabacdadcacacdacaadbbddecaddccdabbaeecdadabbeedcbaeeaeebeededcdbbbecdaebacbbdccccecbdbdddbdecdeecacbbeedbeeaabdedadbaaaacadbedbdecdcadcaccacabadceaaceccacddbecaaccaceecdaedebdcebaadcddadddaeeaababbecedbbadcbbddbdebcdeecbbeebbacdccbebaeabbbdebddabedbbbcccdeaecebebdaadcececcededaaaabceaadaeaecccbbddabcdaabebdcedccacdbbababbebcdaceebbeedeacabdaeebaeabaccecdcdebabdddcbdaadddceaddacbdbbdecbeabddeabacabddcdebdbeadcacaedacaabaeaebddaeeedeeabeecdacbcbcdeebeabdebbeccbabcddcedededeccacaaacdcbddacdddabeacbaedbcbaeceaaeacbaedcdbebcacdeacbeedabbbcbbaaaedbddcacdbbbecbcdebbaceebceeacaacbeaeccdeabbaeabdbcebedebeaeeddbebeabeddabceeaedcaaacdceebbdebbcbcdeabadcadeebadcbbcbcadcddaacaeddbbeeedddcaabcadceccaedbbdcebebaeebdecabbbbaccdadcdabecbaecddaeeaadeccadaaabdadddddbdebaedeaddebebcadecbcbdedbddebdbeaeeccadcbbebdbecadedbecadbeaadbeeaabdebddaeebbaebadadcddadbeecedbcceaeaceebeccecaebcdebeaeebecdebcedeacccaaeaabecdeaeedaabbcdebcaceeacecaeeeeeabdcddbddeedadabcdbbbcacbcbdeaacaedacaccaccaccadeeacaacdebecaeeceaeaecaaccdaddccddeccedbcebbaccddaedebbedaadebbbecaeabebabdcddcebaddeadddaaacaebcbdecaceaceecbbbbcabdcdcdbebcbbacedbacceeecdcdecdadaaeeeeebeacbcaaadceebacecadbdcebebadedccbbeedcaeedbbcbbaaeaeabbdedcaeacccddcbebaeaadddabdbdeeadaaccccebbdbaeabacccbbaaceaeebbdcdabeecbaebbbdbdceaeececbbebabdaebcbcadeebadcdbacacabecceededacdaeaaddaabcacbcebbedeaacdecccedaeccbadbacecdbecbedaccddecbccaedbcbbaebaeadcecbacccadcadcddecddadcddcdcacbacccccabedeededbabaeceacbadddabaabccdbbddcbbceeebbccabaadbeaddbeaaadeadbbebabeeedeceaacadeaaceaebbcaeeddbdccedbcbabbdecacbbcacdbccbdcaedaecceaacbddabcbbddcdbacaddcbabaebdbeddbcaddabeaeeecdbccadceebabedbecdedbdeeeeaabaebebcebcaceddbbcbedadadeabaaedbceabaddceabbebceeddacddbbcbecebeecabdebeacebeedeecddcceedcaaeaddaccbcdcecadddeacceddcbaadaddcadaddaceaabdcbcbbdcccaaedecaecbaacdeedeababdcacaaaddadbaaacacccabeaecddebdcbdeeecbddededeaabdcdaaebcbccbeddedbbecedebebccdcedadddeccedbaacaedbcabeeedbbaaeeabddbaeeddadabdcbcccaddcbebadaccaddceebabaacbdbddbaaeeacaadcccbcacccceaeedeeabaecabdbbddbbcadbbcedaecddeaaacdebcedeaecacdeaceaeeedddabbdbbcdddbdcceaddaabdccbdbaabeedaeddabcaacaaaaecbcbabceaeababdeacdcadacbcbbdcbdbbcdbdacdbadaebbceddcdaacddbbbedbeebeeabcbedebdcccdccddabeccdbdadbcaadebbabbbdcedcaaceecbdeccaacadeececaabeebeabbaaecedabeccdaabaedebcecaededbecbbccdabbbbbecadceadeeddebcbadcededabeedbbeeecdaaaebbbadbecbeaddbcccbeaecbdebcbbecdddcdadbadeecaabaeaaadacaaaeabbbcbeabaeededeacabbaeddbadcceadcebcaacaddbeceddaedcccdcaeddcadeccbcdeaedddcdcbeedeebbceddbcbccecbaceeddcbabcdeabeabcecbbbeabeacbadcceddceddedacbedecbaeebdabadbaedcdbdaaecdaeaebbdcccdebdadcaeadaebababbedbaedcededeceeaabeabddaeaccacdcebacbceacddedcbcdeadeeddcededbdeabeedaddadcbeceedbcbeddccdbeceadadebdaedcdaeaaaddaadebaedabbcaacbbeedbdbededbeebeaaddbdababbabceddebdbbdccbabcabedddbdabcbdbbadeadacccadabdccecccbeacddbcaadccbaaeecadbedbdbceaaebaadeccecdadebbaecacdecaaeadeacdebebcaadbabdabaccebceeedbeaeeaebcebbebedeababcdddbabbdbceeacaceabdedaaaccbadecbcabdbcbdeaeecdbaeabeaebdeddabdccadadaacabeaeaaddcabbcaebeecadbcbeeacabedabbaaacedadeadabbeccdcaaaaabacaeeebbacdedbabaaddcdbdbadcebebebcdcddecccbedbabddccbcdbcadbddabbbdabbabebabcecdcaddaaebbcecdcbedaaddadecbeccdbebededecdedbddcbcdccbbaccabbbeddaebbabcecabbbabcaebddccadceeeadbaceecbaadbdcebedcadbedccedceeebbeeebcacabdbdbdbaaccdcbdbddbdacbccecaeebddbceadeccceceddeddcaaacaacbadeaedcdbbedeadeccacabccecaacaeaddcbaadabbdeeadcabedeebbcecedcabdbebadaeccaccaccadbabccdcccabeddabcacbccccedbcedbebdabcaeaeeaecdabdebbcbadebaacbdaacdbaeabceddbaacaaaadbccbbbceecddacecbceabbdabcbabdaeeabbcdbdacacecddabdeecaeaeddcebcceeaeeecbaebcedbbebdcecedebbabbbdcbbbcacabbaabdbeeebcadadedceddcabdbedeceeecebbcacebeaeecddeadbeddadeaabdbddcabdbdbbcacacaaadedcccbcaeecaecdeccbceececbcdaacbebddaadeddebcdceeccdcceecbceaabbacbccccdcabddabebdbbbccdeadcadddadccbbbcbcbceaecddbdddecaccbddacddddedeccebbeabdeaaeebbcadddccaaddbdbeddcbceacaadabbcdcccadeddbcaccddaccebdeabebaccadeeddabadbcdcddbeaaabebddcbcaacbebdddeaacbaecadadbdaaedaddadceccaceeeabdbdbbacbeeddbcdcacbdccddceacaddbaaebacadaebcedbcacbadbeaecdaedeeaabcdbddcedabebbbbabeceabdddadaacbbeddcabcbcdcebbccccdeedaedcabceaaaeeacecdccdaabaccaeacaeaaaacbccceecbaddbbabaaabaceeadcebbacbbeebeddaecdbcbabcbaabddbdedeaeccccdaeaadcaebbccccbacccdbaeaeabddaedcbddecadceaeccbeeadcbaedacaaabdeabcaddbcebabcdeedadbeeaddcaebbdecceeeaebbdaeddddbebcbbbdcbdbdbdbbaeaecdaddadcccacacabdedeecbdababbaaccbcabbebeddbbdccdeeecacddeedacbddaebebaabaeabccadecdaeeddcedadeeabaacbddcddcdadbbaaeaabacdbcaccddedcabcacdaaabbbccaddbaabcebcecdbcadabebeebbcbeceecdcddcecdbcbcababeedadeadcbcbbbeeeaaababcdeeadaceeceecadddabbadcdceacaeadabedceeeedabbaaaeadbacdcbcdabebcbacadcdeecbcabdecdeadcedcdaabacbbdaedddddddbbccbdaecbcccecbaadbceabcdcaddcacdadaecdeacceddaecaebebaecbebbeeddbedbccdbceabebbaeceaebecaedcccdcaabeabccccabedccbaebbcdcaccddeacdbacdbbdedcbaaeeacabddbadeaaeceaacbebadadcbebbaeeadbbeaddddbdcedebebdacbbeddcebaaaeedeedcabbdddebbedbbeccebbcacbbceaaacbbaceeddaedbbddcaeeaecaedcbadcbdedecbedabbadaeaacdbcaeaaebddebdbeadbcbddabadbcbcdccdbaaedeeedbaeaacacadeddbbdbbdabbeedbbbcdacdaeadaebdbeabbcdcabbaaaeaaedeadacbbddabcbccaceceadcedbebbaeacacadddcceadaadbdbcdaacabaaccbcdddaaeaabbedeeaeadccdceabeebedcecddeaaecacacbdbceeceacbdeedbeebcbbbebdbdbbceceabcabcdacaedeeaabbbbeaaadcdedbaccbbbdbaacacacbddccddbebccbaaaacaceddacedeeecaebeabebececeebedbabdaadbeaaecbbceceedbedbaacbeaceeabaeadebaeaeebdcaddabbbdbdebeeebeedaaacaceedaeebadbdedddcaccbccbacedabcacbeeeabbacaadcaabcbdaccaccccdbddccededadcbbecedcdccbebcdcadcdccbeeabababacbcbbedaecdeeeacccbddbcedceadeeaaaaebbededdebcaddeeddeddadbccaaeaddcaaeeabbbcaeaccdcecddccabecdadadbcadbedbedaddeccdaebaeebdbcaabadbcbdecdbebdadbcdcebaebdaadbaeecaeaeadebcadebebadaabeeadcaccdaebbbbbddabbbbcaaceadaaedcdebecbcebececcbdedbcbceaebcbcdcdbbecebdecadcdbbcdbecbedeaaceaecddcbcbdddaceebaaebceaebcdbcbcdbbaebbdebdddaacacdbddceccedcdeeaedbabecbeacdabdcaaeadbaecdcbbbcbccadbeecbdcacdebddebaabddeacbaadaeadaaaddeecbdbaeedaecdbdbdebbbcdaacebddbebeabcddedbabaddccddaaadcaaadeecdeebdeabacbdceeebbcbddeaaecedaebeadbcbcaaaedaccecdcadcecbbababccbcdcceeddbaaedaeaecbebbebaaeccaecceaeeccccccebeceeaacaebbaddeabebbaebadedccbbecaecdcebeedadbbcaabebbbbcdecaabddacdebbaccedacbbeedacccaaacbcaabcbddeecdbbdaddceededccacdabcedcbebcaabcdcadacccdeaacbdbeabadbbbedebcecaeceeceeecaeeeeccedbdbcbcdbceeeaecadaebacaeaebabcaeeebbbedddcceeeaceaeebcabacaeeeebdabdceeacecdeecbeddadbdabbbdecbdadbbecccacadccebbadaadadcbdbbacbabbaaebebdeccebedeabbcdeabcdeececdccabdedcdbeadbbdddbaaecbdcacdbccaeeeaaddbbeccbabdcbdeaddceecdcdebcddabdcdeebedccdccdcadceeaceddaaddddebeacddcebeeccbeaedccbdcaaadedeaeabceeaadbcebaccdccdcadceaecccebaabaedadaaacbeedebecaaeacecacccddbecceebbccaeadedbeadeebecedaadcbddbcbabceccebadddbdeebdeeeadbecccbbdeabacbddeecdaebcddceccdbdacabaaeccdcbebeeeeedccadecdacaadebccbceedeacabbdabeddebbeadbdbdbcdecddacccddbeaceabdbdcadbdddaaccdadeacbdeddebdcecaebebabdecbaaacebcedadaeedadbabaeedacbcbadacbcddeecdcaadecdaeccbbcbedbdcadaecacecebeaedeacaabdabcdebbeedadcbaebdbbbbcecdbedcbabdbdebbdaaccddaedddacddbbbdeeebededcdaebbbceedeccadadddadcdaacdceaedeeceddaaadccdbadadaadddcbbaedcdbbbddabcbbeeeedbddeebddaadabeceaeccdcbbdecbcbacaeadacbedabbdedaececcdcbdecadaceccaccccaccbcbbbdacbecddeeddecadbdbeaabeaacddddbcbbdeadbcaebeaebdaabccacdbadebabdbacaddacdecebcdeeaacecadbaadbbdcbabaeccababbdddbbcdaaaadbeaaaeacddbeadbdcaaedcbdedeeedbbddddceaacaedbaebdddecaebbeecbebcebaabcabbdadbbcddcdcaabdccadadebacabebdaeebdabcdcacddbaeeedadecbbcadbedeceaaaecdabbcdbdcaaacdcdddaedadecbeabcbeacdeebaddbadeadcacccdbbcccbcebaaddaabadabbdbccceecaadadddebbbdeecebdcbbbebabaebbddbcdedabcadbaecdcddceeeceebbbebedbadbbecdceacbcbaadbacaeceadeeaedaebbacbedeacbaeedcbabcacdeeeeebcdccbceeeedabdbbeeabaecadaeacdeceabcddebceceaabdebaecbccbceadebbedcdacbbdaccdcebdebeaaabbcccddbcdcdddcbccaadeecdaebdcebdaccedeccedaaddecacccdeaedaebcdcbcaaabebaaadaeddaabdddbacdedaedbbcbccbcdcabbdbaeecdbabbaacacbdaebaaebbddeaaddbdadabbbbcbeddaccdbbebcbcbddbeadcdabaeaeebeecdaeababbcbdbbacabddadbdabbdacbecdeddcbaedcdebcbdcacbbdeabdddacebdcbbeeebaadcccdbaccebbbacebcbaecbdccbeccebdabedaabadbdadcdcceddaeedeaddcedebcbeeddaceabbccaaecdccdedbbbbdeebdbedaacbedaddbadcabdcbecdddaebebbaacebddaeeedbbaeddaeceeaeeceddaacebeedceedabedaaaedbbebadddeacadeacddcbddbdcbcebeebadeadceececbdbddbcaaeecadaceecdcbeecaadcaeeabeeccacdbbdbdbebbbebaaedaaddbdacecbebbceeebdbcbbcedcdcbeecccbcddcdadabcdeadccabeeadebaeedebdacedccddabdabcbeabaddeaedebedacdccecaacebbceaaebeadcaecdedecaaaceebddceddeaeabcbeeaedaaebdbbaadeceeeaaebbabbecdeedaedaaacddccbccdaacceacbebddcbbebaadbeaeadccccdbacdcccdabcbccecdacadacaddededddebbccdcadbeedeebdeeccddcdddebbecbbebeceaebbcdcdbdaceadbebabcabdedddedbadebbdbdedaaecbeaedccaebcddaebedddeeababcedaadeecebeeedbbcaaceedbbdddebebcacccadaccdcddcceadebdebebccecaceccbcebabccbceaeabcaaeadeabaabccabaecccebbdaebbccdbbdacaedbbddbbeedaabdecebecbdeaedcbddadcccdeeeadeebcdcddcbecacedaeccbcecaceacbbeaeaeddebddbdbcdceadcaaecbeecaccecececddbbbeceacacabceaabbadddceccedcaeabdddeddcdcaabcbbbaeeeddddcbbddcacdbdaaacbeaaadaeaabdbeeababdeeaccedeabadccbbdeeedebabdbdcdeaedbbccabeecdcabcbaaadddbeabeacacecebcbccbdedbccaaaddbadddaaccbbedcacaecbbadadaeabababecaddbceebcdebcbcdcdacbacdaccdacaadaacdbedaeacecbbebedecdaccedcbcdeebaaedaddbcaedcbdcbceaebabeaeeaddacdcdbadcbbbaadbdabbbdeedbbcecdacdecebebaabdccbdbecbbaacbeabecbceadbcabdbcabcbeccadadecbbadacdecbcccbdacedaacccabdebeaeedcecbbccbadacabeceababacaebbaaaebddeaecbbacbbbbacceebceacaeaeceebdcddbbeeacbaadecccedbdadcbddcacbacdddacaadedaddabccdaacbedcbebccdbaddbdccbaeddaebedcbeebedaeaabcebaaecedbbbabdcbaedbdbdbabbebbdcbcbebaabecbbedcbbcddcabdacebeedebabdacbdcccaaaccdaedaabacbddabecbdeaebddaeadbadadaadeaeeddececdadcaaaecaaadbdeacceceeccaeedeececdacccebbcacdcbeddaaadeedcaaaebdddecbbaacadadeaacbdbabdacdadedacbaaaebcadbcdddebdeadcbccbdcecdbcacadeeceddeecedbdeadbaaddaccbcedbeebbeecabececbbaaecccdeeaeaacbeabacdadaeecceeaeccdeacdcaaacddebedacbbbabaaabaeceaebbdecdacdadbcbccdbcdcdcaadcdcecddebbbdecdcbddeaebbeedeceddaadadecaeadbbadbbdbdeadeeaaecdcdddbabcaacceaeaceaaaeeeccaeaaccebaeeacdbebabbeaaaedddaedeaddacbccdeccbacdbccdaeccabecdbaeeaabbcdcadbdbdadcdcbcbcdacaadadccaaabaacabcaeddeabaecbeaccaebcabccbaacbdcaacedcdedbcbdbcebbbadedaeeadbdbadbccebbecaaadbcbdadadaecbadddbbaabcbeccbcbaadcebbbeebdaaeabbdeadceecabbabdabaadbddeddaadecccceedaccacbaabcbbbdabaebeedddeceaacaedacccdeddddcbdaedceecedeceaabcccbbbedcaccaebecbcbadeaabbcdceacbeeddbdaabeddbceacbbebbceaecccbaddccaaaedbcaccceccddcedbbcbaebccebbeeaecdbebecbaabadadcecbddacbbddbcdeeeabbecedeeabddaacaeaaebbccbcedddbeebddddcddcbaeaeadbdedacbbceebbddedebcadeebacbeeceacbbedbeebeeebbcbabaeadbaedbcbeacbcbcccbcbaecaaeeceeaddabbcdbcbbcebaddcbbadeecddbaeaddbbadcbcbcceaaeadacbaccbddbccdaabeebedcbbabdaabdeeecbadedbadddbeaceabcaebaccbcdeccbddebcabdaddeaaadbbbdacebdcdbaeaedeabcbadccadcabadedeabdbaeddbcbabbcabacbbadbcbcceaedeeceedccaecbdaceccccaecaecaeceeebabbddeaccebaabdecadeaebeeeabbcceeacdbdaeabbcbecebcacebacebcedeacaccbcbcadbcbaeedacbeabdbcbcbbbaadeebabcdaecbabedeadcacdecbccdcabdaaaeceaeedbdebcceeababdedcedeaeeaddaedbcbedebcedbebdaedddbbbbddbacceceaccbcbccdceaadbebbbacbaabaebacdcecddaacceeaeaeaaedbacdcddcecbdbbebdeebeaabdbcacebebadeceabeaeeebbdabcaeddedddcebcdacdecacceacbeebeaecadaaacebbdcaabcbdbaceecbeaeadaecabadedbcbcbbaaeabaedbbcebbebdacadcadecdbeeaeedaaadddddebbeecceeeebcccaabbedaeabaeeecccbcebeaecedabaebadccbedbaaadcddddaecbadacccbcdedbecaceabbbadcddeaaadadcedcdadbdecbaacdcbccebdabbeacadbeacebcccadbcacabdeedcbaccabceceabaeecbcedaaacbeedcdedaaddebbecdbbeedcdcebdabacbaddccccdabebeaeededdbddececbbdaaaceacadbdcbdbbccddadebbddbdcdcdbabeebecebeccbabccceceacbaaeebcbaedaeabddcabcaebeebdaecddbaaeaddabcccbebcddacaeaecbadaacbaebbedbadeaeccbbeadccacecceeacbcdeceebedccbdacdbcecbcbcddccddedbccbaacacbdedccaddbaceceebcbddabceeceaceeacbacbddaecaddebdaeeccabbeadecdbebcaabddedebcaeaaeeebcbeccdabaebbbadbcacdddececaeacaabeaacbebeddadabeebddcadedadaedbcebbbaabaeaeceaecccdccbbdbaabcebebbbbcabcdbdabeecbdcaaeaebbeccbeededbbcedecaaccdbaedeededcaaedebbdeeebababdabdaabbacceadcecccbbddcaabacebaedbcabbddaaaabeebbdcccdceadbabcedddcbcabadeeacaaabedaedcebdbaaedcbcecebcaaeecaaeecdabeeeeecacceaacebbbdcddecbcdcaacbdeabbbeaaccecabbddbccdbeedaaccbbccdbcadbdbbbbcebbbeddbbacedceccababdddaecdedbdbdaebaaccebadecaadbaaedcedeedbabcbadacdbcdeabbdcdaaeedceeacecdadeccdedebeddbaeaddeeeaeabbdedeeccbceaabbacacebeebaaceeddddeccdeaeabdbceaaedaeebcdeebceaddbbcccadbbdcdebcaccdddccdaabbbbbaaddaeedbadeabbeecddeaaeaaccbaecccebdbddadedbcdecaacbadeecbdbecedcccdbbbdacacebcbacbcaedbcebabbdbaaccaaabcbaaadbadcaabeaadadabaebecddeabaedcabeeedddeaaddbadeacadecadacbccbcebbabacdecdaeecbebdacddbdeceadeadbaaddaeedecbedcdbaceaaddeccacedceeaaeacacccaaaccdaebcabdddcdecccebccccecbdbcddeceacbcacdaaaabebececdaabdbaecceceebeedccabcebdadeebbdbaeaaadeedadaecdebeccddcdabbaedbccbdedecbbacebebaaedbabebaadaaeacccdbdedeeacacdccdceeaceeccbacbabcbcbbbcaccaacaaaabeedceebcaccadbcacbedadcebacccaaeaecabcdbcbbebcccdeaaaeaadaeeeebddcccaebcaeeacecbbdbbcbcddabeadbbebdabdcddbbdcdacebbceaedccddbbeebabeddcaccacaaacbddaabcebebbccedddbdcabbbacbddacabbdbcbdeedbbbdebcbdbabacacbccdeddebbaabeddbeeddbddeacecbdbcaabaeecacaaeaaacbbcebbbdeccbdadcbccaceddaceaabeaadecaeeddddbbeededaeadbadedaecccecacadbbaaccaecaeaaaeaeddadaaaecaeeaccbdbbbddbeabeeadaeeebcbeeadeccabcacdeaedbddcaceebccacdaeccadbbcedddadddbaadaacabdbcbeddddbddcaebaabcbcdadcebdadabdeaaabbbddcacdeaacedbaecebdabbcddacadacdeccdaeaebabdbccaabbceabebbedcbdbdccdcebddeedaaacdadcebecbcabbaeeaaaddacbdbdbcccebdcbbabecedcedcbacbbeaccecaceeccbbaccbacbceeeceadebebddaaecbeabeaaadccceecacededaaadcedcdedeababdabbacbbeaddaaeeceaebabcceebaabeaedaebbcadcaadcaeccdbbbeaaebacdccdbdddbebbedcceadbccedbecbdebcecbaddaadbbeaaacbecaaeaceabdedaecacceeddaaebaedeadceeacbdbdddcaceedaceeadeadbaeaadbdbacbddadbbcaaeecdabceedcadbeeaaebecccbceeeaeedabadcdeacddcdbdebcaabbeaaadeaecedeeeddbcdbcbdbbcacedbebdbecdbaeeeaeeeeaebdbbbbabeccaebddcdabaecbbeeebdbbbdaeebbdbdcddeaabebebaddadcbaedaebceeacccccbeaadcbcadaaeebbecdbabdbeedbcbbacaddbebaeeeeeddadceebcbdbccabbbeadeddaebcedcedbdeabecaaecdaaaadabeebcdeeabcabdcebaeaaaadadecadecbeaddbbdcacedaeaebcaceaeebbddbedabbaebdcaaddaacdbccedaaaaabddaddcecbacaaebbaddaaddaaaaaabdadaeaaeebaeecdacdeeceedcdebbeaeaccbbbeedbcddbadeebaacddcaeecedecbdcbddeacbbceeceeaaeddbabcdeacdecdddeedccbacbcebeeeeedccbbeeacbadaeccccabbcbddcaababeedecdaaabeccebecdceccdedebaceaaebccdccdacabbcdedcdebbabeeebbdbdbdedccedbbedabcbbaddaaeedcdacdcbbeeeacbcccbdbdbceacecbbedbbcedeeabeeaeaabebdcadaedbdbcabeeaaccedbdeabaaececeabdcdbdeaeeeeeaaeecabaaececacdbaceeaaaeeaaeedcdacdbdbbabdcebcbcddbdaccdebbdaeaeaeabecbabdebecaababdbcecadecdbdbbdbacdbbbdabbedccceaccadeebdbabadadecceedcadbdacaedadbcceccdcaadcacbadbdaaedbccdaadcacccbebeaeceddceaccdbdbdeedaeacaeeeeabccbedbabddceddcecdbdacedbedbedacebaededeebeededabedabceddcaadeadccaeeabcbcbcbceaaaaaaadaacaaadedcdcacecdaecedacdeabecdceacadaebdbbbbbdaaebebcbadaabdeeaedaaccedaaceabbecadadedabeddeddecbbbbdaedccdebceeedcdccececcbcacabadcebeeaccbacdcbcaddcbeecdcdcccaaaddeebeeaeeaadebbecbebbcccdceeaabeedeaeeadcbabcacabcbdebbcdceabaaeceaaadbebeabceceaeebcbbdcbebddbedcaecdaaecadacdecaeedeeddbaaaabbdecdaddceececeecbabadaacbedbdcbacababdeabbaddabeeeddedcdbdcbaadbedbbaadccdeedeaaaaaaeaadbcbcbadabeeeaeacdbbdccccdbecebbbcadaabcdcaceabbeeceeabcbcbbecaebddeaddeebdeababccdebabcebcdbbcdcbbacbdbdbbadaebebddcacaaecbcacebeabbabeaeeadddebbacaaddabbdabccbabbcceeebdccbdecbcecabadbcbcbdaacceececbbbbcdbacdeceebeecaadebdeccabcabdabeadecbbebeacabbebbecdecadcbadeeeeaaecbbdedbecddaedeaddaedaadbeaaeaacddbdadedaebdbbeaceacadaadecbdedecceaddcecabddacaebdaebaedbdacbaeaecceccadcabdedcbadaecebbdccccabedadddcbcddbbaceccdecdacbadcdceaabcccbccacbdcebbebddabbbcdaabaccacebdaaeddcbcaeebcaebdaeceeaeadadcdaaeabcbcbcbeadaceaecadddcbccaeabaecaaeadddebacbcedbcbdcbbaddadbbdbebdddcdcbdeececcbcebadbdcecdaeadaccebbceaddabdeadbdcedbdecbbeceeebadeaddaababdedcaeccbaeabbabbacaacbebcecddddabbbbadabbcacecbaeabdaecbcbcdcbbbdabeccbeccadcaceabeadacbebeddcaaabeeaaccdcdadaceacabeeecdacbbaccaadeaadbdecddbbdadbaaaaaaeeebabdcdeadcccacbbcdeabecbccbdbeedcdadbbecaddebdcabcebaddaeceebcaadadadecaaedcdbeaceedcdeaecddadddbdbccedadeabaddbbbcebbeaeeebebccabecbdeeecedbabaceebdcdddbccedcdcceaccaeeeceaccebecaeebbceeebaddadbedceeadaabecaaebebcabbdaaaeaaaacdaeddebcdacaadccdbddcecdbaeddaceaeecabcdabdebeaacbddcdaedabcbddeabcebebbabeebaebddbeaddedcaaeeacbaccaacdcaeadbcbacdabcadbabbeabdaebbbedeaabdaddbdbebbbdaeaceccebeebcadcebbaeacdcdbbdddeabcdeeccabaacccecbeadebebeeeecccedeabdeebbdcbcbdeccecbbabcceecdcaedabbaedcadaceadddccdcbeccedaedbcbdebdbeaaddaaeadcdccedbbadbaaddeeabccdedaaacabbcbaaeddaedbabcabedcbabeebdeaeccbecabcaacaeddbdbcceeaaedaedbacecccaedcbaacacdcaabddccccbddbebaceddbccaeaebbaaebbdeecdccbcedaceacbdccdcdcccbaebaccbdabaacbabbddaddecdccbdebacaeecacbdeecebdbddbacacadaaddbdaadcebedbeceddededcecbabddbccbadcaccbcbedceaceadaceecedbcddaaeaadbccddcceebeabcdaceeadbdeaaccccdcedcbbcdccbbdcdbebaaddebacacdecedbdbbebecbdceddaacdeebcbbccaabecbcebddcdddbeaebdcdbabaaaeccecdeeaaeaabecacadaeccbbadaceadeaecbddcccbbbdadbbbcabecaddedddeabbbebaddaccaeddedbbbcdecbdaaacbbbebecbecdbabdbbceeeecdbedeeadaabdebdddaaaaddcdabeadebedcddecbdaedcbadbedeaaadbdcabceebbeecebcbedbbdbbceebacbaedbabdaaeddaacbdbeddadcaedabeccaebaceeddacbedadcaebadeddebecbdababbdbaaeedebaaaedceaedcdceecceedccdadacdbbcebbaaecadbeadcddbeebbabbebbdcccaedcdbbebddceecccceecacdcabbbcaddbabceaccdeecbaabaabaacebbecacdeabeaebbdeecaabcaeddeadbedadacecbecaddbecacebbdbddbbeeabdcadeebaacaaeabeaddadcbcddebdeaceacbecdaaeebbdbbcebadeabeaabeebbaeddcaedcdbcadabbdbccbbcedebededbeedebbaceeeccababaecbaebededdacaeeeccabccceeccecdbbddccbaccadeadeccebcecceeddcdabbdcbaaaccacccbecacdadaabdadedebedeabebbdcaceeeadaaebecbbabcdcebececccabdcebaadacecdeebabdeeabbcadbbcaeeeaeaaecacbceedecdbcceaabaecbacbbaceeaeeabaeedecedbedeabeaeccecbbcbdaebcacbacbeadbebacbddcccabaebeaaebdebceecaddecdadeecedbcdcedacaebabbeadaacdeddbceabbabdcceadcaabeaecddeeeabccdeeededdbabeddabdbbadaceeadbaaccecadcaaaddedcdbbeabbaabedaceadddcebbdcbcceabccbedabecceebdbadccaceecaeebadcdebcdbcccaeadcaeecbbaaeacdeeabeaeadddaeeedededdbdadeaececccdbabcbebdcaddbcdbcbcaecebddbdcaacebcacbaaceadaabaedcbebccbabbeebbccdbcadeabbcabdbabddebcebeeedbadccaecdadeeaebbdbcaecdbbbbaaaaabeadbdbbaebebcdeccabdaddbeaaabaaedabbbbbbdebceebdcccbeacbccbcbdeadceacadaeadbcdebbcdddddbaedddbaaebdcadeedadaebdeeceaeccecabbbecddabbadadabebeddceeaaedbdaceaddceddcdcbdcaaadeeddbecbdbbccddaaccbadaaaebecbaccdddeeaccacedbebbdcddababbebbedadbabedbadcbedecbabcbcadebddbbedaedcdabcacecbacdabbadcceabdddcabadadedabbcadebccdcbaeddaabcbcddddadddcabaccacddcbbceedeabadecdcbbaddbdbebdbccdcbebddaeaedabadeaeebeddbaeddedeedadbccaabbbececceeabdadeabeccddbadebeeeceeccbbebcdabadbbbccadddeeaacebeedecdccabccebebbdbdebbcbbeaeacecdbadeaaaaabadcbdeeeecadbbeacbdcacbeddccbacacbcabdbacadceedeeebecbbaedcaecdddaeceacdaaabacecebcaebbadbbacccbdcdaceddedaeebababaecedaccbbdbedeecdebdeaadadedcbdacdcacaeaaaedbabbaebeeabcaaecaeccaeacabeeddeadbadeddbedbcebcdebcebeadbeeccbcbbeccebdaedddcbdacdcbeaccaeebddeceabcacbcededceabbdedecbcbaaeecdecddeebcbebddceeccadbcbceecbacebecaddebcbabeabadacdeeecddbaaecccaaacbcecacacebaceabeebadeadcaebecdddcbeaedecdbadcdbaabadcabcdaeddddbbabaaeddcbbbccbcdabaddbbbddbedccdbabccaebccdccddcacebbeacbecaeedddebdcbbbdadcddcbebbeabbebccbeedceeadceecddedacbbacdbbeddabcebbbebcaaebdaacedadebdbaddbaaabdbaacdeaaccbddacaeaecedcedebdabdcbdaeeddeadbdcadaaeacdaeacbdebbaaadecdcccdecedbcbbebcccebacbaaccdcdaaddcdacaaddddceeeccbccebecdcdcdacbdcacecbdaaddbdccbbeadebedebbacaedbecbaabddddbaaacdadeeebabeabeeecbbbabdaceddacadabaddcbbbcebdddbedbecdacbacedcbebcbdeadcbceadceeeecedcabdadcbbdbccebdaedbcaaaaccebcaeaedebdddcbaddbebdddaeddeeebddcdecccbdcedebeaacbaecadaaecddbcbcbccdddeccabcdcaeccaececbaadbdecedddcdacedeaabaddbeadaaaacceabbdeaadababcebbabcccbebacdaeeecddabdcebbbceacaeaabaebeadaeacceeaeabacabbabdaadceabceeccdabaaeddadcebaebbeceeaaeacabccbadaedbbadbcddcbbdadaeababdbeaebddbeccbbdceedddadcbaccddedeebaedadaebdaeebcebbedcacbbeccdabbedaecdebbeebdcebeabaceacccccadaabadeaebaccdcecacbaadcebddcddccdbbaeacedaacaadcbbbdcebcddaccedabaacbcaadaaddbebbcbbededcaeadeadbebcbcbebabbcdcbdecdebaeeccbabbccbcbbdbeeacacbedcadeeeaeedbdabccaaebccdceaeeeeebbebeeeaadaeedbddddacaabaedcdbeaabbaaddbeaeebbccecdddabcedecedbdeeabdbaeabebcceeadbaeaeeaddeedbbaedcbbaadddcedcaaeeaebcebccccbbaeeeddbaebddbeaeebddbcaebadbeeaabbadcacebdccacbdcacdecacdeddabdcdaddedeeccdcbcbdbbcedabcdcceacaeabebacedbdebebecacaaadadababcaedacecbdedbacedadedcebbcdacbbddddddadeddbbdaeaaeaeeadcbaaecebdaceadcbebdddcacabdcccaceeceaceccebcaeccaadccbeddacccdbdbadbbecbaabbaccacaccdbbdccdbcbdcdbdcadedbaabcbdaeddbdcbaababddbdaaacbaecebacccadebdddeacccccdadeecdbddeaaadadaeeaeeaddabdeedccaebeecddebebaedebedcebdbdeceedaceecdabcdbccccbeceacabedbeddbcceeaedaadddecccdedcbdabaaebbabaebcebaebcbcdbdedeedccceccdbbaceecbcdcededbccadadddcbceaadcacbdeddbccbceaedccbddbeadabaebedecdbbcecedddaaebbbccaaddbddbcacbeabcabdcdbdcecbccdbacecabcaacabbdbcececccadcbcbddaedebaeebbbceaeacbedbddbeaceceeabaadedcbccddaaabdacaedacbeeaebacadcccdbebbcbedcdbdaeeeccecbcecbdaabbacdbbabdaadbcaadcddbedbedbdaebccbeaebbcadbcaedabcceddeadaadedabceaccaddedaadeaadebbcbbcbcdabdebceeeddbcdceedeecdcaadccdcedbbebcdebddceceaaaaabbdacacdbdabdaaeaaeecbaddedceeebbbeebeddeadddabddaceeccaceccbacaecaccaddaeabeaeabaeabedebbcbcbdcccddddcbeddeddcbedcaeedecddcbccbaedeeeadcabeacbbcdecacdbcccbcdedeaaadabbdcbbadedeceacbaedaddcdaaccecabeaabddcbaebbbbcbbcbbaceacabbbdcbdbcedccdebcdbabcceeaedbbcaddbdadadbebccbddddbdbeacbbbeeebcbaecbbdddbdbebadaeedeeeccceadceccadadecbccdabcbedacabcddeeabeaebecedebeaabdaebebbeccabdbadaaabebbcacaadcabedadebebdbdaacccdeaedcccedcabcaeccecdbccadabadbedbaabaedbcbdbdeaadbaaabbeadabdbababdbbeadedbabbdcccddeedeacacaaeaabccaabccdbebbacdaddceddadecbdeccaacbbdaacccadddeacebaedbccceeccccaeceeebccbeadcbeeaddbadbddcccbedcabedddbabbabaccdeddcabaeddccccdeecedcdedddabedaaeeedbdbabaddaacaadacdabadeceabdedaebacbaeeacbbbeeeeabccdedaaadccabbacadceddbbeaacddceaeabedecdadcebbaeeeeadbadbdeacbceebeabcdbacedadcadddbacadadadeeedeebabcbbbedabedbadbccdbcccbbdeadeddaeeeaabcadaabbbadbeceaedcdaccdaeadceecaccbdeacebedeaceaccebadbdbebdecbaeaebbceecddbbeaacacededbdaceaeadacbeeddaeaeacaacaaabebccabbcccbbcccdceacedccbbcddaecdbeccacececbdbddcbcacadeeaacdcdcacdecdebccbaadedadddcaecddbdeabdbeaabaeeacdeebdbddaecadddedcccdcdaaccebaaaeeedbcedcabdcaaeedbeadaceecccedbaaaabdbcbdaaeaddbdadcbabccbabecdbdacaeaedecbebcbcecbdbbbbabdeceaddeaedbdeccdbcddcddbacdaaadbecebbcbcebbdcbdacebddcdeccaeaeabbaccecdbdbbaaebebaccdddccceaccdaccabeceadddaaebdeabebacaaacebcaadceadaeabcaeacbbbbabadceabcbebbedabebbcbccdedbaeccadbcaecdaacdadaccbcdebdaaeadeaadaddecccabcedbbcdebabaccbdacdacecacbebcddedaecaadadbcabbdcdbdbacbdbeaedebdebbaccccddabeaaceedaedbeeddedceacdeebbbaeebabaaaabedababdeacccbcbbcebddeaceeabcbabddabccaceeaccccdceccdecbbccecdccedcaebbcceddcacadadababaeadddbacbecdbaabbabbaccbbdcecddbcdabeaacadbcbaebdebaacdadecdacebaadbbdbbabcbbbcecceacadccdbcbddddaabaaeaadceecadcccabceaecdaaeeeceebaeddcdecdceecadddddabdeeccacedebcdaeecdbebbaccdaeaceaeacbadcdabbacdbbaecdadcabcebbbbeaadcbcccabadbcaaaecbcedbcdbeaabbdbedcdbbabdebcadacdabaacdeddecacebabcdbaebecdddebccadcaebddebbcacbadbeaaaecbbabccabaedacaedcdcebbaedaabeccebeadcaeaeddabcdacdddaceddbdeabbadebaaaabaaeeedeeaccbadacdbcbacbdbeccbaccdebbadcdeaaebcbaacdecdcdbcbcccdabccddaeccebdaacbceebbbebccaeeddaedcacbabbcceaeaadecdbeaaaceecbabdcedbbcdcdcddebaddbdddbadcbcbcecdddcaeaccdcbdaacecdcaebedadbcccdcdbecaabceaecceaecaacacaeebeeeecbcbeeadcaaaabeddeeedbaabcebbadeebeaedcaadcabeebdbdceeddbaeedcdaebcbcdeabccbccabebabeebceddcdebbdaeccbedceeabdcbdbcaaecebeadecedcadabbdcabaaabcadaddeecaedebdceacdebebaaaecbeecddbccbaeaaabdbddbdadecbeacdddacaaedccaaccccababdeaaededdaeceebcedebdeddbecccbddedbebccdaeccbeaceddbaecdadabbabdadbeadacececcedeccbaebeabbabdedceadebddecaedaeccbabedaaacaeebbacbdbacddbddaaccaacccbdaecccebbdecaaecbadeaacecdacebdeeedbabaceceeccceadcacedabbaccadedaaebeebccedcdeecabaebbabdaacbbaacbdbecdadbbeeaaacaeeabeccdeeeccbadedcebccdbdcdeedccbaadbdbbddcabddebcdabeeabceecedaaccdaebacbabaaecaeaadcbedeedbbacdccceadbcaaccaecacbeedbadcecccdaaeedbbbbaaadeddadabaabeabbceacbbcabecbcecbdaddcaccccbcbabadbeacddedcaabdabebebbcedabeebebcdbbaddebadceabaecbeaceddebdadeceacddacccbbbabbbcecdebbedbadbccadaebcbcdbdbbdcebeacacbbdcaabcecdbdcaabdecddeebaecededbbaecaabdceedcaccdbbadddeaaadaddbaaedcdebeeacbabdbbdadebddbeebddaddcdbdcedcbaadbccecaeebbbeeddeabdedaebbaabbaedaadaaddbbbcbcdddbecdbaaecabecccdebdcbadadbaebbcedaeeeebadecddabbccbbcbcededabcdbbecccaedeededbdcdbdabeacaecbeedcabbdaaaaceddcaaaeaeaecacdddedacedabbdebaccdabbecdabacabebdbbcdabbbbecadedaceddebbebdaccbbabaebbbbbcabdabccbcaecabadecdeabbaedcaaeccdcbbcdddbceccebdaadaaabaeebcdbccadbbbedaccbeccbdcbbcdbbbcdebbcdeaebbcccaeadaeaecceebbcbebeaeecacdbedcecbdcaaabebbcadedabccdeebcadccdddcddcdacacdbaeecbcaaddebbeccebbabdcbccedadebeadabdbcbcbcaedaeacedbaeeedcacaabbdcdcbdecddbadbcabbaadbacccdedccebacbbcceadadbabccacbbeacbbacebdeedeabdadacdeedaacadcdbadabbaccccbcaecdaeababcaeeedbeebdceacdaaeabdacbddeccaebcabcddbccabeddedbdedbdcaaeeacddabbbcdebbabccbccdaedeaeecabcbdadbaabeddbdddcacbaebedeebeacddedbacbebccbceeeeabcaecccabedbdeebebbbadeaccbacbedaeeddecbdbaabdbcdeabbcadadaaceaebaebdaaabeaaeeceacebabedeeabcdcbdcaccdbbabdabaeebccbaccedacacedbdadaabeecdededdcadbdbabcbecdacaabedabdebadaabaeabccadbbebdedceaebcbcadaceaabbbbcebddcbbdabadecaadbeadaccedbcebddbaccdcbbeacacebbebbaadecbcddecbabbcbeccbadbeceabbccecbcddddedbbaccaeeebdbdaaeabdacacaeadbddbbbdeebaeeaabcdadbacbacdabcdacbccbcbaeadbbbaaeabbbacbeccdeeedbdcebbaabedbaedcdcaebdccccaebaecbeeaaddbebcdbceccdcddadaeccbdadebdcbbedaabaeadedbdebdabeebaccdbbedceadaabaceceaeeaeccdcdbecabacdbeabadccdbbebadcbacceedecabcaaadadaeedabedecaceabbcddcbedadcddbadebbaaecbaedcdbaeabdcabcdcedbbadeecbcacaacbaeeeaebbdecacbeaedaecebbcbccbaccbdadaadddacaedcecabededccbcceaaaebdeecccdcdddebcebacdedcbcbbdaedbeaccbcedbceaeacedbeaeeceebbcaaecacbdeceacbceceaeebaecbbbdaccbdbebbecacdbaebdadecbdaeeabadbaebabecdadcdababcacdabcdeddaedcbcacabcbbceebcceadecadeddebcbebdcececacaceccadccaededdccabdecdadeeeddaccbecccaebbbcaebddaeddeddddcadbaaddcdecbbcaadeacbedcdacbcbaeccccebedeecdeedbbbbbbbbcebacecbacadddccebecabebeddcadddceaeedcdeabaccdaeaaddebaceecaedbecadcddcdbebdadabdbbdccebadccedcbbbdaaacaabdabecdaedbdbbdcddbbdecdbeccbaaebbeeacabcabedbacdbbccdecbbcebecadcaddaddedebbadbebdecabdccabbcddcaaaaecceeccdeeedecdababbcbeacaecaaeaaeadacaaddcaaccddaeaaccdaacdabadbdddbeabccbbdbecddabbaeddababebabacadecabedcbdccbaddcadacabebaceedbedbccabdaeacbdcdabbeaceeeedcebceacbbbcaeccbcbbdcaaacecebcecdcbacbccdbeeddebbdaeecbcdaaaddaebebadbcdadaaeeaadecadebceaceccceacbadebeeaababeaaaccbeacbabaddcbdeeeaedddebcdbaedbceacccaccccadddeaadceeaaccedcbcedeccededeadbbedbaaaabcebaeedaecaeaedddccbbecbebceaaaccedadaaededdeebccdaeadcaebbdacbedcadeeaabaadeacacdcebacbadecdaeedbbdcbacdeddbbebdcddedcadcdadeabeeecbcbbebcaabaaeeaadecececdeddacabddceabbbcadabadcdccbbeaacadecacddbbdcebddccabbeeeddadadeeabddedbbbbccabdcbdeabeceebbcaaeadcdadbbdcaddaceabecbeddddbeaeceddabdacccdccccdedaceabecabebaebbaeadeecadbededdcbdcdaecaacbbcebbcdedbddabecceaebcbeeeedccaeceabeecaaacebddcdddcdcbbcdeaccdceabaeecaeadcaceceacbcabeeeeceaecbddbdeabdcebebbbbcdbdceaadbcecbeabbedbdbbaebdbdcccbdbbdcabcadbbcedabcaeaceaccdcbeecddceeaaebbbbcebddbeaccbeecbbeaadaaeddabcabbdabcdbeecdedeeddbcccaebdeacceceeacedecacbcbbdebcdddccabbedeceabadceddecceecaddaaabccddcddddcdcabdbecaeacdcabaabbbbcccadcbccbadceaacabacadcedeaaabcecddbbddcacdecbccadbbacdcdacecbdddacccbcdeacdeabcccbcadccebadebaebcbacacacedabecdddeeacedadbeacccebdedcddbcececeaeccbbbabaebeaeaebebeeddbbeeadedcebbeeedebbbbceecbdebdbaebbabeedeadceeaddebceadaabdbbbdaeecccecbdecbebcbeaedaeddebddcbacaecbdcbeabbabdabbadccabcdbacddeebbcbbadccccccdeaaceadcacbaceeaabecdecdeaadecaebbbdeabaabbdabadeccceccabaebdbbeeacedaedcaacbbcacbeaabddecdaaadaaaddbbddaacaecccbebdbdebaccaeeabceaebeaedaeaecdbdbebbdeecccebcdeabbceeebdaebbcddddbbcdabeabeaecaadbcebaaaaddabbbaaeceacedbeddbedeedcabdddeaeedddbedbdebeddaaedaecabeadadececcccebbbccaeaeebacedcdcbdcbacceceebcdabcbbbcedbeebeddbcaebbabadbbacbabbeaeeebdcbecdaddeaacdeaaeaecbaeecbeaedcecabaeebacebbebbdadddbaedededaddccbaadbbbdecccaaaeeceedbdcaabcaaeddabeaeecbdaacdedaadbceeaeeaeeddebaeecabcaadaeabdaebebceddaecebeddeeadbecacdadcbaadacbdedddadaaaedaecbdbaebbaebceeaaeecaadbbabcdecbbdbddcddabdbcbdcddecadaaadabbcebaacacedeeebeeecbebdbebaedaaebddeeeeabcbecdadbbabcecabdbcedcbcedacececcccaeabebbceacdccdcadbcecacebebbadadaecbbdadddececdecdaeecdcaaacbedddbceccaccaaccdbacbcaedaecadacadbcedccedcdebebaadbacabdbeaadaecdddbeebcaeecebbaaabbaeebecbeecacccdccadcdcbceccbeececcacbaaedbebeabbccbeaeebedaedbaedebeecdaaecbcddaaeecbecbcdedccedbaaeaeebdaecdaadaceadbddbbaebbdccbaccacdeadcbaecaebedaabecedeacdebaaddcceaecbedcedecaeabeeebebbdbdbbadddacaedccabcedebdbecdeceddeacbaddacddadbbceadbedbbcbdedcbeaaacbceecdbbabdaabebaaedcccaadeaddaaabdedcdacebdaeadbaabcbeeeeeaacabbdbbedadeedacbbecacaaaedebcdeaaddccdbcabbedebdcbabcabcbcdceaebacebbcdeedaedaccaebeebcadbeebcacbbddbcdcdbbdcdbbdeddedbdbdeaabdceebececceecdbedbbacbcadcbdeabddbbaedeeacaddaadbbaddaddcbaceeebbdaaddbababdbeeadecbdaeebdebabaccbeaecaaebaecaacdebecdaecababccbddecbaaebcbaeebccbeecbecbeeccecabdddcecebeeadeabaeeaebcceaecadebbdbdbbddeccdcccebcbcecacebbecdccbeeecaeabeaaebeceabcdebcdeddedecbbadeaecbababcbccbcbbaedbbbcecdacdecceaeaeeaeadecbcbedcababdaeddbecdbbcdeaaaadaeedaeadcbeedebbadbbccadaeedcbabbedabdcebcebebecedaddaccadccadbcdabeccaaedebddbdabaacbeeccdbadcecdbaaeeeeadabccadeeaccaacdcdcddcdcdedbeaceebccaaeaedacecccdeeaeaddcbeccadcbbbbabeeabcadcdbdeeeeadeabaeadaadedeecaaddeeeabdbbadceddddeebdabcacdbdbecbdcdecbaaabbaabcceaadbceabbbbaeaebadccbdadeadacbbbdeaaeabeecdccdceecbdaccbcbdcaeaaedbbbbaaeeddbbcbadbcaebebcbdaeceebcddbcabeaeaeebbeccccaeebedadddcbbbbdbddacdeeeaaddecebededcbaaabdadebbccbacbacadedbaabbdbbbeceddccdbbacaebbdeeddadddabedeebdddadeebceadcaacbbaedddbecddcecdbeedbcbebcbaaebbbacdeeeedddbcdaabdacbbcceedcecadacecaddeadbcebccaddbdacacceceabdbbbedaebabdbabbadabecbbddeeebebadebaceedeacedbaaaadcdaebbdecedbcccaeeececdceedcabdbeaabecdbeababadcdcbaddbbcdcdcadabbbdddaebbbdbabeeeacceccdbeeceeabccdbbbbdcabbabecddeabdcbbdccacebcbacbcacbcccabeedecdabbbceaaccabebcebaaaeeabbbddacddeacbbadeebcadcdcdecbbbbbedbdcbbdbccbccedabcbedbbdcedcbdbebaeddbdebcdecadbddacecbbcececcdcbdadbbaacceecedabcdcccccabbedcdcaccaecbdcecdcbbceabddcdceeadeedddcddaccbedddedcacddeacbaabdadccedecedaabdcaaccabedaedcebecccebeacaedbbbaaaebaacdecdbebcacebdbacebecdacbdccaadadedbbbeeebdcdcbbcecbeeedebccecdabaebbeeddcccbeaadacadbabedddbbaaadccbeeccdedddaeedeaacecdeeabdeaeaaaebecdcabdbadcdacaaedabedacabbadbeebdeabcdebdabebcbcdcbbaaedbccdbdebcaeddaedcdadbdbadaaeacdaabacabadebabcbedadbbcadbbbcadeddaebdecadccebcbcdbbbbbbdcebcbebadcadedbaacdbddbbbcacdcdedacadccdccbebabeedceadeaccabdebbdedeeaaecebedbabeaebecbbaddbcbecbecacebadbeedabecbabbeabbacaacdcddbbcdccbbcdeaaddaacceceedbcbbcbcdeddcebdcebcccacaebaedddabceccdeabeecdbbceabbbacceddceebeabbcaabbbecbeadcadbecedeadabcbcabcdceaedceeaebcecbccabeccccbdccbacedeececbdccdabdbdcbbcdaaecebebdbdeaadbadcddeacdeedcebebdcaebbbeeaadadcdbeaebeebdbedbbceebbbaeddccebbcbcedadaeeeebbacedcdccbaebbdbcdccccbabbddcdbadbeeacacedcaadabcdababecbcacccddeecbbdcceebcabcaebdaeadaccdccccebbcecdedccecedadaacedcdabaeabdddcdeeebbbccdcbeaeaeaacadcbdbbdebcdedcbcacceabedcdbeabddadecbdabcebdacabdabcaccccdbdaccaaeadddaeadbbcbddeaebeddadbdcacbcdaabdbdeeeaabcabdddadbbaacbdeeadbdcacdcbcccecbddaedbdccbbcdcdacbcaaadaeadceedadeebdccbdcadaddeaacbabbceddbadcccecdaeccdbebbeacccbcbaaecdbebecdabaacbaddbcdbaabacddedbeeeececbbcbbbeacacabaececaeeecdaeedabaaecebedbdbaddeebbbcbaeaebaedbdaedceaacbeeeeaecbbacedecaaadeabebbecacacededdbbdbdaacbbdcecedcacdaddbabbadeeaeabededaedbdecbbebcdebbacecacadadaaccecbcebedccaebcebcbeccebeeebedaececbcbadcecaebdcadddbdcaedabdbbbacccecedaedaecbcbabbacecebbbeadbeeaecabdecabeddebdbababdacdeadbabbcdddebaadbecdaebaadceceddbacaaacdceaeeabebdddcdcdceeabeddcebdeedbdcbecabebbeaaedcdedebedcddddbcceadebdbecebccbaabcebadcacaeabeaceebdeddbacecddeebcebeedaceeedbecebabebbcaecddcedbccebccdadabaaacaaedebbcbeedabcabbbecdbeacccbedbbeebddaddddaeedddadacddaaccdbbededeedbacbbadeabaacbdbbcccbdabadeadceadcabdcdaadeeecbaaddeaeacbdacbdadbeecaeadbccdbddeaabcacdedbbececceeaddddcbaaebdcecdcecccceaacabeeaecbeccdcecedaddaabbcddebedccceaedccaaeaaeedddaebdebbdbcaeedbadecadababccdbebcdaedccdeedacdacacbedddcaaaaedeedceabcecdeeebecccdaeaeeaeecdaadadbeceeedadebadebbbddebeeccebaadeeddbededceeabbddedaceddaaabcbceeddbadbacbaadadbaebdedabbcbededbccdcaddbccbeececedabdaedcbabeeeaabeecccdcabbbacbdcdabdaaaabacbdeeededdaaacebddecddeaecbdebebbbeaaadbeaacbcbaeedcacbadecbcaeeeabebdbeacabebbaaeeadecbcdaabeddbdccdbcdcebbbdedabdddaddcbedbdabaeeebddbabbacecebdaddbacbbdebcaeaedddebbecccbeabecceedebdbaaacccbaeaaadaeacbeccbbcdccdbcdadcacceecbdecdeddbbaaedcdededcebeaabcbdcdaadbaaeeedabdbbdacbaceaddbaaccbadedbcbddeadabcdebbcadcceebaaaceabeeadaedebbaeecbbddddcddeececbeeaedbbeceeeddddceaaeeacddabbccbaadbcdddaeadddebcedebcbedcceddaccccaeecdaadecaaaeebdaceabcecaccececbdcdcaeeebddbaccdeddacabedbdadddaccacbcdeeeebaaacbeaaecbbbbcedeebccacebccdadbdcdbdebeebabbddccbeebadeeacbbaceddcecabbcecaddcecdbceebbadedbcccbaaadccabaeddceeadbbbceecbaababecacdcccdbdadabeccccedaecbbadababdcbeadaeedcbecdedaeeebcdddcbbeaecddccdddbaecdbdbbbdeededbbecaeeebcbcadbdaabdcbbdebeeccaabdceeecccabcbadeabaaabeadaabdaadadcebeaccbcddaaeceaaaadeecbbeeeebabadcbaabeabeebeeccdddbdeeaeadecadababeddceaddcceecdcabbbcdceaeaaecdedcdeedebeabbabeccdebaabebdebdbadaeeecaaedbdddaabdadcbcccaebecaccecbcdacaaabecbbbeedaecbaadddaceddccdcaabecbaacaddedddacacbdadbcbdedcebcccbdcebabdbdeebbadbacebccbaeaadebbabacbbacaadacbcddabeededacbedbbaceeddbcbbcbcabdeaeaaabaadaacbadcaabcaecebebedecebebcdddbecdbbadbbcebdabaeadadaebcacbaeeebaeeddedbaeedbdccdcadaedcaebdbecbeddceebbeeeeeccbbcacdaedaddcabdddddecdaacbedbcddeeeebddcddbdcbbbadcaecacacdadbebbedeadebaceedabeeddadeadbaeadeedaeceebbbdcedcecbeeaeccacaebebebaccdbadebdaecbdedeccebaaaaeaabbceecbeccdabbeeddeccbbacbedccaebbddcaccddaedecabbeabcccaaedcdcecbebbdedeebebaecedbdabdadddebabcaceeecabdecdedaaaaaceceadccdcbbdddbedabdddedcbaceccdcadcecceaebcdebbacababbaceeaeeaccecaabbabeebaddbcaebcebebcbdbdcceaecdeaceebdbccaabcadccbceebecceddddebcaaeccbcebcceecabcbeabbacabeceeabcbebeedbedbeaceddbcddcbdcebcbeacbabeddaaeebcbbacbecbbbdbaedadcbccdbaddcabecadcdabcadbdebbacebbcacecebcdcdbcecbdadaaccabebbdecaeeaabcaaecdcbacbeaebababedbdbcbbbceadbdddbedbdeedaaebebaebcdbeeeebcdaaedaecdbaeceacaaddecceabaceceeeeaeaaecccbecbdacbdaaaebcbaaaaabcaeebcdedeacbeeacdebeabaecebdabdadeccceceaaebebdcaddaacbdbcddaebbadcacbdcddbbbeeabbdcdceadaddddeaceccbcbbcbdbedeceddcddaceebbbeddeeaddcdebacdebbeeabadebacecceabababccacdaacdcaddeceaddcaebdbbdaeaaebcbcbacdccebadabbdbabaeddcbeaaaebebabcacedecdcaabccebceadbdebbcdcdbddaacceddbababdedcddbaecedaedbcdaaaabbbebcebdeabdadddaceceecdbdaabedcaecddbdacadaeebccbdcabcceebedcacbdccbabdadcabacdecdccccdcabcadecebbededeabaddbcaeeddebdebecaecbccaaeceacabbecdedaeadabacbcebdaddecddeaabedaadeebbcedbaeeebcdadccdbbbdccdbbdaadbddbdcabebbbaedceaaadecaacbaececdddcbbeaebdeaaaacddeabaedcbecececbedbecedccddaacedabcbdbceecadbbbdeebdcaeadaaebebbaddccebcabcbebdadeccbcaadecededdcbedbcabebacccbecdadbcaaaebeeaabcbccebbbccbedeeedcecdbdcdececcadbbedaaeacbdcbaecaebdaaddadacccbcdcdceceebadaedbddeabcccbbedeacbbadadbadbbcaaaaeadccdcddcaacececbedbcbbcabcbcddcbaaabbceddacddebdbdeeedcbedcbaccecbaadeeccccbadbdddecdbbaeaaccccbcecdcbdaddceacebaccbdcedcaceecddedebccbbaccdaeaaaaaeadabebbeaadeecedbcbadebaeabacceabccbccbccddcabdecebccddcecadcdaebeedbdddbcdbbbddbbccebdeaacaddabacdeaaadacdabecbbeababdcdcddadecaeacebbcbcbbaeebeccedaacebddeeebbddcedebebbdebbbcaaebbeebecabdeeebcabeececddcdbcdecaadaeeebaacbcbdbaeabbdbdbaacddbcecaebababaedeacdeadeadceddbbccbcdaebadebdeebbddecedbbcebebbacbbaccbdaeadabcadaeecbeadbbaadcebecceadeccadabadeeccbedadccbcedbaccbdcddaaeaddabeccaadaabeabaccecceeeabcbbeabdaeeddcdcbeaaebdcdbcceaddcedddeedadbabbcdaaddcddbabcbdcacceedecdbdaaeacecbbaebacbcebcadbdebcaaedabbcecccbdacecebbcdddecbedbabbceecabaecdcebbedecdcadcdbdaeeeceaeabccbdaebadecbbadabeeacaecdbcbdabebebacacabcabbabcbaaadeccedecacdebddcbceeddbbcbbdcadcaecedbdecdebccbaaeddbdcbacacaaeeedeadbbdceebacbabceaadecbbaedbcecbddaaddbeecdcaddeedaabbedaccdaeaaaebcbabdcabedcaecbdbdbdddebdcbbcdababedbebbabaeebaabdcddecaedabeacdeaaebedbaadeaabcdbeadeeacdaabeccdadeaedeeeeacdddabbddabdeedcdcdbeeabbdcdbadcdecdaaeedbeebdceaeacabedeeabbbdabcbbcbacdadcdbabacbbbbbaebacbbbdabbadcebacbaadcdddeccdecbeadcedbecacecbaecbdadaaaebbdbdbbcdaecaeeaedbbddbbececbeecbacdceccacddccdcdebedeeebbddabdabcdcdbdeeeebdbcaaeddedeabeedbacacbaccdedeeacbebcbbbeddadbdebebdbddbbbcbbbeababddcabcdebecedebdbdbcbaecadeddcaadceddecdbeacbeadacaecbbaddeccaeadbecedadedccaebbbddeeecacccebddcedcaeddbdeadeeaeedbeacdcadceaedaeacedecbddaeccdcdcddadaddaeadbbeabdcadcebebdddbdbbdedaaddddbcbacecceadbeeeccebecacecbeeebdbeabbeeddcddbdeaccbdbadcdbbcdeabdddacbeeeacabacbcceddedaabecbaabdeceaddbabddaedcdabddcdaeecbacaaddddcdcccdedeacddcdabdaeceacadcbbcbdddbcdbeccdccccaaaaadcdcbccdeaacbadbeeaeadbbacabdacedeeeeeaddacacbbbbecaaaaebccddbadddedbdeebdcddedceebabadadabeadebdeeebdcadcaddadbebcebcedddbbadabaededabdabcbabccccdadbccbdddbadbcebeebcaeaabbddbebecadceddeacdbaddbdceebdbadaaaccadbdcbbaabedbabeabbddabdedeecbbaddccbbaeeddddddacadbdabddadceeaadccdacddeaaedecadadcaedebbdeccacabdbecdbeebddaeddacdacbabccdcdcdeebeaebeebcdadccbdeddbccdabacabdadceceaededdaaeebbadcdcedbcbaeacdebbadbeeebbdbeacadbcadbeabceacbeaeaebeebccbcadadaabbadabebbadcabcbadabbbbbccabacaebdbdcdbdeaceeabbcdeebedddbbdeecbeadacaaedcbeecaacecabcbeddaadceacccdceaeccdabdedaebdeeccedeadcccdebecebeccaacbaedaeaacdedadadcbbadbdbdadcbbdedecdcccdaddcdbcaebdcbabaaaedbbabeebcaddbecbecccccbacdacdedeccbcadabaecbeabbeeadbeeeeaedaadbddbbeceababcdbbbddaeeaecebcaecbbbcdbbceaceeaebccbddddaedaabedcaeabdcaeadadbbddbadabcdbaeacebeaeddabccabcbdebdcbecbdadaaeebdacaeabaaadeaeebaeeabaaeddececdcaacdebdbbcbcaeaadaedddbaeeddbdcaecdbbabeaeeccebabcbdbdaeabecceaeebbcccbbccacccddbceccccdcaacadceacbdabeaaebdedbaabebdebabebaebddddacdcbedbaccbeeaeceadeeecddabebeacddcbcabdbaddbebbbdeeeaddbbeedcbacceaebeadcecbadadbabcdaaabdcadecececbeacbadbdcebceccdaadedcccedeacaeeecccdbccccacdcddcbcbceedaecbadddcbcdcaccabacabedbcedbbeabceeabcebbeaceebddbdbecacaecaedacceeabdedcdbecbedeabecaeccadbbeddeedaceebadcbdedcbdeeecceccbdadbaadedbdedebeacdeeaacdeabaebcaaeebbedebbebbceebedccdccdcacaeddaaaedeacdeddddaebaaaacdedacdeacccaeeeebbbaeececbcaccbeccdacaeeecedecbcdcdcaebeddabeedcadcebccaabbaadaeeaeeedcebdbeddcbeddbccdbbacccbbcdcbcbddaddeaaddbadeedecbbdbebcdcbceaaabcaecbcddbdacbebacddaaccecacedcdebaebeaebdbcacbedabacceeebbddacddbbbcdaecddeccaabacdcabaaacecdedbadcebcecaaaddeaddceedeeeaddcaeedebeacdbbeacaadddbbdcaadaeaaabdeadedccbcacedbacaecdadcccebdabbedbaacdaeaaecdacdbdeedaaadabdadecdddbbeaccaaaecbdddaaaeeeaddcdcdeebceeaeacbeaeebbebabcddbddbccebbbbcdcddebacbcbbcedeabeeceeaccdbccddbebacbaaadddcaccaaacbaebebbddcccdabbcbbbddbccbbaecaeadbdcadbedbecbbcebaacbedddbaebaccccbbbaaaddadaddccbbacdcdabcebdaecaebadcceaebcaebadcbddbdbeebecacecaccacdbaaeabdccbddabcdbabaaebedeebaedcadbbcbddcccdddccddcaaabccbdebbabbdbbccdeeaecaceeabceadceeecdbcbbeeeaabaaeaacbdeaaaacccbbeadcbebcaaaabccceaadcdbaeedacecaacbdaaeceabebbaceebbcdebccadbbbcdccdcdecbbcbaeadeacccdedcdaeeceaceaaabacbbecbbbaddaceddbbacaeacdebddbaeabdccedcbcdebdbcddcbbdddcadbeacbdaadaeecddccdceeeacaceddcadbbdcdbdaceaabedccdebdcabcebdabeeededdeedcebbdaedceeebabeeaacaeebbbcebacedecadcdbaacdbbdcabbbaeeddecbdacebdcdaadedaadddcdbdddabbbebeeacbbebdaeabacbaababaebdcaceaacdeddaaaadecbcadecadacbbcbbacdacceeeddeabeeebeaebabeebaddccbdcddaaccdbbbacddccadcebdaddeedeaaaedaaacbdeebdabaaaabbaeecabaaeacabeaeaedcccdeeabebeccaccbdbcbaddacebacddbebdbbcbdbcdecaedebcabcdecadeddaaaebeedaddbcceadededcbaeabcccdbcaababcbcadedcebededeaaadcaaedcdebaceccbcbededcbddedaeecdebabbcdedcaeedcebdbaebdecccbbaeddbcdbabccccbdabceeeaeaedabeaacdbbaecebbbcebcbabedaeaebcedbcebaabaecaeeabccdeaceaceceaccdbebcbdaacdecaacbedbdddcbeccacebabaccedccdaababdbdcbcebeadebeddadcdacdcaddbadbbceeddbaedcebdcdcdeaebdabddedccaabbbadeabdceddcdeebccdcabeabedcdabdceeacbaaeacdaecaecebcebbadbdcdddabbebbddaaadacbaddcaeadecddccdddcabbecbedeedccbedbcddbaeebeaddcccbebcedeebdecbacbaabedddeeccaacaabbbcebdadebbcaeaadaebacecdabbeebaeaaabcdaaaacebaabdecebcdaaeaadaaccaeeecaacbbdcacadebbdcddaeceaadabadabaacbabaeabbaabeadcdddeadbdcccaebebceeebccdbebeddbaacedcacbdbceadaeedeedadebdbebbebdccaeeababdedaeaecaceaeabbbdeccbbbecadbcdedbeccecdbabaedbdcddaceadbdabaeddbdcbddebddabceabeeeeddbdcbedeacabdbebaabcbdaddecaaaeabbacedaeeabbebdbbdecbacbbabddccbdadeeceebcadbebcabcceabebbebabacbdeebabecacdddbccabbadbebccebbabaecadcccebcbcaadccceceddcadeccddccaedcabcdccaaaebbdeddaebdcbcdadaeebdcedbbeeaddcadebbebecbbbaeaaeaccbceceaaccacbbbbdeececdaaacdccdbaebcbadaaeeeaeedcdceacdaaeccbbaadecdaebabebdbacaadbacccdadcabedcceeddbbbcabcdabdaccaaabbeddbdaebecccbdbbceebdccdaacdbaaaedbceacddddedaddbeedbaaeddaadeecbbccdcdecbbcbccdaaeadcbdabedeaabcbbaddaccdddbeaaaadcaacbeccaaecbccabbccbebbbbcbbececceeeddaabaaaacbebeacbbecbebcbadbebabdbbcbbceceecbbedaadccceaeaeaceaacecacbbbaeedcbcabeeccadaaabdbcdcbacebcddbcaabcdaeebcccbabdabdcaccbedcbbdccecddceebacdcadceadaacedaddeccbcdaeedaaeeababcdecbcccbecdbebcbccdaabbddaccaebcccaacbcaccdcedbdeaddebecdcaadaacaebcacecbebddaabaaaeeaabbacceedbeeceeddbbdbcbacadbdedaececcecbbacbeaedbbdeaecbeaddecadeaceeeababdeedaeeccaeeebbaebcceedaeacadeeabdebdbeebaadabdbaedaececbccdaceebedccccaaaedeacbbddcbadbcaccebbbbccbeeabcaaaedabcabddcacabebaeecebddcdcbcccdebaddccdbbbaeceecadcccdcebadaaeabbdcddaceabdebcbbeacebdaeaeacbbcbecadcdaceebdbeecebcccccabdabbeaecccaeeacadeebdaecbddacddabaceeedebaeaddbacdddecdcebacaaeacccbbaeecbbeeaabcdecacebcbbacbdebaacdaabbaebcdcabcbdcebdceacaeacebbdabbcccabbaaeaacbeedcdeddccbedceaedeeeaacacedeaabaecaabdbbbdadbbaaaeeedbacdaddcdbecbccedaaeecaceabceaeaeceacbaaaaceddabddddadabaedcbcedadbecaedabeabebddedeacecdedabdadccbaccacedbadacebccdeedcbadbedacdcabdbeaaeaececdbaacddbeceacabcdbbaadcebeaabcaaebcedcbdccddeaabbaabddeeadedcdbcdeecbcdcbceebcabcaadadaadcbbeaeedbceddadadbebeaddbcbcbbbdebdeeedaecbdcdedcddaebbdeccabbebdaeddbccbbccabeaeadacecdacebcdaeccabeeaeaeebdbecdadbcedbcecdcddbbddaaacbcbeedecbeeddcdbeabbcdbcbaaeccaeacacaccabbdecbeaeecbdbeedbbdeeaedaabddaeceadbadcceedadbddaddaaeabaceeebdccbebbeaeadbbccbbeadceddadbddaedccaedaadcbaccedbeaeeeaabebdaeaebeabedecacbcebddceebcbecbcecdcabcbeeaecdadccebabddcdddceadcabaeaeecceadacccddcdeddbecceaeebeaadcbbcccadbcabbaecccdceadcacacdebabdcccdebaaecbebeacbdbdbbdccbaaeeddcbbabdaeaeebdaebadecabdedecdbdcaecddeaabaaeeededaebebbbebebbeabbebdbeddbcbcadccaeaceaeaccedebebcadadbccacbceebaeddcbacbecacbdcebecbeaedcddaeedacdcddbeacebaaaebdcbccecbccabdceeecaacacdcbcedbdaeacdeebdcdbeaaadcadeeebdbbcedccdbbbadbeecbcbeebdebadacedcedcaaecdcecbddaadddebabaabccaaeadcaeabdecaceadebedcbdaacbadaedddcaaebbadceabbbeadbcbdbaeaaaddceeaccedcedadeebadbababdcecaddaaaaceeacdabcebaacaeacdaadccdcccedbeeaeabdeabcbcbceedcbdddcdbaabaeddcdbeaebdabaeceebebbceddecedbacbcbccaeabadeaeeccecccddbcbbbdbeabbeadeadaacbabcecadabbbcccabedbbeaadcdeaecaccedcdababdeabaaacedadbdecbeaaddacdccbeaabbdacaeeaddaddebddcbbdbdbdebdaabbbadaaecdaccceecaeadeaceceacabecedacbdcecaedaedeeedaaabbedaccededabdddeeccaecdddabddaedecdddababeebcaaedecbcaeecabeeadaaeaaaaadedebbbaeddcaadbcbdbadcddedcdcbcdbcabaeddabbebadeeccccddacaadabcdbebabeacacdccbaaaeaaadcccdbceecdcaaabeacaaaeddeacdcbaadaabbeaddcccddbecaaacbcdacabaebbcceeceedcbdcacaaaabcccecddcdadccdbbadeeabbccbacbeaabcddaedcabaeeebacbbeccddadbcbeabbdcaddcabcaedcbdbcecaeacbdeadbebbdadbadaccdeabaccdaabcbadeaadecaebcdbeccedcdeebdbceedebaceaeddbaacabecadcadbedaabdddbebcadcebbadadaeebdebeedbadddacccbaedddaabbddebcbacbedeaacccecbbbbdcdbaedcdacdecedcecaaabcdbabdbbdcecceecbaebcbcadacbcdccdebecedddabcabdbecebcedacccacbbbbdcddbbaadddbccdceeeeedaaadbdcebcdbcdcdbeeadbbcabeaedbcaebddceedcdaebdeadbddedbdaeebbbddedabbccbcddeadcabcdbabbecacdbcadcbbceeddadbaeccbdeacbcbecabedbcaeaabaaceedcbaceecaaaadbeceeaedbbdebbddcdbedbcdeacbdaeadcabbbeacabaccbcaaeacdbcedbbedeccaccbadcbccdbbeacadcdddcbaebacdbeabaabdadbadbadcbadcccaaccdacabbbcdaceccbbadeccbdddaaedeebbcceeadbebdecbeeacbbcccbaaabdcaebbeaabacdcdeebdeccdeedcaeeeccdeddeeeabeacbbcbbdeacaaaaeececdcceebdbbcbcccaabbccadadbbdbadabbceacbeeeaebddbaccaebacaadbedbcedeeeccaeccdeeacbebacbeddeacdaadddececbaabbcbbcbdceccdcbdbccadbdadaeaaedeceddbeccdeaacdbaecbcadebadeeadabaeeaebbeaaacbebcadcdbdaeeeebbaecdbecaeddebabbcdddcedeeaaedeeaddcabbdaeebdabbcbbdcbdbadccdecbdceecdeaddcaaadcdcabbddbadadaceceedeaeeadeaeecbbcebdbadedaabaacceaddeabeaedaebbeadbadcadcccaaacbbeeedbcbccdcddeaaaddacdcbbdabedbbcbacbaacebcdeceaaeeedaeabecdcacdddeadebcaeeabedbeedabadaaaeadaabcccadceebdcabbededbceadeddbeebdcbbdbeaaedebedbeccbbeabceadadcbacdbedabcbcdcbdcbbceecaeceddaebeaedadbadcccddabccedcaeedeebccccedacdddebbdbbdddbbdbbdcadedbadaaaebdbdacdabaceaceedbabbbcdceaaabbabeddabdadebedaecdcebbbaebebbbaeacbbcdaebaacbcbddeadccceedeebcbdeaccbcddeadebaeacedbbbdaeeadcebaccdaaadabcbcedababededdbdceabaaacdbcccaecacebeebbcecbbbaadceceedabacedaecbdadecdcebacbeadecadccbaecbadcddeeeecedeaaeeaeaeabddcbaedeeaeedbbcaceebdbacacdaccddbeebebeacaeeacdddeaebebabcdcbeccdbeacaeaecbbdabaeabaddedddeeebacbbcaaeeccecccceadeddcdebdecadcbeeedbeddecedadcbdadacbaabceadcbdacedbabbcdebdeaaebececadeaaceeadddcdeaceecdcedadccbccaecddeacedaddadddecdaedcabebebeaddabacddcccdcaeeaeabbccdeeaeadbdcacdedcbdebddebaebbacdcddabeddadabaeddbeaeaaacbacbbcaecaacaaebbbecedddcceababcdcbbceccbbabedddceabbaaaddbcceabcbdbedaeddcbbbabaacddaeeaeaddecedadbddcbdebbddedccbeedceabddaeaeadeeaebaedebcadccbddbcaeebbcaadcdbccedbebddddddacabeebcdddccbdccedecbecadeedddaccdbdebecbdaeddbcdbddbacedabaddbcdddedbdddccaadbaebaddccbebdadcccdaebacbdecaddcbbeebbcacdebdbdaecdebbaebbacbcbdaedddaceacbccdeeddacabcbbcdaaecdeeaaebdebbaadaaabdbddacaceedbbeedeeeacddbcedbeddbdbeaeddaeeacbeeeddeabaabecacaccccceeecebcddbaccbddbeecdacbcecdaebebbaeeaaeedeadbbdbdaddadbdbadccaccdddcbebebeabcedcdcddcaccebeececdbaadddececcaaaecbeaabddcebccedbdcbbbdedebbccdeecdbbdcdcaebcedabcbddedaccccbbdbccbaeccddcaecdecabaeebaedddbdceacbdcaecbddcdbceebaabeadadbebabbcbdadcaeedeedccddcbcebbdbcbebadbabebadebcaadcaecbdabbcceacbadeeeedacebcabcbcbedcbbbcdebbbdbbbadeceeeaeebcedcababadbebebbceadacdcbacedcbbadadcdeccceacbdebeceeebebdbedcacbbbdcbbcabcdaecebabedacdcdecaeebaadeeaaaebbdbeadddaeddeabdeeedaeeabbbbaadccacccbbbdedaaaebdcaebcbedbbbbcabceaebcdddaacddebeccbebddaceaeddbcecbbcdcbcddecbddebabaaaddccaddbacccdacbdeccdebbcabebececbcddbbaeaeceabeaeeedadeaaaaaddacaedbcbcaedbcdeceebbadceddbbeecaaadacabaddaddeeddaebeedaeecbbcadebcdbebeadaeadcdbabcedabcebdddddcebbeadbdbeeabdedabedddbedabcacbbcebdddbedaacccaaedbddbbebecaceebeaadcaecdbabdcceedaadaddccbdecabdeebeedcebbbaddbbacabdedcdddcedabcadecebceeccebecaccabcbbadcceebbaacdbdceddeadcdbcbceaebdbceeacedddbdbcbeeedaebceecceccebaeabeaebdedbdabecddabcbebebdabbedaecbaabecddbaaadddddabdbbcdabdbaacebbddeaacababbecccdedbaddbebdbbbcbbaddbaadbdcecebaeaaabaedbecbddaaadcdabcbceebbaebcaedbcedbeabdaeeabdaeeddbeadbcacbbacbcecccbdbaaedbdcdcaccedbeaebbbbeaaaacebdbedcbbcdeaebbbdddedbdbacdadeacdbeadbccbacdccdcadeccebdeaaebcecbccccaaecbeeddeadddabccbacbaedebdcdbbebcceebcadbeacdadeaebddabbcddaeadbbbabaebadeeebaeeeeacabdbbdabbdeaaeedeaccedccaaccaecdacbacdcdabeceeeccabccaeebeebbcabbdcbadcbcadceeecdbaadebdcccacaaeeeeeeaaeecdcbcebcdeeeedbedaaabbabecbabacedbbacaeeedbaeebbdbbedbbbcebadecdedbdbdecdebceaeeccdcdacceadeaabedecbcadeceaeebedebaecbabedaedaaaaaccedecdbddccbbcadbedbceeedcbacbcdbadcbdebdeedaddeeceecabdabadaaeaedeedabedceeadbebeabbedccbedcbddcdabadbdbeacbcaaebebcabcbdcaaabddaddbbbcbdeeeeddcadceebcbadddbcebaabeeacbeecaaacbccbeaeebcccacadcecbeabeabccecadcccbacdbdcbcbcdabceedeaebcdddcceeceaedbabcbadceacecebabdbbceddcdbdeecabbcdcbcacacbbccbabaeaaeedbbadacebaddbbdeceabddaaecbdcdebeaadbcabdcecaabdaddebdaceacaedcaccbbdbebdaebcedcbeacbcaddeedeeadbcebebcdabcadeabedcbbbdaacceacbbcebbcdbbbbbcbabcaccdbababacabbedbecababceabbdcddbacccdcecadbecbeddacbbedcccdbccddeaacbbbdaaccbbadeeceaaadbbcaccccdccdbaedaddcadbaadbeeaaebddadadadbdbcdbdecaaaebecedcadaeaaaddcebabcdcbadadddbeabcdcdbdaacabbeaceddeccdeeccdabddbedbabcbecbaceddeabdacdbeccbeeebcedaebcabedebdccdaaabdbecabbaebdccdbcbcdcdeddbceadedaebcbddadcaaceeecdeddaccacaecabcdcabaeddddccdccbdedabeaeaaabddccbcecbedaedddadedadcbdadccaddbcdddaadedbbaaadaeadbddaeaecedeeaaebccaadecaaedcadbbeabcacaeeadaaedcebacacbbdddcedabeeabadeadecdbcdbeecdcddbdebdbcdbababaddddecacecdebabbaccccaddbbedecdcceecbeaddadadaadddbedcbbdceadabbecbedeaecdcbdabcdabbdeeeeadadbdececcaadcbdbaceaecbaeedcebdecabacdcebccdbbceebbbaeaccacbdaabacdacbbdaabcadddadadeecabeeadaadcbecbdbcebceeaecabbeccededeceedcaaaeabdddeaedabdabbdaebbbacdedcaccccdcdbcdbbeacdaccceaeedbbeecdabddcdadccdbecaccebbdeeaebdeeaddccbeaabedcddeeeebbbeabcacdbadecbbadeebabaaaeabbabbaacccdbeababaedbacecbbedbdbaebdeebebddcebeeecabcbccaedcabeacbcceeaccbcdadaceebaadaddbbadcceddbabaddddcceaeadacaaedbdbdbecdbdeadceabdcabbcdececebebddbdebcabedcaaeceedbddbbcceaceebeadecdcbdeaeacddbacddcaaeeadadcdccabceedceecadaadaaeecabbccbabadaeebbaebebceeaabeabadcbbebcbddabcaeebdedebdbdeeaebdaddeebdeeeadcaabdcaecdbcebceccedcaebaeaebbacaebeaccdbbaadaaeababecdceaebaaaeadaaadcbcaeaaddbaeaaedbcebeabeebaadbeddabbecaeecaccadacedaeedebbdeadcbeaebdccdacaeacaabbdecaaebeabedcbaacebedacedddcabadcebcbedececddedcbdceddaedecaebcddbaacdcddbbbbbcccbdacaaabaccceedbabccbdccddebaaedadbbecccdbeccbbdbcaddebbaababbecbcdbaacaecaadeeebaddaaebcdeddbacebbbeceeadabcddeadbcbdcdbebeaebadedeaebddbcbbcbbdbabcaeeabbadeeacceccccbbebebcebceadaedbadbcdaeedbebedcdecdbbbaabeadbdedebeebeaedbcdababcccaaccddcbaddabcccbcdeeaeeccaebabebcbdedabeecdbdeecbeecdcdcdecadedeeebcbbcdcadabbddcaececceadbecdbdbdbbbdbcdddbaebbeaceaeeadadbadeebccedeceeebcebecbbbcdebabcecdeedceabbebcadacdbcedaedeebadaebeacadadceeeeeaedabecadaccbbaaeabdcbdaaadbaacebaaaccdeaeebccddedddbabdedbdbbaceeabbdcdaaabbccecedbbabcbbeabbebacdaaddbcebbeaaeaeceddcdaeacdebcbabebdeacddcacebbeaeecdcdcaedaedbdadaddadbccdcabbdcaeccdadeeceeabaededcdacaceabacababdceedbabbaccaaadbdaeccdeabaebdcaccbdbacbabedeadeacbbabddceaeacccaeceebeecdddbdcbddceddbaedaceaaeecabbeaeeecacbddadccebdaaeabaaaedeebdaeddedecaaaadeddabceaabeceddeeddeaceabebdbddbdcdcbbbbbdebaaabeeadbadcaecbacebacbeeaccdaedeacacaeeeeeabcadddeacadabcaebabbaeadcacdcdedbedccbaaedcccdcdaeddaedcaaccaedadedcbccdaebbadbedebabadbeaaabccdcccdecdaeeecbcbacbbcdadbbcdadcddadeebacbdcdaeaebeaebcadbbdddaebdacbcedeabdaaebeacbbddcaacabdbeeebbdcdcbcbcadeeceeaedccdbabaaccdeeeacbbcadbebccceeeaeeebbdbeecadaecccceaeebeabcdaececabbadcccbbcacbeabdaebbddabeccadbbcadcacaaebbbccddddabdeacaedaeebceaeaddadaaccbdbecbeecececaacaabcdaabecbbcacdecdecbdeeebdaadabdaeeaecbdabbbbdaeebaddcebcadbccebaeaceecaaaacddaaddbdaeeababdeadcadabdbbcccececaaecedbdcbdbddeeaeabebeacbecedcbdabeededeccecdccacadbedccdaaebecbaaabcdbcdadeadaddbbbaaeddeeecaedaeaeaebdaabeebabbbdbeaeeacdaebccacadebddaccdceedeabcedecdbbadbabdbeecabbcbdeccaaeaecdbebeebedcebdbbedaaecacbbddecbcecdededeacebeccbcaadecedebeddeadcecaedbadebdeebeebcbdaabaaceecdbcabbcaecdcbbedccbccdededcaebdaedcbbdacaeceaecdbccabddbeebabcdbedeadacdeeebbeadeadbbecdaaadbeeeceadcbadaeddaebccbabcedcabbedecbcdeeaeaaaddadaeccbcecdddbeaaaaeacacacacadaccddcebaeeeaabcdbcdddaacabecdbeaceceabcabadeaaaceedbcbdceedecebcdbcaabbadaccdedaaecbdcddaacbaddadcabecadebaebabaacbbeaeeebcaacdeadcbbebdabbdbbaedeeacdcccacdecaaecccecbcccdcecccbadbbbbeddebdeabedddbbebbccaadeeceedabecdcdebbeedecaddccceabdeadcdbcbdeebdacdedcebedddaeaebdcccbeddeaceecdaaeccdecbecacecceadbbceaeeeceacbdaaeadbbcbdecabcccbcdbbdacacdabcacebaabdbbceeabacbeedcaddbdbbddbdcbbbeaaccaecaddeaabdcacaebabbbddbeaeccedeeebeceecdcbadacebaaccbdcdabcdacdeecceddceaddcacdecebeacbccdeccedeecbbcbceecbdbaacadcbdabecaadedeaeaacbebcacbaeaecbaadabbaacecdbbaedaeebdbdcdcaeeacbdcbddeececbeaedaccddbdbddeebabcbddddcdaebbcdcaceddaeedaeaccadaceccceddbbddadcbcdbbbaedccabeedecbadeebdbacdaddacbbbadddeebacddcbdadccbddbeaccbacbecbeedbcbabadaccabbaaececebbeadabddabcbbcbbdacdbdceecbccaaedecaceeecdecacccabeeceaecedcedbaecdbbdcaadccaddaececbbeadddbdacbaebccededdaacdcdeabaabddddabaebcceddebbebdaacacabbbcecddbcacbcceadacccddeeabbeaccbadbaddbbedbcacdedaccbaedcbdbaecbebcaceaaaaaabeeacddecabdecdabdabeccecedecabecdcebcabceaeeadaabedcebcbeaaadaeebbbdcbaabcceebcdcabbebadccddccbceecdadebdedccdaacecddcdceccaceddaeeebbeaeecccaeaaeadbbaabbaaeaeddbbadaadcedbeeaabebaeeaddeecaddebddbaeeebedadbcbeeadcdaaeccbedaabeaaacebccedcaceeaceaddaacabecdeecbdcadbeeebcaddedbedebecdadabbcbeacbccdcaacaeaeeedcdaecbeaeabeddbddbbdeedbdccdedaceddcdebbecccebdbebdaacedbddcaaaaeaddbeaddabecaebddababbebdbbcbabbdadcbddcceadededaeddeebccaceedcdbcdcceecbebcaabacabbadcbadebcddeceedcbbeedecaddcdccddcccbeeeadaeadddedcdcadabecbceacdeebeebadbdcbedebecdbeebcaebacedbbbecdddebebdeebccdbdabbebbbcdbbabaeeceaddbabebdbaedccedcabcbcadbddedeedaaedcbdbdadcedaccddeaadaeeacdcceeeddcaaacdacaaeedecdaecdedbacabccaaeccbcceaabceadbdcadccebaadcceedcbdddcceaeabccecebebeaeaddbbcbccccbdbedeeadcebabeaceadcaabedeacddaabcbabbeabdaccccbdbdabbeeeddacbdbbbaadccbdddeedebbabacdcbcbbdedaabdecebeabaccaaacdbcdccdceeebcebccecaaecbbbccceaebaeddaecbbadbeaeaaaabbebeaeecadababaeacdaedeeabadaeccdceadecedcabcdcaccbeeaeccbdcbbbccbaccddbedbdcccbbcaeedaaecccbeececebdbceeceabdcaacdadbdeaeeecddcbdbabeabddedbbddbcdabadacccccebeedeeaeecbbaedecceadcdbbcadcdddaddededdcabbcdcaaeadedcadacaddbbbceeeeecbcbebceadeedbebeaacbaacbeeeecddeeebddadbeedcedbaacdcabdacbedeaeaddbcbadadecdadecaccbadececbdaaaeadeceeddbbdaaacdbbdbaabbdcebeeaedcccbccdabcdeebcdaecbbdbccacdebabdcbedeaeacaddcbdbcedddcdcbbbacbcdaaedccdddeebcaadaccccaacebacaedcdedcbaeaacdabbacebedeceaabcceeaaaeebcaecacbdaebeddcaeaeebdbdebadeaebccbedcaeddadedbcdaccbecccdccabecccdaddaccdbbeadcbecebbabeacbebcbcbedaaadbacaecbbcdbccaabbaadbbaaebeaecaaceeaedddeddbebabdccdccaeeaddbcbeaacadbddaadceaaabcddebaedddbbaecddcaeddedbeeddbcbcebcccaebcccaecdebeebbcabcdaadeeeadadcbaeccddadbbaaaecaabacabeccbbedaeebabbeaacceebdaccabedbadcbccaeaecbcdceaebaadaededddaeaaabbbaebbbeeabcdeccbacdeedcdebbbdcbdebbebedbcbebcabcaecbbbacedbecedcaeeabddeaaeeddcdcbacceabbaacbdeecccbddbdccaddabbabeeddaadadecdbdacceddddcbddceeeaeecadcacbddcacbcabaaeebecedadcebcbaabdaeeabcbbccbdededcceacdaaaaadeeedecdcdedcbcccccbdcdbbaebdedcbdcecdecbaeadcccabbabeeebebaaaaeaaabdebbaecbeaaeaddbcbabaacccdcbeadbdadacadbbbceacedabccaebdaaeabbeccdcedabbbcecabdbceecbadccaaceebcdcbeceadeeeddeebcbddaececbbdbcccaaddbeeccbeabdddeecbdbdebdddebaacebcddeeabbeaccceccdccdadbedabcaedadaddabeabcbacaedacdeacaeadcbaaccacbdeaeecdaeabecbbedbbeceeacddbacbbbebeadceabeeeedecedabdacbeacadcabcdaedcdbdbdeabcaebdcdcccbbbdecaebaecbbdcdeabecebadabadbccacdebdadaeeeaaaaabdcaccbecaaaabeeeccbaeadcadeeeedecdbaddbdcccbdadbceedcaabdeeccecbeddeaecdeadcdebebbbbbedebadedddadddbecbccbaadcedbdbdaabccbbdcaabaecbaeaecdbbeebdcdaeaccaedaadcaebbecdababebadcbedadeebeccedcaaeddaeaccbaebedbbeedcacbbcceebacaadedccedbeddbabceddbcbaecadccaecdcadbccabcabaeeaadbdedaccdacbbecccabeaeacedabaacebbeebebaeebbdebbbebbaebcbaddabaacdbdbdacccbcdceeecbcabdbaedaddeedebcccbecaeececceddaaceebebbbcadebcceebaaacccbebedaeeaabebdbbaedaccddcddbbbecbdceaaeccdddedebbeaccbbccbdaedcdbceeaecebecdadcccceecbdebbbcdcadbbdbbbaaaaeeadbcbdadddddaddcbaabeadaaededaeeabacaebbcbdbddbabcecababcddcbaacdabcadceabeedabebadbeabdbcbebeeebcccdeabebdebccebeedadeccbbecaaacdddaabedebeacbeabcdddebcbedcbddabeedcbdacabeacbbeaeceebccebcdcbdacadbbeabdebebbcbcbbecadbbebaddceccceaedccbbeecbdbceebcdbebbceebcacccbedeccbbdadcabaabbececeaacddebbbdbcebdbdbeebbebadabacdeebcceebeccbbbdbdeedabcbbeeabcadbeebbdbeaacedbcacbdedccaeeaaaddcabececadebdacbadcbbeeaccababbadcbbbbedacdadabeedbebaeeacbdbacddadbcabbaaacaecdeccdeddaaebccaaedabbedecadaacdebaeaebdcdcacaccaaaabaedceebcbedbaaedbebcacecbabdebabaaedcbedaabebaadebddecbaacddcabedaedcebbdebabeaecebebadadbeecddeaebbacceaaccccaacacdeaccccedcaaceeaccccaabecaadeadbddbaeecdbaebdeccbccdcaeeeacbbdecdddcaeeacdbeeedbbcddabbabcaabbcbcecaebccdebbeeaeaeecbbccedecbaeeaacaecaebbccdacbacecaaabcbeccabbaeacccdccccbdddbbbccacbbcdcbbbadcaaebeceedcbbedeeaceabccdaedeacebbebdbdeaddabccabcadaccbdbaccbdbbdceddaabdcdcadeddeeeabdcdbcebacdbccdccacccecabdceeccbeaeeaccecdcaeabdcbbbeeeaedbddbedeedbaebececdbbbadcdaeeeacbeaebecdebacbbcaccccebddedacdbccbbababebdecddcbdcbccdedeeadbbbdaedceeabddabbecaeddadcdeceddcaeebaedbddedadaacaeaadbaadacdeeaceeabbcabededcdeeacecbabeddebbadaacebbecabaeeeaabeaccedcadddccacbddeceddbadcaabadeacaaacbbeedebebcebbbeacceeacbbadbbbaababacedcbedabbbdedaaabeecaacdaaeebadeacabaebeddeddbddbeaccceebbbeddcbdbacdaeedbbeebceeedeccababcbcaaeaadaeddacbcdabbbaaedcdbceabaacccebcdddbeaeacaaaeeeeccaddbbccaeacbaecbadcdbddceaddcdebecbceabbecbcddbdbaedbeaaaadbbcbdacdbeebabadaececdabbecbabdaaaddaedbacabcbcdbddaeeeeecaccbaeaddbcdeaceebaebbabbdabbcddbdacecdaeddeebbcebdbcdbaaecadcdadaadcceacbacacadbbcdaecdadaceacdbdacbdeabdbeddbaacbbbbccdedcbacbaabcbaecdebadddeadcedcaaaaeacbaccbddbbccdeeeecccabcadaadcddbaeaadebbdcdebdacebbcdedecdbbeacbdcddeaeceecaeedbdbabaeddccadcbdeddbbedaceeebcdabccadabeaaabcdaebecbcdedeebabaaeccbdbcecdeeeaeeadbdddcdbdaeeabaeaacbcebbadecaeeaeabbdbdbdacddbcabebaddaeadadcceedebbccccbaabdcdccbddadbcaaacccebababcabcacdcbaeceeabeebebbeadbdacccabddedcdaaecebebeadeadacdbcebbcdcadaecdebcbdadcadacdddcedebddbabbadebccebbdddadcaabbdcdccbbdabdcdddadddbbdebadadacabdaeccbecddcdadeadebcdadbadcacdcedbecceadecdeacbceadbbdcdbcbecebccccbbcedbadccdaaddbabddddcdbeeccacdcaeacccadddabaebaadebceaadecaadeacdcdcaddeecdeccbcaaaceaedcbdeebbeedbedcaabccaceccceccbcecdacbaeeaecbadccbcabbeeddcaacbbedaaeebeadecdaddbcadacceaddbdeecbdeedbbcdbebcdbbedddddccbaccbbedaadaabdaeebdcabcebdceeacceaddbaabbdadebdbdbdeecdeaaeddbcecbadeecaaaaeddddbebaaabdeeaebbbeccdbdceeacacbaabaedbabcdeddbcdecddbadceebadeaeeaecacedcbadadcbbbdcebebaabaebedcbbaeeaccdeabcdabcddbaddcbbeacdbaeebdecdceaaabaebeadebacdecbdcabaedaadebbecacacebdacebbdeaeedceeabbecaebdbaaceebeddbacadaacaeddedbebcebabbbabbebbdbbdcbbecaecdcccbbdccbcadabebdaeedaeacabdcccedeedcbccccdcbcbbcbaeedeeadddadcdcdacbceebddaabcaeadbceecbcaeaacaecbbcbeeecdccddbbbaaeabddcbbbeabdedbdeaedebaeecaebadbcaaedaeeadbceeacdcecbdadeeabeceedacabbaeacbabdaebbbceccbddceddebdacdabccbebadaabeaaaebcdedccdcbebdaeccecdbeededecccbbddccbbcdcbcdaadddcbeeabddeecbbbeeeebbbecceecdedbbaddcdeecacebeecbbbedebcadccccadecacbecdddbedabebeccbcaeabbdcbeaeebdaadebcdedcdccdebccbcbaaaddaecbdeddaeddbecddcebeddbbebbebcedaabbadaecaabeaeebebabeeabaeadbbdebaaacecadaadabecccaeebdbbdecaaaacdbeeedcaedcbedebabeaeaabaeeabacbbadebbbeaddabbeeeaeebacdeeebbebcddbcbabcceaaacaaeedbabceebbeebaddeecdaddbacebeadadeabebdcdbabeccadedbebbbcddebaebedadeedbcecebabacaacdadddadbbcacbaccbaabacabcbaceebeaedadecadaaebdebdcecbdcccdbabebeedadcdaadaebaaeecddcdeaceacbbeddccdabddbacccebdbebddceeaedaaeabbceebeacbcbbddeabeaccccbcabacbbdbccceaebaabccdddcbbabbddacbadedbdcdeedcaccdcbbeadcbcbaceebcaabccdcecbeaaaeacebacccbceeceddecaebcdddaedcbabbbbcacacbbcccacdaaeeedcaeddcadbabeaebcaadcdcdbaccdabdadcbeaacccbeebebebbaabedcdddadceeecdbcdacbaedcadebebdbeeccacdaedcbcacecdaadadaeaabaceceecdbdccbceaaededebcacebbeeaaadccaadddcccecedadecbbddecdeaceebdceeceeecdcdecdddedabaeacdcbddecedadcacdecbeeceeddccdbbcebacdccadeadcbcaabbdeeaeaaeebcdecdecabddadadcedeebbbedecebacbbaaecadabcecbaaabbdeaeedededebedaecdbddccadecbdeeeaeceacaabdaacbebbaabdeeddccccdebddedeacacbedbabddaedaebcebacdaedbcdcdddedcccabccadceebccededecedeaedcbdcaeedddedeccdbedaabcaeeebaeddbdcacebbbeabceecbcbeeddebeebadbccbccdedebcbedbeaebabdaddcbcddaddbbecbeaecdadabbaddddaeceaeedeabbdbdaaaaabbceadacadcdbeebaeceadeebdaddedacbabdebacadddcecabdadaabceeedeeaebcddbdcbcedeeedaecececcdcaeacddbceeabebdeebaeddababebccddccededaebeeeadcdbddcdaeaeebbbdbbbbbbdaacabbcbdbdacbeaeedeaabbaacbdebaebabbcdeadaedaebdebabdceacbddbeadccceaabeeaeaaeeecbdddcedadbcceccdcdbccabbaadbdccdbedbebbacdcebbbbeaeeecebccecdbbcbdaccccacbaddaabebbeadeabeccaedeeadecdaabaddbbdbedbdecacaccdadaacdeeddddbadadcaacebdebeedccdcbddccdedcbeedeeddabeabadeddbdecdcdddacddaeebeeccbaeadcceecaeeedaabceecabddacdcdaacaccdacbebaadaccccebbbddcaceaddbbaecaadbcdbabcccddebacebbbdabcdaecacbdbddcabeecbbdbdddaddbececededbedccebecaaaeeeabecaabedadeeeacedcbdaecebdebdcabcbbbebcebbcddaddbccbcaaceabdbcadbaebdceebedbcacdddcedaadcecdecccbbebebadbdebbcbdcdadbebedeecceaecccbadbebbcedceaecccbbcdeadecbbeeccddbabaddaabdeccdccbbebdeaccebdabdecabaecebbdeecbdddaeccbbeedbcceeeccbacecdaeceabeeeeedeedbbbeddababedeacbacddbbdbcecdbdcbdbebabadeadbdddeedebaeadddebcbbddeadacccdccdcebacabdcceacdceeeabdcacabceeaadaeadcedcdeeedbbecaebdbcdbebecbeedaabddacdbadacaaaaedbbdacdacbabdbaacdeccbcbcabeeeacbdbbcdeabadceacbcdcddbcaacbcdccceaacaddeabacdbadabaadabbaedcddbedbaddbbbecbbedcebccbaaebbadcebecccdbaabaacccdadaeaedcbecdbcdcdeeadbaadcdcbcddacabaadbddcaaaeebcaddbcdddcacbddbddcebaedaebcbedeaecceebaebdbcbcdadeacecbbdcecabaacdedeaccbcdaacbdedadcdbaadcaeebdcbccccdedbeadcbaaeaabbaedbeeeaebbdccbededbcbcedcccecbcebbbbbadeebeceeaabccababcbcccaecaddbcbacedeacccdaadebaeecceadddeabbebbaadbbeedebadcebeacadaaeaccbeecabbccccadacdedddbedeacbccedadcdbecdaebbbdeedbddbacdbbabeadbcdecaaadaebbbabbaeadccaeeadccdeeeaaaaeecbbecadecbcabadaaddecaadcadbebbeadecbbbacacdcbacdaddddacbcebbbeeceaacbcbcedbeabacbeabbecbdeccebaadccadbebadecdaadacdaeebbdeedeeaadbcbbaedaeeeceacababcdceaeedeeaccaadbadeecadedddaceadcdbebbbaaebbcdadeacdacbbaaaabecbabcbcedbdadcececddbddaddeebdedaeedccdeebcbddbdcaabbcbecaecbeceebaeabaabebacadaebabaecbebdacddaccaebaebdebababebbdbaaeebbaaaadaebeceecabecdbdacaaaaedbabaebaebeceedbebacdadbebacabdbbdcbbdacedccabcdabeabddeacabebdccdbabcccaaddadbbbcdaabddbccebdbaebcadcabbbdbaabaaaaabeeeccbccdcdaaeeabddbcdaabdbeedadaebdaedbedecebedddbadedbddbecaccaebebbadebceecabbdeacbbaadccbdabbdaeddeebceccaabccaacccedebbaccdccceacbdeabaeebaeccebeccabdcadeddaacacaddadbbecccaacaacbdacdeaacbabebddcddbaaedebedbdaeccdbdcbaaeecebaddcdcdbeaacddbabadedadceeadaededbccaaebbeddceaebbbabeedadecebacbeceaeceeeeaccdedcbcdadcdcdecbccecadadedacdebaebdabdbededdbdaebccaaedbeacacddebadedaaaaacdeedacceaeaacaebdadeaaccaedbbbcececbdddeccdcbbbddddebdcccbaeabcaedbecaeadaaeccedeeeacbcbbddaacbddcacccdadedcddebaecbeeceaecdaaadccadaceccedaeaecbcdaabdaeeceaeedceeaeeaaaddcabeeeedddabebceeaacadcdddebbdcdbedbeedaeaaccacacddaecbcdcddbacdcccdecaabdeeebbbdcbddccbacdbdecabcecaaeecdaecacbdadcaacabeddcbcdbaedeebdbdabcdcaaeaebaaebdaadddebbcdabadacaaedadebedaddbcecdbcbbabdacdecbbadeabcdcedcebcaacedccbccbbcdebddeadddcebbacbdbdedddbddbcbedecaaaddecaaebccedcbaeecddaacdaadbdddbbebadcceecbaebdadaaaddcbcdcdaaadcbddcacebcdddbadddedaddbeededeccdbaaababbdeadbdbbddcadaaeddaacdbeebeeeebcadeaaabbcedcbabeeadeeeebeeaceaacbdaebcaacedeaedeadbcebdeabedcadaebccccbbabbbbcccdadadcbebadccbecdccabcecbadcdeaceaeedcaaeeedebebedbebdcbdcacbcabdecbbbecaaaaacbeceaacbadaeeeeeccdddaaccecdecbeaeaeaadbdbaecadccbacadaeadadedcbebabbabaceccabbeaaecbccecccdeaabbbeaebcbadadbacdbbebcddccebeceebedbaaaceadddccceddacbeeabdcedcbcbccdcdbbdcceebcaaceeaaecbaabedbbeaaeeededcaceaaabeabacdbebddebeeceabccccebadbaedabaccaedccababacceeebeccccedcccdbdebdabcebbdedbcbabeaeedcabaccbbbebcdaaccedaeeceabbcedbceccdaaecacdacbcebaacbcacabceacadbecacdcdabbebbedecdaedaebcdaebbdeaaebeaecabbeeddbbacebaababdbaccebeeddedccecdaeddceeeaeceddcacbcaccbbdbaeadccbadbbeeeddeaaababeaeddacdbdedcadcbcdbcaaaabdaabbbdcccabedbeabaadcdbddbbdeecedaaeceaaeeebcbbccdcdcdeeedadadbedbeaeabcedeeceadeeaddbadeaddecebbbeadbadbedddebaeaaeebecddbadddcaceabdebcbccdaddbabddcdcccebbecddaeadecedaebcdbebcadecbdbdccdccecedcbdbbdaaeeaddebdcdcccedbaceddeadecebbbddaacdddbbbeddbbadcabdbdaeddbddedadeeabcededbaecbeeaeaeeeeadcdaaaccdecabbcbaeadcbaeabecedcadbbcbbbbecbaedeeabdabbcecedeaedbecaadbdebaaaaeeecabaaebceebdcaedecaaadadddedaaebbdcddaeddbebdeaedcdbdbcbadebbccdeedcdbebbbdbebddbeceececacdaaaceecaaaccddaecedcedacceadbccedcbacdaecceccddeeebeeeddaeeabecebebcbcedbeccdeccabdbaedaaadcdadbaaaebacabdeaadbaeacedddbbcaacbddcdeecccaeccbeabaccdbcbbabaaeabeeebabcbcebadeabecbcbdaabdbedaabdeeacebcbbbadabdbbabecedccdeedecdddedbaaadbdcaadabaeecbecbddbcceeacdadbcdaaeaddcbeacdbecbcbaadbbebbaddcadddcdcdeaccaabedcabebcabceccaadaeaabedaeaecbcbdbedddcabebbcddeaccdeeacdabcedadceeeccddbbdeceaeccbedcbebdeeabbdebcbbdebdcdcabaaeacedeceeeaacaaeaaabaedceebbbedbeccbcdebaceccbadcceccddaceadadeeaddacebebaadabbdbcbdbedbedcbcdddcdcdebadaabdcbccbceeeacebdcdbececbdeeabadeeaaeedecabecbecedbdacbedbbaeccaaaaaaccadcdedcebcbeccdaaeedbcaccbcecddeceecbaddccccabcceaceadebbabcecbbbbdddbbcaadcacdabecaeeeebdcaeadbaecabdeeddddeecccbebcedaeccdaedbebadeaaccdceebdaeebdbebadcedaccaebeadceecbcdadbcdddeadbecacadbbecdadeacadbbabddebbdebadcecaabbceebecbbaedabdabdedeeabdacedddbbdeceeadccdeacaeaeeadbeaaabceecdaccbbaeaedbcbecbddacdadadaaacabbdabbbcbacedadabbebcabdebaecebacbdecadaeceebcdeedeeddaacbabcaccceeaccaedddeacbacdbaecaabbebdbebbebdbcdddadbdaacebebacbdccdcbeeccaadcbcbcccedcedecbaccbcaaddeaccadcebdcebdccdadacebaadbbaaadacbcdeccacadbaaddcedddaebccbeeeaacebabcaadccadecdbbddcedaeecbbeeadbdbecdaddaadbeeaecceaeaedeacdacdcecdaeebbaddcdbbcdbccbacbadaddecbedeadbaaecddeeeeaceacbcebaebbcbaacbacbeaaceaadceeebceddcadacbdadeacecbdddbecedddddcbeaacdbaceccadadacedbbbeabdbbbbceaaaaaccccdbeeededbbeddcebebdaeaccacbddabdbcbaceeaabbaedbaeabaebdcbceaacaeebbacdebdbeeaddecacedeeebbdaebacdaecbdaaaebaddccdbcccadcaededaeecacddceaabdcdbebbbadeeccccadaceedbaaddbbdaacdcbbecededeaadbdecabaeaaebddeedceabdcebaceeddbbdadceceaddbdeacdcadeeecdddcceccdedadeacaabadeccddeebddaedbedbacabaddccbeeeccbccceeadeabcdddeaedcbdceadeccecdacccbbbaadbbbecbaedcdbbcdbedadbbaaddeaceaadbadedeeaeeddceeecccdddceacddddcbadbbaeeadddacdadcceecbbedcbdbeabbecdddcecaaabcebbadaccddbccccdcebeaddeaeddecebadbbcaabbaaeabaedcbbbcceeeaeaddabbdaaddedbcacecbdcddeecbbdcabebdebbadcebdeecabbdadbecbdadbeceacaabbeccbebcbbdcacedddceebdabceccabcacdbdeadddccaeebddedbdabebacbedccccbdadcdaddbeceeddeabecabdedccdddcbdeadcebdbbeceecbbbabddccaceddccdcaddececedeeecbcdbcddbcedaeadadcdeedcdabdeabcedaebaaadabcdcdbaaddeaaeccbeabdcbabcbaccccabadbeaceaacedceacdacabeeaadedbdccbedeeecbacbecdedcbbaddaaceacecdacbadbcebbdaabeaccdcccebbacabeebeebcedabaedadaecbdbbaabecddedabdebddcdeadccdceabedebcaddeeabbbddaddacdbcdcbdaaaebebebddbeebdecdbdddbebcdddeaebccddeeddacccaecddedaacdabcccdcaebbccaedcabceebccddeccdbdaeceedabdbebdbccbccdebdedeeaaabeccdddcedecbcbadbcedbdcbaceedbedbaaadceddbcabbcbaeccadbaabbcaddbeaeadadbcbcccabdaeaedbcbceabbedccdddcccdeedccaecbabbeceaadbeaeadeebdcabacccbaaacdadaacaecdaecdcddaceaceeedbeddecaaecadedeaaeacbdedbcccdbaaaeddacdbdababdcaddebabadccedebdcacbddadeadebabaddddbdddaeeeaccddacebedacabadeebbaeeededdbdceeabbceecedcaebcbecdceebeaeccbdbcaabbaebbcdaaededcbdddccbeeadecdabbacbceecdcbeedbceeccdbbceabcebccebaebecccdebdbccaecbedaacdeedceeebdcdaadddbaeeadbebcaeabcddedcdbcaceeadbacaedbedbacabeeacbaecceedeeacbabadbbddeaddcdecadadcbaacdeeacbeddbeccecaecddeaebbceeacbbdedceabadbecbdedaeadaeabbadeaadcabddcbeecdbddaabeabdbcdbdbdbabbbeaecbdceeadddacaaeabcddedecdbaecaacdcecdecacdaadccedcabeaecbbadcdeeeceeaacadaacdebaccdcddeabeaecbcaaeaeecedeaedaabdeceebbebacebadcecbceddcaddbdaabbedeedddecbececbcbbcddcdcebbceeadcaddcdcbeceeebecdadcddeaddcdbabcddbeebcdddaedcbabbceadacccbaeebccbabbddabdceacecaabcaddcbecbdebbdddaadcdaaccdeeebbbdecddcbceeacecedebdeacbbaeadcaacbdbdaadecbaecedebdeaabacccdcebcadcdbdedacdcabcaebabeaeccdbeeeecedbebbaaeecabbadaadebcdcbadadedaccceccadcbbbadebdaededaceeabceccababbbdeedbadcaddddbdcddaebbeebecdbcbaccbeeeaecbadbedabddcedccbeeeeaddecdedeeabbabeecbeeedeeadababcebbaeacbbecdebacdbdabddbabddbaacdebddcbeeaabebecdcdaeebdcbdacabcbdabaeceeddceedbbbccdcadeadebbbbeaccbddbdcbeeceeacebceedcebbbdcabccaacdecdcdbdcbbebeabdaacceccbdeabaaedbedbcdabbaebabceebbacdcdcbbbcdaeaebecbcaccdacdcebbcaeadedabbdebcabccabdebdbcccbadccbadbbabebadccdbaccdeaecbbeeabbceeebaadcbbdddbdcbbbcdecdbedabacacedaebdcdbeceaaceddabdabeebcbcedddcadbadebaddeaeccaecaeccbebbcccaaabedceeebadabcdbecaeedcaabedcebbbbbbabbbdcebabceacabaaeaccecedaaaeeaececbecccacabeecacbbdbeaacecccdccaeaaaeeaecccabcbcbedbaaabcaebbedeceaeaabdbbdddeaaccdacbbcdddeeebcddccaaaeaebbcadbeabcadbceabdecebabcecbbddceebacdbbecdecbdeccbcbaececbcecaedcddabaabceaadbbdeaccdedbebcdbdaebeebbbcdcadabbdebaeaadccdddadccedeccadbbedbcccbaaaddeabbaeddcceeeebceacecbadeedcceadcbbadbdbecbdcbbebbecdcabeaccbbdecaecabcbcdcdddacbeddbaaeaeaddcadcdcebcccdbaeacbdbabebdeeacebbaddaebaedaaaadecdccdeedaaeebcbbbdaddcbccecdcccddadcdcdeedeadcbdbeaaedcdbeaaaaddadcbcebaadacbeebebeaceedbcebccbdcbedeaececbaaacecacdbbacbcedbacddddceaccbdbbddaaeadecdcaddccaaabbdcbabbabdbdeaaaedaaeeccbcbedcdaccaabebcabdebcddbbdcbdbeabcdcccaacdbebeddebadbbdeccbaadddbccdceabdcaecceecceaddedbdccbcecabeecbeeedbeeeeeccdecccdcbabcedcebacedcdeabeeccecbcaabeacdcbeadecddeeeeeadcbeccebdbdbcbacbdecddcdbaacedcedcadecacccaaeeccecdaebcaacebedaacacbdceeaecddbabaceaadebdecbbecccbaeecdbeaeddbdbdaebbedbacdbaadddcbeeccddedaeccebbbdbecddabcaddcdabeaeebadcbcecdaeebdecbbcbbcdcbaceeecbbaddddbeddeceabdbbdeccccdcabcdacbaabdbdeceecebcebaeecacbdabacbceaaddeebbaddbddddecddaacaacabecbbaabcedabecabcbbecccdccacdddcbabadccbacdecacaddedbabcbcebbbceeebacaadabccdeccabaccceeeedbaddadbdaaaadbbeedeaeabdeaddebedcbebadeedacdcdaeaeecedaeaebbbbadbbccbeaebbaddbcebaabbdcbebcbeadbeabadceccdeddcaecbbaccdacbcbbbcaebeccbabaebcbeaaabdbbcbdaaccdbcdaadabcbaeceeeaeebbcdcabedbcbbdbdeeeadedabcbccbbbccececbdbcaecceecccdaadeabebdcdbbeeccbeadbccccdecaeebbabedadeeedacaceaedbccbbbaecdbbdebbdcdcbaeebbddabeabbeabcbdecbcdcbcbcbdcbedceadaebdaeddbbdabcbdeddcdabcedededeccbeeabcaeadebccadaeeeedaedbeedbaeedecbadaadbbeccdebbbaacccecbcacbcdcaabbeebebcaebbdebbeeaaccadbcebbedcabaeecaaaaabdecbeceaecadeaacddaccdccaddaeeacbbecabcdeaabedbeedacdcdbbdececdaeecbdcbbecdbbeeddabbccddedabdddaaabbdabcbdaeebcedceccabaacededcceaebacbbcccceddcbcabcbcabbddaadcedbbddaaadebcccaabdeebcbdbabbedcacbbaddaabddbcbedbdcddeabeaebaaccccdedadabeddacbeaebececdeaeabaabdaedbedcccddeeebceeeabdbeeddcacbbbabbaacbaddaceeaabadababdbccedcddddeddbdaedadbcdbebcbcdaacedaacbbeeaaeacbdddcabcbcbebbbccebaebedcacbcacecedebecbbddddbbdcdbaeebabeabccccadbeccdbcccbcbdeadbacccbdadbdaebaadadecbddecdbdbcbbdceacabbbaeabbbbaecaeaababbbdaabaaebcbdedcaeddaddadcecdbabbbbbcbddedcceeaaeebedeeebebbaedbbeecdbadaeaececeacddebcbcaddbdbebdadebeabbeeccdcebdebaaedeacddddacacdeaadcdbaedabdddddeaebdaabcdbbedeeeeadebbcbebcacdaddabcaaaecbabeaacdbcaecbacbebaabecedeedcacdbdedeedecaedeaedaaeccbabccbbeccdbcdbeeedcabcdaececdebbaacaeecdbedacbecdabadacdbbabcbddbdecabedeaecddbacbedbdbaabceddebbaabaaddbcabdcbdededdbdcabcacdbaecdbadcbdbbebcddaedaedccbdccabadbbcdcceebbdadebeeabbbbeeddaccaabadebcbcdbdabacbcacbaeedcebabedcbdbbcedcaaeccaddbdabbbcbdcdaecdbddcabceabdedaabcdedeeeabdaeaacbcececcadccebaceaccebebdcbbccadeaaeeebcbababecccdabdeadbcbdedccadddecddcadeebcebeacebecccacbccecdaeecedaacacaccddaecbdbecbbebabedabeaccebabcdaedceecebdeceaaaccedabccdcecbbdeddecadbdabccdbbadadbabaabdccdaaacaddbceacadadaadeeddcdcbbddebcabbaaeeccdddeeecbddbbaaababcedcdaecbbdddcdaedadedbccaeecedeacbcebadbceaecdabbedceeecaabceecadacbcdebaeedaaaaacdcccddcabcabcbeabeeccadebbcaedaeadccbdedacbcbbaaccdedabdbbcdaaaddbbaabacabcccededcbaecaebddbeaaeacbecbadecedbdddeaaecdedbdbdaccccdeaceaacddabbcabbadeadcecbedacbdbddaeabacbdcbbbacacbdddedeadddcbdbecbbbbbbaccbaacdcdcccdecbcdcbbcabcbeccabbeabecedabbebcbebeddbebdaccdcbeadcbbbcdbaaeecdcabdabaddedceaeebaccabeaabaecddeabbbbaecedbaebcedeabbbdbecbcaacccabaccbeaaceabdddeebaedecaedebecadbcccbecebdeacbedcdcebdbcbcbeababdedeceaddacabcaeadeabebebeebbaeabbeddadeaebdcdecabdacdeacbceeaebacdccebddabcabedbaadebbbdeaeeebabeaaccacddbbdecabeeadadddceacedeaccddbdebdaabeedaeabeaadcbdcbdeceeceaaeccabcdcceaedceaecaccacacaccbcbdddcaccdbeccbcabaceeedabadacdaeaeaeeebaadcbbcbaebdaaecbbccdbcddbeacedaedabbaebcddbccedaadeccbecceeaaadacdaedecdbabeedabdcedccaadcbecccdbdacddcbdccabdeaabaeceaebdcbacdcecbbaadbcabdcadbeabeabbebeddcecbebbeccaaabaebbacabecdaacdaebbecebecaeeeabcbcaaadcadcbdcbdebaaebebabbbddeaedddaebdbbbeaccdadedeacddbaaeeacaadacdcceadccacbceecdadcdaaeeadaccbddebaaeeeadacdaaeddebcacebdebbdddadccdcacbddbbabedacbcbedcebecbdcdaaadddaadcaadcbccecddebaabdadaeaacacdeaababdebedccedeceeaccdbaceaebdddcadeceacddcccdcebbdcbaebeccceebdeebddadaedbebadeadbededbaeaacaaaaeeeeebcddeabebacaabbaacddbabceacbddbdbcebeacecedeceaedadbadaccabadbbdecedebdebdbaeadeceadabcbccbcebbedbaebcedbdeaaddecabeaaddcddddcaaeccdaaccdeebaabbceaedcedacedcddcbbdbcdddbcaeeecaddceacebcccedacaaedebcdccedaaaaeddcaadaecdcedeaeedaacededcdeaaedaedbebcbaddbedabbeacceadedaadcacbbcaedcabdecbcaceedeadeedbbeccccccaabcccaccebecdecbbcbdbadebeeabbadaabbedddbeadedacebcecbbeebcbbacdceecdacbaaaedeacdaaebadebcbbbeddcbeaedcebeddbdaecbeddbcaabaceeeeeacaaebbeebbcaadbdbbabebbeabeadebdedaaeeabdcceeceedddebaadadabddedbcdceacecdcbaabbaadcdbcabdacacbbcccadedeaecdbdbbcacabdddaddeebaeeddeeecebdaeeaacacedddcaebeabdaceccacabbeccebcbabaabbabaccdebaededecbbeddcedddaaecacedcbcdadaeebcebaaedcebbbcccdcaadadccabbccccbddacaaaabdccedaadbbebdcddbcabceceebcaeebeaebecbbdcbecdbebcaaeceaebeaebcddecaeaeedabbcbcbbedeadcecbedcaeeaedeebbdeabeaecabacccdcdccbdbbceecbcdaabeceadaecaecbdbdaebcadddaddcccddaaceccebddcbaadcecebcdadaabcadacaadceebceeceacdacaaabdaecabedbcddcbecdadadacaebbaebeeeadddcdeabbcbbcabaeccdecaaadedababccceeadedcecacaecceddecadebeadedbbecceddcabceabacdbeaaadcdaabaebbadbddeddedceacecdacacbeedbdcbcbadcabeddacbaeaaaaaaabeccbcababbecaaeddecccaacdaeaecddbeccebeaaacbbdeeaeedccbcedbbedabcbedaddeecbadacdcbebddbcbcedbbeccdacacbbcecaacbbcdbeeeadacccdecbccabdaedaeabcecaeccbeaeadddccdcaccbcdcbcecaedabbeeaaacadaebaaedddbaaaeddddbebbdcbbcdcdcaeaabedaebbabbaaedddacbcaebaecabededadedbbbceabdeccdababdcdeeacbedbecbbdcabceeeadaebedbeaebececabcbcdcaadaceaecbcbddbccdddcbbdaabbddaabdaeecadcddeddadedbadbeeaccecdeacaeacedbbaaebccbabcbcebebccbccacabaabdcdbcdbaddbadbbdaddeaeaaacadaadaebedacbcebacedeebcdbdbaedbaaddebaebdebeeededacddccaeededbbbadcbdceabbdcecdaecaccdaeebdaceecabdaadadedceddecdecccdaedcaaedbeeedbacccceddcadeeacdababbdcacbdcdaceedceaecbaaaaaebcecdedededdaaaaececeedaaedbdaadabcaedceadabdddbaeeecdeabadecbbbedeadbbabadbebdabbbbcaeddaaedceecccebecbdabccbbdecdebecdbbdadddeddbcaddaeecdacabbadedeaeacceedbeddabaaddbbcddeeedabcccbcdddbdbeebcbeeabebddaeddeabeaeadccecbddbccecbddccabecbbdeeddbddedceedcedacccedaaaaaabcceedcaecaaceedcccbddaddceeeabbababeabacaaedebedbacabbacacddbdadbdadebceedaebaecbdcaaccabbececaeadddebdadabecbcebbbdbbbcbbaddccbbabadacbdcbdadcbdecaabdeaaecdacaaaaeccecebdabacbdddaadaedadaaebedeacbdaaedbbddbdedeeabecdeacabaedaedbeeeacbceadadbacceddeceadeebcedcabceebddbecbddcedcedcccceacbedeeaacdecabaacdeaadbcddaeaeacebecbabddcbedcaacdbbddaccbcebeaaaebceeaeeabaabcecdaebcecbbdbedaeeeadeeddcabdbdcbaaedcacdecbbcabcdbdeccbbeebabebdebacdbbeeadeecbacbcdceaeadcdeaadccbacbadeccadeeaabaaabcbabdaeceddadbacbbaabaebcdbeccccbbacdedbddeabeeeebbbdbcaedaebbbdcebdeaebcadacebedcebbceeeeeadbbbebeccbdadecaceeabbdaebdbbaacddcdcbcbbbecbababbabddedcdacbbacdabbceedadcaeacbeabedbcecbbdaeebddacdbcbcbdecaadeccabaabcdcacabdadadceddcdaccacebdeceaeadaecdbceddedaaeccbeeebeaabbbaeebeacacdedbcbcdabdeacedeacbadececcceebdaecbebddeacbbbedabadbcbdeddaacdbdbbeccacdbebaacbacebacadeedececdecaeedcbbbdeedbccecebcdbebacaaaddbbacdcdbbebedbbcaeddeecdaacccdcdeeadadbcbdcbbaababceabecdeeeaccdbdbbceabcbbceeceacbdaeecdaabdcbeaeeededaaacddccebaacddaaecdcbdccbdcbebedaacddabcdaeeacaeddddadaadaddedcdcddeacbaebadabddeecccacdcecceaabbbababbdeeeedcbedeabdcbacbbcdaabededeeacadbcecddadeeecaacedccaecbacddabdcadacdbcdcebdaedceabeeebebaddbbeceedddadbaaadcbdecedcdcdeaeabdeedcbbedccbcdbbbededacabdbaeaaecbccedaaeecdcbadaeacdbccabbabadbdbdaeacbbdbebcdebcbcecdacdbaadeccddeaababcabddeceddccacdcbeecebcceeeceeedabbdadcbdaceadaaceeeedbccacbdcdcddbeabbcbdabaedeeedcebaaabaeeadbecbcdabeacbabcbbecabccdadacccbedcdddcbbdacbabbbdacdeacecabeeadbdadedbaebadadccddebceedccdbbcacbeadbebaecacabcdbdbedeedcabcdceaebdaebaaeedcbaeeebbbdeebdbbcedeeccacbebcccabedecbccedcdddbccbbcaaecaecccedaecdbeacbceecebcedcbdadcbedaecbedccbbbcbadddbbedcabbdcabccbcedddaaeebeaaebacdecdbeaccdcbacddaabacdababeceaaadecbadbeddddcaeedbeeadedadbebdcaecaaedecddeabdbeabacbacdaebabbacecdadcecddeeedaeceddbdbcdddcececaadbdaadebbeddbeeeeddebdcadcbdaeabadbdabcaecaededecedcacaeceaabeeedeacaceeeabaecdcedcdacddebeaabbbeebcaadeebabcbbbaabdacceaebddbdbdbdaeeeabbbaeaedbbddbdcdddeaceaacecbaeaeacecbcbdbbdcdbdecbbdacdbedacdabcbdbdaddadaaceaadbcabecaeaecddcaadcedaedacdbdacccaedbeecabbcedacbecaeaedaceecacdadceaacccddbeeaecebaccdadbdabeeacacaaaeecbccbacceeadbbcaaaadbbcdcceccdadcaddcdedebeddeabddbabbdebdbaccacaadaebecbceebdbeaceacbcdceeedadaecaccdcaabbeedbddbbaaaabeaabacdbaeaaadcbdcbcccbaeaebcedbcdeacecdadcedaccbecbbeeabadbdcdeecaeabbccdaccadccdedecdddddaedeaddadacdabeaddeeaaceccadabcddcdadaeeeaabdeabecadcdaaeeddbcccebbeceaaececbbebacebcacaecbdddeaebdbecdeabedeceababadbbbcbbcebbacebdceaceebbbebbcccedebacdadecdeecedaaecccaeadadcacbaedabdbaaddcebdcccabcdeaeabdeaabcacccdceaebbceeedbeaaecbaccccbebdcabcacaceacdebeedabeedbacadedbaaaacdeddbcbceaabbbaecedbbbcbcdcdcbacdacaaecadbcdeaecacbecebedabeaabceccbdcbeecbbbdbcbceddcbadabbcdebedabcdcbedecdcbcddbcbdacaaebaeeccdbccaadeaccacedeccbeabaeddebcadeecedabeededbeacdebbcabceedddabaddbbaccceabaadeeddaeaecbcaccbeacdedbdacacaaeabaeadecaaddaaebaecdaadcdbbcbcdedbeabacbeacabeedcddadcaabdaaeddacdbeebdbecececacaeaabeddcbcebcaadecdbdcccaadddedecddebdaeadbeabaadddadbdeedcaaaedbbeaddabdeaeeaedadccbeedcceadacdaaeddabbcababaeeabcbdaacadecedaccddcdecbcbedcecadebbeebbdccaddeeecebeeecebabddccbcbddcadedbdbaedaabbceadbccbdecbddecdbceddadeeaeddcebceedceaeecedbdcbccdcceadbcbecdcabcaccdceeadabdbceeebecedddecedeccbdcaecbeecddaedabbbcbcdecadeccecebeeacacdddbccedcdbdeeacacadcdcebebdddbabacbcdbdadcabcbbedacbedeeeceeebcaeeddccbbcaccbaecdcbcdccabbbeecbdccaacdcddbbbcacddbaaadecdbdceaadebddcabeacabdeeccecbaababacdaeaacaddaeaadddabeddedcceccddaaaeaacaecdacacbbdecccebecdeaeabddaabeaeceaadabedbcebcdaaeecacbaeeacccdcdccdeebabceecdeeddcdbeccebceeddcadcdbbbccbebcadaebddbedbaacccacedcccbceabcdeeeddcaddeeadddcaaabdcadccdedbdebecabeeebecdedeadeedabdebececdbdbcecdddabcaaecbecabedaedebcebceecececceebececaedecbaeaceabaceebdeedcaaabadbdbddaabcbbcccaabbeddadbdcceadaccbbabedcbeeadbebbadcddecceeaaecebcbcecabeaeebecdbabedbecdbedaadacdacacaeaecdccddadcebdadceddaebcaeededebebececdcbedbdedacebceabecaadbebedddddbdacdcccedbcdcddceabcbdacedeabeeacbaabbceeebccbcbaadeaabcbbebecebcbaabadcecabbeddedcbbadebaebdcdbeeabbcabebdbccceaaabdaebbbbddecacddcaeccaddacabacecdbddddaeebbbdbcbbcedeebcaebaddaeacabdebbeaedddececaebcdbdadddbbdeebaecbadeaacbcdeebecddbbbdcedacaecacccdceabbdcabbecceceeecebbbbedceaceabccaaccacccbeaeebaabcaaabeeeeecddeedbabbabdacdcaccecbcbaeceaeeecbbdeaeebcdbbcaaaecdcebadbcdcdcebbddcdaededbcedbdcadadebceabeeadeadcdeccddccdeaecdbdcdedbacdababcaadbaedeeeeecabddbcdddbbabbacdbdacbbacdbedbddcdaccbabddbbeeccddedcaaacdbabadcdadbeacbdeaaebabebbdaaadbbbaebecbbdbeacdbcbdbdcbdeaebeaebdaabcddaaaebaaddccadaccbadbbbdaebbcddcebdbadccccabbacaccbeccdcbcccbebdedbeacdaddbecdcddeebdcbceadacbacedcdbbcceececacabdeabdeaedabbceccceceedadebeebeddbebbaceedeaecabebebccaacbbaeeabcdcaebbdbcccebdeabbddedbccebaaecdcebcdbbdebcaeedcdbdabbedcbdeacbdeeccecbbaceeebecbbabaadcabcbacadcbdaecaabaceacdeebccadadeddacebcdcdbdddbbbbbebeebcceddaaccebbdadeabeedcdbceaebcacabceceebbaeedbaeeecdabcdaaabdeecbdbcbdbbbdaeeadceecdbabcddebebabbdaabaebccaebbecedaebdebbbceddaedaabbcceeebeaedbddeabaeddadadbacbdecbcecdadcabcbadddbdadbddedadbaeccbdcdbedaaaddeebaeadbceedcabcbbbcbdcadddaecbcabaebaadbeabddbdcadbbcbdadbcbcbecacbedccdaebceeedabcacbbabcebcbdccdbababedcdbcadcbdbdadcccbeaecdbaaaabdebbbcbccbabdeaacebddecedacaaedeaeedadeeecbeeebeeacaecaebbeccaccaecceacabaadcebcdacaebbbdcecbdeacaebaccccdcaecebaabebacaceabdcceadeaaceedcbddbaeecabebdbcbbdadedededadbaecededbdddbdababdcdadadbbdddcbdcbcdcaccacccbddaddcddabaeebeccebcbceccbabcaeebbeceaccdbacbbeddddddaddaeedcdcbedacbcadbcbbedcdceadeabbbbabbbdaacdadddcededddeeeccbecdbbedacccecbddbecaedcbaeceabeebbddddceeaedcccacdaceeacabdcabacbcabacaeacbdbaedddeddddbadadbccbbcbcedcdeddecadaaeceeecbecbbcdeecdaeecbbabbddeeabebcddeeacdbdebeceddadeedebcbbabcdadbaebcbaaabdacaeddcbeccaeabcccdbcbaaadcddeddecdbdeebdeeddabaeecaadcebdcaabeeeeaceddebacebeacecdbebddcbdbbdabdeaaeeebabbdebdbbcaccebabadadddeecadebaadcdbeeabcabcbdaeedeccaaddcbaaabdbbbadcdebbdeaddbabddadcedeaedbbdccadcbaeddeecaabdbeacbabaedacbaaeaacdaeecdcadabcaddeddbdadbebbedbedacaacdbceeadeaeeecbaedeecceccaaecdebbdccecddacacecbbdcedaccbeebcdbbcdbddcccaaedccebcaeeabeadeaedadabcecaedebedbbdaabcbdeadbbedadabccdbceebeccceccbecccbcddcdcdcbbcaabcdbaabdaaedabdccbcdbeaacabedebaadaeaedbedeaaaadaeeecbdabcdacaaaeecbbaabddbcecbcddddcdbacdbceabaaecbdebdbcddebbabacbcebaabcddbbbaeabbeccbaddeadcbabceabdadebaaacaadabdedabbacaebbcbecbcebecacbadbeedbeacbdcadaedeaccaecebeedabbebbddacbddecddedcdeccbbbdbdbbacaeededcdcdcdbdaaaedeabadbabaecdaaccedbedaedbdcedbeededdbababeacbeabeaeecddaaddbbebedaddadcdaaabeacbbeccbceaadaebecabeedcbcbecbdadedbdddbcdebbbeedcebeedcedebcecdaaacbdaddbaeecaddeaacbccaadbabcaecddadbcacaaacbdebbdbeadeabdabdeabecaacddaceebebcbdadeaebcdeececcaaeeaccdaabadbaceedceaecddaddcbbceaeaaecaaebeecdaebdeadaaebddbcbdecbebbdcecedbddceceddbddcdeceeaaeabdcceddecbddbeeadcaebaacdccedabdcaceedaaeadcaaeddedeabceccabadbcccddeaabdcbdcbcadeadadbcdccdeaabeeceeceecbcddcbacdbbbecbddabceacbabeccdbcecabebbcdbbbcabbddbdceeacaabebabbaedacbeaadadadeabbadebbeabcdeedbebdabbbcbadcedbcbddeabadecedbbbeeacdddaadbaeceebedaecdbbcabaedcbbcddabadbaecbcebbdbeaddecbabacaeaeadcedcccbdcdaecccdcdcddccadddeabeddbcedabeeabcaadbbbceeddaaabeabbecdbabadabdbdebdddcabeeccdbdecbebcbbeebcdbbcbbdceeaadbaedeccbecbdeedddcebbaeccbcdbcbcaeedeaabeecabcddceddeebbaeecebbcbdebabbbcdacebbbeacaddddaacaecbdedaecadcddbedbaecbccdebbddddedcdccbccbcabeabbabdddadeacabeecdcbbcdceedcdcababbaaceeccadcdcbcabcecbedebaeedeeccaaebaedceeedabaaaeeebdccabcbaaabecbaedecdecacdbccbabbccebbaccecbbceeccadbdcebcaccacbeedbaaeaceaacbbbebabeddbaadeedbccbcedeaebeaeccaacdbbcbeaebcdcadeaababcabccaededcebaddbcaccdbdebdccccbdebaedaddeceaacbbecbabdeabcacbecddadeccbbeacaebbeeacbbbadeccbdcadeeddbbbbaebaedadecdccacdcabbacadadedbdebeeeeeaecdebddddebeedeededbcaccaebcdabecaabbcbabbedadaaebeaceaadaaeebbcdcaddeeeddccaaaacceeacdcccaceeeddaceaecbceaecacbdeadcccccceabcbeddbadcebccdecdbcdaeeabbabcbbebbcdeceacededeebcadaeecbabebdaeacddaacabceeecbbeeeaacceeeacbbabaceebdadeecdaadaecbddadeaeedccbacccaaaabbaecccdeaddccacbdccbcbbacbddebceaabddccdccdcaceedccaebecbacbcdcceaaacccdabecacdbcdcddabccdaabaddccdeedcaacaabbaacbcccbdebeeceaeccbaabdabdbdedcdeeedbbdeeabdadadaacbcadbaadceaabbeddcdedbdcbeaccbeaeceeccabccabdaeaceabbcdadbbecebdeabcabcebbccdadddabcbbbecdabdbdccedcacdcabbbdeeeaeaccebbbeaddbdbcbebdceddbaeebebeddababacabedcdccaeaecaeaecbdaaaecccabcbeddcbeeebacbcebceaeedeababdeeddadcdbeaeddbdbaddddbcbdaadccadedceceeeddeddbdaddbecadadccbdaedcceedcadbaeddacbcbddedddcbbbddcaabebccebdbadddbcbedaabcedbababecbcdccddcdaeadabeeebdcdbaebedbaabacedccaacedaccbaedcbcbedcbdaeaeddbcddbdbdddcbeebebccbaacbcebddababadaccebadedbabdaaececcacbcbdbacebebebdcaadbecdaabedcbabbedeecbdebcccbaadbeebddadadcedabadbcbeacbeacbbdeddbbcabdedaacaedbbebccbecebdbaabeadbcaecdaabdaaeddddbadadeccaccdabeceaeacaecbbdbccddcdadcebeeeaddbcdccaedcbeaabdedddcccbdbaddedbbdadebbbdbcecbbadcecebadbbddcaddccedeeabbeddbbaadbcbcbebaddbadceaddedadaadabceceebbaeacebedacacabbaccdcdebbbeeceabceacacbadbdbcbeaddacbedcbecbddadbddcdbedacacaedbaccdddaaebeabbcbeeceaeeedeecdbacacbcabddeeebaebdbbddbaaecdccdedebdcddddcedcdddcadaacdedbceebeacdcacbecbccebecacaaabddcaeacaedebaedcdebeceedbcdeedaaddaeddadeedeedcedbcadbecbedabccaeddecbadcaebcaddcaeaacdadbcdcebcacedabacdbbcdbdbcaeceecddddeadcaeaebcbcaaceecdbdededbdacdacccbcdaceadaceaccaeaadacaebdaeeebcdeeddbcdcdbbcdcedcbacbbbddcbaccdadbcdeaecddccaaeacccecebebccbaabdecebddcdbaabdccddaedddccadaaeeccebddabbaaacdecaedddaecccaddceaebaecdedeabccadaeebdbcbdbadbeabecdcecdeccebeacdcdaddcbddbcbbddbadebadabbdcaeeccbabdabaecacdceabacbdaddccabaadabcdaddedcdbeeddbecbdccbbdddacbecdbbbbbcedeacacdaebcaebdcdcbaebedcebebbdbadecccecadaabcdbdaaaccecbdaccbccaeedcbadacbccedeaadaecbeedcbbacddcccabaabbccbadbebbaeadecbdbedebbdcaaaeebcabeeabcadbbbbbeeaceceadcdbbedaceaecdcbdeabacaeecadbeddbbcadbeccaabacabcddaabdccedddbbecdbcdcadedebceccadeeaddabbbbddcaabeebebedbbdecddabdbcebadcacadecbcbdbecddeedaacbddabbcedbedcbacccdecbdaabcbcaaddaeeeedbeceddcdbcbacdbaacaddbeeecadbcedaceedcdedacdadadadedcaaacbebceedacddcacebebbdbcbddbdbecddacebccdeaedacbbaeadcdbaaecceabcbecebddbcebceccdcbaaaebcaabbeeacaaecdabcbdeecddedadaddcccccbdceadacceeebaeaedbbddabbacdabedeabbeddeceddcbbdbeddabdbcbedaeadedddaaecbcecaadbcbccddecacaceaecbbccabbbeeabddabcabeedabcbeebeccdabcebbeedaaeeeabaeccdaebdbbddbbdbaebaedabeaaebdbcabbcdceacbdcaeebddadebacbaddcdaedceaedaabddcbabacadedaeebeedbcaeabdbedebbcbabdaaeccbdddbcdabbceadbbaaedebceccbbdacaeeedacdceaecccdbebcbdceaacceeaddeadadcdadedabbdeedeccaaddaecabbcccddacbdcdcadebebccdbbddbddebabeedbdbccdeddccaacbebcecdccbcbabebabeedceeecebaabbdadaaaabcdbcecdcadebbadbaddbcecbadeaaadaaacddacbbcdccebaacbccedeececdbeedebdeabeeedcbbacbbdccaeedbadebabcecaeeceacbdecddccbbadbbabbbdbcdeccaddbaadeedbeebecebcdbbbbaacabddabaecdaddbcdaeadadaaeeaaddaaaeaebaeadadbadbeecebdadeecddadacecddabdabedaabbcbbccdaeddbedccddcddbcbadbdcddbbdaabbcdcbeaabbcecbebbeaacdacbcdbeeccbccabddbdeaedcbbdaccddcdaaabeacdecabcababebdaedbeeebdbdadaaababaebaceaaeceacbeecebaabcdbdaddccbdacabaddaeebbcabbdeedbbeeccbecbbdcaabcdcbcaceedadaacebbdcdaaaedcddbeccbebaedddccbeaccdddbbdcbeaeacaacedcbeddcbaddaeeccdcebadecbadbeaecebbbdddceacccdaeebcdcdbdddbacdddeddddbebbdcbeebedccaaddcdeccdaedbebdedebbabadbeaccebaeaebbcddcceacbedbbabdcdaddebdedaacdcecbbebeccbdbdbdbacaabecdccdccaedcbcedadbeaedcbdeaecccdaaddbbdecdadecadccbebedcdbddcdddababddbeabeccdbcedeadcbdbaceaceadaaebbbabcdcdaaeacecebbbebbcceeceaaeaaccecaaebcaeebbbbbbcdbcddeaabcaaeadbaddebddbdbadeebbabeeedecaaccadabaeedbedcacdbcccaabbeacdabccddebeacedcabbbcbdbeddeabdaebbbdccecddbbaaebedcaceeceaaecdcaabcaddddecccbacbabdaebecbccbbaebcbbdecbaaeaceaaebbdeaaacbeecaaaedeaebecbaaaedacdebcabadaaeedbbbdaaeebbddebcaaddcccaaecddeeaedccebdabacdeddedebcdacdadedccabccbddebebbccbbaaebcabdbddcccccaeccadabbeddbedabeebcdadcebddaaaedbdadbcebaeddcebbbecbbccbdadaaddcebdcdaaadccaedeedcbeecebcbadedacacdebeebecbceeedcddbdaebdcbabbbcebadcadbbeabbaaccdccdaaeddabddddbcecebecbabeabdbccebbdadedcdebccddadeacaeaedbdceeeaeccbbadeadabaeebdbceadbdbccbccdaceceecadbabcaadeadedaccddeeaadabbdeaaadcacabcbbcadddaccecdecdbadddcbdddddeacbdddbebbabebceebedddadedeeccebdbdbdebbabecedecebcccedccbabdbbbacabcbbcebddacdebcbbadaaebecedccbaacbcdebcaddeceebcbdcbdccbcaaadcdbcdddeddeecebcdaecdecbdeedbdabebdebeebcdcbeddadaecbcdaeddeebcdceacdeadbddcaacccaeecbbcbbababeebceaccabdbddeccccedceaeaeaebbdcbbbcdbabeadcabedbddadaebdbedbeadacababadeeeebeaacdaaeccacdacacbdecdcecdccbaedbdcceeddadccdedaeddeeedaebceacdaaeaecbddccaacdeeebceadbbdaeabcdcecceddcbbbcbdbeaebbaaddadbdebbaabeaebccdacadaeecaaededaecbcdbebdbdabcddadcaadecdabbadccbdcbaeebadacdeecdbeeabeccbaeacbaddaacbcbccbecbebbeaabccabdeaeaeabbcbcabcdbdbbbdacdbdaccebebcbcbecaedccadbceaccdbeeeadbcdacddeaaaaebcdbdeeadeaddcccedeadbbbacdcadceadcbacaaccedbdeeddcbebeeccaebbececeacccdaedaaaddcecaecccbebcbeaaabaddcccedeedddebaecdaabecddeebcddeaccecbaebecbcbbceabebcecacdcecaebaebbcaabbceacddcdccebcaedbceceddbacbcbdaeacbeddcccaacbcbacbebccbdadeaeabbbaaaedbabcebabeccbabccabaddcdbbbbabadeebbbdebcdbaeededeabddeeaadaebdebeededebaeddbcdcedcadedeadaebadacdcdeebcaeaaeabbcebaccececbeceeeecbbdaeeecbdbcebedbcadbaddbadbdeaaebceceecbebebdabadbacdaebecdcbeecdceacdecabedeabaaaaadebbadbdbedabceaebeccdbbabeeedccdcaaececbbbaeacebdbdcaadaaeeeaebeadddecadaeeacddacdadadeeadceabeaebabcddccbdcbdcdaeddabbcedadcabeeadbacadeaebbdaaecacaeedaadbacddeccbdacbaaddccdbddbceaaacdcaecbdbeabeaebaaeecebeecebceeabcbcebbaecbcabcabeaecceedecdcbceedccbddddccdacdbadeabbadcbaedbbddbccdcdbeaadeababeadebedbcdcaecccacbdcbebccbbbdcecaacadcdbabdadcdddccdebeeecbbaedeaadebbaeacaccaaacbabebddbedbadaccadbabaddccbeaadaababaeacebbebdbbacdaaabbbddcdaddcddbbaebabaebcebedebbebdaceebabcedacbccbbaeeebecbbcadccceaebbccebeaeedbaebdbddaeaeececcaacdeadadadeadbdedaabdadbbeebdbebaddaadbaaeecbaccdeabcdeabbdacbbbddebcaddeeebaaedbdabdeabcacbdceedbacaceabbeccbccaaadaebeccdbadedbeeacdacebeeeebdcddccdaaacedbadddaeaabeadceaaddaebcddcaddcbaccddacdaedbdccbbbedeedcadadeccdaaaebcbbbdabddaadabbdaebaedaaaeacedabedaccaadcedbddadceeccddbedcaadbaeddbdedccacccbbdeeaacbcebbddbedccaaebaabededbecbaaceabddaddedabcbaeadcdbedcbaacbdacacddccccbddaeedaaadecadadbaeeabebbebedaaadaccdbdaeaacdccabdeeacecddeeacaecccebaccbeeeaaeeaaeaaccadbacedcceccbacecedacecacdcbedbcedabedeadeecdadadbaedbdddecebdbcebdcabebabecddbaecedacebbeabddccbcdbeadedbeaaecbaaacbeacacbeabbeeececbcaabecbdbeccddadcbcaaacbbdceacdcebddadedbdbbabbeeadccdeceeedbecddebbaabacbecbdaabaaeebaddbccbbcecdcddccbcbcccabeecacaebcbdedcddddecdaebcdaedeaceadcbdadebcbabddeebaabdccaebecacaabeadceedbeddbbabbaabcdbbdbdbbcbeadcdbbbaccabcaecbcebaddaeaacbbbbdbcddadbccbceeaeeeaeaabaebadeacdbeaeaeebaecaccbdecdebedadcddbbeebbbacbeabcacabadaaaabcbaeedbeeedcbddbeeeeeeeabbaebaaaddaeaaadaeecbadcdaebddeebbabbcabdbadaeeadeabcbcdbbbeddcaacebdadadacecaebadbbdbaecacbcacecaedcdaacdbcdeccdadcaededaceccbdddeaccaddaedadccceadcaaeeedddddadbdddcbeddbbabcaaeedebaeddaabcdbeebdeeacddaeaebeaaeeeaddbeccccebccbeceaeedbceadcaeeaddbcabacedeeabddbcedaaceaeaadaeebebabcaeeaaeacbabababadacccecccbbdccbeadadcadadccdcaecaecddbacbbdbceeedebcbeadaebdcbbdbedabcdcdccadabdeadaadaacbebeeabbccaceadedcaceeccaabbbeaabbecebcdeddddeaaecaeeebcbacccbcaebdddadaedaecdebdeecbeebdeeaadbaaeeeeceacbcccaceacdbbeaaeccdbdbcdeaacadbdadbeedaedebcaabeedccaeeacdcaeaaaeedebaeaaccbceddcdbabaeeedabdbbecaccaaccdedbabdccbdaeeaadedbcdcdabbcaabedcaeaebddeeaaddbedebdeebabbbacebeadcdeddddcdadabeddadaccaabcadddcababbcceecedcbbbadcccbdaaceeaedbcdbdadccecacaeacdcdebabbceeaeceabccbbaadcaaadbbbdabeedbbedbbedeeebebdaeddbbaadeecabddbcbbecaebddecddebedeaacaccbecdbeceecaeeaaecddcdabcbbacddeaedbeabcaddecbaebbccaacbebcabaacceccccbdcdcbdaebdaccaecabbcaabacceddceccbabacaeaecacebddcbaaabdcdcdcddaebaddaabddedcabcaaddceabbadabdcacddeecacddcecccaebbcdbeaccbedadebaebebaaabbebdbbaaebaebaceceabdeddceeeababedaaababdeeeebdeadbacadcbdedbadaaacbadebcceebacdbbdccdcdedcaecdbecadcbcdcbeececdaceabcaeabbdeecedcdbebebbecaacadebadcdddbadabbaacdeaddebbebecbabccbdcdddecbcebebbeddeddcddeacbcbabecedadbcbdabaedeadacecdbabbddddabbdebeddebeaeaecccaabaccaaceaabeaeedddebdcbbeebecabaecdbabbaddbdacaccddaeadcdabceecebacdbcbaaacbdebcabadedcaaadbdedbebabddaacbbbcbdebceadceaccbacaedaaadeededaededdaacbaedaeabacbedcbcaabcbbceeeabbbcabcaecbbddcbabbabceebbccdbeabcacecddeeaebecaaaaddbedcdcadedcacbbdcddedaaeebaabebbeeadaedccedcabaadbcccccbbdadbddbbdccbdadeacabecdecbdaebeadcdebbcbccdbddabdecaaadcabdebeaedcedecddaaadddccbecebdcccbaeaedccbccaeaaaeeccdcbaaadbaaeaebbcebaaebbddaaadcdadbdaacdcdbcbacbecebbceaabcedaaabaebcecaaecaaadeddbbcbcadddcdaddeadcbcdcaeccaddeadcaddbaecccbcecdcbedeacdaccabcebbddedcccabedadecbceeacbeeeaaaebbcabaacbccccacbeccaeaacaecceedbbceebaaccccbbaecdbdddeabadaabdceeaecdbcbcccddbadcbdebbdcdabbcbabbbbdaedbebbeddddbcadaebbaecbeebeabaadceeeeeaedbdaabedaabcaebaaeebecdddbacdcebeeaaceeaeddeeaececcaeeebebbebcadaacdcdcebbcbecccdcedeeaacaddeeeadacddacccabeeeecbeaceabbcbdcaaecadbeedddcabcbdeecadaccbebdcbdbcabdbccaceceaebccaabcdaadcedbcaaecbdaaabddadcebcddaacedaabebcbbabddcccacaededeeaaaeeaecedbdacccacedeccaebcaeaaabeceedbaadbbdcdbeaabeeebbcbdddebedcaacdcdbdacbdbdaacaeabbeebbcceeeebeeddecbebeeecaecdbbbabcedcdbcdaccdedbdcaaaedbcbebbedaadeeabdbdbcbcdebaabeaaebaeaceaeaedcdabcdcadeeabdbcdadbaceedebcacebcceebcabcaacdbdbeeabdcdadabaebdaadaaeecbbebbaccebadeceddabacebcddbeeabdeccaebdaeaeebdbeeeaadeceadaaeccacaacedebadceebbadeccbbaeedbdaadbeabbeeaedcceadbbcbdebcecdccacdebeecedbcbecabdccaddbcdbbaeeaacdaaddeedeaaebeeeceadccbdaeaebaebaacbeecdcdeeadddeebdabcecbdccedbcdebeedaaebaddedbadeaecbcecbadbeecabccddaebbdacdcbbcbdeccddedddbadcbecacdccdceadaaccebaccdaaabcbbaeceeeeacdcdabacddcbaebeacbebedaaadbbcadcbebcdaedcacbaedeabadeeeaddbbacabddbbcbcddaaddceecaeacccddedbdedaeddbaeddebbcdeeaaeeaaaddceeeeabeddebbcaaaacbbdacaacbebabaeedaaebcaecdecbaecaceccbdedbddecadccdbddbcbeadabddeebcdceeddeadebdadebacacececaadcaaddeeededecacaaabeeabaeacbdaaadadaadddbaebdbebbbdbbeababdcdcbcccacaeeaabadcbeacaaaeaeddcabaaaaddbcddeccaeaadeaabdbedcaaadaecbaaededaedcecaeadaabcbaecbaeaabddebbcbbaacabedeaceacbdcacecbeddcceeededaeeccdeacbdaaebdcdbbeeacddcccaabdadbdaacedecdddaccaeedadeecbabaaddcbbcedbbeebacbaadddcabcdaabeabecbbdeccebeabbcbddecaceabdceaedeedbabcaebeeebacdededbecdaedabeeddcaccdbdeaacbeaccdaccdcbbeebddaaabbddaeacdabdaaacaaebadabbebdeeeecaeedacccdeecaeeeaecbddcdccebdaedeabbcebceeceabeedcdaecdbaeecadddeeadddabeccdebebeddbddccccbeebccaeccbdadadcebeeacbbceaeacabadeceeeadadcaadabebcbabdaebadbaaabaaebeeeaecbbdbeebeacbcbebdadccbbecbdcecccdadaebdbebcbedabdccebcbbbbbeedeebdbeeacdadcedadbeacebeadbdacebdacacdbbdbaaeedeecbceedcbccddecdbcdbcbcecabaeaeeaadbdcdbadebccedaedaacdcaebceaebdadcedebbeeecdbcddeaeeabbadbbcdcbabaebcdceecdbadcaccadaadaadeecadbcbccbaebebceeaabcdbcaeddacdbdceeeccaabdbccdcccaaacaeaccaadebbddaeedddeaddaaeadcecaccbbecbdaecbdebbdecaeabddbaaaedcccebcaceebdabdcacadcecccbdaeeddaaecaadabcdcaacabbbcaacaaebbacadcadcdedbeabbaaeecbcdeceaaeecbcacaaddaedddbbdbadeadedaabdbdccbcdebaebabdeaededbbcaadeabbbabeaceeeddcbaaeaedbbcaebaeadcbcadbaecadccaabcebedcabcbaececccdbbbaaedbeecbcaaadadcdcaebabdaeceadbbdeccbacbaacdadeebcaddcbcbcdacdadbabbebbceaeaebbeaacecabaedeccbbdabdbaebabbebbaaaeaeddcddeabdceaeacabbecbabdebcbebbedbbcaaeebebcaebddddadeaeecbdaceaecceadcdaaabedbececedebdcdcaecccadbbbacedcbcdabbbdbabcebdaeaddaecaeebbbbdebceecdaaacbddeaaeeddebadeaeceaedeaeddbccabaeacdbedbabbcaaddaaabddbdeaabbbbecddcdbbecdbedabcddaadbeddbeceaaabbcacabaacaaceaccdbbeacaccedcceebdaadcdabadaeacbdaddbbcdedbddcaacedecbabdeebdbeecbbdbacbedbeebcceabdadabcbbccdbdcaaddcedaeaaebeaabaedeeaabbbeccbceaabacccebdeabedebdbaaedcaeeeadabbccaebdbcabcdabeacbccdaaabceedddbdbdadecdebdbbddcadaeadbcaccaaddedaecadbebbabdedcbdeeeeddcaacaecaaddebecabbbbeabbdbaaecbdecebdcdceaddcdeabcdbeabbcaaaaeadddbbcceccebaeaeeededdeccccbcbaddddbacbdbdcedbeeeaacabbbdcdaabcaeacecedcbbeadbbeebaacabbabeccaceaadcaaeceedceadabcaaecbcddcadbeeadedabcdaadcbdbcaedbbadedabaecbcacccabbeaaebeeeebaecadabcabccbcbdadbdbdcaaeebeddbdcccccaedbdaccabcbaadacacbdbbbdecdbcdbdbbbaeebabbdbbbbccbddcdeebdebdecedddaeacaaddacbbdbbacebcdcebcdaaecbebbaebababbaeebdccceccdbdeaeedbdacebbcaebddbcbbecddbcbdeaccbadaabacadecdcccaaaaaadaeacbaeecacabadbbabeebebaabcceaccecacccbadaabecaacedcbceacecdcababcbebdaaadddbebcbeebbaccdecbcabbccbedacaaacbaeaaaadcdaaeeddaeeadbccadbebecaebbcddabdcbbebddadcbedeadecbcdceabddcbeddcdeeeaeeabaeddaeeaccbecccdcbddddacbdbaecbeeeeecbdadddccaebbaeadabacecdceacaaadcdecedecadcecbdaedcbeedeeeadaebbbaceebdbabbeacadecaddddbabcbaeeeeeebaacdabedbceabbeaaedadacadeeaadbbacbbecdebdaadaacddbabcdbedcecdebcadeddcbbecdaaaaceeaeeebdbdcbaebdadabddeeebeeccebecbdddaacaadacdcddbbaeccaaeacdaaebcebebdebeddcbdccdcadaaaeddeeaacbcccaebbadceeadedcbeddbebbdccebeddeeeddbcecedccabddaecdabcdbcabecceaadeeaeaaebaadbeaabcddaebcceaeadecccbaceaaddabecacbaacbcebbdaedbdaeeedecdeacadcdadccdebccbaceededbabccbaccaebcacbccbaeadbcdbbbbbbeceddabadabedddcedadacccaecaaadeacadbdbcdaadcdbadbdeacdccdcbcdaeebebdbdaecaadcbabcaedcbadebdcebaeabcdbaccaacaaaeececaaaedcaadabcecaecacabbedbddaacbcddcabeacdbecbdbcdcbaaacdbaeceedaabddbbebcdbacbbeddccbcdcdceeaddcdbaeddbebdeadccadeedecedccedddacceaaebaecdccaadbcccbedbaadacddbcdabdedabedbbceddadcbbdecbadebaaaecbebedbccdbebacbabdcccaaaeaebcdaddbdcdeabbcebedebedddacbbaabaaeecaceeaaeaaeecbaebceadacabebbdaaddabcdaedddadcdabeecebececedebebddeebaeeeeeeeceaebdbcbbcacbdebbbcdeecbeacbddeacdadaccbbbdbdaceebccccddabeccddddecbbabcdbeedcbeacdeaecbaeacceacacacaacebccbbeedbdbedcaacbdababbcdaecbbaddbddbcdbcbacceaeeddaadabcecbacedcabddcdaacadcdcacbbdabddedebecaadcbdcabceabbbbddebcbadcbdeedbedebebecbabdbdaaecccadadcdcbabbeabbabbcecbbeababaedcabacdeaceceaeebbcaaaadbcdcbeadaaaebedccddaabdebdbdcbdbceaccccdbbbbcdeaddbeaddbacacacbbabdbdaedbcbcebcaccdcbcbeeddebccaaedaabbdedecdacbaaddcbedddbcaadbbdccaabdebbcabcedddddbabdacceebabbbbaccccedaaebeebbddcdeecceddddcacdcceacbbaeeccbcedbcecdbdbcbdeeddbcabedaebaccdbbdbbeeddacceccccaddeccbabababbabecceabcacedddccbbdbcacaadcdcaacceacdcdeedddeadcbdcbaaeedacecbbeddaaaeabecccdcdccdbcdcdececbceeaeaaaacdccbdadcabedcebdbbbbdbeedaecdaceededaaedabbedddbebcbceeaebbeacbcaebccdaeaebacabeacdeebebbaeedabbbceecbbbaebdedebdadcdeebadaddcbeeaebaeabedadbcdcbceababcbbceadecdaeacadecbccdeabbecbccbadbdaeadcceacddaaabddcbddcdbeaecaaddeccccceddedeadaececddddcdadaeccbbbebcdcecbeeddedecdedcdedabbacbeeabeecacceaaeedceabdaaacadeeaaadccddbaedcdacaccacbbeeaedabdabeecedcbdacdadcdcccccadecbdaeadceaeaabedacdadedbeeedabdbbabcbaccaebeaeaaeebdbdeceecadccecaebbbaddbcdbddadedbdebecddceabcbcbbabddbebbacdddebceeacdebdeecbebabebacaebcbedacbebdeaeadebdcbeebcbaebdbdcccecacecbeacbbcddcbaeacbcdbabdbaccdaabaadccddcacccdeaecdbebbaaeadbbeaebebbcbaeaceccbedadceabcdcbbebbcbdebccbbaebecabeebdaddececeeecbecddbabeebdbcabdebacaeceaccbcabeccaaceadbecebceecdadbcecaadbacbcdddeaeccbabacebbabaeacaeeddcebeabdeaadbbcbaebcacdaecbcaadcedbdaceecbdbdaeeaecbeeabbddadcbedbaaecedcbedbababcabdbbbaebcbccdaaaaecdcdcadceecbdedabbacbeaadcbceccdceddebebdaacbeeacaceabcacbebddcbedddccaabbebacbbdbbabdccacacdbebabcadeceaedddbeebaeecbcbbaeacccdbedddeeccbecccaecaccbcceeacecdabaeebaedadcaadaddceedeaceadacebdcbdcdeebdeebadacecebbcedceebbaedeabacacecbaabeadbcbdaadcdbcedcacedaeabaadeebcccaeeaadaccbbddcdaaeacedebaaabeedecaabceabaaacdbdedccdcbdebaaadedeccddaaaddbeeedecaccecebcbeadbadabbedbcbcdcbbbdeacddceaadbddaebdbedcebbacaadcdababbdcbdcacecdbcaddddaacabbdedcdbcccadcdaeeaadccbebcddadebebbabbbdcacacaeaabacbabeedddbbaccebeacedcaceedceddcadbeedabcbdbcacecdbbaeecaddabceabaaaacdeabadbadabcebcdedaadbbebedccccaccaabeedaacebeeddbecbcdebdeecadeeaccedcccaabbeddcccedcebddabebcabedbabaabbcceeabeceddbecbcbeadedceaaceacbabbeaacbbbdaebeabceebbadabbdbbcaaaececdbdbadbcbeaecceacebebccddddddeeacaebabbeeccabdccabcadadeadbcecdeecbcbaecadedaccdacdcccdabaeededdeaecaebdbabbdbeeadcbcbdebadedcbacdbcedeccadbccbdcedaadebdebaaedbbbeeedaadcecabddacbccbdbdaccbccceedbbecbccbcbbbeecebbeabcbbeeecbbbabccadeabbbaaeecbbaabaacbbebbeaacbdedccbecdbeddacccbaeebbdbbcbbbddadaeadcedeeaabdceecdebeeaaadcdecebcdcbddcabeadddcaeaaebbdbeacacbecccbbbdbdebedbcbcaecbceebdeaaadcdddaddadadeaeccdddeadaadeccabbeeeeadedceaedbdbdcadcdbebdadbecacdddaecbaeadbecdacabecbeeaebadddabbebccecabdadddabecccccdcaecbdabeedeeeceaadecadabceaebebeeaadbeeccceeabebaadecdbaddaaeabadcbccbcceaecbbecabeeeebaeaddacddadaaebcadeddbdceceabbbcdeaadbadbddacbdaaeedbbcaceeacdaabbbdcceabecccebeaaaaaabaacbadaabbabdbcebcacdbdbcdabdebdabbdcceadedcebdeebedcdcbeaccdedbaceebbdcecdbabbeccaddeeedceddecebcdcaeebbbececbbcbddcecebcdddcbdbedabcdcbcaadbdeedecdacdcdededbccacadcebeaecacedcdaeeecaecaacbecbeceedceddbebadbdddbdedeabdccbcceeaebbedbeebaaccddecbbbdddbaccadcbaeaacdabbaeadebcecedeeeddacceaadeceaabbeabdaebdebabbecebbbadaeceeeccdeacabdebdeaeedcddaabbdacaabeeabdbdbeeeabdbeccbcddaedebaddbcadaeabdcbcdcbcbbbaadeaecebebdacdebdcebbeebbccababbdaebaecddcbdcbcebabddeeabbbcddcebeddbeaeacadcdbabbacdeccadcbadddcaadcadaeaecceeeababbbcebcdbcaedebccdbeaeebddbcdeccbcabcaeebbccaceadaabbabcaaaaacbecedaddaccdbadedbecacababbeadcbabaebbebebeabedceabadccbcccadeecabadeccdbebcecbacbdeaceeabeabbbcacdaedaadcaecbdedaedddceadebeddbceacbabddbdbeadbecebbaebdcbcdceaaeadcacccdaddbbeaeeacabdaabcecccebeecadabebebdbadebbdeaeedeeaeeaaedaabadedacedacabbeeecaaeceecedccdbecabadbbadbbdcacadaedadabbcedcebbabdeccdacecdbccbcacbcaaeebebbcdcbbacbdecaaddadaecddcdbcbeecccebdcbeaabbedddddebbbaebcedeccdedadcaadebecaecbdbaedbadcebeeaaeaeebaccebceaaebadbdecdaaaecbebcdacdccadccedbeabececabccacebacdaddabdcbbacbbcaadadcbadbbcaadeeaeebdeddbbbbeacbcdedddecccaeeeceddadecccdcceecdccddebedacaebaadbeecacdeedadeeadedccdddccdecdbbaacbeddabaaeaddbccddabeaacebbaedeccbeecabdecbcdbaabcdbcaecdeeadaddacbdceabdddddcdbdadbebccaeeadabddedcdebeacbdcadeadccacacbccbbacaeaabddccdcdbeaadbaeacdecedcabaaaadcbedaddcacbabbaececeadbbcbedceddebbbbecaadcdbdbddceebaeaededdabaadadadcccadabbeaddcaecaccaaecbabadebdeaaeececdddebceeecbeeaadddcaccbbacadbcdcdabbecbbcdbebecaebdcacabbecbeddebeaeeabddbcebcbcacbccbdcecdadceababeddaccababedcebedcaccdbeecdeecaeaaedbeeceeeebbcbcbcdcbadbdedbcadbeadbeecadebceaaaeacaaaabceecadabddbaacbeebdbaadabdadccadebdccddcdebdedbcaeabadbdacacdcdaeccadeadeaadebebeaeceeaaeecbeeeeaaeaacbaaddbdedacadccdabeedbdebbbbdaccbdeedbcceacecbcbbaaaacaebbadeacaacbbadcdebbdaddbeedccbbcceabddabedcecbabdacabdcdbccceeceaeccabddedcbceaccdcbcdeecccabdcaeedccaadecbecbaeeadbebdcabccdcddaccdaaaceebdbddebcecccddadbbbccaeaedbcecdebcebedecbbbcbdedecbdcedccaecbceaeadbdbbccdccadaaedeaadeabceddcaeddedabcdadbbbaacbeceebaebdebadcaaeadbaceebcecdadeacedddabbbdcadaadeeddeecedabdabdbdceddabeabeddbddeaceaadacecadcbcccccdbbbeaadadaaecbcccbcbaeceadedbadcbbcaedbaedecadadabdaedebeeacaacccbebeccacccaceeeddbdcdbcdeaeeccdbcbddaaebecaebeeeecdbabaeceaccbedaadaadcbedbbaabdaebebbcaceeabdcbbedddeaadabdbeecbddeaeabceaabbebcaaadeeaeceaaaccdbbbbcaedbbadaeeaabcdedbbacabcceadacdbeecaccaddcbcbdccaeacbaacdeccaacddcaaaedaddedeaededeacbbecedcbabedbccbaaeabceecebeaaaaeccaadcceeadeaeaeebcaaabdbabbeebaebcaccacedabcceeebeecabbbbaeddcbdaeaaeaddeadadbdcbbeaacaecdeaeaecddcadaeeeaeaaeeecbebadabbcbbecddcbbddadaebebabcbbadceeeaaebedeeaaeccdceaedebaeedebbecbddabbbebbebbecaaabaaccacddcbecccaecbeaceceeabacedcddbadebbdceceaeeabcbaeaaaccebedebdccbacbcecbdebcceaaaadeadadcdbabeabdeecebddabedadeeddadababdeaeebdeedbdcaccceaeaadabadbcbdedeadcadcabcedbdacaababbdebceeddbccaedaeacbccdcedeeadaecaaeebeddaadbedbadcdbaeecdbdccdbdaccbdeceeaeababbbbebbedbcaedbeeecaddedcacebbaecaacccbbebaacebecccdcdabbdcadcdbeebbeeeecadcebecedbbcceebdbddedcabceddcebedacdaeedceadaadbecbcbdecbedcebcaeaecbeabdacedecdcacaeddaeecebbcedadeccdacbbedaebbbbeaddabbcbeaacbbacdeaebdbecbdeedadecaabbbdaabeabacddbddbbdaccddbbebcdbebabcaeaebaabceaaabcdcbaedbccbebbeadeeebdcedaadaabaaecaeeeaeecddacaeccbddbadbdbbaadddeccacadaaccaaddabebddcdebeabacbbbceeadacecacaccbabdcebcbddeebbbbbbdcadacbcdbbccbcbadcbacaceadeebbcbbdccccedceecdeeddcdbcebbedcedbdeccbeecaaccdcaadcadbcdcebaadbeccedbeaeebecbaddcdbdecebcbbebcebddebcdbeecbbbccddedcbaaddaddaaeedcadaedcaececcdebadbdcbedbbcbacccdeabddacbaddbdbebdcecbcbabdeeeeccceacaedbebdbbcbeecaadbdaddbacbceaedbbbcedeadaeadbebcdbcaeddebedabddbedaaebdcbcbcaecbdeccbceaaddbababbcdceddddddbaababaebddaebbbddeeccadecbacaddaceddcaabeeeecdaacbbbbbdeddcedabdcbaecebeecbdadaaaaedcaaeeaeaaddccaedcaaddabdeadaaaeadaeddddcbedbbcbaaebdadddbacbdcdacabcddebcbbceaebceaeacaecbaddccbebcadecaaeebadcabcceddcaadacdaabaaecaacbbbebedceecadaadbbeedbccccdaeeabbdebbbdaddaacbbaadacddcbbeceaabbbaeeeeacbcaddebcaaaecdcdddcebeabbbbcbabdcebacdabadbeddcaedabcbababdcecddceeebcccabaecbcdcbbcaccbdbbbbaeebccacecebbdecdccbbabebcdbcbddaddbddedbdbccaaaeaebbbceaecbdbadceaceeddaaedcbadbabbecdadcabcacecdaeebaecabaeaeeeeacebebdaaacbcabbcaabdcdadebabbdbeaceadeebdcaaecccaadbbcaaccdcddecaceaedcbbdbebdeddcddabbabcbbbdebbeeccebaaaadabebedbbabaaceccaebebdadaddeeaabedbdeccdbaebccabddadcbbbdcebbbebcdeaecceeccaabebddedabcedecedacebadbbabdbbedcebdaedccbacceadbdabcddeabdedbddaaecaddcdaedabbaadeedecdcceebebbaccaccbdaaececcababcadbdbecbbcaedbabdcdebdbbecbbaaebdabceaacecadaaeacbedbedbebaeceaaccdeadebacbeaedbbeaecaebaeecaaddcadcaeeaecbeeaddeedbbeecdbabdeddbeaaeeceeeaaadccbcdeaceeabacedeebaecdcbcacaeddedbecdbeacaeddcaaacaedcdeaeeececceeaccededabecbacacaeacaddbaebebdccdeddbbdaedeeabacccbbcedccaadabcccbbceaebbbdcbdeacdadaaeaebbbaaeeaccdaeeaaedacecceabaadceeeeebccdbeddaeadacecedccceecdecbcccadcdebbebeddadaabedaeddcebccbbccecbeeeccdacabadadcdccbcaaabcbbcbbaebaedbeddaeeedeeceeccedcaeecddbeadbabadeccbcaaedaaabbaabdddcbeaaacbbbddbdebebadaccdabceedeacadedaecaeececaaebcdddbcbbceaadbacbcaecbbaeeaadbadedacdabcdcedddbedcdbeabccaddcbdbccdceadebabdceacbbeedabecddaedcaccccdacadebbceacceedabcabbeaecddbcedccddebedaeedadbeeedebbecebcdaaeeedabdecbbcdebccedddadadadcedcbbeebddcdecdcdcaaaaaaabecebbdebccaecadbaedeaadecbbadcbbabcbaadeceadbbebeccdbdcebbadabcabeeadccedbdeaaeedddddabdeeaaddabaeccdcccecabdbbacbeccbadaedbedbccadedcaaeedcdcdeeaabbbcbbdbbaaceabbeabeaebcbdcbbdcdebebabbbdbaecadbbdaedecccdcbeccdbbdcbddcbbacadedeebeebdeebededabcaedccaadaaeccaccbbeedaaedecedecccdcdddcdebedcbbbbbedcbddbdceaabaacbdecddddacadecaeddeadccaaeccabdeebeddbdcbecbeecdaaaeccbcdddaabbadabcadbaaabadbcaadcacaaaceccdebedddaccddabccaeccbebbbccaeedccdcbeeadcecbbceacbaeeddebedabdbacecdcaaebdaebacaeabebedbebbceccebebcbbcdbbedcecaddabeadcadbddbeecddaceebdceeadecdbbceaaeeadbceaecccabcadedcceaeeddcdccccdabacaddbdadebeabccabdabddbbddbbdaaaaacbbcbedcbccaaabaccbcdacbacdaadcdebcdadccdcabdbbdcaaadadeedddedbbcdbabaeeccabdcaeebaddecdeaadabbaadcaaeebbbeadacccdbeabdecbddbeeececebdcaecbaaddbdddccaacebdecdcaaddabceededaaeaaedeadddcbaecebabccddecdaeacebecceeccdddecbdedaacadbecbdcaaececdbddeadedccccdecddddeeabeaddeccaedaacdceaaebdaaedbdaccabadacecebbabcbebaedeccddddcbbddbadbebcadadbabbecccbccaadeedcacdaeacdaeecbdaecbdccdccaabcdbcaadcbbdceedbacccedbdbabecaaebeeccaecbabaaddcdebddadeaedddddcadbeacadedabccdeeedbcdadaeeebadcacbeccbeadbbcdabcebddbbdaadcaaedcbeebdbdeaddabdbeaccdadabddcaebeebeabddaccdcdeebebdbceaccabddbbdacedeaadacdacaccacedcdbeaabeadeebeaddbdbaceaaaebaadccecedccedcbdadaebbccaadeeacbccedeceecbcbedaeacacccbcacacbbeecdcaaadaeaadadecdbbebcaebbeacdedeebdacbbaabdeaeecdadbbacacbdadaaadedbcecdaceaaaaddeeeccdddaeeebbddcaccdabaecceaaeddbbaeabcbaceecacaeaeecacdccbbeadaaddacecdbbbeabdeeccceedaeacedbbeeeaecaceabbdeeaadbbcbeeaaedecbeedaebddeebaeaeeaeddabeacccdceccbaadeeddcaddbbabcebadddebdadbeeadddbeeccaddddecbaadabcbaeabbadebcacaeabaadadecedadcbcedccaceeecbaeaddccebbadbaadbbeacecedceeaeaaaeebcbaadedaabdccdeddaedbbdeecdeacceeecadaeabacebacacdddcabcbceddbeceadcdeecabbbaaeadbbeadbccceadacacdeeaaadeddeceeebcebcbecceedeaeedbcedcebeebabcbdccbddaceaccbceebeeeebbadbaebeddbaebdcbddeddedbaecaceaabaeedacbebbbaacdecbeabbcbeabeacaddaaddeedbadaecbddbcaccdcabcdceabdebcdceeaabdadeabddadeacbdecdabceadbedadaaadccaadbecbeddbdcbaebabcdecaacaaebebddbaadbdeedbddeedacccccedbddaaaaacaadbdbbbeedcacbcaceabbebaeceebcdaeccabecbaceaebecbecdaebcbdeddedaceebaeceaabaeebdcaabbcdceecaedcccacdcacdbdaadbbbebbdcbedaccbbdbbaddedecdcbcedcebbecdacaecabdccadacdbbbbeadeecdcaedbbdcdddbcbcbccebbbbcceacddeeceeaedabebadadddccdccbecbbdeaadbdbaaeeceddbcdebaadabbdeeaebddaebbeedacdbabccdebbedbbebceacddddeceaacdbcdcedddbaaedbedebbcededddeaececedcbedbbeccdaabaaadcdbabbdedebbddccdbecdcbaadddecedecdbeadeebbabdcdbbdebeeedbaaddadedbbeabcaaccdbcacaaecaeeaaeceecccebabeacacbeddbdcbaeecacaecbedbaccbccacedacdadeedacdabbecbbdcbadaeaabbbdbdaeccaecdcdbcdaededcdceedeaddebebacecdccdaabcdeceacadbadccdedbaaeddeccebcbbdacbdccbbacdcbedadacecdabbcddeadccdadacdeceeadaacdbeeecdbcedecbadeecbbaeccbdcbaebdbccedadeabcbcebcacdcccdadeeecbedcdbbaaadcaceceebbccdeebadcbbdebcdbbbaadabbdddbabacaceeabaabecebacbeecdbaacceeebdbaadcdaededbaebbaadeacccebbeadbbbbaebaebedaebaeabdbcddaddcddeedaabaaaaeceddcadbeeeebccbdcebbeeaaecbcdbecdadcdebcaaeceaadcdbceeeedebaaeddadeeebcaeaabdcaaececcddddadebeaeddeecdcabdbeacbbaadbabaadeebdbbecabddcebdcadedddcbbaaccceabacbedeecacaeaeabadccaceaaabbccbcebcabaebddeedbaaedccadcccbabbdceaaecebbdecadcaacebddccdaeeabbdcbecbeebecdedddabbacecdbecbeeaeadeaeaceedacddaeccbabbadcdadabddccbeeedaeeaeedcadbeeacaacceaebaeaccebacbcabbabaeaccacaedaabcdacedbbadaccccdaceeeeaebeacbdbeeebbdbddedbceeeabeeddcdecdcacacdaebdaedeeebeedbcdbacdcbbadbabcdcdbecbebbabdbddbccccbbdabcdbdacebdacbbbbaaaacccbecbacddbebeaebddabedaabcbeecbecdeebaeaeabdbaccabbdacccabeecbebdecdcbeeabadaacadcaeccaceebdebadeaaaaacbaecccbceebaaeecddddebbabbcaedacdadadcbdccbeecbeedbccdedddaabbccdceeeacdacaaaceaeaecdbacaabaedaceebdeaaccdebebcbbddbeceadebbbbbcdecdeebdcbabbbaecedaeceaebbddcccebeedbacecdecabcacbdbbabeadabeebeaabccdebbadebdaaebdbebcbabbbedadaebeeeaeeedbeecdcbabcabdacddcacedbcaadcaeebddccbdcbeaeaddaabaecadebcaebbcaccaacddccbbdcacdaecbcabbaceaaaadeddeaedbebabccedddbeceaedccdadbeddcbabbcaadedcdaaccdcacdaaabebcdcddbbedbecdceebbcbacecbcdbcecdbbeaccdababadbcabbbdcbdddadcaeebabbceaeaddccbcdabbbdeebedaeeeababadaedbabceeadaeabeccdddcbceddedcdaebdeababbacceaaedbebabdaadcdecaabacbdaeaccbdabebaccccceeecbceadddccbabdbcedbaaebaaeddbccabeadbcebecdbebeebbececccbdecdcdacedbbbbbedeadcdeaedadaeeebddddacceabceebcedddaaaabccecababaabcbdeeccceadddaeacebeeeaecdcdbddddacacaaaacaeddecebecdbeaaccbdbbdcdabacdecaebbbbbeeecbabadccdcdcaebabbdccdbebdaebeccbbebceadcecccdabedeaddccccadbdedaecacddbaeecdeccdbcccceceeebbcdddadbeacaecaeeebbaddbdbddaabbeadaedddbdbddbbabdaeadcaeaabedacaeabbdeabdebaebaeacaabeeaabeaaeadceeadbcbeeeaadaeccedebeaabaeeaadecebdbeccdaccaebeeeedbdaaaaeabdddcbaccbddddddbeeddaabedddccbeeebbcebecebdaadbebdcbeddbaddacbacbacbabeeececabccededeadcbceacbacbaaeaaabebcbbadcbddcbbdabaacbbeabdbabdceeecabaabcebacbeaddcdbebcddcbbaeadabccddabcbdedeeaaebadbceccedecbaedacedbedddcdbcebdbbbccaaaddceececcccaecbbdeddaecedeeabcbdacccbbcedcdcebdeadcaeceabceeaaadbaaccbeebbdcadabbcacbcdcdaadadbaaeacebeddcebbdcaecbcbbedbeacdecceccaaacdbcceeabebacceeeebebdaccacaacadaeadadbdcdcccdebadbbaceeeacedcbeeeebddcacbdddcaebdcbaabccaabacdcdabdedebbbcabdececaaededcadaaaeccbdaabacceebcccddddecaebdadeaebaabdedcddbdcbaaeaadebbddceeacceceadecdcddaedeceadecbbcaabcebaecacdabdacebcbecbeccdbbcdcbadccdbebecbaecaeaceebbbcaddacddeeaebbceecbecdedeaceeeeceeccccdacdbcabcccdbebeccabcaeaccecbdebdaccedcbcbeedccabcddccddcccaaeadddbabbeeedbeabdccbcdaaaeeacbdcaebbeeddbdccdeaaecccceaceacecabededcccaedeedccbbdeaaeddedbddadbbcdebdbaccaecaacdcbaebbdccebbdbaecbceeacabbdccbeedeadedecdbbaaddcedcedeadedeeaddeceaddddcabecbcdceebedcdadbedbcbebcabbceaeaadeeedcededbabaacdebbadaceabaacaaaadddbcbedbeacddeaccabaddcbaabecdbccaddbcbacccbccebebdbccadebaeabcccdeccbcacdaeaecdcbebaeddbcaedcbaeabaddbacdaedebdbabdccbaaecdabbdcbeacbbbdabcbdbbceeeecaccdedbcbeabeaacbcabeedbdbeebececacbeaddebeaeadcbebdcaaddbbbbaedeeabbdcaabeceebebdddbeaebecdbaadebbddcddedcdeaeeceeaabbbcdeacecdccddeacaaacccebcbbebecbadcdadaaddeeaebaeecabcbaeabbcddbacdcdeebdcbbddbcdedcaeeebdecbebdebbacbdadedcedcacbbbcbbcbeebbaadebeeeeeeeedebbcaddcdaacbedadcdcbacedecbdadebdcedacebbebecccbeddcdedabddbadcbaeedaacbcebdacccdadddeddcbbbabbeacbdeabbaceedaaaccbedbdedabcabecbcbdacdedceddbbbdedcecbbbcedeabcebbaaecdeadecccaabbdacbbbadeccbacaddbebbdaabdebcbbecbcaaccadeecbeaacacbcbbdeccebbeeabdabebddbaaabdabadebecddbcadebbadcaaaeddbbaecebddebcaacceabdacebabbccbdcabadabdcdcdeccacacedccdbebcdaceaabcbadcedebbbbedebedbdcbeebbecaaaababeebcdbcaecdadbbaadcbdccbbddcbdcdbcabbdedbaeededbcccddcedaaeeadbeddccbadbeaeacceaabeeaecdbccbcbdbedaeacbeedaedadeeeecdbbbbdcbdbccebeacccacbacdcebeaaceeebcbccaedaddbcadbeebccaaecdcdcccebbbaaaaeeebbaaddccdcebcbdcaeaecbaebaeaabdbcbabeccbaaecbccaeeedbaeddbddceacecdddecebbcdccceacbaeedbceeccedcddebbeddbdcceceacbdbbbebcedaccebecaeddcaecbdeddcaebeeecebcecbaaedaecdaabeeedebcdcdcdacbacaccebaeadccbeedeccccadbbcdaadecdaaeccbbdcdcadeececebbadcacbdccccedbbaaeabddbddeacecedbdcbbeabdacaeecbddedaaddddddbbdbceaecaccabaceabceededbccdcacacbdbeadcbcbbebbebabccbaaacbeeecbbbeaaccbacaecbababbcedaedeaebbebbadadcdbdebacbabcccaaadebeaabbdbbbccadbdebaecbbcadcaadaedeacbeeeeceedbadceeecccdadbbaebdcaaacacadabdabdaadaddebccbddcadbccdaddcdeacdeceaabeddacebaecebadbdaecbbcaeaabaccbaaeccccadeccbecabcbbaabdeebdbaedadbcabdeeadeabbeaedabeaadcdadbbaabacbacbcdbadeadebbaecebbdeadeddbcbeecadedcdacedcaebdabbceebddcbeebaacbbedacdbcbbadddbadeecdbeaaaeaaadaacebaadcbabeaededcbdccaadebbeeadcdcacdaaaceccceccecbbebdcddeeabbbdeccbdebeaecdbaaadeabcdcdddacbbcedbaeaebbdddceacdcbebcaaccebacbdaebdbbaedbaecaceeabaeaaadcaaaddbbebbcceaaeecdecddabbeedadbbbdaaeeaeacdbedaccedadecccdbeaabdcdecaccdceabeaddebacbaabcdcabcabccddabedbbceddaebddcdbbbdbdccdedaacabbaeeeddbeedaddbbebbeddacabedabedcbabdbbecaceceebebdccbbbaecbebcedeebbcacaabbbcdeecddddccdbcadddcaabddaecdaabbcaabeadcbdbcbddeecdcacbebbbcdbdabeaacabeacdedeedaadecdbabbeacbdbabcccdadcacaedcdccbadbaddbeaccebaaccedaaddebbecdbdebeecedaeabcbabdacabbeeedbdbbbddacaacaccebbdbdedaedadbdcecaddccadbdcebcbacdecdceeaaaecdbdbbaaaaaeeceadebbdbbaebbcadbedaaecaacaceedaadbabccbcbbddbdadbcbbcacbbaeeadaeccebbdbddbcaecaaeaedddcbdbcbeeeaedaaacadbcceadebeacaadedecebebabacaedcbedcdbcdadeceacccecebcdcbabbabaceebceeaeceabadcecaeedeadaceeadaeddcedabcbddbbedbddbddccbcbbcaacbdddadcdcabcdaddaeacedacbcbbebddaaedcdaecbbdbedbdabccaedcecaeacbeadcacabcadceeadaabecbaecebeeceadbcbdadcaedeacbcaebbeacaecccabbacacbcbacbeceeeadecadcceabeaedeaebdeddbbeaaddacbdeeedaebeeabbcabcdcbedbddbeacdcaddabcbdbbcaaceaceacaaeaaaddddbdaaaeaaebbbdcabdbeeeaabadabeacdadeaecbdcbccddeeccdaddaeddbccaaabaeecbcaacddbdcabeddaecbccdcebbcaecbdaedaaaccbdbbaecaeadbcdbeaaabdeabcdaaabeddbecabeaceaaeddcdadbcabdcdcabeeaabbbcaaacddaeddecaecaeabbbdddcecbbdacecaecaaebaeaaabcadcddcebdcedaeeebdcdbaabcbacdbabdaaaebebabccadaebbbcbabecdeceddbddbcabdeaddeabceccaaabbaadaedccccbcedadbacaccdeaabdcdebddbbecbbacaaedcbaaaeedaecbeaebeedacabedddaeeacdccdcdccbceabdeaabbeeeebceadbdebcaeebbeaabdeebabbbcaabdcdadeccbebbbeebacebdedacbddebabcbbdeeabcdcebbecbdcacdddabdbbccaadeedbdccdbeebceecedbecacbbddcbecdcecaedcdaeaabcccbaacdcacebddbdeaebccdcaeabdedbeedacbaccebdadbebbbeeccdebceabaccedbdeadedcedeaebeddcbcbccaadbaacdcacdaabbdbbccdebeebeeecedacdbeacdbbedadbaebbdaadddcacecbabeaebaeeccdcdacbcbadaeaaecaedaeacbbadaadadeacbebcececadccdcecccbadcedceeceaebaacdaebdbeaebdeebcadcdebaccecaebeceebbaeaecededaeebdaaebbbadaaaecbadbddbabbaacecdbaabaebadcceeecccebaeacbebdacbdaccbdeedccddcbbbdddddcdecbbedabbeadcdbaacbeccaeaaecbaacacdbddadbbccccaeeddadbedcbbeeaacabdbddbceebadabbabdedababcaeaadbdaeadbacadccbdeacbecabcebacbcadbedbbacadbaeeaccbdbceadbceaacbcaeceebebebccddabdabbaddedebaedaeccccaddddeccccdaacbccabeabbaaddbdeecccdbeeecabebdbddcbebbeacedaedccadccbdededdaceaabcbadebcbacbeaaeedcdcddbceaedbcbccbacdadbdbacdbcaccadaedbbbdebacadecceaadebcedacaeeaaeabdecdbedaddccaeebbeaacedbebdbecbbbbaeeacbcdebaeedbeddcbddbccaabbcadcbbcdcecbcccacbcddbdedadecbebbcbeadcbeecdbdcbeddbaabcbeadeecebddbdbedaeebdabaddeeecdbaeabaeeeeddbaaaeecddcabaaddccecbdddabcdbeeabdeeccbceaabcadecaccbbdccceeccaedeeadddeaecddeecbbbeecdacabbcebebeccacccdaaebcaedcbbadbcaecdedbcbccdebbebdcdadedbbdbdccebbcdeebededeaeabccdbaaacddabdddabdeceaeaddaecbaabdabcbbcaebecddccacdebaecddccadbdbabbbcceacabeccdebabecceccacbacbdeaadbadaacebdceedaaaeedbacadeeaedaadcaabecbeabdaaadbbaacdeaabacdaabcdbdecbeadecebcaebaebbabdceababeceebceaaaaedcebbdacaeaeebbacccdaedbbdcacdacceaeaeeaaddbccecacceaeebadedaaacbccbeabdeeabacaaedeeeecbacebcbeebcaacaeeeacaceaaeaddadbcbcbcadedcaaabadcaaeabebdaaedcecbbedcdecddcadcbddacebedaeaaecbbadbcdeaecbbddcddbbbbbcbebccccdddaeebaadeccadaeaacceddcdccebcabdbdbabccceeabcbecacdeaabaabdaedadabbacddbeecdaccaddddbdcaaabeedbeceacceaaddabbbbceaadeaaebbbebcaeabbbabddaabcadaebeecbadecdcbbbeceecabcadddcabddacabbddeabcbabaabbaadbebccedcbcadbdcabaabbcebcaaeeaeaaddeedbabbcedadccdcbabcbbceeadccdceadbbaeccbacceecadccaabeaaaaedaccaaacdeaabeaabaccebdbddccceeabbdacddebdccddbccdcecdacdcddddceedcccebdacceecdcaddabeacdcdedbadaeeaeeebeaeadedceedbbcdcebbccdcbbacebcdecdaddaacdacccaecbbdcbdeebdbbebeabbddabebddeebbbababccabdbdbeadeacebaabcadcbdbceaadbcaabbabcabebdcccbedebbaedadabbdbacbecaacccecacccbebcdbebeabeaeebdbacacedaebeceaacebdbcddeadadcbdbabeabccdecedbacecbdaeeaacddbbdebdebcccbebebebeaeadddbeeabbabbbeddbaecedccdbbacacaaadcabdbabcdddaddabcbcabecccecaceddaceddeabdbdbaaccaaeecabbaaeeaacacaaddcdabdbcecaedbddaedcabedbacccaedcbcdddcdcecdebeaaadacbbcabccbcccababbddeaaaaecddccbcdebacaabbebdeceacadaddaabcecdebebecebccdbadbcabecabcdadbbcdddaccdecadacbacbdaabaebeebbaecadeacebeecdaecadeeccdddcaededacdeadbeacaeeacdbdddbbecbdaadbdecadcdaedbedbbebdacdedeabecabeddcdebdaeebbbbccbacaacecabeecacbcceabbebccaecebdbeecaabdcabebadcaacabdcecbcceeccddcebccdcccdadcdebaccabbcacceecdcabedaaabbcaedaddedcbceccccbebadccaedecddeebebdbeedeeeabdddcbecacccaabbdaddbccbbeabdebabadebbbdcbeabaabcccbbedededebdcdaebaacbbcacadcddbbbbacdeeebeadabddbdadedecaedddddcaaeedeacabadeeaeeadddeebeebbaebcdbedbddceddedecacccbdbecbdacacdbdcedaadebeddbdbcebeaecbbdadadbccbaeeeacacecbbdcebaecbddbbbbbacbadbadcdeceddaeccdddecddabcbbabcddbdecaaadbebbddddaaebebaedbdcbedacacabbcbedcdeedadecabcbaccddcdcabeebdaabdedbddebaaeacdbaeecacbdedbdbdcceebadacbaecbcaedaaedcdecacbaadaeecddddaceddcacddadcbccbebbdbdaeaeccdcccccbaaabbecaaecabbcceacecbeedddeddeddbacdddadeecbecedbbebacaebbbacacbdbeebaaabbadadddbbddeadaaaecabeaadcbeadaacececeeaaededcaeaeadcbaacdbbbecdebceccabadcdacedecbcedceaecaaeaeceabbccdeacddedbdceadbdcebedcbacedebdabaedecdaabdeeabcdceeecbdbdadeccacbcebcbddadacedeaabcbdbceacbdacdcacaaaccdeeebceacbdddcaeeabcdcdeddacabdbeeecaeabcddbabccccdeccbcbaddbbaebcaecbbbacccabbbdddcbabdebedbbabdcaadacccaabdbaddaebbaeabdbedbbebceceebbabeceddbaeaeeddeaccceceebebbacbccbebeaacdcdedaedbcdecddaceebdeaecaeebeaccabecaaedaecbdcededaadbbdbdeaaacdecaeedceeaeabbdccebadeedaddaecbcacabbebceceeaeacebdcbeeeebcbabecdedaaccceeecdabaeccbdbececadaccebabadbebebddabcbaaabbdbabaeedaabaeadcaeccedcbcebabeeadadbabebcebbdbcdbebdebedcabbbacaeecbcbbedddbbceddbeadbdbdebabdddaaecdaceceeebadbceeacedbcdecebadbdedcabadeabddbebecdeecebbbcebededaeddcccaaecdedddbcadbcbaeceedbaeebcedaadcacccbedbebebbaebdaecbecadbabaddbecbdcaeabdaeeeaadcbaceebdbcbbeacdaeabeaebbebadaacdbeeeebaeebaadcaedcddddeacebdbcdcdcbbdeadcdacdaaecedcdbddbcdeedeecedbecdccdbeedaebdbdbbabcddeabaddaebdeaedebdabcbabbcdecbbabddcecabcddaddddceeeaedbcccdaeadadacaadbdbaaadccbdbcbebabbeabcaaeeaadbccabcbbadeddcecbbcedbcbebbadaabddbadcbdeaeacbdbcbabaeabaddeccbdeddabedaccabebeabbbadadceacbcddebcbddebecbabbabaeeabcbddecedcdebcededcdacecaadedebcdbaeacdbaccdbadadbbacceedcbaeaadebebdbabeccededecdeaadedbcbeeadeeadcbbedbceccaaedddaebcaaaacedbecacadcaebaceeadcdcacaacbbbaadacaebdceeebcbabdaebdcacadecaaeedadbaaeaabdacdedacecddeecccbcbdcaeaacbabcbdabbcbcaadeceadaaaaeacddabaacabdaaeabcbaabcdcacadcbdceaaeceebedecbecbdcddeddadbaceaabaabceaebaadcaabbbbeeaedbcbecaeacbcdaedbcdcdeedcbbbdccaecbeaedcadbcaadbebeebaddaecaaecbdaebbddccaedccecebebecddcccdedbecbababccedcaaddbabeedbabcdbdaeccbadccbccdbdacaedbacadceadbbcdacabcbbedcdbccbcabeeaaccaccbbeceedededdabaaecbabcccdccaaebbbeaddccdabdeaaeceabecdeccbcebccdceacdadceebbaacdcdeeaeacadbebedaabaccdebedbecededaedeecbaddecaecddcdbedaaeaeaadbebeecbebebdcededbdbabcbaadddbcbcbdcabeceededbdaacceeccbaeeecbacccdacdbddbbcaabeadebabdbbacedaebeeeeddeadaebdcdbdcebdbdeddedeebaecdecbabbeabdddeaacbecaabcbdecedaeeacdddedaeebcebbebdbccddecebdbbdcdbbdbcbbadcaeaceaddbeabeabeebcbadccdedbcaaecccabccbedddebdeccccaabbaddcbbcddcdecbaddaebadeddbedaabbeaebbeeeedaacecadaccebaabebbedbabaaeeccdceecbadddcbacecdcdaddbebcdaebdbdeaddebbbaababcdadbaebadeabebdadaeeabbccbdebcaadbebbeadbaaebcceaddeaacdddadbaabaadeeeaacbaddddecaecabacadabacabaceabecdaebceadcdbcbdacadaeaeecdbdcdeeababacebceecededeadbdaaeeaedbdabbcecceacebbbedaebdaddedbabcbeabadadedcbaebabbbebeaeaccdcaaaadbbdceceadaadeacceddbaaeebacaaadacbbcebbeaebdbeeaeaadababbdbececcbeeebaabcaebaecbaaadbbebcadedbdaddcebdcaedeabaddaaecaabaacbdebddbedbbacbbbdcbadedcbdcdbdbacbdebeedaacaaabebdabaebbadacbacadcedbaaaacdbdebbdbcaeccdddcdeccaedabeadecbbcdabddcbeebececedbcadddadaaaabccbdbaaceabedacdcdcdddceabdadadbadaaeedceedecedeebccbedadcadbaebccbebcdbaebbadcbdcecebcaabacbcecbcccbaebaaeecebaeabebcdebbbbcdeacaadbabedebddcebdaeeacaceacdddcaebdeabdebebbaadbacbcccaaabbecabbdcbceddeacdbbbaeaabceaeadeeceacbbadbccdccdbbaaabaeaabecbcbaeacccebedecccbddcebdbbeeccebbcecadaecedaeabbbcacdacadaeeedaccaaacaddcbebbaaeaaebaaeddcebbeeadedaeeddaedceddcaddcbddebbbcdeaaaabccbcdacccbcaaeddacddcbadbcacacaabdceaecdaeeaeeaddbecbadcbbceabedadbddddabccaacadccdaeabdbcedbeaeaebadcddbbbdddebddabaeccbaeecdcadbaeaddbddbaeeabbadbdeebcabdddebddbdddbaedebbbaeaedbeeacbbaadaaaaaedbaddbedaeadbedeacddbddbaaacdecdcbaedcebebebadcbeddebdcdceacdbdaedcabcddcbecebbabddeaaddcbbdbeabbdedddceadedeaebbdacbaaeaebccdbbeeceaabbeaebdccbecbacceccceaeedcdedbedacceaddccabccbebeecbacabedaeabcbdcbbccaccdddbddaccdcbaeeaeabbccdcbeddebebdeadebbebdacbacddcceababeeebdcdbbacadacdaacbdecddcadceddaceeeeaaaeddabebecbeabeedaebadceeceeadaadbbcdbdebaadecbdbcbecceededacdbebbcceeadccceadecebedbdbadeaeedcdadacaccceacacbddaaadcdbdbcedcadebbdbacaaeeebadbbcebeebdcbbabeaebcdeabdcabacdaedbacecedaaeaddbeeceedccecbbdddecaccceddcaacaeebebbddaacbadebecdbdbeaccddeadaedbcbcdccaeaabcdbadcacedbaeacaacdcabbbaedddbdadadadabcbcbbcdabdececeaabadbadbbbcbbbbbdbbdaeebcccdbccceabeccdbaaacabbabdadeabdabdcedcaecbbcbadaeedabadcdaecddacaaacbdeedebadbadbbcabcdeeceebcaeeacebecdbeabddddbcbedbbcecebadbebcbdcaebaaececaacaedebacdaddcbedecddcededcaabbbaebcaaaaabeacbbbbebeaeeddaddbbddcbccbcababdebaeccaabedeadbeaccccbccdbbaeebacebcaceacabbdaeecabcdeeeaeaedcbcdbecaddeabeadedbbeeebdecadbedbdbecaebcacbaaedaadbadcbbacbdcdeadeddbbdccbabcbdbebbacccccaccbdeccdbdadabcaecebcabbdaeaeeeacebeddbdadabcdaabebebdeadbaaecacdeaecbccaeabbebbeecccbcceaaacbdbeebeadaaebbdbeecdebbcecdebeecbacadaecebddcaaddaeedcccaceddbcadebcbdaebdceebcbaeaddeccccccebbdeaddebdddbedcdeaedcaeadedcebdcaedebeedaebcdacabeddbcceabecccbebebaedbeabddbebdecdaaeccbeddbbcaaabccadbbabcbbedeabeedabdadaabbdddadeccbcebceaebebadcaaeadcabeddeeaecdaaaacccaabaedaadddddbdeeeecacbbcaaaebeddaecddbaababccdcbbedebcabeebdaeededcdbdcebddaebaededdecddcdbcdaeeaadeedaddaaebebcdabdabbabbdedccedbabaacedaaeaeabdaaeedcdccebbdecdbadcdccadddeddabecabcbaedbcabbaebddeddcaacdbeeaeeaeacedebeaaaeccdaddcccabdacbeebcabededdaadaadbcecbaeeaddcdcdecceeccaaeeeeabedceaaaaddccbdddabaedacbcaedbbacecaacdceeecddcbdbdcdcacabedeaddcacdacaaceaaadacbaececbdbaababeabcecedbceacaceabcaddecedceeeeadabcdeddeedbdccdaddbeccadadddcbbacbeddbdbcecbdabeaeaadabaedecadccdeeccbaacdebabaaeaddccbeceedaadbddecbcddbcedeebeeecbdcbceacaeabbccbcbbdeecbdbbbbeeebcdabdcabbdceaadecaebdbecdceeeedbccbbaeddebbebcdaacddadcbcaaecbceaeebdaedabacbbeeccdbbeeceaaeaeaccbabbcabbaebecbbdaecaddbbbebaedebabebddacabcdadaccdceeeaeebdbcdadeaadabecddaabddcdaeddabcbdcbeaabaacbccddcedaccddcbccebbeccdeecbcccbddcdbabdbcacaeaadeaecddcccdbdbbacbbbbbddcabcaadcadbdeeeecbdaacdbddedbaaeccebcdebdcdcedaedecdeebecdedadcdedaadeaaedbacacdbabcacaacedadceddddcbdecdcdaceceabdbceabedeebdebadddacbeaaeabbcdcceadacbaacbbabedaaadbebbabacccabeedbaadcbccecccedcacddadeedcebbebccbaaaccbcaadcecabbaeabcaceacaadeaaadaacbcadebecbcdaadbecbadccaaeabeaaacdaeccbbdabcdcdbabebedacedbeeddbecdddecacaccaddbbeedacacecadabacbeaebaedccedeecebebdbdbcbeeedecacaddcbabadcdbbbdcdaadcedecbabebdabbadbdebbccdddeaedcddcdbadbdbebecdaaeeddbaedbcbbaabedcddaeecccdebdbbedabcbdabbcbacdbbaccddedcbcdaababaebedebbccbceeabdacdaababceeaadabcdaedaaeedbdcdacbabacadebdacccabccaeccddaccbbeabeadaebabbcbbeeeeaddeeebacaaeadadadcaecdeddddabcccbbbdeebcdcadcbddebbeeaadebbdbcceabacebdeaaeeadacabebbedbadbeabdcadaecbaacabbadcababddbbdeccccacabccbebbeaeedeabbdeacbbbbededebaebbdddcdabdabacecdecbdaccaceaebeeedadaadcdaddedddeebcbbdceccaedcacddcacbddedddeadadcdbcaaddeabeceebddbbbedaaaaabbacebdebbdebceebebbaecdcbbbaaabdacedacedadeceecacdaecbeaaaccddaeddcebebebdeaebadaaaadeaaaadaadeeccdcceecddebebabdabddceaaccbeacbadabccbbcdedeaabbecaeeadeeaeceaebbadaadcdcaceeaaedabecdaaabbadcdddeeaaaabbecaebadedbcecdaeaadaaccdddaeceeabebbcccabebaddccadcdadcaccbadbbdbdbcabeceebedadedebcdcbaedbbcacdbcdcbcbbddbecdabbccbbdcbdbcbebebadeccdeebccabbbbdbcdcdbaeedcbdbeaaebbcbaaeabbdeacdedddaeedadccbebedcddeaecbacebccdecbebbdcaaeaedccadeadbcebcbadbecccccaaaadedddacaceaeacbaebacdedbdbaeecddaabdeaaebeabaabcaeddccdaccebdacebdbeaacdeddbdabaddddccadddbacaeecdccbeeccdeabbacddbbeeebbdedeadcccbedebbaecadbeaadadeaaeacdaacecbdbccceeeccbedceabadaddcacabeeddcdeedceadeadccabbbebbeeaaeceabadedcaeabaacecdcdaadbdbeedadaeeabbdcebbbcbacabbeccdacbbbcebbdecbbbdaccdacbbaedccacabdbcccbdbbebadcbbebeacecdececdbaabecacbbcecdcbaceccdddcecdbbeecaabaddbbedcdddcaccbcccdcccebdbccdaaebddadaeeceacacecdbebbabcdbdbaccceaebcaceddeaceaccbdbcdbccdcdcedbcadceadecbcabebeddbecddbeddbbdcecbbeedeaaccbcdcdbdbabaeadedbdceeaccedbeebdcbdaeaebeebadcdcaeaaeaaaddeeabcbaeebaeecaccebecdcaeddeedaccabbebbdebabaceebadbaabdeeeeaedcebaecabecabdeeebcdbcdcddeccdcecdddbdceaddebadcccddaacdceaacbbdbdccbdcceedcaacbdbddceadadbcdcbbebcbecaebeddabbbeddbeccbabbcbdebbcabcecdebccdddbdcaedcdcceddbadbdbbcddcdbaaecdcbbecdbbdaecacdababbbccbadddbcedcaaecdcdebbdcacddcdededdbccddaedcbacdedccbeddadddddecadbebbedcecbcaeaedbcbecbebeccdcbacdedbcdddcbdaecaaebadadcdadaedddecbeadacacdbdddccdacdcedcbbcedeaaeaddecacbbbbebbbbddccdedcddbeadabeeecdccdebbbabbeeaabadddcbaeaaabdbacaeebdacaedddcbeeeebbebbdbaadcdccaecbebcbadcdcceeaaaedcddbccaedacacbadaeedaabcacdcbdbcedaececbadedcacacbbadeeedaecbdaeccddceedaabcccddecbdacabcddedbadbdbcdbbaaacabbbeaaedcdebedecaecbadccbedadcabadbbdcdbceaabeedaedceedaaadddbddbdbaecbaeeacdacbacadaccdeecbcddbdbcadebabbaadebaaccecccadbcceabbaebdbeacedbbcdadcdcbdeebcdbecdeaaeacadddcdebbeedcebaaaaaacadbbaccdbeccecbceebecaacdaceabeedabaaabcadeabdbbbbcdacceecbebcccbebbdddeaebaddaedbcddceadccbbcbaaaecebeebeeacbecaecbedaddccebbcebbedebaeddcaccaeedecdacebeaeadccbcacbebbcbebdeebaabaedebcaebdaaeceebadcadadbeceaeecddcbbcadeadcebdeeebbcabdccbbbecbcdbcdcddcdcebddacbdbdacccabdadcbdcbaceecabbecebaeaaaeeaaeabeeaebbedaecccbdbabaddccdaacabecaaadeecdbeccbdcbddebbdaabebeecbcaecbebccebbaeadaedcdabbceccbdbaabccaaabbeedaaecbbeaaecddecabeaecbaaadadeecbacdccdcaabbbdeaaceedcdddeabedecbbccdedaceedbcadacacbdcccaebdaedaaebbdcdaaecbaaaededbabeeadaedbbcdaeededaedcaaecaaaaadaaedebdccddebecbeecaeaacaabcceadbcddddddaeebacecedadaeaeebecdedbceecebaaeecbdbaadbaceaebcbbdcdeeeaaabeadebebbdccbddbecdaeacaedddedabddadadbecacecadedadbaedaeababbcaaaedeeddadabacdcaddcdcedcabaaeeddeeddddbbbeebcebbccdbbcbdecacbceeacecdbdccdcdaecabdcebbabbaedeacbeedabbaeceecbddcadbcaeedabdcecdeaccdaeebdeaeccebcabddaaccdcaadbcbeebeccacaabebdcdaeabdecaeaddbbabcabadcaaeddeaacecaecadedccdabbedeabdaeaaeccbbeebeedadeeecaccbcacddbdabbecbbaccaaaeaabbeaccaeecccadeeabddbabcbcbeededdbbbbbebbbeeadaedacbbdebebccecbdeccecbdbbacddbbcbbbabbcedaadadeaacecdeebdeddbaaedeedeccbababccdabbadbcdabdcccacadaadeaeddadacbdbecceccebccadcccaecacdacbbaaccddaddbcdcbeccbabaeddcbdeeedabcbccdcbaabcdebbeaddeebcbbeceacbcadbbbcdbaadaabaaecbbabadadcdbededdcbccbbabddbbebdbdbdceeeddabdabddcbebbabaaaedeaaadddcebbbeabadcbbdededddbdbebdcdbccddaacaccbbadcadbbcecbedbbccedddcdbceccddbebaaeecbbbebdcbacaacbeaddececebabddbaaabaedabbdcbcdecbbaebcdebbbbeaedadbcdbdeedadeccdebbacbedcdaadeccebcebbbaeecddeaeedbcededacabedcadcbdcccacddbdedaeccebebbcbccaecceddbacbbaccdacbecdcdddabcbacddeacadbcedbedaadbdecdaebbbdeaaeeddecebdebddcdbdbccdeaacabcceeaedaddbedbadeddcbbadbbdeadbadacddbbbdbcbddeeadeeacbcccbceedeaedbcdcedccecabdbcdaceaededbaedaedceececdaadecededcabaebeacdaecddcdcadcbebcabecbebadddbcbadccdebbaddaaaadecacecaabbabceeaaececcbbdecaebabecdaecddcbbadcebacaddbebbaaceaedbbbbcbbebeaadbecbcbdbaccaacacdecccacadbbccdabbaccabddeececabaaedebddcebdeaacadcecaecaeeadbacacbbdbbacebaccbbbaceeeeaeeecbabebcebbaaddacbecbbcebaebbecbbaecbbabcdaecaaaecaddcbdaadbbceeaaeddecabbdeccabadddacbaaaacadeecadcbccacebaaccbebdaddcbbbaebedabdbacdadebbabbbacecdeaebaeecbeaddbbabadcbaabccdcddeecebbcbbaabcddbccbbacbdeeddaecabbacaededadbadecccbeecacbdcbecdccbcadeeeeaebebeedccccbebdcdedecbaaedeedecbdbebaeacdaccedecdaabadddeadaccebadededbababaccdccaebcadacaddbcaeadeccbbdacacbcaecbddbbdcbcddbedbaecaaabccdceadcccbbdcbaceeadeaeccdeedddecaeceaacecddccaaceabdbdbeaeddebeeedaebabedeaaacebbbcadbbdebcbcceeadceadcecdbcdadcacbebabbeeacdeaeabeceadbbcbcbbdaedcdddeaabaccbadbdeedcdedcacbcbdcecdaabdbaecdceddbcacacdcabbabcddabbebdcdcdbaceddaeeececcbbeadabcbbbddbacdccdcedbcdaadcbdebdeceeacbacecbcedaeeeaabccbccdddbebbabbbdedeadeaacadcdaaaeccdaadebaacdcbdcdaeccadcacdddccbbbbaababdaeeccbeccbcabccaeecdddaebebaeabedbbbabbaeabdeeaebaceeecebdaddcaccececeaedeebebaaeaaabaabeccdeeedacbddcceaaadbdcacdadabeaccdeebdaaeeadedbaaebeabdbbebebbcaabaaadadbbcddaeebdeebdbdcbcacbabedebaabecbeaaeddbddedcbdcaeaeddccabedcbdceddbbdbccbebdedaacdbdeaddbdbbaedaebedccaaddcbccebaceedbddeabbbadadadacdbadaddecbcdaeaeacaaeecbebbaadcbbeebeeadbadebbbedeabbabbddaceacebbdcebdeeadcdaccedecabaecccddedacbecebcaeeecbedbedcbadaadbecaebbbdddcccaabbadaebaabaecbaadabbebcbaedbbdeebddeeceabebebbecedcecedeeacdcbdacccbbaadeddcbbdadceabedcbdabdecbeacdebbacaaddcbbeecbcbceaccdbabcedbcdeddbdeceaebaaddceccaebdbbabeecebddcdacedebcaaecacbcddaaedcdcebdebcecaabdcebdecbdcedcbbdddeadbbabceeabaccddeeddacbcacbebebedecbaabbeddbebcceedabcabbddbaeebbabcddbaccecccdaabeaeaecaeaebbeedebddcdbeeeacecbcbeddaacbedbcceaeadbabbeebcdbbabbadecceaaabbbcabaebdaeebbdabeaccaeabaadeeaeeacecdbecbbabdaacaedebccdbdacbcbeebebeccbbaddddeabacccbebdcedbbcabeaeecbaddcdbecadebbeeaceeadbceeedadcedebcceecaacdeececeecadababacbeaaeddbaabdbbaccaacbeeceecbabddbeebedceaaedbdabaeeedcdcbbbccdcbcddbbcaebdeacabcadaaabbedbcbcdcdebecbccaeaececabcadedbbedddabedceccbecbedbacadbbbbdaebceccbacabcaccbeadaeabbbeeaeecebdadbaaebbacaadbbccabcddcaeaaadeddecbbdcbdbebdbeaeacedecbdbceebbddaccbdadcabedbdbbeccdecdacdcadcdeaeaedbebbddcbadaddbdebddecdaccececcddaacdccbaccaadcebecbdbbacecaacdbbbdecdabeedbdbdbbecaedcdbadcbabebabbacaaacdeadcadbaecceeaedccabeeddabbbcacdaabdbdedadddedbcacccddbbabaeececbddbaaceeadbbdebedcaeadcdcccacccaabbedbeaaeaabcdbddbbdddbdaaccdeedaabceaeddeabdddbbedddccadbcaaacbeeddacadbebdedcdbdedaeeccddddbbeadbdcbbebecadadccbcecdedcdacbdcabcbddbabbbddbccaabbeecacedccedbcaeeeaaeaabcecaeacaceacbbdbdbcaeeebadbbeadbaebdacddaebecdaebeceeadbdddbabeabccbbabadeebddbdeeadcebdcadedeaeacadbcbceddadaeeeabecddcebecccbabacbcdeacebacaabcaedcddecccedccdcedebeaaebcbbcaadedeebcdadbdaebbcbcaaeacedebacaaeaeaeccbceeebbecacadcabbedebdbeededdaadebdbabdeedaadeaadeebaccddcbddccaabdadcbeccaacbeeadecadaaccbdecedaadbdcbcbdebaacdebabbbbaeeccbccdeedcabaceacbadebacecbdbeddccbbaaaeccaadcacceaeeaadbbeddddabeceeebecabedadaceceddbbbeceacdaaedddcccdebddcccccbcdaacdacabdeeeaacaaddabacebabbaedeedcbeeedebdaedabdbecececeabdbedeacdbeebbbeeeedeaebbadacadedcbacecebaaacacbceaeccdabccbeaabeedececcbacbaccdadbadccaeebeceedbcbebebeaccebabbadabdddbabaccebcbbecabddeeeddcaadaccecbcaabeababeaabdabadabccebacdaceecadebbaedabaebadbceabbbadccdaceedebaccbcebdceddaacedeecbbacceebaddcdecbadebccddecdeacbdacbecbcecebedbecbabcdaeadeeaabacdbaeddaebcbbcdbcdcaddcdebcebcceaadbeaccdbdecebdbdbcddcdeabbeaddaeabecaeddcceaebeeccaececddceacdcbadbaaceeccdabbedeeeadcdaabeddcdddeecdbcbcbcaeeabdcebeecceadccbebababbadeacebbdcbdcadbdebeaaccbeccddbbaccecababadbbcdcdebeeebbbdabcbccbaccbeaececbdecedebdcababbdaedeabacdaddbaeeaabcddedcbccebdcababcaabcbbcadedeabcbddacbeacdbecbbbccadbbadbdbbabcceaedadceccdeeedcdaaceddceedcedcaaeebbbbebcacaccabadebdcdbbaeacebcebbbbbaedeeabbdeeebbccedbcbeeeebecbecaeeaabadbaabccaaaadcaeddbabcededbddeebdbcadebbaadeacbbdabdceeeaedeceeedcbaceccaddebbadaaebcaaaccdbbdbcdbbbedabcbdbebacadbdbdeecdddcedddeaccbaeecceaececabadcdbcbababceeebeeadadbcbdbebecadadeaacddabdeeddedccbedaadacadabcebeabdeddebebbeecabdbdacabedbaedebbdddaebbeadaaecdacccceadccbececbbcaaaadabacdaaededaccadadacebcabddddacdbddabaddaabccbcdccbaebeebaccbabeadbddeecbcebbcebbcdeaecdeaebbcccbcdeddcbdcaebdacabbceadbadadbbeaeacbbbdbeccdedcabcaccdddaededceabcacbcaebbdedebeecaeeacadccadbbaaadaeedcbdbaaacaeeededeacbadabdedadabdaaabbcbaacccdbaadcbccdcbabaaadbaaeecbbebdcaddedadbdacccadcbbcbedabadcadeacceccdcddcbcecaacdbbcddcdbcdcebedbaebcbdbcceaecbebcecdccccabbeeabaaedcbedcbcdbbdedadbbedccdadecaecadadebebbadccddbbbdcabcdbbdbcaebbdcebccedcabcebabcbdabbcaeccdceebbdbbabdcecdebbbdecebcdccccadcbbdeddabcbbcaadbbcdbbdecceedebaeedaecdccadedeecdeebcadbeedabbaeeccccbdedbadcdbabecedbbabcdbdccceaadddacccaaaacdbdbcedcaeddccedeaeddcbebdbddedebdeeebbbcbcceacbdbbbeeaedbbccbccdeabecaabbddecbeeadcbdedbaabdedcdbcabbbcedeeaabeaaadbcbacadeebebeaddbacecabbaeebdddeccacbacbecaccbcbedaaaebecacbdaadbbdaacbdaeaabcbebeeaebeaccbaaadeaddbebcbcdcddccdecddddedccdaebbeadcaeabbeaeaddcdebbebeeeabacbcbcedaacbacccdeccecddddedaacabdaeeebebdbabacdacbebdeabcddccecaccebcebbbcecccebbcdbeebacbaebcedeeebccaaadbacacdbbccebcdedaeeabebbaaadedebeeedebbbcbccedbcaabaededcbcbabbdbeacadbcceeddaeedbdecaabeaceaedacbeaceeecededcccbdadeaeedcebebcbdbbbceeacbaebbbebaacacdbaeebdbebaacbadbdedbebebcaabaebacbdebedebeaaadcaecbdaebeeddcabdadeaeceeaababdbbebbabedcdaaadeaabaacecbcbdaaabebccaadddecaaaceabcbecabaceedbaebaabbecbcbaabdbbaaeececdeaaabaaccbbeaeceaecbccecadbeaecededeecdecbaedaecadccceededcaccabddaddcddbeacbdcdccccbdbcdcdbeadbccedcbbdbcdbcabeadaedacbdcabedaeedbdddbeeddbcdeccdcdbddbaebdbeabacddbacbcbaabeebbaaedaaaeeadaacdebdbcedeaadcbcebcecbddcaddbcaabcbbbbcdbcaeeedaddddecbdaacbccddcabecedebdceebaacedbbacebcecbdcddacaacbbeecbddceaebecbcdabeccbbcbcedbdedcdedeeeabaaacddbbaacceebbdababdedbaeedbdbaccbcbbebeaeaceaeddeabdecbdacadaaeadbeddacedbeeccbeaaadddabdadeadbbbaccababdaeadcdedcdbbaccdbebbebddadbcabbddaecdbddedbdccdabebcbdeeebbcbddddbecabaaaacbbccaadccedbbcbdaaeabdaacbaececdabcddeeacbcbcadcdebceceadcbbdeaedeeebbecaabddbeaaeabdeeabecbaabcaddbebbbebebbeeccccabcbaedddbeaaaabdeebaeacdabcdbdcaeccabbdeeaabdbbbacbeeadaebdbebbaadcabaeceeeaaedcebcedcadeaaddeeecaaadeddecabbbabecbcdceadaaceceacdaebebceaeaecaabcececbbeeecbeeaeccaeaaabddabeeecebcadbaeddeabdedccdcaebeeebdbbaacacbeaeebdeadcbbeceabbbbbbaacdcabebadcbcdecdbdecbdcdcbeeaeacdebcaedcceecadaeddeceddeabdceddadadbddbbcbeddbdeeabbbdebddeaecddebaebdacaddeeadbadceeabdbaadabbeadbcbdcadbadaadccacedcacecccbecbabdeaaeaadaecebadceeeadbeddecbeebdeedbecbeceabebdbecadebeadaeeaabdcabdbcbcbeabecdeabecaaedeecccdcacdbddbcbbdaabcaddaecbbecdebbdcdeaceebeebeaedccbbaeedccdcccecbcacdbdddbaeedaceeecbedebbbcdbaebedbccadabebedcbebceccabedbabbcadbbeeecdaaebebbacebedbdbbebbaacbbbebcbcbcebeeedadeddbacbeedddabbacaebacceaaebababcebdacbacbaacaabdeeedbabcdddbccbdacdcccaddadecbccbbbcadbaeabbdabbdacacbaaaaebdcbeadbecddcdbcdbbadeadbcbbadddcbdeeabecddbcddbacebacdecdbdcbbbdebddadbedecaadcdbabddcaebaadcbebebecbbcedbdeebeadcabcceddceeaadebecdcbceeddaeddeeebceddaebbbcddaeeabaccebeeaaabccbdebeccbcabdaedebaceeeaccaabbaccebaaacabaadeaebbcdccdcbdbaecdbacabaaeddbddedebaecaaddeabdbabdeecebbeddebceebbadddcaaeabbbbdbaeaaeeeaeacccccdaeccddbdaadbcbbdcdeaedbcbacbdadadbbcdbbdbcdbaabbaecdecccecaabccabbecebbabdbceaaededcdbecedebedbcabbedacddabbdceedeaeceacadbbdeacbdeeaacdeacacacdecabeaabacbeeceecdcaaeedabdcbcbccbbedbdbdabbbaddbdcaeecdaeccedadbbcadcdbccdbadababaabadaddddeccaacedebbbeddecacdaacedcdcaeebcdecdedaaacadbabdcacdbbeeabdbeacdedcbadbbeeabbaecdbaadeddadbbbcadbeecaecdcabecbcecdceddddaccadabeaeaabeceebbacbcadecebacbdbaeccdcaacdaedbbebcadddddddecdceccdeaaaecbcabccacddebdddddedeaaaadbdeadcdeaaaebcddbaccbeabcaedaddeeebeebaceebbeeedcadadcdaeaacbeeebaddbcdaccadeebaedbadaaeedbceaaeabeabecdbdcdbdbdccebdcbedaeadaabdecdaacecbdedbbcdadbceaeacbdaebcdeeacacdbdeeaccaecabbcedeacbdedeccecbdeabdaeeaadabbbebdaecedeebcadeedbedccacdaaaababcdcaaaddcdcacdcceabbadabdbeabbdbaeacebadbcdcecaedadbecadaededdcbaebaacabeedbeedcbaeadacadbcbbcaabeaadaddeabcddedbbdebcbcbdccbeabdeaadeceedabccdaaccdbbbbdacdddcbcadcdabaacdbababdccadcbbacedbbcadeebcedecaecdbbecbaabccccbebcaaabadbbeddccebdabcddbbbdcbabbdbcbeebeeacaddedbcebdadacecbeacbddddaaabeceabdbbeddbebeedaadeddbabedbacecebbdbdcceebeedcddedacdabcaeadaaaddcdbddaaaabcecaadeaccadecbcccecddceedeecebabbecaceccebeedbbcdcccbdaeddcbabcebdbccaaadbdabebaeecdaeabbdacdbceebadeeeaedaaaadedecdcbadcdbdeeceebccccaaccbaaecbeadaadcceabcebeebaababdccebcbcbcebdcbedecdbdccebddbcabcadeebcdbcbdcbacddacaceebdabaeabaeecbbcbabdedbeecbbecbedeeaebabebdceecdedecbcadedaaeabcbeeaaccdeeeabacabcacedacdaeedbccacabccaeedbeeedcbacccbdcdeaaccededabcbbbcebeeddbeaaaddbecbaadbbedacadebaebedcbbccdeccaedeecbcadaebbdbcaaeeeecaebbbdbaecdaeddabebedccdebaadaebbdacddddeebdbeecdacdccadaeddebabbdbecaecddeaebeceecbbbbbaedcdbecbdddabdebddadcdcacaeddacabeedecbbcecdbddcecbeaabcbcecadebeaceadcddababaaaedcaaddeeccedbceaacdbcecdbdeadbbaaadceaecbcdeccdccaebccabccbaedcadccdecccddbcdaabcccacececcceabadcaedadbaebdecbadeebbdeeacaeeddebbcaabecbcadebaeebedaeeebaadccaacdbaaeacddbeabbeaddaeccadeaeebeabdeedbacebeeeeebcacbdbeaeedaacaaeebedbcecbcdcccbadecdddcedcdcabdeeaebbeccebeadacedabddbcbeebaeebddebcbbadaddaebbeeadbdacecaccadecdaaddeabaccebbeaabeeceeebbcebdccdbaebbbeacaddedacbebededecdbbbadadbbacbebaaaaadaddddedaeccacdaaaabdecbeaebeeedddddccaedeedccceecebbbaddebaadaedaecaaebedebccaddbeddacdbcdeeaccacacaccdeaddebbcaaaeecabbbeedbadcacbdaeeccbdcabaebbeccdecbcddcebebcbedeabbdeedabcedeabeacbbadbaacbbcddbebdecbbccadabcedeaacadcaaaddedadddadabbbdcbadbbbabceadbdccedbdcedbbcedddbbbdbbcbceebecabeaaaabdceaaecaaccacbcbccbcbcabadcecaccccabcbcbdddbdaccccacebdbebddcecaaedbceeedaeddddccebeccbeaceeddcebdbbddddeaeeacaeadaababeaeebcbbcdbebedcabcecdaadbaaeacedacedbdaaeedaedcbbcdedbcebcbccdcddbcebbcaeaaabbebdbcdceebacedcdcbcbcdedaeedeacadebdbccdbdbdccaacebcaabddbceaeeeedbdbbbacaabeacbdaeeeaeaaceacbbdecdcecdadbabaadbbaacdeedeabdcaeceebbbbdbdbdabacdccbcaaeeaaadcadcaecdecbeaceccbacccdccaebdaceaccceccaebdebbaacddbcbaecbacccdeaaabacbebdadcccacdecadebbbddcacbebcdbdceababeaebcedacebacbeeaaeddddcadebdcdcccbacaacbcbededeaaeeedcaeececccededcbeedabaeabadedadeebdaabacccbddcaadcacbaadbabbacbaaaeddabaedcdeaecbdaeadbbdaedecdebdcbebdeacedbaccedceaeeccdccdabdbdcabdbdaeccdecceaadddbdabcbabaeaccdddecbedcbadaeecbcbdbacbebabdebcedcdddccbaeabbaedaadecbccdddceababbddabcdddbbddadcecaababbeebebcdaacedaedebecdcdaaabbbceeaadbaedbdddeaeceebbddbceeedecdaabcaacdacbcdbccbdeadedabaebddeabbcbcddaebadcaebaadaddddbaadeddecacaecaebbcabcbeaeaedabdcdacdccacabcbbadcbbdccdebebebdeaabadaedbdeeaccdeeaaecacaaadbcedebbecbaccdcccbeaebdebbacdaaaddbaecccdbeecddeadcadbbacececdddcadeedaeeeceacdddecedecbeebbebcdeacedcebcbcceaacabcddaceebdeccbcdbeabbddbcbaecdbcbdeceacaaddabcaebbcaadbbbdcaebbabccdccbadbeabcaeebebdadaeaddabbacebcecdecccdcbeacaccedeecebbccaeaaaddaecdbedebdebcbceccccecbbdaccedebdaaedabadaeecddbbbcaeaaaecdcbbaddaccbcdccabbeaaeeaaaaaabbcaadacaeadabebebbabbaccddbbeebaaeeccbaaecdaeabdcdceacddaeabdeedbcaedbdaabeeaeeaddccabdebcbadcbcbbcbbaeeaeeeebebebededbdcdedebadbcbaecebdbebabbeeeccceadbaeabbdcbbcacbdadebddedebabaabeedcebebeabbbabedbcdbbebabebdeeaeccbdeacecaacdbeccabeaebaaabebceabeadbbceaccecdccedcdeaddedaaaaccbdeeedbbeabbeecebebcebbcadbcbcbccbdadecedccebcbebdbdabcddacccaacadeebbdaecccbaeaacdeeceadedadbaabecddcbbacecdaacabdbaeebcbdaeaabcadaddeeccebcbbcacbabdcbbeddcbabccaceddaacabdcbcedaecbdceccceeaabddeedeecdaeaecaddecedacdbbebcaadebeeecdcecdaddbaccecbaceedecdbaabeadabadadacacbccaaaddddeddacdbaedbedeaceedebcededbcbbbbaabbcabaadadaedabddcdcbcbdedccdaebeadccbaceedecdcaabbabdccdcededccbccdbbddbababacbcaecddbcedbbbeabcbcceacdcdebededbeaadaaeeceacdecaeebbbbcdbcaccebecadacaadecbcbbcceeadaaecddcdabbceddccedebcbaecaabcdbddebaccaceabbbbebbbcbdaabdabeebbcebcecceebcdbabaecadaaeceacddbccdcbdbcbbaecaedebbdbdeddacaadbdbdeaabebbaeeaaaaaebcbebdeedbcbdccceebccbdbebaadadbbedaeccaedcbbcedcececebddbcdbadcbcdcbccebaddaedaabaedacebceadbdeccbadceeabdeaebdbccbdbbbbbaeaadebebcabaeacbaadbcdeaebbeddaabdbbeadaadeaedbdcecdacdadececdaebeebccaaacbedddcedddccdacecabdabeedbdbbebcedbaedabcabdaeaccceabedbcdbceedaeccdbdabaeacebedabeccedeccdbcabcaabbaceabaaddabcedbbadccbbbbaeaebccabdedcedbdccbdbcaeceaabacaaabaebbeccdeabaeaadabdacaaddadadcecbbadcbcdbddddadaedabbbabdcaeccbabcbbbacbabcbbcdacddcbdcadbadecebbccbbeaebddecacbdceebbbddaabceecceddbbdeeeabbedceeeaeccbbececddbcceaeadbadbbbcacabecdadbbeacbebcdcacdcdcabcaeebacbedacaabbcdecdbcccabcabacdbdadadcbdcadccbedcacdaabaeabdaebdbdbbbdbdcebcbbedabcdeeabbdcaacceebdadaacddcdebbaaeaaeaedbbececcbdbdbaedcadcddcbadccacadecbdbbcbbcadbccdedadbdbcbbbbcadcdaebebcadddbacedaceeacabdabeebbedabedeabebabccecebeaeebcceebdecbdcdabdddeaecbeeeadeabbdbbdcbabaeecdbebbcebcdaeadcabeddacbbeeaccddcbebbaedbcceddbcdbecbedecbeeddaadbeeaebeceeaddcbaaabddceedcabcbecdcadcdedcbbcaddadecdecbaeebdacbadebbeaacaadcccebaeedddbdbcaaddbddcabdcddadebceedddbcaecebeaeacbcdaadceebbaecdbddaeeddcbdaccdbacaccbdeccedcebeccaadbeabebbabbdbeaeabbccbebaceeecebeaadedecdaaddccadcdeecaeaedbcbcbbecdaceaecdaabbbcadccbcbcccaeecdceceecaadddbcdbabedddacdaddebcadebacaccdebddcebbececcbeaaedaaabbeabeeaeaecbadaaacbacbaadebdadaaeeecbbbecbdebbbceccbaeaeedbdbddaeaccddeebeaacddaeedbcbbcdcebceebdebcdaddaebeddecbebededcccbecababbabbbcbbacdddcacaaaaaedbbaebbbebddddabbdcaccebeadcceebcdccabddcccddedbdcabcaebdaedcacbacceeccedebccadceebaedeeabacaeecacdebaaabaebdceddaaecbddddbcaedacbedaabbbbbddadbedabeaddbddeaadcbeccbcebacddaaccdeccbeabdcdeeeddcccecbadebdccbebbbedcddaddbceaedebbbaebedbaabbcdcdcabeadababaedcaeeddcdaaeaeaaeddcaceaecedaaaadcbbebdaabeebadaacecaaccededeabdbadeedeaaaabddeeecbabbccbbdacecabcbdccbaacbdbcbbbbedbaabacbebeabceeddcbebeabbdbacbcdbddaadaacdaacdaeededcbdccbaccbebbcbbdacabaedceeccbeeeabaaadaadabadadceddbaaddccaeabbdbabbdaeadcebecddecadccbbaedaddaadbdbadcddecaaaebacabdcdecacddcddeededccadcdecdebebeadebdaabbdadbcaceddbbdddddbdbdebdacabacdbadcdaaeaaebcbcdebeccbcadbaacaaacaccedabdadedddebeedabbbcbcbadcedcabeabeccebccdbacecabdceceaaaebaedabbebbdcacedeeccccaebebeadbcdaccbcdeacebbddaaaecacdbcbdcbbabcebeaeababbebdebbeacdcdcaadacebebbbbcbddebbbabddeadcabeaaacdaedbbeabaaccacacccbecedbacdccaccadeeddbbdeabacdbddacdeceaccaadacabdccacddbcaaeedadcdcbcdebebbbcaecabbdbdcebbaddbadbcdeabecbacebcadeeaeaedbcdbdbabdedceecaaaedeaadbcabbeedabbdbaacedbccceeddacaeadedddcebbbeeccadaaccdedbdcceecbadedeaebddacbbcbddabaaebdbdeadedccbbabcdbcdbaabceecdeeaabbeddcecdcdcceabecddbeeaecaecebebeaabaeaacbbabbaccdeebadeaaaadeaaebcaccbdeecdcbaedbdcbdeadcbcdcdbacbcccdadeabbcdcadbeadecdaceabdbaddbeaebdbaebaababccaaebeabdbbdaccadddbcbbbebddcbacbeeebcbbecbbebaaaacdcdcbaecaceccdeadbbcccdcbceadaaddbeccadbaaecaeccacabdcbdcaebcacbaddcddbbbbdcecebaabaabaaabdbceccabedceedeeaedeeaecadbcaceacaddcaabdbbdbbbbaabdbeeedcacabdaaaecdaabaaddbdaccbadaabbcdcccabacaabebbdebdcdceacaaabbcddbccaaacadcbcabacceebabbcdcbddaaadcacbcbdcdbccdacebadbeaecdabeeeaaceaadeddecbebaaeceaedbeedbdedccbcccebeeaedbbdbbaeeaaaedcbeaecedceaebcbbdacbdccedebadaededeaebbadceedbdaddddcbbdeabdeeecadebbdaccbeacdcacecaabaaacbaeddcdddcbedacdaeabaebbdbcaebabddddeadbdbdcadccebcabdbbcbabacaebcbeedbacbecdbddaadcdcdaeebeacccdcbdbdbcedaabbddddcdeeabaebeebcadbcbebcadcecaddddcacaceecedbdaebeccadeddbcbbeecccddacacedebedaaddbabebbacadbdecbceebcbcdcbbeacadcaccdaacdeaceadadebcccbebaecabbcaacbdeccacadbaddcdccbcadecabedadaeabedaccebdbdcdddeeaeacebedeabebaccaecbaadcdbbedebadbcacedebeedecdbddeabeeadbdbdceeeceeebdaeccacccadabadbacddcbbdeecbaeeacaaeeeceeeededdabccbcdebedbcdceebeeedcdbeedcbdebeedeedccbcecdebdeacdaaeecaddcecddcdcdccebeeeecdacecdaaccaeddeeebdccabaebadddcecbdbdedbaebddecacdacccccaadbedabbaabeecbceeeedbbebdddacbeabcbcbbbdbadddeebeecebecbbeeabaddbaedcaadeecdabcabdbceecebaddadaebbcdbeeacdadcbaeaacecdbddeaeeeeceaeacbedaabdeaaacedabaeedeabeecadcbdecdbdccbceeaadceeeddbebaedeabdcdeaddebaccecaaebdbeceeecbdadbdcbcdbdabdeebddbadecdbabdbbdeecebaceadceacddbdcbceacedbbcacbcdbdddcbddeabbcdcedeeedbbaddaecadddacbdaddecedededdcceccaeeeaecaaebcdeabddebcabcbdebaeadbbedcceebcadbeedaeebcdeeecebdebdacacbbacbaccebbeaebcbbadccedceaccdbdbdeebccaeeceecbbccdbddeadccccadddebcaadbaabbaeecaeceacbebdaebebaedecbcccaccdeddddcecdbbcdbccbbceabedebbeccceecacaaeedcacbcbaecbbbdecbdbbebbebacacaceebbdabdeddbceaddbeaeadecbbaecaeeebaebbacbcacecaaaaeccaaebebecbeeccccbcbdeacdcceeaeaabccbdeeeeeeebacdaaeccccababbadebdbecabeecdbbbcbaebaaedddacaebcebdbcbaabacaecbdbededdbeabcaeddbaeaeaaeacdededdcdedaadcdaceeaaebdeeecadaebdcedcedebbdcdcbbdecceebdaeaadaabbcecccdeedceecdccaeabdecaddeecdcbeaeccedecdebaaaebcaeaabedbdecbcbedbdbabdcbebdcacaeadcbebaebcadaacedeecadebabdcdcabbcebceeabeddadbcccecddbddbacedbaebccdababdbdddddbbccabdadebcdabdcaadddabcbabbbceddebaeeeeacedeedccabbcaeadccecadcedacbcccaccbecbbaeaabacbebbbadebbabacdcaababcbcbddabbcedbdddcdcbeeeacabccddcddeaadcbbcdbecdadadeeccdbeddaabdceebecaecdebcaceacaeeeecadddbdaecbbecaadeacceebabbcddaacedecddebebaacdbbeedeccccdceebaceaadacacaecaaecedceddebadbabaabcaadcddbaacbcabeabaeaaadcbacccdebadcbeabbddcbdcacdbdebbbcbdbbbddbcadaecbecdbcbededdbcacaecabaaebdbceddeddbbabdaeeecdbcdaacceebacbbecbdccbbadbaeaebbbeaedeedaaadabdaacbeedbccbbbaedaddbdcceddddcbccdcbaacdbccaddececceacebcbcaccdadadbabbeddbdceeddacadeebbeceadaebeabcdaaededdcaadacecdbcacaccccbbbcbcdebbedbeceeeabbaedcedbddaadddcaebdceeaeccbccbaebbaebaecacededabeebdebeaabdeabedbaaebdbaabdcceaeacaaedbecbdeaeabbabccbdbcadaebbabebeaeeedbdcabedeecacbcecadebaecdaeebaddbaabdaeddaacdabeddecdbcebcedadddbebddbcacedddcadeabeeeebbaaaeeeddeacbdddbcccddcbccabcbcaebcaaaddbacbeddbdaccaaceccddaacacadbdcdadeecbaecadaabebbbddbeedaabaeadcdaecabcdddebbaaceeebdbceeebacceaedaacdabdbdaeebeddbccdeeaaadddbbaabbabeebcbddbdddcbdebedcaeeacedaabcdecebedbbeacbecbaeabeeedeebdaabbadcbbbedbaaeadbacaacaedadeaebdddbbbacdaacddccaacedbecbebeadbedbdaabdcadedabcbebdedadcdbbebbcdaebecacababbbabddeebbdddccdaecbeaddcedbdcebacccaacdbedccbacbdebadadceebddbbaaeadbbdceacbebadaeceeccddaeecdadbecccaeadddbdcbbcbbccabcebbeacbebeeecbdeabdaebbbdeceebabdaccbaabdbacadecadadebadddabccedadaecebcedecddaadedcbacdbaeaccaaedbcdddcbceedbcacedebeacadbaeaacaddecacacbaceaceeaabdbeccddcaabaadbcebddddbeacedacbaaeecaedeedbdededadbaaadbabcccedacaadbcbdaaccccdadebdeeaaeebcbabbbdbaabcdbabbbddcacdddeabbdaceedcedadcdbecbedadabccedceaebaeccecdddeeeaabeeaeeadbbcaecaabaebcdccbdbdcbbcadadceedcdaaccbebeedecababbddebaeaeededcbaeceeaacdcdaaddcadbdeeaaccebdeaecaaabbebecdedbceaaeeeaeededcacbebecaeeecbbaadebeacedceadcaededeebeadbcaedebcbceeaedeeebadaabdeacabccbdbdbddcaaebacaebbcbaabbedcaabaaeaaedeacdbedebeadbdcebeacadedcbbabeadbdaecbcaedcdbcccaacdacacddeecbbbababedccdeaeddceccdcdeabdaacaccbabeaacdcedadaabbacebecddeebebbbebedadacbdbbcbbdaeaebebdcaddcdbdbaeebaaceeaeadbdbcdcdcdccbdbecadebbdcadcabeabbdeaddaadccbcaaabedbebacaaccabcedcbdbacdcbbadbcbdabccdbdbbdebdbcaeebedaebbebcceaedcabddbedeeaaedabccbdbeccdcbbaacebdeeccdecdcaeeeaadeccdebadbcadddbbbddedccbdbabedaccceadebaecabdedceababbeaaedaadaebedeebebeebccdabdebbcaadcccdcaadcedcacecdadaaeeedcdbccebcaeddeabdcbbcdabbcecccbedeacadddacaaddbebccaecdeccacebbdaceeaacabdbdbadadcdebcbdbebdebdcbdbbceeedddeeccbcadbabbabecbeceacdeaadaedacaeaecebbdcddaeceeabdbddaddcccebaecaeceededebabbecaabcdeceebebecedacdbeadbaabbeacebaccdbadbcbdddbcccecdcaedbcddabedcabbbedebcdbcbeacaeeacbcbebcecaabddedadeddebbbbedddcbbddacbccdcabdbcccceaebebdbebbaecaddaeecebecdcdaeccccacbbeacdaacdadacdebdcdaccbbcbeeedacdabcdbdaadbcddebbbecacdcedebaeebaaebddecaabdebedceeaddcdecbabeecacadcabbbdeddeaaecebedcddbdddcaadcedcebaeaaaeabdbeabcaaacdaebbeebaeadbceaddadaeddcacdbabebebccdedecdcbadbacebabaebccaddbceabbbceccaaabdddeabbdebecececddaeaebccccbccecdebbbcbcaeccddabceeedaccaacdecddabcdbcbdbdaceebccdbbeeeaebdbdcbebdbbedcdaadebdcabbeaeedbcccaebddaebcaddcbeedeebcceeccbceeeebbcacbcadbdbcaaeccdbbdacaabbeeaacdbacdaccddeebbcedbadbedbbbabdcabbcedaecbbaeacedddaeabccdadaebbaadadeddbeeeedddbbdbadeabcdaeaeeaabeeedeccecaebecedbdcbddbcacdacedeecdaeacddcdeccbedaeabdbbeadeebceeddceeacbcbbaabbedccaeeacecdddebdddeaabbacededbcebbedbcdccbcededcacdecbabedaabddeedecbecceaaabccccebedcecdeccdcdaacedddecceedcadbbceacaaaecedbedaccaabbadadbacdaadbabcebdbedcabbacabbadeaaddbdbcbacdcdccddacedbdacabbdceaecadeceabccadaccdbaacdeeaeccacddeadeabbaeacbabdababeecddaadcdabceceadeadddcaaccadcadedbcadaeeaeccebcceeacaabdeebbbeedccdcaeeedaadbeaddaacdeedabababaeeceaaaeddadeebdcabbabdeadddceeeaadabbbbbbccebbaeadabcdcdeeabadedbcbcccdbadeaaaacbccaedabaecdeeaceeecabccacdbbaecdaebeededecccbbacabdbbbddadbcebdcbccceddedceaddcbbbdaceccbdbcbaaebecdebeebbbebeceebabcbbdbdaeadcdbdbebdecccdacceebbacadaacccbcdbabbbebbbdaeeeaeaeebeecaecbdeeedabbdecbccdbcaebbbccbceacaeaabbcccadededcaabcbccbcabaaadbabeabbecbdcdbabdeeaaadbccbbebbdbbacccbaacdccbaaeaacdaceebdabbacbedbbcaaddbcbddedcbbbbedcdbadeebacdbabcbcbdebddeeedeeadadcbdcebaadbeadbdceacedeebcecaaddddaabcecdabddeeadbcbeecaacbcceedebbaedbccbbdbabeedddcadcaadaaabbbeebbcababbeadadeaaccdbbbdddabeedabceadcaddecbbecacabaccabacacbaccbdbebcdeddbabdacdcedeeaaeaacbadbdcddebeddcccaadcdbdbabbdabedbbcdecaadabaaeccbbbacadacccbabeaeeebceaebbebcaaedddcbccacceabedebacadcaeacecbeeeaaaeeacbeadadadbddccbdcebdceabeaaeceabdbddabacddddcbeccdcacbcadcebcacbbaaedebcbadeaaeaedcbbccacdaaaebbdaeddbcdcacaddcaaacebcaedcadecdcdcbccdeebbeabcceadaeebcccbddedbdcaaccbbebbcbcdeabaaaaabcaebacdcddedeedbddadcbedcaabcadbebeedddaacebeeecbacbedbecdcebaabecbedecbaebccceeeacacebbddecddcdbedaecebebaaabecacbbaeadcacaadccecdeebbbbeadcbbecacaaaeeaaeeaadbaaacedbbcabbbbdbdeabbeadaaceabeeabaabdaaecadbdabeeedeeaeedcaaaedbeaeadcbccbbdeacdbacbccbeeabcdcceedaddaedcdebadbcccbddbbeaebaaebbaeeaaadddbeeabcecabccddbacdaaadcedeabbbdddcdbeaeecebdbedcdcbedbdcaeeeecbcadadaddcedbaceaaddbbaeecbcabbebdaeebdeeeaeebaabeeebcdbceddbdbadcaddbbcabbcbabebdcbbbacbbecaeeeabdcadddacdbadcecbeaebcbdcccaabcceeeaecbadbbaeabccddbdceeeeeecdebaeebbbddddbeddceabceecccacbcabdacacbadcbbadecdbeadaacebdacaabdacbbaacadcbdddbddccebaceceaccebadcabecdbabbbaeebaaddcdaaaebcbbacdbaccaebcdcdeceaacdbeebacdadedebbeebdcbceacccabcddedcacdabcdbdbaacacedbacccaaaababedacdadeeeadadcbadaadddceddaecaaadeeecacccdddcbdbbbcccadbdeaecadcacbecddcaddaeeedaedbedadccbcbeadeeaeeddbeaddaeddbddcecdccdaeeacebcbecaebbbcecacccecedeedcbecbcdcbccdeaabeccaebedbeeebddceadadbeecccadbadcddecabeeadbadbdeeeddebdddcccbcaeecadddebdeaacbdcdaececddbabbeaadbaaeabdcddbbaebceadbdcacabaacdaeceeacbacdaebceaacedddeabcacdaaecbaceaaaceabbaabbebaaaeaceaedbccdabedebdccbebeadbbbddcdbeeeecadcceccbcbacdaaddcdacabcccedaacdceaabbeabbbdcdcabecbaecbddddadcdadbadebcbbaabbbcbabdecabebcadabcdccebebceaaabeadcedbeeaccaabebcbbccbebcbbbbaeeaeacbcabdcccbabdcedbdeeddeacaebeecabcedaddeddeeddeadddbecebaeadbddddecdbadcbcceceeabbdacbbccaddeacaeacdebeeeecbbccecbabbebdbebcdbaaaeaccaeebdaddacdeeccebbbeeccecdbdaddccbadbadadcdccbeeebbecceceaeaadecbbdabdbbcbcddcbcadcbdbbccabdeddcbbcbdaadaedbccdbbcceedeedcdeeddcadcdeaedeeebccaaacbaadbeeedbbcacacebadeeeaebcaccbbbcbecebecadabdaccbaaeeceebaaaeadbcaabedcddeccadabdeccdaaedaebbdadbcbeadadedcabdbebdaacaaeedcecabbcaeadddcebbeadcbabaddcebaceebceededaadaceecbddbedcaeababdbcddbbdaecdbaedaedcabbacbcdadaedcabddccccbbcceeedaecdccdeeeedbedbabeaadddeddacbbaaabddbbecebddddadceccccacbcadbbcabbaceeccbabbbdceaaddbcebecdddcaededbaeeccbbacaabdcdbdabbbceaaadcdacbbabaaebbbecbeaecaaedcdebebbaababdebdaeaabeacdbcabdaeaeddddaabddaebdddaceceadeddedabddccdeadccceeeeaeadcbcdaecdeebcabacdabbcddadbbaaacbcdddbeadbadbecdeaabcceaecaeeeeadedccddebdedbbbeacdbbccabcdcdedbddaeaabcaedebdecdccadcbdddedbbcebeededbeddebccbbdaceabcabdbddcdbccadcedccbedacbceeacaabcccdbddebcdebababbecbadbdbbbbecbeeecbdceedcadecabeaddbddbbdadbdaeecdceccbcccbcdbceaddbdaebbbceeebcebcacbeadbeedbeaedabdddbeeeacaaeceaddceaccedcdaccaebdaabbcedabbdecdedabedcedadeecacbedeeebcdeaecdcbecaccaeeeeceddedddababaebddcacebcdaedeaceedbcdccdecadadabcbbcaadabeedbaddacaebaaadcbadedcdedeebdcbceebaecbcaccabeceabceadccaedebdbcaccbecaadcddeadaebcadceccaedcbccecacaceaddaacaadacbdaccddaeebbbcdeccaddeaccebacdccccacdcbdccbbadbbabcdcaccbdaddcacbeeccbdaeccdcedebeeaabbbdacbccbdbeaadebabcbdcccabaedceeddbcadeeabddcbabdbcdcdbcebeceeedaaabebbecadeeddbaadceaeebbdaaabeacbaddcaeadccbaeadacacabcccaeedcceeddedcbabbaacacdeedbdbebbeacbcdecadbcdbcbdebabecbaacaaecdddeaedcdbccaabbccaccdeeeaadabbaabbebaddaadaaaeecbcbbdaceedaaeebcbbcbcddcebaccbaadacababacbedcbeaeadbbbadceacaecabeadbddcccbadabbbaebadabbaadbdbccceebbcadddbacaeeadadaaeeeeeebeaaacabcdbbdceebbddeecbcbddcbbbccaacddacdebdccaaccdeaacabadaacbcacdbdcebeeeaedeebadceacbabddadcbddaedbdbbececccbbebecaedcdccabbdeeaadbbbacbaeeadaedcaaadccabacdbbdcdaceaeddaceccdadaedeeadebbbcaceaedcabdebedaaddbdaebceabccddddcdddbcccaddbcbecbdebadbdbdbbedacebdbdcecbecdbbdebceeccaadebcaddadbbecbaeabdcbccabbccbbedadbaecabcddbcbadddbabedbbbbebeddbbdccbbeacbcadecddcbcabbaedbbdddbbaabbaacecaeecbccbcabeceddeabacbbeecbbcabebeebceeedebaecbaeebeaeedddaacceadceacaaedcacbdeadbdeabbcdcdbbdbaedbaedbcabbcdcbadceebadcbeedaaddcceaeaaaecdadacaacbdbbbadcddebaececceccccaaacccebcaededacaacacadbdbbbbeabdbebdbeebdaecadbeaaaaeaceebdbababcaacabccbeebdabadbacebeeccdcbdccdeaaebdcedbeaaddaeacdcbedcbaacdbccccdcbbbeeccbbcdccbdaecbaabdadcdcdecebeeceacacbedeccbacbcbbaceceeaaeebaddacbacceabbdbaebdccbbdececebdadddbddabcbaadadbeeeccbdebdcabacceecaddadccbcdeccdcdabacdabcdddcbbababceeeceaddcdccebcdcbdaebedddcddeddcbbcabecabaeaadbbbebcbeddbccacaebedaebaabaebbacdadabcdadccdbeadbaaedebebcecdacdaacadeccceabdcbbbabdacaebecbddbddbbcccabbaeedacaeeeecdeeacbeadebbbbbeabbeaedabcbbdcdcebdcccbaacaabdbdddedecdaeeadcbeeadcdaceeecbbadbbbcedcdacaeaeedccddceaecdaeadaabceaaecdebcbddcdabdbcdcecabaddedbebabdcbcebbdebcbbbbeaecabadeadecbdeeddaeadbbccbdcedaedcaadedadedcdaaaededbbbdcdeeebdbcdcecdbcddeebccedeeacbeaadacdeaeabedbeedbeeddccedcdcebcbbecbccedaedadeaabcabcddbadecaabebbbdcebecccdeedeaddcadaebcaccccbdaaddebcebbdeabaaeebbddadbabdabdebabbbdcdeceaadecdeeaadabcadbabadcedbedadaaddadacdacbbccbeadaebecddceacebadaaceabebeedecaaccdaaebabbaadbccdcaabcbbdabbadeebededaeeababdeddeeeeeadecebbbaaadcbdbcadcdcabdbdbdceabdbbabeddabaebaaadeeeaaebdaaaebacebcebaccecaabdbdbdbabbbeeeceaaabcdcbdaaaccdddeddbacaebcaaabcbebbaadcccdcbacdddedcddcdccaecbecaaabeaeecbbbaecdcadcbadabbdccebbecdcecebadddcbbaedeacecdacdacdcabbebabbcbcaecccaecbcaccbcddbaebcbaadeeecedaddbcbbedcdccccaebeceebaedbdaceabcbacdbaabdaeddcaecabedadecebcbeaacdcedcdbebecbedbdabdadbdabadebaeacdbdbcacbdcaacacdcedcabaedeadeceeabdcedbedaeaeabaedcdbcaaaaccedbdaaaaecbbbdbadadabbccadcbaaceddedacbebcabcdabebcecceadaccbdceaedaedcceaccadbebcbacbcbaaebcbdcdbecddeebdcbcdaaaaeccebbeeabcebbeabccdbbbdbcdccdcddcdbdecbcbdbcdebeddaceddaddbcbcadcbcedcdddecacbdebcadccedbaecdbeebebabbbaeabbcedeaceccecccaebbcbbddddacabacedaaeeaacaaaacbebabeccbbacbddddaacbadddbbbeedcdabaddbeeacebeabedbceaeedadbcdadcaaaadedcdeeeacdcabbdcadeaebcdbdddcbabbbadaaaadeecdeabacbadaaebaacaaeabaedaeebaddcaaddddddebdecbbbeddcbececbcbdeadcdcbbeadcceaaccbadabdaecdbdbeeabaaaaaeabdbdecbebbbdcbaadebbaaeebcccdddcecdaccddbacbbddceaecdecbedccdceddeecebaecdecdcbaededecaedbacdecdadaeecbbcccbaddabcecebdecceaaedbbdccbeaeececbbcbaaebbbcedeedbddeeabdbaaccbbbcdbacdccabdeebcbbccbbbacbebbebbdacccbcecdddabecbcadbaababccbabeebaeddbbbaceabadbdbbabaacebccdebaddebaeadcdcecacededcaccdedbccbabedacacdbcbdaacadedbdaddaeadabebacabeddbcdedbaeaebbcebcacabaeadcaaacddabeabcdcacdbcbcbceabcdedebbeabaaabddebdabbbcdbaddbbbcedacbdcaecbeaddcaaaaacdacbeeabcdceaaeecaaadddeadadadcacacddeddcceedbdbaabdbcbabbcadddaeceaaebccbceaeedceadaddcdecbabdccdcdbbaddaeaebbaadeccabcddcceceececcebeeacccabbccedbbdabdeaeecacdadcaeeeecdebbdededebbbdabeababdebebabbdbacbcabacdcbdeaeeabcadcdbbdadbddddaecbdcaaeeddedecaaddbcdeeabeceeabebdabbbaecedcdddedceebbddbedcebacceccceceececbdccacbcdbcadbdeadbcbdbceaecbcbddbacaebedbdacdacccbedacacaaadedabacbdebdacdcdbdaeaaaeecdcdbacbdcbdabccbebdcbcedecdedcbcceaceaaceebeceacdadcbedacedadececccabedbabdaeccaececabecbbbcadaacaabcabaeacadebacabcbeeaeadaeaebaaaaaeaaccccddddedcceeecbeaeeedeecbedaccbbcedddcaaadadcadebdcecacdadaeddedddedeacbaaecdedddbaebbdabbebdacbcbdcdeabdcdcdeabbddadaabdeaaadedccdaacdbaaabcdaaccbabdbeaaeecbaeadceeacbdeceeaebddbbdcadbccebdbeabeedddddbceabbaedaeccebaadcadeeeaaecbdcbecaebeebeccaeceeaaecbebadacdebaeacedbaeececdabeddbdedcbbdeebadabbdedabeadecdcacbbedccddaaeccebcddadcabbaceecceedededeacbdcaeabaceaaadcbcbbaabeaaeedacbadddecddaaedcbdbaeedeceacedddabebcbbeeabdabebeabbcdbcdabcdbcecdcaeccedbbdecaeadbeedddacabbdaeecddababeeecbccacddaccccecabdebbebaebadaaaaadddcaceaaecaeddedbadcaadbebaebeacaaabaaceaceddbdbdeccbeeeccbceaaebddbbaaeabebebecdbddcddeaedcaeadebabcaabebdabcbdaacdaebbeedeaaabdddbbdbaadeabccbccedcbbcaacdbbccbadcdaccccdaeaedbdadeceeacbcebcabbaeebabeaebaaccbedcaddbcbcbbaddacdaddcdedcabbbeeeccaeaeadaacbdadcdbeadeecccaebecdeecadbaebaeccbaebebeeeaadcddadcacaaaccdecadebcdeaeebcbaeebcaaeacbebaecdedeccbdaecacbbbdeddabadcaabbdbeaeecaeedacdeecccbcbdbadebcabcebaddcaeaaddbaecdcbebdecdccceaccebddceceaeedabbceeebcbebabdebbdccebcebdcbccabbcdccbaddcedbbabebbcdecccdedcbcbbadedbbdaebedbacacbceebccdeeedaedcddebccddcaeabddcbcbddeadcdadabeeddddadacbabdbacccadcabdcbbacbadebdadccbbdcbecedeedecadcbaeaebadebbcceadbabbbbeeccccbcaaadeceebceecbcabdacebaacddeacbaedabdedaaacdacacabaeabbaedaebbadacbeedaaeedcebbeeddeecebcdccebbedcbaaadaeecaaccebabaadecbebecbdddeaebaccaecacdeaebbecedaccbebadbbeddddebcceebdadaedecdeddecbcdbdbbdcacccecaebceabdccebdcaceeceddcedbcdeabaeacacdcaaadbdcebacdbeeaebdadeabcaaabedbcddcacbbdbabccbbcbeeecacebeebceeabaedcbceacaabebebbabcacdecaddbbdcedaddecadcaeccacbeecbdaecabdacdddccadbabdaacecccbddaebcaabaeadaabcbaeebceecdbbcabacdcaeeebcbddbdeceecacabcbddbddabaccaeaddcaddcbadaabaabcaaacbecbdcdaedbadabaaddebbbbbabebecabedcabeabacccdaeddbdcebabaccdcddbceecbcdcdceccdbeadaeddebedddaddceeaddaabdbecbdaaedaeaddbcdbcdbadddddecdeabbcadaebceccabacccbdcceadaccbbcedecdbabdaddadbbbcedcedadeeaccdeadeacbcdcddedccacbadbaeeebeeabaceabdcddeeeaabeccbbcbcbbabdcbaabbdacdbeddaeabeacbadbeedaacdceeadedbabddccccdeadebdbaabbacdcadcdeeceddacbcbddeaadbaeddeaabeaacdadadcddeaacceecdebcbacedababcaaaacbcdaddbadcaabcadcadaaecabaaceedaebddbdcdeebeadeeabcdeedededdcebcaaeceaddccabbadaabaedcccedccdeeadcedccbddeadcdabcddbbacdaddbaddceddedcaebedcccbeaeaacbbbaacdcbdbdbdcceccceeeddecbbbbaaedebeadaedebaacbaeddaaedbabecacbdeacbeeaabaeadadbabbceaacdbceecececadaabeedcdcacabbadacccadbbeacaaedcedadccddceacebcedacbcdcbceedbbeeaaedeaecccbadadebdcabdddedeecccdccaadceebcdeeaccbdbaadadabecddcebaccedddcebeabddacedbabdcdaedeceeedcbdbacddeabceedadcacbaedcdeeaeceacbbddccbadeccaebbcccbabbddcbdadcddedbeedcdcaebacbdbdcdcddbbcadababedbddebccedbdacaecdedeabbeddcadaebbbcdeddacaaccbaeabcceaedbdbbecebcbadcadeaebdcbccaabecceabaabeeccdeedacbcbcbebceccaaaceadedbabbaddeddeaedaabddcabecceebcecdbdcebbcccbebbddeadcbbeecbcceaaeccbbbcdbdeebdceeaaaeaccaeececeedcbcdebedaeeeacacbcceeccaccadabddebccadbdcdeddccdecbeeecaddbdaddceecdbcadeaceeecabcaebdaecedceeddecbecabaacbdbabbdccccaebaaacdbabbddaecececcdcbabddebcdbadadcdccdaaacedaeacdbbdcaabccabcaadeaabeddccbddaaecaaccbcbddebbcdecdedbbbcebbebddcbbaddceaadececbdbdaeebcedddccbaaceabeedabbdedecbdadacbccdbbbcbdcbeeeadbdacbadcbbaadcecabebbcddcceeecbbaaabdabacbbdcceaaecaebbeadaddddeedbdaceabaabbeedadcacbbbeacaddaadcbacaaabddeeebdcacbbdeeabdcbcedebbbdcaabaaeeadabacbcacecedcbabdaacbcccbcabbbebaabeeaabdaedcedeababaecbeebeedcbbbcbebbcdedcaceacbadcebcadcdeeabbeaedcbcabdadaedcebbddcdcaaedaceeaeeebeaeacccaedaeccddcaaebedbaeeebdbeeacbdbabdaeaeaececbbcedebebeeedbbdaebedaecacdddcaaacbebcbcebbceeabacdbcdcadadacaedeacaddadddedeebddedbebaaeeaeacadcacbccbcebeddecbcbdedadcdbbcecdbabebdbbdbacadceeccbaccaeabbadeaebdadaacaecdbbbaeeccdedceaadbaacdebcaedaebbeeeeebdadeeaeecdedaadaebebbeecedbbcbedbbedaaaddaaabecbabacbbedbdeabdeadeebbbbdacaadbadcdecdacdbdeabeaeaccdedbcddccbaeaddbdbbcbbabdccceeeadbeeddedeeccabbaadacbbeaaeaeebecdbaebeaedeacaccebdbccabdbaddcaaebbdabbcddbbdcbeeebacabdbdeddbeecadedaccaedecccabecddaadcdbdccdcceaabaedcdbbbbcebcacedcbcceabdbcaebccdcdebdaabddbdababdbdaadeedeeacaadabbcdccbababbbcbccdabadbadceadabbaebddcdbbccdcadbbabadcbecebeddbeacaaedabdcbddccdcdbabeabdebbaeaabcbddcbbecbcbaacbebabcedcedabebccabccedcddcbecdeaeeededceedeebaacaeddbaadbaaccebedecbbadceddddaacadbeaaeccbdddeebbcbcbededceeeacadaaeaddebcaedbaeddaccbcaabbbabcdacbabbeeaeedbabcdeaedabaecededbadbdcebbbacccebddaebceeabdbebcbcdebedbeebbdbcdacdddceabdebaeecbccacacbebcccadbbdadeddaccaddceecadbbaccbdaddccadedacbedadadcdaeadbbccaedccbdadeddacecdebedeecbcddcaeaddabedeecddecbeebdadeeaedaeeedceabbebedececeeebaebbadddabdedccaadaedeabeecaeedecbbeaabaadeccbacddbaebabcabacaeebccdeabdcdacedcddaecbbcbaecadedadebddbcdceecbbdcdcbcdcccaeeceedabdbdeebcbeddacbceebdbeadbbdbbcebdbebedcacddebdacdecedcdeadeecceabeddbceecdecdddcdcdcabddbacbdccccdeaeebadcbeeecdacbbecbdcacbbcbcdbcbbccdadcaecddbeabceceadebedaeaddeabaeacaadeacbadebaabddcbbbaaedaaecbcabecaacccdadaebeedcecaedadeeebcdabcabdbddeaccaeddadaaeeaadbeabaebdbbaadbaaabaaeabaebaadccbdedbecbbebdcceedbaecbadbadbbbebaeabebdcbdbedcdaabbacdcabcaccebebccbbdacabdeaaceedcdebaeacbbaeecacbabceccebcbbdabeedbcbecbecdddebceedbbceeacbadedeebcebdcbccbdceadddecbceccbacbaadcededbbebeedaebadbbdecedddbaeadedddadedccdbdaadbcdbaaeeecabaeddabbbeedeebcdcadbdebececccbbacaaacbceccddadbcdbceeaceceedbaecaecadeddbbdebecbecceeeddadbdaaccbddbdbabdcacdbaeccddacadbbbbccceaabcdbcdcbdcecebeedadadbbdcedcaacebdaccccaecdacaacadecbcaedcbcbceadacebdbcaddacabedabcdceacbdbaaaadcdebdeaaeceaeccbcdbdeccbeaddbacdcbcedcadabbacdaceeaaedacdeecaaeaaaddeebceeeebdedcbcaaeccadcdeabedaccdbddbaaabdbecbbabbdbdeececceaedcdeaeadeabedadceeadeebdccbaccbdbcebeadadbbaedbdedebdaebdbdcaeeaaaaaabaebbaebdaedeeaeebaadbabaacbeaceecddaaaececdcdccacbeebdcaaddacbecbdcdbdcbaacedecbdbbebbedaecdeacbbcebebbacaadbbdbaabddddabbbdccbabbdaabcacbcebdbbdaaccdeccadebaeceaacdabcbaaedbecaedcedbabaacbbdcddaacdacbaeaebdbceecebeecdeccbadddadbcaebeaebeecadcbedadedbcccaadcacaaaddbddabbbcdddedeebcabcedebbbddbeecdcdcacbacaddadbbaaaeacbbbecededdecaccdcadccccdbbaccbccddceaadbcdcceaaaceedbcccebccceacacaadacadaedbcaebeabcceebeedccdedcebbabcbbadadeaedddddbeddaeadaedaeaeebddbeccebdcbcadaadbcecaecebeccedeabaedccbeeebcedbbeaedbaadcdcbcddbeeabccadccbcbedddcbcacdcabbedcdbaedbdaaadbbdcaaabaccbdbbabdeacebbeaccaadccccbaccaeeecabeacabddbbacebeacbaaebabcdddbddadcdbcbdbccdeacaeeeaabababdddadccbbcaccaeeddeeebddeceaacdeeaddcdebeccedabaeddbcdedeadbbdabcebedabbedaabaaaebdacadaacebccdceabbaccaadaadeecedcdaddcdcdaeedebcbedebdeadecabdadeeddaecdededebcaaaadcacedabcbedddbaebdaeccedddddcbceedccdbdaddcdeeacedeabdaaeadbeddcacdeecbcdabbedabecabceddccceecbddbdccedbeeaabbdddeceddddadcadbdebdceeddaeddaaeadeaabeabdbdabeaeddbdaceecebaebbabedbcdaceaeeceaeaebedbdbdcadadccdcededcabdbddacdcbabadbacabcbebdcabdabaecaeebecedeeacedbdddbcddbbeeacaeaabddadceeabdaabeebaaddeadaecddbddebdddebbbacecbeccedabacbbbaebdebacadcacdcbcdeabdbdacdededeecbcbbdbeebdadbdccbacbceceeebaaadbbbbcaaeebcaedcbabbdcabcbecaaeceeeeaedecbeecbedcceabccaccbcedaaedbdbdaadbdeaecdaaedabbcabbebebdbbecbeebbceddccbaebcbadddccceeeacaaddeedbadcdecddedcdbbdbeaaaebaaceeeddebabaccaaacdaeecdebcaccedbbbbeecbcedbbcbbbecbdcbbcdddeddecebdaadcecaedcbaebddcbbaccdbaccaeeaddcbcbeeddcacdccedecaeaedbecbcccdaabbdbdbddbcddacccebacaebaaecdcedecddbcdbcbbecaceddeeecabeaabdbbaabebaecaacadeacceeaaeabbcaabceebedeaaeddaccbdaabeaaabddeddbbebeaddbaaaebbabbbbaedcecbbbeceadbbabeddabeecebeecbaacebdebccaedcaecadcbccdabdedbbcbceadbaeddedddbeedeccddadeebbbeadbaaadadeecedcaabccbebdbdeebdadccccceeddcdaddecddabaccdbaaacbbbbaecebbdddcaeabbdadebbeccbeeebbcebbbccbccdddcbaeeeadceeeceaeecdbdbbdcecbdbbabbcdcaeebecbdeceebdaaedecdecddeaecebdbbadcabceddcdddccdabacdaeecdecdbcadeddbeccacbceeebaebbddedbaaaabbeacecabedbedaebccecbdbaeaebecabdebaddedcbcdaecedbbedacbdebeaeaebbcdaceacbedbcbbbcedbcbdbabecebeebdcecbdeceebdeccaebbadababcddabbdaeecaacdbdddcdcdcecddbaabbbeaedabdbbebeddeecbdeeabcdbacdedeadcebaeeedcdeebeccedcddebedbdbedbdceecccbbeeacbcabcccccedcebeeacdbbeddbbabddcddcbdbaabccaacbbccceabacdcdeccebeaeedaceeecdbbaeecdabbdcdcaebbdebbbaacdeeeeaadadcaaceeacedccebebaddcdbcebeadedeecdabbcdbedddddcdddeaabbccaddaaecebecdededdcadcbebcecaeebcadcaddabdabbceddbdedecdbbbaeacabaaedebaccbddacdbabeceeedcbccbcdeeceebedacaaaecddebdaedcbbdaebbeeeaaadebebeaaddaddedaecaaeaadeebceedcaaebcbacbaddaaccbecaeebaccdecbdddaaceedbebcecbcaddcedbdcaccbdddbebbaebcdbdbbbeacededdcaddecaaecceacacdeeebbcbbbcbbdeaaaabaacdbdcecdeacacbcdddeacbaadeeebbcccebadcbbebbddeccbbaaeeabceaecdeecbebdeccdbeadaebecbdcdbeecaaabdbaaacadaccedadeebbabeaebdcecaebdeaabeedabdbbebddbdacaceecabddeeaaadbdeeabaeabadbabeccacbebaeeddaaeedbbdcbbacdbbdbaacdeadadbdabcaececdcebdaaacbadccdbaaaccceabccdbbdaeaabdcdacbbbecbeadccbdeedaaeccbadacbcdabdebbeeaccdbcaeccebbcbaaabaaecddbbecdcbdbabeddbadeaaebaacbeabbbcabedeeaadbaacebdbaddcccedccddceedadeccdcddbedacbcedacbabdacadeaeeabbecbbccacbdbcedbbdbbeeeaddbcdbbdadbdacecdbeddeecacaadccbeddcbdabbceeebaedbacadebacadacdcbeaeacacdabeccedeacadbbaaecbbbcceaeadddceedcaedbcdcbedbcdaaacabcabdecdcabccbbecccacdcddeabbddbeabbdaeccacaaacebecedbddbcabdccddddedccbacaaeaedaedcbacededadacceedaadbccbccabaacdacbabbdeaebddbbdaeaeaabbebbcddbcecdcaceacdecdcbdeaadeebdeeaacdadeaabeeaedababbdaaaebccdabacacaccaaaeebdaecedcbcbbcbedceadcaaecdcaddcbeaacaacaceacdbadbabcdbccdecebecadeddadccdebddadecaabccebeccaebccedecbececbcebddedbdacccedbbcdbccddaecbeaeaeaedeeedbcdcababdceccceddbecbdbbdadaebccdeadeedaedbceaebddbdedaddadabeabcaedbbebbeaddbaabebadddeebdedabdadbdaccdedadeeaaaabbddbeeadeeacbcbacdeebcccabeeaeddbadcdeddeebbacaacdecedaaedacebedabbedccbceabbaaddcebcbdbbcaebecbedbbbbcbdccbdbaeedadbaeaecebeeaaaaaeebacbaaaadeecacaebbeebebcdceaeeeccecdaaccaabeabbcecdebddcadceccdeeaeabbdccbeedbedeabadebdcaddeaceaacbaaebbabbeedeeccecdbbbedbeecbcbabeaccbdadecaadeaeeeeeddedbddcaddbdbaabdcaccabcbbeebbeccdadccddbdeddbcdaacbddbdcabddccbdeacadeeccbadecbbbbbecdbcaaccadaabebdaececbdddebddceabbabeeadbeeadccecaecdddbcbedeceecdccccedaedbcadebbcbdcdababacdcdeeddcdddecdcbbcaaaaeddbdabaaeebbcbcaecedbddeeebdcecddeedbadeacabaeaaeacadebceecbabbdacbdcbaedcbcdacddedbacebbddacbcdedcebaeaabcedeebeccccecaaaddeadeabbeededdbbbeaacbddbbddeecedacddebccdaaaedcddbcddeacedabbeedbcdcabdecabcecdbdcbeadbeeccddaabacbcdacbaddaaeeaddbdccbccaacbaacdeadaeceabcebbeaeeddeecdcdeccdcacdbbaeebedcbeeeabcabcacaecbdcebccaaaeddcaaeedabddecbeebdbcedccaebccececccadbbecebeedacdbbaddabedcbeaeabbdeabbadcaebecebedcdbaabeaedacccdcbcbcabdcdabdeddcceccabadcecddbcadcddccaccacedabcabeceebdbcceaaabedbacdadddeccaaaaeabdecabeabacbbdbadeaddcbceccdbcdabbdcbabbdabacacebdbdbeaccbccaacebeedddbcddbcebedaeebbceedbaeddeeeabcadcecdecdecceedebbabecccbedaaacdcacdebcebcbabccacabeecebebdecaacdcdccacbceabdbdaaccaaedadaaaceeedceeacacedbdacbbcbaabddeaccccbddacbbaacecdaadebacbaaabeaadbdebabbbacecdaecaacadbededaabdbbacedcbeecddcabdacaadeedebdebdecedcaabcbeabddcaccaeacacaabaabebaccdeedadeaaceeebaaeaebcdaeccbeeedecbaeeedbcbeecdebeabbcdbbacdebececabdeccdebcbdeadccdcdccdceadbebccdbbaceedbabceaaacdaaebeddadbdadcdbdeeabdcecbecbccbdaaadebecbdcbcbdceaececcebedebccabdbaacdbadeaddbceedaddbebeccebecedddcceebbedcadadbcbbabcccbacbdcbddcdebdddacdcaaeaceedbdaaedbacbabeeaabedacbcecaeeacdcedebccbbeaaadddbdaededadeddeaedecbadaaacadebdbaddeeaeaacdcbaeabedcdbbebbeeeedcabeddcbeeebdaeecbdcaacecdbeabdecedcdcdccbadbcaabcaeacabcdbbdacabdbebbbaaebcabddabdcdcbdacbcbcbaebddbacbedabaccbbeecaeeccacecbbeebeedebecddadebcbeadccbbadebabadcabbaadaaddaeebbadbcbddcdaaecaaaebcedebbdbebedcaedbbcbaeedbaadbececddccdcaadaeeeedacebbadecbbadebcddddbbbceeeeeddbbcedbddacebecebedeeecebeedaecaeececceacdceceaedacbcaeecdebbecccedbebabeaedaaacacaceaecbeeaedecabbdbbdadcadadaaeedecdceecbeabcbebecddbdbcabbbebbadcdcabeaacaddbeceecccceabaeabdbaacbbbbabedbeaacddebeeaeeeccaebedecaaaeebabcabdeeaebacbbcdbeccaaddecaadaeaebecaebccaabeaedebcaaedbbabaaebbbdbdeebdccccaceadbcbdeaddaeedaaeedeedeabdceddaabeacbdedeebdbedabbaeacecabedddedcabcabbdaecdbcdccaadbbaddecdbebbadacbadaddeebcbdcccaaaccaadbcaedecccbddccdaaaaebabdeecedadeaacabddcdddbeaaabbaedcadeddbdddedceeadeeeecbadceedeedeabcacccaeaeaeeaabbcaeaabbedbedebddabbbdeeecdacdbedacdabdcdcdabaadcbcacecccdbcbbebaabdbedbccebcedecbeddeabbcacddadabcaccdacedaccaceaabcdcaceedbbcbeedcaccccbcabcceabaabdcdaaeadbbbebdabecdddceceeceecbeceebbbbdeaecdeadeaeebcaaaadadaadbccadddabcabeecebaaaeebccaacdcbdaebdccaacecbbdeeabdbaeacdeeaeececdadcaedacadeeebaaceccbadbebeeebaceeeadbdeeedcbcdadbddbbdceababccbbdaaabceddcdbaedacdcacabdeabacdcbbaeececcdceacbcccdaaabbddbdadcdbdbdedbdcbdeaebaeddabebcacdadbbcdabaaacadcaaacacecceabdceebcacbacedebcaccacadeecaccdebcecdabcdaaaecbaeddbaccacaeeedeedebaacabbaeadccddeeacecbeadbadcadcdabdcdeabdbceecabceeecadeeebbaedaecdebdcdaaaadbacaaaabdbadeebccbbdbaacabeadcabcbbdcbacaccbbaddbacdbecbaaddddbecccebcbecbdcccdaddeecbeeaaddaebadaaceedacbcceccacddeeaaaecdabcabccdbdecbccebbacdcdedbdaddbaaaabeacdcacbeebaccbeebeacaddadcceaeeccbceabebedacddabdabcbdbeccecbdbeaabccbbadebaaedcbcdacdabdceeceecaabbbbdcbcaaaccccacebebcecaeeddbccebdedcdccbbceabdcedbacdcecbbeadeddddaccdcdcaccacdaecccceabedccbedaeecddbbedbacbbaecccaaceadbdeaaabbdebdbbdcdbebdbecaadceaacedbacaddebbadadcaabdbccbeabbeecceeddadeeddebdadbdbacdaedebaedeebbecaacaacbddaeccaabebdaadaecaaaedcedcbdbdbecaaddbcaabeadcdaccdbdaaecccccbadedaceabaceddebdebeadaddaacadccbeedebdbbdcedbedabbddaebeaaaeccbdacdaecdedededcddccdddcbeddaaeeedcabccaddedcacbdeddabdcbedbbbbbdbedbeacacdeececebddccababcbcbbbaecdcaccddadbaaccacaddabdabdaaceeaecbeeabceddecbbcacbabebbccabbeaadaaadadcadbcceebaebaaabeaedadebddeadbbaccaaccddbcacebdbdcaaeaceadeeedbbeececaadeedcccddbcadeccadddbaecbbcbbaeecaccbdebcbdeddddebacacaeaebbbceceabaaabeddbcdddcdcebdceddeabacdebcbebbdedaeeeceacabdeabccaeccdbbeeadeacdbaadbebbcbbecabadcdedaaecacaebebbddbdecbadcecabdecbbbacbabebacdceaadadbdcecaaaedeaebccedbbdddbeedddabcdaeceaaeddcdbdaddaeceecddddbebaccccaceeebbeecccbbebdcdaededaeadbacebebaeceaeaaaeddaebadedadacedbdccbbcebaedbdbddbdceebecddbacecaaddeabdeeabdeaaeddeacebdcadcdddaacbadeacdbdaaaabbecebeeeebaeaadeaadeebaabdabbbdeedcdecdacbecaacbcbbabedcaebcbdcedeaebdaddeebeeeaeedaddcaedcccbeeccadecbadeaabcadabebeddccbadbaacbebeadcabedcaceeedbcacbbedeebacbabbbccbddcccabeaaedddbceecbddcebdacedeeaecddacbbececadaadabadcdadbbaeebabeaabbdbcdebaddedabcbecbedadeabedaaabdbddabddbaeebbabecccadbadbaeaddeaceebacceedbcedbacecbbdbaaaddeccabdacbabbddbdcebbdedccacdddaabaccacdcccbabbeeeabeedbacbbdbeabcaccdccbdcdcbceabbacabebbacbdcbbaacaaceaabbbecbbaaacbbaecabeebeddcabccbabadccbaadbecdcdcddedcdaeeaaecebbbeedbbedbaceeddebadaacadcddeedeadcadeedeaaeebdceceeeccbabedbcbbaeacaeeaceedccdbcaaeacbcdcbcbbecbbadebebeeceaabceadadcdeceadbcdaaaacbaeeedbbdbeeebebeebeaecacdeddeeaadbeeebedbcadcacebabbccbeccabbbcbacdbbeacceecaecebbbdbbadccebdcdeccbceeabdeebdaaeaceecbcaacbaeaeaabdeaabadeddebeaceaddddabedeaacbeddcabbdcacaddbedcbccebbebaaaadecbcbdaebbaabebbabebddebeeebbdddbbabdbeeeecedccbaedbedeeaabbeadebdeabbeeededaccddadecddddbdddedecedaedeececdbcbecebbaaaaebeebbcbdccaeccedcacbdccdcceabeaeecbedaabadabeccdbaccdcebdacedeaacdbadadccdeaddcedadddeeecabdccdbaedeabaeecdbddbdbedaeedcadeecebecaabbdebdaadcdaccdebbdeacbbebaabdddebbdaabbbcceecdeedccbaacaacedbabeebaabeeabbebadddbdbdebcabaccdddeabbbadcdacaebeacabbecacaedadebbbeadbcbdabbaedabebeadbeaadbdeedebcdbdabaccabcadadbadccbcedbdbaadeecbcbecabdaecebdccdabcaeceacceecdecedcecaaeaaabbbaaaeebdddaacccaacdeccacedccbcecacdddbdbeeabacdbcdabaddecedeecaaecdbaeddddaaecbebeaeccaecabebcbbcbbdccabcdedeaaadcaeececababbcebeccaedebeaccecdedcdedabbcdecacdcbaecccdbbcedceeeebdebcbedebecaeccdbdeddaedcabeadaeebddaddcdbdbdcbcebacdaadddeeeaddbbdaadbecaddabcdabbbcbccaadcdccbbeddaddcaedceebcaeedcedeaedddbbbdecdedcaddbaacabadbbeccebaedaaecedbbaecdbeddbccabbacecdcdeccdadabdcdccdcbbaaddcacbebbaaaddbcbdaadbecebddbcddbcbaecbeeeebcebaeaecbabebdaeeeebcaccdecdcdeeceddedccbeecdcddbddcdeabbcadceaeeddbabbcdcaeaceebcdbedabbbcdccdcaedbdcdbabddcbecdbebedbcaeddbacddbeabcdeedeaeadaadcdaeadbbbdcbbdbacdbeecbdaacedbaceaabeedbebdbaaeebabeadceaaddbcecadebeadeeabcadaebadaedecceedacdabdedcbdddbbabecbcdaeccbdbacaebadedbdaccdaabbcdcdbdeedabadeaaedaaaccbaddadedeeaecdebbbeeccaedcdcdadbeaaccbbebccddeaabbbcdaecebabdcebcdaaccccababdedceeaaecbabeebdaceeecebeccccaeceeaadcedbaccacceaedbbebcebdedcdbbddaccbcdcddcaedaaebabccaaeeecceadaedaeaadebbdcedbccacdcaebeacabbabaddabcedcbdbaaddaeeeaadbaabecabeddddabacdbcdeccceceeaacdbebdaedcabebccdeeedcddaeddddbcebbedccabccbdaeceeccdcdceacdaadbcbadbecaadabedcdaadaccdccceedebcaebccadbdebceadecacaedadadedcbeeeadeacaddeaeddeeeecadcdcccedeaaeacddeccdacecadebbcdeaccebeecaebddbceddadddceeacdbcaecbcaccaabeedeedbddeecdbecdadeeceaabdebcccdbabebaabcbecbccccedebbdaccadebbdeacdebbccbcaccaceebbdaceaddededcbdbbbbeeddcedbadacbceccdacbcbaccbecddddebecddddddbeecebedccaaeccdcacecacebdccdaeeccecbceacedaecdaabbbcecbacaecbebeccbbcceeeaabdbdccbacaedcaeacedaeecdadeeedaebebacbccecbaecadecbbbcacaedbdacdddcdaadbacdcddbaaeecedddabadbabedabaaccccdaedbdaacabdeddadcaceeeadbebbccadaccbacadccabbeaedaddacabecadaadbcddccdebbeecaaccabccebbadbeeedaeedbdbececbdceccdabbbdadbbeedaaebcbeddebdccdddaabeeabdbaaddccbeadecdbbabdcdbeeaebabacabbdecececcaabeaababbabdceaddcaeadbddbbcebaacddecaddcebaebbacdbadedadaaadbeedcaebcabdbacbdbdeddebdbcbbcecdccdabddceacbcddacdbeebaeedecebddbcaeeeadbcdbbdecdcabbbcedeacccacebbddeaedbdcaaccbbdddacacbceaeaceebccbaaaddeeeabaabceddbcaeaeaacebcaaedacbacabcadbeddacdeaacaaeddabebbceeebeebcdcabbcddcdcdddbaedeececceebbbdaebcddaceeabbdcbeabebdadeccadbcaacbabaccbdabbbcaccebdbceecbaedabacebedeeecbdcceaeedbbabdceddbcdcbabddebeebecdbcecdabbbbbcacabdeacabcacbabdaaeacbbeadacdbcbacbdcdeeeabbebeebeccbcaaeeecbacaadbbecdaabbacdcacadbadbecbaaccbdedcceeddcacceaceedecbceddceadebccbddcbabbdaebbdbbbabecbddbddddabbcbadeedbecadeadbedaaabcbebeccecbebedbaabbbacedacebccccdeeedadcbddaddccbbcbdebecbebedbacddddccedcdecbaaeecbeaeadddddebcaeaeeaeadaabeaedcecdaeceddaadadaddabaebdecddcabaecddedabbeaceebdebbdeedcebcecebbcaebcdebdacbcbddecbcbeeadceebdeaeeccabdeddedabcdadaedbebdebdaccbeccbdaeaccebdaeecbbadcaebadbdabcaedcdbcecedbdaceebaabebeadeeeccbdadaedaddbeabbeabdcaeaaecbcbacccacdecaaecabdcebecdabaeaecacdcdbbdcbcecdecbacddccdbaecacccdbcabceeeccccebcbdabbcacdccaaceabebcbccadddcdbadbbcdbaabadbeeceeebbceaeaccccccadebbcaeaaeabadeaacddebcbcedceebdaaacebedecdeccdaaaecccbbedccdcdadbbaabeacedcaebeeaeaaccbaaacbdbeaddeadbcecbbbdedcddbddddababbaaebaddbddbbeaccbdcdbbdaacbaecdbcdecadaadbaaeeeebbabdcbcadcabceebddaaddaceeaaebbebddcebaeeddaaaeebddaabdaacabaaebdbcceaddceacdecedcbadbcbcbededdebbcabbdbcbabbeaeaecabbddacaaabcdedecbaabdbcaaccdddbdecccdcbebdbaedbdceaeecaadaeedbcddcccaeccabedaddceabcdbeaeecbaceabbbbbbcecdabaceecaddacaaeeedaddeabeddeaebbbcdcdeebccdadeeddabeadacebeaedabbbccbeccaecaccccdcadaaabdcdbbbbabacaedaabcabecdcbecdeaeaecaedaccdeccabbeeaddebabcbecdaaaaeceacadbdabecaaeecceddcbbbceccacbbadbaacbeaddbeeddaaabcdcccceecdbcbbeebbbcebcbbbecbbedbcaecdbeebdcebdacabedbcadddddbbabdbaedbaeeabcbbbedbedabccebaaeecbdcdbecdaabdaeedaaeecabedbdbebecceadeeeddceadbdbeddbcdceaddbaceebcaeeceaabdacadabdecdcabcccdcbbebaaedbdebedbeacbeebebabbeeeccaababadbcccdaaabbcdecbdecceadbbddddbabbbdacdceecdcdcebcccebbbbbbccbdbdbcdbebaabcabcdabedbcbeeadcedcadbbacaeeaacdadedadaacadcedeebacdacbedaeeabacebcebddccdcecbabbbaceddadceaebddccdabdadcbbaecbbaeeaaeaebcadabdaedbcbedbbcabaaaceabbabebccaedbeebeeaeadbcdabaabeaaaadcbedcaebacbccdaacddcecededcabbcadabebeebbaaebceaeeaecedacebdeccbaedcedcbaadcecddbeeceacbbebdacdcdcdbebbbcabedacadaeeeceaadceccdeecbbbeadddbdaaabaacaeebcbaaeeecbcccbecedabdbcedebeeddbaaaeeedbcabecbeebcdcaeeeadeecddcbebbeaedcdbcdbdceaaeaddcbececbbdbeaacdedbeaedeeebabceaccbbeedceabdecbebcbebdcaccdcedddeedeaabecbeeecbcabadadcebdccbccbaccbdcdabcaecadecebdcbcabbedaacebbabcbaacbdedeccdacdecabecbbbdbaaaddecacddcaeaccadcebcbebdcbaadbbaeeabdcccbacbaebdaddcdcdedbdedaaaedccbcdeebbeddbdcecddbdddeadcaabbbaacdedeabdbccdaebcaaebdcabebdeecbdbbecaddbecbaccdceaaabccacbdaecbabebbedaeedeebebeeeaacacdaaaccceeabccdebdbccedeccdeadaecedeccabadaddccccaebdecadbccbccaccdbdeabcaebabcccdbaaceebedaaeccaceccecbccddcadeabaecbedaececdeaeaedaaccdcdddaecdceddcdaaccdacbeebdabacadddecadbebdedbeabadcdccebbccadbbbbdeaecaedaeaaebddbcadccbaddcdcedbdbbbbeedbbebaccbaaeccbbaecdcebbecbddaadaabebdbacbbaccdaaeadbcdaeaceedacaadcebcadbaceabbaaececcdccddcdbbeddcaabcacdcbdcbaacdddddeeeeddcdccddcdcbebbbdecbbbeabccbccabaceccdceeceebaeceacecccbbdccbcadebaaaebddcceadcecabaeaedaaeadbedceaabecdebdeeaacaceccbdbecccdccbdbabeadabbeaceddabededbcdcbdecbdbeaccedcabaddecdcccdbeeddbcedacdeacecbeedcdbccdbbcbbddbbcecbcaeabebdcccddaeceedcedaccababbaacdebabdbabcdbaaeccbeecbbdaebdedbdbdecedcbeababdcccdbbcdddddabacadeeddaeeaadaaccecbebcaedacaaddabbaacbaeedcaedacecccbaddcdcdbdbeeeeabbcaadcbaadbcaeebaaddcdddedbceeedcecccbeacdacedbaebdebdaabdcbcccaddacdecdceeaddaaeaaedaddedceeeedeaeedeadacdececaadcdbcebcbaddebcabaecadeaaebaacaedcacdddeadadcbacecddddabaccadbcdacebebdbaaadbaaeeececeabebbbbeeabbacaebbddccccceedeceebabcaeebeaedbddaddadadeabacbededdddbbedddeeebcacdcbebdbeeadddcacededcacbebeabedabbcbebbceeaceeddebbaacceaeebebdcaadebdadaadbeabddaadebaccbcccbedbacaeebbbddeedbdbcaaecaacaeedbddaadbbbdaaeceebdbbcceebdbdacacaeeabccecdeddabeeaacddbebddbeaaebdcbaabbaededebdeecdbcddbbecebdacecdbadcdeaabddbbbebddeddaeabbbdceeebcaeccbbaadacebbadadbaacabdbcaeadbabbaacddeabbdeebdcedbccddaecbedabdbbbabeaebabdbeeaadaccceaddcbbbddbcadaccedabccedaabdbecababcabbaeebdeddccaeccedbbadcbdabbdddaebeacaceacdcaabeeececadcdabedbdbcecdcdeaecebeeabdecbdcaacdddddaedaaddccabddacdadbeeecaaebbcbebdbcaaabdccaabcbdbcdeeabdacdbcaceaeaadccdecaadcceadcbbeebcabededbaaaaebbecdaacdcadbdbcdaedacbbcebdedccdbcbecebceaceededcaacdbebebcbebbaacedaaedaedeaecaeecddabbcccdebdecbcadcadcebceceabeaacacacccadbdaaeddeddeddbdcbceabcbaeeacdbacedcdabddcebebdcdddeaceddcdbcaddbaedeccdedbadcabeacececcdbdebecaebccaabdbaeecaeceeddadaccaabccdaeaedcaeeccecddcdddddbabbcebeccbeaebabbbbabddaeebccabbcddcbdbbeecabddcdedecdbcdbaedabcbaeeecdebedabdeccecbacdcebdcedcaacbdebcdaaebcbbcbdaaceceecdaaeacaccebebbaccdedddecdddbdebbbabdddaaacccaeeeaeabbbebcdaddddbbdedecedccabbabacadadceeeabdebdadabeaabacdebddedebcdadeebeaddcbcbbadebeeddbaedddabcaebeccdcdadbeeecddbecabbdeadebcbbcbbaedceaabaeeeabcdaecbbddcedcccabdceadadadaebaebeaabadcbdbdcdedcbbdddbedaecbdbdcbededddebcabdbccdebcbbccbceeadecaabbbecedcedaaaaecbcceeddbbebcccbaeeaebaaeccacabdcbcbcaacecccadddbbeddccebeedadcadcedceebaebbdecbddadaadebbccaeacbbdcdceeddcbdcecbcebaccadececbeeabcddacaddeeeadabeaaeadccdaedbaacaaabecbeeddbdaabbacdbdccaabcdbcedaeaedabcaeccacebdbcdcdedecccdcecaeecdebacbbbccabbeadcdcdcbaadbabcecabcddecbddebeabbdbddbabbcbbadbddcebeaabdcdacdaedaebbcbacdbaccdeaaababeceebdaabdcaccadcbcedecadadeeabeeedbbbdaedeeddcdccbeabacccccddecdadcbaebcccdeccceceddccdcdaccaeaedecadcdaeeadbcdcebcbeeccebabaacceeddadbddeebecdabbabebeabbdbaecadcbcdeababddbbcbcacbeacededacecbecebbedcedebbbaccbcbbebbcbceedcebcbaaeaebebeacacbedbeececeeddadeaadaecdbbacaeccdbdddeaedeebadeadcdccbbedceacddbaaceabdbabeabebdbcbaddeccdbbdbaaceeabdaedaecbaecdabcabecaedeeecadaacabecdcdcdbeebdcdabecebcdbcaabbdbbdecacbcddecedbbdcbdbdabacdaeaaeeaedddecbbdaabebcabbbeedeebadabcbaeedbdddbbdcaeebecddedbecacbdceebcabbbaddeaaeadaaeeadcceadebbebeeabaadcddceedacecaedeccdccadbeadbbecdbaacbdeecbadbbedbecbadcbcdddddeccdaecdcadcebebedbbebbbcecaaabbbebdbabceeccabecbccdacccccaebdaecdbacdeabeedeaeaadcaaecccdbeacdabbadeddacaebebbbedcbbeeecdcbcdceaacbbacdbcedebecabdbacbddeeccbaedcaededeccdbbdcbbbebacbedcdeacadedbccebbbeacaecbcdeadcaaddedaebdedabbadddeececeddeaebdbadedcaabbcedcbbbbbedbcdecdedecabbbcbeceeecacedcdaaaacceedddcdbebddeacadcccbbabddaebceaaedbbeeeedceeaaaaaacedcbebdbbabdccdbeaacaecbedbabebeceecbdaeaeeedaddceeaddeabdccadbadaedddedbabbeedbeeedddabbcbedcdbdacdbdbcbeaebeddcbdcebecabeaeddaccdaaacadceaececbddbbebbaccbdeceaacdebdbdbebdbdecadccacebcdbacbedbadaceabbcdedabedebddcabedcadeabaceabbbcaabddacdadaadeeaeaaacbaddcabbaaccadbadcaeecebdceaedeaeacbadddcbbabbceaaeeaddbabaadbbeadbeacaaeacbdeeccccaededcadcbeeaeebcabecdbcdbbddaadaedbcabbdecbbcdcdcacdebaacabbcbacbabddddadcacacbdbdeabcedccdeacdbbcdbdbaadadebcccddddecceeeaecdeacbacceeebadeddbbeeaddbaacacdabaedecaebebcdccdddbdcdeccdceaabdeccbaddbaaecebdcbeddeceebaacbdabdbcdebaadbebdaaeddabeedbbdaddcabccdccadceaacdbbeedecbaabceddcbaecbbcbadcabaccaeaaabbbbbbdcadbbdbdbcaecddbceccbacaeebdacaceeddbdbbeecdceceeeedcbeeaeccecdcdcdbdbebddcbcdaeaaceeadcaaacaecaeebcbeedcbabaddcaabddedeaedaddccceddbecdaadbdaceeaaeceeebcdcdeeacebdeabcdcddcddecadcdeeaadaaaebcccebbeadacccbbccabccdbbaabcacdeaceebeccbdbaacabeaceeaabeeeebbeddadeadcaabbdbdbbccdecccccdbacecdddbcaacdacbbbeaedcdabcaaabeeeecbbbacebbeadeceaadeaddabeacdcebccdaaaacbebdbeebabcdebddbcedeaeeadcaccebdecbdaeebcdaaaeccadeababcaadaabbeadaabccaddbceadcceaedbcdababecceabbcdaabdbbbddaddebacdaeebdbaabbedbaebcdcacdcbcbeebaeaeeaacdbbaeaccabdccacdedeccadaeddaeaacccbeabbcadbccbcdeacdeedeaaecacecbcabbacbcabaddbeecdcedbbcdedcbdbcacebacebacbceedccaecbdcbaecebedcaebaaccecbaecadebbdabddcacddccaeabdeecbbaebcdcaaeccdcdadaecabeaecbcaacbdaeeedbcbeccbedbedcdaddddeaedceddbdebecdecdcedbaecadeabdccbdcbdcadcdeaaaedabcaeabdcbebedebcaeccadddbadeabbcaaddecdeeacaaeebbabcbdecaeecabaadaaedcedceaaecddcdbddbdaabeaaeacbddbddcdddbbeacaaeccccaadeeedccabdcaaebaabaaebcadadbadcdacdcccadacdababaddebacaecedaaddcdeabaeabcacbdcacdbdcdcbeeaeacaeaeedddaaededeebacdcbadebbceaeceabdccadaaacccdcbdecbcadaedcbbbaadcaabaeeceaadbccddaceddbbbecddceeaeeeeaceadebdeadcaedbeeccddcedcbcebdacbaddaccbdbbededacccecbadaccdcecbaaecddecabedadcbabceaeebaadddbcdbcdbbeceaccddaadccddcacaedbcabbdebcdceebbebebdbdcedbaccabebddaedccddbccadbdebadddebbadddaadebbababcebaadbacaadbdedbeeadcbcaadcecbeabababdaabbebdcabbdaabecacabdbabebaeacdbccacebaebdbeddbcedbdedebeacbdaddaeaaddcccdddbbaabdcebeedecaeeddbcadcadbadbdaaabeecbeadebcbeccadcedbabecaacdbdbadddbbacaaaabebccbcbabcdbcccbbecdbdccecdcdbbeaaceebebaaaacedeeeaeacdceebacdddbdcaaeddcaadaadccbededbacdebcdcbcbbaecaaebadccdaacebedceccceededcdcebdccedcccaadbaaabdaebcbddaebecdacbededeccabcaacedecbabeeebdbbadeabdaadbecaedcaadebeeccdcdbcbebbbbecaaeebceebeadbdccedbbbaeddabdddeceeccabbebaacdbeccebdacdeddbbbecddeaaddceacbbdecdcabdecbbaaaeaabdbcbbdccceeeacabcedcdacddcecaacedcbcdebeddedcceabeaacdececcdebdceeadcacacdbececddbbbbbdebcabcdbdacadeebacaddccaaebeaabceeccecacbeceeccddddebbbdcadcccbeddcbaaaabbbecbdbbaecdbecdbaecddcddcabbcdcaabeecbcebedaaadaaeccbcbdcededbbcadabdceaaccdedacacabbaccdecbddbbbacbaaeceaebabcbebabdacadbbbdcbbeabbbbcaeabaeebcacceddceeabccceacdbbbddabacdecbadeebcdbbdcaccbdbdbebbcadbdaaacabecdcabdceecdecaeaecdbaccbbeecdbebadbaeacdbcacdabeaeddcedaaccaadcebbddededbcdbceabaebcaaebaedbdcecedccaccdabbdbdcaccbcabadbdebedacaddbdedcbbedecaebbaecbbedeedcdbddccaebdbecccaabeeabdebaeceedeeabbecdcedebabbcedecaddaeddaebcaeccccbdcdacbbbeabbbbaeceedddcaaebddbebddacdcbeaaebaddceebddbcbacadcbbdaaadcadcbcbcaabedcceceacaeddcedbccaabebdacedcccbdecacbcededbdbdedaeeabaaddbccddaaeaeccbadceadbabeceaedbbeebbeeeebeaecbcebcabbeaaeaaedcedacabbaacceddeaadeacbcbbaedeaaaecddaebdebcadeaccbdbddaeaeaeecbdbddbdbceedcccecdcceaabbcdcdcbdcebaddadddcaacecceccdcdccbdeebcededeadaabccadedcaadddcdaeedccbabcadeedceaaebeceeacecabcecbeeccacaeaaebaaebacbceecbeaebdcaaaceebabacacaceeececbbddcdeabeabcaabdbeabcdaaceacebaecbddcabebbddeeceecdddddadceebaaeaedaededcdbeaceeabeccacdddadeacedcaebdcedaeaacebadaaacaeeeeccdbcbbeaacabbcbdbdbbbbdadcdcdbdaeeacbaceaaceddcbbabcddbcdddeeddeddaabdbcebaedecdcbaedebcbeddbcbbbeeecaacdecdeabbcdeabcbbbeebaceebddaccdcdeccddbdbbdacbcbabcddedeaeacdacbdeedcbdecccdddceabadaceabdcebeeeedccddddabbddddbaeabceecacadabeeabedebbdaaadebaeabdabcecdaaaeaeeeaeecaeeececbbeccceeeccdadbebecacdaaeddebbeebdcdeedaaccbbeecccaadebadbecedaccbaebbcdadcadaaecdeebceadceaddebacacdbcebbaadeccaabdeedaddbecbacbadaeddaaeecaedbdeedceaecbdddccdbadabbdceccdeadedacaebcbdaaeeceabdddaaddebbecdbbdcbcaceebdcdabdccedcadaddacaaeaadabcdebcecbaeeadeccbebaadcddccaeaedbdbbaacecdbdedcadbcbabccaddececaecdbeeaaeeacceabbadeaeceaaceceaccdceabceccdaadbeabdecdaeebedeccaabdccabcbebadcacdbdadddbdbcddceabdabadaecebbdccccabebbecdaebddcbccebddacaededdacaaadceceacddaecdedeedbbebaeecaebecbbcedceaeccccbdbaeebcdadececcbcbbddeabceeaedcaddebecbdedddabdbdbbaddeebddaabccaeaaaecbbbaeedacaededbbaeaadabdbedcbbbbadaaadadabebcbeeacadbedbdbecceaeeaaacbcddcabaaaedbcddcbabdcdbcaddeabaeccdbbddecdbaabaabbaaedbdeabcdbadbcbcaaabbbaacdadececbddeadadbbeaedcaacbeeeebdaadadecadabddebeccccbedabdaababbbaeebadddccaeebebedcdbebdaabdbedcabecdbcdcbdcaebebbdcacbadeccaddbdbccbaccdbaebbdcbdcbecdeadcbcbaedadbbbebcaebaaeaceddaabcaeedeeaceabeaebaeeaabbbebcabccabacacdecdacdbdaaccadbedadcbadabdbddeaaaacaedadcdbeaceecbbdedecbcdbceabdbaabcaadebccbeceaaeeaeaedebaedebaecedcddbbdabdeabbcbdababeadbdeaddcaeedacbdebbdebadaadcbbaabcbaedadabebebeabbbabddebdbddecbebabecbcdbdecbadbdcdbbadaeddaabbceedcabbcdeecaccecabddaaadbceaccccdecbdcebcecceeccebbbdceaadcdabceebcecaaaaddbaaadcbcadacbdeaabdcdecbccdddecbeddceecbcbabadceeadddcadbdaddbcdadcccebdcebdcccbadaceaccbbbcbceaaaebeeadecdceaccedeaabcbadddbbecdbcbeeeecaaedcdecebcaebddbcdcdddbbaaceceadccdbeeadedbaaaeedbebeeeddbdbbacaadbbbaaddcaeacadcdadaabdaeabdabdeeccbbcbeadeaceeeaaadeeccbecdeaedaceadbacdadbdcdbbccbcbbedecddeccaabccdcbabadaaedddaecbaacaadcbdaddaabecccabcbdaedbdaceecbccccadcdbeeeaceaddbabbcabbecebacacaecaedcaddcababccaabddaceabaedadbdceddbdedcececdaeddbdaaaadebaedadcabbbcaecedaaecdaccccaaabebacadcabacbdacddbecbdcabedbbebdeaedaebaedccbdceabadcbbeebaeacaabbbbddedeccaeeeccdbcaecdccbbedcccccaadcebeabbeabcdbdabcacdabeeeaedddcbeccacbbaabeaabeddebbaccecbdebebbbdddbbbebcdcbbaedadabebbebbccceeecddebbacabeeaccdbcaedccacbbbdeeecdeaccedecaedceddeceeaeecbddbdbecddbebbeadbbbbecaccddaaeeabdebabdeecdcbebbabbebbbbaccdabccaecadaadabcebcdbddaaecbdaecdaebcbaeadedeacacbbabcccdccacbebaedeeadcedcdbdcdecccaddbcdbbaceaadbbacbcdcdabeacdaeddbeabebddcdedaecacacbdcbdadcaedecadcdddeeccceeebacaceeedabceeaaaacaaebdeaedddaacaeccceaaaabbccebdbcaeaceeacbabecabcbecababdaaedbcbdaaeaedeebaecedebacccbdcadaecdeccbaaaabdeeddaabacecabeabbcdcbbbcbdcebaaeeeadbeeaedececcebecdbdcbeadacdbdcbaedcaecabeecacaddcdebccabdabaeecbadecabdcdcdbdaedecedacaacedddbdbcecccbdaaacbbbcccbdcaacbacaddaebdceaedabcaebdecbadaedeebdbebeeeeaecebabedbdbeeaeaaaddbdeecebcbbaaceccebeceeeeecacebbaaaecacbacdaeddeebdaccebbccecaabaedaabecedbaacaebdcdceebadcbcdccacedcbbacdddcdacbdcadeeaeadcbbbebcdbebdcdbccadcbaecdbaeabebcbaecddbedacacebcdacccceaeccbecccccccdadbbbedeaccdcdceeceeddaababaedeebbcdcaeabbbadddabbebaebabedbadcadccdcadcaaeceaabcddbaaecaacecaedccddaddbecabdeebdabbbeeaaebdddccaaadbcbbdbbadabcdcdddceedadeadabcccccacaaccdbdbaaecdeaebebaedbbcaeadedbbeabeceacbdaaacaddebaadbeecbebbdedccecccbddbedceaceacedeabbdebccceedbbacbeedcccdebadedaccccbaeccbabdbedcdeddaeacebbdecacbabcaceeecdddccbadeaaeadbaaaecbcbbddedbeaeccebeedceddccebadeccbcbeddbecceaabcbbbcaaeadbadbbabacaccdedebeabacadddbdabebddceeeedeaaebccbaaeaccecaaadadddabbeaecbbcabbecccbecbecaddbaabecaaeeedcdaddeacdaabcaccbecabebbedabbddeabacdaeabcceaeebdbcdeccddbeadceebcabddbbcbbedbaedbceaebabadccebaebdcabdecebcbeabbbaccbdbcaaccbcbbbeaccbabecbbddeabaddacdebdbbdeadaadbdedeeadbdbcdccedaadddbeaedcdeeaaaeecdaacdcecaccddcdaeacededcdaeadbdcdabeaaadceadbdabacdcbacaceedcecaeabddbbdcdcceeccadcdcccdceadecbaeedeecdaeadbedeeaeadecadeedeebdececbbdecaeaaccdbaaebeebddbcbdaabddccbdbebbabeceaccdabbbbdaadcddaaacdcadacacaeaabccdaddcaabcabdecbeedbbadacbdbedbbabbdbdcecdccbbbbebdbcbbbaebadbdbcadddeecbbdcbaaedbaebceeaabcbdebbbbdbacceebdbadaddacdcdcbbaacbdbbaeceecabeddbbebdcdcdbadbcaadeadeadcdecaaaddaabcbbadedcaaadbbddaceeaeccedaedeedabeaaddbdcedcdccedaccdcddeaceabcbcaaeddddbceaacedabbecbebeceddadcbeeacecdaadccdadcedaebebedceabbccaecbeacadecbaebbdecabcdceabbceeeccaccddccdbbddbabaabceecbaddbacdacdecddcecdbdbbbccabebedeabacedeaaccedbcaeceadeddebbbaaabccbdbedeecbeedbecaabedecebbaecaeddbdcaecdacacbedaedbeadaacdbecbdcebacbecdbaadddeacccbeacbeddbbbccabdabcdabedccaecabbeccbaadadacbdabeaaceaaedbbaadcbbbaabccacadbdacceacaacccaacaeabdbadedeacaaacbdabdaabebabbeabdcccccbddbcddcdccedcbdbacacbebdaaaaaadacadaabbaaeedccacbccaceeddeccecbdbabbaceadebdacaaebcbeadecacaaecbdadaeedeecdcbeacadcbcceddaeeaeaedbddeadaaadebeabdeaecbccceabeacdeccdaeebdabacdbbbbddbddaaedcbaaeeedaddbebeceeddceeabcccbeacabeddaedeacaedceeacccabcbbaaddaecbcadeaaedbeedbcbbbbacedbdbbceaebedcedcaaebacbecadebaceececaadcbbeeaaebeaeacddcbadbcdecbedeeedabbaacdcccacbabbcacaedaacbedabdbddadacebdcedeabacadedeaaccbdbadbccababdeeaeeadbbadbecbacbcddcbeccebeeebdbadebedcadceceaedeccbadbaeedcecebddbdacecbeaeddabbadecbecabaeeacdbbeedccedebddddeabeebeacdbdabbaeaecdadbadebcdcbaebddbdbabcdcbeddaebdababdecdbaedaaddbcdaebacdacedacedbedbedccdddedbdbbdcdeccddcdeaedebbcbeacdebcdacebeccbdeeeadbdcadcacedcadaccddedcecedbcdcbcadebbcdaaeebeeacaaecbcabedaaeadcedabccdabcddecbbebecedebccaceeacaceebbdcccacbbbacecbecddbbdedbdecdaecaebedbabcdddabbceddacacbedabdeecaeeadcecedaeebdbaedadacdbacabcbebbbcbaddeabbcdcacccdccaaaddadcbcceaccaaeecebeedabeddaadecbdddaabedacadbaddaeeecdddceaabcaedadeeeaaeaeacaabccddabbabdacacccabacabcedcddcdabdecbbadacebbecccdaaedabeddedabaaadcaddbcebceaebbededcacebdeedabceeabacaacbdbaeeabdadcbaadacedcdadeeabcaabaedbeddaabdcddabdaabeabcbabdaaedeccedacabceaabeaeaeadaebdbbeccccdebbbeaccecdaaeadceecebdccaabbbdabaabaeddebacdaeacbdbeedcdedeaedaacbbdcbddccdbeddaddcaedaddcaecaaeebdbbcdcbcbcdebdaadccdeddabbcdaeccccddacaabeeeceadbabcaabeebdbbabbdbcecdbbbaaacbceeccdaecdaedbebeeadaaeacbabbdbbabecceedabacdcaaabdaccabeddedbdbdeabcebcdeaeeeabaacddacbbeabadadceeaddcbacbeccabbedaeeebeeaaaacaaabcabcdbbcaebbdddcbaaedccdeeeeeaaaddeceedbaabdaedbcccbeadcbdddceadbcbbddcbcaeeaecdcacdeedeadccdceacdbabbbbdbcebdaebdeccbaaabebbcaaabcdeeebacbbaacdcaeaedeeeeeacdbdecabcadebdeabdbecebeaadcecceaadaadedcddaddbcceecdabcbceacedbddeabaacdaddedbaddbabdbbceedbecedeeaaadacccbdeacaeccdcadecdaaecabbdaccdcccbecadceccedeedebdaddacdcddaacccabaccecaedaeecdcedeebaeecebbdaecbadebacabebbceaadddaccaaecdccaddeddedcebeacbaebcdeeeacecaebebeceaababcbcebbdbdcbaecebbdbedebcaceeabcaabeeebaaebcbcecaabcdbcedaeddaebeddabbcceacebeabeacababccdeaedacadbcbecaadaaaddedacbbcabdddeaebadaaccdcbaacedaaadcadeececeeaaceaecddddabbebccbcdaecbbcccedbbdbcaacbeecbccbdbbdbccdecdcdaaddacdadeccecaaabebecabaeedebaedbaacabaceacdcbdebaaabedbddeadcabbadbdcaeacebbbeaeacbdcbbecbacdeddddaabcbdcbadaaabaceaebbeaaaadceaedceaeaddbbbbddcceaeeeecccacbbcbeeeadbabdbdadbeceedbcecbadacabbebcbcecbeabcaddaebacaabdedcbdcceecdaeecbbaccaabebedaebaeaabdeaacccbbcdadcadcbbbedebadeaeadbceccebddbededbdccbecadeabcccbbaeacceedeaebabebbcecaabdcdaabcbbecbdcebddddecbdcdabdecaabdcacdcabaededbabcedacbdcbdedacdbcababdeaccedcaccaacbacbddaaebadbddaaaaacceabdcbcceeabdbadcabddbbbdcbdbabcabedebbcebdaeceebbaeaadabcebdbdbcbbcecbaaccadcdacbdcbcebadbaceecacceabaadbebbeaedeeebbabdcedacaaabacddddbddcabbeadaedcbeddcaccbeadadcdcaaabcdeeaccadcccdcbbecaecbaddbdeeadcdeeeebeacacbdbdebbeaaaadbddbaeddcadacbecadcbadcecbeceeecbacdddcaadbedbceadedbddbddedabaeddedbabeebdcdaeaeeaccdaacaededcdbaeebddaabebbcebbcdcdcadcdaabdcbbddacaebcdeeebdaddddbbeabebcdaaebebabececbeacdbdabcbecaeacaddeceebeebaaebaeccbdccdaadedeeeeccaaeeeeccdabceabdceadbddedebeaaeaebdbcbceeddbeebddadcdeabdcabccbbaedaddecabdcecbaeabbaadcdccdddcdacbbcbdddacaadababdaabcaacbaebcebccbcabbbacdeceecbccbcededcbebbedbecdeaaececebdcacedeedeebabaecaeadedeadbeeabaebdccdaaaeaeecbbadabbedebaaeaaecbaaccdabddcaaadeabbedddaddaabbbcbedeacedeeabbdeebdaaebedaeaccedbbdbebaddbaeadbdddabedbadaaeeddabaaacaceadabecaabccaabeabeeebdcdddcaddadbeddeecbdabedddeadeaceccccbbdbceccecdbdaadaadaccabacbceadacabacddeddeddabbdedaecbbcbecadeccdcccccddabdecdedceebcbcdbaaeeebbeecbedebdabbbcbabcbebaadcdeecdebaadadeaeccaabddebbebedbadbceabeaccbdebeaabeaabcdbedabccdabacbcebcebaeacebceebeecebaacaecdabbecdcdcadaaebdaaeaaedededaddddeadadbeaaeddcaceeeeeeebdccbcadceaaeeededbcbeaadddbdceadebaddbacbaacbdcbebeabcecdadbbbdabacbdcedaeaecaeaeddcecdaadcaeedceacaadbceddaccdcbaabaeccacebcccadeecacebbadacacdeddeaadeddecbdbdaeaabaabdbdadaebdbccaaddecbbeedebecbbbeebbbbacbcbdbdcaaceecebebeaaeadedbcadeacdeeeeaaaecaabccaacbbdaecaceedbebddabadcccbdaeabcebddcddaeaeeadcacdadebdaacdcccdeeeabccaeaadbeeaccaabaadddcceadebaacceceadadcceccdcbcebdabceadacdcdbdeddebbeabeeacbbcdbeabbaedbbdacebdadacedccececeacbdbcadbcaabdeabcbeebdaedcebcbcedbdedbeacdeacceaccddcabceaeceeddbecbceecacaeccaadbdaaecbbccdbccacaadecdebcdbeceeedcaadacebdaabeacbbcecabdbecceaabcbcabccbeceadceabccbbcbcedcdbcbcabaccddcebbbcdaebdcedcebbadcbacddbcadceedaacbcddaaccbcbbcdddbcaededdbeadddedcabcccbbdcbebabbacbbecbccbbbeeaabaaacbccbbbdacdabceeadcdcaeeabecbbbbedbcaaabdddbdbdedecaabcccabebbbdcadcaaceeebcedabaaaeecbbbaebecdbecdbadcdcdabdedabdadedcdcceccdacccaaddcedddeaaccdbdaddaecebecbecaeddcbeecdaaeecaddcedbebeedeeeaddeccabcdadbabeccaebbecbebbbadcbbcbdedaccecadaeebacabcaabcddebaabdbccdcedbcaeecaeccdcdacdcbabaaecebcdcecdaddbeaadbbaacecbdaeeaebaecdeaebeddabbbbabeacacdcbadabaecaeaccebdbcaeabadebbaccacbabceabeaedcbeabbbbeaeadceeadcdcacebabddbcdbbdccedeeacedeccebebaabbabeaabececcbaedccecbbeacdbedabbdaeeccaddbceadddebbbeabedeeedaeedaccebbbcaaddaeadbaaadedbecbbceceacaacdaaccbbcddcecadebbcdeeddeaaddccaeaacbddeebebcebcebacccacdacdeecbeddadabebaeeddcbbaebbbadbdcaacabeeeadaeabdaadaeaceeacecdcbcebbcdbbadbbbeacecaedbaacbadeccbedeebdbceccecdecbdeaaaecdddeeaeaeacccedaabbbeeacaebdecacdbdcaddcadcbeedbadedcbebdadadaebbeabcceacdcbeccdcdcdedcabdeedaeaeccedbcceaedbabceaedacbacaeddbebabaadaccaccbcccbdcddadbccacbabeaeaaeadabeddcbbcadebabacdaaaeaedbbcceeebdcdbcbcadececaccbedbaedabbeebbdbebbbeeeabecdbcbbbdbdbecedeedddababacbddddbcebeacdedbadcadbbaebcdacdcebebccdccbbcbcceebedadeeebcebeedeacedebbacacdddedeaaeaadebbeaaddcddadbadcaccbcacbbadeeddcadceabbaccccbeceaeeccecbbecbaeebcdeaebecaaeeadceecaedebbebcbceacaeaadcdcceacedcbdecbbcebdbbdededceaceaeebbedaecedbcbaebedcaaeaaeddceddbbacdabadcaaaddecdbaaeacadceceeccebaccaeacabcddbebebbcbdcedadcdddcdcecebeeadcbbbaeaedaacbeccbbbcaecbcacdecdbbcddadcbbbaccdeeacbbdccebdbaaaaccbddbaabddbddeadcccbadaddebebebebbdbeeeaeaecdabadcdeabdbdeabdbaacdcbbcdaacceacceebbbbaabeededabdbcaaadecedaeaebdaabbbdbabbbdbcaedecbeadecabbaedebdacbacceadddcbccabdaaaecbcdabdacbbecebbcdeaabacdcdccbbecacaeddcadacaaedceebbdcbdebbbeabdbbcedeacacddccedcabecdebbedecdcadecebdecaedccaaeaeccacbbbedccdcbceebbdcdaeeddabbdaccadeeeeccacdebaccdbbccedecdacabaabbbbaacbceabbebceadaddbabecccebcabbaabcbbdbebebacccaeeaeaedacddcccccaabaabacedebdebcccacbaaaeaaacabddbeaceccbcdbdaaedbcbbbeaeeaeacbbdeeddcbbadeeacebaecadcedaaeacadeceaaddeabdcdebeeceabaccceeabbdbbadcbebeadceaceaddcececcdeacdeededbeaeaddacaceebaaeccadeddcaeddabcecdeccaddcbccdccacebaeaaebcdddeebebabdacdbaaadaeadcdbecabdaaeedccdedbddddcddaecbeebedcdceeadcadadcdbabeccbadcecaddcbbaeeabeacdababbbbbcbdadababeccbcdeeabeecbeecdebddcccdbeeebdbbaaddccdcededbdcabcbebebdecebadaacedcadacebedeccdbcadbaccdabbabbaabcddaaacacabaedabceccedeededacddcbeeadcbeaedabebbcbceedbeceababcbccdbdcbbcecccecedccbeaecccedecdbaadaadabcacdeebeecbdcdedacaaebeeebecbebceadcabdbdacaabecdeebcadbebbccccaaaaceccddacaadacbbeeabedeaadbadbcbdcababdeedddcbdeedbedabddbcdbedbddabcceedcecbcbbcbaebbdcdbcccdbeaabebeceaedcdcbbdaaddbceeaecccbcdeedcaeadcabaadaddadbebadedbbbedcbeeceddcbdeebdeadecebaebbecddebdbadbacecaccebaecbbbccdccecdcaaadccdeeacdeccbdddbcbdcbedadcddceccddabedcadbaeaaacdcabcceabccbecbdabeeabdcebdddebeccaeaeedacadcecedeeaaecbcecdebaeaadbdaebcbaaadcdeccccadedaaabbdeaeccabadbddacdbbdcdcccbccadecdbbdeedebceaaebecaecbdedabaebcabdcaaabededddcbddbbdaddaabbedcebebbeeaeabbbeedddbeeebbaedcdbbddeaeacbecbacdbdbcebedbdabaaebadbbccdaceeccababbecdcbedeaacbbdeedececdacaeacedaeabaababccbeacadbbcebeebaddebbbebdabddabdbbdcdccccdeabbcbdbabcebaecebeecdabcbabaaeecbaebbeededbdadbbcecdbbcbcdacddcacdacddebbddedeaeacebdbeeeccdbdaccddddabdedbcbedbceeccbcdebcaccabadeaccedddeecebbbdadcbdaeacdeabccdcbcdeeececbececacccbcaadebeacaecacccaaabacdcccecccaebdacbeedeceedcebcdeacbdedeeeecedccbabbbcbbeccadccdbdbbedaaecadebddebaaccccbbbccaeabbbdebbebabaaaacdceeabadddccdacbaaedbaceeabeacccaeadbddbabdeeebcbbedebcdeadeddddbcddebcedbaeeaeeaedccaddcaedcebdcedbcacebdcdbdeabebcadbbaaeecadbcdbdcccdeddbadeadebdbdbacddbecacbbecaaeacacacecedeabbdeeedeeaebeeacdbecbcdcecedeabbaedbaabdbecbeccdbbddecdadaedbabddcecbcaaaceeecebddebdcaedbbbdcadabcabaddabdbcadacbccdcebbcdbbeaeaaecaacabbdeabdbdbcccaeacddaeaeebabadcadaccdbeebcaedcaaeeedcebaebeddebedeccaeaacdbdacdabaaeecadaadecedbedcedcbcdaeeecbdbaebaecdadcdeaceecbedbabbabaeceabacbeddddadaaaeadbccbacecbcbaacdcbbbeecccadcdcbbcdccaeddedeeeaececddecaaaaacceaceaaebcedeecacadbebacdbcbcabcddadabcaeedccaeeaddbdcedbccdecedadeacebdaeddeebceebadecacaeddcbcebdcacabbeececcebeaaebcebebacabbcbecdcebddaeadedeacbcebdabdccabeabecbeacaaeabcedcdcbbadecabeedbbebdccdbbccbeeeaebdabbcbacbbbbdbaacddeeebbcedadcabcbcadaedbeaadcdaebabacaacddebdcddccabdaebeeedeccabdaacdcdcaaaaecdceaeaeabcdbeeebdbdeaeceedbcacebdacddedabcddaebadcedbadeacccedcdbbdeebceecddbbeaacdcdddccbecdbabbbcbdbbaccabecdccbedabcaccbadbcbbacaeabddbeebbdbcccbdcacbecbcacebdbbcbebddedebaccebdcddeaeeeaddcbbdabebeaaeaecaaccabacbbbbbdecdcbccadeaabcaccaccbcbdceecbedaecaacdaaeeaeadbdaaaedebbabacbcbbaccbbbabdbeebdbcbeeeadcdbceddcbadbeabeeddaeecdbcbaaaecbacceebbeebbcbcbeeeacacadebddbabeeebcbebdcdddccaecdeebaceebcdbcacceaeedbaddcbcdccdcdecdebbaddcbdbdcbcdcedebbeadbaddccbacaccadaaabdcabbcecbebcbbdabaddecbbdedabccdacddbcedcdbbccebacdbddbabcdebbedddbacdedaceaedbcabaaececcdeacaedcebbcebeddaaabdbbbcdebaacabeeecabbbeececcebbdedaaceceedcbbbdbaedaddedebbedcdacedaadaedcbcedccbbabcbcceabcadbeedadbccbdbdacccbcaddbcbdededcddedabaadaccacabcaccbecaacebcacbdbcabcacebdcddbbcbaaeecbaecadeaeabaebcdbbcdacebddbcdddbdcbaadaacbbeddbaaadebabaceaabecddcbedbdbedacddbceedddacddedabdbddccaccbabeeaaeeddaeeecdeeeecaccababdbceebecbedacccbddebecbeaabcecebaaeadbedbacdabbbcecbbccaecccddbebacbbbbbababacbcacdacddacdceeccabbbccccaeaaacbbaecdebecbbdeaebbdbddeeeaededaccbbdcaabdbeebbcdaaeceedebcdadbbbcacbcccdcadaaeebaeeaaddedcbbbdbeabdbeacebcecedcceceadbbcadbbbccababddbdbaecdbdbacbdccaacbadeeaadadaabbdacbccedbbbdeedccaeeaecdcdbecabbcdecdaebbbbceedbbeeaaaacbbdbcacabcbdeaeaedacdbbdaaabceaadededdcaaadeaecbecedeacacdceaabeccbacbedecbccdcaadadddcbedbcceadcdacdedbbebbbbdcaeaccacaadebdbccebdebebcecceedadddbbddcdaeecccbdbdbacabebdbedadbeddadaccceebecebdbeaedbcbedbebdddbccedceddbddcddadcdcacaabcadeadbdabdeeacecbeecbeadddedabeacdcbecdaceccbcdabacabaeacdcebacbbeadadeccadacdbdcddddcccddebeeaeddcecdeccaeddecdadbdccbaadaaaeedabaeadedddcebaceaeddbbeaaabbeceecddddbaedbeadbaaedbbecbdcaacbbaabcdebeaccaccaccecbacaacdbbcaeadedcedbbaeeccbaaeabbeebcccaeeacbbbcedbedbacbeadabdaebcedbcaebeadceccaeeeedcebdbdaeaddeccabbaacaddaabaeeaececabbbdbaabaeaaddacbaaeecccedadddaeccabbbeeecbcacdbdbbceebdacebcccacddababaacebecbeeebecdddcebdbabbebbbccccddcaaccddcbbbacdbecacddaccddaaeebccecaccbbeacbcedaeecbbadaeaaeaadddbeeeeeedebccdadaeacdbacdcebacdcbaeddadadcbeeccedaaaeaceabeaccecdecceccaeeaaddeebcdcbdbdbcbdbeaecdcbbdccabadddcedaeddeeddcaadcbdcacebbbebcdaedeedcaeeddecbddcbbcbbebddeaaecdaacebadbdddcdbedeacdebecedeecdaebdbdddebaedcdbdabaabbbcaccebeabdebddddcdeebcabeccdaeebcabbebbdabacbaaadabaeddaaccdcaccddbcecdaaaaadabcbbacccadacebedbbaadaaedebadbdcdbcecebbcebebadacdbcebaaeececeaaeeebccaacaeebbbbadebbadbedeebcdcbeebdaecbbddedacbbdaacbccaaabcaadcbeeaaeaedcbaeecbcaaedbdceedbbabcbeeddabbbdddebbdaaccecaeacedaeeaddaeeeaaecaebdbeceacbedcdcaecebecddadcbeebcecdcedacbbeccbddbaccbdbcdeeedecdabaebebbddebdeeebccadacecdaaceddbebdeceaecaeacaebecbedebcabaddcccabaeacaabeacdebdecbaebecbcdedcaecadacaeeeaccedbbeecdeebeededdbebcdececcedcaacdacebedbadedecbeacadbbbadeeeabeddccabeaecaedacceaabbbcdddeadbceddccaabdbbcaceeaebaabccceaccadebdddcdaabdcaadebdedbaccdadbddbccbdcddbdebebcbedbbcccdcebabeccdabcbbbcddaaaaeaadcdacccbecbedcbaeddbeaabecdeaaaecdacdcdabedeebaabeacdebecacbeeceebeaeabcdceacbabedadbedeabeaeebbdcdccbecdceddbbecccadbbebbeabdaabdaeedccecbebcebbbeccacceadeebbadcadccabcbbadaacdeaaeedededeeacaecabcaccdbeeadbcbbbcdcecddecebbbaeeabcccdccddeceeceeecebcbdabcbeeccaabdaedceceaaededbacdceabadcccaaecabeeecdabebdddaedbebeaaedecaeccecdecbeabbdaaceabeebcceecacceebaaeacadcccbcadeebceacdbcbcaacceeeaacbaeaaeecbebbbbdaecbbdbdbcbeeccaaeadacbaadedeedeceaecaaadabbecbabccebdccdcdadecbeecdecceadabdbbdcbdaabceaadedaadeeadebcabdeeaadadedbbdeaddacdccedbacaceaaaaacdddedacddbdddcbcdbeddaeaababbbeaccbeacbdbaaaddecbeeaaecaaebdadaccacaceceacaebcbeeedcbbaeddbcebdaeecccadadadbbdeacecbabbbddcabebcaebaedabaceceeddaabcaacebabaacdeacdecaddcccbabaccdaabbecdabddcbeaeeaabcdbcdeddabcdaaeeceacdbdccecdccecaceedcaaaaaeedadebeccdecebcecdaaebcabcdcddaacebacecedaaebccccdccbeebaaaedbddbbcbbebbccaaccaaabaebddaeedcbccddaccceceadacdbcdadddaaedadbceaabaaabacbabcccdcdbdaeacedebbdaeabbdcbeaddbbbdbcabecabcacacaebcbbdbeaddedddcccbbacbaccbdbaaaedbdebcbbdbbbaabcabbeacccdebedeaeceeeebaddeecddcdceeebcdadeedcadeeebdbdaedabceadbbeaadbbecdabbcaedadecdddaeddccbddcaacdecccdaaeceeeccbcabaceccadddbccabaacadabdcbddaccbdceaddbbceedabaeedccdbbcaedeabcaecdceccaeeaadececdbeedbbbebbeecbedbaaebacbacadacaebbbdbabccccaaeebecebabcdeedbdabaecdedbbabcdccbcdeacaceddbedcbaddcecbacceaebdcdcddaaecadadcdeccaadcdbdbedbecbaaaddbdceabaaceacbbdebebbeeddabccaaabbbeecaebcbdcaadbdbcebaeabbcabedeeabdcbdbbecccabecadccbdaedadeeeaaecbdeaddbedabdbccedacdedcdeeddcbeaaedadabadbdddcbbcacdedecdbeeacaeadcadcdeaecbeceddbdadbcbedcecbcbbdecdcbcecbdbeeceadcabaeabcaeadacdeaccbcaeeccdbbebbcbabaaeadeedbbbcededcbebdccedbebececdcabcbabcbdaebbccbecbdcbadadabdadcaceadaacdabacdebecaaeebbcbbceeaabecdaddbcaebedcceabadeccbccbdbddeaceaadddeacacaddbeabbdccdbcdaedbdbcabbcbaedbdbbecebceeaebeadbdccedbcccdaabbdbaaaabeaecebddebeebadcdaaccaeabacacdbaadeaaaadbdbabbecabacaacaadbaaecdbdeadccdcedbbabbbcbaecdcabebdbebdebbcaabcdaebddcdcbcedddaaecdcceedeeddeddaaacadaeebdbdddecddaeeadccacebbbdaceaaabebdbbcbcbddcdeccbedaaabdcbaaaadadddbaebdcbdeeaeaaacdaeabbedcddbeeaabcdcdaebeccbaeacacdadebcaebbcceacaaeaceaadcceebbaabacbbeacbddcbeadcedabedbacdebbdbcdadbbceeeaabcaceddbceebdcacbadecacedbdaebdacebcdbaeededdbdabdabeebbaddacbadbcdcccdabeeadebdaaaecccabebaaaebadbacebaedaeabedceadceebcbaadbdebbdbebaeedddeebdcedcbbaaadbedbaeceeabdaedcecbdeccaacaeaebdebbabaddecdaaccbeeeadddbecbaaeaebbcebdaccaeaadadbbaeabbdaccdaadeabeebbbdcecaadddcbbcdbacbcbceecebadacbaebeeceacbeabbcddbecdadabeadccdbcdedaceddacadaeaaebedbedbddbccbbdbcaddaaadaccbceebecdcbdcbedccceaecddbeaabaeddabadadbbdcdabcaaedbdabcabcdaebabcdbeaaaeeeaedbeabdbedbbdcdcaebdaabbbdcaceeccbeeeebdcccbceaebaddbeecbecabbaeccaebeddeaabcaabeabadcdaedcbbbdcabedabbdcbdeadaceadccbceddbbcbddbebcdedceaebacddceaecabaccecabaedeacbdaeacddcbbeeedeecceaedccddcdeaaeaecddedeabddbeaceeddadcededdbbedeeecbeebebcbbccabddaaeceeaadcebddeeeeadabccbbcabadcecdccdbaecddbbbccbbcdddcdbebdcaddacecbbcdcaebeddcbdadedecdadbdbeedbbabcbcdedcbdbecdedcbdaaecdeebacbabddcabbedeeecebaedeabbcabbbbeedabbdcdbccaadeceabbdabbecceedcceaccdaaadabecccaeaadaecdaeddddaaecccdedadcdacaeceddcabaaeacebacaccaededaaacddbdbaecbdecedceabeddbdebdcdbabadbbdbbacbeeadeaaabaabcadcdcdddeddabaabbceddabacdcedaeecaeecebebdedabecdccadbebccccbadbdbdaaaedeebebbecacacdbceaaaacebededcdcdddcadaabdceccdccaccbaaabaceeccbadeddccabbbbdaedcdbbbdabededadbbacadaaeaccddabcbbdeadbabeccaddbbbbabbddceeeebabecbecddacaeaacbaaeaaaacaedabcbbbdeceaaeeabececedaaebecbbccbacbdcebbdcccbecddbbbbbbbadaadbebaaceaebaecbbdaceddccaaeeeabacceaeebaaaadaadcdebbeaeadddadbbccceacdacbcdccaeececebbbbbdceeeacdacebbbeceeecdbddaabcdeabaacddcebadcabdbcebbebeebeddeaeceeedcdaacdaadcccbcecacaaecdaaaeddbcbccedbabbcbddbaeaadabccaabdabdeeaddaccddeeecbdeaaacdecededcbdbcadddcddeaccdbecebeaddcddcddcedcaccbaccacdaceeacddccaedeedebceeaabacdedcacabaeeddbddbabbbadaeedddecaaedeedbcccacdbbadaecccebdcecadceeebcbaaccdeaeaacaedccbacbebebcceaccaadebcadddbecceeaebcdbeadaecbedeacbbbbcebaebdbccbcddcbbbeaedbbcbccbcabcbceccbedecbbabbccaedcaabcdaebaaeaeccbcccdaeabebcecbeebacadccaebedebabdcecacabddacaebdeeeaadcddaedbeeecacededcedadeeebbbbcdeeaecaabcceaadaeceeaceebcbaabedbcdceeaadeeecaccecaccedecedbbaaeaaedcdcaababecdedeeaddceebebbadeaaaadeebdacbbcebacaaaebecdaecbcdeaecdcaedceecdbdbaddcacabaddcdeabcdeabdaabcbedcccedbadecccbbcbacaadacbdadeeeecccacaadadebcbbeeecdaacaaaceedebddccdaaadedcdedbbacbccaedaaecabdbaadeabedcbbceaacdceeaddbeccbeeeebeebaeccdcaaaebdbecdacdacecdceacaecadabceeaeabddcdbbcedcdaabebedeaeabaabeacacdcadbeaadbacdeedcbceccabcbacbadbcbeceabacaaebadacaceeaadebdeeebdcbedadeeacbdcbbaeabaaeedacbcddddeeeedadddbdcebbcaeeeabdccbdcdbcdcddccbcdbaccdedebddcebddaaecdbaccaccccddaaccabdecebbbccbbcecabbcbabcedbaeddddddaadcccbabeccababddabdbccbacbbeededdabadbcdebedbabacdaccecdececdadbebbdceabecedcbdcadaaeebcdceddeaceabebdabeeabeedabdaccaadcaccacbedeeeecbbeaecbcabbdaccbbbeccecbdceeadecccbebccdadbaaceddeabaeacdcbccdcbbcdebedacbdccaabbbadddebddacddcdbccaebabbedbabecbabaecaedbbacbebbbddbabbedaddbdbebcabbdceaeddacaeaebbdccbbebbbbaabbddbebdbabaccbbeaecdcedeaddcbeaddecbadbaeabaaabbbbbbababddecbcbaaaadebbdddcdddebbceadbdebbadaaddbaabbbecbebaedecceccdddeaedceddabdbccbddebacebedbdeacaacadcedbdaaccaddbabaeeedbbbacdcaaadbeeebbaacebccbeaedaeddebdadeeeaeecacececaceedaccebedabbbeddbebceeceacbacaddcadcdccdbbcbaccbdcaeddadceebebdedeeaaeeaadaedeaebebbbcecddedeabbabbcdbbcdccaadaaedcaabbaabdddcbecbadecebdacababdbdbdbdbbdceebcbaaaedcecdbaeaaddbaaeaabceddcbaedcbddebdbccbaeeceabdacbeadcbacebcdebbdacaaaebbeaeedeaabbbbcbecaadcdebcceebdcecadcadcddcebbcdadcbaebbedadebddbbceddadaacaddbedbbdaacbcadecaaccadddbcdedeaebbaadbeeedebcacdbcacdbaaeeedeadcccdeddaeebdccebdaecddceededeecbbaebbceaebbecacebdedadaddaeaecabacdbaacdedadcecacddceeaceaddbcedccbbeaaacbaeaeaceeccbadcebecebbbadcdeeaababbcadaaabeecbadaeedbcededbebecddeaceaeaeeebbabbebdaebbcdadedbeddeacbabcdacedddbabdcbedecbeabedccbbeebcdbbccacccceadeccaebbeeccdbdbaddadbbeebababdaeeadbabaddbcccacddaeeedcdbdeaebadbbceebcaebbccbaabeaaaaaebdacaccaaadbeadaabedaaddbcdcebcccdabcabaacbbcabebaeacebadbdbcedcbdaccbcbddeceaebadcdbeaeaccdccacdccadabbdaddbaceedcbdebbebcdcdabdbecedbddaccbaeaaddecccbcceacecdbdebddbaaacbadbbeeeddeacdaaebddcbaeebbacdaebebebbacecabeddccccbbdceadccbccaadebaaecebeaeecacecceddcaebbabaaebdebebdcedecbabadaaedeeeebeedbcceaecabaaebbaaaddadbcaecaddbecbdddadbddcacbabadbccdddbbebbacaeabacabcedcbebedadbacddbbcbeaabadedbbcbdaabeaaabadaeebbeebcecccdcbacbdaeeabbebeeddccdbaaecdaddbaaeebcdaddebbbebdadccaecabcacdeaddbeadcdadbeddbcdaddeabddaebeaaecbdbeddbbdaacabbebeaeeebdcbaeaaeabeaebbaaaecbcadbabcadedaeeedbececdbdcdbdcbdebabccbcaddcabbcabbabbeaaecccabaacdbdbcaeeecaddddbbbdeeaadddaccceacbebeadcaddacdbdccbcbdcbcacbaaadceaedcaeaddccebdacceccceceacbbaaaabbddbbaaabaddcebbccdaeeaceabbaccbaedeacadbbbabaabcccdceedbaeebeadbecdebedacccbabbbdacbcabeeccaabbebebbaeeadcddeccdedeaccbaecdcabcaaecdadaaabbacbaaaeaebeaaebbeeaaceaeadbebcbacdedaaabcbcedbabacbdeddeabbedcaaeadcdeeaedcdcdacbcdbcecdcbbddeaeddbdddcbbdddacacceaddbaaaadabdcddbbcdecebdaaaeadcebecbcececccaeaceddaccdacedccccccdeebdcceedcbbbbdbadaeeeabdabebdabbcaadcdeaebaabecbceddeaeedeaacacebbacacaacbbeaaaeaceacdbbdecdcaeddbabbdadacaeccecbdbdeccccaddeccebeccbabbdddedddadcadaaddadcbecbecbcdabecacceedbaebbeebbaecbcbbcecdedaeecdecacdddcebdbaccdebbccddbdbeaeddddedecdadabbaaecbedcbeaeaeccaecceeacdbaabaabcbcedbacaecbdacecebddaceedabedcedbabdbbdecbbbacebdeeadeabcadcaeeebedaebebdcadbebbcecbbacedcaebdeebedbdbcadaadddcaadcebcabbccedbaeeeabeeeeccbccadeeeceeebaebcdebdbbecededdbeaeaacacbbeddedecebcdccaceaabadddeddabaecdcddbdedbededadbcdbbadbcebbeadedaeaeceaebacdbddbbbbdddcecbdcddcbebcbdadaccbeebcbdbdebbecbbdadbeccdbacbbececcbbccdbeaeccabdecddecbdabaeadacbbdeabaeceebbcddcadcadbdaeddcdddbeddedecaceaabbbbbbaebbaabdbbccdaaeeeeedecaeedeeecaaeccccedcaeaddbcbebbaacbbeaaddeebeaaeababbdcbdedddbedeebdcdbbbdadbaacbdbaaecadcaeabbdbabebabcbaecedeeebbaccdedbbcbcbaeadacecdebdbbcebbdceeedebccbacaccdedeebccdeadeadeebeadbebbbedcebaecddcddeadeecedbbcdeaddaabddebcceebbdbcaeecdedadcedbdaaecedbdaddebccbcdeccbacaedcbaacbdbbededacadbeaddaeaaddbccaaceadddcaaabbebecebaebcacdadedcecacaaebdacdebbbcbeddcebadbacccbacabababbdbebbdececdabdaeeeebebcaabaeaeceadecbecabbcccdaeeebcdadbabadcabeedcbdcacaecbacbdabbbedeacabceaddbadbedecebbcabacecbbbabbeebcdbbeacccbdbaaceaebdcceddeebcebcbbdabbbaebeecddabeddbeeebeacaaddbbcacdbaabeabdadcbecdceebcdccdeceacdcdbadaaaeeccbabeaddacdaadbdcabbbdbaaacdebdebcccaedbcbacebeebddbcacadceabdbeaaabaecbaadbeedadacdabcdbbdaaaedbbcbdccabdbebcdbbdbceebeceaebaebdacaddebaadbeccecceeeacbccdddebdacbcecccaccaaeaecdddcaabdedaeedbededdcdebacebacdceadaccadccecdaacaedddabaeebdadbadacbcccccabaecbeabebddaeadbcbdcceeeeaeceecbedbcbcebcebcbedeeeeacedbcecacbacebedbcceedabcadbbcdabcebaaddacdabbeecccbaceababacebbdeadcbdaebdabddbabdaacecedabbdcbaaaabebeeeacaecdbadeeaaeaceedaaeeccbdacbccdcbcddecaecaecbbdadedcccadeaaecdeaebbecedacabcbbcceeededacebceaaceebcabccbdeedabededcecbaeeebedebaceeecdadcebcbaecdabdcebecabaaedbabddacbdcdcccdbcbeaaddcdeaabeccbaeeebdeaabdacaaaeabdebacacbadaceaeabbcbeacccbaccbaabceeacdaedceabcbccdbaaecaacdbbcdcaccdcedbebadcdcebecaeaaabcccecdadbebdcdbabccedcaccebadcccdbededaedccedadacdcdabcddacbebbdceebeddecaaabbddcccaecdabbecdadcbbcecdeaedabcddaeaccbcecededbbbbcdddeddabcecbcbaaeebadccdeddeeeeadcaebecbbcabedebadbcedaeabeadbeccbabcbaacdaeddaaddbeddbaaabbbbebbcbdeccebccddcbcbdbaadaadedeeedaeebcaadacdcbbcdeaaeaeaddcaeddbceceaeadbdeebbccedebccdddecdaedacdebaceacdaedcbcdeedbcddcbcaaaccbaedaeedacabadedddacdccdceecdeedacebaadaaeacbeacaccaebdbedbbeadbceecccaabbdabeacdddecabebaeacdaadbccedeeeeaaabacdcbddbcabacdceedcadbedeccebaeadbdcecaebcbbaebdeeccacaadabbaceebcdacbecdacdbcaaceccadedbcedcabbcddbcecaaddaacbdcccedbbcabedcaeaacdbdccdacdaaacbeceecdccaebddbdcedcbeacdbedeebeaddabadbababdeeedbadadebcdebdadbabcabddbebaedbbdddeecacabacdcbdabcedbdeeebabbbcaaebebaaabbeaceecbabdacbdedebddbdeeebbeadeaeadeebadbdbdedbacaeacddbbddacccbbcacabacbcbcdaaddbbaaaeabbcccedadbacecededdbabadcbeacacdaceeedacadebbaeabeecdcadcbcccabbbdeeecabdcaeceedbbbebbcbbbeaddbeebaacddbcceaaecaabedebcadddeedbbaddecaaacddedddbbceaccbebcdbdbbdaedeecbccaddeeebbaeebbacdbcdcecccacebeeceabebbedeecdadccceabeabaaebadabdacddeaeabdadbdbdedecbdbebbcecabadbececadaaedaeabacdaaaeebdbaaaddacbbddbdbcebebbaccbcdaddeeabbbbdddaceadcedbbdedcaddbcddeaecdebdebbebadededcebbaeedeccdddceaeeebabbeaabbababcdebbcaaedbbcddcaaabbecaddebbdcaebdaeedbeadababeeaccdcecaebacecaabebbdaabceecadabdcbccbacbdbccceceebbccbcabcbaccadccdcabdbbebdcbacebbccbdddaadaacccdbcbebdbcbddcacdbdcaaceedacebaaebadecbcceecaacedcacdbdadacacbebacceaeebacceabeaceeeddeabbbeaeeaecaaaacbdceecdccdbcaaccedeaebecebdbebaebcddccdbdebbddcbecabbcdeeebcbcaeccbbabbcadabcdebabcaccacedecaebcecccadececcbecabcdbdcecacdbadaaeeeabeaeaabdbdbbdcedaadabbacaedbaeeeeadccaecabdcbeaeedcebbccdbcececebcdeebcacdcbabbcbbabbdacadebbecaccababecabebbcbacedbabebacdcdabedaebdcdebcbbdcedbedbdddabbabbcaeeabecdceccedecabbaedcaedaeaaabdcdcbcccecaceeacdbcabdcbccdbadeaeddddaccaedcaebadedddbedbdebeaebaaaddccdadcebbbaccccbecbaceecabedccccebadcbaabaadcaeddbdccbdcdbdbabcdcdeaeedadaacedcaaceeeaceebdbaddcbdedddacddbeeeecdcdcbccdabcbcddbdaeebeaaeaabbadecdacceaeaebadcaeebdcaaddbbcadeebebedcbbecadcccbaacdceeedaebbbacdebeebebcecbeaecacedcecacdabdacbcbdabbbcaaecdcecddaabebcdcdbcbbdddcaccbbadedccadebbbeaebdbdbaeeddecbbbaecbcdaaaeacdadeceddeeaabcabccdeeababdccdbebbceabcabaadbcdbceabdcebbbadbedebdeacbebaeadacabcdcbbeeccecacdeaecececddcddccdbcbbbbeccadcdccdcdcbebbbacbbddbeabbcbddaacdecebddeaebcaebdcbbadebcedcebdbcbbababbaccbdddddbecdcebacbeccabacebbabeeceaeebadbedaadcbecbdbbeccebdebddbbdceddedaccebdeccbedbbaddeaeaaccdbbeeaaadaebedadeaeadecaaddeeaedbcbeaadbcdbcdcdbcdaeaebedcaabeaacbecdbbbbebddaccbddbecbddddeebcdbceeddabcacebbadbdbbcaddccbadeaacddaeeebccadadeceedbbdddedadbabdeeadcebabceccedaecaebbeaabdeeeaeacaececcebeccbbbcddcdedbbacadaaaecaabadebabaadbbdedaabaeddddedcbcddcedbcdbaceccdcdddabecdcabdacaadceebaeecedcaccddbeeeccdeabbacecdcabddbbdbacdcaaccaedcdeccacbedeecadbccdddacdaddeecbdbcecdeaadbadebdcddbadbcabcaeaadebcadbeebdcdecccadbcecaebdbeeababceebdaebbcaaeaccedbdcddceccdebeacbeaeccdcebeebbacddabdbbcababcccbdaadcbccdcbdebddeaabbadcbceebedebbebceccbceaaddacebeecbedbdaebddddbcbedecceccddbaeaebcaaceeeaacdcbdaedebeececedacebebaeaaebbdabaccdbacbebbaebddaaacdceeaaaeaeebeababaccdadceddbbccaddadddaebdbdddeecdabeddbcdeaecededcdbbcabacdccdcebecceceeabdeedbecdcacaeebeaecbacbcecacbdeccdbadbbabdeddbabcabdbdcaceadbbbaadbceebabaaebccaddcaecbeadcbedcaabdeeceacbdebbdcdaaebbdeaaadcecccdaebddaaacdbbecdbeccacdddacecdedebaabbdcecedcdaeddadceeacabbaecdbccecbeaeaaeaedbcbdbecedcdccecceedbaaceebabbaeedbabecdecddbecacccbcdaebacbbebcececddceeaeabcbeaebabbddecbeabcaedddcbbbebbaeadaecdcaabececedcbeabadcacdecdeedcccbaccabcdebceeedcedcbabcabadedbabccaadbceddedeaaddaaceadaeebdbbeacbdcbbbbdbbceebeabadbdddadddebaadececeebbbeeaaebecbedcddadbeebbedacdebedadccdbbaeabbdbccdebaebddcbceeabaceabaaccebacaddbcacaaeedcbcecedbbcdacdaaaddecdbbcbdbccbdabaecccaeacebaeeacbeabbcbabbeaeaeddddbaabaddccacecaeddedbbbdccedaedaaeceebbcdaaddcddcceaabeacdebdadecbabcddecbcdaecdeebbabcbbbdacdcbcaaceacedcadbdababbcbbceeaacccaebdaedeaabeececdecbdecbbecbeedbecebedaceacbcdeacadbbdaecdabbeaebacbebaddbeacccbdaeccceeebdbdaecbeadccedcbeabcebdddccbeabecabbbbbbacdaaebddebdcbabdeaceeecabecebddeedeeedbbeadbecaaeddcbcccbbbccbdeacebeadcbbedccaedbedceaeebaeabaebaabacbbbeabdcbaadeeddabebcabceedbeadddcbaadbeddccedebbaaeebadeedbcadcbebbaacbeacbddbcbbdadcacbdeaacaabbdbdeeaaebbdecadbecabaeeeccdbdbabbaaecdaadabeaebbaadbaebbbcbdaebeaaababedceadcbaeddbcaccebaabebbadaaccbdabcdaeddcebccdcabcaebbbbbeccecbeeeaddbccdddecaceeddcecddeddeedeedbcdedcabcbbcebcecabbacbdadcbaceccebcccabcbabbdbcedababdbcababedbbeeaaacaabceadcdabaadaecbbadbeaebdaabebadaeeeaaecdceeeccadacdbeaabdcabaadccaceaccbbdeaebccdeaedbbcbdceebecebcbdeeeddadebabbcaeaacaacadaeadbabccabcbeaaecadebebedcabbeaedaddbeebaacaddbabddbbcaaecedabbccebedbeacbaaedecabaeccabadedbdabbcebdbbeeeacccacabaeebcbbeaeebcadceccbcbaebbadbdadebdbdbcacbceabcbddddadebcbbbbabcddaeaedbeeecbbacdceeeabcabeaebdcbcbdbdaeddeeebebdcebbeaddcdbcacaceecacccaddcbdebddcdccadbaeaabdeabeccbddbdcbdeaacedcbdddababcaceadadcaeacaeeddaebedddbebbbaaabebceeabaccdebcaceddbaaacbedebcabeadbbcdebbcdeeceddeecebeaeaccebadeeeacbdaddccbcdabbbeddedaedcedccbdeaeccccccaadaadbcebceddecbbcbdcebaadbbaaeaecbeadcceebdccdaebcdcdddabeeacaaabcbbecdcabbbcebbdadeeadbdacebceaaccdeeaeaadeacdeebeebeceacddcceddddcaceabcecdeebaebddabcebebadeaebcbdbbdeadbacebdeabadbaaeceedaeaddecbecdcdeceeecbaddcaaadbabedbedeedcebcedcabbebaeaacecdcdccedcdbacabcccbcacdaeabddecbbeeacbeabcbcedbeacdccbedacdbeacaeacddbddccdcaabbedecaeceebdedebddcedeeadcdaacbcabcdddbdacacacabddbebebcdeaeadccdeccabeaedbbecbadeddccacecbbecadcccbbacaaaabcbaadeebacdbccbcaadacddccbbbbbcaeeeaaccceddcaeaceeaeeabaedccadcbececcbebeeedbdaaacbeebbadbaeddaabbccddcbabbdebceceeaeeeabddeaababdaceccebbbdeecbccbddbdeeedcddccdacabcbbdcabebbdacdccbaccdcbbcdddcdabbbcddceddbbbabaecaddadccdbaaadcdbbaeeeaabaedeeedbadadeedbdccaabdcecedecccbaedccededeadedceebacedddebaacdcacabddcacacdebeeabddcbaabbbeadebdddacabebdebaadcedbedbedebcbdcdaddbceebacbecadcdaacaebedbdbbbcbcceeaebccececadbaebcadcadcaddddecabbccceceeddabbceeabaedadeadedaaebbadbaeddacdddbcdeebcdcededcaedadcdecabdcceddedacdaeaeeaeabbcddbecacaccebaddbbaaddbedbdaaceaeaccedbddacbebbaaececebbbecccdcdbaaddaebacbbaeadeddabdcabbdceedebabececceaacbaeabbeececbbdaabaadeaaacdbbdecddbededcaadaabbdddebedbaddcaecdeaeaabddeecaebbbbbecdcbecbaecbaeadcaaacaedcdeacaceaccbeedacaacdeaababdabcceabdddccdecbeacacbcecdcdadeeecaadaeaeeaceeedadcdcaebdecceaeaebaaacadbccaeacdcaddedddcdadedbceeaddeaececeeebebadccdbaaeaecdacacabebaacbbaebeebeeababeeecccdcecdeaeeabedebdcebdadbebeccecdedddbdbacbdebbdaadebedbdabddbdecdcadacbbbdeeeedeacdcbccbacedcabeadbeebdedbdabcbbeabcaebeaaccecccdaeecccbdeddeecededbeaecceceeecaabecadeeeadbddebbecccbececabeedaddbdbddececeecaadaaaaaedadedbcaeaaccebbdedaeebeaaacacbbddeabdacaceadddaebbdebedabcaceacbcdeeddbaebebecddbedadcebecabdbbdceebeddadadddcabcedeacdecebecadaceccbeeaddcdcbbbbceeebbdacdacaecebddebabeacedbaeeabcbddbbedbccdeccedeaaedcbcccacbceebbbedeaceaccbeceddaebdabcaaabbacbbbcaddeaddabaebbaabaebbbaeeeacabcbbbbeaebceddebdeacddcbacdddbcbacdaeaebecebcadadecebecbebeaabcdddeeaacbabbacabacacbacdcacabcbaeedcdbcdbdedacbbebeaebaceeddaabaebcbccaacedbcedaeaabddbbeddcdeaddbcecbdcdbeccdadaddecbbeddeabdbcacdaddacbdbedeeeddaceceeeeabceceabacdcacdebbaeebdbedbadbbbdbebcddeaeddeccbcabedbbcbcdadaaeabbadeedbbdbecbabbccdbccbcebeacdaaadbabedaddeccdcecbcdeedabcbaecacbcadbbcaaebeaeadcdedbdaceabcceeededaeaecbaedaceacbbcbbcdeaaedcaceebadbceecddbacebbddbaedadcaeeebabbbcbdeceddebbeecbbccbcccaaccbddabadabacaebcbadbdedabccbacddcccbdceaaaccbdeacdaddabbeecbbcdadcccabbbeccadadbaaeccbddaadecacceeaedabcaccacaaeeeadaebdbbbeeebacddabbedbaaceadcecccccaeeebeceeecbabdaadbaeadeceaceacebcdcbeaeaccdbeabdedcbcbbbcaddbbababaceecbdbdbdedcceeddccdacdddbabeadbdaedaddecebeacebdcbbcbaecbccbbacccddabaadaeeeaadaacceddcabaabcceaaeabdceacddaaeabcbdceedcbacbdeeeecbaeedecbeaedcdbebaccedbaaddcbbaedaadeabebdcbccddeccbbabdeaaeadcceabcabebcdceedceabbcadedbdcbaacedecdcaddabeedbadcdedcbdbaecbdccbbaabecaaddceaadedbdabaacacbaaadacebabdcadedeabcbaaecccaebedbeccdaacaedbcaaecbadcbecdbcebcaccdbaeddeddebbdcaebbacceabacaaddbabdacdbdeeddcceeeecacccddbbbdabeecaddcdceaadbeaacbbbaeadecadcdbedceeebadcddcaeadbdedabeceacaaaabcabbdeceabdbaedaacadcaceeebaddccbeccaadcccadeccbeaeceaedcbdabdbcbeddbcadbdcdecebbdbddacbacbbbcbbeeeeadbdaceabeebaebaddcbbbeaeddceccdedbdbbbaaabedcdebcabcebabcaccebaabeeccaaabadbbddececdccdaddeaadeecdbdbeeadebdabecbeabcadcbedddebddaaabecaeabadccdaeaddbabbacbacacebbcaddaeeabcadadcbeecccddedabbbddccdadbbdebadddeacdbceeddbdbdecceccceaabdeeeacedbcbeedcdbabccaecccecabcceaebcabedbccdddbbeaeedeeebacecddcdaeeecdedcdeceeaccbdaddddccdbbcbaabcdbdcacaaaadcbbbcccedcacabaabddecaeacadcbdaebdbcbddedbbbdedacbeedebbbedaadacceacebbebabcddeeeaaeeaebdecdecabbbbbebcbcbcbeccecdeceaddaaecbcdaeeaeaebeccddcbebeeaaccebedeeadeabbadaeeeaddbedeedecedabcabadecedaeedcddeeebcecadbdabeecbbbdcaaebdbbcddcabecdedcbaabdbbdcdaaccabdebbdbacdebcaebacabdaabaacdcbaecaedcceeeaaaececacabcacabcbacbdcbbcebdabdbacbcaecabdcccebcaaaceebeabbdddbdcceeaeeecbbdccbadcbbacacebaeccbcecddccebccbdcbcacebaddbdbaccdcedbbcccbaacdedeaacabbabedabeeaeaededdedcabbcdaedcacdbbadadbeaebcebcdeeceedbeacaadeedecccecaddacaecbaecdbaedcbdbbddeddeddbbaebbaddadeecbcddaaacdcbdccaabcaeeacabaeaddbccbbdbcdecadbbbaebcbaaeecdaddcadedbbebbdeddcdaaceaeebdebabbcbbecdceeabcceeabadccebcaecedecaabeabbeddbbacababdbeadcdedddaebabbcaebdcddadcedbabacccecbdddcdecaeacedaaebaeebaceccbaedbeddceadbcaebcccdebbdccaabebbdcbdbcdeaccceaedcadeeccabaecaaaadeddaacbadacdedbcabcaddcadbaceebbdccdecbebcbdcdeeebbbecbccadabcbeeecbabadacbcdaabcdaacedeedbbaedcbaaabdbccaaddaececbbeeebaeaacbdcbbaeaeccbbdbeadddbedcbbeceeebedcdeeebededdcdaccaddacdbecaebcbaaccaccbbdcebbadccdaacadbcbcbccebcceabeabccdbdedceeabacbaebceeaadaaadbcacaabcbeabbbdeedeccbadccedaeccbecbaeeadbdbddbceaecaeceeddbaeceabeacbeecaaeabcebcdbdebbcdddcdaccebbcaddbedeeadebeddddedcccbabcbcdbbbeacbaaddedbbdaaccacbbaeaaaecbcbaaeeedbdecaeaecdcaccaedbdbeecdbcbaacdbabcbcbceececdbcecbcccddaebbadbaedbabaddcbdeedecbdbbceddccbaabbdccdceaadaedaedbcaaddaebdebdbacbbcabeedbccccbcacceeccbbcbbdcebbeeaaeaeebdbadcbabaeeeecdbaacbaabdbaaabccabdbcdababbacedddabeecaaecdbcbeacdedebededceecaeeeabacbadcbbdaaaddbaedccebabdbaccabbdbeaeeeddbceeedccacdbbdedbddaadaacccaabbadddbabdcdabdbcdbcabbadbbeacddceaacddeddcbdcecbaeadbcdabdaeebaebecaacaabedbaaceccddbeaeebcaebdecbeadbbddcbcbeaddebeedccccacaedebadddbbceeaceccceacbdbcbbdaedddbedddcbccdaebaccedadebdedadeeceeccbdbaceabdcbdbeceeaacbddebdeacdbcabaeeddccaedccbaaebbacabbbeedacdebadccedaecdaaaecaaeddeadccceccdadccdeceedcdbaeeacbdaebddddaecdcebcedceeaddbebaeacdaeaaddbbddddcaecaaebcebcacbaadbaaeeaaeeebdbabacaaedecbabecccedcdeaddceaeddabedddcdbbcbcddaeecedceedaecbceeecacabaecbccabbbcaddaebccbeeebeadcaadacabacdaacdeeacebeaeccadbcebadcbedbcabecdccbceecdcacaaabacebdbbcbdbecdddddacdeedcdbdedbdeacbbaabcbcaeddeabbbddbacbcebbeeaabbdbeaedabadaeadccdcdcbeeadeeaeddabdbbcebcdaaabcaceeddeddadadedbbdbeadcecbdebcbaebdbccaadaddeecabeaadccbbbecdbcccbcdbebdabecddbacceddaaabcbeebaabeaddacbaacbadaceddcaccecbdeaeedcaeaadadcacaebaadaeeeccddbeacbcdabbbecbcdabbededddacdeeeecdeeaecccdcceadbdacdcdeeaacdddebbccedbabedecbeaaecccbdbcdadbbaecaccecceddabbdadecedabcbacecbcacecceedadaeadaabbbbcadedbeddbdeedadecbccbddedaebdbecbeccabbeeeecbddaeeceadeeaabaebbdbccaedbcabcbbceadedacdebaceedddaeaeccbceacbcedebeaaccdcbbcadacabadcccbbbbeccecbceeecdaeaaedeebddeceababdebbacacaebbedabadadbdbbeaccdceabaeaebaeddaedeedeedddebaecebddacebaecaecadcbaebbabcbcacdbdcbcbcacdacddaebddabbbdeceaadeeddbdadacdabdebccedbdddabaabdcdcebcdbbebbebbdaacdddaebdaceacadeebeaadebdaeabbaaccedabbcaacabeecaecedbdeaedeaeaaaadaeccceecccaebedaededcdabdbaccbbaacdbbaddacddebdacbbabbbaaaceccbdbeaddccadaabdbddbdceaeadcbebddbdadabdeabcdbeaabbbeaabeadacdcebbcddadbcaaaaeaebaceeaabcaebdaadceacdcdbedbbacaabddbdaaccbdbdbecdebdddccdebebeeebacceaaebecdddcdabbbdccebbddebebcaaaaebacddcdccbbdaecbeccaeeebcdbdcddbeccaaedddababdcabdbdabcceccdceddeebbccbdbdcdabbacdadaceeebccabbcbcddcbacabeadeeecacbcaeebbcbdccbeadbeceebdadedccebbaedcadacbeacabdadbbaaccebacdecbedabeeeccbedcbebcddeaaebeeeebacaceecbdddabbedcbadcaedadeeadcadcdecebcbbecacaaaaeadeebdddbacaecbeeecaeccabcbaedbedbcdccdaaaecbbcaccacbabddaaabdcebcedaaaaaacadaebbcdbaadcaacadeacabbaeaeaeccadcccbacbeecadecdcdababeebeedcbeaebbbebacccbadeeadeecbbbcbdeeaeaebddbecebadaadeaecccddccbcccdcddcbeebdeebebbccebbacddaababbedbeeccaebebeeaedccdacbadecccaadcecbebedadbddedecbbabdadddaadeeaedbeccddbdccddaacddcacbdacdcadcedaadeebdaaaecabeaadbbaebadcdbcdedbdecbeceeedebcdbacdddeeccdcccaedbdbccadaccbbccdeebbededaaecdbdebcedecaccabdddadcdeaddcaaaeabacdeddcaeebceeabdadacdbbcedbccddbdcacbacaeddcabebccbadaebdbecccceaeeacdaadaacbbecaabdebdbbcbcadebdedebeedcdaeadbacbabddbebeeeebccdcccaaaceceaaaeebeaaccabaceaadbbabbdccccdbdabeaeaacbabbdeccabeceaccdcdadaddecaadaedaeadaebaeecaabaeeccdbedecbcbabacbeccebceccabceeecdcedbbecaceabeaecabcaeecacdedeedbbbbdbeadedecbbdeaedebdcabebaababcaadceadcbadcecceadccaeeaadddaabaaeeddddeecdbebaecadccabaadeaadbbeddadeceeccbccdaaeeaeadebcdadedceebeeceddbdbcbabedbedabbbdaebccdcbceccccdadbbcbbddbbacddedadedbbbbecccabcceeecacddedbbddebbebeeccdcecbccbbbabdeabacbbddbacdcabecaabecababdacbccdbbadddcdedaaeababecdddbabbdedecccdaccaccecdedecbacbdacecabdabcccdacdeaeabcbdcadbdadbadabedcecbcedbadcecaaceddbedcccaddebedaababcbbeeecadceedeeebdbcebbcbdeddeeebcbaaadebaededaacadcebeedecbebacbcddccedddbddeeacebacabeaebcbdedadbbebcccaaddeddbbadcacdbcdeaeadbedebebbbaccbedbbcaaccddebcadababceebdcceeeabacdbdddcadcaaeabdcdceceeaaddbcdaaedbedbedaeaeccededbabbacaeddbbdedcaddcaabbaeebebdbdeedccadeabecacadabacedbeebedeebabebddaaddceeeeccbecdabebbdcccebccebccebdeddabecdecadaadeaebeecaaaabcbdcbacdcccabeaecebddceaeacaddebddddddbcbeebceaebbbeeadaeaaecaabebbdbeaeaebebeeedaabdbecceadedededccdebccdaeecbdebecddecbeaeebdcbadcadbeebebdbceaddaeadbdacdabccdccbccbdbadcbbcacdcbedcdebbbebcdccdcaadddbdccadeddbeecbccaeddacebdbcdabaecbebcbbbcbcccbeeadcedcacecbdcadaeccdbaccdaaecadcdcbaadeaeabbdeecaadbbeecccebeabceabbdbcabdebdaacedddabbbdaaacbbbeeccbdecedeeadedbdeddaaacdddeeacacdbceebbeddeddbeddcabcaaabbdcacaeccabcccdedcababaaaddadbbaaebeedecdecacbdbadeabbcdddcaeecdbcccdbbabdbeaeddcaaecdbacbcadedcbbadbdadadbbccaabbeedcbccdccabcceadcbbaeeebeacadccecbdcbebabcdeeabdabdbaaacbacbbbbeeacdcaebdbaeaacbbbeeebeabebeddeebcdbcdeceebddbbeaecdabeaebedcdbdbcddceeddebdceaebdbbcdbeadbedcbaaadcdeeaeaebeaecedcaaedabcccccbcbcdddaabaedeeaaccebdeecebdeeeaaabbdaeaabbcdbdbbadeaceacecabacaacecabeaecbaccaeabdabacecaaaebdaacaaccdebcebcaacabddbcbdbdddcababdecbcbebccebbbdaccecdaadebabadeebecddcbadbcaccdbabcdebaddccabecdbddbeddedebceaeaccdbcaebedaaebcdeebaabcedbecdadddabcdaaaddbdbbebdbacedbcbddeeabadedddeacabcaceeaacbcbccdcabbacedbaaccbdddedeaaedaebeaddbdecbbddaeaaaaabaadcaaabbaeebdbdaaebecdcbabcebeaeccebadacacbdbcbddbedeabebcaeaeebdaaccaccacbbbddccdaccaeebdccacdebaebceadbcdddcccddcbaeaecebeadcabacdbbdcbeccabcbaebecadbacceaaadaedabaaedcccdecbbbccaecbaaaeaacedbcccdddedadddeeebeecacbdbccebeadcbbdebeaaacacebbebeceebbaeedbbebddabbcdeededaaabaedeadbcaebdadbeddcddcdacbdbacbcdacebebcaaaccaecbeabbbbdbedbaadaeadebaebddaddddaecedacdebbbcabcdedbcbcbcaacabbeeddabcebcdadadedceaeeabadddacbcbcebecacddeccdcdcecdddbaeaeeddcebaeaedaccbabcdcddeaaaceceeeccceaaeccaebbbebcabceedecccbcacecabbecaaabeebeebdbeeacceebddddeeedebcadbadecbacdecdabadbdceecccedabddbaaaddaccacbaacaccddbeddedebabedeeadaccbcebecbcaabbabaadbaeeededacaaebbaccacaebbeccaaabdcdbcddecdcdcaecbcdbcdddeeaeebceebbcdabedcbddbccccbbdaedadacceedeedabeabcecbbabccaadbdceaebaeaccdadddeddaaaccdebaebceacbbaccbedddccacadaeabaaecddebebccccabbcbecacdeaebcebbdcdbdecbdedabeeceabbcaccbaababcedaebdddbadadbddcebaabddecdecbdeabdacdaedacabaecacaaaebabaccaeeeeeeeeadeeccdcdddcceddbddeeebaedabedbbddeecedcaddedcababdcbaaabebcececdcbbecbdbeadecabebdadddedeeaeccbbebbaabbdaaaecebaabccceeccbebbacdbeadcabaeebedaebeeecabceaedacbdbbecbbebaaaeabcebaccddcbeadbddbdaccadaaedabcaeeeedaaaadcbbcaacbabcbcedccecaceecbdddaaaacaceeeebdeaddaeccecdeedebdddbbdccdebdcadedbbabbbedabcbbcaaeadecaddceececadecddaeaaabaacdccaeeaeebedeabbaacddcecbadcecdedcacbdeebaaccabdecbabbdabeeddeeadaddaeaedebbacecbabbaaeddebcaddebdcebbaedccdbcdceeecbacebeecaeebdaadaaccedabbabcbdaebadccdcbbbcdbdadcbeebbebedbaeebbebeecebeeaeecdcaeacddedcdeacadabdedbaeadaccabceeaedecdeeacebeaeaaddcdddabecdebccdbaecebdbaaabcedcdcdaceedddadcebeabbabcaddaeeaedcaaeceaadecbdcedcbebbbcbdcaeaddabdddbcbcacccbdcdcccedeacacaecbaadedbbadedeaadebeebdeeeaeddcbcdeeacecddcbeeadceaebdcebccedaedadcdbbaededaadbaaeeddbddbaceaeacdddbcceaeaaeacaaecddccbaaebbdbabebbdeebbebcdacbadbbbaaebccbbccccaacbbbdbaddbceabcedcbbbabbbcddddccaeecbcecbedecccdbcdbeedcececedaecbedccacaecbddbdbdcecebccaeecdebaebabcdeeaccddeacaccabccbbcbdaeddbabeeceacceeabbcdddcbebaecddadadbeeaadeceaabdedbdadebbdeccccadbaeceeedbadbaacddeeccdbbdccdceedbceacbeeaadacbbacbdecdeaeddaddceeebaaeeaedebeebbeeaaaacbbcebadbabccdabcadddedccdcdebcceaecacacbacbadaedeacddcabbacdadaededdaaeceaaabecccccdadebadbadbaecceceadaabdcceeeeddebdaacedeccccbdcdebebdddeccceaedbdaecbaacbbeddbaeeeceaedabbaedaacdedbeddbcaebcaaebaebddeecabcecccdaabbccebdbababbdebcecededdcdddeeecbbdedadbcdbdccaeacbeebacbcbaabbbaedcbbededcddadebedbdbccbaededabeecaebeadbcbceadcaabaabecbeacadababcecccadbdcacbdcaccdaaeddbbedbacabcccebbcebabcdbbbbccbbccaaadcdbbdedabcbddcbaecebeaccbdcbbbadbccecebaccbadbbbecaaadbdacebeddabecacebddcbccecebbaaadabdaccdbaeabdcbdccabdbcabecbebacaedbccbededebbbdabbddcbeaaadddcbecbcebebbddeeeecaeacceaccacaacecdcabbdacdaadbccdbdcadabcbbeceddedeebaaacbecaabeaebdbcdbdccdecdbaaccbeaebecebaaebcbbdbaebecbeaaeeeecacbbbbedaaecdbbbdbacbeceacebaaacaebebcddeddcbddcbebcedecaddbcbbcddedbbcdbaeaaecbedadecccacabdeeccebdcbedaecadccdceadccedbcadabcdeddddcbebdbbeaccdcccbdbbbadedcdcaeadbcaddbacecccbebedcececddddaabadedaebacdacbebdecacabedbdeeddcbadbbceaabbaaaaddaacecedeaebeedecadecadceddddecdacdbbdeebcbbacdeeceecadaacdbaccebaeecbbcacdbcdcedeaaddddabbcadcdaddccbedddaedebeedcadbbdaecbdaceeeabbaeeabbeddcedeecedbbaabababdcaadaceaeabaacadbcbdadcccbabecbeeedebedeeebaecbadcbacdddcddbecaabbecaeaeeaacdedbcacccbdcbeaadadedaabdbbaedcbaabaceeaaeabddcdacdcabaeacdababaeeddbbbbbbabedcceeddeebdaeaccedabbaaececaecaeebeebeaeaeabbecdebececdcbdcdcadecabacbeedbdddcaebdbcbabacddbacaccacbbeebbebddceeaacbbedbcdbdcabacebacbccbbcddcaaaeaaccbbdabcdddddaccaaceaecbdcbacedabaaecceeebdbbaacbdabebbedbcdcbebeacaebcbabedccedccdcbbeecdeccdbadcdcccbeceaccdaabddeaeadbaeaacbebadcbccbcbeaeecdeaeaedebacddaedcabeabaaeadcddcdedeebcdebaaceedceadecedececdeeaebaaedbbbbabbccabdcbcbdaadadecceceeadebbaaceaacdeeccabbccacaccdaaababacbaceddaceaebabdcddeabdebecacaeccaacebcecedbabdeacabaaceadaadbbcddabbcebccadeceaabedbdbbabecdbcaaaddbcbbcacbdebaabcdbdcecddaebbebdaadcdacacceecbeeedeeedeeaaabdaeebbbaccedbeedddbdcebcdbceeacaadeecdcaabdadaeecacebdecbbbaaadadeacbedceaaeecadaecceeccacaaeabcbebacdabcddebdcdedcbeadaddbbacbeedeeebaecebedabeecaebccbebaccebdddbbbbebccedecbeeabbadeabededbdeaaecdadbcbeecebadbdeeaadecdabdbacadcceeddbeaaeccbaaededddcbdeedcbddebdbccbbaceebadaaceeeeabadaaabebbacbbddacabadacbabecdcdcaaaaaceadddeedbbbaeaeeceecaadcedaadaabdbbbbdddddbaedeebaacceddecabbcccebabeddbadbadbdaedcadbdebccdcadcaeeaadeededaeeddbdebceeebbeebaebebacdadbaaaeaaadbdabcbedadadabcbccbbacbabbbbbbeececbeaccbbdadcaddcaeebadebdbddecaccdecdbbbbdececadaebdeddbcebdcbbaeeeabeadbbabdedaebbcecdbcbabddebabeaddaaedbcbdbdcbbbebebdaebddbedadbbadadbbaeaeeccdecaadcbbcceabdbbbdbabacedcaccabaccbacbbcadcdbdeacccdcacebcbdceebbbacdadaccadadaabdccbeddaecaeebacdbedbabeadddcdddbcbccbdabdcbdcaddadbedcdbdcdedcbdbbacebcdbbaebaabdbbebbdadaeebaaaccdaeadcdacdbdbaaabbdeeacbcaccccaeadaadaaecbaaccbcaccdecddcaecbecdaeceaddbeacdcbdedbabeccdddbeaaaeccddccbaeddbddbcaabcbedebabcaccbdbcbaccbaecbcecabdebcbbccbdeaacbcaabaacabaeededbacdedeecaddcdbdcdcaabbcecaddabbbcebeedcaedabbbdabddcdbebbccbaaebcbecdceeabdbbecadbceeeabedabebcdbccddbedbadbdaadeccaabadaebccabaaedccecbaebbceeeeebcedebebcceaeaceabbacedabecdbcacdeeecaaabbebdcaadddbdbbacebaeccabaaeaecbcaaccdcceaccceaabbabaddcdcedaccdecceccacabeeddabdeeaddabbdbecdccdccadabaadcbcccbddcbebcbaabbddbbbddbdaaacabcbdccaecdccdaaaddddeadccddbddacddbecdebccbccbcbbebdcbbceecbcbacaadeadcbdbdbbacaddacdcbbdbcbdebcdabccaacaeaaccdeedacccbdaabbbacddaebdceadbbbbbebeeedcdbdbdccddbaabecdbcbbaddbecbcccbeccdbcceaaebbabebaabeecbbcedaaeabeecaceacdcabebacdddedcbceaedeeaabebbeaadeaaabbbaaabbeeaaadcdacebaccebbdddbcccdebabbdbdaecadebeeaddcbbabeabeddeabbdeaaebacdbdcaedccbaddcddcdccdedbbdaaebeaebcaccbbdaaababcdbdbaebecabcccbdebaceccbdbacecbdeaecaddbcebdebadeeceeadcccddcadcebeaaeccaabacebeeaeeeaaadeeaeadbcdbebdaaceeccadaaacceaeacacdaceddeebabeddbbeedccabbecdaeecbdcecaeaebaeecdaacbcdcebcacecbaddeebeeabbaddebdbebaebaedddaacccadcdedaebdbadadebaaeeeadaedbedddadabdcceddeadeecceebdebbacdebeebbaeebbaeaabadeedeebeaaddeedcbeaddeacadecdebeadeddbeedbecbcbebbbdbabccbeabebdbacbddaaebbdeccbbecbbdedaccdbdcdcaeaebbcaceedbddddbedbbeceedaceeaadedecccdceacddcbaacbdbcebdddcebebadeeaeeecaceaeaadccaeaacbbceaaaacebaeedeeebbbddaedbddcabebdadcccaaeddeadaecccdedababdcaebddbaaaeadbacccabeaeecdedbccbadccadbcbddacceabeeabddbbdedabeadbcceabdbbbebeebeaebcdcbedccbcadaacecadbdedbdaabecbdbddeadaceeebcddbdcbdcbcaebacbecaccacdaaaddceebddcddabecebeebedbabbeadcbadbbbccdedecccaeedcebaadebdbcdbacaecdedcaaaaaabdbcabbacbbccbcdeceebadabddaecdcadbcbbabccbcecbbdcbdbadcbbeebebeeaddbeeaaabddebbeaebbbabbcadcceceeecdaededabcebcdadbedacdaaadcebcecedecadadcdacadaecbebcedcceabbdbaaceedddbcbdeabdddccbeccaaceedabeaebcbcdeccdcaddcabcbeaeabaaccbbaebbbeacebaaaedcddccbebaecdcbccaabccdbcaaeecdcdbeceededdabbbdedacdceecbaeacaddebdbacdbadaeedecbaebccbdccddddbdbceadebbebbabebbdcdcaeaadacdcddcbbcdadcddbbeeccebeacadceccdaceebeeaeebaabadbbaecbbaedeecbebddccdcdaaacbdcddacdadbcaabeabaedcedebcaebcedaaeaeccccbabcbdebcedcbdbabbaeddeaacbbaabbcadbacabeabdcdddaebacadbacdaccebbaaaaeaedabbccbeebcecededacdbdbdaacbbbcaddaccdcecbdaeeabaeaddeaadbbcbddbaeddecbebabbcecaaeadeeaeedccdaeaebeccdcdddecadccdbccabeadccdacbdcabadadacebcbbeabccebdabdbaecbaeaebdbdcaeeadaeddcaabedaddcbcbdaceddaedbadacadbebbbdbcacddebbeedbaedacbdbdcbaaccadbbbaeccdedddaddaaccdcabbaebacccccdcdaccdacbddcecabcbdacaebbcaceaaddeabccbbbdcaeddcbecdebbddbaeaabedbacecabcaceeaaecebeabcbecaddecacacaeddbcadaaeedbabaeaceccadbababcecabcadbeaebaddccedbeeedceddcdbbdcadebdcacadacdbaadccdddaadcdeeecbebbdcaeecedcccebebdbaccecccdeaecdedcaececebbecbebcebcdcedbedcbedbeedaaeeccecdaaacaeaaeeadcbcaceabcdbdccadeddbdaeacdedbadcadaaeebebacddcbcebeedabdbadcbadedadbedeedaaaeeaaddecbadddbbcdcdaadbeeaccdcecacbadbccedaeebecdacccacbaabaecaceacaeddbaccbebdbdabaedddbebaebedebeaacedcdebdbcdcdedabbaaebddeceececabdceccecdebcbebabbdcdbbbeaababbaedacecaecbaebbaddaeccdbccbecbddcadaaebeeebeaaddcadcbcaeebaedbacaaddeeeaeaacdededbdedcebaeebcceaddeacdadbdbcecbbbacdaadbcbebaccdacadcbecccaeeeccaeaeacccbdcaacbeabdbeabaacccecdeaacbddaacddbbceecccbcabceebacedecedeccedbcdbbabcebddcaecdcdaeeddbdddddebcbacdcacadcccdeabcdacbbbabbdeeeeebbbbadaaddccaaaebbddaaeecdecebdbcbdbedebddacbadbcbdacccaeedbccaadbabdbebdeeadacedccaecdcdbabaddbbccabeaceddedcaaacabdecccccbcebeeecdeeaaaaebedeeaddaaabeeceebcaebceceddaddbabeceabadaebcaadecaddbadbcaebabaeceeaeebeecaadceedaaccecccaaeeedbbdebbdedaaedbebdbccedcdabdecdaccddbeceaebbdbecbdccbbdccccddacedeaadcaeadcbcdeaadaabbeaadedbaaeaaebecddaacdcccbcceecddaaeeeeccabbebaabebdadbebaaeeeadeedaadadbcdbebdbdeebeceaaaadbaecadacecbddcedceaadeebadeeddaadddbdcebdbdceebaaaeeddbbabaabcbabacbaecbbebcdceaabddbbbeeeebaeeebcecbdecdbaedddbaacebedccccccedbbbabdacdedeebcbdbbdcabaaacadaabbdeadababcecacdaeacceddadbeeccdcaabcbdccbebdaedaeadbabaacdcbccceeadedbbaccebaedbcadcbeaecccbceabaadabbdeaeaccadacbabcdabdaabbdccaebaebdaceeabcaeedaaccdadbcaccabacddeebacaabbdcaecdaecdcdddadabcbadddabbaadaedcddacddaddeecbadccadeabaddecdebbdcdbaedbadddecdbcacdcdeadadcbcaccaececeebeceadadcdaddbedebbbbdcbedbcdadaaeeeadebadacaadaceabcbebcccaeaeccbebbacbcdddabbeadeacababdeecdbdbeabeecabaddaeceacaadbbbdaccecceaaabdeaccebdecccedeedeeeeaacdabebedccdeadbeadaedcdeabbcbdeebbcbcacdaebbcaccbcdaedbabdeeacdceeadacbacbeebaedbaebcdeaaecebdaceacdaddddcbdbabaababacdedacdcaaaecdabeedbaddecacaadbaaadaeedadcbbeebacbceecbbbeabbabadeacbabecadbcdaabbceeaaacdaceddaeadaadbbdddbacacdaeacaadcbeddedeaaabdaaebadabdaedbaebcabedbabccecdeadbdedebdecaeddecdebbbdacddebadcdbedacacdabedddccdbdcbaeabbbbbbaaeaadababebabdcecebaceeecdceeccdcbdeaeeddbccbcccbcddaaedaddcccbeaaebdaadcedcacdabadecbaabbddaadcebeedeabceedbbbcaeeaaedeabbddedbbbcddcaebecbbecbcdacaaeaebddbccdeaabbacadcbddcebacbdbdebdccdcdcbbbaeaaeacedcbceccaabebabdcbabcbcaaacbdbbdeccabadaabaecedbccdabcbacdadecceaccabdceccbdceebcdacadacaeaaeeeacdbedbbeaeccdbacceeecbaeaddbaedaddceebadbceaebcacebcceeacbceddadbadcacddaaabbbdcacdddbbebaedbaccabdaedcdecdeaddceceadbbbdbddebbabcaacceeaaaeeeadcbebceeabdbcedceabdabebeacecdecbdbedaebeeccbedeebabadecbbeacbcbdddbcdadaaccbcdcdaedbedaeccdbeceabaacbacdabccecaaeccaeccaeacbdaccbcdeebbcaaeaceeccdeeeeabbeacaaceeaacbccadbcadcbdedbceecdcabcabecdbeddecabcaacccdccaccacabbcabbccdaceaeccaaceddebbaaaddeedbdeceabbdabaaadcebcecdaceaedabedeacebeebdadabebadedccbceecdbcecacebeaeeaddbbcebadabecccebbebadbadabadddbceacbbdebaabeedceeddaedceeecdcecabdaaadbacadaecdaecbbdbaadcebabaeabbdbbeebedccaebeceecbcbadeacbadccdacdbebcbbdbaebbedeedebbaaccdbaddeececcceaddccbaaeccceeddabaaccaeacbeebccdcbbeeeaddaeaeeecbebcbbbbcbacdbadaccdacccbccceaeadecebeacaddcaccdecebeadcacaddedcababaacacbdecbacaebeededcabaeeaeecabdebccbdeaeebbbbbdbeedccaebdacbbcedbceccedabedacebeaaeadcabdbeadbdaedbabbabddbadbcacaedbcdebebeeceedccbcddeeabccdaecabbbeaacbaeabadebcdeccaccebdaaedddadbacbbdeacaadccedabcddccbdecdcbedecccbebbecbbeccdaaeebdbcaebcddcecbaebcbaeadaaacdeabcecedcceedaceebccbcdeedcdaeabcacaedebbabdbcbbacdeeeebaaadacebeaaceeeaeecabdcdaddbbdabcabbadaecadcbedbbedacbdacbbbabbabaaadadaececededdaeeabaeccdbcccceadacaabdcabbcacdecceccaecebcaccbaedebbecedddcdadcbabdadabdccbbbeceebabbdcbbebadbacceccbeecbdaebbdbeeabbdeeaaebbccbaccceacbcedaaadececdcaddaabdcedbdcbcdcaeccbbcbadcbdebebbdacdbbcddbaddbcdcadddbceaadedadddacaecdedceadadaddaceddcdeaceabdccceccaeaaecbdcbcbddbdaccadbbabebceddddacbeeeddadbabdabedabbbbbdaeccaddaebdbedeceacabedcacaaabcaabdeebbbeedbbbaabeacbcaebabceeddcaebbdcdadbcbcdebbacddeeecacadeacedaabeeebdaddebadebcdcbcdebabedabbdeecedeecaaaabddccadbbbabadbddadcbdeabaecccbadbcaedadcbaaaeaedccebddadddecacbdcacdceabbcbcedcdeccdcdeeccdeeebaabdcceaeeedeaaaeadbdadbbcbbcadcbebdcdeacbbedcaaccbebeceaacbdcdcedbaabeebbccaecacaccbccedcedbcedddadecdedcceacebbadebdbbcebedadebccebbcddebaeeeecbacecabbabbbbdeedccbddebbdaceeeecaaebddedbcdbeecbecdeaaeaddedbbdcdccddacbddebbdbbdddeacbdeaeebccbecdcdeedbdbebebdedcddccecdaabdeeabcdbbacdbbcbbccdeebdcaaadcdecabdccdbbbaebdaeeacadbbbcacbbebcdddbdcbceedaadcedbddccaeccaedcdeecbbabcebeedcaeabacabaadbcbcaecaeabaddebecedbcbacadcccccbdaceadecdeadeeadbcdebbecbdccbcaaaddddaaecaadcdbebbddecabbbaedbbececdcdebbcabaabececebaedeabbecbaabcdadacdeeeddbdcaddcdcdecbbcbbcdcdaeaaedebaeeedcdcacdcaaceaedabcbcebebbeeecbcdeccdaecddcedbaeaeacbebcdeaddcbdbbcdcbccbeaedcbaebcccaeaeaadabcaeaaddadeeacccaccbbccdcccbacaadbeceacebcebedbbebcdbeccabbedcbebeacebbabbcdaecaababdeabaeedabdcccbdcbabbcdebdeadbbcdbcbeebdbcaabedcaccabaaebbdccdacbeeeadceaecbdeecebdaeadbcedacedcbcdbebdacabbdadecdaeebedebeadecdababedaaaedebacbadceaacbbeecaedeedcadbceaebdcecaadedcddccebedbcaabceeeadeedbbeabcbeaccacccecacbeccbbbadaeaeddadcdaddcecaabcbcaeaadbcebbcdbeaadbdddccbabdbececdabbdbaeadbaabedcccadbddacbedcddbaecedbeaccaaccdbbcbeeceedcbdeaeecadccbbcdacacaaaeabadbdacebaaeaebaecbbadbabcacceedbcaddbdddceeebedddbeadaacbcccbcdebebdaaebaaeeceedacedaaececdeeaeeabbeadbadcccaccdbaeeaacacbaeddddcbaedbadaeecbeeeddacdabbdbcecdadacadeaacdcbceadbdedbadcebcbabadbbbbdeedbadabacdcebedbbeecaaaebebbebeaecaaadcebbdbbeddceeeeabbbdcebdcbabaeeaaceebaaebcbccddecabbbaaeddaecadddcecceecbacdcddedabedebcbbcaecbedeaddeebbdcadbcedacebcedccabcbdcaebeadcbcaeeddcdadadcebdbcabbbecabdabacbadcedeacdeedaedeeecdbbaeeadccabbcdeebddbbcbeaedcddacbcebcacaddbebdbbbcbadedbbdbbedbaeaddddaaccecdcbadaeaaaceadcdceadcbeceadaacedaccdddaeeaeebcddcdaddcebbedcacdaaeaaeecacebeacdcdcebeeddacdeadaedcceedebdaabbcdeddbedcbdaceceedacebbdeddacddbaebddcedebaebbdcbbaeadbebbeabbeddcbadadcdbadccdcecaccccaeecbbcecacadaacbaabdcedadcaaddabbbbbbabbcbadadddbaadbbabbeebccbbceeacceedaacbdddabeeedeaaaacbbabecadbcdbceddcaadbcdacbcdaeedecbeaaacabebedaadccaaadeccacdddccaaecbcbcbcddebbdceacaeadaaaaebbacebbbaddcacdcbdeebbaadacbccceddbcdeacadcbbdeacaddbeaccbacaaabdaadbacadabdabecacceabbbdaeaadededabbdacbcbcdcbcdeeddceceacdebcacdbbabceeebddedcddbaedeecadedaacdbedabababbeaedcedaacbbbbdcaeccddddbbaebdecaeebedecbacbcbabedebeabebcadbdebbbcbadbaeeebdaeeeadbdaccdcdeaeadcacaeccccebdaeddddbdabeacbeaabbacccebdacbaaaddbccecadacbedadeddbcceaededaecadebdddddaedebdedddbdeebaaccceebdcddebaaebdebcabdbbeadbecaedbcedeeccbccaeacbbeaebbabacdccbeddadecdcbdabeecbbacbcebbccbbcdedaabccdbddadbabeabedbaeebaceadceebebbbcbbceededbaaecbbdbeaabaaeeecaedaccbadeeacedcdbdbeebedceaaaaeecdcaeeabcabeecdcbacabaeebcbbddbaccacabaaecaeddbebbadedbcecdcdacaaaeabaabaaeecaccbbddaacebecadbbbceeeedabdaddeaabdacaacecedcbdbbdebdbbcdcecbbcccecdcbacddccdbdcceebbbbdaddebdadedccdeadbacacaeaddadecaacdbbdeaebadecbcbaaaddecdaeadaddcaccdcebbdeabbcacacdbcbcdbedaabdabdacebeccbecaddcebeddddecdacbaeedceacbaceeeaadeadedaaaddaaccbcdcceeedceaacaccedbdabecdaaadadbcaaccbbacecbbbecaacddeeadcaaacbccabeccbebceeeddbdaaeedeeceedeaccebdabaaecabeaadeaedcedcedeedacdbbececbabddadcaecdebaecbabbbeaacdecacdeadccbdceeadcbeadcccbbacacaaeaddbdadaeddbcbdcbddacdaeaddedbdbeaecbaeababeaadbbbeeabbebcacdebeadcaacbdacbeeaadccbcbeeccdcdaaedeaecbcbedccebbcbbeecedccbadeabeaaecbabcbaceddabdeccbddcaaaccddbbbebcedcabcedacaccbdddaccdeecaddacddbdabedddcabbcbbacacaadadcdecdcdbdacaeecbedccbbbaeeddbedeeeadebdbdecbcbddabcacbeaebaeabadaaeccbaedbeccadaceeaeeeacbbececabdcabedebdeadaadeadaaabcedeaeeecbdaaedaeabbdaddcbbebddeebdbbbadaedcdccdaeaaddcabecbbcadaedecacbbbbeeabbbacccbddbbaaaaaadcebedcabbcbbaceaedcedaddacebbedebbeacabbeeeabcaaeaaebabdbcedacdebdbdcaebbdedeabedaeeddcdecdebdabcebcacceceeeeaccdccedabbacbcdacceedbccecddccaeaabcbdedcebceccbaedbddaabebccebabdcbccceeeadecbebaacbbdaeeedddaeccbcdbbcaddaedbcaabcebedcbbeacdadcdccebeceaeeeaebecccaeadbccddbeeadcdeaaadcbacbeedeceabbcaebabebebddaadbdeecaddbbdcdcabdadbedabcbccebddecedeaeadadddecbcbedcedceedeccbacddcbdeebedaadaeebcbacbedcaadcdbbbeeeeebebdccdeedbdedccddcbdcbadebbedaddcddaaabadbddddcceccabcbcebedaeeeacaabaaddaddacaccbddabbaeccedabadeccdbaebaebedcbabdedbecdcbbdcbdabbccdebeedcbcacdeeadccadbdaacadaaeebececeeccdeaeeeaecbbabbcaabdcdcdabbdbbaececccaccacdebcdccacabaabaebbeedaacddddcadeddcbadbbeccddbbeaebcecaabcebabcedcdccaddeceabddcccddccadadccaaebbededebecedeaddbadacadecebeebdbbebcedcaabdeabcbeadcbbacbbbadddceaeecdccdacaeeaedadabdbdeeadedeabbecbbddddcdbaaabeaaceddaceababbeadcaebbbdeaadabaabbdddadaabebdaecdeaecbbccbcbdebceadaccdaabaebaaadebbbacebcebbdbbcdceeabebbedcedbeabcbedacaccdbecadbdebbeebbadeaadbcebaeadaddaddbddeeedccdaecadaccacaddbceaedeabacadaebbdbebeeacceddebdcebbccbddebddceeadecdbadeccadebbcbadbedacacaeeeedbabcceddccedbaddbbbababdcdcbdddadbccccabdbeecbbcdbcdacddbcbdeccebdbaceeeeccedcddceaabcbbecedacbcbbeeccbcedaeeeccdcbbcaebecdadecddeaadcabdddadeeaaeeecaecadccbcadecebcaceaceabbbdeadcabddbaacddddeacebecdbcbcbedbacedbeaacdcebeeecabbcdcadbedcceddcbecccecbcdebedebedaaecacadbbeadaeebbeacdadedcdabdbdedabeebedbceddbbdadbaabecdeccddcdbaacadccceeedecddbceebbbedeebbddcecbceadcdccebbaabbbbcdbdcebcddaaaaddbdcbdaadeabaaadbbcccdacdbebbaeaeecaacaebddebbcccddcaecedaaabecadacdbcbceadaaabacedeabeaccdbedadeebdcccadabaceacaabbcbcebebceedebcadbedecdcaccdddbbcccbdcaeeeeebdeeacadabdbdaccedaebbbdeeabbdedcbcaecdeaecadeabdedaabdaeaeebcabdaebcbedcecbedaacecaebdaecbccdcccddbedbedcedcbbababeabdccadeaaeecaaaadadeecbccacdccedccacbccdecaabdccdaedbccedaccededdcaaedbcdaaccadeaadccdbbebddaadbeadceabbddedbeabaacaedcbdaaeaddcbdceadbeeeabdacddbabaeaabdcccdbabaabdadeddaeaccabbcebbdeecbbbdbadbecccecdabeaedebcaadadbeeaeaddedcbaddaabdccaaabeaacebccdaccdcdebeacacceaebeaadceaaaddcabebbebbbdcddebddbbaadacbdcadedacccdabeedeaaaeddbcdabedcadccecdeedddddbdeedaecdebcbcaeddcedaeabdeedbdecccadadcdccbadbbabacabedaddeaadbcacacebadacaddecccdbdbdbabcceaadceddbcbdbabcacbbaeeddadccaaeabcdbbdeccebdaccababdaadaedbccbebabccbcddadedbeccbadddecccbeacadcdcdedabdadbbbabdbeebbaacdeaacdeeabbeeacaddbcecebbaaeaacbacbeeeeaeaeadbddeeebbecdaeeddaaaddcecbdccddbebcebdcdcdacedebbacdcdaaccdcdebeccabcbcdbedbddabeacdadedbcceceeaabaecbabbdaedceeaabcadeceeddedbcbddbadbbdbecdcdadaadcbecdccedacaebeacbdeddcabacdcaadeebccabdabaddcabbdeaaababebebdecbccdaccdedbebdacccdddbedbabadeabcdcdcdedbcbccdbaabbcbccbdedbcbcdccebbcebeebbbbeddeaaeabedaecccdeadbdbdbdaeaaeabedbadabacaadcedcabbcaabcaeccbeeabdeaaadcaadcbdbcceacacbecebcbdceddbeeabdeaebbecbbcaccdadbaaebdcabacadadaabacedbdbbacecddeaebcaaeccabdaecddbecebeceabcedbddeeaddddeeddbedaecbcdceeccbebdedeadedcdbcbeadcebaceecaeadbecdaeeaecdddedbbdacaeeadddeeeeadecaabecaaabaccbadebaccdcbaeabcbdbcadcecadbbeeedbddabaceaeacbdcecbadcadddacdcbaccbadbcecacabebcbadaeebedcbbecdadbeaebeacaababdbbeadcbebeaeddaccceccdedcabcedddeeedaadcebcdbbacaabccaccbcdacbdadbdaeecaeecdadbddbaaadadbcbdaebcbdbcbedaadbbebbdcaaebbcaadeeceedcecbdacdabbcbcdbcddbdbadedcebaeabaedabcadccdbeaddbadebdaebeeadaeecedadbedcecebebabcccbbcedbaabbdcdbecbccdeeccbedcdccbdeecaeadecbebddcebbacadccdccdbdadbcecdaabeebabcabceabadbedadbcaeaddcbadbcbeeeecaecebeeaabcaeaceadbdbdeccdacdaccddcaaedaceacebaeecadccbdbedccdceebabeedcbcadcccdaddabeebacbeeedbdadccdeabecbaacdbcddecadaeaccdabebaececeebdecbaeaeecadbbbddcaceccdcdeaceedaedbbaeaabacbdbdcaaaaaccbadebdbecaeaebbdecadebbedebcdbddeaaeaceccedddddeabadebdedddcceebabdecbcdbecdabbdccdccbdabadadedaaeaeeeddecbbebcaeabdacebeccaebbdcbbaaacebdaebbedecdacdcdddbdaeddbcaaeadeaddbdbcdbeebaaaeedecdaeadbdedceaadabadaeacdacbebedaccacecccabecaeabecbdddbcebcbcccadbadbdacdbaaeacedccbdbacebaadabeccadbaaeaecceeddecdaedaabcddeaeccebdcaecdceedadddecdcebecaedaeedebadacbcdadbdcadbdaeadcdeeaecbcdceccecbebbdebbbebebccbbeeddacadcbbaedbbbdeabaeababdedebbbaccdcaceaebacbaaeeedbdeececaeaabbccdedddbacbacecdceeeedaeabadbcbcccdeaddcdbeadeeabaccdbacdbabcaedcaccbbbdcabdcadacddebaedbebceceeebabbdddcbaeacabdcacccdbabbcaeddbddeedeadedeabeacdaccdacdebdcaadaddacaaddcbbacbadbbabbbbecebbbbebbcbddbdceeaeeacceecccceeadbecdeaacabaadadbcddeebdcaebcdbdaccbccabebecdabddbaecaeaadddbdadaacbdcbabaeabbeaeedbddbacaadecccdbacdeacacacdecedbeedaccedbdeebbdeddecdccbdadeceeaacdaabcddcaecdbececcaddddedcbbadcadeebacccecddbeadbebeeadadebacbdccbebaedaecacdebaddedbcdbccbeeaeccabccbbacaeabdbaecadcebcacbbeeeeaaccdadabcaabbcabaabecebaccddebddabbcaceadbdceadeeeaccdaeecabdecceeeedcbaabcdebeaaebadcbaeebaaddabcecbacddbedbabbdacddbbebdeccecbdccddebedcedbbdaadeccbcddcebbaeebadcdadccdaacdeaaabcbeeebbcbbeceabeebcabddcababdaeeeadeeecaddcbebeeadbbecddcdacebedebbaebeaceedcaadbecebbeedaeabedceeeceeeedebbccacdcedbeebbaaababddabddbdddedcbcceadbabadcccebcbdcceebaeebdebbbaaccbaeccbaddeaccdcaadededcdcedcabececaeedaaabdcecaedddbecbebdabbebcadebbadbccdccbaabbbedebbedbcccdeccccddceccaedccbbbdceccdacbbeccaebaacaecbdcbbdeddebaacbadbddecbeeccbedacaecdecbbddbbadbccecaddecdecaeedebdeddecbcdaeeecadcdcdaebabdbeaaeeaecdcdcebedbecaabedeecebdedbeaaabeeaebbdbabbeebdcadaedeccbaecadccaaeeeaeeaaaceedbcaaedbdaadbababdcdbeebaebaeecabaebedebdbcaebbdbaeeebbdebbbdedbdecaaaedbeeebeebcadbbbeabedaecbbadceedcbaddacadbedcdbbdebbdcdbaddbcbbaecccdaecaeeceacaceaaddeaeebaddeceaceaabacdbccaecebddbaaacbadecaacdbbaeedbcceacebbaccaeabbcbabbceabbbddbedcdeaadbdaedbaeccadacebcdacbdedcceeddccdcccacebddccbaedaccdaeeeadccedbaaddebbecbcaaebccbaeaedbeabbebdaaabaddaeecdeaddebaadbddcaecdedabbaecbbabbddcadbeecbadaebbecbdebcceadedcbdcddbebaabeccbdeeaaacdecaedcbadebeadeeaceecaceeccebcbdbdabdedccdccddacbacabdbbeacebadaedebacaccbeecabcccccbedadbaaeaeedbaadbaebddebbccadddbbeeaaccacecbcebeecadabbeeabaeebedbaacabaeaacccddbbeeaceceaeeabbcbacaaeadcadbadccebeacdaeceaaecbdddacacedacbbaecbbadcebaaeccabecbaaddeacaabbeeadeebaecaddacbaecaadbebbacaeebaaceeeceabecdceaedebcaadbacabadcceadcbbeebdbbacebdbbbccdaaddbaabdddaeacbdbbddecbaeedabcbdbdedceaddbaaaadccbecbaaaecaaddeddcebeeacdeceaedadeeddcdbccddedebcaeecccaacedaedaeaeceacebddcaeccbbbdceeccedcdabbddccdeeedebeaecadeeccbdabddadebbcecddabbbdcedcbcdebbaeccbdaacddbeedbcaaebceebdbeccddeadbbbbbecbaabbbeceebbdcbababbbecdedbbabdaebdaeababebdbccabdbebdddecbbddcdececbdbbadabacdabcaacabacceeaccebaaadcecabaacedcdbcbdcdcbedecbebaeaeebeedacaedeadddcecceeddddadecadedcdbecdeeeaeaeccebdebcbceabbceaabbedbddaddbaaaebaeaeabaabbdadecaaadcadaccaeddceececaabbddaaeeadbcbaccedadebcdabdabaeaebacbebddededabeeaeeedcaeacecaacccbaaaaaebbcadcdaebbceaaaebbecebacdbceaebabdcadcbbdcaaadadaeaccbbebdbeadecacacbcebcacedeaadbcaddcdaddeccddbaecccbaccbdacbcbbdedcdbcddebaedccedcedddcdaccdeccbeeeedabdbdbedeebdccdccdabaacacdcbacabdabcdbbbabdcecdabaaaacadaadbbabcaaecbddbdbdeeecbdcbbdbeebdbcbaaceaeeddccbabceebebabeecabebdaadeeeeeeeacbbbeabddeeacbaaaeacaadddaeaebedbcabbaeccbabddeebebdcaaebbcccbdaaececaaadeeaecbeabcbadcdcccedceaabdecbccdbedabacadbecdaccbdabaedebabdebeceacaadababcecccbbacecbdbaeabbaeeddaebceaadadcdebbaedeebaedbbabcacbeaecdcccceceaadbbbcdeaaaeaacacecbbeecadcdbeeeaccddeabdadeacebbedddadccecaacbbbbabdbdceebeaeecacdaddbacdedbaeeebdeaedbcdddcdcbdebedcbaceecaabcadbebdcabdcaabbccbeebdbaaaeeaddaccaeaaceaaeacaacbbcaaaabaeddccbcbcbdcbbceceacaebcdebeedaedceccabedccdaebabaabbddcedccaebceeabccbcecacbcbdcbdabeeaddeeebeccbcecdebdbdaeccbcacaabcacadbbaaddbecceeeedececaddddaaebebdcdeeeecbaaecdcbdbedabcaddddcdbadbeceadbcaccccaaabbcdabecbaaccceaddcdaedaeeacaedbebbbbddeaccbdeeaedbeabcbaeaccddbceecbedabbeabceacdbcdbdaaceadeedaebbebaebdbaeeebbacdcbecbcbeebaaceedaacceaacdbacbbaedacaeaceeebbbadcebeeeacecbdeaeaaecbeaabbccccdbeccbeaacbaaeeacecabbebbaadbabbaeaedcdddcbedbdacdbbbcaadbcacedcecdeaeacadbcabdaedbdeceddadbaceebecddbdbccdbecdeaceedbbeeaaceadaabebceaadeeadbaeabcaddadeacabdceaeeabbadbabccaaebdeedbedeacaddaeadaadabbcaeceeeeeddcdccebacbddbbdabbbdddcceedcbedceebeecbdbdeaadcbdedcbeeebaadcddbdddaeaeaeeebdbacacbcdaeaaebaaadceebedabdbbeeebdacababcdabdbaabbdeadebdbbaeeaecbcaccdbbdabceacddacabdaebabdcdbcbebcdecbebedbcebdebcbecaeeceeeaecbcccaadbbbebbdebeccbebabbeabcbaacbceccacbabbbcacecdaececbccdcccabecbeadeeeaadbcbdadaceaadadbaaaabbaddebecbecdbcaebcbdecbbbeebedabcbecadaddbddcdcdcbbccedaacceaccaeaecdebbecddedebaaacdaeaededbddcbbccbdeabecebccedabcbbcbebadaebeacbcabeaeeddecaaaeedbdaacedbbdabbcdadbdabecaebdaadddadccaddcecdbedabbeeceebadeedeeadceedcdacddbbdcccbbddceaabbdceddbaebdacabdecdbecaeeecebeeceebbacadccddaaecbdcaccbedabeaddaeadebbacacaaabbdbddcdebacdacdddcbbdcdccacbdeebcbdacecbdaabaaeacaedcedcbcdddacdeaabdaeeaaaebcecdadbdbdebccacaeadabeedccaebcabacbeacbdcdbbadddbceebecadcdeaadcdaabeaeadccdaeceaebeacaaedcbcbaeabbcaacbcbddceedcababbcdcdcaedcedcdadebadddbaebecbbaadedeeedeadcbbdbbbebeeedbbecdbbbacbcdedaaedbbbdddccbacdebddcbbaeadcbedacbacaaacbaaceaaabcebbdecaebadacebeebddbacdbadaeddceaedbaacbeeebaceaeaadebbddeebbbcaebbceabacdacccbccaccbcaeaaecdadccbbddebbceedeadecbbadcebcbbbbdaacbaecddcbdcdebeeabccddeedcccbeccecacabbbbecacacbabaddbedeabaeabaddecaccaaabedaccadaabbeeabdbcccebabcbeacddebeaababbbdcddccacbcdbdbadbaeebddcdbbdecacdbaecdbbdbcbeeeebdbdeeccbedeceaadacbddcdaeabbaccabbadebecaacdaacccbdebccccedbdddeaacccdcbcdaddecdbbcabadcddedbadbdbeebceebdaaccbdbdaedbebcdebdadeabbbcadbadcabeabdaceabbeeaeabbeddbbacdbdddacdeaccbdddedbcebacacedbaaeacdaeeaabeeeeeacccacceabadaceeedbdecabceabbeabdacecbcedbadaaeedabbbbdacaeecbcccdaaaaedeaeaadebbbeecaaddbbbbaeeabcceccedeebdbacddecdedbaecbabbdccbeeccceebdbcdabcacebaadeebadaeedcedcbcecaabeabdebcacdbcebddcedcbdbdccdeeaceebedebbebbbecedaaccadebaccdaabddbabaabedbcedcccdbebacceacaebcdcaddbeddeeceedeceebeababbbceeeaccebcebacebbccadacebeeeaddeddbeddaccacddcaeddddeeaebecebedaceaeabacadcddddaadbdacadbdbbddcedebbcaedadcdabbeddeeaeecccbaaeecdadaaaeadeaacacaadbdebdaecbaedeaccadcadccbedcdcddeeebdbadcceeccccbcceedaedbdacadcbebbcbceacedeedcccbbedecdceceeddaeacdbeedeadbabdaddceacedababbcccbdabdbababdaaaceaaebdabddbdbcebdeccadacdbdcebcebaadaaeddaababbeaabdaaeecbbbaacaccddceaedceeccbcaaadabbdcecdcbceacbdeaecadeebbceadceaddbbdaeaececaabceaaadeedaadbbceabeeaecccdbdadebebaabedecaeaaababccadddddecdbcccceabddcaceadebecccccdabecdebcdcccbccdcdcdedcadcbaebdeabadadaacdabeeaecdabedaecdeadcdabdcbabcebcdbeccaebbebcaceeedbdcabeaadbbdaeeddaaadcaedecedeaeebeaedbccdbacaaddabcdeabeabadebcbcabeaaacaedddadabbdaedbcbeaceccdadacbbceccbeccdecdbdabcdbcaeebadcbaeebcabecdbceabeeebadaaebeccdaaababbddaaaedcaebbdeeedebbaccbcaaddbcdcbcbeeaedcabcaeccaaabeaebdbeeacaacdedeeadbdcdeeaeecbdcddecebbedcdeeceaaaadaaaddaedddbbacccacbdbadcdaadcdcbbecdaeaddcdeaeecbaaaebeadaccbacececcadadbdbbdcbecededabacecacabbbacceeadddccbcecdcdbacbbdcbddcceedccadbcddeabdeeeaacbccdcabaeddedcddedbcbceaacaccabcbbcddeeeccbeddacccedbeedaeddeadbaddddebdbdaeecdbebccecddddeeaadbbaedeebdcbeeccbcdedeacbaddccccceaabbdedbcecbbbcaeabeeedadeaabeeeaeeebaadacbddadceacadceebaeaeecdaaceeccabbbadbeedbcaedacaeebecbebbceaeecddecedcacbeabbcadcaebbddbecdedccacbdaeecaaeaeababcdeaeccddbecbaaaaebcbeaeddbeaaeacecadbdaecaeaedbebecacacaacaccdceccebdcdcabcedaeeaadebbbcaadbaecaacadbcbaaaabbcddddbccdabdececeebabddacbcdaeeccaeccbbbcbbebeabaeeadceaebceebadecdbcecadbbdbbdebeaadddaadbeaeacddecdecaebdbaabeabdebeecccaeeebabcaebdcbbadddbddbacddaaacdceaccecadaeeeddcaeadadaeeaebdbeeecabeaceccaceabdaceeeaaddaccaccddedaacdeccdcbaeddccebbcdbebeedaeacbecdbecebadcdbccbeaccdcddbdebaaaccbdbcdbcacdababeeabaacdbecbacaaabebccbaaababcacccdeaedaddaacdbbedbeeabdadeadeadbdaabbbaecebcddabdcdbcebcecdcaececdedacbaacadcdbbccaaadcceecccbbbaaeabcaacbecceeecadaacdedcebcceccdabecedaccadeabddecaceaeedaacbbebcceeebadbaadbdcebcacdddaedeaceeacebbcdbabeccebbbeabcacbebcdccaebcbabedccbacccbdebbbabcdccaaaadcedddbbdaebccdbbbdbeedbddbeaaeabcdcaddecebbbbebecebdeeddaececdacdacccccdbaddbddcaeaeececdcbedaceeecebcdabedbbdecbeebeedbcbeccecbebaaccaeaeadccebdbedcdcaacbacdedadbcbabaedcddeadebbabedcbebbabdbabaecbecebaadacdbdeaccebdaacdadbaecddbbbbbeaaccbcedcbebdabcbcdaeeceddddcdaebcdeedabddbabadddeebbcaddcaecdbdaacecdbeccaaccebdcabdecbedaadedadedbdbbecbceaccaeecaedeabaddbacbcbdcccdeaccdceebdeecebdbdadaaaddcdcaaabbedaccaeecaabcccbcbbbaeaddeabcdbabdadeeeabedaeccbecbdabdcadababbeecdbcdabcdccbbeaeedcecaaaddedbeaeaadcecdcababeeccccdcdecdbbeeadddebeabdeacbabbbdedcdedcddbaaebbebebcebaabbcddeceadbeeeccdedeadbcebccabdedecebbbebceeeeccdaeedcbdbadededacaeeccbaebcbacecabaaabebabdddcecbaaeadabdceadeaeedcabddabbacadbdaeecaeadbcedbbbdddedaadbacadbeacadccbeeabcecbeeacddeadbabacdaecadaddcebddecbacbceeaebbacdcadebbbdacadcaedebdcecdaddbeddbabdeedcbabedecceababbaddbbbebeeeedddcbcaacbbcabacddeebeabcdccaaddccdacadadcbdecccececcabcbcdcdbdadceddabecdabacbebbeabebadcdebbbcadedcbbbbbddbddcdbecbbedbdeabbdbdececdabeaabaeddccbbdbbeeadeddebeaaaebceecaabcaeebbdecadcbededecccbedcbaadbdebabbecedcdaeeedaabbdeecdbabaecebededecccddcbbbaedeedddccdbbccaeebecbdedcbccbbbeceebddbbdceaebedcccddcabacbcecebcedcaebdceecbacaaadcbbdccdbbebabdcdcdebcdcacabbebcddabcdcaebcdddadbddccbeabeabdbdeedcbcedadddcadaddcecaebbdccdeacabaabbbbaeabdeebdbadcbeeaebdeeeacaebaebeeacccbedeccdcdbdbeccdedcaedddabdbecbbcaacbbccccaaaacdcecacbcbdeedebbddcdcabdbbcbcdcadbabbbebabddeeaceecbcecdacdaecedaecadaccaaeaedddebdbcabebebebaadebeccaccddbddaabceeeacbacbedaaabbeaaacabbeadacbeaaebcaeaadaaaaaadaaecaaccccadedcbabcdebaceddbbbcacbacceccdedaabcebccebabebddccdecadcdddcddbbacebeebdbdbcbedecaebbdecdcbdabccaaaeecddeebabedeaccaddecdbbeaddeeacaccccdcdccbaebbeabbccbaccdbaddeebbcecbaceededdaabebcceadbcacdbcdecdcdcbcaacdbaeadccaebcebedbbdadeaeedcaacaaabbbaddacdaadcaeaaaadbccaedaecdebeedaaddbdccddeaecbecabbbbdeaeccdcaaecadcabeedbbcacbdaadcbddeadbabcedaacbebdaecaacdbbeceaabeabddedbbbdeacecdeacddadecebcbaceadbbadebdabdeddedcbedecbabacbeeacbbdedbedebdbcdaabccaeeaadddcdccedbaabbeaeeaacbabbdcebbeaebbedbccbbcdeaddeeecabacbcecaceebddcaeeeceeeecbbbcecdadacdebcaccddbaceddeadbedeeedcecaaacbaaceccbbbebabdbcdcdecdbaddcbebcddccdeceabbebbceceeebecaabbdabdeaaabebcdcedddbadcaebaaeabbddddeeceebdacecbbcbdcdbaaecedbdeaaaebadbaccbaaedebecaeccdecdcceceeeeabbceedcdaeeebeaaeeeeeeadbdddbeceaebebcdabbdadabeeeeebececbcbeeedbbeedabbcaaadbdababdabbcabddcdacabdecaebbaccdbeddbebcebebaecccdaedebabbebeebbbcbaecebdbcedadcbabbcdcebadabcaddcedacbadeebdbaddcadeddadcbdeededbcdacbecdaacabcbbbaaaaabbeeadaaebbbaaadaabbbbadacdacdedbebceecaedccabbbcbbedceddcccacedacbbabadddcbabeecceececaabeebdbabebbedddedcbeaacedaadccabebdacaccccaaccdbaccbeeacbeadbbbacabedddaaeceddcaaebddbeedbecadcbddceecadbdaeeaedcedabcaabdddeceaaeddeddcebabcbbebeecbbadeccdccecbababeaaaadeedceedbdadeadebcceabbbacdaeebddbbaedeeadecadbcbadbdbcbdbbeadbaaedbeaeaddbebcaacdbbdedcdeecadccdaeaaeaebedbbedcbeecaaadedadccabcaeeeceadbcbeeacbdbacbccbdceeabdbdccadcdcebbabbcdcaeacabdcabecbcebbbbedadecdadcabcedababdaaadbaaadedbddecbdebdcdeaadaebdcaabecddaecbeeceddbbaadababccdcabbbdbcbbedbcccbecaeedddcbdcabdbdaaedeacdbcdaecbceecabcccdbdacebdccebdbbcbccadbbcccbcdbaddcecebdccdebccdaadacbbebbadbcabadcbbddcaebabcdabbceddebeaadebecdedacceaaadeedaebedbdedccbaaecbdbdabbecdaaeecbcdaaacecaedcaebbaedcaaceecadeacaebbcbacbddeadeeedaddaccedbabcecceecddeaeebbaeabceadbbbbbeedcebbddeeabaeabacedbaeabcdeeabddadbbddacaedbcabccccddcdceddedebeedccebaecddcebcbbaeaaacaedeadebaaeeadbaabbcecadcbcccdeddaaaaeadaceabcbcacbdcbedabdabeadbeedbeddaacedaaacacdddbccacebcbbddcacbcbbeaaedebbcabebbbeaabdcaeddbcaebbeeedeaebcdbaaceddeeaceaebdcadeeedccdaceebbccebdaebbebaeddcedbbcbcdeecdedabccddbaebbdbaacabdabccaceecbadcecebebbadabdeadbaedaadecebacaeadbceeddcdbcadecbebdbbbbdeececedbcacbeddbdcbdeadebceacabdccceeebbeaecaebcdddadbdabedeacddbbeebbcadbcaeaadebbbbbceceaecdeacdbdebaecddccbcdecdbeeadacceaddbbbebdabbeecededdceddcacdeedadeebebadabbedaaaaccdbaedabdbdcdbcbaedeabdbcadaedaadedadddedcbbaaabecbceacabdcddaceacbeabddecccaddddbbecddaeaddecdcabbbabadcbbdcadeebcedddaabbddebbbeaccabcdebecdbaebbbdeaeccdbeebdedaccbabaaccdeeaecdabeeedddcebdacaecbcbdebccddaeaeaabeaadbedebbcdeacbcaaaebecaccaacbeacbaddaecccecaadbcebeccadbdadebcdbbdacabecaddaaaeecadaaccacaedceaecdbaecbbcbaadedbeaabadedcabdbbbabaeaaebedabeceebbedddeadacbcdbbddabbdadbacdcccacdebedcaeaabbcebaceabbaecbabcacddbaaceddecbeaabdaeeacbbabadbadaacaacdbecebaedeeedabdeccbaabeebcbeebdabceabecabdbeedaeecedbedbbeedeabdebaadccdaeeeeddceadccaabebcddeadbeeabbeecedcadebbbeaabadebdbdcbaeedcbdbcbebadcadbaeecbeecdcbceeddecdbbdabebacaecaeccccbedaadaebccbecececdceebccceabceacabbdbebaccdedbcdbacccdbadbcbdbceeccdbdbecbadeaeeabdbadaebcaeceadcdcedabeceaeeebcdeedeadceacbbcdaaddeccccdacccabdbdebddedededdaeecaadebdbceeaececdbdaebbedadddadcaceacadccedcabdabbcedcddaccaaddabaadecdcedabcbabddddeddcbedbacceadbdcccdddeeaeabacdaeabbcaaebbeadbbeabbaceddadaacadecdaceabdaebbbddddebbcbacdebdadcdebccdcaddeccbaadedbdbbdbdbaaebdddcaeacdecdeadacbcccecbbddaddcdcdabbbdcccdcadacbaedbecdcebdbbeecddeebdeaeeeddabeecdbabcaaacdaebedaebeadaaeccedaaddecabcebbaceaebeeacebeddaeceaadbaccbbcdbcbdddccdeeadeccdaaecddeaecbaeadbcecbdaccebebcbebaacddcabeddedeceeeecacdaaccdccdbdeecebaeabcccecccdbabaaadbeddceddeacccabdedccbcddeaedbaececddacdcacccabbbadbdeedaadcbadeeaadcbcebbcccddbdbacddeeddbddbcbeeacaebdbadeecdadbcedddcbdceadccadcacdadeacabcddbcbeedabcacbedebacdaeeeeaebaeedabedbaabedacdabccbbeeeaaadebdddacebccddadcdbecccbaedecebcddadcebcbbcbcdaeabcccddbbeeabdbaabbecaecdecdbecbbcbcdbdabbbeddabacdabcacbacacbecaaaecbeebcadecbeabcdbaddcedbdceeeeecbbebaaddbacdacabaccbddaadceecebaaeddaedbadbbbcdecdaaecacedacaebaeaeacacaeedcbaebacabeeaddabaeccbaeaacceaaaecacddcddcadcbeedbdaccececddebdbaeccccbdbdbecaebbacdecacdcbbebdadbcdeacdbeedaeabeaecadbbbeeeabcbeecceadcaeaabaaeebedaddeaabadaeebbedcbceddbedbbeecdeddcbbccbacdcddeaacccbeebbddeccdcbddcbaacecbeedeccbaacadedadcacedddeaadacbbbaacadeeeebebbeabedeadbeebbabaddcddbdbbdceeaeaeedacceecbaedaacbcddacdeaaceabdaeedbcbebdbbededcdbdbaeacbcedadadbcebaaedcacbdddabdbdedddccaadcadabedbddebbdadedcaceaeddebdddabcaceacdeecccceebaaddcebeeeaedcdeeccaaeecbaeddeadbddeeecaadbdedbcbdbddbaaeacaebcbddbecebdaaccdbcccaaabdaaeeeabdcdceecbdcbdcaeeeaddccdabbddaeebdedacddbceabbdadbaecdebbbcbceeabdedcaddceecdcbdebaacddadacaaaccebdacabbebaebccdceadaabcdcccaeeecbacbdadcddaeedbabbeecebbebbebdbddecebdbededcebdaccaaaeadacbbacedbeaebddaecdcddcddaeaecabaeaeaeaccecebaddbcebbaaccbbacccedccbaecdabacdeaedcaebdeacecaabdcaecddcabedacaeebdddbbcbcceebebceeeeceecedeacdcacbcddecbdeaebececebecccbbdadbcacedbbdecaddddbeedeebeaaceaedbeeabeacdeacccadcdaddeeeceaeeddebdddbbbedadbcaacdcbbebbccbaaebdbeeaaceededcedbbbadebedebadedbecdaabcacdadcaeebbaeceabcedacbaaceadcdccbdceeedcecaacebbacaedddeedcdbccabeabcccbbceeabeedecceaadcbeecbedebebecbccdbbabbedeabbddcbaadddddabedcdccabdceaecbdbebabdadddddadaedeaabaeebadcbbacabbaeeaeeacdcdacbaecbbcaeedddcabceddabaacbceaeddcacadcdebdcbebadedeacbeadaadcbacbadadedcbeecdcdaababbbebedddcabaaceabdcdbeeeaabcacbbbdddcbbbceceabeaddcebdebcaabadbcaababaebcbaaeabccdedaebacabadcdcdbddceecbccacecaabcaaaccaabceebebbbecedbaecbcdccdedddebecbbedabaedeccadaadeecabdececadccabbbbccadcaceaadaeddeebebdcdaccdbcdcbbebeabbbcaecbbadadbadebbebdddebeecdedbeeceddbcecbcbbcdcdedececcbedebdbcdacdecabbbeacbbeecdcddecbcccedcdaaabeeaedbaeaabebbbbeaacdceabebeabbbccdadabeadaaaddbedbaaabbdbdaebdadceddaacaebbacaecaedaadbddcadbabcdaaebeeebbbcadbcdbcdadeaecebbaeeadadccabdaddbbccdbbeeeebebecbaeadaabababaaccbcecaadaaccbcbdcbdcccedeaeeadbcdccabebddceeeabdcdaedccdadababbcbeabebdabedccedadbceccbbbedebecaeaccbdedccedecdbeaecbbebaaebaccdeaabceebecbabacdebdadedcaadacaaeedcaccbdaabcdbdeaadeaaadbccecaadeabeeacdeaaeacebeccacaddacabaecbaebccececebdcbcceaabedeecbdcaddececcaebbabcaaeeebdbadecebadecdabeeebadcbbcdededbecdeddbdcdaeaeadcbeadabadbeddebeddeecccedccacdeadbdbeaaabddeadadbaddcadecbdddbccecceadadbecaeedcadcbadddaedaadaaeabbdadaaaeaeaeeadacaaecdcacddbececaeacccebdebaddccacabddddbbacdcdcdbecdaaebbeadbbcadeebbdcebcdbabcdcebbacbadbbdeddedcddaedeaaabadedbdcacaeecddebcdcdcdabceddcdedbccaabdddaeeacabbeabedcecbeddaeeaeeccacaedbbccdcdbcedaaedecaabebbaaadeebadacddceabcdaccacdadcedacdaedcacaedaaacbeebabcbbbcbbdaaebddbecaacedadbebcbdcbddebcbaccdcddedaaccceabeecaddbdeadcababccccbdcababecdbedbbabebdaebabbcabacecddaeabcbdcabbeadceaabaeadeaebcdbbcebaaabecedbaaebbdbcaedddeedeaabecadedaeebbacbcecadbbcabaedeaceceeecccbbaeccabbccadabacdebecdccdabccebbabcccecaacbdceecbedccdbcaaebdbdcdcddbeadacebdbcdddabcdabcedabbaaececacdcbeeaeaabebddebdacacbbbacceededbbdcdacdcaddedadecacbedaecaaaaecabecbaabbeedbddeaddeceeeececdeeadadbdacdcddbeaadcbaedacabddccdeecacbddeaaebedcbcdbdbecbeddcbecbcecabababaccadbebcaeaddcbcddbaeeaaabcaacdedceacabaadcdadaaeeadbeddecbdbbacaacdcabbbbdccbbccbdedbacabaceecdbcaebbebecabebedbaaddaedcecbcebddcdebeccdebeadeeeccdceeeedaebeeabeacbccecaeacbebbecdbcbedeaecddadacbbdbdcccbaeddbcdabdcaeadaabdbabdbbcdbeadebccdcdbecabbaadddcececeaebccacecebcebbecbcdecaeddeaebdeaedbcecabceddaeaddbdeeaadeaebdecbcacccccedadbcdeccccbadedbaeccdccdbcbdeaadcecbdcbbcbddeacdaeddeeebaebbeeaaeebebeebbbbeceacbdebaecdacccecbebcdccdaabebdcdcdcdeaeaccaadbbcddbeeeeecbedabecbcccaccdebadbbddaabedddbbcdbcdcedecaeeacaeebbddbebecaaeedaadeecbceccbdaebccdbeaeedabaadaddbdaeebebbeeceaebadedaabcaabcabaeeeeadcaaedbecbcddaeecaeaecbacadcccdccbccdcdccaebadbebbcccdbbaecbbaeddadebaccccddbbdcdeecbbdebcabadbbeeaacdbbeebbbbdbbacbccbbdadeddabcdcbbccceebdebeaddeabedaabaaeaebaeebbacbbabbbabdcbdecaceaadccaaadabbdebbceebdecedddaceabedecabdcbaccaedaaebddacebaeabbdcecdbcaccebedadccdcbcaeedacdaceecacccaadeecaaaceeedecddebaabbeebacabaeeeabdebebdcbcdeecbecddeabadaaaabbcccabeecabedbcadddaaeeacbeecbcbcaeeeabbdabaaadeeccdccacdccedebceaaabecabdebddedccdecdecccbacdcdbdabbccebacaaadbeaadaaeebccbcdeecebcdeebbababdbdeddebeddcdabcbcbebdbebbdbdeacbcbbcceedcdacdbacdabeebbbaabddadbaecedbcbebdcbedadcaaccbeaaceddaabbedeebbbeadcedcceeedcceccdeaceabcaceecdbaaedaaeadcaaebdcbdbdccedebdddddeebbdbeedbadadeccbccaeaeecceabdeebaceaeaddcedeebdcbbeeddebdeadcbaadabecbccccacaecbedbeddbdadddaaeabaeacdaeadabeeececcbbbbdddccceecaaaaedcaacddceeaadedabaaecababeabcdccadabebccddcdddadaadeecadcacddecdbcbbbeabbebeaaabeacacdaaaaaeadcbebdecccdcdacdbdcbbebdaddcaeedcddebdaacdeabacbaddbecbbdedeadabeeadddacdbdebccacbdcdaadeadddedecddcbbecaabacbedecdeedaaeedcdaaccaaeeadcebdbcaeaedcaaaddabeedddcabdaccaadbadcbdbeebddabbabadbebbadebeacdaaaebeacdbcecaacaaaacdbbebcccaeeebcbadbdaadcdbebbddaeeddedebcbcdbeaabcacebbebdcebdbacacaabccebbbbbcddbdddebbecdacabadddceaeedcbecabedbdaacdbdabeecceabcebbbbdaccecdcaccbdcceacbeceaacdeeabacaddcbeeebedeeebdccceaababcdddebcaacecddeacccddebeaabdbbdadecaaceeebacaeaaabbbaabaaaeeaebadcaceeebddcadeaeecaaddbcccdceadacbccabadedcccbacaeccaeadbcacaebaaedecddcccadaceadaebecedaaebeeeaedeeacaeebcbdcdabdcabdadcabccbbddebaacbebeeeeaceccbacddedebbbdbadbbdbddeabbabdecbaacceedbcdadacceddedddcdceacaeedbeecedcaadebbddcbdddabaabbdbaccddacbdabeeeacaadbbecaddbdddcdeacdeecadcadcbdbbbabeaedaccbabdabdbdabddcaaacccbacdbaadccdabbedcabdecababcbaddcdcbacccbcbecccdccbabcabbcebebdaeeadacdbcbccbdddcbbbdceaadcdddbacedceebdaadabdacddedeaaecdbbbdaaecaaacbabcbabaeecbbbcdeececbdacbbbcbccebcbbeabeeacdecdabdbdcaaeedcceaebddbcbbcadbcabbaecdcaadecbabdaaddecebeaaacaebcaedbedccbdcdbddaaccdaceccebcabbebaeadabbbbaaadcbbdcebecebbccdebeeaeebceecdabeaccaaeaddbbaeeaaebeaaaacaaeabcbaadacbbddddadebcecedeaeebacacabeecaacbdccaeccacaabcebeabdadaeababcacdcbebeebabebebbabeacabaaabddddebbeeedbadaceebacbdadedcdddabaebeacbbdbdeebedadecabdbcbaeedcedbddbedacbbacdddedeebaebbcdeecdeebdadaeeaccaaebdaddebeaabebdadaaceacdddeacecaadedecdcacdaebeaddcbbebeeeadeecadbdbbcbddaaabbebdcdcddacabceaebabbadacebcbbcbeedaeaeacbeccbbccaddaeeaaceacbaddaeabdaaaaddccabcadeeaebcceaaecdbabebebbdaeeccbadaedebecbabeceeaebeebcccedcecdbacadceaedddccbabdeaccabcacdacadcbbebebdbbecbaebaebeedcadbdaaeadeedebcebdedaecaabdacdbaaaeaecbacdecbbadabcddecabebbbabddacaacbeabaeacdaaedbccedeaacdbdaaceccebdceeceecabddbcaeaeccabcdebcbadabcddceebbcaceccedabdbecbbededaabcbceaebbdaedeceddbcedaedcddcdeaceddabaaeeaeacbeacebdccecabcccaecddaddceccaaebeeddacaddebaacebdaabcabbeaecbcdeacdcbacaaadbddddcbdbbadbaaabeeebbedabacebdaaabdedaaeedcaecddeeebccceaceeaceabecbabbaaaeabdaaabcaedddeeacecdeccacebecccaddbdadecaabadccedbebdbbbeeeadecacbcbeabdccabaecabaacbdaeeeaabdbbcbabecbcbcecdaddebebaeaeecbedaccceaddcdbdacaabbebaeadabdadeeaaaccecaaecccabaeeedcabcaedcceaeacbcebaddcbdeddacdacccbdbbabceadabeeedbbecebaccbacdedbbdcdcaedacaeedbbeaaccdcebcdaaadcabbeabacdacbdaaebedbdacedaecaeecdebcdebdeaedbedebeccddecdbedebdccdeeacdedbdaddcdccdaadeeacbdacdcaaeccadaebcbeebaacaebbaaaeecaadeaebabaedbaedbeeacdaedbceddbcabeebceacddcaaaebaaedebeebcdbdbcebceecaccdaaaacbbdbcecbdcbcabcdcacabcabeaecccaaececabeabcdaaaabdcbcaeaecdadeebabdcccbdddacacddbceedbededddcdbbaacacdabddddbccccbabbbcaebccabebeeeaaededcaeaccaaddacaedcecbbdbdbddeebdaddbcbcacbdddaecaeccabaedcbccabeacceeebaddbdbdcdbdebdeddbdcdaaceeebbcdcebabccbcddacdadbcebaccaadcdcacccdbdcbbbabecaeacbaaeddbdebcabecccdcdedcccacaceabbaeccabbdcdedcebbaebdbcdbaccdbaadcbeeeedcaaddebbadbcdceecddccbeceabbabececbdaccddcdccbeacdaaeeaeabdcaeebaaecdacedeeaccbdaadbbcccddadcbcceaaddebddbbaaccabcbbecbddbccacebddeecabbbdecacddadddbdbdecdaddedabcbdbedacecacdeabaccebaabceeaecdeadbeaeabebccdecaedeaeeecebeeaebdbcdedaaeaecdeacceecebdddcddbabebbceeccaabacaebdbdceaacdabcbbeebdecaeebadddbaaceabdcaedaaeaacaacecbbcbaeeeceaeceacaeceaaecbbdeebccdeeecaacdaedaddbabbdccddcbaababaaeccddacdceaeedaaeaceededabadbdbbdcdbbccdadacedeaebbcceaedbcdcabeeccdbcbeccedcaaaceccadadbecdceacdcccbeabedaeecdcabaabddbabadcddcaccbeaddaccdbadbaeddbcdcbedaabbeebeacbeadbebcdabeabececddaeadcbdabdcecaeaebbeadecbddbdebedbccdeeebebaaebccbbcbcadeeacecbedebcdebbbadcdedbabdebadeedcaaaedeadaaebaabebeebdebdbaebaeaeecdbbeaedeadacccdeabecccddbbdeddbedbccecdcbdceeccbaabacdabebdbbcccaadaadcdbbcbddddcbbdacacbaeccaccceabedbddcdbcbecedaadbbadbcebbdbedbecebceccacababcbedccdbeecccebccbcdbecbacacededbeadaeabccccecbdaabbbaecbeabcaeddaadaceeaeacddbdbcbbabbbabdabcadecaeeadbebabaabebbceeaabbdacbebcdebbbbddbeacbadbaabdccceaddeeebdcacbeeceeaeeaaeececeebcdccbccdebebbabadadcbcdeebdcbebaeaadcbcbecbebcdeadbedcbcdadceebdacbeadccbcdccbebaddebcabceadbbcccdebbcdbebbbaceddabcceeecaddbbdddabebeeeacccdbbabeaaddbeaceecdcbbbcededbaadbbcceacedbaedcaedcaebdbceeacaaebdaddcaaaccadeccbdebeaccabacdccaeeaabbddbeebbbabadedaabccdceeccbbbddccbbccbdacbebdbabbcdeddacedadcabbeebaababacbaacbabbccbaecceadacecbbcdeddabdeaddeacddbaaabcbcebbeeacbbdaedeceeebeadebcdccbabeecaaccbbebedaaadecedebddceecacadbcbecabdbadccdddcacaebbceedcaccbecdabedbaabdcaabbeecdccebcdbeeeccbcbebcbcedbdbceebabbdbdbeadecebbbaedcceedbabacdbeaadddbcdaececeadaecdaacacaddbedeecbcbcccaeccbebbeacaebaaaecdbcedcccadabaabbcddbecceadabdcaacdcdcbdedcebaaeddedcddecccbeaeeececabbcadccaaacdaceebdeedbadcaabaedaaacdeddbaaebcccbabdabbacbdddeceddcacaccdcbcaedbacacddeabeecaadaceecadedbbbaceaeadeabbcbcdeaedbbaacdebdadebaceabceedabdceadbdadbebbcecccebeabcecbecbbdadeabecdadedbebbddbccdcbdbaabbcebbaadacaacbbabdecbcebdacaaecaecadaddecccddadebedecedbadabddbaceebeaadcbbddeeaacdccbceaeaedcecbbbaebddbcacdceeeaacdecaeecaddbdbdacccbcdaddeaaacaeecaaecdbaeeecdbbbdbecadbdeddcbeeebdabdccaebcebbaadaaeceabbaeebdcceddcadddecbbdceedccbdcedaaccebcddccedcacbeaaabecdcacdcbcaedeeeaadedadbdecbeecbacecbabeeedcdadacaaedbaaadddeceeeeeadacbaabccebacbcaaadabeadbabdaccadcedaccdedacebbbacaaaeecedcbebdadcbcabbaacddebdabeedaeeceddabeecbdeabeedaacdacccaddeceaadebcacbacddbbaccdceacbcaeeeecdedddabadeeeeaadcbcdecdeaecdeaaaaeceaecabbabebbccaeccabdcbeabaaebabacdadbbeeebbccdaceaaecbcaacadbaadbebaebeaacdbaacbecaebceccdaecddbcecebebbaeaecbaabbecebdcbbadaeabadeccbaaaebbedacbbaabdcbaaecacdeeebdbadacdaaebeadabbcaccbecadeddddddedbbbceedbddbaededbbdcbecbacdcababbbddddeebedebcbbdcdbacaebbcddbdcbcbdaceaeebcdeaaceaeacbbbaeaceecceeeaccaeacecbbabecdeedaeaabbacbccbddbdecccdadedbeaecaacbdacacdacabbabcdbbbbbaebaadecbcebbbebcedcbbcbddaacbcbcddcbabcbbdccdaeebadedbaadaadedaaddabeedacbaadeaeaeaebdeadacbcaeaabccbecdbbdcceeabcddbeceeddddcebdbbcaabbbabbbdaabdaadedcbadbdbabacdcddebdeadbcebdaadebecdbeedacdbedcaeddceaacceaacccacdcaccbbccccebeeacbddcbecbdccbedbeeadeeeacdeedbcddcadbcabaeeeceaadaededaadaeceedebbecaecaebeaeddaecaeceeeaabddcbaddebaaddeeebeeeaeadceeccaccedceacbaccceddeecaaedcaabbadedbbebcdecbbaadedbdccdcdcbceedadddabdabdcbceaebeeacddcdccdcebeeecbdaeeaecadbdeebeeeecbbccadbaecbddcaeeebdeaacbcbdeddeacecdebecaaccebdddddcdaebededbccdbcedbabdacadaccbbccebdaaedddacadcbbccbcceddcaebaabdeadaeeacabedaeabeddcedcedeeaeabaccaeaacbadeebbbcbdbbdedaddaaaedecaeacbbabcbccbcddbcecabcdacebaabbeadcbdebedbabdbaccbcaaeacaaabddebbbeddcebdabdabeaabadbdaedbdcaabcaccddaecddcadcbabcdbabecedeabdeeacaedacbeacadabbdcbebcbadaaabcddeaeceecddcbdeedeaadbaeaebbcdaaeeaeccadadecebddceaebabcadcdddbdeedabdccbadcbdbbdcbddcddadaaaacadcaacadaeededdecedcbbdecaedeacaecaeceeebabdddbedccdeccadccadacecaaaadcacbbaaccdddcacddcabebbdcadcdcbbcaaebcadcdbecddeecebdacaccbebccbaadadcccaaadebbcccedacaeedcceeabdaebabdedaebaabeccaedcbaeeecaaeabaaeddbaddeaeeaedaadcbecabaadecddeadbadceecccbddbbcecdbbddccddbaccccdcccdabdcbbabdecbddaddeeaaccbdebcbadccebdecebcacbcbbadedeaecbcdccedaeebaeddddbcedadacceaeaebbdaeceebacaabadbcddcbcbaaeeaadddbaacaabddcdedeecdecbdeeaecbdcceaadabbbdecdbdbcdbecbedacbdeacacaeabbacbbdccbabacbdaedbadeedeecbbceaaacccbdabcddaccadecebcbccdbccbaebcadbdeceabdadaddcebcbceeaccaeebdddeeaddeabaeaaadecbeaaacaabababbbaeceddaebdaedcaeebbbbedacdadceedeadceebeccecbcacbbcabdaacadaecbedacdbcdecceedcdeadbabebeebbbabdebceeabdebebbeddbbaedcbaadcecdeaebdedabdeaebeebaaaceadaccbdeecacaecabadbddeabaacccbeeabeccedebbbeccdccbbcaeeebcecbcacedcdbcaedabaedbacecbbacbaeadddaaaadbdcedeabeaeacadbcdbbaddeddaacabcddecdceebbbdcacddddcedeebaecebbaeeeeeaeddebdbaebdddadcdcbccbeddaddbaeaaddaacbaceddccbeccadbeeebaceeaaaeeaaeaebedbecbcbdaabeeccadeecbdcaeadaceaedbdabacbddebddeedaedcedbcedcbbcdddcccceeaddbcbbabcbeabdcbccabbaccccebacddabcadedabcbcdddcadaeabebbcababcacbcbdbaadeaecebacdaddcbdcebdbcdadcaddbccdddaabeaacbadedadcbeeabdbceadbbeaadeddaebbadabeeebbaacedddaebdaaebdeceaaadebeedbbecaacaadbaddebaedeedecddbeedadaadcaccaabcccdbabbdaeecddabbddedecdcedeccbbebbebaddabccedaceedeccabddcadcabeabdcbdbcbdbbbccaebacbcecccecbabccbdaabaeedddbebbadddabaacabbccdaadeedecbdaeadbaabbceebddcebceddbdacdcdadadbbcdebedbcaddcebedcadebabeaebeeeaaebcedeaaeabbebcdbbcaddcdedeacccedeedccdaeebcadaeedaccaacaaabeeaccaaeeeaccabecedbebeceabaccaaaacebcbaddaaceddcacdeaabccaaaebacebddbeaabceebcaccdecddedaadeaebbcbcdbaedebaedacceeecedbdeaaababecbceaeadcabaabbceeebdbeabbdcbebeecbceddccbaacdddcedcaceeccbbbeeccabadceebdaadebcadebaeebdeddedeceddaeddeededdeddeeecabaedbcadcceeaadcceeddeecacebddadaddcedeebebdecebcdbecdcbeddeedebdeaccdcddabdaecebbcbddeaeeccadbbbbcebdcceaaaaececdaeabebaaaaaedbbcbeeedbabaebeacbbbcaacdcbaadacdcdbebeaddcabdeddeaacbccdbbbcaacbccceeedbcdbbcdbebeaccbecaaaebedacbeaaeebcbbbacabaaebbbabeaeaecadceedacbadcdceccebccbeeadcbbabaadddebbaecceebbdddeeadcaecceeaebbaabadedcaeabcccbeccccaaeeadebdcdaaadeaedabdcdedabbaeecddedbcdebbcdbcdbccbaabbedcebebdacdebcddcabbbabaacdecacebcddddeebddaeededddaaaccabbbeedcbbdccdeebcaaaaadcdbbeaccaedacebbcbeebbbdbdcdcbeadbcabccbdeceebbceaeeabbdcbaeeebeaadbcbaaedeaecbceddaadaeabaebdabebcaeedbbebeeadbdbbbbccbbdedbaeeececceabeababdabccedcdeaeecaddeaeaebaabaadcabbaeeeddbebddacbdbbdebbdbadcecbacebbdceecadaeedebdeebcecdcedbecbddabccbedeeaddbbcaedbbeacaaddebcbbbeceecdbdaedeebbcccbbcbaaacbdadadcaaeeadabceecdddeaeeeacbeaceebaeabbaedcccaccaeaaadddbecceeaedecebceaeccabcbdebacddacbdbabcaebadbedaebbeddeeceeeedecacaceebdcbcdcbaedccbdadeeacbebbebaeeaabeecaebbadbeabdeeedbdcaebddbacbabbdabddcecaadabbdcedbabbebcdbebbabdcbbdeadaeaacddbbcdbcdadcaaacbcadbedbcdeeaaaaadadebececbaecabaeeaedccdcddddbcbdecbccdededdcdadcadcbbbaeeeecbabaeadccacbeeecaecbeeeecdebabadcccebbbcabdbeeaadaaeaeaaabacadeeaaabddebecbaecaeecbbceadeecdbceddeaebbeebcbdebaacdaabecaccdbdeaaecbcddecedebdacdaabdccedeeeacaaaabaabbbceeccdbbdbebbbecabcaecedecececdbaccbeadbbebebdabcebcecdcaceaabeebddcebeaaeacadebccaaedababccaeaddeeabbadbedaccbedbebabadcebbeaaacbeecbaaddacbeccbccecddcccdbaaacdaaedcedbdeecdbbccaedcedacacdddabddcebbadbbabbeabecbddbbbacbebaedeccecddaacdadecdcaaceedcaaedeabddebdaeabcbbedbeeeaabdcdddeacbcdceacccecdcceccedeeeaaaaeecbbdeeaedcbebcbaebbecbbadaaaacbcbdecebdeeecdaeeabbbdcebbccdbcccddbdbcdcecaddecdecebaddcabaeccabedbaddcdcdbebebcbbaaeadeccdebceebdaccebdacababdaeaadcbaeaeaebebcbcdcdcebbacaaadbdadbedebabcceccbcacebbabebcacbbedaaacbccdbdbabaebbebbbaebbeeacdcdecbdadadccddbecbaedadebbdbdabdcddaeaedbeedebedeccccabedbdbbeecceeeebcedccedcdeacaecdcbcecdbdbcaedabababdebaeddeadacddedbbcbbbaacbedeebdedbbddaddbedbecbacdebcabddabcadebedbccccaadacddcaadcdabdacadeaecdadaabeaeeceddbdcadbceacebeaacdedbbeeaecdecdcadabdcabacceeaaeddeedbccebddeeaaccdbdeddecbddddaceceecaaddcbaeaaaebebcaecbdabacaaddbddeaedaedadbdeeacdececcbebdebcecabaeecaadcddbbecddaceaadcedbcaadaeaeccebcadebeedbaeabcbcacdadbdbcaddbaecbeddcbeaeecaadebeceeedcdeebedaadacaebddbadbadadaaaeaccecbdbaeabbdcbdcadcddababdbbdbcdaebedcbebaebbeadcdeaebecaacaedacbedadacaeabacdccdaabaedccabebeadbbacedecedbaabbcedeeaeabcaadeccbddcdbddecedbbebbdbebdbcabaacddedebecbbdabcaeeceeecebeeeedacacbeeeebdbdddadacdeacadcaeceedecdcceaadaddeaabbbeebbaebaaaabbbceadcabbaeddecaaaebdeebddaaeddecebaabeebbabeaacadaeecbeceaccebededbcbdeccaaaeddebadeebbceeaceecbbceaccbabbccbabaaabebeecdbebbcdabaecaccceabaaedebabccdcbabddbdcedcaedabadeddddaeebdbcdcddebdeccedcceccadaacedacddeedcabbbdbbeaaacedccdaecabccbbaeedcccdecddbcddeceaeeaaceacedacacebccedbeaccbcdecbeedadbebbaecbbcddbadaaedaebbeccbeddadcdddcebcaeededceebbccaeaeaedabdeebcbcddcbcdcdededebbbbdebdddaddbebcaacbeebbcccdadaaeeaedabceaddeceaadeacbaedbdbbccceaeebecbeecebbcdceaaabbecdabaaccdaadbebeedbcebaadcbceadaaccaaadcbeedcacdbeaccecabaacbeacaabbedabddceceeabcbbadabbcbabaabbbddccceedddcabcbaeeadbaabaaabbbdeceabadecbaedcebaaadecbdbddeadcadaadabcdcdbeedcdbcecabaecededdddaeddbabcdabcbbebbcbecbaceaddeeedaeccdcbbeccbadcaddccbdbdccbecdabcaadeceedcbcdeaabccaaacdbaaeaeddcbaebcbbdcacecacacdacabcbbcadebebddedadaaedbedccececeeaeedaebbdddebacbcbbccabebedaadbaeaeeeadacbcddeaadadcaacdabbddcaceeebedaeaacbebaeebcaddebeeadeaadbddedbacddedbaaacddaeebbbaceebeaccdcadacadedcdbeccedbcacdecaecdeacccbedeaadbecdacabdbecbaceedcaeabdedbbaaebeeceddcdcbcadccbeddcddbcbaadcbdbdaedbcaeccddaecaceddcdcccecdcbeebbebbaebbdebbedaabeeadcaebeabeeddbbacdcbbacceaadabdacacbdebbdccbadedbdddaeadddaedccbbcdcbccbaeeeecddcdacdccdbdbbbbcbdaaeabadeabdabaabbbebaaacbbabdaccceedebaccedeebcaadeaaccdbdccebaeaaacdbeeaeecbccaaedeecdeeecbdadadeadccaadccedecceaaeeeaadcdaedabdccdcbaaaaecaaedbebdcdbccbdabdebceeaebcaecbbadedddeadbacaaeeedcadcdadabbccccaeabadeaacbecaeecedeedbaabebcbcdaedbedcacabecbeccedbeebceeaedcbbceaaaeaaeeebcebecabbcbeaacaddcbedeeacccdcebabcacabaabdcaedbebbcabaaaecbaadcbbccbeecebedadebaeaedaceadaededbceebbddedeabeadaddaeacebdaceaeaddbbaedeaeddcabbcaccdcebecbebeaeeaaeccbaedadebccddbabbebeebbeaadeaebbbeceecebaecadadbcdedbeecebdbaaabacaddbcabbeadcacaecccabccdbadeadbcbadaddabcdeadaddadcaebeabccabcddaabddeceebdebadebdceebeecdccaeedbddbabaebeccaabacbecdbeaeaccbedddaeaeacbedacbadeaeebdbbeabbaebddeddbcdbbeaecebcabdccbeaeebdeedecccaecebcdddcdeaaecaadebaadeebabcdabdbceaaaaccdddedbdeeeeebccaabdedecaeedcccaaaeaacdebcdacbcadcacbdbdccbeedaecdebeeccaeaeaedbbaeecdebabcbacdcebacdcacbcabcecbbbbabebaebcbaaedeadbecaeceededdcddacaedcbadceaeceecbcedcddbecacbecdaddeebabcceeadaaecbdcbbbaeadebbbcaeceeabdbdacbebaecdbdeccaebdbbcecccceeecbccabbcaecedeebcbaeaebbebbcbccdeadeadaabbdddceebdeddacceaedddceadaadaeedeccdaabaeecbdccabbebaecedccdecabbeedaaeacceaeecacacedcadccaabadcaeaedcaecabceecaddccedcdcebdcbcbacddbcdbadcadbdaedacebcacabdacecceedceeaecbbaedbecedcaabcadbbcbcaccecbacddbabeeebecbcacadbeccdaddcecaddaacbdedadedceaacbbcebcbaeeaaadbecbcadeeccebcabeebaacecceabdbcceabaadccaacadbedcaaeceeccbcbceddeaddbeaccbebbbbaeabaaebccdcbdaeddbdbddbbdebaebabbbadaedbaeadccacacdcebddbcbccccacecacacdecdceebdcddaeeeabeecdbebbdedaeccddbabccbebceadbaceccdeeddceacbabbbddbccbddaadccdcbcbedabcaaceebeeeeabdeebaebaccabdecadcecaceeccebeadeddadeaaeacaaebbadadaeabaaecdededcbdaeddddedebdcdaeaeceebdddabcccadbeacaedacdcdbeccbdacbacccdccadaadbdddebcbcebededabcbceabcccaeaaaeabbcaabecebeccececdeeacaececaaaeddcbbeccebbeeebebbcbbdebbdeaaeecdcdcacadcaacdcadeaaaeedabbccdebdabecbaedcadcbdadabbdaacacbccebeddcddaabecacdcdcbececbeeceaaeeedccedeccdadccecedbccaedaadcabbbaaceacaddaecddecdceadbceebddceccbbaadccdebeecacaceadddcbbacacdcebeabdccceecbacbadaadedcbaabceeddcdbcdacddebbaeeccadccacaebeaadaebbabdeeaeaacdbddbadbaabdedbaadbeebeddbceebeaaeebdabaedcccbabdacceeecababdaadedaeeadaccaebaaeabdebdbabcaabedbaacedeceaaadbbcdbdebeadcceebdebcbecabebcebeaeecdecaaeabccebbacddeceebdadabeaddbadedbaaddbebabeabaacbcbadbecadadbeeeacbdeedcbaccbbebcddebbacadbeaecbeaceadbedaaccedeedcbdcbbdadbebccaaeedecbabceceecebbebdaadaedbbdbbadedbabddebebacaaabccdbccbcccbeacebdacaecbbacdcedbdcdeababcbdbceeedabdbbddeacebaabbedacdecacebdeccabcbedbaeebbbaabacbadadeeadaeeabcddadeccdcdaccdededaadedceacdaebaddbbdcbacbecedeaabccaaaedabeaaecddccdaeaaaacdeceaebacbacddceaeebaecbeecebbbeebdaceddbcbbbbaabccececbddeacadeaeaceebcadeecbaeebbdcbbbbabcaedcabeacbbbebeebeaaecbddeccbbdbbbdebdaceabadaabbcaecdcebbeebaddadcadbbcebcbbbdbbeaebbabbacaddecbeedcaaddabbbeeecbbdbdacacecbaabebecbddddaabdcabbecdbdcbacbbdadbcbcceeccdbeeeeaaddadaeebcddeddcabddcbdcccbcecaeddabebbcaccdbddcdebebdcbebdcbbdaedceaeebddbadacdbedddcabeccbcecdccdbcbbecaecaaaecdcbbdaabecbaeebcedbebaddcdaadeddcbddbdacedcabadcdebccddbabacbeebeecdbbbcebeddbddcbbeddaebedadddebeddbbecabedddadeedecabcacaeddbbddbadddddaaedbbaedabaceaebdeeeeebbabeadabbbbeeeaebeececbadabdecebbddbabaaccecbbcddabdacebcececcaddddedbebabeeedeeaaaaabcdcceecaebaecdedacdcebccedaacccaacbdebaebaaebadabadccdeaceaebaccdcbbebdccbebdeaddaabcdaececdacadbedebaaeccdcbdbbadcdebecccadeacdaeaaabaceeaecacebebdedabecabeebecdbbceebcdedddcadceeddbbedaeeecbbedcaedeccecabcceceebcbceccbdaccbdedeacaeeadacbbcbccbadabaaaceccbbdddccacdeaeeaeaeaacdcdabeabcbbcdacabadbdaadbdddcbaebdaddadbdbdbedcbaadadaeccccccdceeecadedabddedbdcccdbcaaabecbededcddbacdbdbdabcebacbbaadddccededcdbeaaeddbcbcdabdbabbabceacadeaecdcbdeeddbadedebdabbeeacccbdcbacdcbacdeaedcadbcbeddcdceabbdbabddbececacebededbeddeccccebeaacdddbeadaceaeccdadbbbecaedebddeaaacbaebbcbbddadcbcbccdccbbaeabacdecdeccdeeedaeedcdbbaacaaeeceecbedbbadbabeecbacdebbdbcbbdabeadbabadcededecbebaebedcddceebccacddacdabcceaeeeedaceeddccdecdacadbddccddadeeaceedbadebddcaebcdeaaaadebbdddadccadcdcacaecbcceaeaecdcdeaadaeebdaebddceadaacaadcaadcaadccedecadaacaacaeabbaebedbddbdbbbabcacbcdcdecedaeaadbceadcddedebeadeaeadddaacebdaecbbceaaeabdacedcdacedbebcceaaddcacadddcadcadcbeceebcbadbdcaccadbbcebeddbeadeddeccddbcedcdadabaeaccdedededdedcbdbbbdaeddeedeabceecdaeebebebaeaebddaccabdedacdaeeaeccbdaddaabcadbcceceddebeededbdbbdaedcbcacaeadbceeabbecdbdceddeebcbaaabecdccabeddddcdebebcbdeeddbdcabdbdacdccebaadeccbcdaaacaddbecdeceadcaddeaaeadaaabebcdbcdbccdbdcaceeddbaaababeadcaeeddaadeedebdeacaaedaabbeecddcbccbbececdadadecccbadddbaaddcbabaeeeddbaeedcaecccdceebdeceaaaacbccbdbdbbebaadcacdceabdaeeababadbaeceebcacccdacdaabdcedeacaecbdbbaacbeebcbccabccdceccebceaebbeccabcccedacebadcadbbeaebeeaecdabdceaaeeaeababadccabacdbcccecddddadaceccebeaaceadbeaacaccbcbdceaeecbdcddaccdedbebccbceecddabedaddecebbbeccbedecacceaaebbeebecdddebcbecbecbdbcacaeebabddddcdcbeddebededecaeeebdabceadcbeacbadadedceccbcdaebeecdeaebbddecedbddaaabdcbbbbedcdcbcaacdbacaebbccaebaeebbabdcceedbcaeddeeaaedabdceaaabacedcbadccbeeecdcabdacbcebbedcceecbeacbcdbcabacbddacceacdcddddddbcbebabcbbdaaaebadbbcabaaddebebbeccbcddcbbabdbdabdaecbaabebebdbaedacccdcbaaebaeceecaaacedaccbdccedbdbdeaebbcebcaebaccdeecbbceeadecebebddadeaaeabeacedbcebeccdbbabdcbeeeabaeebaecabecccdbebdbdeacceedebecbabcbcacebbbdaebdbcbbdcbdbddebddebacbddcabbceabdaeddbdaaedaaaccbcccabdecacbacecedcedecdbcdaccabbddaaeebdbeaecdbedbecedbadebaadebeacdcbcacadabeeaccadebdaabdccbccbedabcbdddcbacbaceabaccaeedeaeaadbdabbeabdccbecececcaeaddbbdacecdbdceacadadadcccabdbbebecececbaddbeacceccdebbbeadaddeeacddadcaaecbbccdebeddccdbacebeaceddbeacaeedadbdacdceebabeeeceaabcecebccbdebdcbbddcddaecaacadacedeebeacdbaecbbecaeceeebcbebdebeddbbaaaaabcadeedaebdccbeceaeccbceabebccdeceebaebaecbcddcbaaddaebedadcabecdaebaabddadcdabcbddeebcecceeabadbddbbaddcdccaaaacaaacedcacdbeddbedaaedbadbaaceabbdaacbdcababcecacadbdebddbdaabdcadebebacbddeeebeabdccdacaececdbacaceaececbdddbbedabdbdbabbaabcaacdebccbceabaebaeecdbdccebbacbecbaacbebccdebedcdeaedccbaaaddceebeeceaababbeaeeabadeebccecdeacecceeeccabedaaaeabcecddeaaecedcabdeaaeacecccabbcaaeeaebeeebebeadacceceaebccaededbaaeebabcddbdacdceaacedbadbddaabbccbdadcccacbdbabdeabaaceeabcbbbeaccdbccbcbbdcaaaaceadbcacdaaaedbcdcebcedcbaeacbaccbbbdbbbddcbddadcdbdeeeddaeaaaeeeeebcddbebebcdecccababddaaebbdcedecaddebaeddaedbdadddadbdbebabcecdcacccdeeccedebabecdbaebbdaaabadadbedeebacbbeccaaaabadbbcbcacdabaabbeaaabcaaaecbcadaedeceebecaeebebadcbdbacabceabddbcbcbdcbadbaeddebdebbdedcdcbddbdcddcbdbbccdecedcbecacabadbbebbacaeeeeccaadbdbdcacbdcddeedbebddeaeacbbecdcebbdebaeccdbeaeeaebededeaaddbbedeaddddadeeabdaecdaadbedccdacdcbcbcbcbeebeaedceaacbecaeeabcbbeaccddaeeddebdcabccdadadbdecdddecdeebddeadccdedeeccdbcceddbddeebbedbecbeecabaaedcdbecdaacadcaeaacbcedcdddbadcbdeadcbabdcdeaebacccbcdbceddcdcceeeeaaeebbdbadcaccddaeddadbebbacabaebbebcadccabebbbdeccddeacacacbdceeccebdccdecdcbdcacacaececcdecdcacbcbcbdbcbedcbaacaaeacdcecbdbeebcebbabdbcbceeecdbccebecbdcabecddeacadeedccaadbeaceaacaeeecaabaabaddcecdcecadcccddddbbdbaabdcaaeaadcebaabcdecccceeaaacbedccbbabcdcaadccdaadabbdbbabcbaeadadeeedaceecbeeaabdddeaeabaebeeadbadceaedcbbeeccdcdabbeeadcaaadecddbedaeadcbbedcdbcadbbecdbddcccaedcdebdcbeeebeabedebebaeaaacdbcecabeceecbecaddcbabdcecdcddcbcacabdaaeacceeddbdeecdaaddeeaebebdabbececebdbedaccacbecbdcecbddeaacebbcaceebcaeeeeaaccbdbeeaeaeadaedaabdacdbaeddbbccddcecbebdddbdbebddeadceacdeaadabcecdcddadbbbeebadeeeccaebbeddcbbccdbeacbaaedcbdaacedacbadeceecdaebaaabeedeaccadaedaccadeaedbebcebbaaadddecedbcaaeabdcabcccaeecacdbecdbcedbcbccbdaaeaedebdbbbcedaeeaeedabbecdcbbdebceebeaabdabceebdeebecdeacecabaeebebacbddebbbebcabaddadeccebbacecdcbeccdabdeceeeabeebedbddccedbecbaccecabeddcbecdeaeacebaaddabbdbceaddacaaceeaddcbdbeaceeddcdbceecdbabbadabbaaabbbccabcbeddadeabeeccbdcbdaaaececbbdaebcdedabeabadaeebaaaaeaabaddacddaccaeacccdabadcabddedaccddccecbedeceeebddedeaddcdeaaeacdabebacacadedaccbbdaabecddaeebabdbbdddabcddadbbcecedecabdabadeaabbdbdbaceddecdcebedcbdabbccceccccbadcaedbdcbdcebdeadbdcdcecebaccdcdccebcedeaedeeeaabbdedcaeeddcacbeaedaecbebccecdaadbddbdbeeceecabadbeabcebeabbaceedeebedbcbedcadcacaccccbaabaeaeccebceccedceecbabeccaaaeabdeaddbacbaaaddbcdbaadbaabbcadacdcbaadcccbbecbcbcedbaadadbbbbebbbcaebbeaebeeabdccdacdacebbeeabccedbdcdeaaebbcddececebcacecccbdecdbdbbdeeedaababadadadcbadebcdeacabaaecdeebdabedaaeaedaeccbbaebddabcbecebceaecdeccabeedbddeaabbaeeebabeebcbeacbeeeaecbbcbdcbdeeddcdeceacbedcaabbddedecdcccacbbaddeabecbaaebababbbedbddbdeedddbebdcacbdecebebeaceebacaadcdcdabbdbaedcddbcbecccebaeecdeecddebccebebdbaeeebdbeccebabccdadaecccccecbdacaddcbbaecaaeddeddbabcddaecadcceddcaaeabdadddbaaccaacacedbecaecbecddbebbabdbdbaebdeeebbdbaecbdacaceedaeabddacebccbcddabceadddeebcaecebabeeebcacdccbbaddbaadbaedabadbbbaeccdbabdceeacacddeecacdeddeeccedaaeccbcceddadecdeaeacdeaaabdecbcaeadacdecbdcabdddebcacbbbcaeaaacacdabedceabbbcaeaccabedcdccbebaacadbbbebbccebdcdadeddbdabdebbbadebbaaaacbcdedebbacdeebecbaceaaeeadaccdeadebbddddeaccaeeccdddbdcadbebdabebdbaedbdbadcdbccbceeeacaecdabbdcabdeedcbceaebebbddbccaedbddbceeadaabdecaecaaaaaaedceaccbbcdbaceacbbbebcdeecaebeaacdcbebcdeedcccddbaeadeddbbebcacadccbceddcddddaaddcebcebaeccacedbaaaeadaeebdcadcbcedaaebdbbbdaebcdbceeeebaaeeabeaccedbbabacaabcccdabbeebeacaabadccdbdcaecdebcacddbcccaabdabededbbbcbbbbcadeaaaecaeccccaaaaeeaecbeedcdbdaadaabecacdeacbddbdbbabbeadeebadaedcdcbcaeacecceaacbadbbcdabbdeeadccbebebbdbdcecccadacbdbccbccaddbabddeabeadcddcdadbaaedecddacebdabbddddeaedaddcbcdedeacadaeccdaeebcdbacebabdbbeaebaedcdabaaaebaddcaabeebdbdbccdccabacaadaadabcaaccabdbddcbcceceedbdaebccbdbcbbabededeebcddabcceabbbcecedcbdbecdcabccecadceecaaccdbdbeaadaddedadebdbbcecbbebcabdcabeedcbeaccbcebceaeceecebcdebdbcecbcecceabdbbaccebdcdcdeeaacedaeccabaddcbcddabddbeddedaddbeebdadaceedbddeecddeeabbdbeeeaabeaaeecaecbdbecebcadaaddecbbddcdadcbaabecceebcdabcbcecdcbbdebccdecdcedbcaeaabebddaecdeeaadecbeebaacbbdceaeeccebdddcdbbeabbecaaaeabaadbdaddbadbcacdddcebaeddddbebcddebbcbdaddbadbbcacdbdedaeccceecdbdddadaddbccceeccedebccaaaadadacececccdcababccedecadacecbcbbeaedadaeaeededcdaabddceeaaeaadbdbdccbcdbbeaccaaebbdaadccdacaaedeeabbccabddeeccadddbeeebedcbdeaebddeedbaabaeeaeedccdaddbbdceebeabdcedcabccaacdcbbbdbbcdbdbaeeaaedbdbaddbdbbbccaeeaeddeaeceacaaebcaebbaaeceebbedbcbaebeccbcbadcbecacedccdaadccbadcbeaeedcbbbbedaeddccdadebacdacecbecbcaccdbddaacddaeccdebccedabababbbddeccecbdbdcabcecbedaceddbadddbdcceaabcbcdecdecdbdeaedbbebaadbbadddaabacccacbbbabebecedabbbaabbdaaabedebbaebeeebbceedbabcdabddccdcbedecdebbcaacaacdebeeadbeebdcbceeecdaaedccecacdebdcccadaababdeebadbdcccbdbdeebebddecaebcabedbdaaacbcdaecdecabadacdbebdbbacababeaeceacdedeceaedbadecbabedceaadddbadbebabaecaaabbbceeadbceeeabebddbccbbbcabdcbbcbcccbcdbbbddacceadbbdacebdaebbeeeccdccecdcbadabcbdeadcdebbbbbaedabcedbddbebdabcebbdedbeabbeedeeacceeeccdecdccabdbabaceeeddcdceeeaceeddbbcdcdaaeecbebaaedaabcdadbcbeaadcddcdecadedddbbcbecaadcedabcedabedbebaeeeabdedbeebcbedbcebeddeceeebebaeebcdcabeeebdbbdadecbcedecaececedcbbceebeddcadcbddaaabbabbebdecddaadeacbbdebdccccebeebddddeabbdaeabeadeedabcccbbeccaeccdbdeaeedcebbbaebeaadcaedddcedaedceecaaaecbddaeaaedcaccebddddceabbaaaeccbedebababcabeddedeedeeaaecdadebdcadebdbbbbcbccbdeeedbacccdedbbbbaaebcabdbdecaaaecaeddebabcdbbeaeccdebaaeaceceabaacecdabebecebbdcbededebdcbdedceaaccdeededabbdaeceeccddedeeccdceacadcaabbdbddaeaeccdcdaaebedaaabeaccdebdadabbdcbacceebccaeecbbbedeeabcbbceaaceceddbdbedcbcceeaaccaebecceadceebbedbdcbaebdeedadededdabeabaebabedbecbdeabedaecbeddceabeeaddebccabcddebbccabbececabdccbecbccbcbcdbbcaacadcebbedeadcbcbaeacbcbaddddedebcbeebacdacbceeeccacedceacbcbbeaedbebdcbdbcdacacbcddecaececcdebdcdeecebeaaebaacaacdcbbeedeaabdacccedebeaedaccebbdecdaeabbeedeedbdeeecbcdaacbdbccdbcabdaaedbadccbdbacccaadbeebaceddbabeeccacdbebaecbaceeaedcbdaadaedcddecaededcbbcaacecbedaadcacbdbccdddbaeeedeeccdebaeeacbbeaecedebeeacebdaabbeccbdbbcdadcaeccdebeebeeaeedbabedaacdabacaaebbdebcaadbdebbaacdeaecbddadaecdddaabcaaaeeecaaebaaccadcebcaadcaabbacaeededdeaedaeeeaaceecceaeadadcbacceddbdcedebbeaecebeedbedeecceeabccbddedeaabddaacdccddcaedcbccbebbeedecdbeceaceceebeebbeaeeabaaaaddbeadabcababeebcecccacceaededceaadcaccebbcdedaccdeeabbaceedcbddddbeecbaaaacbbeaadbbaadcbdcccbbebdbdaecbccbbaeabddbcaecaddbcadedaaeaccceeecbdcbcdeeebcbbedbebcbbbdecbdedbbdcdaacbbadbabdeddacbedbdbaacdcaadadadeaccadeecdebcdbbaeadaecbbbcbdeabaedeadbedaaeacaccdcbecddacbceccadcadeacecabdeddeacbcedcccdeceaddacdeacadacceaeeebeeeadbcecebdccccedddaeaeabbeaeeaacceebdbbddbacdcdccdbbcedcceaaeebbdbbbcedaaadbebbdeedccebcbaddddeabaeedceeccdacdcebadcdbadceddaaabcddeaaedbeceabacceadaabdcebdebaeeccedbcbbbdbdeadbeaaeaddabacacacdabeebadbeaebeaeebbadbbbdabbabbbbcaeaabcaececdcebdbdecebdecacbebcdbcbecceceeaabbaabddbeaaadcdeaeaccbdaecddcaddbeeeebaccacbbabdabcabcbedcddaebdcccadedeabaceabccbaeebcadcccbebeccedbdacaeaaeaebadeecebbabbcdabecedadbdbdecdccdaeabeceeeacccacdabebdedcaccaccdbadacccbbddadebccedeeeabbbcbdcdaacdbbeabccabccbcaaedaadcabaabadedeeabddebedebcadccabeceedbebdcdaecdaaceebcacabcaecceceaebdbdbdebacbddddbbbcacdeceedcaacaabddeedacbccaeadccdddedcadddeabcaabedbccaebaeeabeedaeaaebedeccdabaeceeebdbcabbbbdadeaaaacdcbcbdbcadcabdecdbdaabeccbbddabaccaeeaeeabadbcedcdecddbaedaaccddbccacbdcccbaeedddeaeebacdcccebbaacdbbaccaaabedccbadcaecccaeaecdbccbeaabbdcaaecbacdbaccdabdcdcebcbeaecbebabeaeaeaadccdccabaaeedcebaecbeccbccecadcebdaccbceaceceedcacdaeececaacbbadacaddaadbcaeedadceaaccdaaeecadaeddbdcabdeebaddeacbbadbbbdeebbdebbadaebdccdbeabcadacbebdadebeaeaddcceeeacbbeabebeeaaaeadddbebceebcabeddbebaeadbaeaeaeaacaebcbaeeeecebabacabbcabccaaeeeeecaecdeccbecccaccdddbdcadebaededbaabcdcdecaeeaddebabedcebadcbdeeadcaededcceccdadcdddacdeceaaaeadaddebaeeeddcadebbcbdbeadebbcdecaacdddcccbddeadbbceeceedecaaeaccdcdbabbabbaacdebaeeacbbdaedebceacebebbcdddeededcbcbdddabbbddedccbdacbedbcebabacdddceadacdebeaedadcbaaacecbbbaadabecbabaecadedbeddaaeeecabaddcacbbdbdaecaacacbaaabcbaeceecaeaddbceacebcdabaceccedadddcdeddecdcaedeaaebcaedbdcaddedbaecaeeeeecebadcbcbdacbcdeaddeceebeebbdeeeeaaceecddebcaaaacecabbaccedeceaebeaababecdbbbeeabbdaceaaecaabcceaddbecaedcdbaaccceceaabaccaabdbdaadcedccbcaceeedccedbcadebdcbebaeecacceedbdcdcdacecddabcabaabdcbceececdabebcdcdedbbbebabacabacdbacedacebcbbaccecadcacaebdabdcdededccedabbcdadeebbedadcebaaaabbecaaeeeecadeaccabcadbcacaaacddeeecacabecdbceacacbadadabdbdecbeceacebdeaebdbccbbdaeeebbdeceecbcdadbbbdecbddcdacccedeedbebecdeaeacbeedecabdebceeaebaabeccedbdcdacddbaeeaacdeddeabeaedcaebbaadbcbceecdebaebcdaccecbbbaebdcaeaadcdceebccbbeabcccccbdacdebbbeeaeadbcbebcccdbcebeeeacbbaeeecebdcdaeabbedebcdabecccbbdabdccdcdedcbdeddbbaebdbedbceadbddaecdcdaadeaebceddaeaceacadbaeceeaeaebcdbbdecdcbedbbbacdabdebabbaceddaadbcadbebecabbacacccbbacccbbecdcccdccdccebecbceaacebdecabadbabadbbdabaccbecbbbabeebecccecceecdddccadaaaabecaccaadeebbddbdbacbabddcddeddbaaaaaeadbebdaedadbbacddbbcaeebbccbdbadccdbaaedecbcadacdeaadddcddaeccedebeeaaeebcceabebccabaaecbeeddebbeaacecbbbcdeacdcbbbeedbedceccdaeadcdedaedbaddbddabeccaebacbebbcbaddadddbbcadadccdcdecaeeebebdeacbedcccdadbeeceeaebeedeccdadaeeebbedacadeaeddedadcbeeeeeaedaaebabeaaeededebcbaaecdacaaadaadaeeacedecdcdacabaddecccbedacbbacadbbccaadcadbcddabcaadebabddaaecbcbcbebaaabdaeadaaeccdbdaebadcbbdbedcbadceaebdbdcabcccacdbededeebdebbedebdecaadddbbbdecadbddbbdbaddbabbbbbacddeeddbeaaddacbdeaaeadddaadecccebddaadbeacacbcddabecbbdbbbaebddaaaadaccaeacadacadaadbbccbccbbceebadbbabadbeaabaeabaaeecbeeabdacbadcedcaaaabaccdeacaebeceeebbadabbbbaabcebbdecdbbbaceaaecbeabdbdddebedecebcddddcaedaeeccadcdeaebeeddbbeeddaddceddbdaeeeeceeddbdeeabaaaeedbbbbcecaddcedeadcbdccdabadddaccbddedcbdbceaecacccdcdaadbcedcddddadddecaeaddecddbdcaebeeebadedbedabeababddbcbceacbbbceabeaeaaedaadeeadcbeaaadeabdedeedcaaebddadadcdebcdbacddebdbeeebbedbeebcdeeebadaeeedbdaacccadbadeadccecbeedaccaedcdadebedeeaeaaaeccaddabcbeacbaabebedbaecdecccabddcdadaadecaeaccadcecacdecadbbddeddebdcdedcddeaddbeebdebbbdaabcdbaadecdbcbbbaaaaabbcaddedadaadbacbbdaeedeedbebebceaaeeababebdeaeccadcbbaaeeabbcbddcdeebcdecdcbccbcabbcaeeedaccbccdaabcaaddbdadeeccceaecacaeeaecbccbaabaddabdbccacadcbbabccecabdbcbcbdeaddcaedadaccbdaedccabdabbacccccbaaccedeadcaeacadbdadddabacbdbdbceebacbdebdaddaaaabeeadaeebebbceabcaeabdeaeaedacaecbacaabbebaaeceadbdcdacbbababccabdeaacbbecccceebdcaddbdccdbbcbcedcdecebcedbdccabeceaddabbcaceeaedebcadcacbecdbbadacbdcaccbbcdeccbdaceedaccadbbcececaaedeeaebcbeaecdabadcaccdaacdcccebbabbbddcbaaebaebebbeccedaeccaeeddeaeeddccacccaebededbbacbcaecbcbddebaceeecacacedbadbdeaeaceaeaaaadcebedcdcbeddbbcdadbcabaebbcbadcaaacecebcdbecabeebeabccdebabbcbbbeceeeabdbcedecadcccebcaecebcbeccbabdbebbbeaeedaccbebaebebebcbadceebbdaadccaceadeaeaebcbbacadecabceacadebeeceaacbddadccceedcdaecdabbecdccaeeccbebdaaedecbdaeecadeeedcaaceeeecedcbebccdbaabebcaadaeaacbccbebdebceaacdabadcbddcddcbcdeaabebcbeaeebdeeeaaeacecccacbbdcbedccbcdaeaecbceebabbabeaddcccdbedcaaddeddeeaeaddacbdaeabebadbcddbcaebdcddbdddbccaeccaadcaecedccdaabeedcaacceebaaabbeebbeadecdbbeaaedcbcddbacceeadebbdaadadcdaceadbbcdadedbbebdedeeceaeaceacdaddbaaaedddeaaeebacbbeeeacbaeebcdecbebdcddadaecbededdceeabccaeeddadacbedeaddbabacdabecbcaccacaadebdeadeeccbcbcbddecedbbdaacdcecdbabbdbdceabbcadbecdbaddcbddcaeceeabbdcdadedeaadadddeeecabcaadaebacebbbacaeddaadbcddebceccaebadadecaaaeebaaecebeaabbcdeabebcdaeeabcadbecabbdddaebeacaebcaeeaaacdabbeacdadbedddaeeaeebcdbccdbddecbcbabddddedbedeccbcdcbaeebbdadbcdedbddedbcacdaccbedbedcbcabcedbddabcbbdaacebaacebbeceecddeeaabacaecacbedaeedceecdecddacdccedeeaeaebebbbdabaddbbdaeedebdeadadacbaebaededdeadebdbeccacdebbbabedcdddaaeeebdaeebccacecdcdbbdcdaacabbeacadcbddcbbcaeadaedeaedaddeeebbaeedbdddbacedaeeebabebdeacbcedeeeacbecbdaebeebcceecdacdecdccddeaacaccaccbbdcedddeaedecddaaeecbdaaeeaedddcbddcaceeeabccceabbecbeeaaeabaccebbcbbcaadcccecceeaacbecdbecbabecbeaaedbdbddecccedbaaebcbedccbaacecbdddbdcabeadddadcaabdbdbccbacdcbadbacadbedaecedeceeddbacbbcbbdbbaacdbccbcabeaebedceebcbacaddacaeccbeadbeaadceacebaeabaaaacdddebabdceadeadabcebecaeccdbcccabebedbeacbdabeddbeecaddcbbacedbddeacdbadbcdcbeeaebcddbadeecbaebdccbeebbdeaeccdcebdebecceeedcccabdbbaadceabaabcccecbaacaebbeeaccbbbccdddaccdddbbddcdcddbccadeaeaeddbddedcccaceaecbbbabbcdacaceeabbdcceeaebddbeedaebbeeadadabacebeaeebedabdceaedddcbacabbedccdbbddccaabcebabdcbcbedbeccbdddbaecceddbeeeadeaacddeddbceccdedbdbddbddebdbaacdaabacdcaaaaeaccdcadcbbbdeaadbddcbbbccacbdcaabcaacececedaeeecadcacbdabeedacadbdebbdbaeddedbbccbcbeecccaddddcdabdbecdacccbeaaedaceccbcbdbbeddaebaaddbeccabaceacbedabadcbcdbeddeaacdeaebccbadeaacdaaeeacedaacacbdedaedbaeceeaceeadbedecdaacabedbcacbbbecadaeeaeaacadacdccababeeebcbeededddbeebdbabecbddbaabbcdeabebbcaababeaedcbdedeedcbcdaddebebaeccbaedccbcaaaeeaecabaccbdaccccbadedccdcccbddabcecdcedcebeacbcabbcaabebbbccabccbdcbdbbdbbbddbddeebeebbdedbaabceaadeecdcecdeacbdbeebdaedaebadbccbbdbaaeeaccaaccbaecccdbacecedcacbdddabbaedbccacebddebbecbcebdbbdcacdbeedbaabdcebdebcdabdadcbedaaaecadeceedaddcbcccbaaddeeabadbdecdccdccbeadcabcbacdecceaadbdabaeabecdceecacdceeaccbdedebeabbeceaeeeeeabddccbdccbaaecbaceecccbadaebdabcacbcabddcddcdccceadcbcaaadadadedbaadccebdbaccbddedcdaeacaabaebdcbdedeeeaabbeebbadccbcbcddacdeaebacbbeddaeecebdcbeceeaecaedcabcabceadbedaebbaecbadcacedebaeaddebaabddcddbddbeaaddadbceebdaedeaaedebccbeaabcedeaaccbedadabdccccbdcdbedebddddddacedababbebdcdddbccbbabbabaebeeccebeddebecabadacdbcebdbaceedeeaecdeeeebdbaeaceddbccedbabeceddbacbeccdceacdeaacdbcedbeccdbdeddacabaeaabbceeadaabeaecdcadbbdebbdcbbdecdcbbcebdadcccedeabdcdeebdeacabcabedcbaedebebbadcbbeebaeabccdaceedeaddeaebcaadceacbaaadaacddccaaaeeccaebbbdccccaabaeaacaacdaaecebccadacadacaddeacceaeddabbecaccaeedebceacbbacdabcbbbdabbcbaadedebedaebacbdecdaadecdbacbadeccaebdeecbebbedccaddbaacceeecaacccbcbcbbcdcdbadcbbceccdeeeeebedbccceabacaacadcaadadbbbbebeeaaaebcadaabbabaedaddbcbbceeadadcaddceceacaebceaeebedbaedbbbbaabeecabebdecddbcdbeedcbbeededdbebabaacedebcbaceacdcbedceebedbcdeacedbadbaadabeadebccebddeccbddbdddeccbdabacbeeaababcaababdebddecaeecdebabbcabbacaedacecedeeddecddedddbddeceeaabbabdccedcdaaabcdbdbccedbdddedcddeeaceebdebaabbeebcdadcbcaccabcabababaecebdcbcbbadebeaadbedcedecaeaabcbdcebbddecdecabcaacadcddcaddeeddaaeccbeabbadbbaacecccaacbbebcbcbeccebbdcaaaaacddbcabcdecbccacbcabcbcbdbaceabcedcccdeddeecadcaeddccbcddaebbbbaabeeeacacbdcecdbbedbedaabbcdcbbbadbdedaddacedadcdedcdacebbcdadbdbccbbcdabbacabbddcbceddceacbbdeccbccebeaecdedcadcdbaabebcdcbbbadcecabecadcbbccdaeadeceddaaeedeeeeabcbbddadceacdeadbebbccaeabeecacaebdceadaddbdaaeedabcbbeecaecddcdbbcdaeaaebbaacacdeeaaabecbddcaadbaadbbbccaedcadcaedebedadbbecdcddceaeeddcacaeacdaddaacbaecacaaebddabddcceecbbcbceeaeaaecdebbcdbbbcecdacaaeaedadbceccdeaebebecabedbcddeceaacbadceaecedeebbdebcdbaeedbcccdaeeabbcbadeaabcdacdbecebbdeebbbabaeeaccceaecaedecdcccbcbbdaadbaadadbdcaecbacaecacabedacabaddbaaacddadcabbddbcaecbebebaecbeecbbccccddeacabebddccbecbceecaedbeccdeacabdedadeacbdeebcebbddcacdccccabeddabdbeecebebaecddeaaaebbcdcbaadbabdaaaccabccbaddeaacdebcabccbbdeaccaadccaabbbccdccbbddbdbecceaddbeadeddacaecccdbadeeaddccddbeeedabdadacaadabadbaebecdcacdcddccaeadceebceecbaadbeebbacacceddcdaddedaccebdaeeeddbdbdbdcdcccdecbedadbcecebeeaacaaadebadecdadaacecbdcccbeacdbbdbaabcccbddcdbcabbbcaeabbccadddbdcaddccaaeaadddcaecddcaadbddbdbebdbacaecebebabceeebcddeedcaabaecdacecacabcceebcabcaaacaeaabceecabcadeabdddacddeaaeaebccacbabbdddddccbebbadddacacabacecaaeccedaeaeaaddbdaeebabbbcabdeedadeedaebbbbbdeadcbaedaaeddbaadceabccdccbbaebcbceabceddaeeeceedbdaceddeddcbbcaacdeeaeedcaababcbaebaaeebaadbcacaaeadbaaccbdeecabdbeeabaabcaedbbcddbbeacceeaadaeceeedacebedbcccebebbeabeaaeddeadeacacbbaeaceabccdcceabedaecadaedcbbbbbeccdbdbcceceebbdcecdaccadbbdeacebbcbadcabdabcbadbceddbeabacdecedecebeecbdbedaabdccdaeddabcebbcaccbdcbeeccccaeaedbbabddbebcaaceadbbeabbaaeaaccacdebcabedeecedacaaadeebbdcadbbcbdadaebbebbbbcebdaceedbbbadddcabceeedcdccdbbbedaeabccaaddeebbaacdbaccabaacacdabdcdebbeaeccebadedbdebdbdbbeedeacdecddbddebbbbbadeaccbaaeccaccdabbabebdacdeddebecaeaaeaddcbccadabaccdedaabeccbdeadccbaecdbcbeebeddcddeecbacedacebeeedbaedebccbeaebdcdaecaddadcebbcebaeabbdcecabbeecccacdcdeeecedaeebadeadcdcabcabdeddcbcbbeadbcbededaeeedebedaeebeeadceadcdabcccdebcbbbdceadadeaadedebedbdbadcdaadbcedabadcbcaadabceeeacbddaaacbabdcbecaebdbbccbccddaddccccccdadabdcdbddbacedddcdbebaecbeedabdaedeebaaeaedbedddcbdaedeccbdbaabcaadeccaddbedadccdddbdbeaebbadeebaeccaeeddddeebaabbbbeaaaaedeeeaceddcbcdbecbabbabdcddeddabedddcebcdceceeadcbeeaececbaebdccccdcbbeebbdaddeecaeeadedddceacabcedecdbeededdcdbabcecebaaaccbceccbcbbcbadeadedabbadcdcbcecdbeaaddcbdbcbccaeadddddbaedddbacaaabbbdcbeababbcdadddbeecdbbaabeeeaaceaeebedbacadaaaaadcaaceaabebcdcecccebbcbadcedaaeebbbdbecbbdacbccaebbbebabbcccbdddbaeebceddaaeadedeaeebbbbcbceeccaacadeabedadcadcbcceceabecceeaaddbcdbdbebbbeabcdeabacabddbcbdbbedccbaaadedabbcabddeaaebacedbcecbdcbedccceaacddbcdcbacbeacdcdbcecbcdbaabebeabeeddadabeedaeecbebcddacdcbdaeeebbabeadecaacdeacdccbceaceccadebcaeebcaeecddebebbbeeddeecebcdeddcaddabccccaaeddecdebcdcbaaaeebebbadddaaeeddcececaeabbeddebcbdaadededdddcbdacaabadbaeadbecbdaccceeeceebadbdedaaccedaaebdcadeacbcaaccdcdeeebccdaceadeaeccadadebddccdbdebcadbbedccbaaadedddeacdbccbddedacdacbebabbcdceceeabcaaeaeacebceccdcddaeacadeaeebbcadabbacdadbadeaccacebbdeeccebdbabdcadeadedaaaccccaaddeecedbbbeeddcebebceebcdbacdbecceecddaedbacebabdeecddeeeddbbdddccddeddbcabbdcdceabddbbaddeebebbecabaaeabeddbbcacaddaaeaeeccaedeecaddebddceeabdebaedbcddceddcaccbabadbdcddbecabdbacdddaaeadccddddddcecdaecbedbedacabdceedbaccddeceebecdbdeceeabbbcccecaebccacbbccbcecdbebeadaeeedbedcacabacaebddbcbcbcdbdbeeccecebebcebedaeceaddaabeacbbbaeaacebaaeacbdbaabbdceecdaaeaddceabbcddcededbcaedbceddeeaebacbacecdabedbedcbbbddedecaadaecbbbaaeaddeacdedaacdaecddcbedeeeddddeabdedcacccddeaacaacbabbddeedcbaaeddedbaebbedbddcedcadcedceededdeadbeebcdadbdedeadbdccaeacbbbceaacccccacdaaddaaaddeaedecbacceedebabceacaaeedaabeaceaaddcbdbbdbcaceccacdadaebdabbddccedacbbeddeacedabdbdcabadcacacdaccceecabbaeebeaaaadceeeeabbcbcabcbcaaadacadeeebdacdadbaadaecedcbccbaeabdbedecccddccacaadbbdcbbddcaabbdcdbcceadcbdddebbccadcbbbabbcbbdedcadaccdbadbebcbeebbdadbbcdeeecacabdabaabadcaaedaaacaaecabbacbeecbbbbddadcdecaabcaaedaadddcddeabcdaeccbabadaedbbbbdebcbcddadcbceacdeeeeeccbaddcedeadcdbdbbdaeddcbeaacbebebeaaacecaaeebccbdbbeeeecdacebeeecebeddbdddbbceccccebacdcacdebeddccecddbacebdccabddbcedebdeccecbadedeacaeccaacbbedeeddeaadacedeeddebeaaabcdeababacdedabceabacdcedcbbbcbaeeaccaaeecdbebdeeaaabecdaeaebacdcbecbceddeaacbbaecadbebbcebebcabdebcdcddecabecaccacdebbecedeeeaeedceceeacacdddcaebadbceaadaadbbeeaadaddeabecdacececbdababebadccdbdddaaedcdbdadebcdabbaeaceeaeabbeeedadabababacdcedcdbeccaaeedebecbebaecbaeedeadabbecdbbceacedaedbcbddeddacacddcdbeddedcbccecbdacecadaeaedcacecdddbceeeaacabebaccaaacebbecbeabdedebebbaabddbccbedaacaadbebecadabdebaaeebcbdbabddecedeceabecbdcbeeeaaacbccabcecaaaecabeeeabaecabacdebedceedcbebdaedabebbabccddebebbeaaceadeebeddedbdeaaebcdcecbeddccbbcbdbabdeebabaabcccecdadabaddbbaaecacbecebdaeabdbabedbddcedaabccabbeeccedbaaedbacbdaeaadbeaceabebbeccecbebeaceebdceddecbcedbcecbcebedbeecdceceddcecdedddbacbddcacaadcbbceddcceaeccdbbecebbbdcaebddcdbdecadcadbdeeacdeeeaddacebbaadcdcdcadadbcdbddbcabcebbabcbebaaceacaaaaeedcdeeecbaaebbaddabeaaccbecdddcbeebebaeeebdcaaedeabddaebecbbebacddbccaeecbddceceeceeecedccbcdcbdcabcbeeacbdbebadacbecdaddbaedbaccbaecdadaeedeccacaeeccecdeddebbedbebadebabbacdcdcacbaaeedcaeccdcebedababaaeceecbcbccdebabaeeacbddcbccebecbcbddcbcddacddbaaeabbaccaabebbadaebbcecaeadbcabbebeccedbaeedddcadaabcaecdcacadcacecbbeaeacecdcaaaadceedcbeebedbaaeabdbeeecaecbcdceaebddcbdbecbbebdcabbabdbbadebcbeddeaecbeebbecacccddadbaaabdcdcaedbcdbbcdbbdedbbbdbbeadaaaeebcdcabbadbdbdddadbebeebdeaedadddbcdcabbcccdcacdbecddaaddcddcdcbceaaedcbebeaeceadbbccbccbdbdeacbecbbbedddbecbbaaaeeeecbececbaeadecaeaddaabedbecddcbaabdecddaeebebedecdbcbcabedbdbeddddecabaccbadcdebdeccabaaddcdabaabadabeabedcdeddabeddbcadbbdbdceebcbcddabbeecdcbadcbdabedbcacebcebbbebcdeadcbcebbcdceccdbdaeceaacbdeacdacabecbdcbeadbcddbceebccbccdbdadaabcebdbdaceabebaceeecdbeceaacadbbaebcabedbacdabbadceecaedaccccecacaecdeebeeeeceeaecebbdceebcddacbdebdedaadaccbbeaebbbcccedadacddcdedacccedabcdcbdebaedccbdbddaacbcccebeecabaccecdbccecdcaeaacaaebbabcaabecccbdbeeeebcabbbeaedecaeddbbedadcaaabcaeabebeeedcdccbeddcbdbaadbaeaceddcabedabbcabdebaabaabeccdbbdbeeabbbeecaadcacccdceaecabcadabccbbadeabbebacbdebddcdccadccdcaeaedbedaaeccbecdaaccbeabcedeaacdbdedadadbccecbabdbcdecdeacadaddcbaadcedaebddecaadaaeaaeeeaddadbebccbdccbcbacbbdaeecbacadbadeddededadedabbcdacebbcbcaabbbbbaedbcededdbadcacdbaaaecbdbabedaeccbabdaaceeacadaabdeeecabecabcebeeaadbbabeecbadaebecbabddeabbebaadeaebedbdceacabcbaeacbabacadcabdaecadecceedeeacbcabddecbebcdeddcbeccddebedecbdeebbccbeccbaeaddcbaabcdcedaababaebabdecbdbcceadceccccbdceddbbabceccecceaededdaabccbedcabbdebdcbbbedeeaddaecabaebebaebeaadaaadddbcbcbdbbccdaedcdabddbecdedbdbdcccdbeaddadceaabadabdacbaeaaadbacbaeccbcddcbdadaedbeceabcabdebccccabcbbcbaccdcaeedeababcddbcbbbabbbacdbaadccaeededeceeabaaadcceccadacbdaeaaebabebebadaaccacbdadabeaedabeadbaeabeacaeecbecccbecaeaadbbaecdadebccadabeaaacbeadeaadaaddaccdbacbacebcaeabbedeadacbbdaeabcceccccdcaadadaddaaddbaeecacaadbceddaadcebeaeaeceadcbbcecabcccbeceddcdeeabbadaaedeaadabdeeacdeececddbbbdbbedbebcebbaccacdabccecaeebaedecdbcdeecddcbddcdbecbcaedbddbebadcdcedbdeddcaaadaceaadadbecacaddabadcacbdeccadaacccddbddbacbbbcdcbadeeadbdebadadeeadabebbccbbbcbeacaedebddbbccebededaebcedcddbdeadcbbeeebbddabbdececaccdbdbcabdecedadaecaebbeedabbaecceeecbacbcbccaedbedbdadeaedbdebdbdcccdbaadeecbabcedebcecdcebbbccdadbeedeeccdacabbdbddcaebaddcdeecedadaebcddbdcbbaccedccacdeaececcbadaecdbeaeebabbdcdceeacceabbcbebcccdebddbceceeccaeacbedbbdbddcccbacabcbbaaecdbbbccaecaecabdaaeebcdceeedcbebccaaadeeeaebaabdccaeeebddeaedcecedbbbceaabeeddcbcacdeaeabbddbbadebdaaeceeecacddacaacadaccbbaddbeacaabcbabccdbeccdecbebdaeaccecabadedebacadaecbcbbddecadcbdaadcbccaecbbceedecbbcdbdeeddedeeaeacacdccbaddcabccaedbbceaddbdabeaadadeaccddebaebddecebcccaebececaadcbeddeabbbdabcebebbcdceebaeceeacbddadbdeeeaeeecaaacacaaaabbaaedabaaddcadceadececabdaabdcbcebcebdcabacdaeddbbcaebbebdcccbabaedabceeccceaceeaadaeebeeeddccddeaaaadabadbeaededcbcceaaaeecdabbadaebcedbedcbaabdbaddecbdababadebdaebcdedeeeaabdabcabeabeaaacbeeaedebcbdcdeabdedbddaecbabecccbcecbabecccaeacabeeeedcdaabacbcbdcacaeaddacbcebacabccbbadbbcdeaeedeedddeceddbbaebdaaaeeeddeabbbaaecbbbadedbabcedbbabeeeabcbbdbabdbcdecaaaebadddbbdbddbdeabddedeeddcebcdaaabecbcdbbeddcaaeadeeaedbabdcbbceadcbeeedabcbaaabbcdedacacadcbbaeebdecabddadddebeeacdcdacbeebbcadcabceceedceabdedbacbacdeaebadbcccdbdedcdcadeabededcbceddeeddeacdadbbaccdcebdcbeceeebcaddacacdeaeaeddeadbedcbcdaeeccebbbcdceeddceadbbbbeeeecccbaecdadaddaaceebecddddcebebebdeddadebabadebebacaceabbdcaeacbeeccccbdaebcebaeadcbaabeaedbecdbcbdbdabdbdaedddbeeeaeeeddacddadcaddaedccadebadeddabbdeebadaeaaccabcbadbcadeeabdddababccaaaeaddbdbcccebecbdcddeaaaebbaeebeaeaaccdeabbebacbaaaedbccdaddcbeccededacacacbbbbdaecdadcbaaccaeedbbccacdabceedbedeecbbeebbbeebacabecbacdcbacebcdbaadddcbedadbddaeccccacdadacbaebadbdedebeeaacedbebabeabccbdccdcabbdcddaeadbedceceaebdcdcbedeebcacceaadaeaadabeebbacebdaecebeabeeceeabbbccbeabcaeadcbedbebdcbcedcecaebbcbabbbadcdcadbddeacaecdecbeabcdccecdbcadbcdeccdaedcbecabdddccbadddceeaceeeeabacbddccadbacadaeeaecbccabdaecaaecdcceebbdcabdbcbbdcaebbaacecbaaceccebdcbadcdbcdabebebddeeededabccdbbcbddedecaaeddaeecbbcabaebddccbcbeaabbaaacdabccbedeceabdeeabeeaaaaeaeeeccbbccddbdbbaaaaebcadbdecedaebddabecabcaedcbdeeacbeebeedaeeceebbcbdcddababddbbdcdcdabecbddcbcbbdecbdeebceedbbebaccdebcdebadcccccdeabceabedcebecbebcebceccaabbeacbecbeaaceadebababeceaeaecadeebacaabcaadceeedaecddeacddbecdddbdedabecebabdedcaeeccdadaebbccddcbccebcbcbabacdeaadcecdeeadaeabcbebaeeabebeaaabbedebbebebdccececdbebccedabbaaeebcaaeeccdcabcdaecbcbbccbbdcabdbebbadecbbcceeddecacdeebbbeaabdbcbeecbdedcbcaeebedbeeecceddbebaabeddadebcdbcebbedeadaceedcdbdbaebeebcdbbaabbdededcbaceadbbccdcadcaeaeebcdabcaabdbcdaabadbdacbddeaadeaedaeedbadbeecdddeedbaaabdbbeeccccaddabbeaebdadcbabbcdccddecbeaeeeeadecedeaedcddcbcadbcedaaedadedeebeebdbebcaddaeecccaddadeceebcdddceacedcdbbccbdbceeeabbecabcedbceedeaedbbceecabebeeaaaacdcaaaccadcedadaeeeacaaaaebaddadbbcdeedbccaccdddaaaedeebadcbdbecaabdedddcaacaabacedbdacdaadbddeaddddddbecacdbeabbaeaddcabdbcbdcbecdabeecdadbaacceedacdabbcebdeccceeaacebacbdeebddecbacebbedaabeedaaadbcbcabdcaadaccdaacedbcbddaeddcebcdbbacdcabedbdeccbcecaadecdadbacbbabbbceeedcdcecdeebccacadcddeeaebecddabbdabeceaddacbbaddbccddbbedeabaddbceedeeadaadccadebdacdeeeeecdbdddeceadecaaabebceadececeadcaebdaaebadbddaaceeceeeccceadbadcbecadaeaecccbbaccbbbeebaeadbcdcbabdbdeeabcddacaebceddeceebdcccedccdebeebceccbbadadccebadabacddbdbaecbccccecccadcedbebcdcdcacccbbacdeeeddaaebedebcdbbeadbbeaaacbccbedbceedabaecbecbdcadeedadaeedbbbccebebebcbbbcbabedddeaaabaedabdeedcadaceedadcebeeebbeaadeecaeaaceedbedadaceedcdbcebaabadaccdadacadadbaaddeeaeeecabdddbbebbcaeaaaebcaceabdcabbeddeabacbdadcddecaeadeddcbdecebdbaddddaaeeabddaaccaccbdbaadeaddacbddeccbcbacbeccecdbeaccdebeaaabeebbcddebcbbaabeacbdacdedcdddbacaacedacabbdaceddbcbbcadaeaccbcdbabeeaeaceadddcdeabedacdcdcaaaabaeaecbeaaeceebdeeaacccdddeebabccecbcddbabeddabecccaebaeecaddabdbacbeddabccaaabaedddacccdaccbaccaebbeeabcecdedcacecdacbddbdbaaedaadbaddbbddebeccbedbceccbdcabcbbadaaecacdaddaddebaeabebdbdbbdeccaeadebcabdbcbaecaebeecebdaebbdeadeaabeeaccaaccdaeaeeaebdedeabceaaacacdeaecaabacbecacaecbcbddadbbdcebeeededecdeeebdaebcbaaaaaecbadaceeebebedaeecebbcecbbbdbdbcddedccbcccbbebebaebbeeddabedaacedabbdbadacadccbeaaacdeedaedaccaeeabedceeabcacdabdbcddccadacbeeedabdcacdabeaccebddaebdcbcddbaddaeccaecccdeabcdedabbbebadcbdeeddbceddadddccbdccaaebdcbcaaeacaebdacbccbbceecbcacabdbcccdcadcdebdbddcdeeaeacadccdccececbbceaebdbddcacbaeddbaccecdabeadaceebcdacecddabdcbdeaabebebacddbdbbdcccaabebbbbcabdeaedbdbacbacdadbbdbecaacaecacdebacdedbaccdcdeeacbcceeeebddddaddbccbdbabdbaacddeebdceabcecbdccddbdaaacdddacadebbaaedaabcdbbdcebccdaeccdbdacbeaebeddabbbeaeaeeedebccbcddaaccaeddbceedabadedddbdbdcaedeaeacebcbbeeecbcbbbbbcdedcdbeacddbcddceaeceadbccbaaddceaaaebbecdeabbedabeceddecbaceccaebbadbebcadbdcbaadeadcacacebdcdecbaddcdedbaaaabcccdeeccecacddbdddbabecaddeccdeacddecdddceabbcebcccaeecbbcbabbecbcbaadbeabdedecabcbdcceccbddcecaceadbebececbaaacbbdacaeaddedacbaabeacadddbbecbaceaacdeecabcdacdeadddbedbdaacecdcebcdcaabcddaddedbceabddbccecaeedccbaedcdbcabecabbbebbeebedaadeecaeececbaccbeadcdbddababeadbeeadbabcdeaaaaaeebaaebcdccaeaddbddcdebcbcdddceebbabceaedbabcbddbedecdceecbddbbacacbabebbacdccbdbbeaecbeeedecebdaececcaeadbdbbcdaccccbcdadaaaacabbbcbeeeeedadbbacdaaaebccdbaaadadaaceaeeccdddcdeadcdbdcdeeccdbbcaccceecebdbdeaebdadddedbedbaddcbbedecdadeaccddaaceeaddebeddeaaaaaaaebebaebeeababbbdbbbcddecccccedbbabebaebcbadbdbcaebacbbceebdabdcbbddececccbdaeacbeedcadbbedeaecdddbeedbeaeeaededbeaebdecbdeacedcaaacccccbbbedaccbbdecaabeabedddcdacedaaccbacdbdbabcedbbcacbcbeacdacdddaaeecaeabeccaecdeedebadedbceceaceecdbdadabbeedcbdbccecedacbbeadbccaaedbbacddbeadebcbebbbabbdedbaeeaaadddacecbaebecaddcdabdcbcacacdbacebdcebeebbcdccaaeeccabbecaddbcddccccedcbddeebadeedbdadedacbbcebecccadcbadccadabbadaceaabebcdedeeecdaedacadebdaadddbccdeebdbbdaeeeedcbcdeedcceebeddeeeabadbdaedadedeeabedbcecadeedeccccdbeecaebdceaabababdeacdaadaecaebdebdaeeaeeadccecbcdccccbcedebeeebadaacacedbdbabcbddbebaabdbabaeedcaaacbbceccedcdceaadbacedeaabbecbaeedcdebcdeceedcabbeabcabcabacbbadcbeeeeaecaeecacadceaacbbedbcbcccddedbbadbedbedebebbecceeecaabbbaadbceaaacbcccebcbacaacdbbaadbbacddababacadeeeddbcdabcdbeaacbbdcabbbccadbebddacbbcacdcbdaaacdedcacedbccecceddedabdcbcbadacaccebebecbbacaebceddaecacddeacbcddddbeeeaceedcbadbdcccdedebebbeaaaceddaaccaadceaebbacdccbedcdbcbabebbdebccacdbbdbcebdadebeedddbbdecdaecedcbdcebaeebdcdccceebdbecabaadaadcebccdbaaaeaaedcabcecdaeadecddccaccacabdaadbcaebeebdccbaeddeeeaaddbdbdaddcdbabdbbebbdabadacceecadadaaebeadadeeacdddeddecabcbdbdaadbcabdadeacceeaabeecedbeabdcaecdaadacdbbaabecebcabbbdadeebbbdabdcdacbddebdcbcaaacebcaaaceceebbbbcccdccaccbeebaaeceddeedcdbeeeadeebbeaeeccebcbecccebdcbbdacabbadbcdddacebbeaabcdabaaeaddececdbedaaeecdbbdddbcebeadeaeabacadeacdcbecbcbcbaecdddcbbaeacaaceeebdceebbaebdebabcedbbecedcdcbdddcbeadeddcebbedebadaddcdebdebdaaeadeddcecedcaebdebeaabcbecbddedceddbbbdbcebebcedeabcdabcdcddbdbedccdaacababdccaccdbecacabdacaddabdbcbbbeaeaccbcdddaedeaeceedceaaecbeeeacdecbdbedacebedbddeebbebdbcecbdeeacdeeacbbebcdaddbaaccdecbacdeeeeaecdbcadcaaadeebbbbbcbdaebcbeccdaabecdaadceaecdbbeaaabdddcbdbbeecdccddbdbbdcbbdcdeceeaaaedbadebbaeccaaecadebdcdacbcbcedebeababbdddaaadacbeeeeebbbcdcdebcbaddcbddeebeddbedeedeaeccceeeabebdddeccadcedbcbecdcabedbbcaabecbdaaedceccdaaccddacdedcbdbabbeeddcedcbecabdcbbbcabcbdabcbdcaecbeebccabdbddabbbaadacdacceeecaccbcebbddddcbbadacedcceceddccecbbbabaadbdcdaaccaddcceeebabbeabcccbcbbadaabaecebaecddbcccedbdbcdbabbaedbbcebeedbaccedecdccaeccccdcaddbaeeacaeaecaeaaedcbbbcbecedcdccaeabdbebbabaebdceaacbadaeddddaedddbeedbdbddcccbadaeedbbbeaaebbebdabdcececaeacddaabedbedaabaaadceddbeabcbbcbaeeebabbbddbbadbdbdbbaecdaeebcdbabddedbcedbabbceabeabceebbbbaaaecaeaecdbacaaeaadbbdcdcceddcbaaddcbceaddbccbdaeceaedbbbaebaabbabaecdadbbabbcbbacaeeedebbdbddcaeaaeaebcbdcaceaaccddbcdbbcabeceeaaacadbbbdaaadbddaedceaddcbdadceeadabdeeadadacdcedbaacbbbcdbaeeabcebbbcabccbeeadcededdbcaeddacbacdbbceadebdceabcdaeedaeacebceccbbeeaeceeaeedaecaabebadbacdbeccbbdebbddebcabcdacecadeeceadcddceceecdbaebdbccdbeaeceabeabcceaaddacceeabebaeaeeeebedbadaedeccacaaaeecaeddbaedccdccddbeacaeabebedbaccbdabebbaeeeaaadadadaaadbcbcdeddebabdbceedddccddbdecbabcaaaebccbbacdeaacceadaadddbcbcbbecbaeedadacceecbccdacccdcdaaeeaddceddeddecbaeebdbabacbadbdeebecabcaeccdaebbbbeebacdbcbebeddbcbdedededccbecccceacbdccbeecbbebcdbccdecbaaccdcccbabddcdadedcdabdcbceadcedbbeeeaeebddeddbbbdcabdcdceebdabccebccebccdaeedecdcdaeaaeaddcccebecbbecbbdbdccadeebbbcdedaadeedccbadabeacdccbaedbcbddecaecedabbaabbaeccbccbacbbdbccbedbbeaedcbdbaaebbdaaeabcbcddbeceaebcedeaadbcebacbcaeaaceccabeaccedbebabcbdbaddecdabdceedeacabadddebecccebbcaadbbdedccecebddccbdcacaeecbbedbcbcbaacabdaabbaaeeeceaabdaedebbbcccbacbacaccaaddddabaaeabcdccbdaabdedeeebedaaeececebbeeeaededeebdcdbbcabeeddbedccbeaebcbdbbdedbbecbcbcaaeaaadacbabaeadeabcccbdecedbdbaaedbccabddeccbededcaaaecbddceaaedabeaaadcedbbebcbadcdaecbeaabdbbaacdcebbaeaedcadbdeccaecdcdbccdbdbdcbcdceaacbdadacdcbccaecaccccecdbbdbabbecdebabdeadbbacdaecababceeabacbbeebbcdeabcadaebbadadacedcacceeabdddebbaaaebdedbadcbdaeadbcbcdcdbbecebaaecdbebecbbeccbebebaacbedebbbbececbbdddeebadebadcababaebecaeadeccaecbbbceeaaddddcdccceaecedcaabeedcacccaacaeebaeeaabdcbacbdbbdbabbcaebaccdeeaeeeabeacdeaedddeacecacaaebcbeaaaabdcacdaeccdecdacedbeceedddddcdebdaddecbacaadedaeceeabcedaedabcbeecbaeaadcbbbbabccbbbcadeebdcbcdddcacccebeccdbdbcbdbaccbacdaedabbceedbadcacabaebadedbdecaecadeabaaecaddcdbdbaecaccadaadecbdcdaaecbbdeadcaddbbcbbcddcbbdaccecdadaccacdbdebcbebaedeedbbeaeeeaedaaebecebcabcecaebacccdbcdedabbdbbdcbbcaccedbecdcdabebaabaeebcaedabbacddccddbebadebdbacdbcddaebedcddcbcbebbdadceaedacedbbbeeecaabbdaaabdeccbadcabcbbabbeacadccdaeebdcaceabeccdcbcadddeebcbabeaceecceddacedcebaaedddacbbbaeaecbcadcacceccebccdeddddeabaebedcdeecdaacccacceabeecddcbcabdcaeeaddbcecbedaaabbecbdbbeeebdeeceacedceacebaecbddebcceddadbcabacdacbcababaeaacccceebbdebecaedadaedaacceebebacbcbddbbaabcceadbaebcedbccaecdecdeecdaacdbcaaadeecdcbadabaaadacadedbecdbcaccbababbecacdeecbbedeaecbaadebadcbbecdedbdeddadbbacadaebbdaadbbcbccbceabaecacaeaeaadcaedcbeebcaabbdaeeeebbcccdaabeadebacbceaacccdebeaeceacbdadbeeeecedecbdbaaaeebebdddedecaaedbeecadddcbdbdbacabbdeeeadcbddbeaadbebeaebcbbdcadccaaadedaddeebcadbaaacedeecddacdcabebeaadbcbdaaebdabdaadbabcecbbccedecccebcedaababedceccaceaedcddcebddeaaddaabdbbaeadcedbcacabcbddeccbbcddeebbaeabeaabebacceddeaadaebceedaaadbbacbbcaaadccbadeaccacecdedbacedabecedaebdaaaedeabebadccaeddacbbeacdacebacddaaaaddddababaaccaccadcadebdbbdbaeaebccaeebbccbbbdccbdbadcabadececddcacaacbecadebcbeadaacacbcddceedcddeccbbdbddddcaebeaddbedaeeeadeacbceabbeebdeedbbbaeeeaccccddabdddacebadabdbecaedcdabbbdccdacaaaedabdaddcdddededeabeddcdabbacccccebbacebabbdaeecebacaadacdaddeeeebcceebdcaeebbbcccabadacaeebcadbbddcacacababbbcbabceabaceabecdceaedabaebedbaaaaeaedbcdbcdbaebcdbbcccdaeedeebdbcadcdeebbaebdbecceebaddecebbcdcdceddaaaeebddedbaceaeaabcadcaacbbecacbddaccecedbcdbacbbacaeabadcbabdcbaeabeacebebacbcbecacdddddaacedddddcbcaeaebcaccdbacbdcaadbdbbbbbacecccddbadacbdcedeaddcacdbcabdaccebcdcacddbcabecbbddecdcbddecaaedbabdaabaaaacdeddbcbdcdebcdccbaddbededaabbacdadbabbebbedddbeebbdccdaabebbadbadcaacdbeebdcaeaddcddbcacbdaeabdabcecaeceaaeeedddedddedabccbeeccadedacadcecacbdaddcecbaebaddedccadebcbbabedbccbabaadcdaccabccbeebadabcddbcececcadeccaaedaccecbcbddbeeddeeedcbebbaceacdddbecdecbdeabadadcccabcccedcccbcbbeeacceaeaaccbcbbddddecdeebadcbdbbdbbddcecdcdaedbcbaceddcdaeabdadebbaaeeaeaecaaaedabedcaaceeccccdeecedeaabebededbceeaedabeaecaaeacdabcabecaaabbdeededbcabdedbcebacbbebcdbcbeeadcdabceaabebecddbddcaebddaceadaebceaccbddccccbbedcdadecbacdabccededcbebabeddeddcaaaebeaeaeeeeeacaacaaecbebaedecdebeccebdddcdabecacdaeccadcceadabcacbeaecccbecebbebbcdeaacadcddbcbddaebcaacadedbabdacccebadaaadaeedeceedbbddabcdacaecaacabebcccaebdbcaacdaaebddbdaebcdedecacacdaabcceddbbbddbebadaecccdecbdbbbcdcdcdcdeaacbdcabcdbdbdcecbdddabeddeebdeabcbdaaaaecbbbcebbaeceddabccebbbcaeaddcedeebaeaadbdcbddbceaddeeecbeedaeecccedebbaabcacaecbbaeaedbeeeccebbeededbdeacbccaadceeaccbeabedddeccedcaddbbcbebdcadecacebbebcccaeacabadbebeebbaebcdbecaddbedebaaecdbbdeaabbedeeeacebdceacbebbcadcacecedcebdeeaaaeeaabeabcaceaaecbbdbcecedaaebdeddeaebbeeecbbbceebdddbedbcdaecedcbacaecdcbbadcccabbaabbbceddbdabdadaddccbdbaabeebdddaaeadacdadabceaaccebebaaaebaaedadaadaaddcadddcbadeadbcddbdbcebbabcdbebadedcedadccedbccdbdbbaedadeabecccccdceedceacdddcdceadcddceeeebbdddedddecbadacebeaaedebccdccccdebadcadabcdadaeaaacdaccdacdabdcbaddadbbbcaddbdeebbeabeacadaccbcbceacccdbdccdcbaadbebdbcdeabaacedddcbdaaecdcabebbeabcebdbaaedcabcceddeaeecdedbeeeedcdeddedcddbaadadeaabedddbaaaacdecadaddbcaccedeaddebddbeedecaecbebddccaceedcbeacedacbdecbcaabcabdaedeededbcebccbbbbcebbeedbaabaddddadaaddaddedcbebddbadbaeecbdcddbaabcabcbadcbcdeaccaacbccdcadcbabbeeeeabeabeababddebbdaaecbaeebdbeacabbeeaccddcdbdaaaccbcaabdacadddebccddedeceaedacbaaedbebeaddcbaeeddabcdbdbddbdcbdeebbbebaabeecbadbbbebeceaebcaccadcaabaacdbdeeebdcaaeceeaaacbecbbaeaeddbdcccacccaccbaacaaeccbbebdadccdaacbabcaaacdddcdbacdaddaeaddcbeeccececbaebcccebbdcebeeecadaccdedbaeeebcdedceaedaeecdacddbddecaeeaeadacacddccbaebcecaacaabdcdbbbbcabecdcbccdddbadcadbeebbdbdedbbdccdcbabbbdbaedaebecbaedbdbddddabdecbaaaadcabbdaccbdcaeaedebceddcbcacdbbdebdbcbdcbdcbeabcedeaeedeabedaacddbcdeeecbccceaeabdebdadbeeadbebeceeebeebbeeaedeecddeecdcecdaebccaaeaabacaceedacbaeebacabcdcbeeeebebdceacdbbdcaabbccccbcdbdbecebcdbebabbeedbdcaccadeeedabdadbbbdbbdeabeebbbdebeaccbdbbbaebebbcbacabcdedadbbbaababcceeeedaedcbdaedecebadaabcdccceebbdbbedcbbdadddeaaceceddbaccededaddbcacbccbcaebcebcedabcceddbbababebaeddbdcdacbbdaadbaaacccddedebcdaeeddcedbabaacccecbcdddaeecebacccdbeedeecccaeacbadbaeacedaeddbbddcceebcabdeaeadbecbdbceabbccabacddaccbcabaccaccabddacdeccaaeacecaaaabadeebdccdacdccecabcbaaccaaadeeacdeeeaabbdcdabcccabdaadbccdbbbdacedadbdaabbeeeccddbbedeaaadaededdcbedbcccecaccaaacaddcebdbecbbabdeebccbebbbcdecaeabadcaabebedaaddebccddeddcecbbdaacbddcaeadbdcecccdaebcbcbeccdebcaeacabceddddcbbbecbadeabebdeedeadcaebbccdcadeaddbcdeaecccabeebbadbcaeeddacbdecaebaadecbeddeeeabbbedaddcebbdeccdbaddcdbcddedbacebaecabdaaddbcdebbbabdebbccaaabbeaaabdebdeacbebddadacedebbdadeeaabbbedbbdbdcacbccecbcabcceadebececdccccdaabaaabdcdccdbbcdabdedebebceeecddecbadcadbddeebccbabeadbaeaadddcabaddabbabbedbecdbadabdccaeedaadecbdaabbeeeabecedeeadbeaedeadebeaeeeadaadbabdaacbbdddbbedcdebcdcdccdeccbceddabaaeaceacbdaeddbaebdceebbcdccdeacdeebedabddedcebddccbbebdaaacabccebadeacccdddbdeabdddcabcbabacdbbdbbedadececbeddacddbaaabbeceeddcdcddcaccadaeedbddaddbaccaadaacdeecccaabdbedaedbecadbcebeaedaacdbbdbcbbddaaaebdcbbacbbdacaabdbceabdeebabdbdcbdddbbcebbbccccbbaadeebdbceaeeacdbbdbbabbaacdbcdcdcbbebbecdcdcbcbbdbacdbaecaddeddbeaccbaaacddbccaabbacadeeddcbeddbcaeabbdbcddbdabeedcbdbacbaaeaebabbddbdcbbecdbcbcbcebaedbdcbdceaeebcceabedeeeedabbacedebecebabccdbaceeededcdedcabaceddbbaedbedeebecbdeddeabedeedecbbbeacebacccdeedacadbbbeaceecbebdadabcdbebddddbdcebedaacebbeeadbdcdadbdaaeadebaeadcabbacbeacaceadaecaaeaebcaedadacaabedeababaeacacebccccbdaccbdcaebdaeebcedceacbdaacebceeedccaccaeddbadcbcaaeecdbedbbdeacecebebaddaadedaccacaaebedecbbedabeabaddaecdaddcdaacacecbbcdbcdecaecaceccbaeeeeddcddbccacbebcaaeddacbeaadebbcaebeedddebcabebcdeaababbaaccbeabbbeccbbdaeccabedbeeddcacdcccbadcbacdeeeecddedcbcdbbbbaadddbeecccecebbccbbccebcddadeddbcabedddbdebdacbbcebccabaeaaecedbaaeeacecbdecddeedecdcbedbbcddbbededcbceabdabdcebadacdcbdeeddaaddbdbccbcdeecddebcaaceecdecadedeeacacacbabbbccdcabbcabedcecbdbacccdbdadabacecbbbbccabebabeaccaedcdceaeaebcedbbbdecbbecabbdaedbaceaedabeadabbccaabadacacaecabacbbdbdadeabbcecddcadedaabbcdbedcbbcaeddebabcaddabeabecbaebccccedabdaacecebcacedadccbdacacaeaebcadccedceccbecdbbedcaeeecedeabbcbcdceecaeccaebebedbbbbdbdeedbedcdebebbeedbcbeaadadceecccaadaedacceabeedabaeddeedecaabbbabbcbedbcaadccebebbebacddcddceadddbaeebcbdccbaebdbcddcaaeeeddbbbbeceaabdcaedbaabceeedbebbbcbebbdddbdcbeebaacaeccacccbeaaadcdddddbddedabeddaebbabeeacbaddedeaeadddcebbcbedbaeeedbcdabcebabdcdeebabdedddabeceaaecbadecedbeddcccbccddabacbbebcaabceaeacecaceebeeadebddeacaedbaaebbbaccdcdaceedbacadccedadaedaeaedceadbbedabeeebdcbadabdedaaaccbcceacbbbbaccdadceeaebcaababeedcadecdedaabbdebadeececcddcdcbcecaacddcddceeeeeccbcaaabbaadddbbdbbcaaeabddcceaeedbeabcbcdbeddbccdcebcccebacabeeebbecededdcdeadadbaedacbaaecaecdebdabeadacbbdacceaededcebbebbdbdacccaabacdbceabcabebedcaebecdabcbbaedaedcaeaaeddbbcabcacbbacdaadccadcbcdcaadddedaaeaacadccacdbdedabbbcaceabebddaacbebdecabdaeebbccbcbcabacdadcaaddcbcbdeabbeedeeacacbcdedaeeeeaccaaddbaceecbbeaaaceecddadabaddccbbdeacddecddebbadceaedbbaeabaabebcacecdbdcdebccdcdddcdcddcdeedeeacccedcbdbcbdeabcccbdecbeacdceddcbdbecebadbbbeecaeebebcbddceacdbdcabaaecdadcbcecccbcdddebceaaacbbaebcedaadcacbeccecbcbedacabacbccdbdadcceaebcccbbbadeabddcadaacbbdeaabdcaaebadbbbaaeacdbedeadcdacbebbbeebccaddbadddbddddeeccabcceeabaaceacbccedcbcdbeececadbedebceeedcdaabcccbceccaddbabeaabdcabdcbaeaadbebbedbaedaadeedcabdceeaeecbabecdaaaeddbaceaecccbdedebaaceccddddebabebcbccbcdcbabeaedebcecadadebaededdaddcecedcbecabbeddeabbabedbbaddeecebbdbbcccedcbdbbbaeeedceabceeeadadeabeeeedababdaabcbccbacbcecbaceabeabbcceabdddeadddbdbedcdbaddabbeccbeeedcdacebdedbedcaeacacceddcacebecdcccccceadddcdddcbbebedebcdebccdacdebeeeadcbbaddcbdcceedbdbadaccabbdedbadeaccdeabbdaecabcaebcbeabbbbeecccaebbeeebccdbccbdccaddceadcdeaadaaacccebecbadebcbdcebdebcabccaacabedbaebcacbddcebedbbabcedddbbdbebedcbbceacecebdbdaaceaddadddbbdcceeaacdddecdcadcbcdbaaadecbbdbcdaebaddeaeaeceacccbcbcebeadccbccdedcdcdcdadccaccebceaceeebeceacadccebddccebbacbbaaacdcadbdabdaedccdcedabdddebdacacbaebcaeeaeadeaddabcdeaaedadbaeededbcbbeeaceecddacbeeceadaedcbebcdebcebbeecdcecadaebecadcaccdacadaacbcdddccedeebdadcceaeecbabdbedcebebaceaddecedbceebaebecbeeaaeebeabcadbcbcbecdabedcdcabddaddcbdbddcbeaeeaccbdbddddacdecadeadeecbeaabeacaecacddbaecaccabebbadddcaeceaeecdccbbbdaedaadccccdbebcbcdaeaceeaccddbbacdcaabdecdbbbdeabebebbecaadbbdcdedcddeabcacbcddaedbcccdbceeabbabcabbcaccbeccecdedadcabbccabebbeccdaceddbdceacedddcbcbacadbbedceebedcaaecdedbdcdeeaddecceeaadbdaaebaaedddaebbdacbeeebededbbecbcbaecccbbaadbeeeadbdebbeacbaecdcdbaaceebabbecaecaadbbeabaaeedeaacccaedaecadedceabccbacdadabbecbbcdcddbebbbadebbccdebbeccbaedaabbaacdadbbacdabcdbcbbbaceabebeecbbacddecdbaaecedbaedcdaddedacbeddebebccabccedacebbdbadbcbbddbadeacdeaeadeaaecacdcbbccdcccbeaaaccdaeecedadceabcccadbeeceddceccaedabdaeecdbbdaceccacdddcecaedecbcaeaceaccaddabccccabacbccdadaeccabdcccdddbccdcdbbcaecccbeaaceebcaadabcaccaecdabddddccaaeaaaeebbdcbbebccabedddeaadecabbdeecccdececeadebadadbaeabadcdcebedcdbcdeaaaaddbeeaceabdaadaacbedbccabeddaceeabcadcdceaeeedabacaccedbcebeedeccaaacbeeccaadbbcdbbdabeddcadcbaaeedbdddebbeeaabceabeeeddacdbbaeeeecbcdccbdbbbecadbacedaaadeccaebdebaacdebdcceccaaacbbdbdcbdaacbbbeedcdddedbeaceaeaabeabadddbdaccccacbecebbcdebcaaeecaadeecebaedaeddbaaadeebacbbdaebcbaaacebebacecccdcbcccaaeabeaaacbebbdeecbdeaadeacaedeccebbbedbdddcdceadbdceabbbdeaaebdbacaceeaabeeeebdbacbddbbcaddeacadeaeaecbaadeeeaeaeabedbcccbecddaecbbebdeabbdaaaddabcebbbdcebeadccdedbbbcaaebaecceecdcbccaadadaabdcaaecbaebedbbecabcbcbaadccdeabacdbeceebdbdbdbdcecdcaadbcbdadcacacabecadeadbebcadecaddedbacebbdddbbeacccebcbcedeeeeadaabedadacbabcedbccbabbabbcbaeebdcabbceaccbbdddbacccddccacdacdeeccdebdaadceeacacecbceccabdaabbebddeeceadacebebacddaceadbedababbeebbbbbeedceeaadaceddbabcadbecddebddaacdecdbbdcbaedbeecdeddbddbddbeeebeacbdbbbeacceeaedcbeaabcbcaaeeaabcbccbbcbdbcbcacebebaebebcdbcaccbbebaaaeddcbbcaccaebeabbeebbbbadedecbdbbadadbdabdecedcabaedddbaaeaabdcaacdbedccbdaedcdabacaedaceedaebadbaaaeccbecaadeccdccebdaabaaacadccacdbbeaddccbadccdbbacecccccdbbcbeebbcddecddeccdccaeecbdebbbeaeedeabaecbcaccbabaadaabdbeadabaceeecdcccbdaeecabaeacddaaebeeaaaadeaeccdddbdabdebecddbbceddeabbeecddddaebbddaebbececcceebeedbbcacaeddadccdeaeaeebdcdebddbdcdccacbdcccdeedcbceecdbccbbbecabdeaedadaabcbaacdbdbecbecbceecdacaddcbaabbebbaabcbbdcbdbedcecddaceceadeabaeadadebccdddadabbcdacedaeacdadbabcebaedcceddccbdabceaaceecbdbedbaeaaaeccdcccabdceebbeccaabbcdddbaddddddbedbadcdecebabddadebcbdbcdaececeacdbbebeccdedebaecabeadacaeddecabccceabaabdcbdcadbbddcdaddcdcdcaadccecbbcbecaededdabbdcccaabdcbeaecebadadebdaaeaaeceeddecbdecccbcbaebcaedebbcaabdceeaebaeedacbcbbeadaccdaeabcbbdaadecbbcbcccbbdeddaaadaaacecbacbdeddcbaabdcedeceaebccaeaeeebdbceacacabbbdadcaaebbbcdbaecebdbedbdeabeaecdaebeaeceabebdbcbbdbacedabcdcdbeacebdecacdbedbeeeeeacabebaedbcbbcdeedddaacaebbbbdacbdbbebbdabbbbeeddabbeeeadeabacdacdadddeedebccdacbdaaebeedeabebedbcbcedebacbabeeeaabebbcbcbceabdcebcbdeeeadcbdedccaaacbddeccebdcdcadeaeaeeaeccdedaccdebaedeecadcdccebbaccbccedebdebeababaaaecbbbbbdbdedbcedaecddcabbaededaccdcaeedeaabaaeaabeedcbaddeaaeebeeeabcbadacbcbbbebadeededdcccacbeaacecdecbeeaededecbecabedaeecbedacacbcdeeddecabeededcaabacddacaecbcadaceedeebeabbeebaadbbaeeacbbabbbbcbbdcacdaeebeadabaddabdceacaccadeebdddbebeebddbbebcadaeadaaaeeadddabbbdbaadebccdcebaceeeccaeaddeeeddaabbadbcbaddadbecaecbaacadcadabdecedabadeedaabbccecabbebedcbdeebaababbddecbeccebeebddadeedaaeaddccdbeddaaedbedeededbeebbcabbdbdeebeadbdcdbaededdccbceaabcabbddaebcbeabaedbbdeddebedbdcbbbbaedebeedabdcddddbebdaaeebedaddedbeedabbdcbedeacaacdcbbbabebebdaddbacbcceeacbddbdddbcdcbadedeccbadecdabcbdebdeadedbdbbbcceebdadbaeeadeedbccccdccdeecaeeeadcbabdcacaccdeababceabdbdaaadbadeebddcebeebedcaaeebebdabadaacaedcbddaabcdadbecbbdceceeeebaedaeaebdebcaadecdedceabcdbaadcceabdbaebbdbbceccaeadbededcddaceededccdeaadbdecbadcebceacdeceecdeeddcdaabcadabcebdbaadadeecbeaeccdcbabdccaeaccdaedbbedaccdebeaedacdeaebdddacbaacabbeccadbebddedbadabceacbdabdbeeadedbcaaeebcddeddcbcbcbebcdbeaecbdabbeeeeacaecaaebaccdebbabdcbcbbedecbbcedcbeebadddacbdbddcdcdbddddebdacadbddacbadecaadacbebbaaadaccddabacbacdccdbdaceeaacdcdcbdadaecddaebaeaeddadbecdbdeeaaacadeaceabacbcbdcdbadaacbbbdddeababedcabaabdeeaabbdaacccaadcebdcddacabeccebbccceeabacccdeceeddbdadeebbdbdcdceeaccddddbcebdacbedbaadacbeabacceabdaebabdbaceabbaceebddcedabaeebaacceaccbceedccdbddbaeababbdebacebcacbedadcaedacabedadbbcbcbbaecbedcedccdcaaaeabcabdbdbaceacbbdedacebbcabbceeecabcdbaabbeeeabcbdebecdebdceabcdbecbaadacacabbeaadcaabcdbabcddeedbeccecccccceaecacaedbbcdebeebaaaeabaaddbbbeecacabddabbadceeecaaebcebabedbdeeeabcbbacabcaacdaecbacbcbaadbdadbccadcaddaeecdbbeaaceaecbedcbaaedceacebabdedddaeedddaddcbabddcdbdeaadaaabeeeebaeecddcacecadaddabadebeabcbedccebdbdbcdaaeeeccbaabdaebaaadbaccdeaebcecaeceaeedcdbbdcaecbeadababcadabebceababadaeebeaddeebbeeabcdecabdadbcbecaedebcabedaccabdddecbeedccbcdecbaceaeabbebaeeedeedeeeedaabdabbebbedebeababddabebcdcabaacdddabccdaecdbabcbeaedaebcbcecaaddaeaacebddbdaecedcbdeeacececbdeaedcbbecaccaddeebcabdebcaaeeecadabbeaacbeceecbbcaabadabbcbbcbcacbacebcbabeabddeedddaabeacdbdcaeabceaeedcaaeeaaecdcdbbadabedddcbcbeeebbaaeaadbacdcdcbbeaceadebdadaeddadaeccbecbabcaaadadcdbadbebbdaacbaeaabddaeeabebdacdbabbbbcabdcdbaaaceebcdecceecccabddccdcdebbcdecaedccdeeacdbeacbddeaadadeebaeebabccacecdbcadbebdacceacaaecabdddeaccbbeeddadeacbcacdcbddbedaadebeabeeadccdccbeaeeddabccdeaaecbdedbcabababcbdaddaceddbdbdbedcebcccdacbcbdbcdbcceacdecdbabbbececdaaeddedaebaddecaaccbeceabceaceaeaabcddbeeeaeebcaaeeaedcaedacacbdebcbbdeccceaaeccdcddcadbbbbaddeacdadbcdcbaaddbdbacedddbdeddcbdeeebcadbbcdaabeacdcebbacbeeeeccbabcecaaddbebbcdcbdbceaaceabaadbedceaeabababebbabdaccaddabcdeeeabacdecbceabdacdbbbeadbccbbdbcebabeebccaecacadeedbdeadbbdbbaeacbebdececbeaceceeadaeeeceaacdbbbbdabebccaacccdbcbbddceeacddebeeacbaedabadcabbceeeececacedabbaeadaacacacdcaadeadaadccdacdccdabbcecdbdeceeeaaeeeedbcbbbdaeddebdacebccabdbcededaaeadacbdeddcebebabbeddbcddedaacbcabaeeacdddeebaadaedadbccbeedecbbedbbedeaeabaaaabebaccacadddeeabadbdccabdebbecabcdeecddbcccbecbdaecacbbddedebeebbdbbbbddeaaeebdebebdceadbaedddacdbcdcdddaaabaecedadcaccaeadaeeebabcecccccdadcbebdecdccddbbaddaedcdbdddacaacdccaacbccacbcbdccdcdeadebcebadaabdaccbeabaacbcbadbeabbcbeebeaaeadcbedcceabacddadcceadbcebbccbbccbbeeedaecaaccdaddadbbcabdcbbdedacacebecaddabeeddaadbeeeedbecbbcaaccebaaabdbdebdeabdcdeadbaccdeebcdaeceaddeaccceddccbcbbbecccadaeaacddacacdacababdaecaccbebddcadaceaeaeadccbdebbedccbbdaeddeecdddcadeaecebbadcaddaeecbcecabeeceaecdeeabaccedbebbeabcabcbeaddbcecdbaaaeddebcdbecceaaaaaceadceaeadbecbcbcaadceeebbbbcbbeaedbcaabeabeecccbabeccbaeacdedabddcbaadebecadceddcebcaaebceddebbcadbabeeaadceadcaceaaaddeedbcaedecaaebdaabbbbeaebadaddaaaeccbeaddeabbaddaadacaddacdddeceeecbbddebeeeabbbacddbcbaedbacdbebbcdeecbeddebcbbbeaceabbadccabeacaeebdbecaebcaedeeaacbaecedeaeaddedcddcaecbaddbcedbaceccdbacedbeadbdedddeeeadbedcedbddddbabbabebaeebcbaeeddbcbdcdadecbdebabdeaaeadbbcbeeccecbdaccaccdcceeaadbeeebbbabbbdaeabcaebbbacdcededecaaeebaebbeabddecadbaceecaccedccdceaebddddbeabaeeaddcaacbdbecdaedaaddbaaeeeaaaabbadcdaaddedbebaadeadeadeebedcaaebaaaaeeddcacedbccdcdeeabaddbeeaceaedeaceaceeadeedbeedebecccbdadccaebeabbbbcaedcbdbeedeaadcaceccbeaecaeaedeedbbdebcebbecbeebadeebcdeeebeeaeebbbdedcaceaededbbabbaceccbcddeebcbacaedcddceaedbcdabbccbccbabcdbadaeadccbaeadbaebbbbadbddbbdcaaaeebebbadaeedccdbaedbabbadaedaebcedeaccdaccbabebbbadcacbdbbbaddbbbededaabecadbedccccabeddceecccbcaecbddcabeaceadbddedecddcacdaedddacddbdebaecdddcadabdabcabbcdcadeebdbbbadabebbceebabddaddbcaabdbcbebcadcdeddcaaaceebbedaaecbebdadecabdcadadebebacadeaeaaabbacceacacbbeceabccedeaadaddebdecbeeceecaeebabdaecbcedaeedaeacdccccedacbaebdbbdceceeceecdbeaaaadbacbebbabccbbdbbcecacceaeccbcddcedcdaeeeabdebdcddcddbabebdddadaeaeeabceeeedcdddeddeacaedacbbdcaeccbcbbedaadacadcbecddbbbcddcbddcabaaaceaccceccdedeebbeccacbadbeeceebcaebbadcaddcbedcccedecdbbeadaacdabadacaeaaaaeaecdebdcedcbeceaeeedececebbeaadbdbcebeebbaeabbbedbccaedadceeebdaacdbaadccbceccccddbdccdcbebcbbcbebcbeaaecaebbccabdccadedaabceeaecacaccccebaedaddacdbdbeaaaaecacedcbacbdcbbebeceedccdbdcccacabdbaaabeadacdeeecaaccaabcbabaadabbbecbaebbcedaabdadcabdaebbecdcadcbdebddabbeccbdbabcbdadddceaeabdaedeceabbacecbcdcebdbdabdabbdacecdcbbdecededbacbbdabdeebeeecddbecbdedecabaeedcaacdcddecaeadbeacaeaeacbcaccbdceadebbeeedbabdadeedeeaecacceabcacbadbdbcaeaaceaccccbeddccacdcbcdbbbbceaddbebdcccaebeacbaebdecbdcadbbecaaaabacbebaeecacceeeccaeaebbdcbbbaeddcbecdeeebdedeabcadccddaecccabbdadccceeabedbabbebabebcdeaedaeedeedeccbaddebcabeccecbbabaacedebceecdbdaeaecdbbcadcccbaceedbebababbedaeaecaeaabceeddceccaeecaeebeaeadbdbeebaadecdbaabbcbceebbcdadedeeedacdceabbddbacccceeabcaddaebacdcadeabdebbbbacedcdecadcddabdceadaacaaeaeabaecaabdedccbdcccbbedabadbecbeddeadddedddcaeaeadbadecabeeebabddacaaaacdeededebcabcdccbaebedeebccecadddedacbbaaedbabccdccabaccccaccacadcaebddedbabcaeaaaeedbabbccdcaddecdeddabeecbecbdbbecebecaccbedaaebaccaacaedbcceceadacadeaeebbccacdcbcddccccdabdaacaebebbbccededdecdceacbaddaeadcecedbbaccaabdcdabddeebbbababedbaabeeeeeeccdeadbbecedaaabaaeaaeeadddecdabacdeadeaaccddbecaddbcdbadbbedaeddadebdccdddbdceadcaedadaeaddaeeadeedebadbebbedabcbcedceabdadbbbcaddebbdebcbdaeadadbbbddcbcddebebdebbaecbccebeaacecaaaededdedbaaddbcbddeaeddddebaddebebbdebaeebeabbbbabebcacabecbbadbabcbcbaecbbaabeeabcdedbaddecdbbeeebbeccebeaebecdcadacabacbacccbeeaddedbdaccbaebccccdbcccecdaacbebdadcaadbaddaccadadebceeaaacacedbcadebdeddcabccabbdbdccedbadceaaddeddcacbceddaccdaeacbcdcacaccddabcddaabaeaecdccabcaacccbecddcceeedbdbaaacdaebbdaccaaceccbddeecadecbaacdeacdbaecccccedbccabcacdbbbbbeccbcdedabcbcedaacebbaddcdaeacdaabbbbaeeaddacbedadcadebbebcddecdbcabeaeaadceccecbcbabbdcaaceabebcedcceabeceddbebbebecdabaebcccdbcbedcacecabecaadcaecececeeaecbabaacdeeeeacaecabdabdaadeebaecdceeceecababbbdcdadccaccddeabcddecacbcddaaaadaebecdbebbcbbdaacaddacacaddcabcaceecdbbcdeeddaaedbbabcebdaedbbaeeaeedaeaaaedcdbdbabaccdddacaaedabddacceeebbcababddbacccbcbaceeaeacbcbaeeccdaecabacbbcdceabcebaabcecccedbcbbdecbcdccababeceadbdcbecadcadcdedacacadcccbcddcaacdbebeecbdaaceadacddecddcecbadacbccceeeadcadcabecbdabecabcaaeeeedceeddaebaaaaacadccebaeeedcabdbccabedccbbdbaaecbddedcceccbecabbeaaebadbdddbcdebcdbdeeaababcccaeaceeadebbadcececabbecaecddcdeaacabedbdaccdacdccdbcdaddcbcddccdcceeecadebcddccadabddbdcaedadcdddbbbdccadcdeebbabdebbdceceacdaaeacbeecaedebcbacbabbceeeacebdcddabbccddbebbaaabeeeddebcceaeeaaedebaeedcdecacdbabbabdcacbcbadbbabcbbecceaabceddbeceeeeebdececcaccdaecdcbdaadcbcedeccadedcbecbedcbcdadbccaaeeebbbcbadeabbeecabbabcedcaeeebbcbaccbbaecddebdcbdcdedebdabaeabeecdceaeecdbccbbebaacdbddacadceceaabadbbcaddccdaaeccbabeebdcbccaaeaacbbccecdaabcccbeeceadbbacccebbbeedadccddbebadaabdeadacacdccdbdebeaecbdbaebaecddbeddaeddbdbadcdcdadddcdbddbeabeccaaaaddbadccbdcdddaeaeeaacceaccceddaddbcbadcdeaeacbecdeadcdbdcbedecceeacdadcbeedacdddedaaaccdeacabbeeccddcceeeedebddaadcdbaccbdaecaadaacebdbedddcdaebbccbcdaaabbddbcaedbbeebbebaccbcbcbaebdcceecdeeeecedceceadacddaaabebebebddeabdccbbbbbecdcebbcdbcccbededcebbbdebccaaeeabbbbdabadbbaadaceadbceebcdebcceaebabecbadedcdabecdbbcdebeeacccbcdabbaeebaeddceceacdddabbdbaceeacebcbddcecedbbebaceccdbbbcbbabdeeddddcadccccdbceccdeeeddbaadaaebcbdacdeeaccadbcceaabbabebcbedbeececdbcdabecacecccacedccecaebcabbacaeeddaebeeabaaaacbddedcebcadbacedebbdbcddecbbadbacedecceebebabcacdbecbeadedebabeabeadbaaebbeacddeadecbeaddddcbecdcebcbbacbbbdcdceedbebaaccbcebbdcdedaaededbcbeedaccaabeccbdeddecdddebaaebdeecdabdaacaadbabdbdcdcbccaacddeddabebdecaaeeddaeaccaaabcecccedbdacbbacbcbddaaacbeacdcaaedcadaadbebcdacbbeeeaebecbeecdadddbbdceabaeeeeabeddbbcdbedcdbedeaabcaeebadcdceebccbdccecaedccdadbadecbcadadeceacdaabaeabadbcabeeababceebcecebccdbcbaceceebbeceecbdbcadcedbbdbebdaebacebaacdceeccdbbeeabeddeadccbbdbbaeeceacccaabbecdbecebacebeececeeacaacdaddccedbedbbdddcabecdbdbacacbebacbbedeebdaddccbcabaeeacdbaecdecabdbebccedddacaacaedcceadcbebccdabddadcabebbbecceedcddcbcaaedcdaccdaddaddbebdaadeeabeeadccdeceadccaeecbdccedcdddeaebcdeedbdeaedceceebedcddcaceeeabdecdadcaaaecbcdbdddcccecdaabcbdbdaabebaddbededddbcacedeccbcdbddbcaeebdcabeccaaababbcdacaaaccbaeaecceecedacbeedebcebcaadebbdadcabcececadebdddacadeeeebdcaeecbdadadbbcdcdeecaccbeebbdeccadcbeedeeeececdbccbbdbbcecdeebdeaeacedabdddbccbcaeaaadbdebbbbdeacebdedaddbcbaddaaadecbbecbcdaeeeaeaddecaceedbdecaeadcdedbecadebbbccdeebadabceadacededebaacdadddedeebeccadbadebacdeabbebadbcaadbcbaeadedaceeabaaedbaaeecbcedabecdaeeeceaddbcedeacdeaeebcdbccaaccacadadeaddcceadebbcdeaeeedceceedcecebdedadbdabeccbeedbadddceacdbbecbcbbddedbcdebcceacbadaccdbcbbdeabbaebbdceadadcceacabceaeaeaacbbabeedceaadcadbccccaeaccbccbceebabaddbcccdeccdadbaeaaccdabdaadaeddbeddbccaeaeaeccacdddcecdacebadedbbadccceedceeeaecdeaecddedabcbededaeaabbabbaddcacaeeaabcdbebeccbeaeabececadceecaccbdbbdccbadedaaddddcdadebadddccbabdacdedceddbaeaeebaaeacedeeceddbcbbbbebcbedeecabbbbdabededddcabcdaeabaadeeeeeedabadddadaaabdabbacbebbcdebaccedeabaeceacbecbcdeabbacdddeebebababadeeadabdbcceaaecebacbdbebeccccdcaacbadbcecddeeececbddcaaacbaabceaeaeebaceadadbbcbaabcedadaacedeecceeeeaceeaecabbbbdeebecedbdbadabbecdbadbdaaeadbccdbaecadcbadabebdddcadcbeebdbbbddcaedbabbdbbeddbaeeaaeaaccceaaadeabeeaaedceeaececabaaecdcbedcdacbcdbebcdbcccebabebdebcbbdedcbadbddccecdcecebdaeaedceedecdbdcededaeebacdcccaadaadcaaaacacabeaebcbdddaccbadcacdcdabeaedbbdaccdabbcebbeecccebaeadadcbddebbbccddececcebbacbddabcddeaaabeeadadbbbaccacaadebccacbabbccaabaaebaeadcbabceeccbbebcccbddabecadbaedabebbddecdcedadaadaeaebcbadddbcecbcbacbbaecbecbaeecaebbcbcbadbbededeeeddabcaedbebaebdebbcaedacbeaddaabacbdabebceebdaceceacccbbebacacdebbcabdaaaadadcaecaeecebabcdbeddddaaacbbbbeaeabbebecedecabaeaadbeeecdbbaabbbeceaaccaabbccebeaddbcdbedaedeaeeccbdaedcdbcbccddeeedccbdaacddedbaeeeeadcaaabdddadacccbbaabccccdedbaacdabebeaadaccecccbaebccbbdaddccbaececacdbbcbcededaabebddedecacaaeceaadcecbdeeabdecdddaddccabdcaeccaebcbccaeaadcbddacedddddedcaaaeeeeeccabecdedacbeaadddeebccbdbeddcbdceabacecebebeeadbeeeacdbbdecebbdbbddcbceaccdbcbbebbdaccebbdecbcaeaeeccdeaddbdedadbcaedcccbbcedcdecbcccaceccadeedbdeacaddcecbbebdcbadaccccbdeadabceaeebbbcabbaacbdabdaabbababcdbcebddcdaaceaaddacecccdeccaedaccdbedabacaddeadaeddabbdeacadadaadddcaccbbadceaadabcedeeaeaaadcbcdceedddddddeedecabcdcbebbdeedcdbecebebbbcaabcbdeababeecaceacebccadaadedbaaebdccecbbccddadadeaaeebbbacaacbddbddbedaecaebacdeeccaaacaceddeeaebeadcacbdddddaaaebdbacaabeedbdaaacebebeeccccbdadadcacebbbebbeacbdbdeddebedcabcedbadaeecdbdcedcabeabcceacaccbecabbddececadcddabdeabcebebabadeecbabeccdeadceaaebdddbcbdebbeeeebabadceeaabbecdecbabcaeeeaeaaddabedcadcddbebeccadeecdbaeadaaaaebabeaaeadcbbbdddedabaeebbaaceeebadeebbceceacbdcabbdacbbbbdedebbacaadcbbcaabddcaacdeddaeebcdcdaceccecdcdeceeecccbbddcbdcaededceeacbdbeecbeebeddbcdbebececbaddcdccbedabdbacbbeecedaddaddedaedccebedceecebcdbddcbbcbcaaeabbbdddbebddcebdabaeccebcaabbebeadadbecccdebdbaaccaeedeeacdacaeadaabcdeccdbbcbbadaaecdbbbecaeccaaacadcbdaaaacebbaebddddbdacdebcadebbcdccaceddbaecedaecbbbcedbadbebaadcbaedceadbcacceadcbdadeaeaebacbcaccccdbedabcdeaaadddbbcbdcdccecebededcedabceddacacebebbdbedaaaecdbecbdadecadaaaddeeadeeaadcbdebeaeeeaeecebaabacebeeabcbececcccbbcbacbebecccecabedecdadcbedcebaebaacbdddbddbdbbedbeeeebddaebadcaccaecadbacbcccbadacbdececedadadadbbaeaacbcaebedeabebacaadaabdedcceccdccacedbdaaebecebdbaedadbaabdcabacdbeeeddeaeecabdcdcaaaceaabcaeeaececaeaebbebeccacadabacaebdcabddcacbbbdecaaceadbbaccceaadccadaaeeacccdcabbdaabeeabedacbecedabcaddbcdbeeddbbedaabbbddcaacdcdecdeeebaccaccebbbaacccdbbdedddecccdadeeedaceedbdabbdcccebdbcaecbcabaabedaceeabccbbaeccaaedcccbebcbbbbbbacccadedadbabedccabdacceeadaadebecacebbbbeccaceaeecedeaaadedbbabddaaddaacadebbbecbdbdbdddbecaccaeebdacdacbcedeaaebabdacccbccbbecaeedeadedecabbabdabbdeeabaeaceeaeeeadabeeeebcceecddddedcebebbcdbdaadcdcbbeecdeeaedabcbbbdeddeeabeccaabdaeedadbcdcaadcddacbeeddddcdabeadebddeedebddcdebcacbadcdbbcabbcdbdeacdeeeabeaacbcddaababcebcedbaccdddecdccabebaededceecabdcaccadbaeeeeacecadbdebcdaedcccedabbaecceecedbbecabcdececbbeccddecaaecaadcbcebaaaaccdbecebadccedbdbcaecbcecbeeabcdaaabedcaddbdabedeeebedaaeabacabeacdddacdabddbdbbecddcaadabacacacacbccdaccedeebcedacbccadcaadaaaeedbddbadbcaeabadcdcdabdaebdeeddabbedeedaededaaeadbdeddebdbbbcdedecaaeadebcbbaeadeeccacaeaaebaeeaceddcdaeddcbbddeaeebcadacebaaddaebaadaceadbbdabbecdddbacecabdeccabbceeadeacebeaeeecabeccaaadbeabeceadeaecdebeedbbeecdcecbdaccebedeeeeecaaeaccbceeadbeedbcabecdaadeadbaadbcdcbcbaaedbacddddddeedcdedabeecaeacaabcbeeeabcccececdcadedbecabdeedcbcbeaccdcbbddbcaaaccccceebcabbdedabeacebdcaaecbddccebbeeddabadecbcddbbaabddadbcabadbababaaadddaddddeceaacbdcbeeeddcbacbdccdaebcabcedecacccdebdceaedaadecacbecabbdcecbdbceacaaebbdbacaccaabdcdebbbeceaeceddcdbdccadddbeecccdeacdbdbbeaeacbecccbaeaabdacedcdcbebacbbdbaedeecddbdbeddccbdddbaddbbceaabdeeedbdbbbcceeddceccdbcdedcdeeadcbddbdbecbdedceeeaaacadddabeeccbadecaaedacecaedbbdcdbceedaaddadbcbdcddaccceecddbbedacadaadbeaceaeabbabbeeebbbadcdbecdadeeaceabacdeeeeedcdbceabdedaeacdadaadedbaeaedddebababdbdbbceeadbeceaeaeeebdccabeddaddaaceabbedcecbdcceeeeccdaceedbdacbeaadebedaeceadbebadeceeeaeedeaaecbbddedbadcecaaaedadbdceddedbbeeabbedacddbdcebcaeaebeceecbebcdacaaadbaeeeaedabcddccbdceddaeecbdaebccecdacddaaedbadbedabcddecceaeabdbbdcdaaedbcdacadbabbcbccdacdcbdebdecadbdeecbecaadedcebbecbbdbcbdbbcaccccacdbdbebcceeceabcdabadaeedddebdddaeedabedcaeddeecceadcdeedddeabececedaedbbcdcdcbdeacbcacdaeeaaccccbddebabcdaedbeaeeeeddebbacbbaebddeedadcbbecaeaeddbbcddbebbcddaebcebacebcccbbeaebeeaadeecddadbdabdaeaebbbdbbcccaabcdeddcbcedaabbdabebebeacbdabdcadbdbaaceccbbebdcebacdaccceccdaaaadeeedaacadcccadeeebbcebbaaabeceecaceddacdbaeaeeecddcdebbddcbbbccecebacecdabdddeeedebeaedcaeedaadeaeeebccadeddbdbbcaadcceceaedbecddbbeccecdbebcddebeebaabdbdabeaedcbdaeaebaebbdabaadbbbceeadabddaceaeeedadcadbdcebacdccdbbeccebaaadaeccbacdaebbbaecacccdcdbdbcdedcbdbaedeeddbcddccbbaeddbcccbcbbcbecdedbeeccebcaadadccbecbcebcbcdeebbbbbadaeaeedbebdaabdbadaaeedbbadbedbeaceeedadaeebedddedccebabdbcdeaecabceadeeecadcecbbadabdbdaadceadaaccbcccacabbcdaacebcdaecaabdaddeeaedcbbbbbdbcdcedbdcbaeaeacedebaecadcecdbbaecaaebcdbdeddbacecbeaebecaacccbddacbacdacdaababadceacddceeabeedbeccddebeeddddbebccdecccceeebcbacddbaeddbbacdccbeeeddcbdaeaabdecdbdcaedccdeedbceccabdaeecabcdeeedaabbeaabaadeabdbccebecbbccdeaabceeacabaeeabeeddebccaebeebbcabbcecaabdaeabadcddbcbdbeaccccdbeeccdeacadbbbeebadccceddddbdcdecbaedbcbbccbceedcbdaaaabdebbceaddcebdcaaeaeaaadceeebbdebacbadebdcdbaadaacdeeedaeeeacdadebadbcbaecbdaaeecdbbcdceddcbddaeaababdadcaedcecdcdeebeeaadeeaacbcaaddbadcccccdaeccdccdbdaccbaceaccaaeedccbcaadaaccbacedcbbbbaedaddacecadacbabcaadbdccadbbeedabdddbedcaeccabcccebdabdbacaedebadabaadebeeebccacceddeccadbeabbeeabbcebdbcbcadaacebbdddbcbabcccdaeacdecdeeecddaabcbbdeedeeacdecdbebaaaceddbaaacaabeecebceccdbbbaaaccceaedaedccbcecbbeedbbbaabadeedecedeacccdaadcaeaceeeaadcbceacebebcbebbdbaedeaebdabcadecdadcddeddbadacdbcbaabadeababdacceceedaabecdbbbabbaeeddaabbbaecdbdaabadbcabedbabdcecdcaecadeabbeaeeadcdcebbebddbabbbbcbcabecbcebdedbaadddbdeabebaedccdbcdcbdeaccadcedebdceceaabeebccdebadbcecaccacaecaeadcdebaceabcaeecbbdadedeeadcbebdeeabdbdadbbcabadecdbecdebbbcbabedbceeceeeeaaeddaeaacccadbcdbdeedeedcaaacaaceabceaeceecebeceebdceaacaeebedcbabdaeeddaaabdbabcccaeacacebbcbcaacebadeeaaaceeccedbaaedcbecdebdabbbdeccceeebabdacadaeabcbeabbbddccbecbeaebaaacaabecceaabaaaaadbcaaaebabcebbabecdacddcebabaedbdedcdbdbdcedddadeddccdceecdaedcebbceeccddcbaccacbbbaecbadaacebaeedcaecccdeddecdccdddbdcaebaecaceaecbdbedacbaeeadecedeebcabbdbcebdeaaccaaecaceddeacbececcbeaecceccdeebabaabeeccdaacabacedadbdbcbdebeabebaaeeccdbaecdaedeeaacbceddeaacabdccaeedacaeeaddaacdabbcbdddbccbaacbbebddbdadbaacaabddaeabcccaacbceeccbaeaeaddddbdebcabcedecdeeabcdbacbdabeaddbbebbaeebdcbaaebbddcaeacebbccbeabbcdbcebcecaececaccbdecbdaaebdabadecdbdadbecbebbbabdadedcaedddbedcbbcdbdeddbaaddadddaedbccceadbbbcdceaedbceddaadbdbbaeedcbadcbdacecabaddaeadaececcbbcbcadbabbebbdadbbaebbbaecbecedaeeeadbbacebabedbdccdcbaebbcdbdeeacdecdbeddeccceedebcbecdacecabbbcabbdddcadcecedebdcebbbaadddecedcecaacecbddcceddcbeebeaddbdaebaaaabadaeebdddcddccddcebbeeebaebdbadeaddaaecdacacccbdbeaceadcddeebbcbaeeacdacdcaedeebbbedcbdcbaeabccabbceeadedcaaeaaadeebdaddedacedbdaaaededeeacbedbcacedecadbdeccdaeeeedecacaaeabbbaabdcdaabdbeacdceadcecbbaccccdeedaceceedbdeacdeabbdbbaadbdbbaedecdcecedcbeccaddebccdcdcdbbbcebecaabccadecadbbbdcdeaaceaebbebbedabbcacadeccaaecdaaceccaeddebdecabdcaaeccdcbbecabbdabaccdebdbdeecbdcdcdeedecedebaaecacaabeabebdedbaccbddacbcbddaeadaacbaddabecbcaceeccedbdecbbbcacaccedcbecdadadbddadcdecaaabecabbbeceeaadeeadeaeccdaeebddebbaadeacdeebedebdebbcdbebecaadaabbebcdeadadebbaecccdccbddacebedbaebbbdeeeddaabcdecebddbdeeacbceabedeaeeeadbbcdbcbddacbbaeabebccbaeedeabeeeccacaacacdeeaabbdcedddbdedbbdeecebdeceadddbccacddaabbbbedbbcecdabdcbeecdbbcdeecdddaaaedaebdcecaebaaadaeaaeecccacabdebdbecdebabadeaccbebdbcacbbcbcbbcedbbcbcedcadadeaeeebddaaeddddeebdcdddbdcaedeeadbecdadcdaebecddaeeacbdcdcadbbbdeabadaddbbbaeecedbdcedbcaededecdabbdeadbbdedeeabbdbcadbacceabccbdaadeebdaddedcbaabdaddbccdbadaabedeecedcbeddabadbccdbeabaddadebcbaaeabebebcadccbeadedebceddcdddcddceebdcdbcbcdacedceccbdaabbbbaeeebebbedbaabdedadbbaadaadadbbcccddbbbabcedabbdadeaabbddbeeebdddacacaaabeadedcaddaecbeecbecadccbcbeddccdabdebabbbbcebeeaeaaebbedeeacbdaabcdbdadecddbbbabccedabdbaeacdedeeaeeaaccdaaeacdedabdabcaaaedccaebeddcaacecaedaaaeaddbcecdacbabcdceeccaebaebacaadcdaaabdaaabebbadcebaabbabcdeeecdbdcdeeacbbacddcbbdeaabddecdbbccebcedcecedcbceecaabbddddadebdcbedcddadecbbbeacadbdbcbecaecddebacaeddebbeadccdabdacecdaacbbcaacadeedecddcdddbaacdcccbbdbccbabecbcbbeaddbdcbcaabceedaebecbdbeeaabbcdbcaeccdbacdeeeaeccddcecbaebabddbeabbeecbbcebdeaaddbcaaddddbcdbcadcdceeeeccaadebabeaeacdacbedbcbaddadcbddbbdcddebbaeeabaceceeccaecbcededdaeceedcbcecccebdbcdddddebbdddbeaaeadbdaaeacccacacdceadcbecadeeddeabadbecbeabcadecdaecaecdaacbaeabeaaaddabbdacecadeadadbdcacbcecbeeeeccddbedeeaabdaeabdeabababacebaddcbcabcabcddaaecccdbdcecbaccebbcadbbcabadeeccbbeeecaecaaaaccadadebbedbeccecaacecceedbcbeeadabceeeebabadaddadbebccabdbebbadadcadbedcbdaaedccaaadcbbddcbcdeabbbebbabcbbbebbbcecebaaabdccceebbcdedbeeabbeccdebdbdbddaecccbbdaddbbedbaadeacccdcbdeeaedbcbdebdcbaccecedaacacbabdbbdacecdcadbeabbcecdebddaccabaaaabecdecebeedabaccecdabeadcddadcbcbbeabcecebbcdccdedcbcdaeeecdcdecdeedcdbaeedcaacbeaeccaaabaeeecdaedbebecdddacabdbaeaeccbaadaaedbedeacbcbcbaaddcdbadbcaebbaaabaeaaebecabdedacaadbebbeeceedbacadbcabbaeeaecadbcbbcadbddbadedbcbcedcbdadebabeabecbaddbcaceadccccbbcbddeaccddccaceeeaccebebaaceedbcbeebedcbaeaddabecebbacbecbaeccabcaeecaccbcddbecbbacdeebaedaaceeaadecdddccbabceaecaaaebedbeeeaceeecdaeddcaaaacaddccbaacbddeadcdcacdadbdbbddcceceaaacaddecaedbcdadbbaaeddeddeccaddebceadcdcebabecedacedaaeeacdaebddadaaaddeaccecbbabbecbeeacceacccdddbabbdcebcdbebbeacccebbabbbbcccbccdeedeacbcbdbaaedceadabcbecddcacbbaacbeabcbcadabbdecacaecdeaccbccadddccbebadeccccddacbbdbeacdbddcaeceeacbcdddebeddabdeadccadebeccddbececaebcecbceaddccdbcecbbbebceddeaabceaeabebbddeabcbdceadccebbadebbaceadbbcadcbbecaedcddeacdeeeebcbdbbceaedcedacceebdcadbdbaaecbbbdabebaeeaeacbdcbbadddddabaccbbacdaaaaaabbeddcabecabdacbaebecbaccbdbddeccdbbdbcaabdadeedaabcbecbaedecccebbdbaaaebdedcccddaeccdebeebaecccaaabaadbddadabbbcceeacedeaedcaccbaeadacdbdaaaaabccbeaeaaeadcecbdcbadeeaaddbeaacbebacdbcaecdcebbebccebeaeacadebcdbdaccbedcccabcabbbddaaababdadbebebbaacaeaeaccebbaecdcdaeababceedaaecccddaebeaeabdebdecbeedaebbddadcebbdeabadddecdceadaccceacddaecbcedecbbcebdacdbeacabacbcecbbebaacdebccedcbddeddddadadacceeeabaaeaacdaccdcacbecebeddcbdeadecbaadcbaeeaececebeeaeadcccabbbcdaceacadcaaeeaeaccdccdedcecbdcbdeeeeadeadebcaaaeccbbebcebccecbebdacdbdcedbacbebedbaedadebeecbacabebaccbeabaacbbeeedadedaeaeaabbbacccdaddacbdaaebbcceeacceedbdadbeecaecbaebaadbdddbdccbbeedebbbcabdecabccadcbeeddceceacedabaaedbadeebeacbeedcabaacacdcedeacecaddbdcebbeeadeaabacaaaaeddabcdbaaabedbaaddcaaecbeecbbbecbccacacecdcabdaaecbbdcdaaacceabeeeaabbebddcaeaedabaacbcdcadccabdaaadacdcdaceeeccdbbccbeddcaedcbccdcabcaeaccacdbcbeddabececeacdeceeacaadebdcbcaacccdcaaccbcacdeacbdbcebcbedbbcbbcbbeceeebeeaaabdbbbbbcadcbeeddecedbeacbaecabccaecacccedeecceeccbebbbbbcdbdebcdcdbbeeadeaeeebbdcabeceebeaeeacceaccbdbcbaacaaebacdeedaecbcbbdbcceaebceabceeaebcaaebcceeadcadddaeccdedcdbbcbeabbbbadaabbaceedcaabccbebcecceaeadedeeeddbeebbcaacaaaeedeaeebbcedecbcedaadcddaaedecebbcacbaceacadeacccdeadbcbbbedbadbdababebdeccccbabdcaeeeaddcabaacebccdebdbeecaaccedaeecccecebaaeeeaededcacacaaddaddedbdcdabeebdcbeaaebdabaecccabcdcddbccebbbdbacaaeabdddceacddecaebabacbcedeccebbcbbdcabecceabdeeeeceebdceacbccedcbbdcbbaecbaddecaaeaedbedadeadbdececdccadeecdeeebdcbaabccebdeddbdecaaaeaaaaaedbbdcedcdcbcceeedaeccaeecbeebbaeaaacdddaeddacbecceaccbaccbdaeeedbededdabaabadbdacaaadaebbeddeadacabdcddbdeeabdaeceecbaaddbbadaebbcdecaeaecddbecddcdbecabbeacbdcdbbacdeedceddaadaaedbdbcebbcceeecbdacbcaacdcbbcbccecdbedcebcdebabebeadbdacdbeeacdecddcbbdcaceaeadabecaebcdeaaacedbcedeeaebcdcaccabdcdeaebbdcaccbbccbcbdceccbecbbdadecccddddbecacccbcddbbeeeebbaddbeacaeebacaccabbacdbcdadbeddaadddbcdbdacecddebdcadbcaddacacdacbeeacedaaacbbcabcebdeeeadccacaaeecedcbecabbabdbdabcedaedadccbaaaeebbeaebbcdccbaecadacbedaebaaeeacdddadabdeacebedccebdcadeeccadbebabaceaeccabbbdceddcecddeedbeceadedaaaabaedabecccdcecdddecceaecaeaecaebaccadaaabbccbcaeaaeeabdceaedbabaeadebcccecdacccdcddeabecedbabceaacecbceeadcecbdccccdeccbaeedaabeaaecaddebcdeaebdbecbbcbdbdaceaebcaaadcdcadddaebddaadecbdebbaadcacddebeecadeacaaccbdbccbeacdcaecadecebdedbcbaaaccabedbdbedeccabdebbbbeebcbabdaabbaadbebbbbbdaddcadccebccaceaccdcdcbcabbdacdbaccaaddabbcccbeeadaceecadcdabceaadbaeabebebabadeacecccdccebcbacbebddbdabacdcbeebcbecadacbbcaaedaccaaaeadbeaddecdedbdddceaecececccdbcdbbbeababeabbdbdcdcbccceccdbaadaaeedbceaaceedeedbaebaeddabdddbceeceaebdeedbdcdeeadeaaeeaebdaaceeeabdeabceaaaaeaebdceeabababdcadebcbeebdbdbcceebccadadaddcbcbeceedadabdbababcdbaddbbdeccdeddeaebacacbabaccbadeedebaabcdedeacbeedcdeecebccdabdcaacacdbeecdbbdebdcdabcbdeaaaecabadbbbcadeeeebebdabdcdbecebedbddbbbdaadaaaeeebaabedebecbaebebaaedaebaecbadbedecababdabcdbddcbcaebaebacbececbaebdedebdaaccecbdcaaacaabbeeaabadcbcdbcdcbadddaeccdeacdeaecdbcdeceebaceabebedbbacdeacddbcadaabbcccbacebcddeecabdebcdccacaeddaeeacdaecedbecebeeecdcbacbebdedebcbbebacdaecaeccaebcdabbcceceeaeabaebdebbccaaddbedcbbebeecbbaabaceccebebbeabbacebbdeaadbccbcdebaedeebacacacbbeeecceaedadddbdbcedccbcbceabeabebacadbababcdecdebcbbbaadebbccceceddbceeadbabaecaacdcbabaadebaecbcadabddadeaedaedaccbdadceedebadaaabeecaedadabebebacadebacbabaaddeadebeecaeddadaadaeabebedbbccadbdaeeeccbedbedbecbbebccebcededddebdccaadebccbaccaaceeacdbbbdcecbcddcbbeecbbcdcaecbedeacdeeddaabceccebdebedeaeaadcdcaccdeaeecdeadcbdadedeeeceebaeedeaaaabdbedcdcecdebceaaceeddbaecadddbeebabcbadacbaddbabdaccbbbadddabaccdcabdeebdbedeadccaeeadbdaeabbcbeaededbacaebebaccacbbccdcaedbcccebecbaddceaaadaeeeabccabbeabeececadbbecdaaeadcededceebdccbdacceacecdbaeacebacadcaababbaeadddecaeecbedcaeadaceccbcbdcbabebccecbcedbadbeceddebacbbdddaadbaadabadbebdbacdddedeebdedbcdceedcbaecccaaadbccaedbdeddacedcbadceadbaacedbbceddcedeaacbbceacabbdbcddbbeeceaaaceabdbebdddccadabccaaeabbbdcaaccbbcccdacdadecedceaabcbbedaddebeacadbbcdbbdceebdebdcdacebaedccaeddbecdeeedadacbddcbedadadddcbcedccaebcceedadeedecaccbdbcbabbbadccccbedbbbbaeeeaceebdebadecdceabaaaddaeeaadbdbccdaccadddbbeaccbadcbedbebddcdeeadcacbbdadecddecaeadeecabddcdeebecbdecdbaecbdbdabdcbcebeccaedbacceadabbebdbadebeccaccdecbdbdaadcabddacdbbdbbddbeabaeaaeeccaeacecabaeddcccbaabcbbebbeedaccdacaedcceabbcdbceccddebdbceaabcabaecaeedcaebbbedddecbdaceddeebebabbbddcebbadedbeeabdabbeeaaacedaddbcadedcebbdcedecdbeeaeceaacbadbaaeecaaccebbcceedaecdceccbcbceecccacadeaddcdacdebdbdedadcdaedecaedbabadeeaeeaddbcedebcaabceccbadbdebedccbbddcedccbbadacccceaeaacaceaeaccadeedbaadbdebedadeccedaabcebcdddbbebabbddbeeddbbaaaccabbccdbdeebcaebadbcaaaadaedaeeebededcbdeceebaceadcbdccbbbdedabababadaadaceeaedaaccbacaeedebabcedaebccbdacacabaaddbbbeaeadaabdbbeecddacddcececeacebcaeddadedcdebeeccebcbedeabeeeeaaaebbebacecbabbcbcabebceecebddaadaaabcaeadcdbacedabbeccdbbdcabbcaadbecaacbabbeccbbabdedcdbbabcccdceacddeeeacaaddacbcabcaaadedeceaabbeeeedbeceeaaeadbcebceedaebdbededbcacaebbadebbecdbecbbedadbbdcdcbbaacbeaebdcceecceeeaeecaadaacdbdbbebdaacaccdaddebdbacbbeebcbbadebcecbadecbdbacedaeadbedcecdddbceadbeaabdbbbdaaaabdbecbeeecbeadbbababceaaabecdcdeabaeaeedadeccebaeeeddccbcbcdbbcedecaceaaadaccbdedabacececaeaaaecdeacdcbbdadcebbbbebeceaedacccaaadbeccebaaecebdbeddccbcaceddebaabaaacbdceeccbdcbeebbcbdeedeaadbeebdbabaadbedadbbbecedcedeeddebdbbbcdadecadaeedceccaadbdbebabcccaddebededbcbcccbdccdaddeedbaaebbcaaaaddcbeacdcacaecebddaddcbbbdcbeececbbbcceaceabbbcacececddbdeaacbcbbbaacebdcebaeacbbedeeacbebacccacdcabdbecbccbbbdcceeecbacbecbcdbcacaeeaedabbbadebeabbbdaadadaabebecdedbaebbeecbeaaddcddaacddaccdbbedecddccbcaaedcddcaaeeedcecaccdedabdcedbaaaeecdedaceecbadabddcedaecddedabddbcaaceadcbbcabcbadbbedcddceaecaebeaaaecacddaeabdbeeaebdeebbaebaacaecaebacebabbcdadbcabbdcdbcabbebbadadeeabeaeadbceedaaccbeaabcdabcbdebacdaedcdebacbddeebabdbbcdceccebbcabeccccdbeeaecacdaacbcadaaeeacdbaccedbadbebadadccdeabeecbabbadbaccdaebeedabdecebeceabcecabdeaeeabaabbacebcebededaddcdeeabceddadbbadacaddecabebebbeccacbcabecddeeccaceeabecaeacdcdbdddbacdccaaccaacceeaaaaadbabadcbbbaaeabecccceeaacbcebacbbcdebbdacabdabccbcdccdbeaaddedbceaedbeabcdbbdeddddceeeedcccccececcbabeebdddcebaaecadcecbecabdeedbbebcecbbadacabcbbeaccdbdcbecbcbcbaccceacdddcaaccdddacadecccbdaaebdcaebaabaaaaeecdcaadceaacdcaceebacbadeeeabbcaababaeececcbdddcaaaeedcdeaedddcdecebbccadbdbaddeccaccaaecadbbabbeaccecbbccaecebceebbaceccdbceeaabcdbbbaaedeadaaaeaaaecbadadbabdbdeeebcadeedbbecbaacaeaaeacaeabecaaccadacacedaadbcdebccedaacceeeacabecadacecbbccebcaddcddcaaebbcaecbdeeebeecedeebcdaabecbaecccbabaabacccbecddcbaedeeadbcdadcbeaedbeccbaceebaeadcadcaceacceabddaedcaeadaebbaecdaeeddbedbbcdcaaeedbdcdbdebaddeabdeecabcdccbcabdddacbdddcddbeeeccdedaeedabbbdeabadccacbdabeaeacbcdebbedcabbdbaccdcedcaedcecdacbcdcededdacdacabecdceebdaccbaaddddcbcaecababbedcccaadacdedebeeebcdacceebbebccccdececcdaabbbeacedccddeccbbdcdbbaebbebebeadcdbdaabaadacccbadbbbdebadacceeedcbeeeecdbbcabccdacdeeeaecabacbdededceccdddddeaccabcccdcaeecbdcdcbdcdabaeceaceeecbdadcecccaddeadeaeccbeebdaabcedbbbeebceceeccddddccabceedaeccbceadeeedbeaaeadedbbabbaaeeeaabbccecabcedccceabdbdcaaacacdbeaeaaabdacacdbccdedceacaaeaccededdbcbcdbccddebbdddbbcaddcedbbacdacbddbecdaecbcdbaeaccdeeccbcccaeedaaaaebccdbbdccdbedccacddcdecedcbcedbacaadeaaddeacaaeceabeeeaadaaabececaaeccdcccaaccaaebbaccdedbeccdbaeedcdbbddeadedcccbaaebaedacedccceabaaadeaccdabebbeddedcdedaeddeacedbbddcbdcedccbdcddbabdaaeddeccdbababadceaebedbaeaedebaccbceedbaaaedecbbeeceeeeadabaadcecadadbabcacddeddaeebaabebbbebbebcabdccabbadeaeacecebeaebeadcdccdbcaaedeabeeacdcbaccbbebdbeceeaddaecccbcbdaaadeccadccabbceeaabcddadeebcaecbedceccbbbaedcaaedaedeedccdceadeacdbaeeadaacbadabccaadaecdbddadadebbceeaccbcbdbabecabadeacbdeccbaaadbacedaceabedacabcbeeecbcdcabecddaadddeaebabaddaaeaebcecbeddaceaacabdaabdbcedcebaaceaabecddeaeecbedaecdaaacbeedacccecdcbdeccacadbddeebebdcaeeadebcdbaedacecebcdceeecbeedececbecaabebddebbeaaebbdcdceeeeaaebbbdcabaeeadbaebbcceabeecdaecbdebeaaaedcbcddeaeacabceabcbbedecabcbbabaaabdaeaeeddeaaedccebcedbdbadbcaeabcedaebeeaebccadedecadbdbbabeccacadeececaecccedacbddccacbcddacdebbbadbaebdbccbeacdabdeeaacaaddecedecbbadbedcecbcceadbedbebdbcdbceaccccbaaaeeeeedaaacabcdbadabbaacdbbdecdabadcaaaddeacccabcbdeabcbedeeeddaeaaeecdeabdabeadcddeddbdccbbaacdccacabedbbacbbecaadcbabaeecbbcdbabbcebacccceeecbbaeabaeccccdceebbbcaeeddaacabedaecbadbaaeebdcaededbadaeecbaeebcddcebbddeaadecbbedbdedebdecacedcbcabbacaddebdcecbebeabadbeadedbebadbcedeccbcdddbddbceebeadaeeceeabccbacbdaceddeacbbebcdbaabbdbbbdabdedbdbcceceacbdbabcebdecdabbbcaececbaaeeaaabadbbaacbeaabbebecbeaadabeadaebdcdbbdacdedebdcaebaaaedaaaddedacaabdcccacdcbaaeceecbaebecbbcedabcdbaaebaceababcaaaeedcebcddcdecadaaeaeccdcaaeaccceceadabeccdcbecdddeddaeadcaedbcdcdbcdaabdbbecbccaceaeaddbcdabbcaeebbcaebedbdebdbbeabadedebbeebdacadabacccaceccdebdaaabeebddcebcccbbcdcaaaddeccdebaddcaeacadeadcdedbdbecdacdaabeeebbdcdaededbaceaececbaecdaceaebedcabbaccecdbebcacdedaeadeeebabacaaddbbbebbeedaeebdadbdcdceadbadaaacdebebccccebcdcacedabbeecdebceaddaaecaeecceeceabbedcdcbceddacbddddaebabdeddbcbcececdbbeeabcabaadcbbaecbdaabacdbbcbabadbedcecbecedcdecdebcbebeeadbaedcaddbdbbddccecadcdcbbdaddceddbbdadeddbbcaaabdaeddccdcbdcedaabeceddcbbbdcbbbcbaeabeacddadbcceebadaaddaebaacdacceeedadcdcacbecaceabbddaedceecdaadecdbdbeeddbdcddeeeeeabbbbacbdccdaaaeaddbcecbebebeeadecdaedbdeecbceadecbdaceaaecdedecaeaeabbbcabddceacdaededbeadaccabeecddeaaabbbeaaaeebdbeeaeeaeadbedcaeddcdbdbdbeccbeaeadcdbbaaeedcdabbbcccdedceedcbeaecaaaaeabeadcecaaadaceaaacaedaecdcdcacbeedbcabbbcabecabaaedaedceedaaeebccecbebebabeccbdaabbabebcaebceadbbecbaebbdaaaadceccacacbaddacbaadeccdebbceaecddaeedeaaedaabedcacdedabcbacbaaacceccdadbbbbcbababaacddeacebbecaeedbdebeedaebabdacbdebbbddbdacecdeeaedaceedebcaecdabbbeadbacabacbbcabcdcbbacdceadecbddecceedaaedbdaedabdaaabcbaeaacbabbcbedddcccdecdabebecdabaacdcddabebdbaabbdedbaabbbdcaebaeeabceecbbbeedddebeaadeaebcabadbedcdcaaeccccdcdacebcbcdbddaebabebdebadeccbddeddcaebebbbbdebdaecbedabbbceeeedbebbaeeeeccaeaadedaaedcbadceceaecacaceccbbdccedcdecacacceaeedceeadacedaeaabcedbdcabceadeadcebdedbbaeabdbedeecacedcbbaacdbbcaecbbcbadccadddaaccdedaeedcdabcaacecacddadbbdacadbdedcdbddbecbebdcecebdbcadaacbccabaaadeeeedceddeedeacbdadeacaababbadceecbecaabdcabbbbaedeeecedaabcaddccccdadcdbaeececeaebabcbbadaaddaeaececdacaaabdedbdacbbbaecdcbbddeccecadddabbadceaecdaddddbccaddbadecdacbcddbcbabccdedcedadededaecdaedddbcebaeebbecabadbbaebebaaabdceadadaaddaadaaeacdbbddacbcbcbccadeadddddbdcaeaadeecbeaacdecacdcbbedabebbaeedcbcaabaebceacbeedacacbbaacabeabdcacdcadeacddccadeaaacbaeaaaaeababdcdaceeacccebabeeeaeeeececaddeabdadbaccebeadcddadcbcebdaecceaaabdbcaaeeeedcdecececebbeddcbbcccbeeaedbecbaacdbcdbecbdebbdeeaacbdbccecbedeaaddacceedbeddcbddddcebeddddbcbdbbdeebeabadabbdbedbaacdebeececbeecedcadddbccabadceabbdebababdcdcaebbbdaaaedcbbaeaaeacabbbddbeeacbcedeadaeeaadaabbdabdbedaaadcabdacdcdbcbbbaabdbcdceccddabbdcddecbdbdeebccaaebcaaaeaccacdcbeeeaecadbdeeedcccdaecdedaecbeacbdedebbdadedccecebebadbaaadddaaaedbdcbceaacebddceeacdeaaabadadccdcebebccbdaaaabebeebaccbdceeceeaeaeebcbdcddccebecbebdeaacedbcbdaccbcecebdbebdebabacbebbddbbcaddedcbccebbddeeaadacbaaecaceccdcbabeddabdedeaaadebdbddcdccdcbededbdaeaeebcedbdaedecbeecaeddcdcebbdbdcccccbbabcddedaeedecddcececdedbceedaabbdcbabbaecbadecdeacdebaaedccacbacdcddcedacbbcdaacceabedbeedcacddbbbbebedaaeaebcbceeebbaddbdebabaceeeecacbeceecaecebddcacceacecadadacdbbaebcceccbabaccdebcddaaadecadeabdccaebbcecbccdddabadaadeaeddeeeedacdbbabbeaadaceaeebdabaaceeedaaadcbdaadaadaaabebedebbdcdbbbaaabdeceadbdbbddbedecbbbadedbcbebaecddcedcaeadadeaededbecebaaddbbaacdddddbccdeadeababebcbaebccaecaddeaebcedaabeeedeaeddcbaebadedeebedcdeebcdabdcabacebcbabbdabeadaebcaaeddbaeecbceacdbcdeeddeaecdaaacbcaedaabadcebcbaaaaebcbcdabddcebcaadaaccaedadabbededeaceecbaeabddbdecccdeabbddebcbaccdaebecdbddabbdaaaeccbccaacceaccbbccccaddbbdcbacaabaebceaacaabdecaacedcacabbaaeeadbdaeeecdabaabeabebebceaacabcbbcaeebcabeeaacdddbcabecbeeabcbcdbaedeaebcaebdbedadccdcecabdeebbcebabbabbbcceaceeebcebbaaaecacebcaebcceeaebaadbbecaeacedebcdbcabeeaaaebbdeddbddcccecddaaacdbadbedceebaebbdecddeddbedebacaadaadcabaebdedcbaeaaecaeccccbadeeecacccedcbbbaaaacaaeaedcaeeeadeecebcbbabdbbcacbadcbbecebedebccdedabaaadbebedddbaabaaecdacbbbaceeabcbcceebbedaabacaeeeaceeecebcbdcaeccebeddedadaaeadcdecadebbedbdcaeebabdccababadceebeeedcebaadacbbeebedaeccdcacbeaaecacaeeedbabbddaaceddbacebbecceadbbabcccddebaedeeaacaebabababaebbeaacbdcbaabcaaeecdaaaddddcedcacdabbcaedabedbabbcddccbdbeccdbdbcdcedbabacabbccddaeccdebaebadacdcbddcddbcedebaabdcbcdaadcdeebeeabeaecdddcdeabbacacaddbbbabddebdbadcacbedbcdaccccbbabeebdecbebadedbccaeadbbaaeebaceaaeaebeabaacacaccbcaaacbcaaecbaeaceabecabccbeedcceddeadeeeadeddeabcadcbdecccbbaaaddaedccaacbbbabdddbdbddbeecaebcaebaccdbcceedeebadeabcaccbecbbebeabbbceeabcceddbecdebecedaaaebbdcbadebeddbccededecaaaddbaacdeccdedcbcbccaeccabcedbdccceccbcbdbdcccabdbbeceeaaabbdebcabbddaacabdcbaaaaecddadcbddcdccceebdeecdaebdaecebbdacdeebdeedabbadebeaddaceeaecedbaeaeabecaadbebeacecdebbdbbddceebdaecaeabdbcaeaaccdcaebdcbebdaabeadcaccaaddcbddcbedaaceabbbcdbedeebecbabcdceacebedcbbdebdbeebeeabbdabeacedcbdbbbabbddadaeeaeacdcbbeecaaccceeabaecbbcddddbedaaaeaacdcbbbcbceabdddcccbaadeaedcddccecbdeaedccddceaadbaaebeacdebcdcdedeeadeecbebbebbaaabcceaeecbccadedbacdbccdcdcbcdeacddacabbbbddebedeeddaccaacaaaaecbbedeecaebcaaebacdedeebadcecbbecddcaacadbbcbedbdeebddacbcbeecbbcdaadddddacceadbebaebaeeacabaacbacbeccdeaecbabbdcadbbecdbcebdcbaabeebcdeadcbedeeaaddbbeedaebcadddcdbdcbabcbcbeacbdabbbecddbedccebbaccabbacedcacebeaacabeacbcebcbcddeebdacbdeebebebaaaabbbeccdeacecabcdadbabebbebbadccdcadedccececebcacdabdbebcbbcddbbcabbcabbdcebebeeeebdedadbaacbabeebcbabbeeccabaacaedcccbbdceeaedaaaadcdbdacababcdebadecbacddbbaadcbeadbabbbebbcdccdcebebaadaecbedcdcbdbcddccebdaaddedbeacddebbdbbdbebeaabddebedaacbdcbeedaacacabdaacabcddadaabbbdbecdccacabaacdedaaebeabcdddaddbabdeecddbeaceabbecbacbbdeadddeaaedccebbebcaaadacbcaceeebcecdacdcebbedbceecbbccaeabeccacedaddbcaddbebdebdcccbbaabcdcceedecebdacbdaecceaacdaebeaaeeaeccbebbdabdeceeacbaddccadebabcbdbbcdbcedbedceddadcdadcadebedcccecbbaabeeabdececaabddadbabcdbebcdbedaccceaddadcdddaeedcadcbaabcbeccdadcbaddbbcbdbabccaaeabecabaecedaeebedaccdddcebaaaededcedbbeadccbeddaaabadccaecdbcaedccceeddeecabdaabbcbedceedebbcdabcdeaebcdeaeacaaadbbedecbdbadcdbbbebdedeccdbccaeceaacaccdbaaddcdccdbbbeccdbeaecdbbaaabaadabbdecdcebdceaddaebabedbcecbbbdebbaccbdcacbbccbacbdeedddbddacbcebabcbcdeaecbcaeaaedabccaeccbebacbdbcccdccdbbccdcbabdccadacbcebbaddbadbbbcdbbddcdbaaaecedeebcddcaceeecacdabeebedadecddddccaeadccceadbcbacddcaadbbdbbccbaacdbacddebbcbdbecdcaadebebcdaabcecdcddeebdddcaadcdbeededdcebaaebdbeeadecdcabbbedaecbbaacaabceceddacdbaecbbbedcabdbebccadcadbededeccbaeabeaddecaaaebcabbbecbddddceaddceebaaabcdadeddbcdaabeaacccaabebabcdabbdbbcabcddcedebadacaedeedbccbeeaccccdebdddbbaddceeabddeecadaeccbcbebedcdbeacdaeeabbddbdebbccbeaadceaaceccdccdcabaeaacedeaddeadabdadadcaacdbdbdbddabcadecdcacbadbebecabbcbcbacabcecaceeebcaccbadaeaeaedacbcaabccbdadbdedaababeccdaeeabaadbccacedddaddebccabcdcbaddeedbddbbadaaaececaccabbbdddcabdddecddecdbdebcbaebdbeceabeabbaceeeaeacbaddacadcaccdabbaecaebccdecaadceccacbabbedbccbabaaaebbbeeeebbbdedbeaccdcbcbdcabadecacdeedcccbceaedbbecdbdcebbeacedaddabdeaceecbadbeaaacbbabacbdcdecededcadecdebceabccedbdecadeebbecbcbaecdbcdebedbdbadacaaadbdedaadecbaedabcdccbbbaabcaacbdabecedceaeebdceceebaebbccaddeceadbecbbddbbbebecbcdedeaabacababbdddddbaddacbedcdabccccaeeaedeabcccbdaaedbbbccaebcedcbeebcddebaddedcbccbedeaecbebcecaaedbadaebbdbabcedeaaaeccbacadacbebddcaeaaadcaccbedccdbcbcbdecdaabedacbaabbccadacabbdaccaaeeadeacebbabdbaccaebdcddaeebdddcbadcbaceadabdeaedbcaeaedcaaacdaeaaddbdaeddddcbdcbdbdbeabbcdecbeddaadcbebceedadcdebcbacedecbddabdbcdbaabaadcedbebccddbeceabcdcbedaabaacdccecaabedccbaacdadadccdaeecbacebdbeeeebeaeeeeddabedbaedeedeebcaaedadebbecdceabaaccebaaadcacceddaaaabcbeabeadddaebebaecacaabbeeaeddabedaebdbcacacccbacbbcddecbbdabdbeedbadecdaceeeebecdcbbeaecbcdadadbacdcdbaadaddbaabdecdcddaeaecaeddbbeeeabeabecabacedbeaaadceceedcdebaacddeebccedeceadeabddecdeecebdcedebadabaedaebcbebdecccbdcdbeebedceccddbbdebacdddbaeccababacbdebedecbedbdedeedbecccbcabbaaadecbdacccbeddedabaddbeaecbdaabbcaaebdbbeaaddbbdcbcbdbbbacccebeccaecdeebbdbbeaccddebabbebdbccbbbcaebcbaeedcbdeebeedadaebcbbbcecacabddccdbaeddddcbebbcaccbeacacbbddaedaccccdeaccccbeddecdeebbedbccdadebebeadbcacececbdceadaabaeaacecaaebebeebdcdeceebbbeceedbcaeeeedecbdadeddebbddbcacabdebbebbabcebeacabbdddcbdcacdebdcaceddedeeaddedeecbcaddbaaedddcbddabaadaccbcabaccddbbebebedcedbeecebcccecbccccbacceeeacaeddaececdcaedeccceccbeabecedcceeccedddbceddbddbebbdecbcaececcabaaccaedadbccaabcabeacacdadbbaecbebebdaecdabbceeebabbcdadbeadaceeaeadabbbdaaaacebacbadcbaeadbebcdcdbaaeddbaeccebeecadeccddbaedbdaedacaecbabcddebaaaecbeeacbbaebdadaccedcbbddbdbbbbaaeaeaddecccabedaaacabbebebeabdedcaeebecbbacdcccecbdecbaeeeabeacbddcadbedcbaeedbbeeacdadccbdabddacaceeeadcddaadbcdcbedccbdddcdedbdaaacbabebbbcebaaebdeabdcadebacabbebcaadabddaadabeeddabcbeecadeeecbbcebdbaccedbdbcecadacadeedcacecebbaeeacdababcbbacdbcccdeddddaadecbbcbdeaadadccebbeadacabedccadaacebdbaadcebecccbaaddaebeadaedceedbbcbcdeeccbeadabcdceaadcaeeaabbebecacdeaaabdbccebecdaedaccbdccccbdaabdcdebdcecdddebcbddbdebbbabaeabddeeaeaaddbaacaadbadbcedcdcbbecebadbbbbecaaaaaaebbedaaeabdecaacbddceeababbabadbdddadaaaeceaacdedacbecadecebcadbbecbdbbeaebeeadddacdeaadedbdccacdeaccebbadccbcaeddcdbadadcabababbdeceddbccbbebdebdedaebeeaddedacdcaadcddaddebaddbbbdabeddcbedceadeececebdddaddcddbacbebecadabcabbedcadcbacbdadcbcdbcdaacdbdbaeabebacdeacaeadcbeeebbbdeebaeabcaebeabbbccaedeedaeaccadacaaabedcacbdbdcdaedceadaeabaadaccdbcdaaccaebcddedbdccecbeabcceeebdeecdedacccccdecccebeadbbccaedcaaaeeeaedbddedbcebeebeabeabedeaaddbceedcdbdbadedeadebbebdbaabdddaebccecbcbbbeacdaececbbdadabbecbbbaccccbdeeabacabeabecbcbddbcedebedebebccdcdbdbcadadabcdcdaaccdecbbacbbddbeacbaebbedcbacbaeadbabedabbeeedbcbeeacebbbcbdbeddbbbcbbcacebbdcadabbcaeddaddccceaadbaaedceeecdeaaeceacebdacacceddcecaaddaebeabacbacdebacddadacdceacaeeeedbedcecebbcddbaaabacbbccbabdcebcebedeebdccccdecabcabcdbdabbeaddbabbcedceeccabebbbebedebebdcedcdecbdaaceccecaeecbdcaacdbdedeebbcdabdbedbdabcddadcddabccbababbdecadeacbacacabaeedabecbeebeeababdddecabdebbbeeacadedbdddeeadbdebcaedebdaecabdaaacddacdccbeaaebbdbadeaccedaaddaebdbcbcaebdabedebbdecacccdaabcececcbaaccbbebaadebcebacbbebbaaaccacbaccdaebbdbaaeabccebcadedbadbdcaccaeabddbaaecacabbdcabbeceacaeaeecabebbbdcaddabbdeccabbbcbecadbebdbebabacedeacbbbdbacbdabbedddbabaabbebedeeaccacdbaacdebdeedddbceeaaebaabceecaebdccbadbebeececcdaeceabedbccadebaaddcadabadbacbceabdcdeabbabadaaaaccadebdadabbabeecaaabaceacacdbccbbbceabcbabbebacededdebcedcecadcaccaeeeaededbaadddbccccbeccdcadedeabdabcaecebaedbaecdadbbcebacebadbecccaccabedabaaccaeacabcdeaeedbcbecabcdcbcabedddaabeeddcacecacecccadeeeabdebddcbadcebdcebadababcdeacdccdedbdadcbdaeecabcdabdeabceecdcddeedbaeedcabcabcabcadddddbccbbdacedcbddeddcbbdabddcaccebbaaaabacabedcddccccaddecdaeeedbeeeacbaceecdeedcbadbacbeeadcdceacccacdbdcdbeddeddaabeeacceababdcabdbacccbacaccbaaaaddbaebeeaecaccddcabebbcdcdedabeacddaececbadcbeededcecbbecebcaababaadbdcedadabedeedcbbbbaddedbcababccbaddecaabdceccbdbedecbbbbaebacdeeddbaaceecbbaccbbccacadaeabacabbaeccbbdbdedadcbbddacaaddbbdabddcbccddadbabaeacacbdaaddaeedcdaacabbbacebeceababbcdecbbaccbeddbdedbacdeadbbebbceadddbecbeeddeeaaccbaadacecbaaecadadabddcedabebdbdbaeabaacbccdbcababaebeaeebbbcccdeaabdbdaadabdcdcbadbdbeeacbdcdbcdeaececbceedcdcabceaaceeadabbbdddedcceebdaccbeecdeeeeaaadcbdeddaddddcdeccbcabccbabedeeaacbcbbdecccadaecdceabdcdebecceebbbaeacdbecdccadaaeececdeacabcccebbbedbbbecaadedbeacebaadcdaaeacaababddbaadeaaeeaebaccabcdbceddbdcbbeeeebbcadceadaaabedadcebccaadedbecabcecbdabcdabaadcbbcccdaaabaabddcacbecdaccadedcdbcbeabbeabaaeecceddbcbdadecadecdeddacbddabbeddcedbedbebccbcceedcdbebecebcbaacbabeebaacacddeceecedebebdbaacabaddcbbeccdcedbeaedabeddadbcaeaababeabddadcacdbaabaaedddbceccdadcdcccaeadaabccadbecaacdaddacabbebbbbeccaabdabcacedecdaeacccacedeabbcaeddbdecddecdbeabcaaaebaabaccbedebbbababdbbadeddcbecccdbbcbdabcecccbacbdedaeaedbcbecaceddbbbbcdcbdbdbbcdbeebcbdcacdccdacdcccaddcdaabdbacceacbeccdabccebcdbeeecbbdebdacacbecbdbcdccedcaeedeeaceaeebbcdbcbaeebebeddccbdebbceebdcadbebedcceeedadaccbbcacecacddeccbcbecabbaebedebebcdabebebeaceaebbbecaeacadacadecdbbcedebeacecdadecdbcbbeabceaedccbaddbeaeccbebecddeadcebcdedeececdccedbbdceabacceccddcccbababccbbadaababadbddeeceebbaacdddaeeeaddccaeebcebeddabdeeecdccbdeaebceecbbbbeccbbecbdeaaeeeececacccacbadbeaecedcdecacdcbaececedbedbedddeebcedecaddbebcaadcacaadebeacbccdbecdaaadadbbbabeedaadcaadaccadccedcabdcbdcccceeabceadcbcdcbdaaeeeeebebacdabcabededaddedcdebbdcaabdebedbaebacbeadbcbbbcedaedebbabaceebebeeadabadcadaacabeededcaebbbbdaaaceebbbcacdcacccebacebdeedebbabcbaeacdbddabccbaccaccedcdcddcdceabcbbbaacbaedeeeeccbbabebacdcbcdbceeaecdceadbedbbeececbdbbcdbeceaebabadbabbdebceeeeddbecdecabbabceeedecabaacbecdddbcdbeccedbbeacdddcababbbdecdcaadcbdbeaeaabcecbacbebaeedbecaadaebadbcbbdcdadbbbabaeacdcbccbbceabacaabedbccadddeebdedbeebedcbcecbecadcdaccbcaedecdaedbcccbcecacaeeebbeeacadcaeddcccddceadeccdbdeeecacedcaacdcbcbbdbbdcbadaaaadcaacccbaaeaadeabbcdcbdedacbdcbbdecdcceadabbabbdcaaaadceadbbbdecbdebcadcdeadedbbccbddacabebaeceeaeddceebbebedbccaacaaeeaddbdddaeaaebebddaceddbdeeadceaddbedeedcbaacaaedacecbabadcecebebbdabaaeeececbabeeccbcdcadcecebdbacebadaccdaaeeadacdcaabaabdebbcbbbeceeeaeacdcaaaeaeadaaecaceaaabadbeddaedcabecdeecbbaabacdcdbedcedbabbeceeadabdecebaadcbbbaeadcdeccdabdebceaddacacdcdbbbbcdbaecacbebbcceebbcebbccaacddbcccddcecacbcedeccbbcacdcdbcbbeaceaaaabcedcadcecabeabaebddacdeedadbeedabddcbebbccacdcabebedcbcbdccdbcebadebbecbacddecdecbdcddabdcbeababdddddeabedbbcdabacebbeaabcacaedbbdeeaabbbeeacedacdadccddbbdaacaabadcdeadcccbcbaedaebaebecebbddaabaaeebcadbcebedadeaddcaeabacacbabcbaedceeabccdacebccbadbddaeeaaadaabdedccceaecadeceebeaebcecedcbddbadebaddcabceadbddacbeadbeaaddddcdeebccedbccccbdecdbcadaebceeaaacbeadeedcababcaddebccceabadcbdbbcdbdcbbaaebbcdbbcabeeeddcdaedbdaeaaadaeeccbbbdbcccdcaadadeaaceebceeebaadaccbeeebcebaeedcbeedadbaebbeeacdebedbccbedcdabdbaacdaadadecadccabbccbbbeebdeeeeeabdaecbaadcdddcacccaaddcedeaaebcdeaedabaabccbceadabdabbbdbcbeddadbcdcacbddaecdbdadebaedcacceadcbbaacbbabdcdcebddcdcdadeadaadcccdeaebbbdcbecbbabccedcdedbaadbeacdddedeecdceddeebdbdaeacbadcdccbacacedeaceacaabdedbbceaaaaccdaedbbcbbccdcabeddaeecbcbdbecbeceaadeadeaeabacbdabebccedbdccbbeedeeedaaaebdeebdaaaedbcbcadebbececcdaaeeaeaaadacdabadeaabacbebabebaaeddebecccdaacadbaeaadccabdbcdccecccbcebebdebabdbbcedaecacbebcedcebbcecaceaccbccbdeacaeaeccbebedbdebccebccbddeabedabcdcebddaacdecbcdabbededececadebbcbbeebeebaadbbaccaadabecbaebeddaeaccebebebceebebeeccdeeaebaeaabdcceaaaebbededdcdaccbbaebadedadacecbcedbccbebcaeabeddeebeaebbacccdbebebdedececeaaacddeadacebdcedaebbabdaadacbcbbeadeeecaaaedbebbdaccdeeadaabebcdceaaedcbddcbacdbddceebaacbbacdbbedebbaaceaebaedcacadcadcbebaeadbebbcaeccbdaadededabbeacbdbdceddbcceeeecbbcbdcebdaaabcadbadddcbbebbeadadaeaadbebbdbddadaaaddbbaebbebaabdedbdacaadecaadbecadaacecaebadcbcbaeaaeacbcddedaaaaddbcbdbbaecceacdacdeeaaeacaeaddeeddcbddeeaacdeacdceaceabdadeccbbdbabeeaebcbeeeeadcbbcadccdcabbaeeaeddaacadeadcdccbeebcabcabdccaecdcbcabcbdabaadacebededeebdcbebdbaeeebdaebbcbdbdbdedabdcdadcdaebbeaadadedbdabebaaaebdccdacdbacbddcacbbbabdddbaadaaebbaaebdcddaebceaeddbbabbbccdedcdccccaeeddbbcacedbabcadaaecebddcdeccedbdcbcccbedcedcbabceadeaaacdacdaedcadaeaebaaedbecdeabcacabadeabddedadedcdbdaacdaabacdeeddbeaeacbaebceadbceabdeccddcabaebebdbaaaedbcdecdbedddcbbaebbceababbebaacedececaacacbccbbaebdcdecdceecaacdeedbdbdbadabccebbbeacedebccbbdebdebbeeacccadcbccbccaadecdcdbedaaecbddadbcddecdcdebeadbeeaeeccbebbcdbbaaeebdacbbaeceeebececcdceebceededcecbaebacbccebabeedcecdbcccbdadbecabdeabcbcccebadadedeaaaedaaadccddcadccecbebdbeceebadecebbbcdabadacbceaaebdbbcbbaacdcdcdbdadeaacacbbdbceadecccaebbbabacecddbecbecbcacdcccebedbadbaaecdeeeeeceebcbdbedbcecabdacbebeaaecdeebeaebbeadcbaccabeecbbbdcedaceceaceacbdbbaceedecbaeedcdebacecdebaaeadcbbadabebcbdcabbabebbcdaedebcecbdecbdbebecabacacbbabddbceeadeabddccdbebeaddbbbdbeadedadabbabcbddabdbcadcdebeeacebebccbbdbcbaedcadaeaedacaabcabcdacdbccddcceaeddacbcbeddcbbdadbebaedbadbecbedbbeaaacebbbbcdeaccccaceebebcbbbcaaeebeeceaceebccacaacdeccadbecaecbdaedcdaeccbdaaaaabeeedceecaecdddbdeddbcbebcabddcebaceaeadbcbaceedebaaedadbaaebcaadcaeedddcabbeaeeecacaadcbcdadbbdcbcaecdacaecabaeaabedccdccccacceedaaecabacdccdeecccddeebaebdaacdbaecaecebdbdebdabebabdcabeceabacaecaeeebbedabacddccddacdacdadddaeabcaecabdeedcbbdcadbdbdedbebbeedcdcabceecdeadaeecaaabccceddbddaeabacaccddcdceeedcdacddabdadeadcbeabbbdedcdecedddddaadebceedbebaeecbbabddecdedabdbbaaecaaadccceedaaccdbeecaecddadaabbcdeedaceaeeadcddbcdeccbbbaaccabaedacdabedbcccbdecacaceaccaeaebaaeceaaaaaeaadceadcbbdbddceaedeeacbaaeedeeaddbddebbdbcadceeaacdaaecbadbcdbbedcbbebdeaaebcbbebdeabaaebecdcdababbdddcdbcecedadedaececaddbdaeabbedcdaaacccdccedabdeacdebddccadbaeabcaecbbcbabceebebedaccbbdbaebceabcecaadbedbcabbbedcabcdedcbbbeaecbeeecdeebccadabcadbadbeacdabbcddbcdddbacccdcdddaddbacbbabeeccbadededecddcddabddaebcdcaaadabdacdeadeccedceaaaebbececcbdeeacdaccaddaaacbaaeceddbececacdaacaeebadccdbaedbedebdccedeadecabaebbeabacccdcdbebcecabcbcedaeddcadaebddcbaecbdbeedeecdcbedadadedceedeeabaeabaededbdcbdeaeeaabecdddccdbbadadbcedebbecbbdbbbbdcdaaaeabeeaaaaeebeccddaebabcecbbdbbcaabdaeeeeddaeeeecddcaebccebcdadeeaecdbdbeebbeeabdeaaaeacdeeeeadceebabdcebbddebaacbbcecbbcadbbddccecaacadcdebcccbebbcdeccedbbaeeeecdeababaeebdeceabcbbeeeccdcdbbedceddbadcbdcdcbaecaceddebbeedcddbaeecebcadaaebeecdcacdccbbaaedbeecbaaceceaacbbdabeebadecadeedcedcaeedecddbaeaecebaabeedabdaebdcaceadeaaabeacecbcaebddbdaededdacbccecabacebedbecbecabacebdcabaeccaeceadaaabdbbadbbeacbabddcacaaedbccedbeedcdacbacdadbdddacdedbcebbbebdcdcdebacbddeaeadbbdeaebadcaeceecbaecbdecaeeacdacaaeabecaeebbbcbcdedeeacddacaedbabdebacbcbaeceecaaedcdbcacdeeecabecbcedccdaceacabeadcadacddeeabbacaeeaaedbddccbeebadbdcbbbcdbbdebbacdcaedcbceebaeceacecbcaddcaedcadeaccbecbbdeedeadadbaeacdaeccedcbabbdabdbbdbcdebdaaaceeeebccaecebddecdabdaaacceedaeeeeddbedbcecbdddebddeaaaaebbabaedcdedbeecebaddeacaeecaccedaaaaceecdcaabddbcccccbbbcdedabcbcaccbedbcedbbaabeaeecdaecabeadaccdaabeddbcacbeacccbdcabaaedabaedcaaaaacbadbeeaddcbcabeabdbdcdeabeedaacbaeaceabebdacaedecebceddcdcdabbdeacbeededdecacceaeebadedebdedbeedacceabadeedabcadaaecabebcbdebabcacaecdeeececbbceeeaaadedaeeaeccbdabbbdcaabbeeaebeacaabbaabcdacedabcacaadddabbeedcacbdeabdabdcdabadcebaeddbadabedeaeaddecbccaacbcaabecdcdbabeedcdbadaecaccdbcadaaaacedcdddcacddcacbdebacebcadcccedddbbbbedabbbcceeeaabccbebadbbbecebccabbeacaaacbbabddaddadeeacdecbcccbbbaecccbbbaadddaaacbdcccacabaeebeceedecdbcbccabacddbdbaebdadabdceebbcdedceadecdececddddadeaaaaaedeedbaeddddabaeebeacdcedcedacdacbacecadebceaacecbdaccacaeebaacadebecabceecaeaedaaedddcaecaeaeacddabdedaeddcadabcaabadbccdcbbbbedbdaeccbcecccdacadcbceabdadecadabbaaecdebedaceccaedcacdbedaaddaaadececbabaacadbadaebcebdeaaeacdabecaceacaedebacceceecddeeccdbaccdeccdeaecdddbeeaaeedbacddcabcabecedcccbcedcddcbdebceababcecbdaceaeeacbebcdaceadecccedeaccbccdddcccadebabcaedccacadbdebdaedbedeeecbdedaeadeeaaceeabdaddabebcbdaacaaebbbeebdbdceacdeedceceebcbadeceddbabaceadeacbacceebebadacccadcbcaaaecaddebdaebececdbeddbcbbecaacbecaddedbebecbebeadbcacdbccaedcccbdeaeaaababdeadbcacbbbdcedeacdaabeaadbaceaadeeaebcaeaacdbeeabaaebdaedecaaabadaeeaebcebbbdaabaeeaecaabdedeebedbdadcdcceadccbecacbdcecceebccbdeebaedeecbcdcdeeacaeaeacbcdaebeecdcdcceedadbbebeeeabdacaecccacbdddabeedcbcceacdeaebbceeaeeebeeadbbcbbecabeaceaaecbbeededabcdcacdaeebbcddaaeedadeecaadcbdabdaedbabddbdbaededddebecededcccdcbaaecdedebaaabcbcbaeeeadbbcabbccacbcabedaeeeccbbabdecbcbaaaacaccecadececdbabaddecaadaacceacdbbcccceebcadecceaabbadacdabbbbabceadaebedbdcdabbcddeadecaacdaededdccbdedadcbcdedecccebcbadeaaddcddaeceaeecebdeeaecddeaeeadbdcadeceeeedeccbeecdeebedbcbacdbdcecdaaabeadcebdddaedcedeeedaeabcdccacbbeeacececeaebeeeacddedabcebaeaeabeaeeacaeedcaedbdbdbcecdaaacedeaadcedadeeddebbccbeababbeacaaddbbcaccecbbcaddcaccebbacceebadcdbecaeeaaededcdbbceacbddaecdcdddcbeeaaccdbdaacdddabecabbcceceadccecabbeeebecdaeeddcbcbabadaebdddaeededecabddabdccdbccedceacebabdebceacebdbceeecaccebadcccecdabeceaaabbcddaeabbdebbabecdeaaeaccccbcabeedccaabdcdacaaaebdddaecceeecaeabbdcceadbacecebbceddccbcadbcdbccbbeaeadcccbcddaebdbaaaaecaaaabdddceaabbaecabdbebccddeabdaaccceccdecbcacdaebeecaabbccbeddbbdcceddaaeaeaabadcbacdcbaacdecbbabebccebcbeacaacbdbeedccacdecdddddceaabbcadddedababbacbacdceedacdeeeaaebbbcceaabbcedebdebaecdabcdeebadbdcbdbddeeeecdbddabeacaaaeadeedceeaaebbdbcbadeebcdcbcdecbbabbccaedccdccebbbbcccdacbeecaebaeddbadbdcdacaedeeadcabadcbddbbbdacdeabcceeecbccccaecadedbbddbceaacdcdceeedddcbcdecddadabadccabdaddcdacdbeaacddecabdebdddbcadeebbcbddabeaecdbebcaebddbaeedceeccabcaebcdebcbdbaddadcadccccabeabeeebbbbbcdaabdbccdcaeadcaeaecaeacbaeddbcaedbbadcdccbddabcaccbcdaccecdbebdaabbdddbbebacabbebaebaedbcacbbceaeaaabebdbdbcdcabadaaaddcbacecaaaecebbbbadaaceabedeedecaacdcecccddeacadaccabaabdbdaadabbcddbcbcccbcabaaeedcbdbeebceecdcacbcededaeecabbaceceaebbdbacdaacbedcacdcaaceeeacbcbcbccccaebadbdbadcaedbeaddbeaadcdeabbbbeddcaeecedcdeadbbacabdebcabedeabbcdaddaadeeccaeeeaecbaaabbdcdabdadbbcdbccabeaacabbaaacedbbcdaceaedbbbcbcabadeceadecdcbdaaedcbcdcbcdacbabebedaaddadecbacbebcebcbaaaedabdddbabaccbccdbabdbbdedecedcaccebaecabbabccaeaeaaecaabcbdeeecabadabbbcbceebaedadeedebeddcaddeeadebcdbcbacecccebbedebacbacedccabcbddbcddacdebdceceeaeaccaedeaeebabaeebdeeacbecdcabedccaccedadcedbecbcbddccbdccacbeedaabbcbaaeabadcdcadececccbccdabeaeebeeebedebeaaacaacedcaedbbdacaeeeabadbbebdddbbabbbcbbabaceeeaaebdabcdababdecdacedcdacaaedbdbebedeadaadbcaeccaaddddcbcaebabbcceceddecacbdeedbbdccbeadadccaeccdaabbddaaceabaceedebabeeedcdaecbcacedbddebdbaddcdabaceeedabbcdaabaeebbcbbeaedabdcbcacccbadbceaababbbdadbecaedbdedbebabdeddcdecbeebaebeecebabbceddacabcdddedcadcdbbbbbaddcddececeabbccadbcdcbcdedbaacddcdbdecabddbbcaadcbeeeebbdcadcdcbccecbeeedbeeedcbaabbcacddbceddaccceddbadaedccceadeaaddbeaaeeeabcadddbaedaccbaceacdccedaaadaeeadccddeaddcbebbabaaaeecbebbadacdeedbdaeccccbdaaaeabbecbabcabbbaeceaccedbbcdbededbaadccaacceaacaeacaacdcdbdaeacbbebcecaabdddceacbaedcccbbedbbaebbadebdbbceeaeaacbdceaadceabbeecadabacdbcebdcbcadcddeaccbebaeeadcecebbbcdeaceccadcacbbeacdaeecbddecedddcebaddacadbdbeaababcaecadbeededdaebceeeeebbcdeaeaeeabdbecddedeebbaaaddcebbabbedbcbabcaadedcadcbadcdeeeaaccebacdeadbeabdccacbbabddaddbeebaaaecccddbabcbabbcabbecbbbdcccbcadeaeeceaceceddbaaaadeeaadebadbdbedebaadcbcbcdcacedebeabdedaaddceabaaccecadeecdbeeecbeeaabeeedcaceeddaebdedddcecaccbeaddbbacabaacceccedbadbeeeedecceadacdeeebdcbdbeeaaabdaccabdadbacaebaebaeadcdccbccceababecacbcbaadbbadbddceadcaaedadccabcdebbbdaeeecbdacddaeacbdbdabcbddeeadbdacbaadcdadbaceecdcadcdecdcbaddadcddadcaeecedabcbcdebacceeabbbddbcbceceeeabdaccabbbcdabbdceaedcbdeaebebededccdaceebcdcabbdeacacdebddddebdbacabecdbeaeecebeedacbeeacbbbdcdeebaadeecbcceeceeecebddeadeccacadcbdbadedeaceadaadabcdedcccaececddddeaabddeabdaeebbededecbaaedccceeeacdeddebcdaaccdcdadcaddcabbdeabbdcdeadceaacacaeecaebcddbaddceababccadebebecbdbecdcdbdcbaabbceacdadeaaddeccacdcbdeecdebcdbcdaeadacccdcbcbadceeaceaaebcdbbbecbbdbecdcedabaebdbaebadddddeadbecaedaacacdcdccadedddbdbadbcccbaceeddbebcaeccbcbacaabcebdacbbeebddeeaacadeddeedeaaddbceaddcbcbcdcccebbddbedeaceabccedeeaeccacbcddedcdcdcededebeadbeaadaeeacaacaebcdbbcaceeacedcaadadeeecaeebeddcbceeeaeacaedeacbecbbbbeabbccccbbcbebaabdaabbcecaccedbcbeaeabeedbdbdbccaaddcebdeaeccdcbceacdeaceccaaadcbcebcdbedeeeddbcecaabcabbdccbabcdccccceeeceadcaadaeeadaeeeecceeaedeaaddaabebacccdaaabdadeccdeceeacbbacbcdacdeebaabbbccebabaaadeecacacbaacbdbdceabdbbaecaddeabbeeacedbdacbddaeaeeddeaaccbbdabaeedbdcabbabeeaaadcbacdbcdcadbdacceeababedbdcaeeaabaeaebceeebcadbdccbecdbcabcdeabcdabcebbdbaedbddbcecbdcecadbadaacdaccbebdebbdaadbebacebdaaeddedaeecbdcdcdeadddcdabadaddddacccaecececaadcaabcdbbababecdbecbebadcaedaccebadeddebecedcaccebaaadeceaeeadadaeeaabccdbaaedcbbeeaabdeaddccbcbdabdeabcecdacaeacccdabcebebcddcdacaabcadcdabededcedabaccecceddecaecdaabbbecbbcdeabdbbcaddeedcccceaceeabbcccccacadabcbdbcdeaaeccceeebbdabbcdacbcbddaaacedddbcadebbcaaadcbeacbdabebeeaecdeacedcecbebabebdcabdaebabedcedaeebeddbecbdbebecdabbcddebeedccbedaebccaeabeedebcbbeabeebdebeecdaedeebaadddaceedaaabaeceababebebbabdcedcbebdcdbabbcebbbbaedcbaeaaaeadbedaabceddebddcaacdcdbbacbeecdccccabacbcbebbddabcbbddcdedcbdcadbdacbabccbaeeebdcadeccbeddbbbaaeaacbeebcadaadecdabcbaddcbdecedddcccaeeabdcccbdcaacbaaeaeaebedacebbcaaedacabaaedbaecacedcbeededbdbdbbdceadcdeedeecbebebcbaaaeeacebaedcddedadaebbaedcadbabdecedadebacbbedddeacbeeacdabbeaebcbddaeceacadabdecbeaacebecdeaaabbededdeebddccbbbdeeddebdddcabecddedbcbeaeebabadcdabcbbaabccaebbbbacdedbccbdeebcededdddbecebccdbedacddadacaadadabbeddbbcecbaabcbbaeaeadacddbcdeecdbddcdecdaecbbbcbbeacdbbdcabaecbabecebcacadbbeabdeaceedabdbeacbedaaccabdeeadcdecdeeadcddcbdabcacdbcdaedcebbaaedadeaebabcbddcedcbdbaececdccbebcbdceeacdcaedbadbcbaededddadbbebececaacebceaebbcdebddddadbbccbcbdaadbbebaaedceaebbeaaedccaecdddaaeccdeadadeaebaaecbccbcecddcbdbcbbbeebababedbcceeedebbccdaddadebdedaaaaaddcebceaecbedecbddcaadbabeaccdbcaeccbebaccdbabeadbbcedeaccdcababdbaaaecdbebddbcedadaadddccebcacdabdcaaacaaebedddbbabacbdbccbbddbcedddcaecdaddbeccebacbdcbdcccebaaaceecdacddeebcebbbdeccbbaadbabdddbeecebcccbdbaacddcacdebbdbaacdbcdebdcdeeadacdaebbdcdceacadbcbddbedaecbcaebadcbbdecbbacdeeaadadabecdceccedaaeadbceeaddddbbdbaacbbddebacdacbdeceacacccabdebdcacaaeddbbbadbdaddeaddedacadecbcedddaccedeacabcdbabaceeedaaaaebeecdbeecbababcaebbeddaceadccdebababbadeedccebcaecaebaeccabdcbeacaaaaeedaeeceaeeaacbbeddcbbdaebdbcaedbeeaaebdceecdbbcdbbbaeedcbadaeeeebbeadabbddaddcbdccacdbddcbdeaacbdeeadceedebacdddeabdadbcbebbeeeedcceebbcbeacebbdacebdcecdacdcaaacedbbcdbcecaeddcebcabaebacdeaabaeabccdaaabbbdbeabeceaeeccabceaebbdbacdccadcddccabdabcdaebedbebadabeedccdbedcedccdbccdbaacbbdbaeaacbcdbdaccaeaaddbbeeaddccdddcdbadadcdeeaedcabeebececeabcbeddcbaabadbabbbcddecccdebdbdaaaaeeaecadccbcbcbadeebbeabeddbbedcbccabbaeacdeebacccebedcdcceebdebdcacbdebdededaddeeecbaaaaccbacacdbdddecabbbbcbaaeeeebababaadaeedabeacdabebcaaccbdabbeaccacdedbbaebddeecaacaccbddedadccceececdedccdeaaaedeeeceebecdededdabbbeabbdaabdcaddeddbceacaaabaeabdecacabceceeaabecaabddececababdeaecebeeabcbbaaccbeccadaedbdbeaeedbcddbabdddcaddbedcedabcbbaeecbbedecdabbddceebaeebceecabbdbbcaceebcdebdcaebddedccbacbccadebbeebecaaecaabbdaaeaedecdabedbebeddaabbebbaedaedacebcbeeaadcbbebdeebaecdaeabebddddeabbdcbbeababcdeccccacdcadedadaeebbaddedccebeabdccdbeccabccdebadbbedcaadeadddadacbbddcbbbebdcacbabeebabadaebbaadbacbabdebdeacedcedccdcdbcdcdbbecbbacdedabeaaaedcbcaedbddebaecddeeabebdcacbeeacbdecceeaedcdebdcccedcbbacdabbacecccdadbdbaadacabaebadacbeebadeddbdaaedaeecaddcdabcadbeceddbbaeeddbacdadedececdcbbebeabbaaeedceeaaddbadcacbcbdadbbdeeedcedeaacbecbdbbdbccccbaebccebeceaaaaeaebbcdcebdeddcbbbdacdcacbdaaccaeabdbecddacaeabaedcbbbbedbcbcdabecebdbddeaedcbbbcdeceeccddbdedbcadabdcabceeebdbcdadcbebdadbedbceabceeeabebebbbabaaedebbbcdedcdedbddcccdceecebaaaabdeedbddbcbbeaceabbbeddadddcbacadbcedeaabaeecedbcdcbebabaaecdedbbcbbbdcceebcddcadebcedbddaeadadcaddebcabdcaedbbcedcbaaebbededaaebcadedcbadcbeccbdaeaddaeaedceedbeaabeccddbecaaaccbacddbcadeeeecdeddbacbebdeedcdbbaadebdabaaaacaeaacdabdbbbeadeaaeecabececabcacaecbeaabdabbebebaceecaaadddcadadceacaadabcecebcaedccbdacaccebeeacdeccdbeddaddeecbeeaceeadddadbdcaecdaacddecdecedcbeceaeeaedaaccddecbdbdadbaeadeaebbcdceaebadaadedcccdbccaebdabdceedddeceadbcddaaccebbeecceccedebeebcddaeebcdeaeaeccbddebabbcacebdededcecccdaaabaecbaecbbdbdcbebbeeebebdbccdbedbbaadebcaaaebbbbbaecdcdddebeebdbbcebdcabcdaceeabebacaddeeddcdabeceacebceecaccdaaddedabbcaceecacaabbeaccdeaececceecdadcbcebbcccaadedbabbdaacbaccbccbabbaaacdbeaecebaeecaedceadabdaebbddebdccecbeaedbcccdbaecbcebeeeabdbbecbecddaeecbebbbbbbcdcacacdcedcdcedcebaedbcaedcbcedbcacbcddaebabcbbeedadeebbeecebcdaceededebadeaecbcdccaebebcaeedecbaebdeaedcbccebebcbedaebebbecaeaadedbbebccbddedcbcaecaedbbecbeebddcaabbceecbacaeeaecdccedebbedcbcacdbbedeeadbdaabdeeaeecedcededebeeeaecaddaecdebeeececbacbeddcedabaeedcadacdcbecadbddbeebcbadcbbcadeeccbddddbedeabbebccecbeceddbadacdddaabadebeddbcbacaaabdeaeacceeaecbdcadaaccdbaecaabbedcbbdadbccdeabaceedbbcbdedaebbeeaaadccdeaaaacdaccdacbcddbadabbdabcceaaaadbbcdeeaeacceceabeadaababceddeabbaccdeccebceadadebeacabbaddedabdabeaebbbbcbabdccdecbdcaecadedeceeaccdcebcabeaecddbdaabecbddeceaedadabdecaccadcdaebdaeccbdeeedadeddbadcadedccaebcdcabecceedaccbebaaabcccbadcedaaacaaeadaedabbeaeeceeebebcccecddcedbdbddedcccdabdecddbcbedddcbabadaaaeedcbbeccddabbadedbdacbceecdecadcadecedaaecaebcadabaaeabdbcaabaddaadcdbaaaaccebdececccabdacccbbaddeaececadabbecdcbaddccbcaedaccadeceacaddebacebbacdddabaecdbdceebaadbbbcbeebedbaeaeeebbbdebddaaaebbbeddcdadedddaeabadaaecbdaabdecaaebeaabedeebecadcacbabccedcbebbcaeedbbecebacbdcbbecccadadaebedadcbaeddcbbaeceebebeebceaabeaabddedcaedeaebccccacaabcabeedeceabbbbbcaadeecddbaebccabdeddecebcdabccbaeeecaeddbceaaeabeedbaaacecadbadacbbbdbbdededdbecdceededcbbaedeabccbbedcdebdeaecbbbbdcbbbdcdadcddadabcbcaccadccaaaabedbecdcdbcaabebedcadcdbecaeadadbaeabceeaeeaaabdaeddbbbccdbdbaeedcecdadddddacbabbdcabdcacdbdddbdaaecbeeedbacaedadaadeabcdaaeabedcebbeabccdcdeaabccdcaaeebcaebdcedbccacbbaaedebdbbeebaeacbdaabecedcacbeebadebcbcaebeaddeeecceebbedadaaccaeacedadeeebdbabececddceebebecdbeaddcdbccdddceddbadaabedeacdaeacabbdedbebeadcbedeeccbbabbadeeaeddeecabececaacdecbcbeedcccacaeacbcdeacceedbbdabccacbbdddaddbabdecbcdbddddaecdcbcbecadeaaeaaebeaaeeaababcdcbaadbbdccbbcedbedeaebdadcbbbcaaccedcdabcedebcaabaceabaecabbceabaaeadcadddcabdcecdaeeecaeabaeccaccbedbdccabbaaddbbaedabaaaebddeaecabecbdeccabedaedddeacacaaeacdbdddabedabaaeddabadbbaeaeadeccadeacbdadadecacccbaeeecddbbbdeacddcedbbbeeebbddecdddccbaceaedeeacecdcceecbaebccececacddceeabcbbaceedccdedaeccdabebdacdebdaacbcadcbeadcccaddabdececeaadacbddcbaccaadeeddeaacaececdbddadacbdcbecdbddadaddecbacbcbdcbebeaceeacaabdcdbdabebecaadeabddaaebdaddaebeadbbebbecbcaceacbadbadeacbaccbeccebdbdaecccdcaebdeedccbdbaebddbccecdeccadebdccedacabacdddadcaeacdbcecadcddcaedcbdadcadaddedbbcccbcaedbcdccdeadbeeabeedbbdaccdccdddabdbcebbdaaecdedeedddbadaacacdabeeabebdcabdbabddaadcdccbeacaddcebecedadddbbddbcdbbcaeeeccadbaeebabadcdcebacedbebcaebbeadaebccadbacaaacacdacccaaedadbcacdaccdbebbbbdacaebdceebcebebecebaeaccdcbbbdedcedabcdebdcbdebadbdeddbbcadedbbbcdbebbddacebdaecdececebbcbccdadceeeaebaacbdacbeececcceaecebdadcddacebdedbabeeedeabecabeecbaacaddceabdeeadceeabaabbedeadeaabaccdccecbdddbacbbeaeabdacdebaaedceebdbacdabdadeaaccdddbddcddbcaeebcecaeeccddeceecaebbcbcbbbebeceaaacaabadaaaababecdbaababaeceeeddedbbabbaebabcdbbbbdbabcaddedcdabecbceaadebeccdbbaccadaeabececcabeccccaccdebdbeccdebcceacbdccecabdbacebbdddbbdebeccbcdcbdcdebdbcaabadecbeeeaabaccbcaecdbaaecdbbcebbeabebcbcddcdabaedebbbcaddaaacbeebbdaabbeebabaccbaecedebdcdaaddbdbbedecddbaedacaeabccaddcceeceaacecbebadbebdbeaebceddbaccabaabebededdabeacedbadaadacbceacdbbbbdddcacdacbaadaccbacdadcabdabdcebbaeabcacaaddedbeadbceaeacdbabaeeebbbbadacaabdbdadddeeedeabedacbbbbbcbcccaceeadaacaabcddcdebbecaacdcaabdbedcccbeecdeebeeccedacabcaabeceeaeedbcbaeedeeedabbceaabdccdededccbeeecacddeddadecedabdcbdcceedccadccabbedabdbadcddeecdcddebeaedbecebcdecbdcdbdaecbaeeeebddcaacbeebdabdaaddabdaacaacdaecacabababbcdcdaccceaaedbdbaedeedbcdebdeadcecadbbdbacbecabdecdcbcedcaecedaccebcdbbbbeeedbcbbdebeaeeecdccbaeecebcbabddcdedcaedabaaaeaebccbbbbaaeaecbadedbbebabdedaeabcadceebbadeedabbbdebdddcacdbcecaebcabbcebcbbcedebbdaeceabeaaebcbecbcceaebecbaaaacbddbecbbbdeaeaedaccbddcbbeebbacdbeedcedbeceeccaebcceeeaddecdbacebabadabeabcdcbddaabcbddceecdcebadbbecdcbdbeadaddddbdccbbdaaadbeceaebdddaadedcadbaadaeecccededbeeeaabbeaddeecedaedbabbeceebaceecabaedaeedeeccaeceedbcecdeabbedbbebadacdaaceadbeccecaecddcacccaceeeadacedaabedcbadacedaecebedaebecdebdecddbadbcbeededbbeaceacbdaddadebedbdbaaeacacddbcdbdeeddaeedbadbcadccdeebddcccaaeddcaabbbbcaaceadabacadbbbaceaaaebbcbecedbcbaaaaadcecacaaaeeeebccaabecddedbcedeeeadaadbadebdbaabcaaaeabbeaccebccccaaabecaddecaedcbcebdddbdcabcbbcdaddbbaaedebdedcdbeeaecadeadadcadabdecedaeebedaedeaadabcccceeebeebeacdbedeaacdbaedddcebdaedecaabaaaeecedbcacededddceacdaedaeadcacaabbeaecedeedceccaebccecbdbabccddabcedbeeadbadecddacaccbccebbedacbbeeaeebbbaebdaccaecccdcadaaeeebcdabedcbcaeebeeacabdabbccededddbabeaebcaedbcecbdeeaaaabccbeedbebbeaebbeaabbdddbadcaadadbdeabdebacbebdaacaebdacbccaabbddcadaddecebddcddaccadcdcdcaeadeedbccababacbcaabedaddecddcdddbebcebedcaaedacdeabdbbdbdccbebdbddbaceaacbaecaccebedbdceeaccbbbdbcadedddbddbbbbaedbcdbadaebedebaeecddbbbdebbdedccadcddabadeccbbdaabcddaecdaaedebbecedcadabbeedbeeeabbeadadddacededdadecbbbdbeebdecedaddbaccccacacedcaceeceabcdbcbbcaaaadaceccbcaeedeeaebdddbabeeeeabeebbcedddbeeddceddeeaabbaebdaccedcddeadecbddabbbdbaebaeeabbdbcedbcbeedbdceceeadccecbcebecdaebddedbaaeaecdbbacadeaaaaeebdbdccdadaeacdeaececcaddadbcecabeaebcadcdeacabdcccedacbeacdbbbbcacaceeeaaebacbeeeaacaedbccdceaaadabeecdbccdaadbeedeaaeacaaedadedcabddedadceedcdddceeeddadbbebbbadeeaaedcdcebeacebcbcbacbaaaeecbbabbbebdedceedbacccedcabdecaddbddcacaaeeadbebcbeedbbbedcbdecdbbedcaceacbceecebcccabbaceddddcdabcbbbedeeddccadbbdcbccaaeabcbcadbeeebdecaabeebbbebeeadcacbbdabdaceeeccaeebaeaddeccbcbeeceecdacddecabebddbbedeccebccabcabcedbeebcdecbccbaecbdedbeaaebdbadcaebbabddebcdbcccbeacadabceebbabbcdcddcebbabcdbecddeabdaceeededbeaabbdbebeebcedbacceddeaaacecbbedabaecdecadcaaabedaecebdbbaadceebbeadcddcbddddacdccdebbbaecbbaccccddeadddeadcaeabbabeeccbbeecdeebabbeeaeecaadcaadcbecdbccdcaaedbdabbbcdbdebcbaccaccaeebbccdbddcabebaaededbeacccddbecdedacadbabbadbdaaeadcedeaddccdbeeaeaccbbaaddbbadededbdbdeadabecceeaeecdbbcaacababbbecbbbedbabccbcbdbccaebedecaccacedebaadcddcdbdbdadebaeceedaddabceaebeedbcccebeeecaccdccbebaabaeeecadbaadcdbdcdacbeaaedacbddebdcccccdbacbceadcbaceaedddeeacebadeedcaeacbcbaebaddeacdcddeacabdedcdbaeaebaccdacbbaaaabaaccbabeaaebecedcecdeaacecaecddeaeacbcddbaebdaeedebbbadecdeaaddccaeeebdeaadbbabbcccddedacbecbdaedeacedcaaadabdceedcbdcdbbcadebdaceddebdbbcaadeaabbaceceedbdddacdeeccaacceadbceaacdecacaababacdddceceadacdcabdbbcdbbcacebbdaceeabeabaaabbaccbedeccebecebddbedcebabddadeabcdcaaacaeddbcddaccacdaecbddeecbddcacdecebacceecaddbebcaeddbddeebcbabaebceeacacacadedeeadedeadaeeabaeedeebbdedbbebdbaaacdddcbaecbebcedbcaecbdadbbceeabadbbcbedbdbbaaebebddbeecdcedcceaaceddaaaadbabdbebaacebbddddbdebeaaccacbadddbbbadcbeaddaabaacdadbddeadcdcdacdbcdaadeebdadcecedbbadbbebacbabcdbebadeeccebbebeebcbdaeecaabcccdcdeeaacdccdedddbbcdeabbcaadbccabccccadcebeccccadbbacddbcbddabeaccbaadedcdeabceabcdeadcaebaedbabdebcabbbdbbbcaaecbdeecbabccecaeaeddacbecddeddaccdeebcccdcdaaaaeabaaaddedabaaeeacaeddcabdccbddadcbccedbeccebbbecedbadaedadddbebccaedaadbbdbabbdeecdcacaeaccebbbadeecdccaabcbedbcdacddaeeeaaaacaacadaacbdecadcaeceeccbbdcadddabecbcabccbdcdbccaceedcadecbaeedeaeeeadeddeecbcceaecbeabcdcedccbceecdbebcbbdedbceeaedcdaeccdecbadcedbccbdccbbadaeeceebceeabcebcddddcadaecbbaecbeebacbdabccadabdcaaebddaabbbaeedadacdecececcbdcccbadcedacccdddaebbdddbeedbccbcdceabcbedbaaaabdacddddbccbeeabdceebcaaabadccededcbadcecaadbbadeadedadbedeeeededddeacbacbaaaeadcddedadcdeabadeeecaeeaaababbacedecdbbbdaeacdedbcaebbbdaaabadadeeccbcdecbdcbabccacbecebbcbadebbdabbccaeebdddeabcbbbeebecebddbdabcadbdeeebbaabeaadeedadabdbcecadecbddccadeeecacbbdbbbeaabaebcaaaeaabeedbebccbddadbaceaecebaeadeaebdbcdacdecdeaeeedcbdcbcddebccddadacbaaebeaccecabaaebbedededcbebbbadceeaebecdbecacdabadeaaaebadeaaabcabbbdeaeedbadeeecabcbeddeaaaebdececabbceeecadabedadbeeeecbcecaeecabddddcaebcbadcaadeeaacdadddbbabaddbadecbecabedadddcababaedcdeecceebecaebbcbeaaaccaaeadeadbcdcacabaedcddadecabeebcceebaecbbccdceeebdedbdbcaaaaabdbcddbaedcceebacddedeabebcdedcbdbdcedebcccacabceaccbaebeacedcadcdbcdcbebaabebacdeacaeeceecebedaaeccdacebcadcecaeebcebeebdbbaceacaddaededceadaeeecaceadeececbcdadeaeedcaddadeddeadcaedcceddadedeeaaabdbaaebdbbbcedccbceabdceebdebeadaabdacbbbeeadeecbaacbedebccbedacdcaaddaddcaaddaeeebddedcaaecddeceaacbcdadcbececadebaeaeaeececabdabdcaeacccaddaaaccebabaaaecbcbdebeadcbbbdeedaeebeecaddcebcdbcbdaadccbedeeeecdbcecbdebcddbdeaeaecddebeddadaabbbadbacabcaecbccecdebeedaedccebbdcacdeacacbeedbadecdcebcaeebacbbebabdbdcdcedceaabcadabaeadaebdddecaaadccceecbbbdedcabceecaeddbdebbbebcedecdabcaeecedeaaebddcbcabccabddcedaabaedbcdecbcbecdeeaaddbddeaceccbcdbeaaeddabeaacdaacecbadbaddabeacccebcabbdcbaaceaaabbdccaaeaccebbdbacecdeeeaeecdddeaaccbcbecebadbebcddeeadbdcadaebeaebedaaaebdaabdceccedbdeeddababebedccccceaccaeaacbbbcbdddbcbeeeccacbbabcbdeaddcebebbeaaeadccaceceeaebbddcbceacebeadcbbecdbdacbbedbbeddedaecbedbdadcaabedeeebaabcedcbacdceeccaedeadbceabbceedcdecbaddccabbcbcbbedcbbedbdadccaabdcdaadeabbaabecbaddcddcadcdecebbdeeceeaddddbececaeadcbdabddccbacebdecbacbbbadedaccccdedbacdeadcaddeaeaeedcacecaabebcabcebcdadccdedbcebcebcbdcdeaabcebcaabdabbdbaebbdbeddbebbadbcaebbbccaaaddcbaacedccdaacadbbbbbddecaebaacbcacedcdbbddbecdacecbaccedbbcaeaecabcddabadbbdaecbdceaccbadcedbdcbbecdcedbbdbaacdbedccacadbceeadcaecccdababaccdececebeececcdbbabaccdbecedbccaaeacadbaacbddcdccebcbaaedcecdcdacbecaaebddedbdbedadcbceacdadcdaabcbbbebadaacaccdbccecedcecbaeedcadebbdbacdabbdceebeedaabeabcaeadadebcddcbacdacacadebbbecabbcbdbaabaaeadacdacbbebceddacddcddadcdebeecaceebcdbbabbacecedccebddedcbdccdcabebcbeccccaaacddcbbbcaebeadeabaaeaaacabdbdcdcaacddbaabdeaaadeaedaebbbdeecedabdcbacbccdaacacbccdaecdcaeebdbbaedbdadccebbcacadabdceadececaceecdecdcbedbcbadeeeebaccaddebedbeceacaabbedbbacbedddaaeebdbddacbbcccabaeedcbbeecedeebbdebcddabcdccdbdadedbaeeaddaeeebeedbebddeaddddddcbadacaaccbbadaebbacceecaebeaeecacaecccbcdcdaebddaeedbeccecacbbeccaadcabccaedeedaaeacbcdddddecadabccdeceaadcbedbceedabdaebeddebddcabbecbdedccacaebeabbbdbedaedebdabcaaccddbcdcdbbcbebeceaecbacececaabcceeabbbdddedabebadceaacccbcaeeecbecadeebacadecbbbccbdadbaceaeeaebbddbbaacceccabcecacbbbaceddecedadaabeeeddbadccaeddcdedaacddedeaaeaedeececbcadaaebdbeecdaaadaececcdadacaeabbabcebcdeacdceaccdaccabdadcdadcaeeeaadbccaeeabbeaaebcadbdcbddadbbeedbbdaecadeacddaebccddaacbeedadbbdbdcabceebacababadecbbdaecebeacdcbeddcbbaaceadbadaeaabecbdccbbbdccccdcceedcadbaeccaebadeebadcddecbdbeeabccbddaebaceacccabbeeaeeacbbeaebacebbedabdcecdededeeeebaaacdeabbeddbdeedbbbbcacddaeeabaddabcebaebbddcecdbadacddeccdbaebdeccaaaaeacbebbbcdeecaabdeebecceccbcaebbeaccaacaddaeaecadebecdbcddaacbebbbdbeecebabddabcdddbeeddcdaeacedabdedeedbbeccebbddbccbebacbeddbaeebbcbcadceabbebacbbdbadacbcdccbadaaeacebdeeeabbbedbbcceceaacdaebbdcacaeeedcbcadddbdeaaaddceabcebcccbcbbbedbebbaaadbbbbdbabccaebaedcbacacbaaddebbcedcadbbadebaebeacccabcbabbabeebbdcccbddcaceedacadcaaeebacdcbaccbbaddacdeeacaceecbbcaabbcdcabeaaeadacccbabaadecdeebaebdadaadcbcaaadddbaadaeceaaeadccbbeeaddcddbbcaaaeccbdadcaeeaeceabccaebbabddecaddebdcabdadecdedddaaebadcdebeaceaecdbeccadbbcadadebebbeebeccddeeddeabcbceadddceddcaacadeeaebeaeeabeededdedaedacebedebacecadcaebadadbdeeecedcaaeccdcaadaeacabceeabeaacdadecbacdacaaddcaebcecbddacccdbbbdeadaaaeebedaaacccaabeeceabeeaccdeebebaeebdabddeecedbeccadcddeeceddecbbdcacaccedbeccbabceacddbedcbcabaccbaedadecabaaeddaeeddeccebdadeaaeddaeadaaeacaacedacdadeedadbcdddedebaeecbdbbdedbeeddadaccaacdaedecccceacacabeaeacbebbadbaaddbedbbbbbbadccaddabbcabedddbcebebccddebaabbbdbebebaacbeeebabedccaeabcceedaabcdccceecbabcceddcaaccbaddcdcddaabecdddaadcebbbebdeebebbddeacaceceeaeededcbccaddcacccbaadbdadaabcaecbcebcaeeabaecbaadaaaacdbecececbabcbececbdeadaabcdcbaeedabccdaeceedcbbbccacbdbebbcdadaecdcedbdcedeecdcbddccdaaadccaeaccbbebaadeedecedbaadcedcdeebadcabaecdbaaebbdaebeedaaebaaaaecedbcdbcdaedecbeeadacaaaedceadbdeecbbdadbbebcebdbcbdededdeeadddedbdeaebeeceeebdabaccadabaabeccdceddadeaeabeddabdcabbebebcabeeceecdeedccdcbeccbeaebebbcecabdabdabacabbbbdcdeceacbdbeccbbdeccccadaabbebbcdaeacdedddbdeacdbbbbaacbccedacbbebeeedadcedeadcadcbdcaceabebdadcbcbaabeeecbddccaaabbacdcebaaeaccdcccbbaecceddcacedcdcdbadcceebeabdeeadabbcdacdbadccdebceaacccececcedbbaacacaeecedeaeecaeddbecdebcbcaaebbeaebedbcacdeadcccbcbeaadaebbcaadddcceeebccbbaecdabbdbeeeadcaccbddbaccdacacdaadbadbaedeebcadbcbbdddceaccbdcaeaddbeddabaccccdccadccbcaabdaadcdabdeedcdedaeeecdcaebdacddbabdcccdecccddcdeadaeaeeedecbeaccaeaccabbcbcdabcabebeabecabbecbaeabaaeebadeeddcedbcdeadcbaaddcdaddbabadbaddecaaebecedabdceaccbeaebdbceccebbeceddeeddcceaabedceeeaadcbdebadbddebacbbecaedddeddeadbeeceeaaeaddeebcbaceebcaacbbbdbddeabadccccedccedbedeababdeacabaabcdecbebcabaddadaeadeccbbbadebbbeaedebdabeeebebdaedcecbddeaeebeecacdabcdcedaacbecedbcddbbeccbecccbacacdacbcadbedccddaadbedcdeeecddccdcbcdaeaaddbabbdbedabdcbbddeedadaeebedeaacbbbeaaeebbbeaeaeadbeabeaddcacbbeecccadadccdeeabdccdabddebdaaddcddddebeeeaeccbcddceeebcabadabccacdebceaeabcdcedbddbabedaaeeeadcbcdbadcacccaeeebbdaaabaccbabecceccbddabbdccddedbddeeacabcdecdcbbacbdeeeaaadaeedeeabaceacbddacbaabaacaaaebbceebccacaadebbeddceacdccdcedbbeecebdedaeeddedddeeabcdbcceceeaeaedaaebdaecadaaecbebbbaeeddbdcebaddecededcdebedcdbdddcecccceaedcbcbebdaaebeccbdaccbbaabbddabcaadbedbddccabdccaeeeccbebcabdaaacddcdecdcceacaceecdbcddbeebaeaabcabcbaedbdaeddadcecbbdccdacaeeccdddaaeecdcadbececeeaeceabbacadaedddaaabbecdcbaacddebebdbcbdabbceabceeedbedebaabeccaedbbabbcccccecadacebdcebcbcdbbdbeeadeeaebddccceaaececdabbbbabebbcddeeaebaecabcecaecdcabdcadbaeacebdccebceadeaabbcccecacdbdddbceadbacabbbbbbbcecebacddbacdddecebdcccbaedeedaedaaabaaebcdcaaaaaedbbeebddbceeadbebebacdcdcaeaedbcaaaacbdedebedbeecedccdceeddecbbeedcecbceabebcbbbadccedcecaabcadaecbaecaccedbddebdebaacebbeaeaedbbccdecdebbebeeeeecacacedcecbcdabddcdeccedecabcbebaeecbeaecaaadeabdcaebacaadadbaaeaaacaaabbeeaadcbdcdaeeabbeeedbaadccbcdedbbdcbedbaeddeacdbbcaedebbbbcaabaceecacdbbaacdcaeeacdcacdcdeabaabebebadccbecbbccebdbbeaccaecdcbeadebddddcebaebbcdceddaecbadedebeddbbbadceccbcebeedddbeddcbebbddadbbdcbbcceaceedcbecdecaecebccebadaeabcddbeabcdadecdaedceedddeaeaaecaebbdcdecddcbecdcadaabddccabcdbdeaccacaecbbcceabadeeecceababcbeebbdeebbabbadbcdaccabeececcccdababbaabdeeddbaaebedadaadadbabdcedbeaaeabacbedadecdceeceeebbceaeabadedbadacebaadbdaaacccbdeebedeeaaecdccebecabccdebebacbdbceabcbbaedbdaeceaabdbeaecbabaaebabbddadeaabbdceacdcdbeabdacebbdaaaeddcdacbacdebabcbcbcaeaeaadbcdaaedbbacceebbcdeccbaabeabeeaadbaabdcaaedababadbbecebbcbbabbcaebeecbaabacaeacadbdbceaddbeddadbcebedbbacdabdadbbacdeeeaadabbdbeedeecbccdaebaceedccbdcdeaeaababcabbcecedccbdebaeedceceecdaabbeedccbecabaeeebddbeceaacdcdcaaecbcadacdceeeeddcbdbccbbbacdeacdcddbecabcdbaddeccddbbbaacdedddcaaecbbbaaacceebdbbcdbdaaebbedcdaceebaebcacdeccaadebabcaaacbbadbbcbabedebcececabaadbeaccdcacbcdeccacbebebbcadbeebcaebdbdadcaadcbecdcbdeeebbcedcedccdcdddbbeaeacdcecbeabcadebbdcbebddbcaebeabccaceaabaacbddebdaaebedbacdcdeedeaccabebeaecbededabceadcbeabaeebceacbeabadddaeaeeadbdaecccbcadcbedbbaaceedbddddbdebdddedaadbabcddcbcceacddceedeacbcccaeabeabdabeaedddecbedeccbcabdadcdbaeaddeaecdebdabadaadddaeeaadcacdbcdaeebeddeeeeaebadbdeaecdbbcbdeeabccacbdadbbcedbeeecedbabdbdabaceeaeecacebabdcaeecadcdcdcedebabceedcbeddaeddbcdcbcbbddbbaeaccaacadcacadbecddabbbadadbdadbeceaedeacdedbcadeadbcaadeeecddcdacebedebddeacecccdbdcdcebebdbaebcadaaebbbdddebbddbbabeaebeccadceebabaeeccbbceacadceeccedcabbaadebeecabedebebcaecebacccdacceabbddcaccdacababebcaadcdeccedeeebdcedbededcdaacaaccdbedcdebacbcdacaeeadbaabdebcdceaeaacbcbdabdacbcdcaeadcaeaccedcecadaaababaabbebadcbbcaacacdddaceebbedcdccddbbaacceddaaaccddbeceddbadaddcaebbeebabbccbdebcaddeedcbbadcccbbcbecaaceababbcecabdbdaacbbedbcceacdabdeebccdeedaccbbaacacdccccdaaaccecebdcdedaaddbdabacabbedebadbcdcdeaeaceaabedebcaccaebbedbcedacebbcacbebaecbbacbdccdeaaacecceabcdeabdaacccddccdaaeccebcaddababbddccddeaaabdabcceececbdddccbeecbebcdcdadbddeabedebdeaeaeceabdcbdbacbebbaaaeeaeeeabeaeccbedbadcdcdcbdabedaebdbcabddbeaebbaaeecbdebddbabcbddbdcceeecdebcbdcbcbadeebbbaebcabcbbddbddeeeebeeeeceeedbbbcbcddacabaadeceadbbcaedcbbaceedadeacaedcaaedecbaebbdbeaddedbceacbecaadbadacedbacddadcaebebdacabccabccddaeaccbabacddececceacdadeccccccdceeebabebdceadebeaacccdebaeacabbcdadbcadecbadeedaecaddbdebaabebceeccbaedebceabbacaeedebdeeabacedabdabebddbeabedccbedcdcabcbeceaabeebbbdcececdaedeeeabacbdeabcabceeaceccceeeaebbbbadceeebabecceedecbbdbcaabacdcdcbceeebdeaccabbdacabdecdcaeedadccaeabdbbbbbcecedebdaddcdaddbaaddaddceecbddaccecdaaeabccedcaabebedecdaeddcacaddcadbebaaebaeebcebebcbecccaeaadaebbbeddbdabacadbcbccdcdedeecabdbaeddaabcecebadcbcdadeadeebcdeeacadbabdecdbebeaccdadaecceaaccacbbbaeaababbcbdbdbaddedacddbadacadbeddbeaebeaaeeebcadbecdeeaebbadddadbbbbebddcdcebaaaeaaaadadceaecadcdcbccebeabeabddbaecaeddaebacbcdeddcbeedbbbbcecaeaeeeacabebbeecabebeacdacebbdaaeeacdeabaedabaedeeccecbcdcddcebeaabcecbadbedceecdcdaecbecbadaeedbcaeabeacbbecdcbbbaeabcbecbdacbdeeecacbeabcaecccbaacdedabbedccbaabcabdebeacccccbeebdcdedbaddadebadcebdabeddcceebaadeedabebbdbaeeeacaadcbeaadecbcbaeebdcccdeedbdacdacbecadbbddbeabdcacebeeabcdcaacaeeadadabccbbadcedddbecbdabbedbbdebddbeaeabbbdcbaceaebecbecaabadbacbecabdbedaacbaebcdbcaededcaacaebaabbabcacddacbcabceceebecdcdadeedacaabccdbaceacabedcccbcbaaeaebdeabdbaccdcaabedcdcabecdcdcebcadbdedbdbdcdcedecedbbebbbbccabeadddeeebbbeebbdbdebeddcbccabcbcadceacecceaeaacbdcbbbbacadecdbcaceacceccbaeeaddbdaaddaeeeeaaaaccbedecadcbcbbbedaadddecddedadbdbabdabedccaabbcbaadbdedeeaccbaaeadddaebbdececcbadaacdaeecddabcaeedaccbaecdbbadcaaaebbadbedaeaadbebeddabccaebaacababebedbacdbcdaeeaecdaeccaeababbddcdaebbaeecdbaadcceddabeedbbdbcaceeebbbceedcacadddbeeeeebeacaacdddeaccdaebdebceddeabacdbaedeedbbaddacaaaebadeadcecacaedbeaccacbcdccbebdeddbacddcecceecdcbebcdbeabdaedebaccbbabdcededbabacbceaeaedbedcbdededbaeecdeeddcbbbdccbdcacdeebbdacbddbcbbceedcabddcccacededadedccdbbeeaccbccdadcabcbbdeaaaadcdbcdbedebcbabdbcdceabbbaebeebcbcccecebedeeabdbebecbcbdeabbbabcddaabbeabdbeeabdeabbacebcededebedcbbcecbdeeddddabccababebbbdbeaaaacaececeabdaebbacebddedbebaebdabdceeccdadadbdcbaddbcbbaaecdcbacdcebbbebbaacbabadebdddcaccddbaebccdeacededccdebebccaaddceadabadacaecebbdabbddcbccebdabdadadbeadaadceacdecbaacceebedeccebdbcebbcaaabbbccabbddedadbdeaddbbebbccdeaeedccebeadcdaadcdebabdecebacdadceeacbaabbbccedcadadbaadadcbdeebdcdcdbeeadecaebbbeedbebbebbeeddbbcceebbecdbebdaebacbaeaacbcdeaaccbbadccccaedeebcccaccbebeabdaadeeddbcbbceacdceeedceebaecebabbbcddedcedbddbeadacbddbabcadbabbacaecdacaceddadaaaddcedcbdbddedababdeadcaebaccdadedbeecbcabeeceedcbccebedcebeeaadcbdddcceebdaebadccadcaaeebebeddbbeeeaeeabebdacacdaadbcaadecaddaaeaedcbccdacbdccaacaedbccbecbcbaaabdbbeedbeeceaddbcbbccbaadabaebeecccdacdeaabadbabaecdeaaadedecdaadeadbbcccceddceabdeccacdebceadabdaedecdecbdcddcebaaeaabcabadbcbaeaadbdecccceaaabbabedbaabdedeceabddaccdedbcdbbabccdabcacbcaebedaadedbdaaeacadbcbbebaccdcdcbcaedabaadbbdccbdebbccadecddddecccaabbdbddbcdcedbddeecdedddecdeeaccaebcccaabecaeadaeebbaaeaeacbccabcbcaeebdedaabcebdbacdeeaedbbcebceacbdbdeccdabeaaecdbcbcbebbbaaaeadddaeccddecbcbdaabaaaedbddcdabaccadacbdededddcedcddebccdaaceadeedecbaeaecadddeeaadaaddebbcaaebddacbeebddbcdbbaedadadadddeabbcdbeeeaaaeddacacaaebcccbaacdcdbabadaeaabdbeccbbabcddadeedbadcbbdeeeddadddaedebeadcbbceacedccdaacebdbceaaeddaababbacebcdcecadecaedcbeedbbebeecdcebdbeeeaebaaacadacdcaadcabbaeddcdeedbeebaddabcccadaaadbecceabbeecbabecbdcbbaeacaeedbabcdccaccbaeaaeeddbaaaecbdddbebedaadabbcdeecabdaddaabbebbeacccebbcbabcabaadcdaecccbeeaabddcbaedebbddccaaaaeebcdcaeeababdaacdebaebadcacaadecadeaccbbbadaabecbebdbaacdcdadcbeebccccaabecccbdaecbaabcceddbadaebbbeadaddcecdcbacbdcdcbadebaaaedeedccbcdaaeaeaecabeececaedddeddcbeebcaecebbebdebcdababecaabcaedceeddadccbeacdbdeebbeabaeddabedcbddedaeaaddaaaadebeaebaedaceebadcdaeaceabbeedcddcddcedeaeebdcacaecaebbdbdbcabcacbaabdbccabdabecbcddbdcdbeaadedbdcbbeecbceaecdbdbacccedddaadbdbabedaeacdadeaaaaeaeaecdccaebaecbcbadeebcdddaecbeebdececdcaeddcabebcbbcbbeddebdeaaebbcdbcdcccbbbaeacbdbddbdbddbdeeebeadedeebccbeddaabeacaebcebeadcceccdabaacadaceeaddbdcadeeacacaaeebaaacececdcdeadecdaddeaabaeabcbddecdeeaeeededbccdeabcdbcbaceebdbdedccabedcacbbcccbbeebedbeddebddeaecccdebeacebebedcedacbeabeaeebaedaaedbaaaaecaedcbcaebecbabbeacbbddbadbbdcccdabaebeaeeccedcddabaccbdebeeaadaadacabdbcdaacdceeaacbcebedeaeadddaccbdbdbdccaddbdddebcedbdabdaccaccecbaeedecccccddadeecdcadbedaaaddbcdcaccbdaadacbbbcecaeecbebdacddbcadcadcaeebcdacedecceaddaaadaddedbbbabcabdebbcbcbecadbadccbdcbdcdbbacdccaeaaceadecdcabeacdbeaecabacdaeccbabeeeaccccbeabebbccabedccbcaccecaebedcacbedbaaeedacbceadaadbccacbabbdaabbcbbadbeceebcbecabeaadababcecdeabeadecaaceceeacecaacbcadbeedbdedcddaabcdaabedeaacedabeedddbdbadccacabbebdabebccbeabbaeebcbbbeacaeacbadcdacacbadcbddaecadccabbececaadcddbceadbccaedbdcbbcbeabbeddeaaceecadaadabaccabcbcdbbcacdaeaaedddabdccbdbcebbdaacdbcdbeaddcbbdceedcbcbbecabadbecabcdaebadbbbdeecaeeaecbebbccadacabcddeaeaabadcabdbbbaeecbbdcdeadbadbeddeaeeceadabaabbedcadbcecacebddbebccdacdedebeebcecccdbbdeebedbcebedeabdbdddaedcbbbcdedcccbcabbabdcdebddbacbecdcaedabccccdcacacbededdbbacbdcbcbbdaddaaaaccebcbeaedcabdbdababbaeaccacdbcebcacdbadcbdcadbecaadddcbcecbbedabedddecebcddadeceacbbabdbdecebdddbaddebbccceadbebccbadddadcdbcebbdaebadabeacedeebcedeedebbebbedcdaebdcbabadabbdacdcccddaecbcbcbcdbeaecbcdbaadbeddbbcadbcdebccbdadbabdbbaadceddcdddacccbdddaecbadeeeeabaceddccadbeecbebbbeddeebbedaceaaaeebccedbdecadcddcebebdcdaebbcddbbbdabdbbbdbedcdbedbadacbdcccedaeadaccabadadbeddacaacabbcbbdcdabbecdecbbbabbeedbbaadcecdaccccaaecaddeabeddedccbbbbcbecebbaadeebcecadaaabcccdceedbbabaadcbebdcadadbedddbadbecaecebadbdedadaccddadeebebebabeacecbadcaaaaecebebaabbceacecaeaadbccbcccaccabccabadeadbbceaceaaebbdeacaeadcaadabcebddeadbcdaacbaacdeeaaedabebcdecbadabbecbdeacedabadbcedaeddcccccccabcbcaedbaccccabaebbabadeccaebbcbcddaaceabbeddddecdbaeecedbdcdacecbddcbeceaecebeabbcacedecbaeccebbaadaeedecebddacddabecadccaaaeadceaabdddbcbecbaeeacdbbbaaabeddccaedbcbbdeebbddceadcdcbccecaaacbdaaebacabacccaddbdceebdbdcebacabccadcaecaeaebdcdcbaddedbeddcaedbbdeaaedeccabaaddeebadacddccacbaaddeeaebaccadaaddbbbadbedeebaddbacadeaecdddbecccadbedeeccacdedcecdbcdedeaebaccbdaececdeaeeecdabeebdbedcbaddaceaededebbbaccedccaadadacedbacccdbcaaebcccaacddaebdbbcceddabccedadedacbabacdcccdbaacedbbeaabacacabcdaceadabcacdceecebeddadadaddedbceaeedcbcecbeaeedacbecdbdecceecadecabaeddaedacacacbbecbddbbdbeacdecddcceabedcdadebdaecedccaeabadacbaddaacddbedccbeaccbbcbabdbbbacbacbabeabbeaccbbbdbbdeeeecbacdcecdbbadabdaabdceeabeaabddaecbcbdcdbddcaccbddceeeceabeeeedbbaacbedbebecabdcdcbaddaddeeaacecebbabddebadbbcaeacdcbacaaeacddcbacdadbceaeebcbdbbedabcaaccbabeddcccbedacbbbbbcdaabcbeceaabedbecaaaadcebbeebacadecdbddbaebcbdbeeabcadededaaccdbccaabebbacddbbeaadeaeacadbceaccbcdaeaeaeaeadeabbdcaabeecccdaadcaeacadabedbaebceececebbadcdeddeddaacbeebcdaaadacbdbcbceaadaeadbebbebcdabaccbadbeadecdedecccaeacddbaaddccbdebebaecbcabbbedaadeebabccadbceaccaeccdbeaebebedeeaabacacceadcbadcdabccdbcaacaaebeaddccabdababaeacbddaddacebcceaccbccacbeaeeabeebcddeacaddedcadceecaadcdbdddcbabbadedcbccdaccabebdbaebeadedeadaaadddaaeaacdadabccaceebccdeeddecceaaeebceaedaaebceeaeccbedeccecdebdcecbbadccacabecccccdacaabdceaddbaeabbdebabebbeabdcecdcadebadbddcaebdeeebdabccceddcebbebdeaaccebcecaddeccccbcbaebdaabbaaeeaecaddebdddcbccbeadcaccaeedbdbaeaabcddaceacbebbaccbbbabebabeedeaedbdaacbdcbadcadddbbaaeaccbcbdbeceabdedcaaebcacedaabaaaaabdedbaceddcdbcdbdcabbbdcbaeaacbdabdedbbcabbaadcbdebbadeccbeeacaaabeeccbdcaaddeedcbcdcccdcdcccecedaadcaabbeccabbbdcbbcecdacbeeacdbaddedcbbeedccadbddbaabeaadcbdadabedeaaddcceccceebccbeebeaccdceebbdebdcbbaccbbdebcdacaaabbaaccdeccbcbeecdaedbeabbeedeeaaccabcaaecabdceaddbaebaceadabcbadbbbadcdeccdbcaacccceabeababdcdceecaeceabeebddbaebbbecaddcbcabeadbdabbaedcdeedbdbececcedaaddcbdbbcabaabebdcacdddcddacddcaaebeeedeaabaebcebedcaedaaceabaccdcccbbcdcdcecbdebdddecabbebccadddeedbcdeecceccbdaeccedbeecadacddccceaddadceeeebbabaaceabacededaebdaadddeccdeeacaeeeadebdcaaacaaeabddcbdcaaadcacdbbbaeacbdbbeacedceaaaedcbcbddaeddbbdeeadbeeaeaabcecdaedadceddceaaebddeeabbcbdcbdaddcbcecddcbeeeecedadacecacaedeeadedcebdeddaeaceccdacabeeccaeedcecceddaabccdbebebddacebbebeedbbaecbdeadcdedddddccccaccebbbccbceadacabdaadcdbcddabcaedbadeebcebdeaedacdbddaaeccebcceadadbacbcbceaabaeaeabdbddaeecddcbdcebddcecdbabbeddaeddeeaabbebcabbaeaddebcdbeeaabbbeacddccedebaceadedceddacebcdcaedddeacbbbeaadeceacaeecabeeadbbceceeecdaddcebedaacadabdadbacbaeecedacceddadaedebadeddcdaeabbacabccbdcdeeccdbcbbccbdcbadceeddbeedadcdbaeadeccaaebcbceeebaeadcbadbeaedcececcedcaeebebdddcaeededacdccbcbabecdeaaeeadbdedcccedddbccedecccbeeebacdeeceadedbbaedcdbeaedadaaddeebaeedacacdcbbbcecbbbccbeabedeaedaacaaabaabcaaacacaacadedabedebcbbedaecebbbadabcabdebaadbcbeaaadabbbddaeebbccbcecdddabdacdbaaecadebddecdebbeeecdabbcbcccaabbcdadbaccadadbdbdcaaceebaaadbdaadbdaeacbadbababeadeaabebcaabbceecaaadcdedaabaaacccaceabcaedaaaedccebcbbbcccbecaaeaceedaadcbbbebdbcccbcdcaeabaeaccecedccabdaaedacebbaabcdbdbceabaebbeabacbbadbddecccdceccdabcebeabadeddacdaccdeaccbdcaceadcceeaaacbceadcdebbacbaccbaaebeebacebabaedecbbddebcbbeccedabeeecbbcdabacecaddedbbcacbaabebeddcacddaaaedbdcdeaacabcbbacedbcabebbdddcaabdadccdcdbebdebeebbbceeedeaeadcbeeacdadcacebacadaacaecaddbececaaecbbadcaaddbbeeadacabedacdcdbaeddbdeedbdebaaedbdbadaeeaeabadddbcaabbdbccceaddbedeebaeceabeaedbbbdbaabaecaeeacaeccbbccadaccbddcacaacebeecdeccecbbdbaedddddcdadeadaabbadeebcaacbacdeaacacddbecbedceacbecceebbabdeaacbaabbacdacecbacdebbcbdedcdcbcbaeaeeadcdbeecbbacaccdbcebdedbabbecababdbdbcddeadabcdabaeccbacaabedebaacbceaeaddaeedceebdacccdeaacdbbdcdeecadcceeebdbaddcdebeaecbadbcddbbeeececeebcbdeedbcbcacbceeeddcbeaedeeadaceacdccbcecbdedabbacbbaaebaddbeeedacbacaeaaeeacecaacabacdbdcedcceeacdebdbdbacbebaceaaccbaccbecbecacccccaadbcbcaccadcbdaaddbbeaccccaeeccacaceadebedaddcbcceaaebddebaeacddbdddbddabcdeacbcdeecdadabaedccdebdbedaabbdecdaacaaaaddadadceddbacdadaebebdcdeaaaeaddcbcdabbeacabecbdeaeaebcaeadddeeaeeaebdcdabbbeeeedecedcdabbaccbdaabedebceddcbacabccacebeaeaceddecbcdaaedcccbecdbeadccdbbcdaccdbedbdabbcbdcecbdacbabbcebbaabebacdeaecacededeaaeaaecbeabbcbaebadbacedcabbecdedcccadebabdeaedbaddeceecddedacceabaedceaccdaabbecbeaeecdebeccdaaddddedceeeeaeddabecbbbeaecbdacecceaadbddaabedbdecdeadcaecadebacbacbedbacccbaccdedbbcaebabceebbdeadebcdeeadbaeddbeebaadbeedadbecddadaeebaedaddacdcdacebecdcdcbdbcecbaedbcbbccbccdddabbaaecdbceeeeecdadecbebdbcabddbcdecbccdbccbccbaacaedebeebaeacbadbacbdbadaadedaecdcecabbdabdbddebedbbacbbaeedeedcdbeceaebaeceedddedbceadecaaeacbadddbabeabacbaaeceaabecabdcaddbabbebdcdcaedeeaeebcbeaedbbdddeccacadebaeabcdbddecabdcbbbeaccceccadadcdcbbedcbcaaddacdbccdadabddbcccacecaadeadecadcaadadcaadcdeddbaeeddcecaebbeeacbedcacadbbeeedaabaccecbdeadcebebaecebebcbeaccccbaeccabeaabaedaebbcbabbeeadaacaccaececdecebbeeeaaaebaaaaecaeceabbacbdabadaadadeacecececcbaceecebacaeddbbbdbecdaccecacbebeedcceaacddaddcadaaeaecdeaaeeaaaddeabacbbbdbbcdeccbcbbcdddaaaacabdbcabccbaaebbdccbeeaabacacabcbdbddeedbeacecbeeccdabbdccbcbbabdddaebbccaeddeeecdebaddbeedacedddcbbadbaddceceeeabadcadecadbdadcbcddbeaadcedcdaeeedaccbcaebcecaedcebaaccddbcdaeacbbaedeccdedbecbaeacbcecaabecdbbaadebbbcebacaadbedbedeeadddedebdadbabbcadedebcdbdedaecaeeabcadddaadbadcabbbaddaeddebabadccebacabccbedaacbcdabeaeeedeaceaabddbbaebabddaceebbeacddabecaabbbdcabcdddcdadccebdacecdbeacddbedaebccdcacebadabcdeaaebaaeeabaceaeaadabbceebcceaacaaecedcbadecbbeaeaeaadebdddebaccededdeabbededcbcadadbdccedaecadcdeadabdbadbadcbeedaeddaabdaeccacedcaacdcaeabdcbeebabeadcededcdbdaaabcbbedccbbbabceaaeeaddbdaaadaaaabceebbaacdededaceebacceeadaadcdcabaabeaddabbbceacdaedebaacacdbcadaadececedbbaecdebbeaeaaceeaadbacadabcbdbaeebaadaededcedbeedddbadccbedeebddedcbcdbbaaecddbbaeedeaadbbdceeccaedcadaedadadcebaabdcbcddececedceabbceedddeedadeaaadaccbcdabaacbcbddbabaedbdccdedeebebdebdcbbeaccbaaaeeaecdbaaddabebbeacdbaccaccceeaebadbbdeabbcbabbbeadeabdedddcdaeccacbcdcccdabcccceddeadebacdbeecaacbdeacdbdeddbccdacdedeaeeebedbabdcdeeddaebccddddddecdeecbbbdbebcacecbeededeeddcadbbeedbebebbaacdbbedebdbaacbaabcacbeeceabcebdeeaeeedadacbdedecadadedaadeadecaddeaeacceddecbeedaddccddccabebdebbcaadbabadbbbcdbccebdabaceaeaccccdbceddcbdeacbeadbeaceeddaedaaaaceeceedbeeccaeacdcdbaeaaeaaecaaedcbddaaceccaaeaebdaacbdcdeecdbbadbddaededbcedcceceeaedbededceaaebaadebbcaaadacaecaaaccdeecbcdceededbecbabdeabcceaeedbcecebcadcdacdbbbabdabbabadbdcceecadeaaeaeaddbddabeacadebadaddbcebabeeeebcdccdcceeacabbdeeaacedadedbaeeeabbaaecdbdecbddacdbdccbaabbdadeceeeddadebeebcdaceccbadecaaccabedbbadedddddbeeacbbadaecbcabedecededcabbdedbabbbebbabcbddddcabdeabdcbbdebaadabbcccbdcdbebbbbcbddceaeddecaaaebbaeecadecaaabedbbaeabdcdadbaadccdbaaebcbedabaddaecbeeeaacccbbaecbbeadaedcacecdeabbdcaaedadaabcccbecdebdeeabdbcceccbebcdddeacadcbcedaacaabcacadabcdbcabaeacaedeeeadbeacedabaacddccdabeebbbdccdebaddbceadbadbcecacbaadbcaebcddbbbcabeebebaadaeeebdbaadcbcbebdedbbcbacaedbbeeeccdbdcedeebddbedbcaaaacddcedbaadeaacecdcdeddeeaacaddababcccacdeeeaeccbccadbdcbeaeeecdddceacbaeedaecbccbddeebdbbadbcdabdcdaddebcddbbdeacdcecbddbeadbeaddccdccacdbadcddeedcbaeaaeeccecaadeebceeeabaadeebabedaceaddcbabebeccbedeccacbebbbbedbabbebcbbbbcddeebdabeccaaedcdededbeeebbdacaaceadbaecaebdebbeaecaddbddedbbdbecbbebdadecbcdebeebabacecbbaccddebadcaeaeebcbddacbbeacbbecbaaceccbcacaeedaeeedeeccccbeeaeaabebbecdaebeabcbddcaecabdccdedecceddeaceeccadcabbcccecbcbacbebaaaeabedbadabdcebcddbcabbbdcbaadcbabbeddccbbbeccadacaaecaeddcbcaccddaadcddeecbaecabaabdbecbcbbcdaeeaeceddbdeccaedcbedeacabeadbbdbbacebcebddacecaddbecadaccaaacddbecebadaeddeeeccaceabdceeaaadddbbebeccedacabbbedcddedcdebebdaecbdeadebedcabccaaeececbcedaddaabdecdacceabbaeabdaeaaaacaeababebcebebdcdcebdbdababbceceaeccedeccccbddebdacdaababdaaabcbdaaadbeccaeaeeeaaacadcdccccbcedbebebadeddbdbaecebabadeeaacdbabcccedaeacadcadcaceaabababebeaebddbcdabbbddaedddbbedecaededecaddceeccebaddebebadbcacbcdecbeaaebbaadaebcebeebadbdaceadaebaaccdebbdbaeaabadbebcaedbdbcceddcabcddcbcbeecaeddaceccbacbaddeceddebeeccbaeacdecbdbaccecdaadedeccbbaacdbadeaddbbbbeadaedbccbceddcddeebbbeeadcecabddeabecebecdabcaeeaaadeaaebcbebecebececaedbbaeccaaedaeecbdbaadbedecbedbccaddbabaebeadecdebcddcbeecdccbeecaddbedbddcecaccaacabeabcdeabadadcbeeaaadadbdaeebccaaceeacecadcbddcecdabceddbeaddeeadaceedbccdceccccbaddbdbebaadccedabecaebbdbaaadbcaacbacbcbedecdaacaaeaabbcadababdbbcbebbecadcccebdcbdedabdcdccecceadcdcbdcaeedebebcdddecdbcebeccbedbbeeaccdaccccdabbebeacebdedbaddedeeeabbaccdebceebbbcdbccccdecceeaaedbaceebbdceceedcdcabeccbbeedebdbebadbaadddaabbbeeedebdeddbbcbbedcbadbeccadabcdceceeacedeeacbecdddbadaebdbcbdbecebbcdbeeeaaaddbdcddecaddacaaedddaacabddabcdccecbdccbbbbeeeedbbdbcbbcebbacaeaecacbeceaaacabcebebccdcddeecbbdabcaeecbdbdbdaedeedcaedebaeceadadabbcbcbdaaccacdcadbbbbdeccbccabdbaacadbebabcbbddacddcaccccddcedcddbaecaeeebcccdabbeaaeeaaecdbbaccbaeaebbdbdccbabddccbdcebdeadbecaebbeadddaaaaeeabbadacdcabbcbeccbddbeecedacaccaddcebbaebccedbdcceedbebdcbbdebbbbaabdacedbababecbdedcdebdaecdeaecaccddcbbeeebabebcccdcebbcbcdedbebdeedadabacecebacaccddddcbcadedebaccdadedaddaadadaddcbeeacadadbeadadbbccccbcdcdeaddacecaeccecbaeeddbcdbaacdeeccaacaaccabececacbccebbebcbdaeeaabbbecdaaddaededccebbbedbbedebebbcbcbcdaedddddbaecaddaebadedcdecdddeaeeeeadaaeeddaabbbedeaedcabccbcdbaaecdecacedaceaddbecbabbcaaceaccdbdeccdaecebaeabdbbbdaecbdabceecbccdbdacdabaabeedabbeaecebeeecdaabedceaeaaebeedcaeabddbdbababdaebbdbdeddddbeeceeedeccdaedebbddadedadebcaedcbeecdbdeebdacccaedbbcaeadcdceadebabaadebaecacdccceacbaacdcecadcecbcdcdecbbbbbaaddacadaaeebaeaabdceeedabdabdaadeeeaadebcdaceadaccbedceccadeeecceecdececbebbaadcaedbbbebecaeecbccddaaeccbabaaaddaeddbcdebdabadbbcbeceabbaaaacccebbcbeaaebbdaadbbaecacedeceddebbecebdeedadaebdbededabddbaabbcceccebbeddeeedaccaacadebdecbcbbbcabbabaccadbcecaacbdbaeadabdcecaedbeebdebeacdbcaceceddabdaaacccddadebaedddbedebaedecaededaeedbcdddebedadabdbdcbaadddccaaeecdeaadeeeeabddecdebebeceabcebeecbceaaebdaaceeeebbecbbecebabadeedbddaceeeaaddaaaccbbdeabaeaaccdbabbcdeddbbddeebddeaecbcdaceadcdacbebebeecedebbacdadbbbbabebacecdbcbaadbaebbebaedacbbdebbdeaeceddbbadbceebeabdbecacadddebaebeeabdbebdbdcdcabdadbdacdcedadbaceccabeececcaadceceeabdeaccccdacedcaddaddaeceeebddccbecdbcbdabedbdddeadcaaddaacbaabceeadaebdacbeacedecdabaecaecdcdcbdaacdeacbeeccdddacecbcacbddadcaaedbdbbcccaebebdeaeebceedaabccebdadabdcbddceceeccaadcbaaddadbbcebaabaaddebbcecaeddebcebbdcebdccddaebceccadccdbdabbbecbccaedcebeedbccdcdbdadbabcdbbbceecccbbcabaeeeeaccddeaeebbebdccbdaaaeceeaaacbbedaebcaaacaddabacceebddeaaebccdeecaddbbbcdccbaaeabdebcaabccbaebabdadbaaeecacaccdebbeebcaaeddabbebbedcdebadbabcdbcbdaeeacdbedcbaccaddabacedbaebcbdddaaddccacdcccdececddddaeaabdebdababcebeeacceeaeebedeadcaaeacbbccdadbcbbbcdaabbcbcbdcbeebdbbbaddbeddaadcaebbbddbdeaeeaccddccdeeabaacacbdbaddbbaececbdcdeeddcdddeddadbdbeddbabbcbcdaceeacabdcdaeadbebbaadeeaeddbcabeebceeaeebaeaeeaabcacdccccbedebbebcdeddecdaadedccaaacedaebceccbbeadabaacaebaececdaebdbbebeeecbceccaecaddbbbbacddaaacecdeedcbabcccccbceecadcbecdbbcdddabeabbddeeabbdbccbcbdeebdccedbebdbbcaecadabaeadbaddbddcccceedcddceaeaeaedbdeacabddebabaacbabdbdccbebccabcebedccccbbecdbbbaaebecddbaddcbdabdbdbaabbabdbeecebebadbcdbaacaadbdebadbdbbdabddeaaaedacdaddcebeaeabcbebbeaccdeaeddbebeebceddbecceadebddeedceaccceadbbbaeacaceacdeeeadaebedebecaacaddccbadeecdbdcedabbcdbaddbdcddbdbeabeacababddbaadcaabcbacaabaebaccabcaebcbdacebcadacbbcadaddaceebadaeeceaceeeedcbaabcceeaebcaedddccbddacdbbccdacaacdadebbaccaaaceacebcaabdbabcccaddeeeccbdeeacdaeaeccaccebddbaccedaebaedeeacaaeacbeebdbdcecabddcebebacebcbacdcedbcadadcbceccaccbaacebaeddebdeaddbaddcdebacecbdeeaaacbacbcdddccaebbbbabaabbcaaaaecbabddbadbcdcabccbdcdbedebccadacadcebbcadedcaeeadacabbeadeebeeaaccaceddcacddddebebdcedaaadbcadccadcbcbddedeaadadecdeabbdeeeacdccbcdaeccaecdaedeeebccbacddddcdecdcdbcaeacedeecbbdabdaecdbaebaacdeecaaeadccedacdabcdedabcaccecaddeadecaebcebbebaebecabccedbecadecedcdecabeddcbbdbeeabdacdabdaaaaaceebcdabbbecadabdcadbccbecaeeddbaabeaacbdeddbdbcbdeeccaddceaecaacadbabdddcdebbeecaabcceacdabdbaaaaeedbddccebadcdcdacbdeecbccbabaeaaacadabeecceaccbdcddcadbaccecaedabeebaedececddaabcaabddcbacbbcccebaceccddbeadeabaeacbedbabcbabdbecaddebeabcceeaacacdbadecacbebabbbdabbcecccdcbaeaadababaedbbdbcbededbbcdadbaccbbaeceabbaaaaadceccaabadeebebeeddbddaecbbdbedbacbeabbbbceeeebedcdebbccbdabaebecabceeebbcacaedababacecdeeeccdddccdebbdcbaaabbabeeebaaaacedabddedebbaecdbaebbececaceceabbaecbceceeeededadbbdedbbaaacbeabaacaaeaabdebaeeeaaebebedeaabddcccdeadacacbcabdddeececcdccdbdedcddcbaeeabecdbbcaaebacccbacadebecbadcaebbaedcebbcbabdeecdcadecedbbbababceecaaeedebeeccbbbdedcdccddaecbaabecbaeaceccbcdbaeedbcaeabecdcedbbacbecdccdbadecdedecdbaaaecdaeddceaebddcbcdbacdaceeacaddeceeabdcdadddacdbedbabccdedbcbeabaaeaeebabecdabecedacdeeebbccaadcedaddebedaeebbcddeacaaacdcbcbaeddeeddcdcdebeedebaeaceeabccdbddabcdaedcaedcbeeddcedeeadddbbebbeacdacbedcdddacbbcaabbabcacacbdbbaeeccdcdaaeccadecadeadaabdcbbaceedcdeddaabbbacedaedcbadaedeaeeddcddeecbbebdaabadcdccbcddcadbcbeaadcdddedeacdadccaccdebdeeeeaacaccbccaedbcadadcbadbdeccbcebdbacbabadbbacacadbaaedeccbbbccccdeeeeadaebddddbaacbdaeaeaedeedcabbbabcbbdbbcecadebeccbaabcbbbdcdecdbdeddbbeaecdebeccbcebcebdebaaeaedcedbabbbccacabdeeecdebbadbcdcbabcebddbdcbcdedacaccccdadbbcacecdddacbacbadababdedbeadaedddaddbaabeabadaaddcedcbcbeeddedcdcbadbedcacdbcbcacacccadcceccecdcebcebbececebeeeaabaedebaebadcdcedaeadbdabbbcdacbddeecbbeccecabcddceacebaaebbbcbcabdaedaddcbcaeeeedaacceecbedcdbcebbebaaedeabcadababecebaabecbebbaceebbdbcddeeedaeecdbbedccecebdabaaddcbacdbbeaecdcddacccdeecbdeeabebecdadcdedcaccbedbadbbadedcebddcbeaebbdbabbedabdecddacaabcccbccbcbcbcbddcceadbbbeaedccceebeeeeddeacdcecbaddceaccebabddbeedebdbcacadcaaedeacadccbdcdebbccabdacedbdbbbddcbbdbdcbbdaaacaadcdbeaeeacbadaceebcceaeaeccaedbeadccbecedeacbdebcdadecbacbdaaeabacdddceebaacedbbbcccdbbbaedaceebdbecdbbeadedecdebdadcecacccdedaceebeedeceacbdeeadbbdeddcbccddccdccbcbbebcddcbeeecabacedbeddbcadbebebbabaddaccecadebdbeecdebadacebeabbbcbdadacacdeceedeeeaaccaeaaccbbdbddcbcedabacbddecaaaadaccaebeaedeacdcedcdbdacebdcceacebbbaabcbeedddbccdbccedaddbdbddbeeccaeaeebadbbbebceabdaabadbecccbcdbeaeccadceaeeddadaceacaedebcececdaedcebeddddcddbbacbdeccdeeedccdedddddabebdbacccbabcddeadbaacaceccbedcdeaaebabdedddcaeeedcecabacaeecebbdbacabbedcaeacdacbeaecabbcddacacaabeaaeeddeddbaaadabeaedbdecbdcaebcdeeceaaedeeceabbecdaccdacdcacdcceebcedadbdccbcaecaeccdbbdccccebabdbddeeadeabaeeabddbdabbacaddadeccdccbecebaccdddbaadbbbaabecadbebceeebcdcaeacbcbdddeeaddabaaedadcedabcbdcbecbdbaebcdbbdeabadecbabcebeacdaecaecddddbcceeaaebaaabeaabdbaabecaedabaceebdcabcbaaddebeebbbceaaedabaecacbdbebbbeaaaebdecebbbcdeecebcdeacabdaecdbdebedbebdadaeceadeebbecdbdacedbbcaeeaadaadbdadccaebbcbaebabacddeeaeaebabcdaccaaaeccbeeaddbcbaaedaaccdbdecbedbbeedbbaeaabbacbcbebdeecccdcacbecdbabdccbaddadbeeabeccaedeecabddccadccbcdaadebabaddebaacdbdabaadedeccdaaebbedccdebbcceaaccbeabeeaeabdbecdbbbbaddedacbecbddbecbceaccabbddcdeeeddacdcaceeeddddbcebaebeaedcbbeaebaaeeccaecaececcdcaabcbbabcdcccaabdbbbcaedaaddddaedbcdceeebeeaeddbacddddacdeacdaaaccdbeebdacedeecccedbedaceaeeacbecbacdcbcccecbdaebbcbccdacbedbdaedddbacdebeeeeedcddacbeadebcbeaeabeccbceeadccadaabcbcbaaaecdaeadddaacacabebbeaadbebbabcecebdbeecaeadebcbebccaecbabbcabecebbaeeccbedecbbeeceddceeaccdeccdbcceebadacdaebdcbcccccadbadceabaaedaadbdedabcaaabcecbadcdcbdeceeecacdcaaedaadbaccbdacaeedbbcceddbceaccdbdcdeceeaabdbdeceadedebabacebedbbbaadebcadbdecbecaedeebccadaaadcacecadececeebaaadecbeebdbdaedebadeeeaabaeebddecbabbeebcdccacdcceebcadcbeaedecddcadeabedbbaaebdbeeeaccecdeddaeabbdbebdcdbbbbcccdeaeedbacbcbacbdacacdadddaabeaadcaeebccddaebdbbcbcacbdaddcbceaedecddeeeacebbdaabcdbaceedbeaecdaaccdabddbaccdcedceaabcbbaababbdddcbabbbcdeaeedaebacdcbdbadbbebdddeaebdeccbdcccaddbdadabcaadceebcdaeecdededcbdeeddaacabaebcbabbeeddaecbccbceccddddcecbcaedeeaacaddaeccdeabbabdeadcedabedbdebacaeacaeeededcdeccbadecdbcaccddebcbaaccbaeecdaedcdbbbcaeebddadbeeecebececddcdeabeadbeaddcacbaccabeadbcbecdbabdccddacddaccabaaabcaadbacccdcedccaeceeaeedadeedebeacbdbcddbceccdbbdbccbaeababeadccddeeacebbbaedbceebacebdecacecbbecbdbcabdbcdceacaeeedababacbeacbccecebecdbcacbcbbbaaebabbddbbbeddbedccdcdedaebadeedaddcedadaaababbdceacbcbbdababbbddadbecaaccbdbcbabbccceacdaceeddaedbcaaccbacdecbcabeabbdeebbdbeaacaddcdabbdbdeaabbebbecabcddabaeeecebececcdbedeeaeeeadaeaecdeddaeaddebceedbbebaccbadeeeddeccaaacececcbadcbaddceaedbbaaddaabdbecabbebeabbbedcececebcebcdebccbdebeaabdbabecddebebcaceaeecacbdbdceecebcaeebdacaabeecbddbbedbadddabdaeacdebeecdbeaaabaeabcaaebedcbadeadbbeabbcbbaedaabbeacdccdedeeadeedccddeaecbaaddaddccdabecadaebcebaeaaeadabeebcdbecedeceaebdedcaebaddebdbeacbeeaedaccbbccedadbcddbbbccccebecabcaddaceedaabdbceeeecdbdcbaddabcebaeedbeaeaebcdecbbeabaadaebceabaacbdcbbccdbaacaeaaebbacbabcacdadebbeabadcaeeabdaaabedeaadeeeeadcaeddceceeeeeabcdcddacaebaadcbbdeedccbdcbdabacedceceeaaacdcaececaeaececaddcbbeaccbabcacececcacadadbcbeccbdbdbdecbbeccceeeebbcbadbacdabbedbdbcaabdccecdbbbbcceaadeeabbcadecddebabaaddaeabddbaaaebaadcbeabdbbedadcbacedeaecddaddbdebdcedabbcdbbeccdeddeccddededccacbadabddadebabcdaeeebbaabceedcaebeaeabebcebedbccaddcaebeedabbabaedddbdebaabdbeeaaaeaacecebdceacceacadcbeaabceacaabeebaeececcdaecaacaceeebabeebebcbcedccbeadacbdccceeceeebebdceebbcccaeaedceabbbcbecceadbaaeebaeccbabbbeeebeaeedccedcbdedddcadcecbaecbbbbbcdaebadcbcbedcccbdddaedccbedcdeeddeadaedcecccdcaedecedcbcacebeddbcbabaecaeccecabecaabccecaedbeccdbdcddbdbedcbcbcebcebadccdbeaaeecbdcdbbccbbeaedceeebcddeceebdebbaacdeceecdaeeaeabbececdcceeecbdadbebcecaeeddeeeccdbbceacbacdbcbeabacaaddccaebdedbcdccaedddceedcbbdacdceeedacbeaeaebaecabbebbdeebccecbecabdccaaecdaddbcbedccabdadbebaecbadaadbcdbbbcbabddadedccdebbcacceceddbcdbcedceeacdccaebccdcecabcedceecedbcaceeeaaacbeddbcebeaabcbbcdbadbabdeadebdaaadebebebedecbeccdeeeebcbeaadabbdaabcdcceeccccbacbaaeabecabcdcaaddaecbcbddbdbaecabbddcbebaaceebdabebcebdebebaedbeabadabaeabaabcddececacabecedcdebdedeecdeecbbbecdadcdcadcbebbcebbecaaccebbccacdbaddaceaaddeebcedbdbbddeccebabeeeaadbcebeaddbcdaacbdbddebaccddceeebdebcecbcebeedceaabbeacedaadedecdabaaaeaaadeeabeecdaadedeeabcadeecaeaebcbdbdddacbbaddaecebcbcedbeeeddececedbaacebaeeaceceadabbebadddaceebbbdacbaeabeaccadecbdebceccedaccbeacbceacabebbdbdebcdcadcaeaedeaedcccbaedaadbaadedbdcbabcaeedadebcececebbceedcceccdaeebbcbcbeaeaecceeadaceceadabedeeadbdbecacbcaabbeeaccccbdbbbddabacbdaeababebcddcbadbabbcdadcbcaacabeedcdbccbbeaadceadaedaeeacbecceaadeadebcdacbebacaabccaeeaaacdddbbeddbbddecbecdceaeabcadbcbedbedaceadaacdcedecebcbebbbedcadeeccaeedabeeeccbedaacebaededadbddeeceadbdcdbadbcecaabddacdccccaaaaadcabdbdcedbcacaebaebaabeeaedadaebcaaaabdcbebdadedbebababdbdbacdabebdcaeceeeeaadaeeacdadbacdbebbccedccdbdaddaeacedeabedeacedeacdccdabadaebcebcbcdbbccccbbddbeeaacadedaededbdebabbeccabaebeebaedbdeeeeccdddacddacbbdbcccdccddbdedbbacbecacbaadeedabcecacbccccddbddbdecbbccdacbcadbbceeaeebcbbdcecaadebbccedaacacbbeededbadbdebaeccdaaccbacdaebebadccdaaccbdaebaacbebecacadbbdacdecebeddbbacceddcbbabbacbddcdbceededdaeaaedecbdacaeaddcbcaabeebdebdbbebddbbcebbabeadccaecbcbaeaacaaacdcdbddbdcdececeeccdeeceeccedaaeaccadaabddeebcadeabeacbacddacceaadcedcceeabedcaeadbabbadbcbdcaddbabbdeaaccabcabddcedccbedccedcbdeaeeecaebcadaeeabbccaeedbacadababeabbaaddeaddcdabacceaeacabdeebdaadaaabecbeedbaeccbaddcacaacddbecabeabddaabebecaddbcdadaababacaebbbbeeacecceceebbbdadecbabcdcccdbababdededdbaaebbaaaadcddbedddcdbdddcbddcdddcaeabbabdbaeeaccebdeebddeaeaacabcbaccddceaeadaccccccbcdabbbeccceebedbadcdceabdeddabaadabbecbdadbddaaabebabcadedeaeeadececcddacccddaeebddbabcdaeeeeabeaecceecacaeebbecaecbceecabbbcaaaadadebbabaebccaaceabdcbccacebbbdcdbebcaccdbdcebaadbeeacadddeebdbceacdcabacabedcaaeadabbdedaeebbdebbdabdacbcdceeaebadbdccdddaeeaebbbabcabeaeadeeeebbdebdbcbcdcbeaeddcedabaacbbdaacadaedccdaaadeddbebbdaebcebbbeebebdaaaaedcbcbaaadebccdcaababbaabdedeeddbdaaebedbebbeccababbcddeddcababbdbeccecbebeaeaaacbacddebbdaaeeccceadcadcbcbdceaaadbaececaedeccdaaaebbdcaaceebdbcdedbcdaadcbbcbbaeeeadeacaccdbadadbcdaeaecaaedbecdabbeacadceadeeaccdbaddcddcbbadadeabbcbdaacdbacacacddbdcdecebebbcbddcceebbdabacaccdecacceebaadeceecedbebabdeaaaecebddddebbbabdcaedddeaaaceddcabceeaababaeeeecaccbbabdacceeeaddcebebbbbcdedbbdddbdbdecddedebaadccceebcbdcacbaeccaebbcdbceadcaddeaebedddacabaccbdddbeddbcabaeaabddeececaadcaecbebbdaceceacbccdebadaaaabaccacececaedaccdcaceeddacddacaecabaecadeabadebeedeaacddbdcbecabdaddeacbceabaabaceeccebdaddadceabeaadccbdddbaedeabdbeaaacadbbdbadbabcbbabaebcecdddccbbcaeebbccbddeedabbeecbadecbbbdecdabbeababbdbacdbaccecedbeaceebdcdbbedbadbcaadbcbdbaaecedecaebeaededeaaaeaadcdeecdedaedebdceadbdaaeecbdbacdedeeeaebeebadaeccebaebcbedaaeadceeeddbacdceacecedccbabacacedcacebceddebbaeabdecdeceadbbbddbadaacabadeebcddbebeceedcbdeaeccabddacdbdbabcdeabcdececdbcdcedadabccecacacbbebdeccadadaeedcbcddebbcecaebedabaacedadebbaeababeebdeaeadeadabeecceedeecabaceeadbbbccaaabbbbadcebcbaaabdaabeeaddedeadbcedcdbdcdccadecbaddbbaedbabadaaddbdedabaecbeaeeddbebeadeccbabddadabbbaaacaeabdedeedcbdcaceacbaceaabccebacdcccaedcdcecdecdbbbadccddeebbeaedaebbacdecdacaeeccdecbbdbdaabbeabcbedcebdbaebcdbaecbbbecdbacaeeacbbcbaceabeadbaeeadbbcccaccdbacbeceebbdbabedbdceebbbabeeeaacdeecdcceddccceceaadabeaddddcdbceaaeeacabceeececbbabebecdcedacdaaacedbdcaadebbdceedcabbeadaccabdedaeebbeecbaccddeabcbcabebabceedaebceaadbcbdcadbeeeccaceeacccaccedbbedceabcabbdbdcbadabbbdebdcaaceeaecdececaabaecdcdbdebdecddcceebcccebccdbbeccbbbeebeadbdccbedebaaabdbbaecebcbbeccddccedbabbbcddaacbadcadedbededbeddeaadbbbadaeebecddcddddcccdaecebdccbbceaecaeeaedcbbceaaabcdeedcdcacbbecdbeaaaaebebadabdbbdcddadcbcdbdebcceccbdddeabcddebbcbacabbdebbacbcdbdaaebecdeedababedcbcbebbccbacceaedddeedceceaabaebccacaabeaeecadbdaadedbddbcdccbabdccdccbbcaeeceaeecdaadeeccdaaaabceaeaaccdbccadceececcaeeaabebbcedbacdbecaaccbcaabebcbbedadddeeeddeedbabaaacedeebacecdabadadcadebbaeceebaedeaaabdcdbbaeccddbeaecceddcecaecedcedacdacbbdeddaeeccdebeedbeaaadbdaebcdccbadacaccbceedccbcbbdabdabedaeadbceccbadaedcddadabbccaeadedabbdabdcbddcecdcaccbdbcbadaecbbacabbbccbbeaaeaebddcaadbcaacdacebaaebebcceabbdaebadeeacdeecedaccaccdaacbdcecebeeecccacbddeeebbcabdcceaacdecbedabccdebdddacbccaabcdbbecaececbcebcdeaecabcaaaceaedbcbbbdbbadeadbaaaecadccaacaacedbaaadeebdcbdcaadaabaebbaeddeccbeacdddbddcdcabbddcabcbccbaeaaedbcbeebdccdbcecabbbbbeceadcadaecdbdaaabbabeabdceccdabceabccaebeebbaccdeacdeccbbecbbbabaddaaaabedcaddadaceeecbaeaeeaaacbcedddecdccbbbccebdabebdbdbddeaacdbacaadcbbedddcadecededabcbcbcabcbeabaccdacdbadbbeabcebcaabcbebddabacacecceccccbdedadbedbeccbbbdcbbdeaccebabebeddbabaedcacaacdbaaadaaceeaccadecdecaaebcbbaceecdabbbdcacaeacbddeebbebeadbeabcadacadecbaedadcdaecbdcddeedacbbbdbabcddeacaebcbaecaeabceebbcdaaebcdeeacbcceeedcaaebadccbcadbceacdcdabddeedecccdddaaeeeabebceeaebeeaaebcaddcabebaaddeddcecdecbcedaecaadecbaeeabebadbbeecdcecdbbdccceccbecdeebceddbcddceeceeeebbddbddebdceeccbbdcbebeeeebadcdaeeacabdbcbbdccdbadcbccddaacdaabdeeaeaeeaccddeeadecaeebceeaaeeadbdebbbabbeededebadcceedaccdabdbdcdbbbcbcbdcababddbbedbbebddbdcdaaaddaaedcaaceaeeaeecdaeaccbebabebbbaceaeacdaeddcceeaabacddcbdcaacabedcdccabdaadbdbaeecddadcbddaeababadbbdadacdaabadebddcebdbbaebaacedbaaaebcababaeeabecccaaacdbedaceacaedeadbdbaccddddedcbdaeaebebaddccdaddbbdebecdcdadebbccaebaaebcdacccbdbbadbdccebcdaabaedeadaaebcbcdaaedcaaaacbacaccaadccddbddcceedededbcaecaebbaebeaeddceeedadecbbdaaebddbbbccadccebcaeaeaaebcbaddadaaeeaeecbaedbdbdeccebbaeabeaaccdcdeaebdebbecdbcbeabbdabddaeeaeadaeececedaebbbcbaecacabacedebbcdababebcbedebbabacdadceabbdbdccbcbcccacbdcaaeebdcbedcededbcadbacaaeadadadbeaaddeabdeebddadacebcccaeedbadccbecaacdeabbacdbebaecdcabeaaddcacacdcdadbebcbdbddaababbecbccdbeaeeacbdbceaabcecedeeecaddccdecadedddbcbdcaeacddcceddaddadbdbeeaceaddcbabdaebdebdebcebeeccdadaadaababecbedbaebdcabddbbcbbecbebaaecceaababebaabdabeeadbcbdbbebeddcebeadadbbedadecbdebaeeeddccddaeeaacbdadccddbeccbacddaaddacdbaccbdccbeacbacdbaaacaeebcceeaecbaacabedbadeceddedacbeaabcdceaadebeeececedcaccccbabaebbdbaeacdbadabdbbbccbdaadbacedddccacadbbccbbedeceebcbcebcccbedbdccbadeaabeacedcccddbbbaeecaaedaacddabbecaaebebceabbdbecccbeeebbecdeebdaabdbaaadeaceeebadccbaeddcbaebbabdaecbceccdbcccbaecabebbbebbcdeccaedaebacdccaabcecdebbcbdacccadcbcbcbcbcaedccbcdabdcbcaebcaccbeaceaedcebcaaeedbbaadeacacccabdcebddcabecdcaecbbaebcdadcbbbaaccbcdaaacddcccbcadcdacbbaddddcbbdccccacaeeaabdddcadadcdebdabecedacedddbabeeceacabdbadceeeaccdbdedaabedaddededaebedcddaeeacacdedabebcedaaecacaedaaceadbecbbcceaadeccbaaaecadbabadabdbadcdbbecbdbbcacaaebdadeacaaeabdeadccdbccbebaacccdcacbedbbebcaaebddcaedbbdcebedaaedeaabdebddcbabdcedebdceecbdbccabbbddcbabadbaccadeddadbaecaecadcaeedbdaccdcecabedabdcebaaeddcaddccadecebeeadbabbdcadbaacadcbdceadceebbbdbebacaebccdeabbecccccacddcdeddabaacbdcbdbaeddcbecceacbdeecedccbccbddcceceebeadedcabcbeeeedeccaeaccaecabdcceadcdaacabebdbdbcdadbacebcdeccbbabedacddebdceaeeddaddabecadeecacddeadcebccccadbdcdbeaaecacddceaccabdccebaccdaedbbbdaeaabbadaedbcdeeedbaebbbddedcedacddeadebbaadbddabbccdadeedcadcedccabcebeadecdaaaedaecdbebbbdcbdaacaacdbcbbbdacadbaddeaebacabeaeceabdaaddcecdcbaaceeadbcbeeedadaeceddcabdcddbaebdddeccdccabdebbaadeaecbcacdadbbdabbaacbeeedcbdababdbedeeaeebcbecbbecdbbdbeaadcdbcbbaecbeebecbebacaaeaadccabbecdadbbadececccecbaedddebaaccbdadbcbedcabaaaedceddbdcccebceaecddcacdbabcdaeeeceebceadacaeecbbceeddbadbaddeadcbdaaacbbbaeadeebbaeeaadbedddcdbaebadaeeabdeedcbaeddaeeebaeaccbeedbcaabbedebcaedcaadcebdceeedaccdaecbcdeadacabeebaaacbdbdbbebadeccaaceeceaddebcabbacbcdecbddbcdaceeaaabaecaabebdacdedebbebadeeebcebabdcbebddedaacbdadbabcdeeacceddcccabcbacbacaedacadcbdeddaecabbeeeeeaadedcdbdccacabbaccaededddbdaebcabeeddcbdbdddecbebbbaaaaccdceaeeceaddedebcdddaabaedadecdcacbaaabeeedeedddebeebbcbcdbedcaabedaebccddbcbcedeaacaecdbabddbdaeeeceeedacdbecdcadeedbbcaabeedededcbadcebbccbcabadceeecdadbebdaebbebbeebceabbacdedaddebaadbdbdebdcaaaedccaeccaeeccbbbddabeabbdbbabebaecabedaabcdbbdeaabadabdddcecabeccbcbaaceccdadcaddaebaadcebdcbebedbaeddcddbeaeddadaeecdcacbddeadcdddeeaadcbedebddccddbbcbcbdcbdcaccaabcebdcbdbbaeacbebcaeeeaddecadaeecddeaebdceeabbcacdadbcdeacccddbdbdcccbaededdecdaddcdcdceabcdcddcdeccabedbeceebecebbedbecddbaeecbcaccbbceeceaedccbeaacbeeabaabeeeeadedeadcedbecddebbcddbcedcdcceaabbedaebbebabecccbbaadcdbdaecbdccaeccdeabbcdabccadbceccbdaeadaabdcaddbdabebeedcbdcdadcdcbecbaaadbaebbeeaaceaaebcabdaeecedaddbabccbbaabcdabadddcabcccbdcbaedacbdbcdcaddacecbdaeeadebeabebcbabbcacbccaeddbdbdddaeeddddacaacbcbdeeadcadbaceedabcecaecbddcbcaaeeecedbaaccdaacbaebdadcacddcedaceedcedaceebabcecccbdccacadcccbeaebbaadbddaceedcbedbcaabdaebccabccbbacadebeecddcbccbdadadacdceaacbaccbebebaacaadabaecceccbccedabbadbadadebdeacbececbcbdececabbbdaeddeaadaabdaeeedbcaeeadbdedecdcbabbcacdaeceeecedebcebbbbaaaacadebeeceecceccdaadcbddbcdaeebcdabbababdaeddeddbcabdddbeceebbebdecbabababcadcaadcbcbcacdbaadbdeaedabccbddbbedabeecdbbaadeeabadeaeaccdeedebceadaedcaeecbeeeabdbedddcbdccdaccdcddadaedaeddadbddbbeddddebeaaabecbccabbcbbddbdccaaaeaeccbebcecbcdabbcaaeabeedeeeadecddbeeaaaacbeaadecddebddbebcccdadceeebedceeaeacaadbacbdbeabbcddceddecaceeadaeaebcaaeabdaedcacaaebeedbdbbdbdbceedaccadaeceebdcdbdabbdaeeedbdeecaadacbceebadbaaadceceaebceddebaadddecbdacbaabadcabcbebbaacbdebdcbaddceaccdbdccceddacedccdabdcdccbdadecabeebceedcbedacecbeaaddbbadadcddaeeebabdbbcbeabbaaecdeaedaceabaabebcabaccbccacecacebdcbaceeceacbbbeccbcdcbccabbdebebaacdadcdacabacecacaecededaadaccdbaeeacacaacabbbebcdebaadddedbddeaebaccccadecbeabbddcdbbbbaaccbecaeacbaddabdadeaeaabbcbbbbbcacdebccbdadacdaedecdccabebbebbeadaabcdeaeacedbbddddbeebabaaddbbabcdeebdcadabdaeecdaecddeccebbbdcbbbbbdcdbddedabbecdabdeddcebccebcdeedeaaeecabebdeaeecbdbbdedaeccdccdbdbcabaedbccddacadebcaeadeecabbacbcccabaabdaeaabdddedadeccabdaceaecccddeccaeebedbeeeeedaadacbaabcccaadaeccbdcabaddcdeabeddadaebceaceeaccbbcaddeedebbceedadecdcbadddbadedecceacecacddcaebaacccdeeebeaabaedcdddaeddcececbbddccebdcaebacbaceecbddaaeeceaacedcdaaedeceabdcdedbacccadabdbceedeadecdadeacaceebbaaedecebacebcdaabaddcadaecdadebddaedeabebeadaacbbcaceccceabbebdbcdedbcbdddacdbbacdcbeccaadddcdcaabbcaceebceabaeaeacdeaaadedbabebcebebcaedcdddddbaebecaeededadacbebcbeaadeeaccbabeecebddacecaebbcceadbddbdcbaaccaaccbddebdbbdbbbbdebcecedcbeabeeaeeedbdeccccddcacbeaeaeedaddbdebbadeacebadcdadbdccececcecadeacbbcddaacdbecebbaaaaddbedaedaaccbdbeedcbabbacddbaacbbbabddaadcceeadbcdccbadeddbdbecaccbdeddabdadddbcecbceeebcbaabebecaceccdddbccdbbaeabbebccdebbaaabaaaaadabaecbbbeedddacdaabbdbbedeaaddadacbdbbbebbdeabdcccadabaddbdbdcbbcccccdeeddbbbabbaaabceaeababeebebaacdaabdeabeeeacccdccaadaabecdddbabaeddeeeceeeddccedabdababcbacaaacedecdabbabbeebdcaacbdcbcedcabdccaaccedccebabbdeceabddaaeadbadbdaabeaabadaddcdaddeccddcaeeebbbdceebdaeaeadbbaeacdebacccbabebbaaeaabedcddcbecccbedaecceaeeddadaadeaeacbbcddddddeaeedbebcabeacdabdddccaaedbaeccdcaeddcebdbecebabbebbebabebabebbbdebcacabaecaccdbcabeceddaadebcccbeebcaeeedcaddbeaccdebbebdcdeaacaaebbdabacbcaeadddeceeeddeaccbcdaaddebcbacbcbdaabcddeccaddcaacccedeeeaddbaedadceaceeeaddeabdcebcdceeacacbdaecedbddbbebbaaeacdceaebeadebaecebcbdbdcbecccecdaddadcbdddccedaabeedcedbeacacacbbdabebcdcdcddbebbebbbdadcabcbaededdebacaddaaeccadbacaceeebcebcaaaadeeccbceeccaadcedbebebacceebbeadeabcbccbbeaeecacdbcdbcdaebbbdbecbeebdbeddeddbcbbbcbbadcbadbbdcdccbcbaccecdbbaddeddecbedeaeccdaccbdcceacbbbbabadbedaecbeecebbbdcddcdaadcbddddcbccdbacaaabacbaedaccebbbaadcdcdcebaacaeedaeacabecebbaebcddbeedbedbcdcbbaaaaccebeedeadacdbebeedadccbedbbeedadcddccdebbaacbacacebeeabaaabddaccabbaecadcecacdcbbbedddddaccaedaedbbcebdedaaedbbddaedcadadcbdaadcadadbbebcdbcabaeaeebebbdbeccbbbcdcecbaaaadeeaaabbbaeddecabadcdeedbbbbcbbbbcaababcdcabbeeeeabccdcedaabcabeaeabedcebcdcdedaeddcacecdebeeecbccdabbcaaadbeeccbdbdecbadaabcbdddcedbeabaceeabeabbccaddcaccbbddbcaadcbaadcaeedecbebddccaddcddcabceccebeeabdaecdcbdcceedadccdbbedbdbcbdeadbbedccedddeccbdcbaadbbcdacdebeaddddaaddddabecaacbdedbaadeecdbdeabcaccdabddacdcbbdbddbadbbadaabbbbdeccdabadbaacaeaabddebacdabedeeebcdebeebacddbbaaadbcebdeaadaabeecaeeddcbdbadeecdceaaddcedaebeaacabbcaecaceaabbcdeeecabdccbaabaaadeebbeaeebcbeaadebaabcadcaeebabdabcceedaecddbcddcebedbccdcdbbcbdbebcccdadcaccabcbadabbaaaaacdccdcbeedceaedaaeddaddcbcbeadacabbeccdcbeababbecccdcdbceaacedaccbcbaaadcabacabcdaadacddedbbabdaaaeecdbeadacbdbbdeebaedbbeadbadadaaaaddabebeebeabeedbdeabbeeeccadaecbccabddeebbcbeaeebdbbcbcdaaddeebebabddababbeeabaccecdadbaeecaeaeddcacdadedbeeceaadcadedaaeeabddcdcdcecdabbaacccdebaabaecbaeceababacbbaabaebcacbcdcbdcdddabbcbbebebcccecdbddbeaecddccdcabecdecbeebeaaadeddaecdbceaeceaaacebdccabebdacbdeeddccdeedbdaeeacbbdbddbcaacaccecddbbbdbccccbbceadcbaabbcecabdcbedcbbcdeeeabdcbccdccbbeedcbccedeeecbddbcdedeeeaabbdabacccbabcbdbacbeaedadaecbaedeeacbdeecebaabbbdaaebaececcdaecabdaddccdbbeceaaeabebbbddedddddcdbdbeceacdeeebcdeddccbeddeeeacabdbaaadddecdcaebcdedadceeaddadaceeaadedacebaaaaaedabaddeddbeaddebbeaabddeacababbccecdbcdaceceddcaeabddcebbeddedaacecbbcaaecaccceebedcdbeeaabebbcadeadeedacecceecaabacbbccabdaaaeeddeddbdbbaebadabecbcacdecadcbddcaeadaeccacdcddbecaebbcbecbaebecedcebeeaccbdbdeeaadacaacdaaaabaacebecbabebbaaddcaceaecbecdeaaededaebccceeaedbdebaddcadcdccbcccddcadceadcbceeaabbedcdccbbcedaccccccbabcededaeecbbcaebebaaabaababbceaaaacebeccadacaebcdecbdcbeedbaaedccdbaccabecbaacdeedcaddbdcaeaceeccbecbaebcccabcdeddccccaebcbacbdcbbcceeadddcbeebdbecababaaacddcbadbcadcceaddebbdabeddacaaeeabeebbbeebacdaabaeaacccbedadbebdbceebcbdadcdaaaebeecabaadaebbaeccdaebccbbcabacbccdccbaaabeedbedcbdeeacaacdcdeecadeedabcbdeccbddabcddadbdbeaaebebbddcbdadddeeddbdddedbeaaecadddcdbbecadedbdedbebabbebbdeeccbbceceaceeedadeceecbcacbbacbcbaddaaeedadbddeadcdadacabbdeaadbaaadbecacededbcaaeecdcedcbeeebecdedbdbdcbacaeabaacbbbaecacdcebdaeedecbedccaaceeaadacecbdcddbbebdceccddbcacceabebabbdaeedcabddbbcdbdecddddebcdddedbadbdbebbbadbaedcbaacadcbceadecabaaeabaeaeccaccdbbedbbebaddccddbeaccdbbbeadaccaddbcdaceaabdcbdacdceccbdddbcadddaeebbededcaecaaecacabeeebdbdcebbdbaeeabacabcadcedbdaacdbccddadaecaecebcddacceeccbceadbcdebedeecbceccbdcdacbdcdbeeeabbeddaacedccdaeaabcacbebecbeabcbbaebeaceabaebbdaebadceabaceebabeedcedaeececeececedbcadddbcadcabacdddddecbacbabecaaaadecabbeadadebbeceebedbecaebccbcddcbaddeeabceadababcdcbacaeeeeadeabaccaabadecaaddacaccdbbbecdaaaacecceabcdabcacabdeaeccdedacbeccbcbceebadeccedbecbbabaeecdccdaceceebcaccabeacbeeadbbeddbcdbecdabdbaadbbccbecddcedcacdbcddeabadbbaccacbedccddbcabdbbaddeccabcbbbacbbdabebcdeaaaedbaeedcbdbcbcedebbaaadecaeecaeddeececccbeeceabcedeceaedbaaddaeababdecebadaaaddcddaccaddeaadcdddbcbedbaccedeedbecaabcceeaebcacbbbdbdeccabcedccddceecbabadacebaabadcbccbeedecdedbbaccdcaedbceebdcdeeecadaccdbeeaadeaaceedabdebacedbbeeccddcbacccedddabddcdcbaacebcbddeccadecddddddecbaeeccccbbeececeeccdeabccbadaeacdddecaaebeeadaedcdaabecdcdaebbbeeddaecaaadadadaeabbabbaedbacedbbbbcbdcebebedcddccbdedbdbdcdadecabeeeaebcbcddeebebebebdeebaabcdbaedbedeadccbaeccedbbcddabeadbecccadbdacebdadbeabcccabeaecbecbcdbedbaadddcbabcdabdbcbdbdeaaedbccbdabaceabacddbedeaeccccbbacdbbcdeebcdaeaacecbdbcabbcceeabbccbcdaadcaedeabcaccebeeabaaebdedeebdaabcdcccaaebeeaddcbceeeebecedcabbeebbbddecabcbaadcccbccaecebbeecdcddccadceaeddcbbbedbbeaacedcececbcdbccbcacaacacadbbaeccecedbdadaaeeaeadaeccaddecabaabadbeeaedceddcdcdaeaacdbeacdbcabddadbdddcbdeddeeaabceacabaadbdebcbdeeddcaacaccacaccddbbabeeeaecaeaeaaebecebbeedbcdbcebbddbbadaecabeabccdbdaebacebeccecccdadcbedecdadecbdabdaeedadaeebcceaccbbbbdbaadbeebccaceeeaaebbbcbbedcabbdacadccaadbbcababbbcebaaeaeaaeadabcabebaadbdddebeecabdbdbbbacdddbbeeaadcaaaedaeedabdceeaedcebacdbddaadbcbccbbccebeaeacadeedcaeaaaedbdecaedeccbdebedcceaaebaeaceeaadcbaabaeecdeecdbecaaaedcdcadabaaabacceeeeaccccdeacdabdabccaeedcdbcadbdbeebcceccaeaebeeedcccdeeaaddabcccdbccaedaadbccaddcbceaccbacdbcaeedecadadbaabebbcadedeeaaecaddeacaeceacccedadabcacbcadaaeaadceeabdcdbeadadeaacacecacebbccdbdbaddadaeeeedbaddbbceaedcebdeabcebbaeddbcdbbcdbbdacddebdacbecedddecedbdcdbdcbdcbaeecedeebcabceecaacddaebcaebcabbdcbdcdebebacacbaceccbccbcbbedcdcadceebdecaacecebcaadbecbbccebaaaebededebdabbeeabdcedaccdcaecddaacbddcdaaaabdbeddaadcadcbdbecdcadadcebacddeeeedaacbbdabeaeabccbecbdacadbdbaeebbaaeacaeecebbccddaabbabaaeeddbcedeedbaddbaadccccebbebecceceebadcadbbcebceddbdaaceaeabbecaedeadcacdedadcadddddccedcbdadaebabeacdecccccceeceedcccadeecbbebcbbbbacecbacbebdabbdeaccedbbeddeebacaeeacbcbbedcacadbbacacacbecbdedbcddacccdccbcdcadedbaaaaaeadbeccbbedadcdcbbdbaacaedddbbeedbbeecdcbabbbeacbceabdecaeeccdccdbaabbaecedbabebeadccbdcdbeceeeecbabbdcacceaeeedbeeddbaddbcebddccbadbaabbaeddebdebeedcedecdbcdcdceebbdbeeebbbccdaebcaebdcbacdedabeabccdebcabddadcdcbbcceddebdabbbbdebedbbaacacddccacacbeedcbbccddeaebccdbdbbdacbaadbcbedaacaccdbdbabaeddadcadedabedacadbdebecccdcacccddeeabceaddbedecadadecedbbbacdcedcdabccbccdbdeccacedecdceacbcecceaacebddcccbcdeacdbddddaaebabbbbdebcbeabdaceedbeccaddbcdaebdddbbbdaecdedcaecaddbecdbddcbecccaaeebcddcdeebedcccadeeebbdeacadadabdebceecceadbaccdaddeabdadeceeacbcbbaadcbaaadecdcbceeddcebbdddbcdeeeebdbbbeabaeecbadbcecbdccdeeadbbaaccdceacddadccebaababcdadbcbaeecbaacbbddeeecaedebbadbbaeacddddaebbbaeaadbdbcbabdddcbeeaaadcdbddecaccbedddadcabbebbaeebcbcbaccbceaaaddebcddadbedabaedaecbccbbdbcdbecbaacbebccaddccddcecaeebcdbadadcabdebbbaecbebbdebbbcbeedaaabccbbeebebddbaababaeddacebcdedddaeaaddadacaadddecbebdccacdeacdaecbaddcaedebbcaccaaeeebcabdddcedebaaeacbeebacceadbbaddabbeecbebaebdabceebdeeedebabdcdaacebeaecceccebeccbecccaeeeeeddaccbebabcdedeceebbedaabbcddcadccbbdaddeecbbecaeccdbbdccbcabbabdaebdbdedaacaacaaaddeccbdedebdedabecdeeabccdceaaeeedcedcceedcababbaaeeacbdbcabecedbccaabaabecadabbabedaeceabaeabdeaebcceabbaaebbdadbdecebbcdddebddddebadebbedaaeacccbabaacbedebaddbedebbaacadbacdedbddccbddccddbedeebacdedbdecedaaeabceaadebeaadabbdcaddaeddcbbbccadbeeeccbaceacebbcecbebeadeeacddbaedbdcadcdadaecccecebdadeccbecbebeeeaaadeacbdccbcddddcaebcaeaeeacecbadbedeecddaadcabbddbebaeeeeaebecaaaeebbeaabbacbaddaddddcedbebaeeebdacbddadeaadddadabbdeccadabbadddabccbeadcddadbeeddbbdddceecacadecdedebacabaecccdcbebbbeacccecacabbdcdeeccdeaacceeaeabbaaaadedaceeecedabcbeeeddaadedaeecaadddceddbbbadeaeedcedacadbeabbdacedeccbabdbedaccdceacdcbcdadeeadcababccedccaabcddedebcabddbedaeeecdabdddeceaebcdcbdaadcbdcccdaacaceabedbbaccbaabdddddeaedebddaecebdddababdddbdbeccbdcdeddbabdbdebccbaedecabddebbcbebdbaccdcdaabdadedeabaabdcbcabaeaacbacceadbbabcaabcbadbdeccacecaebcdcbcecedbddcedebaeeadaebddbceaceaccacdaceccddebcdeeeedecbcdcadaadedbaebcaaeaaaeaeeebadccabbbbddabbbceaaaabcbbdadbedccedcbdddeaccddbacabdecacedaeebababceacaeddeceeaeacdededacdbecdbaacbebcaacbeedadadabddcecedbdbcddedcddadccddcdbccbcccadcaacdcecdcabaccdcbacbaeeaaddddabceabcaecaadaddddccdcdedbaacaeeecebaebcdbadececeddbebeededecedeadaadceeadbcaecbebadecebebeedcbcabdaedebceeddbcdebbcbebcebdcdaeaebdddeeabcedbeebecccebbeedcaceaeaceebcdacdeaeabebbedaceedcbacebbbedabdddeacdacbaaddbaedebcabcbadebceabbdbdcdeededbedbdedabdcecdcbcbcdeabcaccdabedaeeceebacbccdbabeccecebeaeccbdcbabcbaaebeaedcbdcdebdebbaecbbaddcecdcdeaaaeeedcccbecebbacdedcbebeacbeddabdecaeabbaeabdbcdaadeedbabddddbccebdabebcdddcdaedcbddbbcababbbaaebeabeeccdbcecbbaedbcedcabdddccccadeccbeaceaadbabeedebcdadbbeaabddbceaacdcacbdcdbbaeacaaadcaaeecebdcebceecddaccacdccbdebdaccdecbbcccbaecbcddebcedebedabacabbebceddcddbdaececdecceccedababdebccebcbdddbeacddabbbadadcbbcdabbaccecebebdedbbdccccbebadebcdaabdecdeaabbcebdcddeddbdbbacdacbcdebccbeeadcecdeaaabcabcccebecedaaebabdbadbacbdcacacacedcdbbebeceeceddeacacbcdedabbccdeaebceadebbaecbbbdbbdacdccadcbadcbabedaacebdbbadeaacceddbccdceccdacbacebcbcaeaaebcdddeeaecdabbceacbeebaaecebeccaabacdbebcbdddebddcbbdbacacdbebbbbcbccbdcccdbdbebeeeedcedadbdcecceaecbdebeeccdbcdeddddedbacadaccaebdbeceeebaeedaaacbacedcedcdadcedecddbbabcdabaeacccdacdbdbaeaecccaacedebdcbbbbadcdddcececbcbbdaaaacaababecdcdbecabdcdabbbacabaeeaccddbaaaaedddddaddcbedbecbccbddaddbdebbecdaceddeccdeeedaeeadebdaebbceaadccadbeaaecbabbcecacceeaaeeccccbabbccccdedbbdddededebbccaaeeaabeaedddaebcaabebbadabbcdbcdbbdeebbbcbaaccaaacdeabaeddeeadaaeabdceaaebadeddeadcdbbdbbcedeeeeddcbbcbaacccdbdaecebcaacedddbbbdccbbedccbeddabeecdeeeccddeeddeddeecebbececbeddbbcebbdaaebcdbceeaedadbaecdbceddbdcbeaabbecadcecdadabbecabebaccacededbeceacbaeebbbcdeabebeaeadaaccaebecbbbccecdebaadabebadebaaaeeebbdeeedeacdbcbacedbabacaaadacbcdbbcacedcccceaceecaaceeadddcebdbdbabdabcccebbadaaebabeaeecbccbbbaddedcdabaeedeebaecddcabbaeebabbdbdcdbaeaceaccaeceaddebabbaeceacdaaadaededddaddcdebbddeaeeaadebaedcebeccaabcdbcbbccadbdaacbbbecdceaeebbbdadeebdcceeadaddeeecbaadabbeadbabaaaeeaccadecebaaacababcdbeceadacaadaebbbebdcbaddedbbccbcddecdbbababbccbedddceaabbadaabdecdeabbdbbeabbcdababceaadccaabdedceeeeecdddeaaecaaacdddacdacdcaaeeedbacccabaaadbcbcddaaeebbeeebcaaaedaddaeecaabdbaaebcecbdaeedeabbbdacebabcabacdedcededbebcebbebbdcdaeebbbcbddaeaebeedeaccbddddcaeddcaceeaebaecdadeaeaaeeacebeabcbcacacaeebcdaaecdadeaaaaedddbdabdcddbaedadbbbeddbcccebebcadaadadecbdaecaeaaecadccdeaacdbedeadeaaceebedcdbceadaccedecddbbacdbeccedcbccedeabcabcabeeaeedacebdbdcbbbbaabdcccdeeaaaeaccdbbbcceeddcaadaabebcbdebbdedbdccbeebceebceebeaaadbbacbcdabcbaeecbddceeaabbccecbebbdacaaddcaddbdbbcceecceecbbcddadbecaceddeaeaecdacdbbeadeceaddebcdbaeabeacedccadbceaddcccecdeabdebeabaecdbecaedbbcabedcdcecbbbcaceebbaddbedeadcbecdabcebcdbeaadacbdcaabccbecbabdbeeebdabaddeaeddcbeacacadceddbadcaeebdbdbdaebbadeecbaecaebcebbdbdaabdcaeacdecaaaeacdbddaedbbeedcacdacedcdceecebacecdabaaeeeddeedbbeebdccdeeacaaeeaccaebdcaccaeaedcbdbdecaeedaeedbdeceeedaddaeceaeebeaedbaeedecedadeabcbeeddeaecbbebececadcdccbbaaaceaacbdeaaecececddeeeaeacddebcbbeedcedcaeebddcabaeaedcbbeeddbebcaeebeeebdeceacabdbecbbadcbbcbadecedceebadcdedbdceaabeadccecabcdaeedbdcbccedbdbabeeedccececbceceddcaddbeacacecdbccddcaaabaccbbabeebacaeabdbeececdcaddcddbacceaccbdeebbdacdecacaadddacceadabdbaebcaacabeaceadbdaaeaaceaaadcaccabdacdccdeabbbadadcbacaddccedcadddceadeddcedceacaaeddddbbeacceaddabbedaebeecceadcbbbaccdcbedecacecaacaadeceadaaaebaeabaabadcacdedbeebaaddbacdebebdcdcbbaaecebadcccbcccdbbcebebacbdaadcbacebdbdcaeebcbbaabdcdbbaaccdcababccddddbaccabdcbeeddbbccccdbcbcaecabcdabedebeabcacecbbbaccebdebcdcdadbbbebabbdbdbbbceddedabddbcdaccecedaabeccdbaabdbdbacebeddbadacdadaaeebbaddbccdcddebeddbbeeedbedbcdebebeaebcbedbbbadacedbbdccbcccaedceceeedabdeebddacbdadddaddadbceeadebdebbdbdaaaaadaedecaecbddccecabaedaeeebdedcaccaaadaadbddecdccbcccaedddcddbadbaaeaaddaeececeddbeabaeecdacdcbbdebdbaaddbddaccaeeaacaddaeabeabaebedcbeaacaeaecabbacaadbacabecccbebaccaeddaeeecabbcceadebeaebaadcaadaaadeededcbcaaaaaababacdbddceaebbcedcbeadadedbdaeaecdceacebadabebbcdbcaecbcceaecececcbddbbcabedeaaedcadbeaddcdadacbccdcaeaeaeccaadacbbdaebbebeadedebedabccbcbeeabdcdeabbdbebecbecaecbdbebccbdeeaceacecbedbebaeceddbeeaeabcbdbcdeacabaecaabbdeaebeabcceebdabebeceddeeecccaebbcddadbebabaacbcecbaeedcedceaadcbaeeedeaddaecadeeccaeaaabcebcdcbbbdcebdbabdabdaadeccaaebbddbdaedaaeadbdbadddeedbbdcbacecdadacbccabcdebcedecebadacccbeaaecbbaaddbebadcbdaadbdadabacaaacaddbbecdbbccbebaeeeaabcbabdaccccaeddeceeadcadbeeebcaebbbecadeabcbeebdcbeaaacebecadbbdcaacacbceadadcbceeadbdacebbebcbdccbeddabcccacdcaccaeeedeceacedcdaccbbabddbecaeeebccbeaccababcbcdcecaedcebdabeabbdedeadedadcdabdabddbdabbceaabeacbbeceecccaddebebbcaccadbebacbbcabaedbbbceeaaaabcebddbbcdeeedeebdbabadedbeebaeecacbccabcbedeaddedeaceabdbedeaaaaeaebcbebcedabeccedbeedbdbbcccecccadacacaacaddcdbdabadabccecbdaabddeaaeaecadcdaecabbcceaecbeacdcaaeaaaeecbaddeaaaccacbdbceedcaadabeaadaeeaaeeebcaeadeceeacbcdabaaedceddcbeedabebecceeddcecbeaacbbbcbbaeadcdbabcacedceacedbebccedeaaeeaccceeeeecdbabbaedeababeeececcbddbccadaaadceecdcbddbabceabbbacebdbabddeeecaadbcbecbaddbaadbddecbbecbbadacbabbbadaeaaeadadadacdebbbcedbdcedeeecdaccaacddbabaecbedbddcbdebdedeaecebccdaabeebcdedbbeeaddcaeeeccbebdaaabeeebceabadbddbacdbaadeacdedcaacadecedcabebdccdaabecedadcbabedcdbeceebaceeaeebeedcbaaddbdadaccaaeaeaceacdddcedcdabbcdbcdbacaadeabdbdbcadeaebadedbdeeeabcbbcdceebaaedbaecceeaeadbbddbcdedcbdaabeeaadbeabcabebbaedceebdaeebeacceaddedbdbbbedecdbaaadbbcceaacbdaaebbeabaebcccdebddcbcdeececebacdacbcaaddbcaadbdedbaaecacbacccacdabdecdaadbddacbcdddaebcbdcededaaecddceabbecbaecbabeececaebeabecbdebdcedeecebdaeabaadceccedadadededaaedbbdbdcebdeaaddeabcacedbdcdcdcabbccbeceacebacbbedebebeaaecbdcbdceececdccaedebbbbceaccdaddccabbeacdcaabdcbdaedbaccebddccdcbdaababcdcdaadddceaaedaceaaaaecbdedbdaddbbdddcebeabebbdcdedcadedabeacceecabdbedcdecebbeedaecddaecacdbedbdcaceabeebaaeeddcbcbcebacdeadaabaeadcbadbcbaeacdadcddedaeaebdaeabacbbdbbddccebcacedaeeaeebbdeabeaeeabeddedcddcdaacecbebeacadcadccbacebedbdbcacdbdaaeacbedbadcbdcabeacaedabaaeaddbbededaadeeeebaddecccbcacbeedecbdecaaddaaeaebdebcedeececcbdaeaeeeddbbaeddadecdabeceebcdaddeeabdbbabdadaaadbdebbdbeeaedccadbbcdaadccbaddbcebbbedcbebdecbbacaabccccacedbbaaddeadeebaeaeaaaedbaabdbeeadedbcbecabcedbbeaacddbddcabaedcdaaacbbacecdaeaabbeedcedadbeadcabbbcccbebaebcbecadccebcdcdeccecbcebebaeedecbdeeeebeaeccdccaccaedbaacdcabaabcccddeccbebcdcaaebeddecddebdedabaeaabdaeaaaeddeaaabdeeaabcaeacedcbdaaeedadccadeadeadadcaceeddaaebcdadadadedbcaabbceddadbdbddceaabccebbbeeabbcdceeaadcadaedceddeebaeeeaaddddbeabeaddaebdcdeebedeccabeceeaadabacabaeacaeadaeacaddddbdecbcabceccaceedeabccbccbecbbbbceddbecaabbebebbdaaaaceaebdddabcbbddaccbdbdbccaeccbccbbaddbaaaedbaeabeabbdbecceeacbddddebdbeedbabaccbcaeddbaeaeccdcbcdedcaeaeccdbaaabccbeacdaceabdaaadaccbddaeeddaabecbbeddcbaacedabcddebecdaebbaedacedacdadbbbaeadbaceadcabcceddedbbddbeebddecdebcdaccaaacaedddecbebedbcadebedcbedaddbadcadaebbdcedcdbbebcddbbccedbdaededcdecbbcbcbcdbecececcabcaedcebdebdcabcdccdeddbbeebdcdcecaabcecdadcadeccaddcacdddedbbcaceacabebbddbdbcbaeeacdcaeabecabddbcdaaadbbceecdeaccbcaabeadeaaeececccdcaadeaaeccdbebeadceeccdaceedbbdaeeeebdddbcabbedeabdbcdbdbedbdaebdecbccdeaacecbabbdcdadedbbeabcbdcdcdceadbaedbcaaacaabcbcbaaceddbcbeccbadaedabecebadbadabaadccceebaedeeaccbcbaeccddcacacabebaaadeadbedbeabddeeaebeadebdabedaacdbcebaddacdaabaadaeedeadbbbbcecaadeddabeabdebdedaeebddeecacaadbeecbccaadceebbebbcbbdacecabbeebeaccdedaaabbbebddbbabaaebccdeceeadabecbeecbdebebedbaeccdaadabecdbcdeccaaaeecaeccdbcceebccebebcbdecedecabaedceaeedddddbebeadcecccaacbcedccbceedeadbebaaedcbadbdcdeedddbcbeceeedbadebcedaaabadaaceebebecadbabadeeabaedebacbceeccebadabababeadcebdbdddeeeedebbdccacadaedceacdbacedeceddcbcbabdecbacebcedcbeeedbaecceadadadacddacaeecdacbbbaeacecabcedccdacbcaabedbabecccecdabaecbeadceeabadacbaabcadaaccecdccabadbeebddbaeebcaacdbaeacccbbbcbecddeeaaddabbbbaacdbbcdcabdacdbcebdceadbbaaedbcdcbbbeaeccbecabbadcbeedcacceacecaabddbedaaeebcebdebcbabbbbbdecdbcabddaccccaedbceacacebbdcaceddacdddeddbebbdbcebedebadadeaeaabaceebdbdabeddcadbdbeedecbdbdeaaacdaaaebcadccbaaacdcdcddcdebaeaeaeaacdcaedbedbbdbceaeadbeadbbdcacdbeacaccddebcddaebebeddecdccbcacddbaccecebadacadcebaabaecacadcbbeacbddddeceaebacdaebbcceceeedbcccbbccbbaddbcdbceebbebcccddcdeeececeaabbbccddecbebddcccdcdeebaabdcececcbdcddadceaabacddeedbdecbdcbecddabadddadcedcadadbdbbbcadeaeebbbaadbcbbcecbdacbabcddebcbacaddeebccddabebbbeedddeadaadceaeaaccdbebcaadeaacedcbeecadaedcecacddcebbceeaecbaadebccabacbccdbaeeaedeacceabddacecabbeabacecccbecceeddedbddcddeccabdcdbaedbdcbdabceddcedeabbbaacccacdadeeeabbeebcdcecaaebcbacdcecedddedacbabdcdecaccaeebeceedeabebddcebbdbcaaddbbecdacdbebaabbdedccbcedadbbaddacbceeeacedceedebadcdedddaccebeccbcaacdceacbcdaacebbedcbeeadbcebedcaccadbdeaddbdececbdbcddaeecddbececddbcedadacdddbebdaedeecdedbbaceebaacebbaeceecedbdaeadcdcddddcecdbaaaeacedcadcccedcbdeaacbacadbbadcddcedaaaebadbcddebdeddacedabedccbcbebaddaeebdadeeedbedddeedaaccbccaadcdbaecabebebddacdabaaaeaaadcbdaeddabcddceedeeeebaacdcaabadedeeacabceacdeceebcddcdeaebcaddcdddeddcdeaaaadeccadddbdcceabcdcbeedaedabdacaaeadebcdecbccabadbcceccaeddbebabdadabdcaaebccdabbbdaaaeeeeccadbcecddcdecabadacddedaeeadccdeeaaeaadcdcaaceedaebdebecedcdeaeddcbddebccdbabdbebbccbaabcbcaecaecaedebcebdabcbacabdadbbdeecabaebcaddcccacabcadbeabbbaeeeacbdebdbbcbadcdebdedebbcdabeecaaebadbdecdeceebddbbacbbeccdccecdecdbabeadaabaacbccaecdbbdddeedebebadddbcdbbcbcedbcaadacddbddabbddbbbeababcbaeebbdaeeacbcecedcbabcbebbaabdbdcccadeceedaccaeecccbbdedebaeddaecdcccadadaeaaacdbcbedadaaceeadebecabaecdbdaeacdacbabbccccdbadbbeceebbdbcedbdceaedcaadbebbbbeeacedbcaccbcbebeeecaabaeaadcbcceeeeadebeabcacaeccabbcceccdeabaebedadecaebacecdaecbaddcaccdbaaadccedbcebeabdcacbceacaadaaacddebcabaeeeecdddbbaadbdebcddddebbaeaebcddddedeceaccbcecbbbbbbbbbabcddbebeeacecaccdcdecadeedeebddcaecbedbdeccbacccaabdcacededddeedadeaeabbecbeaddcebeddececaeadbeabadcaacacbacadbbdaeeeebbeccaeccdaecedbeddcbbbeabddabebbddcdacbdeaadebabaaaabdaccdbcdebededebdcdbcbbadacdcadbdadeecdacdabdcceaaacddbcedebaaeeddcdcbeddecbacbadbeaaeaceddbaccdcbadaecaaacdbdcddabcceacacbbccccceadbdccceaebbaceecadbaacccbdbaaeebcdbbbaaadeabbecaabbceacbdeedbbcabcabcabcaaacabdcbcdbcabedbebeecbeccdcccaecbddacacbbcdecbcaabbedaeececebeadaacdbbeeceaaccbcdbbbdebeaaccbcebacbecbaadcebddeabedaebccadbbcdcabbbdedecbadbbadecedeaebeeaebdadbebcbcadbadbdbceabeadddcbacdedacebbeadbeacdddcbccbbdaccbdbcadeeaaceaeccbccabbccedaabecabacecdedddeedcecaceacdeebabdbccbebeabdcabebabedbbccdcedecccacceaedeedeaaadaeeeaebeebbedbbdebcebbbddbaccaecacbebcbeedddabcaeaadcbeccbaabcdedcaaaabceadecceabceaaebaaecccbeecabddcacbcbbadbdddaeaccaecbaaabaccbacaadbccdabcbbbdeacceadaaddeeddadeebebabeecdbacadeacbacbdbddcededadaadabddbcbddadeebacbbeacddbdbcbbceacbdbbaccacedeabcbdabbadadbaaabebedcbbccbaadaaadaaaeabbdbebeadeebadbceeedeacbcddcedccbdadeacadeeaeabdeaacaebcbbacbccaaadaddeccbeeaabebaaadcdbabaaaceacccecbaaeecdeedcccaacddcbbdaeddabeaceeacedacaaeebddbaeaebcbbabaececdeeeacecacdecccbcbbeaaaacbaedbbadeaddeaaebbeacabadaaeedcdeedbcdcedeadbdbdbdcdaeeeaacecdbdabaeaceacbedbaaaccdbddaeccacbbececabedaccdacddbcccbdbacdeadebaaabebdaadddddabceabcaaeddaeecbdeaebecbbaecceabbdeeaedebbdabcecddaadcadadcedebbdeeceabbeabcaeddbaccdbacdcddabcebbeddcaaeacbacddccebcedacedebaacdeaaedebacbeccccbdacdbacacbaebdaedeebdcbbceaadcaaeeeeacdaabdbcababbdedeebcaadbcedeabadeacecaaccaccaacaccdcabcbcdbeacdbbacabedeadabadbcbecbdcbcebcbbacacbeeadceddcdebdddeacabaaabbabaddacaecbdcbeccbeebcdaeccdeeecdddecdcbedaeeaebbcdcacbbecaebdabeedddedecbdbacdbdceddcdeadecbcdacdbbdbaaaeddaceaacbcaaceacbadaededcbeebbacaabdabcadddbdccceebcabaaebbcbdabaadaedbbeadeacbeadeaeceadbedacacebbaebeeabdadddadcbacbdedbbddbdcdcdadcdaebeaaddadbdccbabcecaebcecaaadcbbeedeaeebdacebdedeeacabcededbbbddbcbedbedeccbdeeacdcdbcedebcbeabeaeecceceaddcadccbacbdaddcccaebabbbccbcdebbcacbaebaecdaeceadbbeabaaeddebecbbaeaedededbaabcaaabdcaeaebccccceebabdbdacdceddddccedbebeebdbeaeceedddaeccdadecdcaeadcaaebcdcaeaeebedaecabdbebcedabbddadcbaaebacbcddccecdeabbebededaccdedeededcbcdcbdaebeabbbdeeaeeeabddeecadddaadeedeaaabbdcabaecebabddebdadbeaddbcdaeebbddebcaabdeedabdadabbebaacebddeadedbbdeeacdaeaeedddabebdededdcadbdcdacbddcabcebaeecacdeddccbecbbabebebebbddcceecdeeedceccccabddeddebecdcabbdaadaecaecbeddceabaecbecedbcbdbbcdadebeeedbacadbbbdbbbdbabbdbaedbcaeabaddacececaccdbddabdcbcceddcabddbaaeedbabadbbbdedaeaacddacdbbeeaebecbbbaaddabcccebadebddadeeeceecadaacdabeeadbaddaccacaaeebecdcbdcabaedeadbdaabebaaebdbebdacadcaeaceccdbcbdeaabedceacbedaddceecebadedbcdcaaaccaceedaeebeacaebdccbebbddbeaeedddcacedeededbcbdeabcbcdcecaacedcaaacaaecdbceecccdeceddeacccecdaacadcdcedaceeebcadbccaaeecbcedcdadbddedacacebbdbbdcdcacecebeedbdeaedbbeeaceeebabaeeecdddaaadccdceecbbdbdadbecaacdeabddaaebcbdbcccadaadacaaacebebdadadaceccddbddcdbcbccadbacebedabdacaecddaaadaeecbebdbcbcdebadbcaeacbcbeddacedcaddeedbacebecbdcdebcacdbeaeddbbcadbebddabbdeeaabaacebbebedccedbacdbccdcecbdaebeeaecbcbeddeabdbcbceeecaadbcebebddbcbbceeaddeecdecbcdebbcadccccdddbcabaedeadccaaaaceceddbdccccaddddebcaddeadaecebbebbbbdedccbeccdbeaeceeebcbacbaadaabadebccbdaebabdaecebdceaeecacadadbebbeddcbdecbaabdadabcbabacebaceeaaaccebbadadeaebbbdeaedbbeacbeeebadbbdcdeabbdaecbabbdbeddeceaebeaaaeaddbebddbdebeebebaadcbdeeeddebebeccabecadacaceedebdbebccaccccbbcbacddcdecdedeadadcdbadeecdbbcdecebbeadbeaaaabaacabeecabaeacdadcadaceeaecdabcddbbbcedecdbdeebcaaeeeaeadaececadcbdeedabceeaaeeebadadedebeaeeecbdecdbdddaddcbccdeeceedecdcaadaedaabdcdacebeabaededeacaebdebcdbcdcedddaaacdcaccaacacacdadabccaacbacacedcadccdedddaecbdaccdeccbaaaecdaeabdabeeedcdbceacebadcebddbcabcebecbdebdabdddcbeabbbaaaccceeaddbdcacdbaaaeaddaebccdadbcacaaceeebbbecdeebccbdbeccadedaaacbdacabbbdcabcededcdbcebcadcbbeedeedeeacccadddaeaaacbdacadaadcbcceeceaababeddbabecadedcdcbeabaddbebbeeeedeacadccacecdbebebcecbadccdeebdcdbdcbcdebdaedecaaeebaabdbaddbeddbcccabedbbdeaaebecabdddcdbcbaaadddbcadbccaddbcdaccdddcbcceadeeaebbdebaecedcedabebbebaecbbaaecbaeebcdbabbcdaebccbadebacdebdddeebdbcaabcaaecbddacddcdbebdabaadacaebcecdbcdbedcbbebdbcdecbccdceddeeeceeadbebbcacdaddbbcbcadeeaaacbbcedbabceeacbedcaadaaebbacacddbcaeacdadbbbbbacdedeccaaadcdabebdbdacaaaeaacbdedcacdecbdbcedadcedeaeaeacbdeaecdbccaaabcccedbcabeedcbaccedacadaceeddebdcdeaabaddbdaebaaaaedacdcbcacbedaeebeeddaddacbbbdeadbedbdbbedabcbabedcbdbaeccedbeabeaeacbedadcabacbeabcaaecddcbcdbddedaaaadecbdaaacaabbeddbaeacdcdcbabbeddddcabeedbddcadeccbaebddeddbcddaadacdcedaebddcdccebdddddbdabcbdacedeebddbaeedaeacbdcaadadbbeebabdcdbaeaababbbdcaccdecbcdeeadddbaedaddabbedeabaadedaaddabbbaabdddcdcadacabcbdeceedebedaccbcababdcdcaeabaaabbccbdbcbdbaceccedccaebbbddccdcdbdbeadbbeeaebecadccaeeebaccaceaddbddbcccccadbccccebadaecaeaddeadeebaabbecaadeaadbaaaabecbececaeddaacaeacebdaaecaaaddbbddbcbebebccccddecedbebddabcddeecdcaddbecaeedcacecaeeeeeebcccacceabcbacecccadaeaddcdbedabdbcbadbeededdcecaedcacecaaeecaebdbcadabdacaeddaacaaeceeccbaadabbbbbdcaeababdeabeeadeaabbcccccbdabddedeeedddaaecbadebeacaaeededceebbededbecebeacabdcadcdcadcaeceedeaabaddeaebcbdaeacdebaabdaedbbdddaccdeaecbdddadbeeccacbebbcbedcebcaeeedabcdcadeacdabaebaaacbaebaacddaebecacdeccdecedcaccaabecececdabadbcbaeadcddedbacdebeadbbbdacccabcedbacbaeeeeedcbbedcbccaedecabbcbabdbbedbeadebceedacadacaedaccadcdebcbacacdccccbbbacadbbeedebbbcbabcdcdeebeedaccccebcdcdbbbdacaaacaecaeebabcbdabdcebbadaaecdbaccdeceebddedebebcbedcbaacbabbebaccacbdbbbdececccbdecbbeceeaacdadddbabeddecadbaeceeaecdbcaaeabacdedabdcabebdcbccbeccaebcdbdaedcbebdceadebebaebeeabebddcbaaebcdacaeaeaaddaddacaacabebeeaabadbecbacebcbabdecdbeebdeabdcaebcccbdabeaedeedbdbaebbbabeeaaedbecebdeadabaaacbbdbbabaebbbbbbccecddaeaedcaedacbddbcbdddcedcaceaabecddaeaaceeedbcbcebeecebcecccabdaabdedbdbebbedeceeeabeecccbaddeeaadacceaeccdedcdebeddeebedbaedcbebacedebabcabdbcdbebaceeeeccccddcccaaadbccaebbceaecdebabcbdbaadcbbdbecbbdbeebbabdbddcdeacdeacedccabdbaabcdcabddbcaccdbccabecdcceeebcadecadddddbadaeeadceacdadbbdcedbdbeadbcacabaadeaeedebcccdbeadceceabdeaeabaeebcdbedeacdccacceceabbbdcbceeceddbcbdbcaeeabadbddeadbadddabadeddbdaedbcddeebbddeecacadcddbaabeebaaeedbccacdbeeeeaadceacacedaaeccecdbbceddeececddccadbccbbbcaedcdedabaaadeddadaaccaeacaebaeaccaccaabbeeedacdaeebcdbecadaddddbadbecaeacbbeaabdcddcdeddbdbdabdededaccecebdcacdccecdccaeaeadbaacbbbccedecceaeabacbededaebbceeeccebacbcababcaeeeddeddebaccecdbbdcdabbdddeeacccdbadcaabcecadceaedcedabaeddbcbeebcdcdabcbbcaaaaddcebcccebbbbdbddceebcdadeaecaddccaacbbacccedaddaeccedebbacbbedeecbabceacbbeaaaacdbcaebabdcbcedcccacbacdedbbcdedeeedbdddcabdeedcaadabbecccddcececedbebbbabcdabeaedeadacdccccaaaaceedabdaececeecdababbcbbbbbcacbdccbecccacbedaaedeceecceeccbebabbbcbadcddbddeccdeedebeecaccceeaabdddbbceedcbbeabebbacbabcdeaeadccdbcbcceaceedccaacdcabcbaedcdbcdccdeaddecbabadbbcdddcbdeccedabaaebbbdeaaababeedbbebbedebcbadebdcadddbdbbdabdeccdbcbcecdbbcacabbccadbeabcdddccaecdabaeaddbecacebadcccbdbabbeebbcdbbbddacbdcaceeaaaeccdcaaaeccebcaaddacbebaadaceecededdeeaecceebcdbdaaadeeaecabdedcaedaecececaddacdcedaacacdeaecadcbeeeceaeaddcdbddddcaeaebdbdcdccbbaaababceadabcccacacdcaedaebacdcbbbecbbcecbbeddbcbccdbcdaacecaeabcdaccddcdccacbddeeadaccbaebcadeecdbedceddadaadeeeebceedbeacdaeaceedadedebeedebaccbaecddedbedaeecedaddaeaeaaedcbacabedadbdaededabbddcaeddcccbeccebceeeeecdebbedcebbeccdcccedaedeadeedaacbebbbddeaeabbecadedbdbebccdcedbdeaebaadecbcbcdbddedbedbddcabeebebddbbdaabdbbecdaecedacddacecbeaabeecdaecddeadadaaeabddacecabdbbcaebacaecbbeabededeccbeadadabcbdcadecbcdcccebddeabdbddaaecdebebdbdebcbeadacbeeaaabbbadaaaedeeeddbeeecabaddbceacebcdebedebbebcddbcabdacecbecbeeddaabbdcaaeccceacaadcaecacbdbaecacdbeedcbdadaabeadadbbbccdaaadbcdccaccdbdeaeecbdebaddeabbcdbacdaebacbcbbeebcadaabbccbaddebabdadeaccaadedadedcdcdebedddaeabedebbddbdecccaecababadaebaaceebcebbcaedeacaddaebbecedebaebbddbbacbeacdcbeaeceecbcdccedbeddecddcbcceccebaabadababeddedbcebecdaeabcabbbadbddbdbccccbbdacedebacdbdacecaeaeaccceaaaedabcaaabbdbeeccaecdedbceaeeccbdbdbddacebdabbddcadeaababccabccbeecbecacacdbbabaaeabecbeaeecececdcbdacaadbcecbaaeadcadbcdcaebbcbeeedcceeaccdacbecaadbbbacacdacccadbcbabcbedeccddeaeeeebeebadeadabaceaaebacbdedbacbacdbeeacddadcacdeeaeaedecddaceedbbadabacebcbaeceabbdbbdcdddcaacbbceeaaaceaaecacdbdeeeecbccbaebaeecdddbebeeddaebcdacddebcaedeccdbbbdcbeecaecdedbabeabdceeecaaeeaebebdccdeadddabecdccbccdaebeadaecbbbadbcaabbcbacdbddcbadcdabeebabedddecbacecdcaabdacaaeedbccdcbedabaddadadccbddadceaebdadbbbddeabcdbecbabcbbeebeeddcbabbaeadcecceabeebeccbeebbacadedeadedbccbbaedeeedacbbaaacadccccacabeebeabddcccddecadcdbbdcacbcebaeaebbbdabdbbbdededaaebbcdddabeabcaabaeaacbcaadbadbdeadecccdedcdadbaeecaabeedabadabbbecadceaccabbbaeaeccebcabeabdeaddeadaeebdaceeedbaacaccaadbadcdadebdaddccdbeddcceabcdaacaeeadbeaeabeceedbeeabbdabaeabaecdbacddeaabaaebdceddeebbdeacabbccabcedecdeaadbbbecdbadeaadbadecbcceedecbebbbcabecccaedecdbbcadcabeebaeecbaccacbebeeeabbbbdadecacdaaaeebbeddcbbceadbabaadbabeceeabeeeccbbeabceeeccaedceeabddbebdbbdcbacbddbcdbebcbbcebbeeebadeedbdbaeeaabbddbdccaecccbdcdeaedcdcabbcdcdedacacbdadeaabacceadecedcaabaaadedbeddbadcaadddaccacbbbcceeaaddbbababceeccdaceacdeecbbcbeedbdaaedbaadbaddcdedebcaebedeaecbeabdbcabacecbbbdcbeaaabbebacecbaceaccaeaaaacbbcbcbbcbbdcacdebddaeeebcdbaeecddebcaedbadcdbbecbcdaeceadbceceababaeddbecbcabccaacccebeaccdabedbcabacceddabadddddaeadaccedcdacacdeaeeaceeeaddaedcdaccdbddaddccecedbdececccdcaededacacecccaededcedebaebddecabeeaccdcadceccbedeecaecabdceaceeebbebdecacdcdaebabcdadbbbabacceaceebcdbebaedcbaebbdcbdcdeecadcbdeaddacedebbcceeccbcdbbdbeeaacbcbecbdeecddbccbeaaeeddbdbdbeaadeaaccdbdccadeadeeadabcaeacceaadeaecccddabdbabeaecdeaacbccdeddedcccdadcbcdadedceaecabeaaeedbccdebcbdcedcdbbaccbcedebbbebeacddbccabadbbaeadeedbcdbbcecdadecdbeaaaebedeedacddbedcbeacdcbeaeaecdecceddeddbcdaeecbaddcaedbcddedcdecebcbdaeaaedeaebdcbbbbebccbaddaadedaeaecaaadbcaedddddbdbaaabcccbbceedbcceeabccbcbaeedbdcbaecdcadceddebaaccbbdddadebbabbeeedecbbabbdddaceaceecbbdadebaeeabcbacdabecaeebddcdabeeecbaeaaddccbadeecacacbeeeeddadaecbbceecbddeeeeecddcacacecbeabcddbabacabaaaccddabdeabddcedccceaadeeebddcbcbdcbdacbbdecbdabbcbaeaebabdaabebdddedcaaadbadccededcdbbadcabedaaeecebbabbbbaddeaedbcddcbeeecaeedcbccebbbeebcebccbccceaeaededadabbeebdebebdcdeedbdacecacdbaeabdbdcbaecbecbeeedbcbebaacaeeaccabaceeeeddadaacedabadeababdbbbddcaebbcdaaadcaceadeddabdaacdebbdcadeaebbacabdbbaeaedecacbddcbcddbbcbedccaebedceadddaecedaeaceebaaedeaaaebaceddbaadeedceddbeceaecebeaaaebedaaeacbadeadedceacbddeabadbddcaddabdacddceabaeacedbdcdaeaccccbaccaeeddabbedeebeedaeabadbdeccaaddcbddcebcdaccbdabcdedbbddecbbeeccbebdbeacabbddaebabbbbaeeeaedeaaaaaecedbeaedddbecebeadcbcccdceabdeebbbacbcaccbcccaabddcbdacaacbebaeaebebcacaecceaceaabbcecdcecbcdebabedbcdadecdedcaddceaccadbcaaceceaebeeecedeeacecedbaeeabccacecdccecbaeedcaaecbebabeeddaebacadaaebceacaebbbecbbebcabaaedeacaebacdbbbedadcbcabacbbbbccababebcceaaccccedadbaaadccaecabaaaaddbbeecddceedacebdddeaedadbeebdcdcaacecdcbabaebdbececaecaedbbbeabaabcdcbcabadebdacbeeabcbbaacdebbdcecbcecccccababdbadddbcacecbcadbccbdeadcaaedadeeccdbaecbadabebbbbedadcdadbdaabcdccccdbcabccaeeacdbccabdcabecabeeeddabbacaaebceeaebbbccbabbceddddbdeacdcacecbeddcedcdcceeddbaabbdedacdaaeccebdedededddccbbddeacdeccdcbecbeeebabedabeacdebaccadbaaebabaccaabbeacdbebceacabbebeeebacceacdabecdbcaccbecdaaabeedddecaccebcaaebbebcdcadecabdcdcacedcabeacebecdceecaecedbccdacdebdeccbdeabeedbadeeebdaadabbdaacbabbbdacacabeacbbeaecabaaebcbbcbbddcbcaaebaccabdeceebceaecbceecadeeedeaecabcbbccbeaecaeecceacaacecbedbaddbaeadaaeeeaaebdeacaacacbadcdadaabbedbdacdbbccdcaaecbeeaeccbcbbbdbdbcceeacddddbcabbcdbadeaabbbaacabcedeccecdcbcaecdceeaedbdbedeceddbeeeaeabaebdbaeabecaeccdedadabbdecbaeeccceedeabdddbdcdceecdcceebaacdadcbbdbeacbaccabeaaaddadccdcdaadaeabdcdbaeeedaadbaceecbadadedceaeddedbacdbcccaabaaabbceccadabeddccabcbebcbbadbedeecaacdddeccdddddbdaaacecdbababdcaecbaacbadcdaedcddecbcaecbbaebccdccdccedcadceaeaadcadcdaabeceadebbbdbebebcdbabdcbdccecddadacbabcdcbbcabbadddcaccedacededededdabaadeaabacadeddaecaabbddbcdceecdcabadedbbadbbdceddabeccbccadddeebcaeccdeabadbebcacdebdcebdecdadaaebebceaeecedaaceebeaadddaaedebededcecbedcbbdbbbccdcabbebaecbabdaeeaecdeeeaaceebabaccdaaeceedeeecaaaeddbbdabbeccbebcdbdaeaabacdedbcaabebbbedaecebddbbedacacdbdcbdedbeecebbaadeabacadeccceeabbdaabaabbaebaceebbdbcadddabeaceaacccaaaccbaedeebbeaaeaadcecaaeddecaccdecaebaadbecaedadecceacbbdcddceeeeacddecdbbebaccadbceaeebdaccaaadbdbcebaacbedeaadabbebceaaaaaacddcdeccaceedebaeebcdebdcbdacddcbbebbdcecebeeeeadbcbcedcddcaebcadddcceecaadcacbeacdecebaaeabbdecbbdbbedccdbabaeedebbcdcbbcbcadceeeeeaecdeacadebadccebceaddaedeedeaacbbbbcdbaacabebededeedddcdbaddcccecccabaabaacccabbecebcaddceddcadabeabdeadeaabeceaacdeaaaeaaedbbaaeedcbebbbeceeabcaececeebcdedbbadbbbbcccccbaeedddcaecbcbabeaededcdbaeedecebedbaabbeecbcedaeecdbaeaacacedccbcbdcbdacceacebdbbcadcccdabebbecbedccbbbadddbdbadcaaeaabccbbbabaeeccebdeaddaddaccbaacceabbdeaccacbbdaeccedbeceeaedeecacadbdeecdbceeeacbdecbddebaacbcbabdddadbaaabacaccdbccbcaadbabaceeeaeadaabbaacecccadaebcadaadccadebbccabbdbddedeacdeaedaabadaeacbbcdaebbcdddbbcbecceacaaabecdbecbacbadccdadaebabecdaddedbeeecacadabedacdeeebbecdaceccbbcdaddecdcbbbcebbcbbeeccdadacbbcaadedaccccaaaceeedcbbdecedbbcdccecadaeeaacdaeaeeceaaadddedbceddaecbdeddbeedecbaaecccebedcbcebaeeceddadeedececceebaadceaadbddedeccdbccdcddacacebbbbdaabadabbebbcebcbedeeacecaaebbebdeedbacadedaabcbdcbbbcceaacecbebdddeebdaededeeaabcbeeacdbbbacddaaacebbcdaacebddeccebceebdecabbbbedadcbcceebdddabacccacdeacebddababbcccabceecccebeebdcbaedcbeaeaecaaededacbaeeabbedbdabbcaedaebaedeacaccdedbbecccbbaddbbbaaeddebadcdbcdaaaacaecbaedabeeabaaedbbebabcebcebddbddccdddddbbccccbaeebaeaccbeaaaadcbdbcdcceeaddddaeedbeecaaabbceeaaadcabdccdbbededdccddddabacedbeedbccacdddcebeaebdadedadecebddebbddebecdbcacecbebabcaabbabbeebdebebeeddadccbdeecacaeacaacedadcededebdeebedcbbebecdbbeadcdadbdeadbeecbadccdebcceeeebacccdcacdccceeedebdaebbecbbacabeededadacdedcebdbcbacbedcceaeceabccdacebabbdaaaeadddccaebcddbdcbbcbacbaeeeecceaaedaedccdeccbacdbdacccbaeaccbaedcbeedbdeadeddbbaebdbebbcaecdeaeeaabcbceddddebcebdddaeeeeeaeacebbabacdbecdccbadbaeddbebccdabdabaeeabedccadececadecccdeaebbbbddaecdbebbbaeceaeecacdeebbbdcabccccbddeaacaaddabbdcbabaccedceececdaaecdeaabdbddbcbeedcbabecdbabdbbdbaceebaddeacdeddecdbcdabeaaacaedbeddacdcdeddadccaceabdacdabdbaeeddacebbcebcdccebbdabeddcaaccaeacedbeabbdddcbebbadccbbeceacbebdebccaaacddccebeccaddeceadeccdadaccadeceaebcaabeedceaabbcaaccbddeadcdeaabbceaeccecbcdddadeeceeeeccdedbebecbddaecceebedabbcbeacbabcdceeebbbcdcaaeebeacaebbbcbdeebedbcdcbbecdcaebebebdedddaeadadbaddeadcdcaacdcaabadbceeedccbabdeacaadddeaceeabbcdceadeeeedcdccedbaedeeaedeabaabbaabadbcabddeaaaecddeecabdeadcbcbebcecbedebccbdecaddbaaceaebdabebcdecdeddceedcbabededbdaaadcabdedbeadabdecabbcbebedadddaeaaeaecceaaccacddeaddadbdabdcddadbaeadadbebcaeebecacecbcbdbbaeadaecdcccdbcddddcccacbceebdcaaecddedaedeabcadeacbabaeaadbecdadbbacbebedcabdcceadadeceacecdbabdecaebdbbdccdaeacdcdabaccececdeaddbabcccceabecdeeacbbbbabbedbabcceecabacabcdddaececbbdcadecbbeacbdcbbabcacaaebabbaddcebceabcecaaceddaabdabebededdadabececeeaadaabddcacebbbabddadcadddbcabaadcabeaddeaecdbeacbaeecedacceeedceedceecedceceaddccaeceeaaacaadbccbbaaadabbdbddebbabddeacccbdebcdaebdaeabcddceddebbebbadcdacceccdebabdcdacbcbaddbaebebdabebceceabececcdacacdeeeecaadecaccecbbdeddecaadeedccabbaeabbaadaaebebeedeeeaebaacbcbcbadeedcbbaddbdadedeeeccebedcedeeaadebeadbbbdcbbbcbbdeddcdbaceaacdcccddacbddbdbaeedaaacdbdedaecebdeadebddbaacdeebcecdebcabdedddbddcccedaceceeddbbbceadbbaaddebbeedcdcabecbeaeeaadecddbaceadcecacdbdaedaeaccdacadeecdcaadeacbbddedaaeddcaaaaaacdaddabbacdbcecabadebcbebcdcbcbccdccadabebbdccddddccedebcabdebbcbdcdedeceedbebcddbeedabaaccaaebaecbedbceddcabcebeadcedbaecbbaadaacddeebebcaeeacbaedddaaacddeedbaadadddccbdedeecaedbeecdcccdaedbeeaacacaadcedebaacaabceaeedceedcacebbdcadeaabbdbcbbaeecadbdcaadbcabadbddaeecdcbabbcbededcabddadbadcccddabbbaedacaddccdeabdebaaaaebcaeadddeecbedaccdedceceeeadcdcaadbddaebbbeabaecbbbdddbbddeeddadbbbcbebaeeabcaaeaceeecbdbabcecbcaddcecbeccbbbbcdcaaddebdddacbecbabeecacdccaeecdcacebeecdbaaddccdbbceddcccbecebacecaecceedcedeecadadbebabcddccdaadcaadebaecbaaebdbdecdebcccacaaaebedeaddeadcbdbdeacaabeebecaeeedcbdbebcaeaaacbdbeeabddaaaeaaddabcaccbaaaabdbcbeabaabebbaaacbdbccccaeaedadcdabacbaebacecbbedcaacbdeeeaaeddedeabdeedbdecababdbadeedbcaaebcbbdabeeaaeaabaaeeedbcbbbdbedeccededcadabedacddbddebdbbeaeccbdeedddabbdecadddcdcacccbadbdebeadbbccaceaddcbeeaeacbeaeccddaeceeedeeaaeaacecddaecdaacbccddcddcbebeecaededdeeaddeebaecdbcecdbcaaccbddaacbaceaccdacaacebbaabcabebabcdeccedbbdbcbacadababedeecabdacbcdccaaadacbbbebecbadbaacebdabaecaebebcaeadcceeccbbacaddeddceacbcbadddeebcaadadccbbdbabaeaeccebadeaeaacbadbcccadeeeccbdeebbeeaabccdacaeceeddedeedaabddceeebcacbcddbadaabdbbeabebaedceccecaecbbcebedadaedadccecbacebcaebbaadaecbeeeadebdbbcedbbbbaedbeecaaddebbddccbeccbebcaaeddebbcadcdacbcbdcbbaaedadabbedeebbeacabebededbabbcabcbaeabeceeabdbbcbceeebdccbbaebbbccbeadeecaabeadecbadeebdacbacacbeebceededdddbacceeebddcaeecbaacaccadadbeccbaddaeacbaeecaebceceaddaaddbdeeedaacebeceeedeccceaccadacacebcccabbaacddbabccbaeeaecebdcecacbbdceaaeeccabcbedacdddbcdadcdabceccbabeeeecabaedcaabdadebdbccabdbccdbaebdedcdbeceaaddbabbcbeddbbdbadbdbbcbececeedaceccbccecaceadcdaededabcdabecaaadecebceddcbeabcabebbbaddbbddaebeeebbcbebcdeaaebbecaaadbbeadcedbecededcbbebbecdaabddadddaaeeccedcadadcbdaededcabbaaebcebccdaccbcddddaedbccdbbaacbdaaebdebdabeccaccbececaecccddeccaccdebbdbaacbebceddbcecceebcbbebccbbcbbcdcdaaedcadcaabbbdaeadcdbbaaaaedcbcedbebceaeeeaeaceacebaeaaaebebdbebbcabbcdcdbeadcadabbadceceaeadaadbbddceacdbbabaadeadceeebaacbcbdaaeeecdcdbbadbcaabbcdbcbcdbbaabddebaeddcadecccdabcbcbcadabbaceabaceabaaebadbbbaaebcdeeeceaccccbbedcbeeebbaebacdaedcaecccbedbeeabcabbcdbeaeeacbdbecedcacbbbceeedcbbeaccaddeeedeedcabeccaeebcedaaccecddbeebbdbebdbbaabbdeccbcccdebeacbedaeaedbcdebaddaedbdcdcabbbbebaebeadeabdcaebdbebecdcbbbacecbadaeeccbebdbbaeddccceaddcaaeabbddaabceeecbeacbabcbdcaaebdacbcedbbaecceeecbadacddeddcbaeebbcdebadacdcecadbeadbebeeaaceaabcecddeddcacaebebbaceeadbedbcabccaaeadcbabcedcededeaaecddebcdbabadbdeaeedccdbbcaccaaddccdbeadbacdeccccacceadcecceeccaeabdebdddbbcbdedeebccdbeccdbbecacdbeeddcddacbbaebbebdbbcababceabcbeccbdeebbbaedcbaceedaacccaebcededaabbdeabdebebdcebabaacceddbdcbbdabeeddcbeccbdabdeeeaecededccaeaedebbbbbacbdabdacdbddeabcbabebbabebbdeebbeeccdccecbcedbeaeacdebbccabdbbabaacedbcacaadecdadcbbabababdbdaeebaccdaedbadbcdacabcbeecbbeadccdedbedcbbadaacaebaecdbcceceadacdbbcbadecbeebdeceabebbbdadebdaeabccdaddcbaeaeacbcbaedbcddacdaecdcbadabeabebecabeaddadbbdeedbeaddebadeaacacaabbbebcadbadaaeeaaeeedbbeacbcedecabbdeddbdcecacaecebaccaeacccbacdadaabacbaebcebccdeabdadbccaaebebeeaeaebecacceaedeadbcaabddbecdaebeabccacdcbeddeabdcacabbaceeaadedaeccbabeebaecccddbcacdacbcbdddbbdbadabaebceadcebeeaeacecdcadeebdaddabbdedbdacdebdecdbcdeabacccbecdbceddeaedeebedbccabeeeddabdccdabcdebcebbbaceededebeadeabdceabadebedbbecceeddbecbeddbacbeeecebbecbdbceaecebdcddcaedddaaeebbbcbdbadedcceabbaeacedceceaeebbbecccebeadebaeecabdeeeaaacedcaeaeaebacbccecbdaaeddbdedcdebcbecaeebeadbcbccebcaabedbeebcbaaccddccbbbaccbdeecbdcddcbaedacdecbbbacdbdacbcdccebbdccdceeabbbdbacbceeabdbdecdbabedebaaecbbccaabbdcbaebcecadccedddadeebacabbceadaddccebceecabdacbdbaddbcebdabdbeadcdcdaecacecabdccbebabdcbeabdbeebdaddcbbbceeadbdeaedbedbababcabbadbcebeddbeeaebdcccccaaaedcedeaeedcabbacbcccadaebdebcccceeebcbbbecebcebeeebcbedbcbaecaaaebacbeedabedcddabaaccdcecedebadddbcdbdadabcabdbedaacaddaeaecebcacaabcabbaacdabcedaedecbbbbedeedacedccacbbdeebdbddebabbadabcdccbcedadebadbbdcebdaaeebdabbbceaacabecedebadacecbcbcabececcedaddcccadebaadeeaeddacddacdccaadaadedbbeaedebebceaceddcdcbdaeddaedaacddccbddbeeaadcbbebaaecdedbbcdcadedddacddbbaeeaedceececaacddbcdeeabdbbaaddddbaaeeddadcebcdebecaeeececceadadbcaaebcbebcbacbebeecaeadcbebccedabadcbcccdeeadcebbdeebadaacaeeedeeaeabbeccddbdabaacabdbeeabbddaecbadacdcededccaadcecccdbdebecbcddbedbdeaaddbddddbeaabcaeaabbabdbddebeaeddecaddeaaccedcaaddeeebbccaaeeedceaecadbdbecccedeabedbcabadacabaceddcbbbadabdeecbccdedadcdbdebdaabdebdeceaceeeccbeccaacacadbcabbaeacaebadebcccbadedcceeebaeedcaecddeadaccbcdceeaebdeedaebcaacddeedcacccccedabecbaebeddcdddcdeeceabdbeeecaccaebbdcbeedeabadaadcdaaceccbdbecdcabaecabadaeaebbdebacbecaebaccbbdbbecabaedbdccceccaeaeecbcbeaacecdcebbbabaadbcbaccbaabaceaaaeadddebcaeacdaccedaaecadbdebeadaaccbdddbbcebabbbdcaeaddecbaccbeeccbabeaaddabceaacabdbbadcabeabaddbaceacadadbbeaedeeacdcbbcbeeddbcacebccededaeebcbccdedacebaaeeabecacbacaabccebbbddbccedceedcbcebcaebebdcbddcbdaadeaeddabaaeceeedcbdeeaedbedcccbdcdaebdeabeaabbeabaeacbeaeeeabbacaeabceeddcdceeaaacaedacdcdedcddbdcadddcabbcadaebbdadbeeaeeabdccadaaaaddbcebebbaabebbadbaadbdcabeeeacebeedeaddbdccaccaaddbcbadedaaaadadaccaeadedbddeecceecebaeedebddcdaceedebcddbdbccedbedbcbddcdcaabecbeaccabaceaacbacdcdbadbbebacdbedadbbadbbbbdebcabaecaceccedbdcabaebbccccdceaaaebaeaabeacabbdadeadbbcccbbecceeecaaaededabdccdeecacabcdccacbeecbeebeeeebacbdddddaececbaecdadeeddbeddcccadaeabeecdecdcedbbccebdaecacccdbacedbbcbbccadcccbbdacebeaebbacdcddcccdbbdacaedcaebadceedcbaeaccdabcdbebdeeadaedbceebaecdadbaededadcbebcecaaebdeeacabbaaaaecacdbcbdbcaeceaedbeccdeecdacbbbbeeaeddeedbaacdaebcadbaddabdeabaeabcdceaadabebdcbbdbcdeedbebacebabbedaceeecacbebacbedadcdaedecdedaaceeaccbadadacbebceaddbecabdcdecbaababadaacceebaecbaccababeecaebadabbeeaeeececceecaeebeadbddbcceccdbeaadbbaccacdecaabbdaeedcbdddaceecbcdecbaaecbcbdcaccbcaebccedacacadbcdccbabbebcdcbceeccbbacbaedacbccecaaaaaccaeddedabdceebddedceabeedaaacadbdaeebebeeedebbcaabccaebbadcbcccacbceaaddeddeeedbbdbcaaacceeadbebccdadccbdbcaabcacecceedebddadbecedeecceabcbebbadbdccaeaddebbecaddbecaaeaaecdeecbabccddbeacbeceecdbebceacbabceeaccebdbcaecabccdccdecbeaacbbedaecdceddbabcaceabeedcccebacbdbdabaaabeebecedacdadeedaaeeecaecccdcddcabbbeedcdaebcceccadebeccddcdeccbdeecbbdeaaabebccabdbceabedecdcbeeccdcdbadaaddbeaceacceededaabbcddadcacdabdaebdddbadcbaeacbdcbdbcdbbdecadaaaeddebbaccedcbdbbbcccaddacabceccceceebdcacacdbcbcdbacddaeedadaabecbadcbeababedbaeaddcadcadeabbdeebcadaeabebeecddecceccdbdcaebceceeecabdbedcbcacccbbeebdddcbbecceccdacaadbeceaeaadbacccbbcaecaeebcdbbdbeadcdabecebaeabadadaabacdabbbaadbecdacbaadcedbedecaadeddebaeaabcbceceaebcbeeedcebbcabbedcbbdeaeeabdbaddacbcdaedeecaaabcddcbaccbeadbdcdaecabaacababbbaedacaaeeedbccdaccdcccacbbeebbabddbbbadceadcaeaddbdbedbebcdcddaaecbedbbadcaeddcabeceddabedaaadbceabbbaecbcecebdaaabbcaddbddecacebbeebbeacebddeeeaaccaebecabbbcabcadcddbbcccededcdacddbaadcbccebbdecebbdeadbcaebeabdcbdbaebabbaabbaacebcdccdbacbedebcbbecdeaacbddcbbebeceeeccabbaabdeddadacdeabbbeceadecbbeaabceccabeddbeacdccdbbaabeeeecdcecacaebddecdeadaccaeaabbedbaebaaeebecedebdaebbabebabadabbdbddbbcdeecdabeccecbcceaecbbbddecbbcbbbacdddbcbaacbccbacccadeaeaeddaecaaadaaddebdabeabbbedacbabeaebeeaaecdbeabaebbcaecdaacbbddddedeacbaaaeadbadccccacddbceaebccacaeeecdeeddedccdcbbeaccabdbabddadbadacbccedebddecdedcdaabeedbebcaaaebecaabbacacdcaabbdeadccceeddaaceeebcbdeabdeaaceeacbdababdebdcdeeedaebcdebdcebdeccecaaaadcbceeaabcdaedcbadddeaecacdebdeceebddabcabcaddadcbbdbdcacaedbdbdaceccbdaadbdaadebbeeddaceecacaadeceedbbbccdddeebadeddcbbebbeaeaccedcbeddcdabdeaabaabccccacaddddaabeddabbbebededbcaeaecdbeccadacdbaebbdbccbadcbadaeaecbeedacdabaececacecdaccdbeabbcdecbececbbaacedbcccdebbdeccacbeecdbabecedbeeaabbbbabaabbdbeabaeadcbcbaccaecacebdbdeaacbaedaeceaececaeeeedeeaccccedcaccabdeddebaeadedabddddcbccacdccabacbdccbbdadcbebadeeacbcbbededcebaeacaabeacededdbcbeabdbbccdcdcdebabacecccdadccdaaabcabecabebecdedebdbddcaecadbddbeecabdedcbeaaebdddeebcbebbaaccceecbdbedddedadceabeeabebebadeeceaeabeeabedebdaceecccaddcbaeadbcbeedadacbddcbdddbdecaacedaddcdbbabdebecdacaddbedaebccbcbbdebbaecaeccaeaceedeebaeacdaeadecaaabaabbaaecedeebdeaabdaabedaabdccdacdadcaacbeaeccacdbebddbeaaaaeddbebcdcbbebcbbddebaaeddcabaacecadcecbdddebbacacdcacbdbbcebeeecaadacadaaacbbadddbddecbecdebeabaebccbccabbddeaebdbbaeaebecabcaacbebebdcecaebbbdeeaabbbdcaeedebbdaeabdebdebeddbbbdacaeddadbaebcaceaeaaceabaececbbbceaceadcebbebbdacaceabceaabcbcddbcbcbdcbaaeceedaedcbddaadadbdcebcdaeedbdacbabdaeddbeaeacccddacdcbedbdbdadadaccbcbceceddecdedcadaabddbdcbeeebbeeceadbbebaeacdeeceecdbdaddedbcdedecabddbeabbabccdbaacecdebbedeaadccbaecbaeeacecacceddadebbebbdebedcaaadecedbcdceabaaecabcbeebbecbeceeacbdeeacbccbceababbdbaedebaeaceecbcddeeecdccbedeaeedebcabbdedcbdbdbddbddaeecbeacdcbcbaabadcbebbcbbacaacacdbeadcabbddbbaaecdcceeccdedaebabeddcbdadebbadeabeebeadacaceeacbccaaccebedccaebbdadeebacdcbdeececbedabdabdbeadeddabeeaddacacbcbcdbdcaebbdcdadcedccacaacaeacdebddeadcbbbcedcedeaacdbaaeaeceaebbeaadedceadedadbadcbeceddddbccabccaabedbcdadcdbeccddaeedabbbbbaaaeeccaaecbabeaccebdbebdebdeedabadbbdaceeadacbddecdccdbcaeabbbddbeeeebbeddbccbaadeeaddbdcbcedbedabdacedbabbecbcaddbbbacedbcebeedabdaeddebeebdbeeaaabdceeddaddeeaccadecdcbaedcbeadbadadaacacdccedbbdbabcadbabaeaabdcbcebacebcabeabdeebeeebababdeddecdaebdaaebeadcdeedecadaddaacdacebddbdadebcbadaacdcaccbeeeecbbabdaaedbeceadddeccbebebcbceecaeeaaedeccadcdcbbddbdbeddbdedebdbbdbcbbeeedccacdedddacedbebeacbcaeebeaaebceedeedcddbdaccaeaacadbeacedbaeebbeebdceecedcbeedbdecdecaddaacbdaeedadedeaadcadbeaeceeaddbcaebdeaaaadaeddbcabdddeeaacbeeaebbabdeeedbabbddaacaebaabbcecaaabeacdabcbcddbdbebeaedcdcdadccacecdebbdcaebdcdeccacadaeedddaceceaddbacedbcbdeebcabcaccbcbdeddcbbddcdaccbbecddbadeddcbcabbecbdcecaddddbcdceaddedebbdbddedadccedbcabaceedabccbcaaeecdacceddcdeeedebdaeeceecdedebcedeacababcabebbadbabeccbbdcacbebcbacbeecbecdecedbdbdaecbdeddcebcbaaadbdadbecbabcdcaecdecaeebacdebeceaebabdcacbeabcbcacaaecbeceececcdeaedeccbebabcbcbdbaeeadcabbcdcebdaceaddbcbdeadcbedeadcedceaebbeaddaaebacdadeedaceeeedaadbaaebdaaadbbcddcdbdcbacddaeeeeaaaadbdcaadbcbaeeeaddadbcbdadcbeddedbadbaeaeaccbeadeecddadecdbddeabcaedebdbaacdacaeeabeabaabbabedaadecbcbadcadeacbbadeedceabeacccbaddceabbccacdbdabedbebdeeeddacaddccdbedbecbcbecccddecbbabaabadddaeedaadddccaaaceababbbbbdccdcacbadbaaeaccbcbbcaccceabaeccaddbddabaadaacadcebebbabbceaecbcacdaaacbbbaddbbdccddaacecddcabcadbceabebdcedddbbededdaddcebabaacecaddaaeaecbcddeaaceecbecaebddbbecccbaddeceaceeeebcbcebccedbadadaacecebedbcdcdceadcddbdcbaedeabeebebbbbdbaabacdccbedbdddbaacacbebeaaadeeeaedbdbcbabadddebcbcdddaedbeecadbdbcdadccaaedadadedbbbeebbeeeabbdbbecdcdcacdcbbecebaabdebaeccaecbeedccaeedecbecddcbeccacceaeecbbccbebababedbdceeeeaebcdaddbeaeddccdeeccbdedeaaebdcccdaacaaabeaeddaaadcbadacbbbaddeabadbaadbeaeeaacadcbcbbaaabdddaabbbaeecbcdcecaadebaeaacabbcbdacecaedbeeadaadddbabdbcddeddbebcbcebbaebaeabbbeeebdaabdaddbdaaeddebbbaacabeebbaccabaddacacabbccecacaaeecdbabadebdedbbeaadeeccbabedeededbcddbbeacacddcbcdbbacbdeceacedbebbbcedebccbbecbcbdccbceadeeeccbacdbdccecdcdecdbcebaaadcbbcaaacdcdcaaacecdcdbaeaccdddcaaeaccdecebdbecabeecdabceeeedacaccdcadadebcceadcddcebcaadbdbbebadabbcdecceaccdeddcdacbcecebdaeeeadcbbbdeecdacecbcdbeeddcababbceaacdaecacbbbeeeceacecdaedeeaeecaedddcbeabeaececdcdcecdceecacbddbcbebaebdbceccdbbaebaebcdddeceadcedaddecbdabceedebadababaacceaceddddccabccbbcedddadaeddbacdeaebbceeeceadbeebcacedacaeacbbeaeaaccecddcecbbeacdddddaeeeadecdddbeacccbbeccecdacecbaaeebddcebebbcaeadeeebcdbaaeabccdebbbecbdeedbedacbeccdacddabbaecccdaadcedcddbdaecebacbcbbdbbacdbbcaccbbcdbcddbceaaceaeabecbdccacececaedccdebbebeadeaadeaceabdcaaceeebcbbcddbaebcedbabeeecbbaacdabdcbeaccaddcbbbcabaceecaabbadddeeabceeaecacddedddaaededcdaeeedbcaeeeebcdbdcbbdbecdccdaacbeebbbaddbadedbaeacadddebaaabdccceceddadbcadedbeeeedaaecebbbdacecacebcedcadabccbbebdbdedcdaabcadcaddcaebbecadaeeedbbdbbceeaecbebdeaacdbeebdbcdcbcccaeebeabdabdedadebdbcdbcbaddcbbbbdabdccebcbecbeeeeecbcbdaaadaecbeddbcbbdbbeaadbcbcdbedceedabaeadacabedececdbceaabdeaaebbdbeacacedbceccedaeeecccedddbedbccbdaacdcccebbbddecccaadeaeaaaaedcbedecaaedaebdebbdabedaadbdbcecdccaeceebbbacbabadebeaebddbbccdeabbdddeadadadbedecbcbaecacebbcdadbbcaadeeebadaccccdddeedcbcdcdadcdaddcacecaebeadeaacbaabbaaecebbdbbeebacbdeeccbcdceeaecebbebbaabbaccedcdaadcbcdbbcecddcebccadeabdeeedcddedecabaaacaeccddeadbdedcdabdadecddbbcbdceceeeceecaeabbabbbeeebacedbbceeddccdaaccddaabaddccacdbaeaaccadbbebecaebaceeabcbdedabaccaeecdecbacdbeadcbcbcecbecdeaaaddaceeeeddcabcccaabbedecddaecbddbebbdcaacccedcecbdbdcaaeabbebacdaceacabadbbdbaecdccceadebbceeadccdcbbccbecaadadaacaeababebecaadbcacaeededaadbdcadbddcadcedddbaabdbbcacdababaececeebaeaeabdbeedececacddebaeabddbcecbbddedbcccdcaaedccedbeddbdacebbaebdbdcedaadcdabadbbdacaebdcccaebdeddccaceacaecbdbedeaecaedcecddadbccaacadceacacccedcbeeaacaaddbadcbebadbcbeaececadaeaeaddcaadeeedeeeadabbdbaceddbeecebbbeebbaeaacbeebdcabbddcadabedddaacceeddccabeddcbcedaaddbeccacadcdcedaaecaaaacecaedbaeecedcbbeccbeedeeaddecedcaceebcecaaaedbaadbecacdecaadeedcdbdddcaaeccdedaaaaadadacadbaabecdaeddcbaaabbedbecddaaebdadcdebdbceddeeaeecbdeceabeeedaddddbabecabaebdbeeceddccbbcddadaeebbdcbebecdaacacdbaeeabdaadbceddeacdeabeceeeaedceaebbaaecbaeebcecabeabdbaaccbbadedbcdbaeebcacccacdebebabaaeeedcbdadbaeccdebeaedbbecacbdeaeabbcaaacebdbaedbacbebceacaeeecaebddcebbaecdaaaddbaebbddbccbdcbaaddcbdeddedaedeabdbbbcbceaacdeeabeaabbbdeedeebdccdacbcbedcbdabcbbabdebcdebaacccedabaccdddabbeebabdabceccedabeedababbcbcacdadaeaceeeacedacecdbbeeaceadaabbcceabaeccdeaeeccdceabbcbdbdecccceceaaeaeadebbceebbbeacbabcbccaaccbddaeddaaebbbbbacedecccaecdeebbcdceecababdbcdeedbcadbabacdbaedeccecebbbecebddeeeaaacaceacbdaeaeabaadbaeecdaebbdbdeaaebcdabccbdeaddeceaacdcccedddbeeeacabbabdbeedddbccecbeaadbeebceeccabbdaebeccdacacaaeddbdbdbbecbceabcabacecbcedbebccacdebbeaadedcdcebebaedbbbddbeaacddeaedebcccdddcdcadabdbbebeacecdedceacdabcaacceecdedbabaaeaeacabdcebbbcbdaecbbddcccbbbeccdcccbcaaccecddcccaeabbbedcbdedededbebabdbaeebbabebdeaaaabeabbdebcccaebbabdcccbcbbbeebccebcecdcdaacedcabedebaddbbacbbadbbceccabaebdddccadacbbcebbbaccbeeedbabaacdadaacaaedbbeadebdacbecdeacaeddbebeebbbcddbabeebecbedaacddbabaadadccbcaccadcddadceceeddedaaabaeadedadaaeeeccacadecbedeaebbeaaadcadadbeaeaacebcadceaeacdeababaaebecbdeaaccedaaebcedddabcbeadddeeabacdbbdcadaababcdadabbccbcddadedcaadeacbcbaecabeaedcccbbaaebdceccabaccbdbcbeadeacaeaccaeabbaceeaacaeaabadbddabecccbcddedaeeebcbcebcdeededbabeaadbeedbabacabeddaeeeeeabdbacebdaddbbadcdacddcbdbeebbbaadbceadbcadcaaacecdccddeeeadbeeaacaecabddcdaccbdaadeeceaabdbdbaabdbedcbcaabdacaccecbebeedddbbadebeeceadebcecdeaeeaaccbeaaeecbeacdbaccaeaddeeeabeecaebbdeadbcacbeabcdecebabbddcbbcabeddcbedeebbdbabdddcaacebdbdeedeccaaaccedeaccdcacccbbaaecedbebcebbbbbdaaabaecacecdaeceedbeaeccabceacdcceadcebacddbbacaadeacacebbecebbdcbbedbcebadbebdaeebccbdbbaeadeedbcdeaadacecdcaadeecdccdbacdaddeaddedbadbdcacbbcecbebbdccbeeebdcabaddebcbeebeeddacddcedecbabacbcbeabdacbcddadbadaeccdbbecebdceeccbaaabdccecaaebeeebecedeeacbcdbbcabcbbeccacaeebecaadacaadaeceddbcecccdeaecdcbbeaaeedceeacedccbdedcdcbdcaebaecebccbbbaeaebaeaeddabadcdecbebdbeeeeececedabebabcdaeaaeeceeaddedecbcbaebbbacddebcdeaddcbcddaaccdddceceaaaebebeecdeeabcceccadcddbaecbecbdebcaddbeacaedcdaeababdabadebcbebbeabbdbbacbbbbadbaeaabaeaddbbdedddebcecbdccddcbeaebeabacbcbcaeeadecedcacecbcccbddedceeabbedcbebbeccabcdebdcdeacbbcdbabcbcdcbbedbcceadadeaacceddbcacbabcaceadaccbbbdbdbcecabbaceedbcabcabbabdbdbaaecebaabbbcddecdbceaecdacdbaeacbcdbddaecbdbaebaabbeeeaaebbeaaeacaabcaeeaccdaeabceeacdaeebbadadaeeeeebbaebcdaebddcccbdeedeaceadecddbaccecddedaecacceceecacbaccacddcababaeaedcaebaeebaeeeedbbecdababeeabceababcedbecbbbcbedbacadcdaedeaecdcaceeaecaeaedeaeddebbadedcaddacaddbbbdeadbdeacdceeeebdaeaceabbbdddebbbabcbddcdeadaebacabebeddeecacaaaadeadebabedadebedcaaadabadbececedaecbbebbbeadedadaddacceecbbdbacdaecceaabeedbcaacaecbaeaadaebeddbaedbecbebacdcedaacaedadcadabddedcbabeebdcbeeaebabcacaddbcceaccdcddecdbbaabecaacecaadcabaacecbcccbabcacbdbebbcdaadabadaadbaeceaddebcbdaaaddeaedcbcbeddbbeadabbeadbcaecabdadabedcceaddbdaeecacebeeaebccdbdebcbddbcbdccdaddaebdaaabecdedebdbcdbaaaedadbdadddaeedbcccbdddeebeeebededacbdbddddbceebcacecbcbbcdbcaecebeeadbcbbbdabcbdbaeacebacaaabdbceecdcabdebcaebaeabeaedabeaabccbaabadebdcedabcbcbbcdabacdebecaaabedddeeaeceaaaeedbacddebdceeadeeeacdaccdadacabacbaccccaddceaacbccceeccceddbddaabebeaedbeabeccbbebadcddaedeaeecebabaedddedadbbbdcedddcceddbceabbacdddddacdaabdbecaeececdccebcdacbadeeaddbadceaedcbcdcdbceeedabbdbbdddeddabaadaddbbeecebeeaaeaedcacacceeaaeedecedceeeebbbeecdaccbebdeacbebecebeccddcedbaadcdbbaadbbbaeaddddddacdaccecaeacbaebecbbeddedccaaeebaacbaeaeedaededbadaccaecdedeabeeaacabccabddeecacccacaeabcccddcecaddbcccbcbbbbcceebdeeadbabacadbcbcbcdbacddeacdececeadedceebdbedabaadeebbdbdcdaeceabddeabedcdcbaecebcedbbdaaaebedeaeeccdddadccacdbbbebeadadddddcddbbaecababdcabaaccaaebbceacaadecabeceedabdeabcdcdeaedacbacbeebdaededdbdbddddacabcceccbdceaaecdbaebdbadaecccecaacdecdbcabbeaabaeacebbeddbdcebedaeaceaabbbbabceddcbabeedbcbbbbedccdeeccddaedcacadecedeedeeaecceeabcbdaedacaddbbddaaadadcdacbeabbabbccbcabcbcacadeacabeebcedeeedcbebeebbaddaeebccbdcccecabdcbacaaaaacadbbdbabaebbeeaddaabdbabbbabddcadbcdcdacdaacebeaadeaeedcbecadebeecbeadceacedeecedddceabbaeebaaaadaaaddddeaebbbdaaacaaddcccbdeddabbaeecedeeedbaeebcbaeeeaeecddeaacbdcdecabeacabdedceeabbecedaacaaebdbdbbcaceebdcdeacbebbecececddbdabecebdabcdeddaadbbcdcbbaadecdddbbbedacaebabacecbebdeddacaecbeddeeebcaabdcecaeecbdbecdacaadaadaeecbedaeccdddcdcdddecbbeacaeddbdaabdacebcebbeacabdaeaeabaadccbdeadeeedaedbdbccbbdcabbeccbbdbdbbdcddddcccaebebaeabeaceaccacaaddaeabebdddecdabdceecbaeeecccbeaaaebadbdedaedcdeddddebabadcdaaebdddebeacdcddecdacababdecedbdcbcaddbddbebaedcbaeaedbdcacedaedaecbdccceabcdeabaddcdcedabecbbddbddebddbddeadcacddbabdeeaeeabeabaadebabebbcdbbdcddaeddaabbdbcadaabccddeeacbbcbebcecedeedbbceeecceaebdbddaadbdcdabbecccbcadbbbecaaebbdebaeadbddbeaabcbadacbcaccaeaaebbbbaeddcebadadbdacebbacebaebdebcaeccbceacdacedacbccbdbdebaaebaebcbbdbebbeebdcdbaaacaddeebcebdecdcdacacbebeeecdaaadebdddbdbaededdccddddaebaebdeccceeaeaadcceebdacdbeeddcebebcdbebeebbdabbbbaddabaebaeabedaecbcbdbdeccedcecdccdddadaaccddeeebbaebecdbebdbaeaedacadccbbdddbcbeddeacaeeeaeedececbeaedeeddaacbedecbedccdddacadcadccbdecaadeadecbbbdcabdbdbabbeacedcbeaeeebebcebdcaaceceedbbbcdeaaebababcbaddbedcddabeaebecbedcbcedbececacacbdddeadccdbccdcadeabbaebdceaaeaeacddcdbaeaedeaaddcabecdedcebaabeccbbebcbabebebbcbadaadcaacbcebdcdacececadccbdecacaaadcedddecccdebdcaababbeebdabbecddeeeccdcaebeedbedaedcaadbebacbdaaecddededceeddbedeaaecabdeceacbceeacdedbccecaddacababcbdadbbadbccbaecabdcdedcaedcdbbbdbbceaacbdedeebccadabedbecdddecacaaabdeedddeacadcbcaeaddedababdabdbcadddecadeebcddeeedcdaddcadadcddbaccaebebaecedbbcabecbdbbdceacbbbdedbedddaccdbadbcbdbbdeebdabeabcdbdbdaecbedcabcbacbbeadeaedcbadcecaacceeadcdacebaddbadedabdbdedaaeceedaabedebbddaaaeadeebcbecacdbdecdceedaccecbbdeddccedbebbddceeebadccdccbccecadceabcabccdacebeddaddabaccacaccebabdaadeccaeabdbdadcebbbadaabceabeeacabdcdccadeeaaedadddecdaacbdecbcbbdeaccebbddabbaabeebcceacdcbdcdceddbbdcdabecaacabcbbcedadaebbdeeeebbdbbacaceaaeceaeaeeabbdbecabecbeedebcdecacbaaedccebceaeedadebeceadedeecceeeccedecbeadcbcaccdcebcddaddeeddcebdcccbebebddbddecdabaeaccaadadaecabbbaeeeabecebbecadedbbdeccadabddddabbbeababbeaeddddaacedacabceaedecebddaebabeacececcdcedecceedeebaaddccecdabeaeddcecdaadcccecbcedebdbbbedaeedeacdcdbddceceecaaebecdeeccbddaedeadbbeabbddbdcbbbdcdcbeecccebdeabcedabcdcdbbcccbceaaabbadbdeeebbadecddbedaaddebdacbedbabeebeceadaadcbebdceddaabceaebacbcddacccdbdacdacecadebdbdbccbeaabcaecceedbbaadcedccbcbcaedceeaaabccbccdabbebcaebbbaaadbeadadcedcddbddceaaedaaadabcbecbaaadeadadeebbbeeadcccadbabddaadbcecbabecaaedceeccadbbedacebaedcbcdadedeaaddcbceccdcbbcceaabcebbbdbdacaadeccbcdabeebdebbedbeedaddecbccdebabecbeaaeebdeeeaaccddeeaebcebbabaaadacbecdecbeeeeeedeebdbdeddbbabbbbbbbcdcebcbccdacbdbcaaaaceedccaabeebeecdbbbcbdbecbcebddcbbeebaccaebccdbabeadcebeedebcaededdcbdecbccbcecebceddcabdadadabecbddbdebcddeebeceaeebdbdbceabdbeeeaaededdbcbaeaebbebeabeceaaceaebeecdcedcbbebdddbdbbddeadbbbebbebcbdebedbddcbccdcddedcabaecadedcbdedbcdeaaedeedceeccaadabaeeaaacaadeaaacaebceaeceaadebacaaedebecceeadebbadabeccbdccdababcaadebaddddbdbabadadcadcccecadcaccdadebeecaccdabeecebdcbdcdecbcededdaadaebccdcccdeebdaeadbeacaaeddecaeaadccdddacbebdcabdebbeccedbbcacbceaddeaaedccaadacdaeadbcacadedccbcdabacedbeecbbaebaccbaccebceddcaaaddebeeabeeeacbacdeebcdbbbecddbdcbccaecacebaccebeeaeacaebcebaccaeeabbaccccbeaedaaaebadadbcabdadbbacdbcacbcbeacaabccbdeededdbbbdaaaeaabccbaeaeedaadcdecbdcdbabedcbcdaacbacaaddbeedcadebcdbcdeedbdacbedaaebadeceeeeebcebbdcdbeedcbacbbcecdabdaebebcacddcdbadeedabeadcccdabbdbabebaacbcbdbcdeccabdacddadaeeabedeebbaacbadbebcddbabdbdabeaeaedbeddaccddeeeeaaceddddbebdceaddaccdeebbccbceddaccbbeceeedaadededeadacddadbcbcdebacdacabebeaeaebececedbbbaeebbcaeebbdedaeeaededdabaecaabdbcaaabaaeaacaaaebbbceaaacecdcdacdcadabeebaaeeadccccebcaaaacddcedadacdbadaededeedcdcddaecbaeabedbdbceaeedbeaecaaeeeabdbcaadaeeceaacebdcdadaabedcbbcadcdedcabaeadbcdabddecaececdbbddeedccababbebcbdeecdbcaedabdaaedceeceaabadbdceadedeeabaeacdcddeedcdccdceacdeadbabceeaededbecacddbbbdeaaadcbeebcabcbeabbdaccbaaebbbaaebdceeeecdeeaabddaaacdddecadcdaadedacedeabcdcebeacedecaebeaccbacbcebbdcaacebebdacdccbccaeccaaedaaddbdeaecdcdddedcccbbeacacecaacccdccdbdecdbbbdededbccbdddccbdcceccdacddcdbabbdadadeeabebcdbaccbbcabdceabbebbadcececdabeaaacaddbabaddaccedceccecbccceacedbcabaedbdddbccbaceadecedaadbcecebbdeeeddedceaaaaebbcbdbabbdecabaeabdaceabadeecddeedddbbaacdeabaeccdadcabaebaabdcacdabeeabecddcedeceeddebeeccdbbeeedbbaabdaebaaeadcaebcddeeadaeddeedbebeaddaebdaeaedaedecbceebecbaccbeaaacddcbdbbdaaadeeabcecaaeecccdbeacaccaaaacddebdcaaeceebbdbbdacbeceebebddaaabbeababbbddbaaaccbeebeadacaccbdcaadeecaeceecddbccaeeeaeabbbbbdaaebdaeccbbdaccecdeceebadedbbbdddaaabdadbdeedcadeabbadacadebaaaebaaddcecbacbdbaaebeceabbcacecbcebdcebdabaccaddebadedebdaccdadebbeedcdabcbddbdaeadaddeedbeccdbcebebaaeaceccaecccdababcaccbcaaebeacbecacbbdebdebddccbbbdeadccaadbebbdacaabedbdeddbbbbadcbdcbdddeceaaecebcbaceeedabcbcdeeebedbcacbdaaaeabdcdcaedacaaadbacdbcdbbbaccedcdcabbdaabaeaaeccddadaedbecaadececcbeeeadbeeecbbcbaebbcdbaedeabbabecdbbecdedbdaeeeddeaacbadcdbeddadcadddadeebbbbeeabacdbacbcbddecdaccbbdccbeccbbcdddeeeeeacacccceaeababdcddceeaebbdabbeebeaaddccbcdadaadbcedbbaeccbedcaacddcbdaddeadedbbdbbacdbeebaeabcadccaaeacaeebdacaacdceedcaaadedcdadddeedcdcccdddedcdbadbbbedebdbddcbbddacddeeececeebcdedeadbdeabadbcdeaabaeccaeeadaceaadeadeeadedebcaedcebdeabececcaacaebdaebacaaadeaedbdacbbaebeaacdaaecbedebeecdeaccabaddbadeaaebcecedbbadbdecdaedcdddbecaeecccccbaaadeccddbccaceaecadcbabebdacbaddaccbaedebbbdedcabecbabeebdacbedcdbceebeedbcabccddcdeccdabceebdeddcdbeaadcaeddaddacdaedabadeecbcebbbeaaebeadbceeacbcecbbaaddecadabdbabeadacbaecbcadbaeecacdebaacdddbbbddcecbcceccebeedbccaadbeeeeaebccdedecaebeaabebdeaadbadeeacdedaedceebaeeddedbaaadecbaddccabbaebadcdecdacacbbddabadcbbeabeaddedbbdcaadebcabdebeccabbbabdcebbbeababeaedcdddddbcaacddcdeaaddaabeaaaeaeaadabdbbdeaaccdaccbecccbcbabbddadddbcbcebaddeeebedbbaacbcecadcdbeebaeabdbabecbcbaddbceeedabedcbcebdcbdcecbedcdadbcaeccceccbdddbaaaaaadeebedeccadbecaedaedbcacabcddbadaabddadaeeeceddcceecbdbddbeeccbcacccedbebdbaeebecbeeeccdbbaaecbdacbddccccadeebcccbbadaacabcdecabbdabacaeabcdccdedcdabcdbbcedeceabedecaedbdabbceabdbecbcdacdeddcddccdeaacdecebbcdcacddbbaaacdacdcebccbceadbcdacabeeeecbaaeadacdcbdaaaddcdddcaeccaaccccaecaaadddeeeebeaaeaedaadcdeecbbabccddcceaeccacdcbacadaebbbcbdbecdedbbcccedcdebbabbcabddaaceeaededccddebbbbcadcecccceddacbbaccbcbdedbadbebbbabadaaddcaedbaabccebbedecbbacbceaebebaeeaeedbececeaccdddbccdebddecddbdeadbbdbbcddbbccecaecddabdeebbbceddaeaaaaeeacbeebdccebeebabdbcbaaceabebacaccdccbdadcbdddddedbebaaaaaadeeedbbeeedaaddceeeaeeaecbdadacebeceddbaeabbeeaaadbdaebcdcaecceddceacaebcebccbdbadbabeeaaedacadbdeecccccccbeedaebaaeddbadeeacccadcebadbbdecedcbbcdceaeebcbdcaebedbeeaeccebedcddabaeddceebcccbcebbaaccaeddaedabaabcceadccbbeababcbbdeccbdaeecebaeaaecaabaabeeadcedddbcadbbbccdddcedeadceabbdccbecbccbbedaccdbdcdeeccccadbdbbacacebcccdeadbeebddeeedbbbddadcbdcadbddbdaadadeedaebdcbcddeebecbadebeebeadbeecbcdcdccbeeadaacaceecabeabedaceddbbaedadabcbbecebbcedceebbecaaeeadadcebcebcbabddaebdaadcabddcaacbeaadeeacdaeddbaeaacbaeaacdabaedaceaecceccbcbeecedcddbeeeabeabaebceaaecccdbccddaccbaadadcedcdaadbaebaebeccaeabddbbaaedbcdaeeeaccddebaebabbaacabcebeddecdaccdacbdebcbaccebeaccecadedabcbacacbeebcbbadcdeaccecbedcdadcedbbeaedebacabebebddaeeebbdcbdbecbdcecceadaccadeddacbedeeaaacdccaeccdbeadcbdbdecdbbecbbaaedcdadddecddbebecadaccaaeedcccccebaeaeeddacebbdcaaabcdcecabcaeadadcacbdcdbecbecdaacceceaddeeeaedebadcaebebbcedebdddedcdecbeecbadeceaeacbbcddbccecbbddcddbbbaddaaecebbcbdbdebecdbeccddbadbdacabbbaccabbcaccbccadcecdeeeadbeedaddddaecdeaaaeedbededebeaddeebdbcbdeccbaeadcbbbeebcabaeadadeabaeeeeadaaabeaedccaabbeecbcedcbaaccbecadadbbebaebbaaaacaeacabdacccebbedbcdbddeddacbdceecbceacbbddbdbbbdacebbabecececaecbebacdaddaaaedcbaebbbeeeecaeaacdaddeacdeadcdbbadcccdccdadccdcbdbaddcaeaecbeaddabababebbdedcaceaddbccbecaadaaedaccbcaacddbcadbeadacbabcebdeecbdadbbcccceeddadebbdaccddbbdbddbeadbedeadeacbaaaaaccbaeebecddaadecbdcbdbebcebacbbddeebabedbebdaaeeeeeedccbdccdeadecbdbcccdedadcdaeeebbdddbbbeddcddebbecdaccceeebcadbceedbaedbcccceaeddadeddecdbacddbccedecdcdbbaecdadcbeecebeaadaecabaaaeacdaeadabaeccdabbdccbbceedaaddbeaeedbaddceecdbedadaadecedabebdcccdceeddcacccaacdeaaabeeabedaeeabeaedabaecedcdcbcbcadeddcdbcdcdabdabaddeeaceacecdcedcaeceadebbbaceaaabcaeadadcdedbbeebaaceecbbedeecbcaaaeddcccbececdcdcdedeccceaaeeadcaeccbddddbddcebbaabdddccbcecdbdabbcbdcdaecddddeceadabbdcdadcbbebaeccdbddbcaecdbeccdccabeeccedbcdceebcacccbebeabceaddacaecbbbbacadcddbbecbeeaaeccaacedbdddaccaabedadaaccdeebddedebcddacbdeddaeaacbbcacadddebadcdabbaacecbdccebdcdbabbaeccaeaebddacbabbbbdeacccdcccdcbbbdcaabbabdaeccaddccdceebabdbdddaabdbeedbdcacabbcedabdbcbacaccbaaacebcddbaaacdcceccedbddbaceabcbdaababeaadbeebbeacacddeebbbbebeeeeeacdcebcddcdbeddbddadbceadacacebacddcbdcdbceebcadcbaaeacddbddbaccaccacadeceeabdacebdbaddcacadcbdebdbecdacdcdbcddcadddcabaededbbabbdbdebecdaabbaeebdeeadaddcbdcccadbddbbddbedbbdaceddbadebbedddddbbdbcbbdccccddbabeaeedeeaddedecceabacbabcaebcdeedceabaddbadebdbccebcbeeceaeeeeeacbadbbdebdebeeddbcdedddcaabcbbcadabedbebaeeeebbccddaabdbdcbdbbdcbccabeeddedcdbedcabebcbaeacbdacdaabbebbcdeeadcccdcbcbcbaaedaabacacaeaaabdbcbbecbdbaeddadbaedbececcdacdaecbcaaaaaaaacdcddeaababadccdbaaecbdceabbeadbaecebeeacbaebcbdbbdaaceccedadabeadaedbadcdabdedcebdbeadccececdbadbdbadadbbaeabebacbbbcacddadadabcbdbeaabdeadceebaabeccdcbddebaeaecddcbadeaabdcebdbcbcecbbaedcebcdbdcdbccecddbcaceadabbcedeaedbcedcdaeaacaaeaebccdcddeacbddceaabedbbdcaedebddcaeeecdebbadccbbbaaeebbebacaceabcebcdbbbcaaddaedadcaeaaaecabbecccebeceeeaebadbebadedcacebdbaeabceeecebacbaddaeebeabdbabedcebacaadbdabebabcbadbbcbadbddeccdebadcdabeabcbcaecdccbedbeebbcecdcbbedcbcdccaebddabeccaaabdaedebaebacaecdacdddcbadbcedebcbdcbbbcbaedeeaaabacbeeadaacaedbaaccebddbcceebcadaddeabbebaddddacecdaaebaedbbddcebdabebddaedcabebbcabddededaebbeedbbdecdbecbeacaebbeaddedebccabdbecdcaeeeccadeeeedaeccbaacdbaceaecdadbbacdebadbebaeeebeeeeddbebadaaddddaccccbedbadddbcbccccbeedeceddbbcaceeeecaebedddcbbabcacdaeedacaccccbbdcadbadeebccdcbddeedecaabbecbcceadeacccbddcedddcedbedaabaeddaeecabddccedbdcadbddeceeeddddeecdcbbcdddbdcebdbbecdddbbcbbaaaeaaabdecaccbeeeaeaccbcaecceeacabaadeedbdeaecdedcaeeecaeccccaedbbcacdaeedbddaecdaabdeebddceaeedaeeeaeabeccadcddbdeebadbdbeedccddbbecccbdbaeeeebcadcaadbbabbaedbdbcdddbdcaddacaeecbdaccceeeadcbaecaecdbcaedeadadcaebcbbcdebecaabdcaabcbbebbbbcdcdbebadcdeacbbdbbabbababdbdceecbcbabeabccbbcdbdcacddcaeccecbdbcaddaeddaaeeadabccceddcdccecbbdacabbcaccaebaddeeceaeddadeaaacbaedccaddbececddbcdddaabedeccbcdebedeeeeebdbdecdcdbbacbdebaadcebacedbdabeebbabdaadeaaadcebacbbaedaaabbaecbdbabeebaeaacbebcceadaddbcabbcdaedeaeadeecacdeccababeddbbaccedabbbcecacecdeabecceeecdecbbeceecabcdbcbdbeaebaebacadabdbbbbacacbcbebdecdabeaeaedbadccadddabdebdeabbaccbddbbaedadaeecdaeabbedbadcaaccbbababcecbccbaacaeecbaaddbecceeabeabceeababdabbacdaabedababbdddaaabaebcebdecebabeadbdaecaebdbeeadeaaaecddacdcaabeabbdddccaaaadcbbeabacbeedecebbaddeaabeaeedaebbbcacdcbbbddabaaccededbcaaadbaeecdcddbdcdbdeaccacbdecacdeadabddacaccdacccbceeeaabeecddaeeeecebebecdeacbcbbecdaebdbaaabcdadbccaaaeecbedbbdebaeecebcdeaeadeedaadabbceaeedbecebaaaeededdbbccebddeeaaaccbcaedacdecbceeaaddbedaddbaadbdedeebbcaebbabebceaabbadcacecbeeacabaacdbcccebeebbbbaacacaeddeaeccabdaeaeeceacbaadbebdcaaaeaccdcdcdcebbbcccedccdbadcdcbddccbdceabacaccdcdbecedcdbacebeeaedbbebbaabecbebadddecacbeeddcddcdbecceddacaceedeaabcacaaeaccbdcecbebeabcdedbddbbedaabdeadcbdbacaeaebabedcddcacacddaceedccbcdcddbecaddbabedeeaabbdbccadacabadcaedeaebdddcaebdeaedbdebacceaaaebeecebcceddeaddcadaabdebebaacadaaabcedaedddcdabaeddcdbcdcdbabcedaeaacdadeabedccbbdcdddeceddacabcdadeabdcacadabaabaedcbcdacbeeeeaeeeccbbedbcadabbdccdaaccabcaceebbaeddeebaeccebcbcbabcddebaebedbacbcbedacbedbeabbeebdcebbbddebbbedebacdeaeadbbbbbcdbccbccaaaebdcbdcecebeaecbddadbbbbdcedaeedbcdaeeabbeadbaedaaddceaedaaadadaddddbbaccedcedeaddbcbdacaaacbadbaddbacddeecbbeceeecbeddcdacaeebbcdecceeedeebaabaecabbcebccdeaddbcbdebdbcbacbcdedaeadaccccccaeedebccadaabccbecbcbcdebadaeadcddbdbcabcbeceadeaaaccebebccdadaaabcaabbabaabbdadbddbeabebbedcacacecaacdcacbccddcabeddceebddcaaaedaeeeebeecbdacddbbbbebccbebeddeedaebbacecdadbdaeebebcccdcabddecebcaeabccbabdbcedacacbedebbbabbdedbccbacdcbcbcebbacdddaecdedbdadcbbdcbecdbaceacdaaedccabeacacbedaaadccdecadeaeeeccececbedccdababaadbaacdbbddeadaeebbccadcbdcdbdbadacbcceaacecbdaaaaaabbcbcbaedbaeaacdecbadedaccddddacecabddcecdbddcbacadacabceaaaaceeecaaaaaececdcaedcadbeabbbdbebabeddaacccddedbbbcbacdddaaccaecbcaaedbeebbcbeaaacecdcaaebadacbaeacadccaecbecbcadbcecedccaabddcabdcbabaacdbbecbeecddabbcddcbdbbceddeddeabedeaeaabaaaabcdcadedcaababdcdeadccddbacdabebdecbccabaecddaecaecdbbddacbbcceadacedeedcececbdeabacbcaddbacbebabeadceedcbbcaebddcbeaddaeaccabbbcaadcbbeacdbeeccebeeeacbedbdaaabddacbacbcabeeacbeaebbeabbbeceaccccebeaeccadadcabbabdcabccbdbcadcacebcaaabcdbdecdeddbabaeacaabcbdeddaceddabbacaedadacbabcaeddeeebaecdacbdedbaeeaaabbdcedacadaaeccdaeaeedbdaeaccebceacebcbeebcaceeaccceaadedccdbdccaadbcdbdbbbaaebbbedcbddaaeccadccabcdbbcbdcbabcdebecdbecdcdccecaeccbedeacdadabcdaccebbdbcceaddceadacbaabecbecedccccaacececcdebbcaccdbaceacbddacbdeeebabbbbcddcebeacadeeababdbbcbcbccacabcbcddbbbbdbddeaeeaeedcaddccedccaeacadbcddcbdaddeebcbdcddceccbeddadadbcbdedeabdeebbabcadecaccaedbcbeaddeaaaccceedcaeabbcdbcacdeeeebccabbbddddaeaaccdaaabcbcadcaebbcdbcccadcdcccdaaabcababaeecaeccbbeccbebcbdceccaaeadaeeedeacbcdeddcacebbedccdcbbebcdceebebeaacecbeccaabcacaebadccadeccbcaebbcbcceabcbeddcbbbecdddddbbdecddbecadcccbceaeaabcedddcbebcdbcbeebaceeccaacddaeecddecdebcacdbcedbbdacdacbddceebecabadeadcacbecbbcadabdcccdccdeaddeabdcadedcecabcdddcdbddabccdddecddcaadbcbbcbbaecbdcabdedbcccbdcecdcaebcacedbcddbbaeadaacebcdcccdbccaaaebeedbbadebebcdacdcadeecbeccbadaaeeeebebcceebdeadbdccabbeeedbeceeccdebeccdcadbaeeacdbcecbbacebbeceadbeaaceabcddeadddcabdedceebdcedcabaabacbaceacbbeecddcbaeddbeaeecacaabcceeecccddaebdaabbbeddbccaeccaceabbbdedbcebedddbbcbcabaedabcbeeadedcabeadecaeedbaaaabdbddcdccaaddadddbcbededaeeadcbaedebbeeeaccccebbbcdbaaaecbccbabddcbaabedbcddebebcaeccbbaaabeddbcdabacebcdccedeadcaadaebcddeccdeebeccdcdadbbebcadcdabcbbdabdddccbcbeebbecdaebcaeeebecedbdceaaacaaebbecbbccdccdbebbacdbeabeedaeaaccbdaabeedbbbcacbebcadceeeeddccaeebaabccecbdebcccccccdbededaeebbdcababccdacddecaabcbeccbddddecdddabdbecedabbbdcdbcbedbcdbbcbcaddabaacdddcdcaaacaebaeadbecdeedccbdaeaddebdedcdcbedaabcecceacacdebeccdcecbabdaccbbebcdccdaddededebabbbaddaedeacaabbedcdadcacaabadbdbdaaacbdedeccebbadcebacbebebbadadaeceabbddeadabaaaeeddeacaaabbbeabacebaceeceececbabdabbaadcebadbabbbddddcaddaededebaaaebaccabaadceeacbadcebabedcaccbabaacadeedebbccbedaaebdbbddaeecdbcbaadaeadccdbdeeadbdacdcecccddecaaecbabecbecccdaabeecbccabedeebbadaccdadccdeeddcdbbccaeabdaccedabbceadcebbbebeabceebecadaaacbbadadcadebdaadcceaeeaadcaccdcedabcbcdabceaececdeecdceeedcbaecbcaaddeadbacdecdabbdddcdccccdcaebccacbebacaedabceebddeaeededbdddbccaddbeccdcecaeceebcacccaadeaaaaccecdaabcacdeadeeccaebbeeedccdbaedcdaadcbceccbcadbbccceeedccbbecabcedbedaeeceeddeaeabdbbdeccabbbaddcbebdbaecbdccacbdbeddecebccbedaecaaccebebdeebedccaeeecaaeccceedababcbbdbbabddacaadcdcbcbeddedaceeacebdeeaeabacbcdbcbceddcbcdcbccceddbbddbbddbbaedeccdcdceccbbdddbadcbbadddebcabbebcaeeabdbeececaeececcbeabbccabbddcbddddececeeceddbddceabbedebeaaccbabcabbaeebbabdbcabbedacbbccdcadbacaccaadedababbaadbcbcecdbeebdedbaaccccdcdbbbaecdddbbeeeeaabecbaaaedbcdddebddbbecabeedececddddacddcedbbedbaccabdeddeaeeaedadcaaacecceeeeabddcedcaadbeebcbecddbbcbcaccbbcecbdabeabddaedebbcbcddedcebdeabdcddbcdbcabdcaadadaaceceeeddccccbadaedddcbcdecbccbbdbdcabaedcebedacaeeccaadddaaaeeaddddbccddbbdbecaedecdbaabcdaeadaaccabacacedeebbebcdbaacaddaddbbbacebbbaeccecabbdacbbbbbdaeeccdcdcdaecaaedceecbdddedcdddbbabcbeedebdeabeaebbdaeaddbeeecdabcedeeaddeeaddcdeadbabdeeeacddaddeacaaeabdcbaaccbcecbdccadbcceecebecddacacbcaeadcebaaeaaaeedcedaeedbbcccabcaeedeadcaeedccdbcebcdebeeddacedcbdebddbecbcbaddbeccdcdcdecdecbedcccdcedeeadcacccbaaeaccaeaadeaadcecceccecccebebdebddddecbeecdeedebbdcbbbadaddcacacecdcdbdbadacdaeebbabaeecebecedbbbdbedbeceeddbdddedcebbbccaadbceeeceedeaccbeaaeaaedeababeadddddebaecdccbaeaddbedcdcbcbdaaebccdcbbedcabcabedabceccabdbcababeebadbbabceddecdbbecddbdcabbbccabebcbabecccccebedbddeeeeebcdcaebdeddecdcedeababadaaaebbedbcbbdcddaeabacccbdcbbcabeadedeabddecedadcbabbcbdddeecacdddabdcbdedaebeabbeaeeebccaeabeadcecebadebeaaaddeeccaaecdcadedbaccbdadabceecbeadececaccadccdeeebbecbbbaedcabadbacedaadbcaaaecabeecbeccebbabeeddcecadccdabdbadaedbeadecdbdedddeddebdcececdeeeabbdbdeddbebabdcedbccbbcdcebcbeaeedddeeaecadacdcbabdeaceccabecdccdbaeedaeededeabecdadbdebeeacddcbceabdddaabaddcbecdeebebbdceabdeeaecbccaaccbacdacceddbabcacabaebbaaeabbbadecadbdddaecbedcbddcbeecaadbdeebeadcbcbecbbccdbdaadedcbcdaedacbedaadacacaecbbacadceadaacadcbeadbbdadbcbaeaabdcecccbdabdeeabdcacceaadbbdeaebadcaddbdeadacdcacbbeeabdaeadbacbdbbbabdabaebeabadaadbdbccaadedbaeadccaecdcaabdeeedbaccedecccccbdeaecbcebbbaeadbadcdabdbdcaadbbeaeeedeabdadceabbecdeecaaccadbbbedebadcaacceadaaaecccbadaaeaedababcadcbaaabccabbdadacecaceeaabddcabddeaacbbbaaccdeccbaeeedcbcbdacbccbbcaecdceccbdedecdeaaadabddcdbeebedcbbbccacaeecceeabaeddeedeaadaeccaeedddbbabdbbdbebaaeeeacdccccbcbecdacdcbebdcaabbaabeebdadbdadecccebaeebebaaddeedcddaadeeaadeecdcebcccacdbdbbdcbaacebeadeadaceadccdedbcbadddabeecaccdbacaaaaaaadcaadbabbabeecbbdcbaacccdacbbdbacceebabdbdabbbddccdaadeebdcdaadcceeccbdcdecedacedcaeedebddababcbabbccdbebbbaecacdadbdceaceaedbccadabeaddbdccecebbcdeecdaedbceecedbbdcddbdadbccdcdedbeedbbcbeabadecbedecbabeaadedcaddedcbbabdecbbddaaedddcdebcccedbbcedebddddadedebedcdcecededaaecdbdacccebbceeeceadeebbdecbbbbaecccadeaebbadadbeaeaddebeeabceecdbdbcdceadebeeaaccaedcdcebdebeacbbeabbaecbbbbebddeaecddcbabcdabdabddedbcecabdaaccaeceeadcceadaadbdeaceaceaaaaaccbceeedcadabbdceeadbcaeacccaaaedabcaddbbadbecccdaedcabbadcabbdceeceeebebacccdcaabdbbbdacabebcedaabceaaededddadaddaaabadeecaedaaebecbcedbdcaccbeaedeeedabecccdadcbeddbddbbebbabaacdcbeceecbeacecccdeeccacbbbedceeecbcecebccdeeacdebeaaeebeedeaeecababcbebaadbcdcedeeaeababebeceebceeaeabbccabcaeadaabdbcccbaeeeddeaaeeccbbbaccbaddebcdadcebbcbddcbacbcbeaeaedebdedbaebcedbdccdcbeaeedecbddcbdceddedebcaeccebbeebacaeddadcbecabadacccbcbaaccabadbcceaebdbbcdbccccababcccbededaaddaeaabceabaaacdceebbddeacdedeabbbcadabceccdcedccdcaceedceabdaeeebbaddedaaaabbbeecbbdbeceebedecccceedcedbececccacbdcecbaaaecdcbdcabbacbbcecbbdeebeadebeddaccbddecbbceebeebbccadcceaebecedecdeddbbcaeaeebcddcdaccdbddbceacbeacaceaecddaeddbbbbebeeccaeeecccbddeeeedbbceaacddbdaaaecedeadbbebcddacddaccecadedddbbcceaaabdcbccdedeaadddccacaaddabbccdcddacdbddaaedbaddaacdecddaacddeeaadaeacecbaaeaeddccdacdaacceaaaabdccddbdbcbeaddddcabbebbeabdacabeeadedecebbaeabacbaacbeabecaeceaccbdaedaaaaedacceddceaeecebbaebebebebacbccaaeaacdbddbaaddcbbbdeabbdbdacbbedcbacadecdcdedbbadeacabbdecddbacdcebbdeccabacacbdcbcececbadcedcededcdeaccababeedcdbaedecaadceacabbaabdceeadbaebaeddedcbbdbcddbbcddedecdeccbdecbbaddebedcdeabbabbcadeddabdcbebceeaccbdbcdddddddabbbecbdacbeecedddababdcbddddcdddcbbedecbbcadececededbdadaebccaccbddbdbbbaebccaabbccdeaaddeabecacdeeaadeccdabcbbedcbabaeadeaebdbeebedcdaadbdbceaacaaedeadcaabcdebeccacaeecdedcedaacadeebeaebaeedbdebddbeedaadebaccadeaaaaceaebbdbdaabcacaaaddeabcaadbabbceabdeeaddcebbdcbabbabdbdeccaddeecdbdeaeacdeeeaecedbbcadacbbeedaecaaabdedcdadbddeceeacddbeecdbecbeabeadcedcecbadcaabdbcbcceebcdbcbcdcdeebeceeedeebdceedceeeabdbeacaabbcabdcaaaccaaeddababcdcebedccbdbaaebecaaccebeadadcceabeccaebcebebcddcabbdcbccbacecdedaaebcecbcebaddeaebedccbaebdacbedcbaaedbeedbdbebadbbeeacdddabcccbcbedcbddadddebdcdbddceeceeccbacdbbbbdcaacaaeacecdaacdcabcdaeeeeebabdebbbaeddbdbdadbebeeebdcdecedcbaebbdddecabbecbcacaddaecaeaceeeabaeceeccadbaebacecaedbecbdceacbddcbcaaaeeeaaeddeadbbabbbaabbabcbebcecdaecddadecacaeabbdcbcbeecebcdbcbccdadaecbacacdcdceddacacdecdeacbadbbcdbdeededdeadaedcededabbdaddebbbeccbcdedbbabaeabdabdedeceaaedeeabeeedecddaecccbebcdacaacdacabbbcbaeaeebbaaddabbcdbcaebecceeeaedbdcbacbcbaadbadcdcdddeddbebecadbadecddcaeadbdccdbdcdbdceeaccdeebbbeccceedccebeeeadecbdbdabadeebcbadaacceeecdbbbedcebbbbeaabcddadabbdececcebdeaaeecadeabebacbcbeabaabedbdbecbccbaaaeebecebeebaccdcadceadbbabeaeadeaabbabeaaedbecaaccadaabdcdddabeaebdeadeadecdbbaabedaecdcabcecdcbebcaeeaeccadebdacaabdbdddeeecccaaadaaeadaaacdeecddacaacebddbedeaacaddddededbecbbeaededadebeacbacbdaccbbbecadabcdddabaebcdadddbacbacbdaacababaecdbaccccbdeeceaadaedabbcaabbaeeadaaccccbbbabaeacbdccecceadebcbcbacdaeebadaeaacbdcbcdbeabaaabcdbadbceeecacadbdabadecbabbcdbddaedccbececaebeaeeeecadabaadaedadddeebdeaddaabdaddbcbebabeaaeaeaddcbbccdabecbabdeccdebdcebaaaebceddecddaddaddbbddadaabecceaedacbceedebceaaebdcbaeaacbccaaccadbebbcacabbebbcabbdaabdcceebacebdbeadcaecacbbcceaadcdceebeacbcbcdbcaaaeaceadcdcecadebaacaedbaceddaabeeddedcabdbeeaacaeeaeadcebaecbcabedabeeecaddddcaabecaddcedceeabdbbeabdcaebcecbeadccaeeaecccddbbddaeaacaeacbcecdedcdeccadcdacadbecadedbacddeeccddbbbeccdddbcaeaadeccaceacaeaabddbbdcdbecdeaeabdcdbaecbcaeeadddcdabbebbbcbdbdbeaaeeedcedbeddcebcaabdbbdbaadcdbccdcdbcaadbebdbebdadabadbbdeeabeedddaaacebabdbcabceededeadebcebacaedabddccbcadcdbaedcdeabcdedaeabbaabdaeccdbaacbcddaadaecbecdddcbcaceeeadbddebebadbddaeaebbacaabbaebbccaaedacacebdcbcdadeebacbacbadacedcddbbdabdcbbbbcebbaecaeeadebbcaaacaaecdaebeabcdcdbccacdbcbdecbccdedbcebdbaaacebacebabbeabdbbcbcccdebecdebaeeedacaaaedebbcadceadadadbcacddbaaaeeadbeedccecddcadedaeeabdeaaebabdbebdcaeabdeccdcecdecdeebdbaeedbacacddcacecaabcdeacbdebbaeadadbeeeacdeeabccdeeeadddccbaebeaabcacbecedadebccdbbecdbabedcedcdacdedaeebadecbbcdcaeeeebbccbeccacbbcaeddacddedadacddeddceeadcecebcccacceaddcdaeabececcecbcaccecdeabeacedacebbdddabececadeaadbabadccddccdbaccdebbaadbbadedadecacdedcebdeadbcbebcdbccbadcbdaaeaecbaddbaacdbcaebdcadddcedcadeabeeebabaaacabbdccdcabcedbcedcbabbcebaaaeecedeaddcdbdcecbabbbddddaabbadaebcaabebcbacabaecadcedebdccddbaebababdeedabcccaecadaaadaddbeccdecbddebcaedccbccaceedaeeaadedecedceacbabbaaecdccedbcbbabddbacdaccaabcdbdcacecaddabbaadeaeacdcbaccaeddadccbedbabbedbddabeeeeaadcacbccbadeccacaeeaadbacaddcedaaeabdbdaccbaaeceeccabebaeacadddadcbdbeeabbebdeeddbcadcceaeebeedcccaabaaabecbdcdecbdeeeadccecdaaccbecdbdcdeacdaddbbeeceadaedbebdcedaeedceacecbddecbecebdceebbdcdbdabcdcaaceaeccbaeebbedeeceebbdecadaccbbaececcababacaaabbbcdaaadcdeaebdccbecbacadbdbeeecbbbdcceccabecdcebdacaebbadacadbdadddadebdecbdacbbcbeccdabcdcccdaebaaadaabecbebabbdececbddcdaeebaeaaaceacccbecddceaecaeaedcdbcbcbbdccaedecaceabdbcbbbbcedcbadecdcabeedbbceebabdbbbebecbbaebebccbdecaaaaebeeabbacdbebdbbbdeeeabcacebaddcbdececbbcdbbdbaddcaebadbacdddebbceecabebcbcdbedcaeadeaaeeebeecabecdcbeedbadbadeadedbdbeadaeddbbcbdedcbaaacbdacbbcadcbbbccccbdebdedeebaacdcadaccebaceadcdaabbbaecbdababbabdaedcdedebeaaecdbebaddaeccbdcecbeebeeabdccdeaceedddbdaacccccaeaddacbbcccdeabceabdaecbcaadabcbadbbadededddbcacccbeaedadaaedededaeabecddcabbabdbccecabaccbdcdbcddaceebbcdacbebacbccbcebecdaeceecbcbbdcdcdbbdeeebcdbdaaeeddbaebbdecaccbbabaecdcadbbdbcdcbedbbddbeceeabdbceacdcdcdadccdaacbaceeaccadcadaddecaededcdbceeeeceacbeeccaedcbaaacacaaddebbedceaebcebbcbeeeabcdccddbbcedcabdccbabbaeadbedebebdcecdccdabceadccebdbddddedebbbdeeddbaddeaadddeaedacacaccdaaacedaaebeaccbdaebbccddeacebedabdcbeaceeaddadaabdcbbececacadbbddcccdecaacbbaaeaaabeceaecacddcbccadedaabbcbdedabdaabebbaceceedcaadacceeebedeabaeabcbaabaadbadbbecaaccecaadaddcaeabbbecbbbddbbbebcebabcbebcdcaabcbdcdddeeddacecdeceadceebeebaecceabacbccaebaebeaebdddbbecbacebacddbdacbacdaddcbcbddcbbeaabddaaeaddbabaaadeccdbedecbcbdddbceeadbdeccbcabddcdceddaaeceaaaabdaabbbeccceceaaedccdaddceacceebedacdbddaaaaeadbdaaaceeeeddbbceeecedbccbdeadecbdbecbeeccdbededcebdedcaecbdbdbeaadadbcabccedbeaaccdcabaabbaccadccdaeabddaecbadbcaebadbccaccccbcaddecdbaeaaaadecaaadbbacbbbddecdcedbbdbddcdaacaeaeaabcdadbecccdaadbbdbbacceecdccbdcbdbbebeaebeccabcebbeceecdcabaaeeabdaededacbcceeeebabbaadaaccccbcbebeddadaceebbccbebabaecdecdecbacbdaceaaaddebbcdbcdacebdedceceecececadcebecaebdaacbbcdacbcdcabdbdadbccebebdbabbeceadeedaeababccebbcecdbecbabbcbebcadcdddcdccdedededbcccaaadaaaebccbdddacabcbbbeeaaebadaabbbceddebeaeeccbbaedabacedccacecebbbabcacdabcaeaabbcecdedaedeadbbaacbaebebbceeddbbaddabcdbdddeaebceeaaeabdbebbeaaedabedbcdadbdabeabbebbbbacceebdaeadaddedeeacbabcdbcddaacbedceddcebdcebbcaaccccbcbdcaabadccccdabeedbbaeaebbddebaaeeebceeabaaeabeaaabcceacceecebbadaeaaeaedbcbcaaeaeccbaaabeebdbddcccbdbdddacbbeeddbaddcaaddddcabdddcaabbdeddbcdabcdadbbdadaecebcbbedbeacbcdebaacecceeedebcaeecbbeeacdbaddbadacbabbbddebecdebcdaddceeaeabaddbbcacbedbabbbdaeeddadeabeaedaccebecdeeaaacebdeedccddecedcbdaeabbacddecccbeaaedcdaedcedcebbbcbbbedecaedbbbbaecdceaeeaecdbceaebedcdeaaceceebdeeecebaccacccadddabebbdcebbeaaeabadbeadadcdcdedeeaeeeadddaaacbadebebcaadaaacccdceedadccbaedadcedaccbdcadadbddccaeebbbaeedddaaacdcbccadeccacdeaeadbeaaaaabbddacaabadaedeaecebabaecbbaadbebebabaedcebeddbdbceecdacdeabaecebedbbdedadaacddbdcedbdcddeabdcccdbacbabcccacaabeaaaddbebcdaabedaebbccaedeaaecaccaaddaeacdabaecdbbeccababadeaebbceeabbbbdaaaaebdcaccdcdcebdcdbaddcbdcbdaeceddacbecceccebcbeabbbccebaaaabceaccccbdaceadaedbcaabcaecdceeaaeeadcaeddeeddebdabdadccbcccecedbddcadbccbcbcaceabbcaadcceebacbaaddcbbeabeccdebcbeabcbbeaceddddcbceaceabcccddaecabdcaadbbbecdcbdcabdcedcdecdaccecedbaceeddbdececbeebadcebcaaabcbeaaddddaeeddcedcddcdecceddadabcbceadbdcddedadddceaacbaabaeacbaaabbcdebbecedbcacbdeabddbabacebccccdecaebbcedeabedaddbdbeecdceabdbdbaaaaabbadaabbdebeaebbbdbddaeececebebabecebdadceeddcdbbadacebcbccaebacbbeaaebaadcabcedddeccdbeecbbabbaedcbbadbedbadabaabbbcdecbcdbbcbadbebbaedbaacccdaddbedcbccebbeacbceaebdcaeddceeadabadaadabcbedcecdddedcbceccdaeacbeeadadeeabcaabcaceacdcccebdcbbcbacbbddbcaaacadabdbdbdcbeecdecdaaccedecacacdadcebececceaeeecdbbeeacebaeecaccebebabadcceadedaabdaabedeccdabebbaeeeeddeeeeebaebcbaecdbcbbbeecddcbedabaeeddaeabcdebebdeeadbbebeceabdabeebeddbdadebebbdacecddaacbbcbaadaeabbbbabbeeabaaddcedbbdcbdddbacdabdddedcbedbcbeaaeaeabadbaaebadcbdbacbebcdccbdadcebbbcbdcdececbdbbbecdaadbccadbcdacdcaacbeaaeccaaadeddbdabeceebccdadabccecdcbdceceaabbbbaecebcbcdbeebdcaccbbaeabbcaccabcacadacebbbdbbdddecedecaaebbaccabbcdcdcbddcdcababeeeddebbedebaecdadecdeeeeccbcdcdcbceaebbcadeccbcaaaacacaeaedceabdbdcbccaabcbcbbaaebccdabaeabebacedbcadebadccdeabbacacccddaeabcaecacdbedbaaddaaabadddbdaccdaeeacecceeeddbcdedcebbeebadabcccaccabaacbaabdecceeeabaecdcecdcaaaeddacaccdaeacdabebcbeadceaecaaddecebdbacbdaabbdeceedaacedaecbabdcedbbbcccecebcdeceaeaebdbabecccbbbdcdeebacccecaadbaebdddceaacbbdddddcdaccabaadbccdcceddcbbcecccabaabaebbccacdaecdbabadcbdceecbacdcecaaeaddeadabdbeadacdbecaeacceacaaacdabceadcddcacbeccaadacbbebbebbaaebeebceaaeabadedaeaacebcdbdcdbbddebebbdcbaddbbbbabecadbbbceccadcaaabdcaecbbacaedeedcccbebacaaeccbdbdaeecdeceedbbddeaacbcdebdaddecedcebaeecaacdccccdadbbadcdccdeacbeeeadabaadddacbebdcecadabdeccbeddecbdceedecaddcecaaeebcbedbdcedacbcadeccbcebaebddabbbcdaddddbebbadeecbccbebcbbdbcdadcbdcccaeccdadebeaaadbbdecccdeedccbeebecdbdaadebdbbccdaecabaadceccbddddedbccaecbcdcbcaabeeedbcddbbeeedebaabcddeddbaabdadeccaddadeecdeeddccedcaaeecaaacbdccedecadeeaaacbcabcabbcdbbdaccaaababdebdeedcddbdaecbbbcbeaddeddeeaadeabbbcbccdcbaabbedcceacecdaddcacadacddaceadabdcdaceeddddedcbadacddecadebeacaeebbedbeeccbcabccacdeccaedaeaeacbeebaeccebedbbadaaddacbeaecedacddbceaebccbcecedbeeddedaedaccecdaacbaebeedbaecaaabddbeedbcaebbddabbcbabdaaccebcdeacccaabcdbaeaacaccdbebdcbccacbecceebcbacbccbabacadbeddccceadceaaeccecbcbedcccbebecebcdcaccaabdaddcddcaeadbedbededcceddbbeedbcadadededdcaccdbdeaabbccdbdbccceabeebbadbabdebecdcccbaaecdacdbaddededbebdacbdedebcbecbbcdccdbeccaaeccbaabdebdbaccdcddaebaedacdacdeccecebaadacdbedcaabdbdcbaededdadabcdcbedabbcaaedeeeddbcbaecdbbdddedebacbbeacdcabecebccacacbcadabcdbdeddbacadceabdbadbbcdcbcdbcbdacadadeadcedaedaacaeccecbbbacceacedcddcabbdbdaabebeacbbeabaccbeeaebbddbcbcdcaddbaccccadbebaccbbcdddbdcabcacbbedeaccddbddaacabdeeaeeababacedeecbbededdcecaceeeabdcbbbbceceebebbceaecedccddaccbbccacaaeebcbcccbaaccecbcdbecaebabdbbeeeeaeaccaccebadedeebbbbaeebddbdbbdceecebdcccedabeacdecadbecbacdaeeaaaadbdcddabbddaebbdbbeaabebdebdeaeeecedbabceebdebbccbdecdcdaeadbadadcacedbdccdaeabdddbbedcbbbbbbcabbedbbcadccbbeeebcdbbcaadcbcbbbabcaeaedbbbdedbdceaeadbececceeccdabeebacdceeeabeaeadecdbbdbdaaebaedbeddcdaeecaaccadcbddccbeccaecedcddbccbedddbdbadeedeaeecebeddaeaedcceadedadeadbadacdbeddabeedadcdbbdcacdeeebcbaaadaeebbadbeebdaddcecbcdeeedbdddbcadaabdbdcdabbedbbebecbedbeccedcbcddaeddcdcbdbeccbcdcdeeaceeacdbceeaebdaeaedcaddbabebceeeebaeddccbdbacbbbabcbaccaeeabeacdedaaeebdddaeabcddabbeddbeabbbebcbabdbddbbdcbbcdeaebcaeadedadacecebaeeeabedacadbaebddaecbeddeaedbbebabeaadaabdbdbcebcecdecddabccacbaecbcacacdeacbbeebeceacbdacdccacbeabceabdeddddbaccadaeeeeabecbcbdccdacaceecbcbbbaddbbcceabeaabccbaccaaecebabbdaaecedebabcedebdaadbccbaaccbbbbadddeebbdaaeebcabcabacbaadbdeccaecbbadcbbeecdabebebdeeceeaecdebeedbabbdcbcacbaaedebcebdbcddbacbabacacdcaedabdaedbddebbedcddbbcdcbabceadcaddbdcdcadecdcdaedbbebddcddcbdaccdaadeecabaddadcabdeaddbabadacaebedbecdcdcbbbabadeaaecbddabdaaadddccdaecddaecaeadbdcbeabacebebeaecbeaabaceddbdadbeaecaecbccbbaedbccaccbeddbcbaaeceaabeabcaeddbedddaabbbacaeeeebdeadebbbeeabaaceacdcacaceacceacaadaadbbcaccdddeadecaccdcebabbaaaccabbaeebdcabdeebecbdceacedadedaecdaadaeccabbeebdbbaadbabaadabeeadedaadcccbdeeecccedeecbeeabdedbbedcbdcdeccdbcbebbacdadaccaadcddecdddcebeeedddaaddebececaaacdbeeeaceedaaabbcbdaeebeeddcedcdadadecbeabdccaeacaaadbeddeddebabebdcdbbccbecdbabedebcccaaaeaabbbbececbaceececbceddddbcdeeabdccdacaaeecbcbcabccacbedaecbdcbbdaabaeadeacabdeebdbeaceeecaebcaaaeadceabaaceeccdeacddbaeabdbddbeccabebaeedaebcecaccddabdecabaecebcdedaccaacbccaadebdcaaaaaceaccebebccecddaaedeaddbbaccbceccaccadcbadcbeedacbaddebeadecdcbbaeecccadaedcaeebcaaeabcabcbacaaaabcdedbdecdaacbedabbecdadaebabaeabcedeedeecbaedbcdbebccebcbabadaabaaeacabddeaddaadcadbcbddcececbacddeaccddcdababeddaecaaabdecadddadccecdeccddabceeecaaaacbecbddbbcbdebdaabccadbbebaecbadcccacebebabcebdbdacedecedddeaceaaceeeddeaabbbacbdeddbedeacdbcdaabbbbbddcaddacdedcbbaedddcbbabcabccaecbbaedaabbecdeeabacaeaaacbddbcdabacbcadcdedacdeecaccdbbddabdeecdadedaaeeddcccbcbdbceaabaeddacedbbcdcaadbeaacdbabdecebddcebecbaeeaccaadceaaeccabababbabdcabaadaedbdeecccaeecbcccedcdcaeadeaeaccabdecbadbdadbbecabdccbddccecadbdaababdbeabbebecdaabecddbeecaeaceaddabdcebdadaedcdeddeadbccdbadaedecceebbabcccebbedaaeddedbebebdecceaedcddddebaebbbedabccdeaedadbaaddbdadabbeeeaeeebcbceeabbcdcacadbabcadcccddabaeccbccbccddaabbbbeccbdbdadabbdebbeaaeaebadcaabbebcebdbcecdacdaaaaededededcdcdaecceecdddbcaadddeedbcdbdadadbcecbaaceedcbdeaebccababebbcddacddbdcedaddbbeeedaddbadddaaadaadcedbbccbaaacdbedcdeaddedadcdbceaebebcacabacccaebadadaadbbcdabdecbdeaccebeadebcbaedbbebceabaacbdccabdbbeeeaebaaacbaaabbcaaeaccbbcabbaadedecbeebcbadbbecccabacbbccdbacdceabaadeadbceccbdecddaceacdaaccddabcaeadeedcdcdadaeedecbcbcdcdcabbaddccacbebeecbeacdcacddcccdbeecbcbcbebabddedbddcbbbbcecebaaeabebcdecaccbcaacbccdbebdeadeaeccddeecbbbbccaeeceecebacccddedaeccddaedddcabcccdbadebabaddceddcdaedcaeaaeddbcebabbadcbcbaedcecdbceaadecbadabbeedacdbcccebcbacddaaeebaccdcecdcecbeecebdcadedcecceadaeceabaedaccecebeebdbdeddcddbcdaedbccebbcdabbccbbabacccaaadbebecebdccebaeddeadbccdbddaaabceddddcbdccdaeeceabbbeacdddaeecdcbcebcdeedbedaccaccccadaabebcdcdabdeddcecacccdebbbdddacababeaebbbeebcaccbbccdbeaeaebabcedcaebdbcbbdaddddccaadadcdacaeacaddceedbbbbcacdccbdbdabdbcdcbcadededbeceabacebcaaeaeeddddcccaaaebbbebacebbbdadeadbdabcbacaaedbacbdddbccddbabdebbccbbeeaebcbadeeacdabcdeaeacbbeeeccdedaaeddcaacdcdbdaedbbcacdaaabedccbabaeadbbadaacdecddcedbdcabddeacbccecabaecabeaadddcebcbbbccaadebbbeaadcdaeeebcbbbebebcbcabacbdaeacdcabecaeceaaeebeaccdcabacbaeddcdcebecccabaacaccdbcedeaabbcadccdadddaaaecdaadcadceececbaddeccbabdbdadeaeaebebbaecaddbbabcabbcbcaacbdcaacedecbeedbbbebbdeebeaeaadcacaaebdedbbcdaebecdeebbcdaaddadbcedcbdbbceeabbebeeaabbedbeeeeabececadcbaebcadccbcecaabbadadbeacdeccbaadededddeecacdbdaccdecaceaadeeddebeaedbedcbcaabbacbebabbbdddaebddccaedcbaecdbadebadbadecdeadadbceeeabbeaabdaaebbdeadeacdeadccbcbeeadcbecaceccebeeccebbcbdbabebccdadcbccdecaaaddbaeaacbcebdbedeaeedbcdeeeedccdebdcabcbaacadaddacddcabddceaddaabeceaccddddcbacabcdadcccaabeaccdcecabbcdbdcaaadecaeedcbabcbcbabbaebdedcabaddebbecbccebcaeeeeadcbeebadcdaceaaedacacecccbebbdeeaedecedbdccddbaeeaeddaceebbaadabcbdaacacacabdebcdebaebceadabeaddcbcabaabbeaceaebdbeecedcabaacdbeaaacedcdddccadeaedbddecddbabdadaeacdcbcbabecccdeeddcbdabebabdddcdebdccddeccaeabcbbaeaeedabccddeeaabdbdecdcbaccdacbbdbdabadbebebdecceacaeecddcbcbbdeacaecbbbddbdeeebaccabdddcdbeebbabbbccaeaedbabccdaeeacdcbcadcbbddaebeebacdaaeaebbdbedaccbdeeebdaebabadadbacbcbadacebedadbddddaeceaceadecebaaddadeadbebeadeeedbcccbaaddcabaeaecbacbcdcabebbdbbdbbadbebdedeecadcbcbcceedbbcaacacadccdbebecacdeaaeebdaabcebcbaaeebeabbaddcaedeeedcbdeabdeaececaebbdecaacbbdcbadacdbdeeaaebbcbabbacdaecdadbeccecdeadcabbdeacbdccebdbeecceeaeedddeaccdacbbcedeebbdbccaaedcbbcdaadcedecbaeaaecdbccaaebeebcbdbbdbdaebdabebaaaaceccddbbdaacbcdbbaadbbadaecdbbcbbdcbdbbaabbdcdebbeecbbccbabebbdbcbbdbbaabcbebbcbaaebddacbacabcaddbaababdabdbecadcaebbbdaadebeccccdedbdbaebbcebcccdcbbbbbeceeeecaeecebbccabeabccbaabdacabdccbbccaaceaebebdcbdeeedebdcadbcecdbccddeeddaeccbddbdedecbedcebaeeebdacceeabbedebdadbbbdadaddeaaabdbcbabbcdccbacdccaedcebaacaeaeacbeaceedccddbdcdcebddbdebeeeeeeadbccebddcaabacbabaabbdcbceccebdedccdbbbeccbdbbedeccadcdedbcaddadccddcceedbeaeeddcebebccacbdcdacceabcbebdacbeedcaebabedcaabeabdaaabcaebbabebceccdbedadbeedcaceeeaeddbcdcacdeaacacecbbabdeceeadbdbeabbbedbbacadbbedcdecbaddcaecdaceacaaaaaaedcedaadcbcddadaacddbaacaaaaaeaadeeaaeaecbaabdbaeccbdedddeacdedcacdcdbacbdccddaedeaecbbeadcdedbcaeabceebbddadbededacbbeebbddebbdaebbdeeadcedbddccccaddeabbbdbbcdddbaacaaaeebcbcecedcdbcbddcecbbbdbcbadcceeebdececbcedadceaaabcecadadeedeccbecbbcdecadbabbeedddacddbdddeeceeccabdbcddceceadbdbadaddabbdabededeaccddaddabacdecbbeeeaceddeceedbececeeeecdceedaeebabcaeeacbbbadbdbdcecbdcaaaccbbdbbdcacdcebaddcddbddbbeeccedcabaaedcaaabeaddbbaaceececabddeccdbbbcbbcbcaebecbcacabbbcaeedbdedadcadedadedaeeeccaaeccaeeeededdaedbbdadccbabeacddddeaacbbececbdecabadabdeeebcdbcecabdaccdbeebbdcadadaaacdbbecadaebcdbdbedeabcacacdbcdccaddebddacacebeecddaaddbcaaecacdeeacdcccdedacbcdaeaeecadaabeacbaaedeeebcccedebedeeacecdbdaadbcddabbcceaccbeeebbabdcaaeeabeedcbbeabccacccdebcdaaaeddacdbdeaaacabdeeeaceedaebddadaedbdcdecaddecdcaeadeeeaeccbeccccabaadbaacdadaeaabcadcdbddcacddacbccacdddcbdacbedeabbcadaeadcaecdaedebaadbbddaabeabcddabaabbcbaeabaaccaaebccecdceebdddbecceccdeebcccecbbddaceebeedbccdaecbedacaaabddaabacbccaacacbbbdabaebacededeacdaadbacadaaedcaccbcddddcbabcddbcbddeeecaabebeaeaaecccdccdbaeedadbbaeeddeecebdccabbcabaeabbddcdebdeaaebacacaaeaccccbccacedbcbddbacabbdbbaabbdccddedeabaadccccdcadeececcacebddcdebbecebaeebbdadddedbdbcbcaebaadbacaeeddaeadcdeeadccccacbadccbccbecbbcecbcddeabdebbdddcbaaddcbbeeabbbbccdcecdebdaddabedebdadeeadabebeadabcddebaaccecaedcaaeebcbadddadaeadabdcbadbebcccebeedadabcdccabcabeaeeeaadcaaccbbcebceddadcbbccebdcedbaecdcaaadedeabbdaecdecedcacbdcbecbeaeeceebcaabcebdbdacbebacbcacecceadbaedecaaebeddcedcebdcdbcebdecbcaacdbebecedcecceaadcecacbaacbbaddaddaddbbaaeabeebeaaccbcdedabdbdeeadacacdcdcadaabaabedbaaabbabbebacdcbdcdebdeaacbeaaadceabaacebebeddbeabbbaeacddceaddbeebddbbeabdceedbaabbedeadeadbbcdbbaccdacecdabeaedecdcdbecbebdcbdaeceabcadecdbabeebeccbcbacbdeadcdddeaabcdedbaeedccbdecdbaedabaaeccadbdcbbabebdddaeebcdaedebebaeceacbdbcbdcebacebedcccdaadaaddeabdaeacccaeedcabcdbaaabadcaeaaadbaecdcebecbccddebccccaccbcadccbaaeddbceeaeeadebbeccaedaeeadadcdeedacbbccacabdbabbbeeadeebbebdbbabbbecdebcbabbcecaedacacdedbaecbedcdebdeccdcacadcbdebaacccaeaecbaaaccabedeeedaccbccdeedbdccababbbebeabdcbeedbaeaabadedccebdaaecaaecaedbdbebaddeccddcacbaeaeeaacdacbeaccabbbeecbbaecabadcabeaeedbeaeddcedeadcaaacdedeeabdbcbbeaacabcedeeeeaaebecececcccdebdeeddcccbceaaeccabdddacbacabcabbdbebcdccaeaeccbdeaeddcbaebebbacebbdccccacabeaccebdeeecddbcbcdddbdccececaccadabedadcddbddbabcbbebcabebdccaaaedbcddddbaddddaeecadacedcaeeebecdaeeccbeebdbaaeebdbbdcbcbbdabcbceccbaecaeaeaceaaddededebdbdbdeeeadbbdebdabbcaaaeeeeaeebedbadbdbebebdceccbeccecbdabcadbdabaaeebdaceeedcadabeaaccecdceccadaaecbccaddbdbccaaababedcdaaaaadecdeddbbadaadceadeaacaacbdccceaedaadcbaeaeecdcbccdcdaedbcacbdccbaebedecdbaecaacdedbdbdbcdadabccecdeceeecdcacbeeedcbebdeaebdeeadbccebcdcaddeacebaceceddbaededaeeedacabeababddacdedabbcbcababeddccdaaeaddbdebaabbbbabbddebaeaaeccdebbcddadcaecdeccaadcdabbaebbacbdbceccdddacdeceaebeaebcceaddcacacebddddcdcdebdaceabadacdbbdeaabacdbcbbbdedbedceacdccbaaddccbdcdabcccabdbbcdadbdddeebedceecdebedeabdbbdbebccceedababcdacebadaddeddddbabbeabbdedebeddcbaedeaecdaeeaccddaccabaebcdddecbbbadcbdacabcdabbdbcbadacaecbaddebdeebebeebababcbbdddcedadedbcdcbdcacaecaddbddccbeecbbcedbdabadbadcaeedccccbedcaaebbddaeddaddccbecbbeaeacbcebbdaadddaeddedbeceacbdcebbaadcbeaecedbccbbccbbaedaaeabebbdebdbacceebcdebeeeedccedeaadbeccbaaacadadbbeabebccddedcbccaaebbdebedbbeddaedbecadacdcddecaddbdbbcbadedcbcbaaabaebaedcbbbaeeccddcacebeddaaeaeedabbbbaaebbbcdecdaeebeaeeabdbcdbeceeebddaecdbbdbabdeebacaebaebebbeceedaaeaeaeaceedcceedbaaccabceebcacbebeebbdcaaeeeeadecdbbacbdcccbbadcbceaeceeaeddeccdebedebceedcebdcbecdacdbedcdcdcbaacdbcbeeeeabbcbbdccacdcbbcdaadbcdaeebbbdbbceeaedceadbdedecabaddaecbbaeecbbdabaeaedcaabdaeaeceacccadaccabbdbbebeedbabeaddcdeeaacacdeadccaebdcaaeddbdecbbcdbeedacbecccdbbdaedecdebaabaeabbdaccdcedabcaedebdcdcebbebdddeadecdecdbaaceaebdbedecddbebcbebededaabadcdbeacbebbbadbdedcaaaaddddddeaebebbebbcecaecceeaaceccacbedabecbddeaecceadaccdbdeadebddacebeedccbbedaddccaaabbacdbdaebbdbecccbbcaacbdebaddeeeaaccdbedecdddaaaccbbeaacabadbabbbdccaaabbacecadbdabdcaeddbcabdeeaebccccecdcddedbbcdabcddbaccdcadcaadebcdbdbeedeadbbdbcaccbaeedccbbebdbcceeececbebbdeedabeaeaedcaeaaacacbabacaeedbbdaacecbbbaacaddcdcabbebaeebcebdadcedeadadbcaebedebeceeecbccbddcecccbcdaedddededdceabdebbecbdabdccaebacbecaccebeeadecabdbdedddabadecbbaeddedeaaacabcdbebedebcaecdeccabdcbbdaaabbabbaeaadaecddccadbdcddabeedcaebccccdddeacdcaaddcdcaddecaeacaaadcbbabeededeecdbdadabaddabdacbeceaeaebbceeaeaadacbdccbbddcabeaabbbaeeeccbbadeacadcdecaabbeddbabdaaaeeabcbaebceabdebabdcdedacabadbdcccbbeeecdacaabbbdadccebadbcabcbbbdbaaeabebddcbeecdbcddceabdceecadaceecdadccbabdceacbccdccaadcdeadcddbeacbbbcdacdedbcebbeaadaaabdbaeebbbcecaeaaabceeaddaccdbadcddeabbdcddddacebbcdcaebcadbbbeedcaeeaebacccdeeaadbceaccabcddcbaecdedcadbaabeaebaccbbbcbcacecebbadcccdcdceaadabcbdabbbdcaddacedebdedecbedccaecdcaaccdebdcbcdbaeebbdbaaeaebcdcddbcbabbacdecbcbddddddceecbabbdcccdbabdecacbbdeaddbcabcebcbcdecdeedcbddccdebcadacbecedacbeaecadeeabbdaccedbacdeadbdbbaceecbaabedcacdbdbdadedccdcabcadbbdedceacdacebbaacbebabcbacadabbbeebcecababeaabbcaadadcdcddaceabdcdcddedbbaadbdceededeabbbcaddbabdebcaecdbccbeadaebaccacaddaedbccecedaccddbedacecbdeebdcaabbabbacaaceddcddcdadebbbcaacbcdcccbaeeedadcddaadcdccdeaccdcabbcdeadeaeeddecedcadbcacbaeadddcdcaaceeaeaeecbccadabbdaddbeabcdaedeebbcdcdabdecabdccebccebccebccbbdcceabbacbbbcdabcdcebbeddecbeaacebeaeeaebdaeedacbdbbbaabdcacaceaacdccaedaaaebbaadbbdcbaecaddbddeeebcaaaedbebbeeaeeecbabbeedeceeddcdcaaedcaddddaccdcdcccaaedceabaaaeebecdcdeceaacbbddadcbebcecdabeebccddeaedabbbbeeaddbeecadeecacdeabdcecbdccaeadcedbeabaebedccbecceceeccecddcdbaabedecaedbebeadcbcbcbebdddceaeddcdedbcbedbdbaeedacedecabaaadddecbacdcabaaceecaccbacecbcbacbcbbbeadecbcadeabcdcadcacdccaedceebcbeadeeddbbbaecdcdddeccaedebdbbabeaedacecadcbaaeeadbeadbaeeccddddddbbeddbdeecebeabeddccdbdceecebeeebcbcaddbbeaacebdcbedecebcdaddabeebcaedaadadadeeedbcbccdcacebdacaaaccaacadbdccddbccdccdadcceadbcccdacaebcaadbbbdeddaaabbeeeeebccccddbacbcbeabdcdbcaaeccaacbaceabcbdeeccedaececdddeadbeeedeccdebdaaebecadeadccdadbadbbceecedeeebbcdcccaececadcdbcdcaecaddbadebaddaabdcaecdabedebaccdcbceadbebcbddcddbaeaabdecbedbceddbeededdedacedbaadcbdedacadedbaccaabbcadbbaecedbecedecccacacbaebcdebbacaeaaaaedbdbecaebbdaeddcdaeecaeeeeccdbdacdabdccadaaedacecacccbebeebddadbbdedabbdcbbaccdeeaebddadcabcedbeabebbdbdccbdbdaadecbeabcdaaeaeaeacdaceeaabcceeeddccddeddeabeaaedabbdbdaeeddaddaadddbebcadedbeecdedbadaeaeeacceabddbeeddecdebaacbedddaccadbcabbbdabbbcdccaacacccaadedbadadccacdaebdedcecedacbeebddebaaebbbcbcbcdeeeadeedbcaaeabaeecbbbeabeceeccceccceabbbbacdcbceabcdeebecdaecdacbacccabceacdddccaaaddebbdedaddbececdedbaaaedbadbebaeebceaedbaccccbaacaeadaacbddccdcedbddcdcccbdbdeaeebebabdeadcbedcbaeedbcbebaeadebebdbdadbbbebacccccbdbdcdaacbeeaedbcabbdbbcedcaaaaacbddadedeeaccdabbebcaedeecaaedcebbcbcaeabacebecacdedadbdbdaedcdeabeaabdcececceaebeaacabcccdcabebdcbdbbaaaaeeaeaaaeacbadaacebeabbacabeecbaceeccbceaadedebcbcbebcbaeacadcbebdcbaacaaebedbacebebbddbaeaedbebccadbdbecccedcbebbbbebecdedecabababedadedeebeabdebebbedeaceeedacecaedddbbbbdcbdebedbdeddaeddddbccaddddbbdbebddcbeecaccabcbcdcbbcacaedaecdaddcdbacceceeadacadccbdbbcecadacccdacbddddddbdccdaacbdcddbeecbeaaabbbecccddbdceedcbbadbceebabcbabcdabedccccabcceacddddaebcabedccceaeddbaabcdaeecdcedbaacebcbcdcacaeaadaabbabcaccaaeaabebecbcabdeaeebabacabcbeeeebcabccabbbcccbcbdcdcdcebbcedaeddcbbeadbdcbbcadddebbbedeacdbcbcdaebeaebdadcadddeadaebeeadbdbddbcebacdcdbcadbaababaeaedaaaabcbccabacbbadeebdbebbdeaaadbbecebdcecdadaddedbecdaccbeaacbedddbbcebaceacadcebacdabbdccadaceaadeabeeeaedcdcadccbacecdacbdeacedcaceabbcacccabaedbabcaebddacaeecaaaecacadaadddbeceaabbeadbaecababacbebbeccbcadcabcdcadbacacabedebabdbeeaebcceabcbeecdcedcbcaecbdeacdcecaceabdddcddecaedacdaeaeeaeabedbddcdbdeacaddaadeabbbadbacbceacebbdedabdbdacdccccbeadccbcbbbaedbcdeadeaadcebbcbcbdcbcbadbcbebababaddddedceeedbababedaebcdaeeccababebcaebbedaecaccacaabbdbbebccdadbedcccadbeeacccaddeebcdbaacaecaceaececabddeebbcdaeabdecbeecbedeceeacacebddedcbddeedebcdacaeadaeadeceaacadbeecabceabaeedbabddeaebcdecbbbbadaedcbcdbbcbaaabacbddacdbcaaccbcbbacdebcadbdeacdbadaeaaaeccacdeccedbeccdcbeeddaeeaadcdecaabcdcdabebbcabaebebeecdbdadbbadabbeabadcdebbbdbabaadddcddabbeddeacadadaebcbcccdebcbcdedbebcbbbedcedcbcbabebedbcbacddadabdbeebdcdedcdcdaecbceadebbebdcbaeccdcddbccacabcbbcedceeceeadcadebedaccadcdabeecceaacbbeaacedaeedebddaeeddcdaaeadbecbbacbddabbdbaeccedacddecadabeabeecdbdaeecddecaaaecbbbbcdaddbbeeacceaaecacececbcecedcadeebcaedcdbecebebddeabadbcdcecbedcbedbbacebadaeabcbeedecebaddabbcaebdecaeddeeebdaddeeddedbedbaebeabedeeecdcbddccdebbdbcddbeadebbabbbbcaadddddbddaaccbedeecaaadbaeebdcbabacdbedbceceabeeaabedadbcbbacebdeaebeddaeeeccbeeececcdbaccaaaeeaaccdcbbcbeecaaccdacacbddebabbbbcbeacadddcadcdcbdecacaadcbdadadcddccdeeadbebbbaceadbceebcdbdacacdeadbbeedcceedaaceabdabcdbebbbbbdeaceeecdbaadceabaeaccdedacdecbbdbcddabecacbebcceeaecbebddeeceddaeccdcdddbcbddecdbedcceecdbcabaaeedeeadddebbaebccddaeadaddeaaacceabdaeacceaadeadddcaddbcccaacaecacbebdddabbbadeebcbaaaadddeabbdbdceacbaaeaedeadbaccedaadbaceadcbbcddbeddbcbdbebebcbdbadbdcaacbedbdaeccaadbebeceaadeacaadeabaabcbedaaacdabbceaedceceacbdcacdcdaddaeddddecaecdcadecaaecedbdaaebcedbdedaddccedbaedbaccbcbccebdebcbdbecbceadbdbccdeceadadedcbccbbacbdadaccdacbaaacabbddaddeceabebddceadbaacaebdcbababddcbadbcbecbdcbadaebeceecebbbcbddedbddebceaaedacbaecacdbccaeeedacdcdcdbdacacddbebeddecaddabddceccbebbbddeebdcbeeacbacbbcdcdcdcdcdbacdbabeecadbdeaaaaebcaaeebcceaabadcacadaacecdbccbeecadcabbbaacebcbcddaeeeeaeedaaddcedbaedcededbeaeaaabcddbdccaaeebdcaaeadbeedceaeebcecacededeedadbeacaebabddcebdadecabbceebbdbddceacbcbcebbbecbebeaededceebbccaadddbcececaabaceabbaeadacbaebeccccebbabcdebbeeaaaeeedbdbbaeeddbcbbaedcdbcdcddcdaccbeadadbcccebdcbbceebbbdeceecadeadcccdcddacdcabdceabcddeabeecdbebebdedecdcccccbdeeaabcccbebddcaaedcbbaddedaccabcbaddcbccacdcbeaedebaccbcdaccdbabcdadcdecbcbedaaadcdbbbbcccddaaeaeebcbabdeceeeddbddabaabadcbdcaaabdecacdebccbaadbddcbdacecadaeaaacaeaccaeabccebbbebdcaeebdecaebdcabcaaaddedaabacdbbdaedeeabcddeddbeacddacebabeecdaedbcddbcaccbadcdbcdbdaacbedcccecbdcbaadbccbbadaabdaadbcdaccdbdbdccdbacddaeebeccadbcaeeccbcdecaaeadceeabeabbaeebbdbacbdddbadaebdeadcebccbddaaedaebeeadceeecabbdeabcaceaabbcbcacecedadabacdbceeddcaeddebaeaeacabbebbedcbeebeebbebadceaddabdabaacbcddebcbbedacecbdbdbdbddcbbbadaeaceebeaabcbcaaabbedddacbcecdacacadedcdcceaedcdbcceaebcdcecebbedbddbeecaacdedebabcacccdcdaedbdddaedcccecdacdbaeeaeadddebcdbbaeeaabbbcedadddaceebebbbadbdcecbdbbeddadccdcbbecdcebebdcbaeeeaeabaedcceadbeeadaaceaddceccbacceeaddbbbeeddaeeaeabddeaaeabdaddbedcaeecdbeeeaebbbaedcaebccaeadaacaaedaabbaadbaecaaeaaacadabebdadcdbabebceacddbcacdaddcdebaeeababccecabaaaaceddeaceececacbacadcddaabedeedaacecebaccaeabdcaaabadbccdeecccbceabbbeaeebbccdacddcbeaedeaacaecbdadccabedcedacabaaeaddccdebcdcbceeebebadadebbcebdeeaeddabcebceaaebadebbadbadbadcdacaccabeecdeceaeaedcbdcdbbabddbcceaebddaacbcdbcaaeebcbcacdcdbdaadecaeecccaadecaecbddceedaceceaadabbeedaebcbbeaaeabadabbabdceecdaccceedebeaebceaeedcbbbedcadabaeabcbeaacbeadebdcaaeaadeaeeadaddeeeecddceeacadaddecbaeaedddcedaedbaebdcccacbbebcccebaedddeadbbaeaaaeaecdceebaaceededcddeddeaedcbbeeddccbbecadcaddcbcbbcbaacbaaedeacbbeceebdbddadcadcedeceebabdaaabcdbceecebceddeaadceacedbcaabccedcabbcbacebaeedbbbbacbbdbcceeebeebccdaddccbddebeabaabedccdadecaabdcccbbbcaecbcaddbecadbebccdeebcbabaecabcaaabadeebdaecedbbcbccabbcacaeecccdbadbcceebbebacebddeebdaeaadacaabdaabaedababaeebaacbcbdbbaaaaababbedcedebdddbddecbccadedbecaceecceebdaababcbbbdaebeabcecaaabaaebcabdcbdbdaabbddcbeeeedecabbbbacebaebaccdbaadddeeacdddaedbecbabdeedbeaaeadcdeacdaccadacaecdcebabbabbaebedeaaeeeebdacbdbddaaedbdbdebedacdbcaceadebbebcebebecbaaaccaededdadadbabdbeadcbcceabeadbddabedcaeadcbdeaabbaadcbbebdedaabbccadcbbdeaaecbecaeadecadbcadbbbbbcaaecaababdccddeacdcedcacbadedebacabbcedabeacdaadecabacddddbacbbdebcdababdecdddbdaaeddecacbcbccebedcbcdbcdbbbaccbccaabeaedbccebadccdbccabdbdddaddabdbdeeaceddddecbebabeeeccbacaeeeeaddeecdaecceaeecbbaaeabcdadeacdadceebabebbcdaebaaedbdaaccaacbaadaceaaceeadececaeecbcabadebbdcacedebcdabeadddccbebbebaecbedccedceabbbcbedbcbdabacabdeaaedaaedcecddcecdaedacedbcbdeecaaeabacedaadaecdbdeaabdbabcacdadeececdabbdcbdaeaeaadccbecbdeecbaaacbedcdeebeebbcedcbdababbcbcbecceaedaebbabdeaadddceedaadbebcdcbebadbcbaacadeebbcccbedadadedcaaebedadabbdbadaebbcbcabdcdeebbddebdecaeaeaebddbbdaedbececaaedceedcbbeeddeacecaccebbdedeebbcbbadbddeedacbdbcebcdcbccebabbddeabcbbadddadcecdeeecebbdededabaabbcecdebbdeabddedaaeeeaaeecaacdbcbddddadbbdcbcadedcaacbbeaddbeaebaedddebadceceddeecbbdebbaeacecccecebadadaaebdcbbebcbececbcdbccdbccaceddaecabceeaabcbaeeeacaedeeacabdcdddceedacbbddecadeaccbedcabaebaacaebaaaeadedbaeaacbddbcedcdbaddadcaecdeacbadaeacbdbeecbddebcaceaceabadcbacdedddcbcdecaaaadeacaeddcebdaababedaeeebeecbbbeeebbaabaaebaccecebecdbcbebbcbbcdbebaeebdccbdbacdbcdbbaddabcaaccbddbebddbdbbdeacbddbeddbcbbdccbcbabaceacccaaccbadedbbeabccecbddccbbebbebcecaaeadeadacbabbdeabddccdbcedccddaaceabcdbbdaceacbbeecbcadbcaedcbebaeebbeecacedbbdadabbeaaaabddbacdbacccdabaeacceadeeaedaaebaebeabdebbcbeecdaedaedeaddaddabeacdcaadbccddcedebddcacebeeacaaccccceadacbccadeeeceddcdedadbeccdcdaabbacaeccbcaccdddcbdadbcbcbbdedbadcbbaaeccbacabcdddeeceeabadecccabdbdedaeadbdadbbeaadacededecccecaebcedcbdaaddabbcadedddebeddeadbcadacdceaaeeedeecaccbbbadacdabedbabcaaadacdaaadbdbbcddcecebdeaeeeccceaeadbdebbdabaeddabdecbbddcdeceebbbecebcebddebccedacabbcddbbdbedccaebdcbbbcaabbdebddccddacbdbcdcacdbcaabecedbbcbacdadbcdddacddebeabecacdbdaacbabeacaaadddcaaccceeeaabbedcebddeeebbeabacbaddbbaaaebaeecedacdebdecdcbbccaccecdaeacbdcdcbdbceadceccdccebcbdaeaecacbccebabbcaecbaaccacaceedbabaacdeaedbdcedaebabdbcccbaaeeceedaacedccdccaaeedbbaeeebaacdeeaabcaebadebbecdaedcbaaccdeabcbcdedacaadbeaddebdaabaadadbcccccaedcabcceedecebbaaacdeaeecbecbeaabeaeebeccccdcdadbebdddecaadcaececbdecaadccabdbcdbedbdbabbdcbbadbbdcaacedccaebbeedcebdbebbcbaabddcadebdaeccdbdbbccaaacacceeaeadcaeadaaecabccadcaeadbbbdeddccaccaaccbeedbecdabbaedccbcaacbaaaaeecabaceddaabcadbaaddeeeabeabeaeacbdaecdadddbaaddccbeacaecabdcebbadabecdbaeedacecaaeadecdbedaeccbbdabdcdabbeabbbaddddcebdcebdedbebcdedbbcbbdbbaabecbcaccbceaedbeabeaeabbcaaccdcbbedabaeecebddecaeaaeeecdbbeccbaaddabdbcaddecdaeeedaceceedeeaceabdddbbdcbbeeedceecbeeddceaddbedbbaeaabebaaeeeebcedbeecccacadedebcddecccebeddbadbdebcdeddecedaabbeacaaabddaeadcdbaddedccaaddeccdcaeddaacabdaeadacbaedbabcaaccbcbaeeeeddcdabadaeaccebaacdbbbaabbdedddbbacacaeaccdbcaabbbdeaeeacbcccdcecedcddaecdeecceaaeebaaceadababbebcdbcecbeadecadbdbeccacedccbeeccdacbbaadceadabcaedadbbabbddbdcedeeebbbbcbbedccbcecaaeeadaabdeaaabdceedeaaebdebebabceeebeaccbccbdeeedddbceedaddadaecbbadecacaaabadbbcdbbbebeeceedabdddcbdbadcadcbeddaebbccbededdcecbbdcbdddeebbbbbebabbdbddbbcddaababcccadeeebecadbbecddaaeeacebcbeecbcdaadabcdecedacdabaedcaecbbcaecadbdddadabbbddbcdedbaaeeaecaeeedeeabecaadcacebdecdeceecdbebbeaadadeaacbbdbbdaddcbcaecceabecbdadbacbccaebdcabaedaecdebebeeccccbdaabeadbcebcaaddbaeecbcecacbdaeebeabcdbcceebdbdaacbdecedebaeebaebbdbeccecebabdaaaebabeddcbbbdcebedbdcacdedceecbbeddaaccecbbcadabebbeeddeeebcbbbbeceeeddaebeeebeebdcbabcdddedddcabaeacbdbcdadcdbebabdcedaadeddedeecaebeabbacaabbedacbddeeecbcedebeaedaecbedcbaececedcdcededcaadeedbbecdbebbcebddbbbbbeeeecdcaabcccbecaebccdbaacacaeeaeaebabedecdcbdedceadddabdbeadccacbdbaaaeabaecbbabaaecbebeebbcecaaaaccaeadacdebbceddbbcdeabeaaddddababaeecaccdccbeecdabbebcabbcbbaacbadeeccbbddbeceadebccaabacecddbdcdecebcdcccadadddebedddaabecbeeeadbdbaeeabbabdacbcbcbbdacaeaebccbdededcedbabedacaeccdedaceaadcbebaebeccadceabccaddbdddbaeadaedcbbcceeabbeebadbbbebddccbcecdaeadebedddbacdcdbbdddcebebeacbccabbcecebdccecedccebdddacbbbdbabdecbbdebbdbcbaccabcaeaeeedccbddbbdaaaeedcddeddbaccddbdeaedbbebebebacaccaabbcbacccbbeeaedadbeebbdcaeeaadcdcddeedaaddcbdaeaaeaacbbdecdddcecdccababbccbbaddbceaaeedeccaaeacedaeabbbeceadaddaacdabeecaddbcbcbabacaeeeaceecbbebbcdbddcccdebebabadacccccbdadddadddaaedaceaaeaacdbaabedbcebecddedcdbacaedecabadcdeadceeeaeaedcebdeecbcdcecdeecdeedbadecbcddaeaacbbbababeceacaccddedcbceaecdebeecaceaaedebacaebcdaddcabdcaaeadccacadeaebeaeaecdeabacdaeadbaabaaaccecbdddadadebeadadcdaddadadabaadbcdaccdeeeeecdebedecbaaaadbeacecaeacaababdcaacaaadcabeabedcbcacdbdbaadccdddedadaeeaaddbadbeecddedbcaeaddbcaaccaaeabcacaccbcdabcbaaabebdaebbeebcceccaadcbbbadccadabbbdbaaddbbbccbdacdcceeecbbebcbdcadbdcceebeecbacadabaddccbddddadeaeeaabcbadadbdaabcecdcdeaaccabedcbdacbeebaccceebeeeadcbedcbceccedcdcaeebcdddbbebdedbccdeabaaadbcdcecdeeedcaccacdaadaebbadaedadcdccccbeccedadaccaceaedabcbbcbbcadceaaebbececedbedcaacdcdecbaabeebaababacadbdadcddceaaceacccbcabcddcdddacbedcaaaadbebdaaebceabaeeeabdddcaeecbcaaacabcdcdebcbaaaccbdeabbeabadbbbdbcddabcbededddaecdaaceecbaccbddddaeedecdcbadadeedbaeccbceeadceccebeeeeecebbbbcebeceaeaacdbbbbddacdcdceabacebadceecbcdeeddabcaabbdaddccbecabdcbcceeabdbdbbddbedaabeabddacccaadecdeadbbaddedcbbebbecccdccdeaadadadeaaadbedaedececcabacbbcbabeecdedabedbededdcaddababadccaaecbceeebdecebdbcaaadbadddbadebccbdddbbebaccdbbaeddaaebeaeccacddbcbadeccabbcceeabacbdccabbedbdadaeeeaeebdeeabbacadedcacadacdccaaddcaedeebaccdcbabddbbadcacdcbdccbccbeaebaccbabebadcacaaddcbdabbccdcbcbaaebccabbdbaecdcbabdaedaeaccaeceddacaeecdedaddcadbdbdacbecacaacbbaccdbabaceddbedabbaeedeeddebdcbabbbccbdbbabddecaeeececedecddbdcbecaaeedcedddccdbcbcbbdcdacabaeceedcabbecbbbebbbbdccdbcebaceadbededeaeedeaccebdbeadcebceabacdbdebaecddeadddbccccaecadaababadbcabcbeeeeeaadbdeddabbcdcecedddeebacdcbedebccceebdbdcdbdcbccabcaababacdbceaaeccaddadbdcedcdedacaaeaacacecccceedcdbadeecabeedcceaddabcbacacecbbdccedbdcccdbaacbbabdeaaaaebbddbbccabeeddbcdabecbdaddcebacaddacdbebaccaacdbedebdaabbdabaabcbdcdbcaadbbbcacbddaabecebacdabddebcccaabcaddabcdbdbcbbceeabdabecaebdaccdaedaddeedbabbecaeecededddcaacabacccceadadbaeabcecbeabeadabebddbecbbceacdddcbebbddcbdabbbbbabcbbbdedcbaededdeedeeeaecaacdccccbddbbeebcbbbbbececdaaebecccccbacddddccbbcddadadceeddddccbbdecdaababdbaaeacdeadabdbaadbabaedaaaddeadeccddacbccdeecbcbaccdccacbcccbdabdedaebdceedaaccdbbabbcbcedadebadbdebaceabaedcbbdaedbdbebaaabeaeabdddedbeeacddceacdedabecaddcbbcdbaacbcaedebcaddbecbdabebccdbcddeaaacbbbebaecabdadcbcbbcbedcaaadcdccbbcddeecbbdbccbdabbcaebabedeeacededcaeeecaadbaebddbceabcacdbccabdcaeaddecdccbadecbddcbbbadedcdbddeebcabcddacadaecdcbeaeeddcadceacbbeeaeaedcceebbdaceaacaaadcaeebcaebcccbccddbbbcedecbddaecdadaceabcdbabebbebeadbbdaacdeabbcbadabbdeabddecccabeaacaedcaacdeccaeaeaeadecbeecaacaaabdaedbcabdaeeaabeaeccabedbbaabbeeeeedbccbdcceeaaebecddadbbcbbdbbcdbedbacdcedeeadccbabdacdbccddaecbadcdcacbadecccccedadebdbcadbeeacdccddedcbebcaecacadccacacdaacbeaaccdeedddcdadcdedceccbdedbbdbbcbdeeababdaebedebdccdaccedcaecabddcebaeccacdbacdbbddbcadddcdebdbacddbddbaddedbdeabdedadbdbcbbccebcbbabcbcdddacdebeecbadacaebadeedacbbaabebcbcadedaabdcbbedccecadbbbbdbccbabceedeaedcadcbdccadcadaebaaaeddeeabedebeaaaedcbeecabedbecdeaeddcaccdcccbccbbbdeddaaaedcebcddabdadbcdbedcdaccceaaeabbcbcbaebdcebedcccabdcceccedbbbccadbccddcdabbedccecaddbedceabcedbdebaedaebaaadbcaedaacdcedbecccacbabdbcddbecaabbecbceeadbccdeccdeddabbdcadaadeeebacdadedbbedccbebddcdcaabddabcbacaacbbaddecaedaeaaedabecbdcbdedeceaebecabedacebacaeccabebcbdadecbdcdecaaedbcbabbedacdbeddcababdcebccdddceeadadcbaceaecebecddddcdeaccddcbccacceccbccdddabcaaaaccabddadbedaaaebccdbceaaeedbabbbebadadaddabcdadaacdbccbcbbaeadabbeadabbeddcbabadbbceaaeaaecdcdcaacbbbecccebaeabeaddbaecccdacbeadebbdeaceaaacaecedcccddcedcecceddddecabccaebbbcbcdebedcecbdeeaadadabebdbbaddccbadadbedbceaddbaababccdbdacaebacaccddcddedebedeceaaecedebebacebdecebebddaedeabacabacadacdeedbcadbbcbbdabcbededeebbaeceadeaaaaeedadacddcbddecbbdcdabebabdaabbbbcccbaacdbbdecdcebbaeaceadedbddbaadcbabdedecdcbcaadedeceaadbccbaabdbbebdccbbdbdeeddadbabbeeadeeebaccedebadecbaaceaaeadeeaabaaedbdcaedddccabeedcdacdaddedeceeddcdadbaebdeacbecaceeaaaebdebebadbebdaabccdceeadbdddebdedbaddcedbcceebdccdabcadbeadabcdeebebbbdcebbacbdbdecbccaeaeeeddbbcbbbecabbbddbecadadaadaaccbbdacdbcacdeaabbaaeababadeaebeeadecbaaaedcddabaebdecbbccedeceddddbdabdbceebdbaebbceddabedeeaeeddebcdddeceeddaacaadadcbaadeeaacaadaaddeeedaaacdccdbabdcacaacbbcbacbadebaaacdadecacacacdeabbbdbccdcdceaaacebbecbabbcecddeaadeaabcaaaecdeabdeebdaeabbcdeadcdbeabeaaaebbcdbdcedaaeddbebacdbdcadbdbaebedabddcdeecabeacaebbdaabaeaddccabebaadeedccaaeacecadbccbeaaaeaceaaddcebbaccaecbcdaecadcbeceaeaccdcaabdedddcbbeadaedaeddceddbedbbbebeadbcdaadadaeebbdedeadbdcdcaaeddedcecbcaeeeeaebaebeabaacccadcdcedaeacaeebceedcbbbaedcabcbedccccddaeedcdbdaecddcccbeecebacdececbedeacaabcebbcbeeaacbbebceeaeebaeaabdceedcceacbcbadaccabcabebcadebabceadbebaabbdbeacaedbacbdeebccddecacecceddccbbabbccedababeebdebaaddcdaedbcaadeadaebbbacceeccdcedcbcbbabbcedecdbadcbddccccdcbdddcbeaebcdceaddeaadbbccadceecacaeeaadaecebeaadedddbdeeedbedeaaedbaabcadceabdaadbbacbeabaaccbcbaaabcabaccecebebdddaddbbeadeddeccbaadbbcbeaabecaaaacbacdceeaceeccdabdecabcacaccaddadedbdbbbacbeaacbacdbceedabdcebccacdaceaceadabdaeedeacebbbbbeecbbaedbcccedddaeeeabbbecaecabbdbcedacaacbbeddbdaccecbadceeeaabcbebcbbdadbbbdddbddaecabbbbebceaabcbccbddaecbebdcceccdbccebbcbbebbdcacadacedbddbdebbdaeaabcaaeaaedbcddbebcdadbadedebeaabeebedcdbbdabbacdbbaadcebeaddbaeeadbbcbccbabacbadceabcdbcbeddeeeebadecddaeeedbcbdaecebaaabacaeaecbeadeaaedabecccadeaaabcbdcccebcbcbedcbcbdaaebedcccebeaaadebbcbaebdcddadbebaccedbbdaeeaccadeaddebbadaddaedbaebbbadaaacbdebcabadcadaddcedabcadebcecccdcaabaaccaaacbecbdeaadedddbbaaebbebbccdccbeebadaddbabdcebbdaacbbedbeacbadaecdaeeedcbbdbaebadeaeaecbdacbcebadabbabaebcadacbdcdcabaaaecdbbcbeceedaaeedbadbbbddeacceaccbbdbdaeaedcceddbdaeedcbcaaddccbeabebeaccaacedeadbdbecedbeaabaadbbdbcdcdccabdbdacdbeccceceabbcdaabcdcdcbbdbadcbdbedacaeaacecdddaeabebadaaceebceabdaeccacbaacceedacaabdeeedecabaeaddbacaecedbccbbeaedcaddbcaadececcccddaaaacabcdcbceeddcdbceddedcccaaabccdeadbbbddbdaccdbcaeeacdadcecaebdecedaccdbaecdbcbaccbbceecdcccebcacddebbeacceeaabaaddedcedabddaddebceacdcdbbaddaaddbaceebaacbcdbdcadcaecdbdcdbdcaccddaeeaddbcdedeabdaaabeeddabaebaaaeccadaddceaddadcdcecdddecbebaadadcdeedebdeebceaaabcdebcabbcbecaaeebeebcebceacdbbeaaaccaeebccabecdcdaeaccecacaeaeeccbbebabdebeaeccdceceadacbbdbbacecadeaeebdbbeebaaaacaebdbcaddccecaceededabbeeeceebaaeedaabcacaeabaddaebdbeedadaeddccedccbdedebdbdbbedbbcaaaacebebbccbdcbcbdccdbecaeaacacbcededdadbbbccdbaabdcbdcadabbdacbbadacbabdccdcbeaeedbbdbdbcccebcaceedcdeeccbecadbaebecbdccbbebeabedbccccbbbddbbcbcaceeaaeaddedeeaecbeccabcecededeecccbbccadabdcaebcadbebbecbebbbaeabbaaeabdabedbbcbcbddaaaeceabeaeddbcdcaedaccdbccdcbacbedcadcaaecaaabdebebececacbedeaeaebeadcdeedacbcacceacaeacedededebeadbdcbcdeedbacaeddddcabdbbcbbeccbacbbddbeaadbbbdebdbceceaaadeceabeedebcceaadbaacddabaabcbaedbaecbdacaecdccaccdcddbdeacdeacecebdbcceaebeaacdaeddedceadbddcebceebedcbcedceceeacaccccddbbedababaeeecebdabcceebcdbceeaebbbcddaebdcbededbaadbbbedbdedaabecdedaedddecaddedcedabecdaaaabebdadbeeaaaeabcaabaeabeddacbcbacdceebddcdccabeaacdaeeddbbaebdddaaecdddadedbaaadecdbcbcceedabadaeeaeadbdadaedadaeaabdccedacdbbaaddbdebcceddbeaaceebbeabaaebebabcebdbcdcbdeaaadedeaeceadbeabdadccaeadabbedcbaaeccdeacadbcbbbddadacaeeabdadababcdcbecaaeceeabdbadeeedabedcbebccdcacddcdaeacaebebddebdbcecabcdbcdaedcebdceedbeecaedaceabbceddceebccdbccbbeccceeadbdedaededeaedcbddcdadedccceccedeadbedbcbedeecbeaecdceddedcdcedbadadbcbababceaaabadddcdaaddebbbbeeaebaaaaaaebdbdadbedecddaebabadbcdccbdaaceaacccacdccaadbddbaecedbebcedceadccacbddacaaaecadaaaccbcccdcaeeeacdbdcbbacebeeaabdaaeaceadbbadecbcdbabeccacbbbbdbeacdabddeeebcacacbbbeabbddceeabbaddadedcecedbaedeccccedebdddabedaaebcddacecaeeedcdacaaaabdeaeedbccabaececcadbeeaadaeabccabdcbbdcaeaeeeebbcacceaecedbeebbeebceadaccdacdbebdadbdaddbbbeaeddcccedbcbccedbadabaaebeecaabacbaeecdebbdbdddacdbeedecbeecdbadaecddbedeeccbccadeedbcbbcddbeaceecaacaaadcccaadaeebaadabcdcebcdebaeedadcaaaadbaabecadbeacaececdeeddcebadeeedcacacbebdceadecaebcaadbacebedabbdbbccedacecbcbdcdbaacddacaddbebdbebabbebcadbdcebeceaccaabaaaecadccbcddccedecbceaabddcdddbbdddeecccdbdceacdecaeeaeedacceebbbddbebebcbcddebccbacbdcaabaecbabbcecdcdbdcdaacbddcbaecbbaedcdbdbcddceadedcbceacaaecadcbbeccbbaabaacdbdebbababeddeddabecaeccdababeeedacccbdcbcddebedcaaacbabcbdacaedebcedcbedddbaddbdcddccaaccceccaceccbeededccceeddbdbdabbcdeacdcbbbcbebbebeccccebbcebbbeccedbdecdaecededcdeeeddbaaddabaddbedcdbceecbdaebccbbaceedaabaaddcbebcceecedbbecbbddebdaadcdbbdcadacacacbcedccebaaabaeceededaaddccdceddceecebbcaebddcacbeebacaeaadeabecbdccbebebdaedbbaeeeebacbbedeebcddeedbdcdbccccedaabdaccbabedeecadbeabbcbbeddbaeebbebeabbeaacdeebbabcecdceddebacbaabbecdddcacaaeeaadedbbaeccbdbaacadccebabbbbcdbbcbaadbadcaecdecedadcabacbcbabeacceebaacadbceecaaeaedbdceebabecaccdccdebbcecdcceabbceccdeebdeeebaaaccabdcacaeeeaabcbcdedcebdaeabcceeaebdcaebebbecdbdaedeadedcebdaedabaebcedbaecbcebeadcedabcebbdecaaacdcacbbaccdccdadaabceacdaabdbadbbbaeaabbebedcdaedaaeaebcedeeeedbcdbeaceeebdccebcdbcccdbcadcacceccacbaabaaacabaccaeeebabdcdabdeabbbbcbeedbbdcdbceddbdceabeaeeeceebcccbaacdbdebdcacbccadebcebddcabddceeabaccdbceacdeabcaadbadaedebdabcbdbaddaabbeedbcacddeccaacadaebdaddadcdaeabceabcccdcaabdbceebddabaecdebcabbbdaeecabdaaedddeecdadebbabdbdeecccbeacaecdabecddeeddacbbdabbcbbeadddcaccdeecbcbdebbcbcadbdebaddedceaebdabceeadbbabddbabddeeadbacbdddedbacbecaaaaedddbecedceadedaddadbabeedaadeddaceccbddaddcdeabbadceadaeddeeadaaeecaeacaceceaadbabeaaeebcbdbabeaabebabeacdcecbdaebeabeaaeddcebbbadaaeebdadddbacddeadcbbbddadedebbeeccdaaaadaaaabdacddebcceebeeacbedecdccdaabebadbaebbdccbebdaaebdcbdaabcdeccbedeccadeaeebbecbcbbeabeaadeacdacbaaceadaeccabcbbceaaaaeeebeddbceaabdaebccabcecbcbdbbdeadacddcdecabedbeeeecbaacbbcdaccbecdadaabeaadbeeebcaaccdebaeccacccbdeccdaeadebcdabcbbadcbbbcabcdcbacabcdbadcedcbddadadbdbeabbaccebbaaedadcbbadcdbcceadaaebbbebeeccadbcaebedcbbdbcededceaddecbacdebabeaadeecbecdcdecbdbeedcbabddeecabbdbeeaedeeeacecadceccbdbabbdabbeccecddebdbbcbccdeaadaeecceaddabbcadddcddadbcaceabdcdcadcdeadeababaaebecaeaaacdcccdeacccddbebacdcdcbceecebdbbeecabccdebceceadaadeabcbeeecaeebbcdadaedecbdadeadbdcddbcaaccdabaeabadbebadbbedaebecbcbbeeadbdceacebdcdbdeecddddeeaaddaaebacaceacbdacecbcdcdadaebadcabedeeacdbaebaadadbaecbdeeadebeedccaacdacbaaedebeceeacbeeccceccddebbdbaadcbadcbabaebbdeedcccbbcdccecabbaedaeaccbcbceecababaceadacadadcedaeecbebdcccaceeaedcaeaeedccdcbaabdcbaacccacceacacbeabbcbcaaaeccabeaeeeaacccaceedbbdabeeebceccdcebcecaddddadeddeadeeacaebdeeedbdedbdecadadbdedbecdbbeaaabacedacdabccdbaddaaaeadbbeebddbdabeddeebcaabbadbdbcdbccadccccacdcccdbccdbedaddbbccebebabaeaababdcddcdeddbbeddbbbaacbeaabebcdcdaccdabdbdecbbcedbbbbdeeeceebcadddebcddbccacbaecdbeaaaacbaededeebdebaedbeaabdbcebbcbddcebaedabcebeadedaabdccdbeaedaaadaabbbcacacdaeecccdeebccbeeaeaadbebabccaeccddbcdcebcccaeedaeeccdebbaeabedbebbbbacadddaecdecdeddecaadddbccaebeacebccedbbbceeabecceaaaaccdadabeedebecbcdaabbbcccaaeecdcdbbeddcddadeadddaebdccbebeccdecabeeddbbaedadedbeadaadbdeceabbaddbccaccaeeeedcacbbbdbbeeabcaedabbacaaaaeedeadcdadcebbaebdebcadedabbcbbcacaecdaaccebcdbadcecbadcacadeedabdbaaaedccbebddaeeedcbbbcedcddcbcebcaaecbacaccbaecbaddbbacaeebebaeebebeaddbebdbddaadedcccabbeecdecbbeceddcdccdeaaeccbbbaabeeedbebbbbacbbcadcbaadcedecbaabbeeeaadcececadaabcdbadedeeabbdceadbbddeebdbeeaecabeceebacddeedcceebbabaeaccccabedbcaceaedbbadbcdcabcdabeadcbdaebdebebbdeacecacdbccdaadadebdeaebebdedaecababecabececedbaaaaeacdeacdcadcadbcaeadaedadacddbbabbbdcecdedaeabacabaeceeccaedebbeebbdeedcbadcdccdaccbaecddeadbaddcbebedecccdbcbedbaacbabcbcaaaddbedadbdaaaccdcaeeaccbadecbbbdbacdbdbcbdcebedabeacceccbccdccbbcaecaecdcaccdbbcdbddaddcadceecbddbdadaaecacbbacadecdbebadbdeedcaeaceccdeceaeaabeaddabeeaddecadacbaebaccadacbecbccdeeeebcbdbacbacbaecbddedddabeeeaecdacbdeecbecbcdcaadeedcaceedcdcbeddbbaeccdcbebbacdcacbceaccecbeddcccebdcabdcedbbdcebcbadbebaccedaddbddccdcbbeccdcadcbcccbbedcbbbbccdecdeabdecaacaaeebeaedcecbaaeceecccdedaaabbeacaeeaaeaebecaadcacbeedbeabcbabcecedcebcaddaedcededbeddeebbddbbccabebcadabcacadcedcecaccadaddbdbeedacbbdaaabeaececaabddcdddddddccbbeebbccbbcddecacabdecddeeceecbcddcadceecbeabcecdaddddaecccebbdcaeeaacebeabeceeedcecbcbbbdbbcaddeadeceebcccbaedabdaccebcebaadbdaecbeacbbceacedbdadddaebebcbbbbdaeaeebdceaeacecccaabceabadaeccebadbacddcdcebdbdeabcdaaaaeddeeacbccceaaceacedbdddccbbbacadbabaaeaedaababbacbceabcdaabaccbcaeddcaabaceeecebdeeadebbeadaebddedcacedaaaaadbeaeeaaddbdcadbaddabeedeaddaecadacccacbdaeccadccbddadaeabdedcddeacbbcceabdcaecaacceeebcdedbdedaaaaacebbbadecdacdaaaacecdeaebbebbabcdcdaceeedcbaaebeaacccccadbdecdacebdcabdaaaabcabbccecadacedbdceabeaebbebdaecccaccbbedcadcdaecddeeedecabadcdeedeecdacbdeeecedebebbabddeaeaebcacedadacaeabcdaadceaeccebacdbaecddcbdeedcbdadccbedeecedcbdddcccedcbdbbdeddbeeecceedbdddbeacaacaaaddecbdecdbdccbbbaabebdceedebebdbacabadddbcaeaeedeabcbbcdbccbdaeaabdcdeecdaabcdcedededeecaeabbacdecbaabadacdbabbaaaeacdacbbeadcbebdcccadeebdeacdbdebeaabccddaabecbeabcedbaeadbcbddadceccecdbebeaceaedcbeeeddeedbdceedaddcddcbeebaccbadbdecccdcbdaacaccebdcbeccbdcdeadccbbccdacaeadacdddadabcbdecadccbaeadaaedecaaebdaccaceecebeadaabacddebdbbbddecedabeacbabecbeacaacdbcedbecdacbdbaccecdbcebecadeeecdbcbcdeddeaeadacccaeeaaceeccebeaabeadeedddecabebdbbeaeeadddecbddaedbbadcebbcdecdeadaeeaebdeabbddaecdccebdbbccbcddabddcdecdececbeebceddecaeabbcceebbcabdbaabcbaaaeaeebcaacbcaeaccbbacadedcbeceebcddbadeedbcebceecbecdbdbeacaddceaecbdcacdeeddcaabceaebcbbccbcddadaceabeedbcdbbdbcacbaeaaeccdecbdeaeeacebacdbeecebaabadddebedadbdceddbccacedeaaedcddedeacccedceacabbbbbdebebccacabacbdacaadaddccecbbbdbedceceaeaadbccddddaaacbcaeebccdcbcedbbabbceaeddddbabbdccbbaedaababcbdcdceacdeeabacbbcadeedeeabadcbbaeabddcaedddeebedaeabcbbebcbabecacaadeeeccbecbbcdbabcbcabaadbacbbcdaceedaeceddbbdbcdeabadaebacbcdddaeadabbecbceceddbcdccaadcdaddbdbbccdcadebeaaabdecadccbbddaaedcacabebeeedaebebcabdaabedcdbbddddbeeaaaacdecaedcabeaaacecaccadadcebbbbceededdcaddbcddcaecaebbccaadacebcdaeabccacabababaceccdeadbceeeccceacbabebadcbaadeceddedadcbbceacddecdcaccdcbddbacbebeeccbbbacabedcdaeabacadbeedcbeccdabbecbaacebdcdeabeaaeebcabcebbdcaceddeeecdccacbdcaebbcbaaaebcbdeddbeddbebeaaebdcdbeeceacdcaeeedbbeceedeeabeeddacdcebecbedebeadaccdccccdbcbaaebaabaeababcdbadcbabaabbebeedbccaeeebbddbabaceadaebbecedcdebedadeeadacdbdadeaebeaddbdbacedcbdebceaceaadeedadeccaeacaeddabcdebaeacbcadacdaeaccaceabbdacebaccbebabddceedaeeeaedebbbccddaddcddeddbcaacbdcccacaaeebacdebcecaaebaeabeeeccdbdcebbdcaeacdeaebaedebbceeddcdaaddccdecdabdceecdceddbbbecbabddeadddaebdedcccdbaceccebdaeddebcaaddeaaeeaccdbbaceabeccbbacddebeeebbbeaababbbbbdbbcccdccdbaccdaedaacaededcbdebcdbadbdabbedbabddcbedeeeebededccbbbedaabbabbadabbbeaddcecaabbddaeaecdcdacedbcabaccebbbbdbcadaadabeeddabcacebdddcaabbadaceebbedcaddaacbeeedbcaebdbeabbcddebcdccecebcbebccdeddebebdceaddcbdacdaecaebdedbedcceeecceadcdcddabdeebacedecbdeceddbaaddadeeedbdccababbeeeceabaacddcbaaeeebebcddedacbddecbbeecdedeaabdcdadaaccdaaddcecdbedcbcacbcbabaedaeaececceddeaaddadaecbddabcccdacceeeddabccecadbebaedaeaeeabddbcbaddccedcabaabacccedbdeeecdbbbcdcdcbcddcddeedeeedabcadedaaaedbcecbbddeadaeacbccaaecbbeebaacdcccddacaeaedcbadedaccceeaaedecebebcdbacedcbaceabceecbbebebaeeabdbdacbcdacacaabbaeebbdeaeebaabddacaeebadeeecdccbdabbdebbadbccaeabceacbceaecedcaaeacedddeeeadeeacabcabeacadbebbcbeeedbcaeeadddbaccabeddccbcdddaeccebabaccddedbbebeedbbebbbcccceaaecdbdeedacbcbcaadeedbdeacaaecacddcbcedaeadecbdcbebaaedcdccaddcbadbdacdcbcebceeabebeeededebcbeecdeeabdabaeeceebcdcbccaeceeeecdbdcaabbceddceeedddceabdbcaebbaceedaebbbbeccdbeecabeeeddbabacbeaedbbeddaadedbecbecedbadcaccdbabdeaccebacceccacacadcebbadbbcbdddabebcccdedaeadebebdcddeecbadaacccbbcdedabecaddeacbeecebaaabbdeddbdcdcaddcbbaaadebdbdaeeccdecbcabaadedabcdaeadccedaddcabccdceddcdecadcbcaaeddacdaabceacdecbadcaddcdacdedadadecaceeebcbeebecbeebcbbeabbdbedcebeabedbcaedcdeacaddccacabceadcaebbeceeaeeccadbcebaaceddedcdaabcdcdcceaaabacedaccededcddaeddadbbdecdaecddaaeaadaccaeeeeebadebccdcebadadbabaeaaceebeccabbcedbeeeacedbdeabadacbcddcadcaaeabebbebeeeddaceaabecdcbbcceabbcdccbcbebecacddebbeacdbadddacdaadecdccddcadaaeadacdcaccbcebecaeadcadeabdeaaebbbeccbdadebedadacbdebeacccccdcceeeadadbcbdbceadddbeaaaddbcdacdbddbbdabdbbecaaacabaaacebebadeccdcecabbeadccccbcbdacdccdedceceeadbeebdddcdecbabccaaeeeaddebdeeaddbdacabeeebecaecbeaeeedbdbbcbccecababcecdaebecdeebbcbeadaeccedddcbcaddeeddbedbedbdcebdcccbbbababbeceaddbcdedecacebecbcdbdceabbaccbdaeccecdaeddbeddbcacedcdcbbbdcadddeeadbcecdaddcabbaecacebaddaabdbadadeaeecdacdcdbaecabbaddcebdbeeedeeabececadbbdacbccceeaaeaebcaedbcbacdabbcecaacdadcdccbdeaeebddabdedeecceddccaddddbbcaeeaeeedaceadbbadbdbdbcbceacaddedbdbdaabccecbcdbccaaecedecbbceccdbbdbdadcbebdabeadcdbeebceabdbcceecdcacabaecdcbeabddbaacecbdacbaaeeaebbabbaabbddcdaadbdabbcbbecaaccbdcbaebbcdeceecbbcbccacdbbbdbcaadaebaeeaabdebeacaeabdeeeaddceceacbdbbeeeaaeaeedaabbdeebaabcbdbedaeedeeecdeddcaaaceacabceccedaebbeeebbbbadabbeceecdbaccebddecdcdebcbaecdacbadcdedbaababcbcdbddcbeeeaaecbbeaceccabebbccecebdedeaaabbcbceaddeeebacbccbacebcdeeccbcadeadaaedceddeeebdabcdadcecaccaddeadaaeeeaccadacdbbdcacdbdbdcacedccedaeddedecddbbbddbedcbeeebadceaaaceeedddbccaaebedcecbcaddeedacdceaddcbdcaedecbcdebcaedaadcbddcadaedcebbceceeaecabdcebeeedcdabeaaacabcacacabacacdebebdbedcabddaccbaeabbdcdbcbdccbaaceabbeebceedbeaccebabeeeaaabbccbcbcadadbeeaceadeeadcbccbaaacccaccccbdaebcaccbaacbabcbcabbbbddceaddcbdeedcaebeeaadcaceaedbecedabaeaccbeaaebbadadcacceaeaaacadddaaedeabeddceceadcbdeeeabaaabeedacbcaddadaccdadadbcbeeedcebebbabeceaeedbdeddaadcaeaeaecdbebeacabbdbededacaacbceebeaddaccebccaecaabadbaebcdaedddabcadcddacdaacdecadbdadbdadaacabeeabcaaaacaaaeeddeebcccbbaaacddceddabaadadedcaaecdecaabceebdabedcadbdabadcbbdccdebdceaecdecabdbdbadcacdbaaedaddbcdcdebceaeaaecaeaaeaddcdbaeedabecbdddebcbdcaebeebccddccbcccbddcebcdccbbbcacbedaabcbbebcdbcbcdddddadbbeeaaddeabdddabbceeabadddbcbaebbdbbeccbebeebbbaabbeaceaabceeebacdbbbabebdeacbbcbeabddddaaeeeeeabeeeaedbaeccabebabcbbcddeeccbbaaacacccabeaaedddbeaabbddaeeaebacaeddccdcbceeadebdbddcccadbaccbccedeecbeabeceddcedcdabeaacedbbeadbbdbebaaeccdbaedceadcaceceddcbcbddacdaaadaecceaadeceadedddcbcdbeedeeacbdbcedebedaecbeddceeccdbccdccaccbdbdebaabbebebcabdacccbababddacbaeeddecbcdbbeaeacdacebcabcccaeebcdadcbabcbccdecdbbdbbbbeecececeabedeeccaeebceebaebedecebdaaaebadbcebebeeaceccaabceeadcaecbbbbcabccabcbeebaaccececabdadddbcbbedaddeabeaecccaecacbcedccabccacdacdebeabbeddadeaeadeccdbdbcadeacdaeeebdbbdeedcbbadaaeddeedecabcdbbccbccbaceaaecbcdbcdabedeadcecdaccaadddbaaceeabdcbeeabadcccceccaaccbbaeecdeadcaadaababddadbdabbdeecaeaeaaaccbbdbaecaaccbabaeddccdedaeeacaaeeabdeacbedceaaadcadebccaeaaedcdedecbbeabccdbbadcbdccedcebedebabdbcddbbbccbaeaadbaaddbaaceeeccddececadbcbbaecebbdcaddeaebebcbbdcecebcadcecdcabcbcddcebabedcdbddddddddcdabaeceebcceadcddcbddbaceaedbecbeaeeeedaeebbaedeacabceeeaeeeccdbdbdaadcaaecdcadcacebedcebbcbbeccadcedcedccabaedcccbddcbbeccaaadcbdbdbbdcbbabaaebaeeeddebcbccbcddadeabdebbdecddbacaaedceaccaebabaecbdbbbdbdcbddbccdcacdddeeecbeabbebadcaaceceecadeceeebecccbcbdbacdcbcdbcdccecaaddebecedbbaaaaebcededabadaaedbceecdbccbecaddbeabdbaabcecbaedabebccededadbdbdeeededbcebbeadddccbbbbdccbaebcdbceadaabbaecaaabbbddccaedacdacddebdbbbdcbeacecbecbccdecddcbceecaadeeeaeeecabeeacdbbbebcaeecdeccccbeaeceeccadbcdabaeabcadceedcbaaceacbdddcacadedeeedcbcedbaccbeaecbedbcabbaeddaddbbaddbdeddcebcdbdadcbcccbdccaeedbcbacdbeaecaacbddcadbdcacacecbcccacecacceeecabecbbbcdedddaacadebacdabddbedabedbacabdebadbadccaabacdebaceccebaddcadcddcdccbeabbcabcccdbebdadaecacabbebeccebaeedddddadcdaaddeaaddecdececdebebdabddaebccbaaaeebcdcdccdaebacaebdabcebbcdcbabaddbccceeeecacceccceaadbebcbcdedcaccecbccdadceacbbcebeebbdbecabdeabaeeadaceaaebdccadbbabdabdbecabeecbeaaccabaaeebecbacedaecdadaabaedbececedccbedcabbecbebcedcadebadbadecddbeabecabccdddaeeddcadeaaedcedacbbbdacddbbdcacdeddbeedbbacccbabeabbaabeaabccbacbeebbbcacadebcebaadbbbbdcccdcbcecadaaabdcbdaaeedaecdaceccbdeadcedccbcdeadbdaecaaaebeeaecaccddebeedeeeacbeddcaedcdccdededeebdecbcedbddedaadbcdcddadbeebacdebccdaacdacbdbdbdceebddeedeacdbdadabeedcedcbdcbcbbdacbaabbaeecbdacbedadecbcabebbddbeaabcbcdbddccbeacbcbdbbeedabcabbcbdacecaddccacbedbebabbdaeacaceccaaeaeebebcbcdbdceaaaadebebcbccdadeccebeacabacaaeabbaaccedebaaebcbcbbcdbbceccbedaeddeeaebdbbdecdecdebccaecbbaececbabacceddcaccacdbecabcbdcbbbcdbbcdbccaecbccaaeeadccebbacacaccddcbadebebacbaeebedcadbcbdbaadbeebcdeabbaeaaaececbdecaacbbebedcedbbbdabbadeaeacbbdbabecbcceceabebeeeeddabcecbeabbababddddaaeddeeebcbcbdbbaeecacabadaacbbceceecaadbdeebdadcdcacceccebcdbdaecabddbedcdcdedacdaaebecdeceecbdddaabdaceabbddebcbddebbeededdbbebdebdadcbdcedeaeeddcdbcadebdddebdebebbddcaecacedecddbcbedaabededdbedceecbdbaaccddaacccabaedbdddedaaaacecaecacdaaccbdbdceedddacddecdcbbbaadbcbedcbeeaecedabeabaaaeddcadccbeabbeedbbbbdcdebedbbccbcddcacceabccebdbecebcabdbebaaaaedddeecdadabbeaaacccbdbcbebdcbabdeebddaeecccacbebebebbcdceaadcebaabecbcaaeeaaecbbbcaccbdeabdbceaddcadaadeaacddacabacecaedacccbeacdcaebadecbedaaebaebdceccdabcadabcdccdecedcbecebdbacbcedcaabdaebecaaeeeeeadddcdadcebeabedcecddaebaccbeedbbdccdbdbccacceacbddbacbcadededbcdedbdddcaaecabbabebbdacbcdcbeddaabacceedbeadaabdccadcaabbccdebddbebaccacbeaaabaabaeaaecbcdbadaacbebeddadecbcbcacdceaebcadbccdebceedabbceebadacebcdeebabcadeedaeededacccbaccaeeccaeacdbededaececeedbbecbbeaecaeaaedbedebddabbddeecdebdbbacccecccedcdabeecdddbcbdeadeeaccdcbdababdadcbaecbacdebdadebceeeecbebbdeeebbcccacacddeabcbeebeceabcddaaedbacbcbcdcbaeaacbcbdccbeaaedbcebbadcbabedeaacaaebadeacceeccecdcacedcdedcabdcadbedddededcbcecedbeaecaecacdcdebabcebbedeceeaeeacdebaeeaedcbdbedabddeebcbaedadcbbbaeebcbecdcdebbcdaaaabbedabadbccccbbcdcbacceecddaabeebaedacbccedeeaeacdabaaadcaebeaaccabbadaacbcddadbedcaadaddcbadabedeebbbddcaadabbaedeecebbeadcccdabaceaccecadbcecbbdbaecdbedccbbabbaeaadeaaaabbedeaebbcdcddbececcccedbdabdcaccddacceeeddadabeaebdbdaeacacbcecdccaecadcccebccdadedeaabedbaaadcaedcdbeecaadccdcdbdaaababcbbbaccbeabeccccbaeeababaaabdbebcaddaeadddcdbcebecaedceadeeaadbdbabdabbcbecbbacabdacdcceaececaebabadbecbeecaaacbceadeddacdecdcbdacecaebecadccbcceaeabaacdadbbebedddebaeabebeabeadecabcaaebbeceadaebceaabddedbadeedbadeaaddeecebbadbeeceebdbbebcdedbbedbaedabdeddcdedbbdbdaecaadebaeeaedcdbcdabebececceebdddabcaeaabeeadaaddacdeabebbcdecebdcdeedcebadbaecadaddddbacccccabecebceebbaaedaeedecbeddcdddeacaeebedaddadbacaeedecaaeaaeacebdeedcaedccbddadcceebebcdcdabecdbeebebdccadeceadaecbbacbbcdcbecdabbcecabadceebeeabecccbbbcdabcbdbbeacbbacbeddadbabdbebdbbadeeeeceedcecdabadebaacabadacdedaaaabbcccbaeabddabaedbddacccecedbcedaaaaadabcdbaeabddbdcceabcdcbdeedbdebadebbdaabddceaeeabbcacadadbcbccbcabebaddbccdbcaddecdaadccbedbeeceddacadaebcdeeaacceacdecaeaceadaedcbaebcedcaaaebdaeacecbdadcccdcaddecabdaededbbacdccadbbbeccdcadbcbbecabbeeaccedbddedebcbcbeeddddbaaeddeddeedadcaaeaeebebababbceaaaaacbedaaabedbccebccdbcaeaddedcbddeddddedceeadcbbaeacdbccbabdbbdcceebdbcbeaddeecaacadebaccdeaebccbadaeedecaebddbebbbadbbbcbcaccceceedacbcbaabcdabacbabeaedcaebdbccdedcaeccaceaeedceabcbdbeaaebecbbebacaedcbeccdadcdbbdeeaabcedbedeecececbbecbaceacdaecedcacccceecaedcbdbdcbaedacadcbbeaaaeeeaeebbaabbccddbdbbeecbbbaecacaadeaeaeebbbdaaeebaddbabaeababcaedaeeabadddadcadedecaedeccdccdbdacecbedbaeaddadbeeacececedeebadcbdbdcabeeddcadbeedabcdedbceaedeebedbadbacbacebbcbbdddecdcedbbacbabbdbceacdbbddabccbebecdabdcedadbbeeaceedeacdddbbadebbbabebcbbeebbeeaeeaeaecebbadaabdaadcdcaacccbebeedccdaceceabdeecedabaacbebaceaecbbecaaddecaeddbaaccdeddeacdebabbaecaabadcddebbddcbabeabbbbceeeeebebcadeebcdaccbbbaadabaecebbdceaebeeeaecdbcdbdaaadabbedbdadbdeeccacaebedbbdebaeadadeabccabdacaedbbceebadddbebeeaeeedbcbadaaaddaccddbccabceacbbedbccaacecaaeadabdaceeddbdbceacbaaebddaceadedeceeecadedadeedaecedcacbcdbcabcdacdbedbeaabdeabaaaaecaaeddbbaadcdcdcedecbaceebebeeaeaebdacbbcbcebceadbcaadecaedaaddacddacadddcdbadcedbeccaaebaabedaadaebcaccbceaaadeeeedbaadddacbcaacdcdabbebbaaadacedbbdaaaadceaedacdeaaddabdbaceababbceacdaabccdbacaababebdabbbacdccdeeceedcddeecababecaaebcbcacabdbceeedcdaeabcbddadecdccddbadeeebdeedbacbbdeaeadabeacceeaebbcabbbdeadbbccbaebeaacbaeacabeceeadeebceedbabebecccddeecbdbaecbcdcbbdbdebdaeddbdbcdabdcbbaacdeedadeeebaecaebbeeabebbbcbaaadeeceeeccccddaaadaacacebddcdaeccedeaecaacdeccaeaeeeabbacddbaceabebcdebcecacbbeacadeabeededddcdbacbdbedbccedecbcdeedbadadbccbaecadcdbadeaaacdaaabeebdbaceceedbabcbabdacadadcdbaeacaeddedccebeceadddabeaebbdcabcbcdcecedceaaaebacceaeecaaaeddecdaedabcccacdecabbebdacdddebcdacbacddacdaceadcbccaecdbcadadbdedbaecebbabdabdbadaccdceaababbdcdbdeedccddeeebbdaeddcbedcbcbadcccdaeceeccabcbccacbebeacbdedaadeedeadbbcaacadeadadacdadaeacebccddeeeedebcdbcbbbbcddcdbececeadcdbddbceccdcbeacadaaeaaacbbddcbbaeedcdebedbedceaaceeccbeacadcaeeddcdadeacbdbaadcabbaaebbcbadcadbbaddddbbceaeceebabbaaacdbeedddedddccddcbbedacadeeeddebadabbaddedabcabaceedbddcaacaecadbeceadbcebdcdcbbcdddaabccceebabedaadbdbacccbcdddbeaccbbadebeccdbaddecdbeaabebddbdbcbdecdedccebbcebbaebedaaeadcbcccabeabeaeeebeadeeebcebbaaeecceeaaebeeedddeccbacbeaacacadaaeacceeececaeebbeaadebcacdaceebaeabadabecadeeedcdcaecbbaacadbccdadcbabdabdaeaacdeebacabbacdbcbceedbacccecacbbbaebaaeebbbadcbbabbecbdaecdeaadbadcacedaadbcbbebdbbabcbcebdeacecdbddbccebeedcbbecceacbaeebbdadabecbaeadcecdbaecccacaebeebdcdcdeddcbaddcbecececcaabdbbcadaeecbccbabbcaeaedcccccacdecaabbdcaeadbebebeebabceddbceeddbbdedcbbaacacbbbeddddeeacbabdbdecbcdddeeeeeaecdbdcbceaeadacecaaabbcbbdeeaaabacaaaecceddeabebecaeccdcdbbdcdbcaaaaeadbdcbecebbaaecbeaebecddabbeecabaccedddbbbaabbdeecccbcbbbdcbcdbaeccbbeadbbcabcccccaceedeccdccbaebeedbeebdbccddcdebbbaebadaccecaeccadddbbcedeecbcaabadaacdbdcebbcdededddbdddddbcaceddeacaabbaaadedbacdcebebcdaceccabeedeceeccbbbbbdeeadcedcdbeeceadbddbdbeadddaadbbbdbbaeaaabcaeacbeddeaaeccadcbbabaabcacabadcaedcecbbaaeddabbacaccebabbaaeedededabdbaabdbcacebecaeedaaccbaecbabdcddacddbaacddaeabcbebabcdaedcebecbaaeddcebeeaceceacbbedceeadbceddadacdcdaaaadcabedaeebcaddceaecdcabbbaacbbcabeeeecacbebecaeaabedaaaebedeeaaaedbbbceacedbbbecdcbbeacecedbcdedcccabcdaeecebcabceddbdcbceeceeebbbacacbdaaeaeaecdcddeadeacaedceeeacdccddbecaacddedceeceeeaecbdccebbebeddbacacceecdbbecbdaeecedceabbadeddbbebbdcbbcbacdddbdcaccabadbaceabdeddcacadaabdddbecdcabeebabeadcececeeadcdececcadcbeddccebcdaceddabecaccbbbcbbeebcbebadcdeabbcdcacdbbeadcecbdceecbaeaceeedededccebdebdcdeabacdbacecccdccccbcebbccdeddbcecaaedbecdabdbaeceedadcccbdbdddebbddbeacaddddebcdbeaaeececeaabaadccccadbdceccdeecececbdddeeeceeaecceabddcbadbeaeadccdcddebebabaaaeacdabaedeacdcdedbaeebccccbdeddadacaeccdcededeeadbbdbccdebaddcceeacecbdcbbbceacbdabdbcaabdbdebcababecdcaaadbdbccddaccceabdddaacddbaebdccacdaebebccedceaebacedcaeeebacaadcabaedcbaeedbdebbcccceaecddadbaddeaabcebadebacebecdbaaaadcbccbeacbadedccabcaaeabacbceddbdbabbbbceeccdbededaceeaddeaeadcdedededebaedcecbeeecebedbbbdddaebceaebedcdebdaaabadbcaebaebcebcecdeeddcbabdaeebabbdadcaeaabddbdbaeabbcbabddadebaebecceadeceadcacbedcecaacaaceaebeebcaeababcecbcbeebaddeccddbcbeacacceeaabbeeceeaeeeadcecdabadadaaeaadbadddcdabbcbbbdcbcaecccaeabdbeeedeaebcbbedeaeeebbaacabdbcbeabcaadbdaaededebdaadcacccbbdbdbaedccbcbeccccbcbeaecdcecdbcddaeabeadcebbdcdbdedabdcccdbcdeccacecedadceacabddeacbaaacbeeecbedadccddcadbecdeddeaeacbbdbeabcdaeebaacbeadecdaadedaaaaaebbabbeaabeeeecbccbecdbcacdbdbaaeebcdecbbdcedcbeabadbadaddebbcdaaeeccccddbbccdaaddddddddcbbaeccabddeceddecbcdadacebceadacceaaeebbaddeadddadedbbaabcbdcdebeaaacedcecdbeceedbdbdbaaaedbcdbdadeddaebeccbecabaddaadebabeceedceeadbbcccdccceeccabeaceabaadbbeaceebcceecdceddbbcebdcacceaabbbeaccebebedccbcdaebbabaddebceadbcdddaccceabddcbcebadebeccdcdbbdeeebeedaaaabeecbabdabcbaebbbebbaeeddcbdbaadbeacdeedcdbceaabadadddbabcdaeaaaaddbcdadcdeeebbbcdbdaceccadcaabcdbdedcdaabdeaebebdcebddcdaeeedaedccbcceacbbdacccababecdadcaedcbbaabebdacaedbbcaadbecbedaeeeedbdabdcddeebdbcdaaaadadceabcdaecdabdedeaacdedaaaaadabbbabcbabbebbcccddadcdaceecaebddaebcccababbacadedccaaabdbddcedcccdacceebecacbbeecbdceaadcdbebeaaaadaccdbdececbaabeddaacecdeddcebbbabaeedddcbcbcedcbebceddcccabaeecdccbdcddeaeaaccaaaccdbcedadceeaddadcbbaaaacbcbabcddebbdacaeaeabbdaceaabbccddaaceecebedbcbabbebaceaadeabbdcdaeabedaadadbbeedacbebaaebdacbbaebceeeeeabaebcedabcaeeaccdadaaadbbcdcedaccbaaeabcbcedabbaecdbaecbcdababaaabedadddacdebbccadaebbcbeceebebcdcddbbdacbdebeecadaccbabaddecabbeeeebabddebbeadaecadaddcacacbecbadaceabcdaabbecedcebeaddcabdeccbbdddbcbeceadaaceecbddcbccedbaabbbcadedadcbeebcaecccbdbeccecbdbccadbddeaabbacdbbddcaeedeabcecddbaeebaaebcbeedbadccbdbdbbcadabeabbabcbbddadcaccaedddbebcbadbaeacebeeeddecddceeaeebbaedddaebecebaaeccebdecdecadebedcbbdddcebeadccdbbdcedeeeabeabadaaaaceaddedbdeadbbbdbecacddabdbddaecdbcaaebaecaedeadeaddbeeeeecaaabcecacbcbbadbcdbccedadcbddbccbbedccbdaaaeedbeabdcecdcbdbaaacedcaaadcddceecbccbcccccbedaeeacdabcaecbdaccbcecdbcaabcccedacdabdabccbdabdeeadeebbbaabdcdecddcbcaccddaddadccbabbadabdceacadbeeceaaceceaacdbcceedcdeeceabcadebebababceacbdaebbdebbbccbcbeaeedabadbddcaeacbecdbcbdbbbddcbababcdccdeaaceacdbebbaccacdbeeacbecdebccdceabacbddeeaaebcdbabaeecbcaabedbbddacacdcebeeabeadccaccddcdbdeeaaeddbbaeccacbdadabddccdceaaddccbebbbecdcdbcedcadeacabddbceeeddedabbaecbabeebeecedadbcdedabcbdcccbeeeadacedcdacdaddcdcdbbdbddebceecaccdcaeaecbdbeadedeaabecdeddabdabadeebbdbdadcedadcecccdaeeddecedebdedecbeabeaebbaaabadeceebccceebacdaaccdbbcdeebbcbbcaecebaacaddaecedbcaabcdebaddaeeeaeceaeebadaeeaaacaddcaddaddebedaadabedbbdccbccdeccbeacaeebccaccaccbbbabccbdacbbcdcbaaddbcedccbbeccaaaacebeabdbbaddeacacccbbcbadcceddedbbdeddccababaadddbcedcbdcaeebacbdcdaabecadbedadbdbbaceabbdaeadcbeadbeddacbcdcbdadbddeacecbcddacdbbdcaeaededbdedacdbddeeaaccbceddcdcdbcceaaecacdcccdbecaaecbdacbeeeaeceeaddaaabbbbdeeededcedabcdaddbdbdeccceebecaeaeeacebbbbccdddecdcdbbbeeeaaddeeadeeeccbebadbcbecbebabcebebdceecaabacddedccbbebaedbadbeecdaebbdbecbdcacdadcdbcebcadbddbaaccbbdedaddacaacadbccbbcbadddcbbebababdabcbeaaedececebeaaddcdcaaececccbdaeadcbeebaacacbedbaeddbadecbdaddeccbeeccbadebeecadcccbccbdcaacebbcbdaeedbbdccaceaeaeabdbaaeccebddbeccddcdcceccbbcaedebedaddadbdeeabbbedececbbabaaeeeeddcabecdeabbcdedbeadaadddbbadbedaaaeeecceeaadebbbaacabcbabeeebadbddadeececcbdcecaedaabbebdcedcecbcbdaadcbcdabebadaabeabcecbcdedeabdbbaecddecbababaceecbbdebbabcebabeaccadedbadaccbabcedcbeaeedaacedbaadbaeecddaebceaebcaeedceadbdccecdbbdcadacdedcabeeadabcbebecebcbadaeaabcecdbaeebcedcebebeceddbccaadbbdaaebddaabaaddeeaeedeacabbdadacddacaddedeeacabaedabddbccedeeaedabaabebbaebecceabbaebbeceaddccbecbeeaecbedcebceebedaeddebcbbabdbacdabceecbdccbcedcdadbbbadbaeeeaaebdbecaedbbdaeceecbbeaecaedaaaecebaaebedadcbcceebeeeabdcbebbbebbdbeeebdeaeeacbedaeecedaeaccddebddbeddccbcdadebecbaaedbbdacbbeadaedcebbacaccccdaddaaeddcbbcdabddeecbaccdbcacdecdeeaaabebeebadcdaeaceeebcdebcaebaeabadacddcbacbedadbdadccdcaedeeabcedcccddcedecdaaaacbbeeeeabebbebeedaeedbcaebadeadaeebcdaaaabcbbbcdedbdcdedadcebbbdbbcddedecccaceccbdaaadcbcbcbdaccdaebcaaeccabcbcdceabedcedceaecddcaaacebababcbccebceceeeeedcabebdcbbaecaeabdbcebddcbbaebeaedaaaebeecbdbecdcaeabdebadbdcadacaeecdbcceacebbebacebddccacaccceabdeceeebcaddbdccbadaeebdcabbdcbceaddbaabeecccaabbcdebcaecaeadbcbeabcbdeeaeeaebebbcccdbccadebaadbeecddaacbcccbbecceebdeaeeabaabbcdedebeacbcecebcebecbceeedacddbbcececeaacacebbadbebebbebadeddaeddaeaacbbbeeeaaaaababccbecdeaeabccccbaeccddecbaeabaaaabdacbaddeceadcdcbabdaceabdedbdeabceedadbecccabeecbeeedcdcaacdedccdbceeaaedbbeeeeeeeeceddeaabbdaddcbbbdbdeebabbbadedeacadaddccabaabddcadbcbeabbbacdbbbabcebdabdddbceecdabccdcdcdcdcaacedacebbbbacbedbdbacdedbcbaeaaeeadcedccddadedaeeeabeecbdeeeacacaadbbebdcabeeeaebeaceacccbeebbaceddabeededcaebeeecabebabeedebdbdcbdbbaaebddaaacbadcaaabebbaeedcdcadccadabebecdedbacadbbaebddcbdbedcbaaecbbabcacceecbdebabdbdaeecabedcccececaebaeaecaccebdbccdbdaccbddabedcddbceeceebdacabddeeeaebaedaacaeadcaceddcadbbeeebabcddabdddabeedadedaaaebdbbbcedccaebdaabaecddcbaacebdecbabcbeedceadebcecbbbaebcaeacacdacebcabdaacecdddecabcaaecddcbebbcdabaebdacbdcaebbaabbcedcdcdecddceecaacecabeebeedbcececdeaccaabddeceaddaceceadeecdcbbacedaccdacdccdbaeacacaaabaaddcdababcacbbdccbbdcecedbaaaeebdecbadaeedbaaddbeadeeebaaddcdddbbedeabdeabaebdbecebcdbadbaadcebbaedaeecaabddcebacaedeebbcedeadacceadbbaabdbbddcbcedcacddeacbcababbdcbeddebcebcccaedbecedbabcabcececacddcedaccbbbdbcdeddbbdbcedaabdbbaacabecbbbebcddebbededcebcededabecddcddecdacadcdacdcbeadbcecebeecebecdadadbddbeaaaecdabcdeccecebdbcdecadebaccebdceeebcedbbaabaaecceccdeebdcabedaecacadbdeddedbaabaeabccadedbacdbdecabdbaabadcdeeedbdccabcebedcdaebdaacabaecbadabcbcdecaecabddaaaeeecaaabddcbcbabaececbeeaeccecabeceeeddcebcaadbabbdebeacedadccddabecccabecbcbadebcdcacebdadbadeaeecbddeecdbedceabaecbcbbacbcadcabeebcdaeddaaccaadebdbcedaeabaeeedbcbbaebeeeecbeddbededcbaedccbcaeadedadcbeaabaeeeeebddaaccbabdceccadcbbbecddcebeadabdeaccbcebeecbbcbbcadbedbcaabbacccbbdabbbbadcbcceacbbbbeedddbcebeaceeccdbcddbaaaeebaddaecaedbeceebabcbcedacacdbdbaaaaeebbcadaceddabadbbdeaebceedebcbbecdeaeeebbdccebbacbccbdcdbddaaedabccdbcecaebcebcbbbccabeeacbbccdcccbccbeecadbebeeedecaebeebcabbbbbeeebabcbdcebbcbdeaedcbcadcaecbeeabdabeeceebebabbcaedcadbababcbbabbedceaeccebeaedadabacbdbabcabacbbaaacccdeedbeabaeddedecceeaeedadbecedeeabaadcbecaddbabadaccceaddcebbecaecbacdaaaaaecedeebbbdbdccacdaceabeabddeacabbdcaebbcedcaedaaeaacbbeecbabbbebebeacbdebbbaaecaacbcbdbeababebaaecadebdedbcbbeeacaeaccbbbbccdddddcbbbaddebdcdbebadbcadcdcabaeaeedadacebbdbeccedaaddbbdbeeacccedabbceedbaebcebbbebcacdcecbabacdbdadbcbdaaeabceaebcaceacabbadabbdbeebdaccddceeeaeaddddebbecebcdbcbbbdbccaeaddbbbcddbdeebdbbddabcebcdaaceeaccbaebaeadeacdaabdbddebcabbccdbccdabedeaceeebcdbcccedbebcbbeacebcbdaaccdbadbcbcccdadadbdbdbbdcacadddedccbcacdaeaecdeebabcceacbbdcabcdbedabddabacdededceeaacacbbccbbabcbdacdebdbcedbacbbdcaabbaeadcdbdedcdaeaaaccbebdeccbbededceaeeeaaadeeaaaddaeeabdadacdbceedaacddcdcbdcdddbdbbdbbddcabbbbcdadacecdbbdecadbddeebacdadeccedcccaabcddeecbaaaeeaabcbeebaedcccebcecddccbdaacaeecaccabeaeabbeacbcdebeceeedeaddeaabbaaeeebdabbbcdbbddbbeccdeeedbbddeeccdbebceedbbddebddecbeeaabdeacbebcccbbaccadcbedbaccabcccaadbbcaccbcbdadeccdcecaddbaebedbbedaabaabdacddbececacccbecedeeedaeacaedddebbeaccacbdcebebddcbecbeadcaedabbaaebcabedaceddccabdaaccebebcbcbbbaaecdeeeeebdbebdcabaedcbdcebebbeaaccbcedcdbedbdeecebedbcdbbbbeacdbccecabedecdeedbddcbecbbdecdbdcedccbaaacdbbbbeccadeeddcccdaeeeeeddeabebbbadedccaeeeeebdbebacdaadedceeeecaaccceaedacacdeeabbbaedaacbbdabbedeaecbadbabbdeabaaebddbdaebcaccddbdbdbbcdcaaddccebbcdacaedbbccbccbdbeecbbbcceceabdcacaaeeaceadcceaddbbbabdaeaddbbbcdcdddbeeeaabbeddcccbdebcccacdabbcaeddebacaddaaeccababbbcddeacaedcaacbbecdcaedeecabeacbacabecdbaaaeaddcdabccdddaedabbbedcdcbecbddcbcbdebaccdcedaaaddebdedaabcecdeeeeaadecddaccbddcdeeabccedbaeadaecdaedddcbdeecabaadbdbceeebdaababbcebcacebbdeaeeabbabbbeeabacbdacdceecebbdaddeeeaccbdbadaaadcdbeadaacadeedbeacbaecbadabbdaddbeebccaababdeeecccaecbebbaeaeceecaceccceacbadadbcdcdecabeadabceaeebecccabbbbecceacdaaeeeecdbebecaaebcebbaddadeaadeccedddadedcadebceeccdeacaaadacaadabacabdaacaccbbeedddcbaebcbbddacedaeebabbbbadcacaddeedcedaaebcbacaeaecbeaabeebccaaabbbadeeaabaaececcddbbeeebbaebdcaaeaeedabdeecebdebdadeeddbeaadbcabcddebecbeaaedbbcacaabdbbdadbcaaaaaeecadabdcacaaaaecbdeaebabaeadacaaceededacdbecaacedbccaeedacdcababcbcdbedcebbddccedacbdebeeeaddbabaadbabeebcdccaababddbeaeeccbadcebdaebbaeeccebbadeeeeeadbeebadabeaceeebaacabddddabdabcdadcdebbcbdaacaadcabddcbdbadeedbbbcacdccbbdaebcdaaddddceeabdeddbedecddaddaecedbebbaeedcbcbbcebadccaceaaeaeabcdbedebddddaabadeccedecadacccbbeeeecceaacdcabadeeccebaaccabacacccaabbcddecebdbbcababcadbadedbccababcccebeaddcdceacaddaeabedeeaeecbdaccaeeddaebbedbeeeddcceadebccedebdcbaecabbddbbeeeeadedeadaaccbabcbbdbacecbebceecebcceeccceebddaabbcdecdacdaccdaaadbceedbadbdbcbbbdcdceadadbbdabbcbeaebdaaeeaaaabcbeaddeeaceadcdbaaaecadbdeadbecdaaebebedaaddececcbbddbdedabbdbdbdaaebbabcadceccbabccecbeadbdbeebedddceacddaedabcacdeabdbbeddadebdbcaadddcdddeeedacecabadbcddccdccdeecdebeeddddbadeccabadeddcebbaacbdaedadeedbaaaaaecebedcbedbbcaededacabdaabeedaeacacccbdbedccecdacbacebeacbdcddceeecedddbdcbbeddeeaedbdaadedeccdebeaaddbdbdacccbbdbaedddbddaeedabaabcbedbdbaaaeadbcaaecdabcaaadbabdbccccdadcbaccadabbebbccaabcbebebaaccbdbedebdecbcbccdcdcdccdabcbebeabbadeabecbbbeaeaccacabccbeedcedacbebaaebcedebbacebaddbbdbebebdebcdcccbedbcbddaeaacdcbbcaadddbeaccbbddbeadbcbeadeaceddccccddaeadaaabcaacaedcdbecbdecddbebcdbdbbbbddaaacdaecabcacacdbbedcededadabcabcbebdaedceacacbccecbbdeabeaabdeadaddcdbbdcabbecaebebdaaebbddcdecddeecbdbbeeebbbacbdcddbbdaeadaccadbbcacdebdbbebdedcdbabdbbbbdddcaabcacbedacecadaadcabbcecabccbbcbceebceaddcaeddbdcdebebdecceadadadebceaedeaeabeebaebaaeadaddbbaebccbacdebcaaebdbbdeeaebebbbccaebaecbedaccdacedbaeecceababcedecabaeccadadeadeabadaabedbcebabcedeacbdddecbddeacdccdabcceeeaabcbbeabebcccedcbaceabdbcdaaebdababbbdcdbbcdeaacddcddbceddaadaabeebdbcbeeececdbdaaedbbdbbebecaedcabecdeedbeebbedaaceeddbdcbadaabcddebeecdacabedaccaedbdbdcedabaadcaccecbdeddeebdaadbaabbdbdabddbeecbcaeebddeacdeaccbdceeceeddabdddcbdbbedcdcecceddecdbdccbedcacaeebbddecebdddadcedeecdccaaeddbbdaeecadcccbbaaaaedabebcecdeeedcebaaeaddcbbbdacebcccabbdcbceebdbaaadbdadeedebeeaaedbbcbaeededcebececaaccedbaeaecbcbcabdbdccdcaaaeddcccecbdbdacdbacebcdccbaabbaadcabdecbcbcedbbbcebebbccdaaacdcdaaebabeeccadababacbdcaedbecbdcdceceacedeeebaceebcdaacaeccddceedbbaedebcbbadddbadcedabbaeacbcddccabcdeddadeebeedeccbaddbeaaacdabcebdedbbdaabadcdebacdbeadaabbbdbcbeebbebecdddeddababcdabcdddcbedbbbccacaeccbdbdacecaacdccddcdddcddadaebadbadbeccadebaadabbdcaedcedaacbeaaaddbabcaeedbbcacdcddbbccebaaacbedbbbedabadebadaeaecbeeddeaaecdcdccedeccbbeaeecdebaeeaedadbcedeedcacabbdcbdedcbcaccbbeeeeccedbaadbabaabdbceeccebcaabdecaabdcdccbbbaababcbcacbbbceadadbccbadeeeebabccbcedccdadeababdacbadbddadbdbbccabdcaddddeaccaaadddbaeacddaaeabeeeadadedebcbdbccacbcdcaebcbbceeccebbbabedcbcbeabccbbdbecdcdbbadabdccdeecbebeaaaaceeceaaedbecdccacaceeabdacaecdababcbedeabccdbecebdcecaaaeceedaebacedabcbcecbbdeccdddccbbabceecaecbccdaaacbdebabbeeebabbdbdbcdccebbbabdecacebcbbcaddbebcaaebadadcbbebcceebacdaeeaadeaecaeabeabdcaeedcacbcacaaeacddebecdbeaddbbccedeebeeaceebadcdcecbaccecdbecbeaceebeeedcbcdbddedbcddaedacbbdbddccaccdeedaaabddbabdbbaaeceaaaaebcccddbeaddaebcebceacbcbebceadeaebbaeadedadaeaaaeeabdbbbddececbcbbaadecacbcebbaddbbeadabedddbebeddedbedadeeaedbeaddbceabaebbbdcaececdddaedbdadececbdaaebadbaaeedbcceadeadabaaedbacadbdabcebccedaedbebdaacccececcaeabbdaddeeadbdbabeddaddbccbcdcbbdaeccbbaacddcaacecbecdedcdabdbbdddaeabadcbacaadbbabeddebbbdacaccceadddaededdecdeecddabeebbdcbebcbeccbddddabbcebeebdddcecdaecbcbebccdeedbddbcacdecebbecadadaaeeaeabaddedbbcebbbbdadcbceddecdcbaeebaeeecaeccedeaedddbeebdabedabddbbcedbeaaedecdecddbbedbddeddecbaaecbeabdcdeececdabecbeedccecbdbceeddcacbbbcedccaccdcdcdbcaaecdcbcaeaccddeeebbcbdaedebdabaceccdddeceabcbcacaebdbbacccaabecbabcaabaddaaaddaadbcdeccbcebdcbdedacbbeebbeeceaddeacabcecbabaccaacbcdbbacadbebdcebcdeacdeeaedbadccdaaccceccaaedcececdedeeecbaceecdcceecbcbbceeedceedbeaadeaecbabdaeeedbddbcacddeaeacdadeedeedcedceccceeecaecbebebcdddabeeaadddbbabbacadeebdeeacbbadccdddbbeccaaabbdcebedbaebbbebaaebeeecebcbbdbbaeceaebedbdbdadddccdbcebbaacaaeabbbddabeaebbecbceddadcadebbebabbbbdbdaaebbcabbdaededaaadbbddaadcdbdadabacacccaeaaeaeaaeecdbdcbbebcbdeebcbaeaaabdcbbccacbddaadbbcacbbdceaddccdeaaceaacaadacacebaedeaeadeecbdaddcccdacbedcebadbbdeddaaddeeacdabeaddbbccadabeabaabbbcbeeeeddcdaaececbdaaebaeaadadddeabeddcdceedabbacbbbaddeebcbccaaddddbdeacbddaeadedebeeecaecdbecadedcceadebceedbdcccebdaababeaeceadbaedbaccedbcbceaeeeaacdedeaebdbcdedacbdcdddeabbbdbcdceebcaaabeeceddaadcdcbbbbbadeecaabbbcdadebcedbdbecbebbadbebbeeaaeedabdeaeabeedaccccddbcdaeededaaccdddeecbcbeadbadabbbadccaecaacccbecbcbaebdadbcaabcbbecbaabaaebacbeaacdbecadbbbdcecceabaabcbeebacbdbbdcabaeedeecaccbcbdddabaaccabebdcaedcceccbcceeadbaedaeebaccdeacacddcecbbbeeaeceaadadacaeaacdaebdcaddacbbeecadacadbecccaeccecdbacecebeaccccbaeeccedcacddeaebbbeacebecbdbbdaedcebbdaccdababbdeaeaceabccacdeeebcabaaedeccdcedcacbbccaddedbedcaabbdebdebacadddadeaddbbaadeadabccbaecadebcaecdabbcaeeaedacdcaeeddcadbbdbeeaedacdaccecbeedebdcdbbedaccacccdbeadedabedbcebdbecdeeaeccbecadbceaaccdbdcaaedcbeeaabaecacadcdcabbcebeeceedbeccdadddebcbacdaacaedacabbcadeabbdcecdcbccdeedccdcbeddeebabbdbedbbbccaedbccbacaceabcbdabedbceeacceaeddadbdaaebedbdababeddbacaecbacedebeadddccacddecbbacacdaaebabeececdcdeccceeebaddcaecebcaaaadebcadedabecccbbdbddecaddcbacecabdaebeacbadbbdebcdeeaeadcdeeaeadeaddddbcacebdcaddcdcaeeeddbbcebbebcbbbeedbcedebeecbdcebabbdbbaabcecacdcadadccbcedeaaeeaaebeaeeaebdceadecedebdaccadccbaddaabddbadabdedcbbedbdbcadbacabbbdacbdecdcdaceceeceaecdcacbddbdbdceaadadcebbbaacccacbbbcadcbaceabadbabbdbccdebbebcbaabbdcdbecbaccbbdddbcbdaabeaeaabbbedaeacdcdbadacaababcaeebbadbbadbcecedbcaeceaeadeeceadcccdebcdaccbddadeeabdecdbdaecadcadbcbecacabdbdedaecdbcbebbcddccdaeeabbcebaeaaceabacaadcacbbdcacbecedadcadbbbdaeccebbbdedbedadbceecceedaccdcabdbdeeacbbdbddacbbbeacbaabbdbcbcacdceccebadcdadeeecdbcbccceceecbeeabbeeeddbcdddadbeccecceadeeedcdeddacdecdaeecebabaabbcdaacdbbcddabcaeeddabecabdbabaacbbcedebcbeeebdcabaadbbeaeebcacbcdbaceeadbbacebccbdeaabdeaaeebeacdeebadcaaddceecbeebdaecaeccebcdeaaaeabadebeaceabccaaacacecbebeeaabcabdacabdbccecaaabcbcbcdaabadabecabbeebccceadabededeaebdeaabcaebdabcedcedcdbdddaddabbebaebdbdcaaceecedbbaeeaeeceaaddbbebddeedbaebdcdbaaeeaceabacbeedceacaecdaceecadcdeceedeaeaeadacadcdcdbecdbbdcebddbaaeecdaacabcbdacbdcdaacaeddecaaccccdaebdcdbcbaebcdadeeeabbaddbdcdadacbadeaaaabbeabcbbeacbabeddbeceddcdacbdbebceeadcbeecdddaedbbbbeecaceaeeabadecbaebbdbaaabdbeabccdeabeedacbcbabbeddeceecbeaaebacacabbddbeadebadacbedbdacebaaadabdbcbcccdecedbbbdbecbcdecdbcdabedededbcadbdbaacadbaaeacabbaaaedeacbaeaccacebcceaeabdaebaadbdecededdebedcaaeeeeaadebbbabaddcabacededbcdbedaedbeabeadcbcedbeeadbbcdeadcdbbeccebaeacbcacaeeedabeadcbaeaeebeadcacbebcabeaeedbddbebdeabbcdcdaaedbaecdcceeceebbbdeaabebcaadcbceaeedbdceddebcccddcbedededacebaabbdebaeacdbebdbebeaacbccccecbccbdcececbaebadabaaadbbebbccaedcebacdeadcdeacaeeaaceedcbbdadcebebdeccadcabcbccbccebaceecaeeedecceaedbbaaaaedcdbdacbabddaacceceedaabacddadabdaabbcceacbcdbabacacdaebcdaeaadbbabeedbceadecccbabbeddacdccedeebeeccabaacccddeebaacbdeceaaaedabdabdaceaddcaabeeaddaeabbeabbdbcbddbdccdedcdedeaadcadacecacceceebdbecdabbdbcabacbbebacedecaccdebeceeaeceebedcdcbeecdccaaedaababeccacaddbcbabbbaeebcbcbcdbbbecaaecabbeecdbdbacabcbacaccccbbadaeaeaaeccbbdceedbbdaabbbcdeabcbceabbdcdbabbababccacbeabcebbdcaacadaceabbaabebadeeabedeebcbdebbdaccebbbabacbadabcbeadbdcebebbceccddbaeaecbecbdccbccabbdebcedaceccdcabdcdbeaacabbedcaeeebdcaccedacbbacaebccececebebaebcaadeddebeaeadadabbdddeccddcbbdcceabeebcadcbeacbbdedacbacdabbdcaabdcdcaccdddaccecbebdcedcdbccedeaeacddacebbbdcecbdcedcabcacecddaadbecbedcbeeaebbcbcceddbeeaecbdaebccdbacceeebadcaceaadbadebebcdddbbaeaedabaedbdbadbcaeccdeccebadebdecaddcbddabeceeacaccbabacaaeacadcdaeadecdaaddebddbecedeaecbcceacdcaedaebcedaadaabbacedaadebdecedabbeabdaccceaedbedebbbcdecaddbbeacabeebeccaceeddbaeabecebeecabdcdccaddecdbbbebddaaadbeedbdccbeaaacdaeebecdbdadababdcbcddacdabeddbaadacbbaeacddbbedcbbbadddeaeaaeeacdabdaeeabdebebbcdbbbaedbeeecabbadabcadccaeeabcebbcbecaebbedeecdabbedcabaeeedcedaabdacdbbcbddccaaccdddbcdaccaeaeaaeaeecdabdeeaeddebdecbcbceadcaddecdcbdabedacdcdaaedcadbbaacdeeddabadeccbbbcbeaacdbcddcaceedacacabdcdaabbabebbeeebaeccedeacbeecbbdeceddadbcbcdbecbbbddcadecdcccdbecbcdceddcbeecdeadecccbcbbaaecccabaacdaacedcdedcccbdaeebeadbccbdaadcdebbcacababaebddececabbdabcdbedeaeacbaaedabcbcbacbdccabcecceacdedaaacdedddcedeacebcdebcddbcdaebdabeadadbddecccdceecaabcdcbdbbadeadadacdcabaacacedddeddacbdabedcaaabaadebedbedaacaaebdbbcaddbccecabbaedbbcacdddbebdceeeabdecddcacbcecdcdececaabadbeadbcaabaceaaabcadccdcceebabcdecebedceadaebaaaddacccbecaeaddcaceeccbcbebaaeaaaaaabeacecbdcccdecedcbcaeebaedeeccbebabeadbeaeccdaecbdbcaeddbbecaaececdceaacccdeeebdceaeeadeaaabcbacecbeeedbdeaccecebacecdedecacbedebddbedaaddaccedaeacceedaceaeddccdaaeecaeabeecdcabcedcabcddbacedaebabbebbeedabbbadeedcbbbddccbcedadbebbcbdbaebabeaaeadeadecabacbbbeaeadebacababbcabcbeedaebaebcbebcedaabbdabcabdebdcecccbbabeeadbecaaaeddcdecabeaedceddabddedaecdacdccedcbccdeceecbeedeebadecedeeedbbbaacdaebcceeebcabbccdeccbaaaeadebdbcadcabcceadbadeabcdccedddabebcebcdccaebadedbccdaceeeccbdbdeccbeccbdbbcaecadadadbbdeccceebbbdebdadcbdeabbbeacdceacadbeeacdaabbababcbdbacbeaeaaadeedbaabdbadeaaecbdecceeeddebebadcdbaebaabadbeceeeccedeeebdbaecbbaeaeabccabdccdbabeebcbcaddcbdeaddbccaebddbdcdeddacaadebccdbddeeedccdcdeadedeadddccbbdebaaceebbbaccdaccbaeaabaacbadcdcaccbbbdddccacdaeabbaeddaeddaceaebbbcecdabccccdceeebbdbdebbdceeabcdacdadbeaadcecacdddaaacdaebdeeabcaecdeedcecadbbcbcdaeabaaadbbbabddedadcaaaadedecdcbceacadcbedccdcccaecddacbabbaaddacbcdeeabcbceabaceaaaedeaddbedeeeeacacedbbcdcacabdbeacebedabdaaadadcecdbeddcdeacabbbaecaaeccaeadaebbdddaeebabcdbedbddacebababdacbabeebdcaddabeabdaadbeeceeedccbdebbbbbbaeecdeeabcbcecbeaeebbaeacbcaabdeabcccebeaeabdbbaeaaeadbdcacdcdaedebbccaeaeadbccebaaceccaabccdceccccaccadcbadecebbcdbbcbdbccebeeabcbceaecaeebdeceededcaceebababdaabddeeeadcddebaddaaadebcccddcadeaedcabcaedcdaaeeedeccbbcebadeebcbceadaaadabdedbcccdcccdeaedeeabcbcdddbeaedccabcebccbaeaeceadccaeaeebabdeabbebceededebbdeacbbadeeaacecedbbdbabcbbeecedbacaedededabaeebcdaeeceacccdcbdddeabdabdbcdbdaeccdceeaaceaaeeadededcaadececacadbbbcedbaabccabcdcbcdcbcdbecddbeebbcecdedbaabbcbecdddcdceccddaddcbdecebacacdbaeadbebedbbbdeedbbbaabdebbebadaccadbeacdaebcdcacdcebebcccccdaeedaebaacaeecaadabbacddcceacbeddcadbbbbacacccaebccdbabcacddbcccecacaadedeeaeecbccceeabbedeccbdeebbeedeecdcccdaddbdadaaaaecbcbbabaceaedcbecebcaddabccdccdcadebeecbedaedadddaddbabbacdcacbededcdeeeadbbdebccbbccbccbeceebadbbccbccacdedaecdcbbdebdaadaccbbceadbbeabbccdccceeceeebbdedcbbdabaeabcbcacbdabecacbebececcabecbeedbdaddaebeddbcdacccbcabcadadddeaccbaadbcdacdbebccacddaaccdaabadceecacebeabbbddecdeebecadaacbdcacdbebdbcaddeeedabbeccaaedabbbdeedabbcaeeaebacadeecbcbccadaabddebcceedaddcacccacdceeaabdaacaeeddbdabadecdabddcceaacbaaacacdadbbccbcccdacdeaddccddccabeabbadbedccebedceaacababbccbbeeaabcdbcbacabeeabdbcaaadcaebcdbceebeaeccbddaccddedcabeeaddbedbbcbaabaeaadadeddeacebabeacaadecdaebbdbacbbcdbaedcbcabcbaeadeeaeccdacbdaaddbbbbcbacdadbcecaebbdaddebdbbcdebcddcdbaedbbeeacabaaecabcabcddccaabccedadcdacaedcdabcacaaccbebbddcedababadcccabebdcaedebcddbeecbdcbccbbcccbacdadebdaddabcaddccbedbbbceeaadbbebceabdedeaeaddebcebbbdcaeadaddeabadbeedcaedcacaacbdbbecacaeebdcabccdcddacaedceceacceccebecebcadedebeebbbbdecabddacbbdbccaebdaecbadaeadccdbcccbecddadaedeccedabbbdedcebabccbeecbdcdacbeaabeaacdbdeddbbdcbadeddbbdecbbeeaaeaeabcadabdedbcdbdddbcbbcdbabbbbaddcddcbcaaadbdcaaebcbcbbceabaddeddccbbcdcbcdcabccbbbedcbaecbaceadcdaeabbdebcaeadbceddaaccbebbbdabacbbcccaadbcebaabcdcdaaaeabebcbcacabacdbbebeeabcdabeabceddbbaabbacacdddaaedbdeccbaaacdddaeabeabdbccbccadeeddeedeabbabeaadbaebeaceedddaedddcdeccaddadcdcdabbdaacbeedacddbbeadedacacedeccbdbbaebbdebabebaaeaccbaeebebaeebdbbbadbeebbadbcbeecdacddeedbdabaeadcbddaecdebcdcadaaececceaacebcbedaeacabeccccaacebadcebcaabdccccdaecbacabbdaebbbeaebeabadcbbadbedbabbecdeeeadbdaddcdabbbcaeddecdaceddcdbaddcedacacaedeeeedcdccedccebcedcabcebedcdcaaecddcceedabcbdbaddcddcbbacaceaceeaddbedcabbbdbcddbbbbdbbaebebbedacbdaeebabbcadecebbecbcbdacdbedddaddbcbdcbbadeddceeabdbceecbddedcebbeabbacbdecbccbbeadeaddabaecdcedaacabcbccbaaaceebcacdadadaacabcbacecabeeedcddaeaddeeaccabdbbcceeaeaeaaaecacedbcbaaaaeabeaddbacddaeeeeacecaaebaddcbedbbeadacdedcceababbeaddbeedbdabaebcaadcaeccbdbeaddedacacdeddeeebaeeabbadccdadecbdcdbaceababebdaeebbebacedabdbbbcbddcdceabdaadbbdbeabdecbcdcbdeddeeacaacaeddbceaeddddabacebaadaacccadaaedaddabbacccbcdedcdbbeaadcbcabaebebedbdbddbaaeebcbbecbdcabceaacdbecebbbdaadeccbdaaadadcaeebdedebcbbccabebdaadbcbbcebdaacdccdebcabedabcdcbabbbebdabcbcecadbbaddebbaaebddeaecceaeeaeddbcdcebaebeedbacbdebbbccedeaeaadcdbceedcdaeaeeedeceebabeaaadadcccdaaabbddcbdebdcbbaddceacddddbdcebcabbaecbabccaecbcbbcdeaaccecedcbdccdadedcdceacedeedbdbaabcaecbeeeececacedceaeacdecdbebecdeaabaaedcaebeacccedaeeeadedddddadcbaecdcdccdbdbdadaaadcbbbcdeeeeacccbddadbadaeaddbdeeedbbedcbeddcddedaaeaadddbeabdeacbdcdbabcabddcedecedebaaccddddaaebebdeccdeedcabeeeacbacbdceaadeaddedcaadcdedebacbeeaacddeadaadbeaddcecdadbcbbdaecbbebeececdcbddcaebcbdcacaadbbcbcccccdbaeabdbededacedaedaeeaeaaeeaeecdbabebcebcacadcbcdbcddeccdeaddccaedbbdebeedbacbebceeddeddcebdcadbeaccbaeaecaeaebeebcdebedabebcebacbabbbebcbceedbcbadadeeaadeaabbaddeedcadcabeadcbbcedeeabcbacbadccedbbcdbcdbbddeedddbcaadbcebeeaccaededbeeebbbeeeaeaedaddabcdcbbeccbcadbbbeebeaddccdeaaedaccaeebaebceaeddddbdbcaaddccaabcedcbaeeaedbbaaeecddcadedabbbcdeaacadeecabbacebcddbaabccdadcccdedcbcddcaabbcbecabaecbebaccdaaddebbdcbeddabddbbbcdaebdcabdaeabebedeeedcaacbcbeeaedebecaecacbcebedececdebcbecacdcaacbdbccdccaaebdcdebdadaabaebacbdecedcbdddacbadcaaddadbbeedecebccadcacdacebbebbadacebcdaabcaabcadaeebdcbcadaadbedebcabedebaccdbbccccdadbccacdabbbacaaaceeeeebcddbeaeeebdcaddcabecdccaaebddabeaaaebebbdaeaeebaeeebaecaaeaabeaedadecaaababccececaadaecadebcacdeecabaebcecbceedcadcbdecbadacceacaaecddbedabeecacbcbbdbddcedaabdbebcaedabcddeaabbbecbdbbcddadcaceeeeccbeeadeccebbdeacbababcebeeaebbcdbdcaeeaecbdeeacecacbeccbadedeabcdaeaccabdbacdbaadbbedddeaebbecdaadbddeebacddddacaeeddbecdacedecdadedaecbcebdedacdadaadbceddaeaeadecadaeddeeceabcabadecbacbaebeecebedcdbdddbabaaaddccaddbddecbbaddabacaabeaadaaabbddaabeedddedaedbeaacbecebcaeceabaabbedddaceedbcabceaabbeadbbeedececcadbddbcccdaaeaebaecabedadaeedeabaecdeceabccddedecacbedcbbabeccaaecaebbbbcaaccddcecedbebbbdaceeaadecdadbceebceacccebacbecaadabebdeeaddddbdadabcdebadccabedbbeacadccbdcbbccccdcaebeaabdceccdaadcdccdcbaedaebdecdbdadaddabbcbddccaabdcedbdeccdccccddacacbeadbdeebcceabcaecaaebdeabceebbeacaeddbeaacbcdeadddddcdeeabedbbdeeeeebdbadebdcaabdcccedcadccbabbcddccaeaaabccbdeaeedeeecbcadbeccabaaacccdbaabddbcbdadacbeccccdedddcaaddacedaadedebaeccdcedcbbcabbaceddbaedaaadddbaacdedebaedccdeaebcecaebbdedcbdedccdbeccedebdeeaebcccbcaedbabcbaeaeabbeedaadcdeeacaeaabadbcbcdcbedbdedbdddaeddeabdacabdbeeebbcbdcecaeaadddbeeeadeaeeecdddebeedcacbacedeadbccadbeacbbdaedabdeedabdcbadbdebdeadecedaebcbdaedecaeaeadedeeedbcccacdbccdbcebeebeedadeaeaebbbcaaccddeeacbebdbacdbbebbdcdbadbedcebdaacecebbbccaadcccbcdcdecaddeacddaeccaccbeaebcebedaccddcbedbeabbeebdccaebdaccdaeeedadcacddbedbeeebeadeecebdaddccbbdebecbbaeacdeedeaebebeadcccebbdedaabaccdbebedcccaacccacddbddbaadbdbdbaebeeedcebcaaaadbbabceccbbcbdabedaaeebbccccebcddcecdabdbcdeacddaacadeeadddcdacedddccceeadbebcecacadcbadeceadceaabedcdedcdbabaccabadadacdccbaecbeeceebedbaacceeadcccbeebaeeddddcddebcaceaddbbeeeedbbdeeebedbebccaaebabeaccdadccbdddbbecaeaebcabdcbecdcdebcadaeedbebcdcebaccdcecbedeaaeeeedaaeceeedacbcddcbdbedbeadcdadbaddebbabdaaabbbadaceccdebbbebcedebcdccacdebadbcbcbddeeabecbdecdccddadeabcedcbaaacddcdeadbecbaceaabceeeeecadaccbebecadccedabacdcbbbbcdddcaebbadcccbebbcbcadeabcaebbbeddeecaccbdcdcbeaeecebabedabaacdbadabcdcbababdbadaecdbaaddaacaeedbdbdcbabacdaabeadaebebceabddedaeacbbccbbcdecbdbeaeddeaacdeedaaaacddcebedabaccdbabbccecbceebbcbcdedbedbabeceeedccedbcdbeadaccdbcbcebacacabbddeecddbcbecdbbbaedacecccaeedaddcdbedadaccacaadbbbebdbdabeceebcebcaeeaadabaaedaaccccecbdddabcecedeeddaaeaccadcbebdcdabcecbdbbbbdddcddbcbbaeecaeeadacdbcddeccdbebeebdbcdcaebadcbcacbeeaeedcbcbedbbaecbabdadaabdaabedceedaadceaeecddcadbcdeabababeeedccbcbdbecbccdcdedcaddccddcebdeaebcecadbdceedcbdddacbcceeebccbbaebecbabbdabccdedbaceedaacacabbadeadaaccdbbabbdeeecbebcbceebcdeaecaceceddcacedeaaaacbcdbdcbaadaccbdedbdacaeccbcbdddedcaceddbccddadeabdacebdaaecaaecaebbdcacbebaaecdcebadbdcabdcbddccceebbdcddcceadeacabccddcdaaecebaebbcaaacbdeddbdecbacdbeaebcaeceedaddabecdaccceaddcdeadeaedaaacebcbeaddccdececadbeebecedecabacedececaadadbaabbcabdcabcbddbabbccaecaacdeecccecabcaedededcddcdaaabcbbacaeabceadeaeecebabcebadaedeaebebedababcdaeebcbddaaacebaaaebaacddeddebdeedcaceeadacdcaaaadecbdcbadbdbbbaaaaebabdcdcacaaacdbddeeccbadacdddadbcebabeddeaeaeecbebacabbbdadcdbdcaddcaeeeebcbbebaaddbceddbbccdebdcbdcaddeebbdbaebeeddacbcaaededccaeecbdbedcceeaadebecdaaebddbacedbbaeeccedcdcdbcaebcdeacbbabdaacadaabadcbaaeecadabaaceacecdcedebdcbdaadedaedbcdbcddacceeeadcedeaeccaacbbacccacbabbdccdaecddeacdcceacadbdadcbedddcbbacbbdeadbdaebaaebecdbaabeeeedddddeecaabdddcbebbeaebccecaaebbbecaaedaadcaecbaabeeaaadedceeeddaecbadbeedeabececdebcabaeadbbaeeedbeceecaecaaddcbaeeededcbadaeebdcbeaedceeccdadcadcbccccdeabcbecaaaeeeceadabbcdededdcdddecbcddbcdbbbaedddbbbedaecdecedaceaaeeaaeebdcebcaddaadbcabaaedaccebcaeadeeaeeeacdcddaaaebccbcbdeeccdcccbdeecacecedbebbababbbccdbcbdecdbbeeecadeceabedbccbdbcaeadcbcccbadddebabcddbbadecadddbabcedeaadbaeedabadaabeaeeeeaabdeaecbedaeeebedbabcccddaeedcdededadbcdedbaeebdceedeaddcecdeabdbcebecacbeadceaadaccdddeeabcbceccadbececebbbaaceadedaeebeedaadbadbcbbdabcbeecaebbabceeeaebebbbeebdccbebcdbabaaeaaacabedeeaadebcbeabdeacaceebbaecdccaacbceebeceaabcaddaaeecbabdbebbcdadabbedbebeabdbbabaabededbadaeadddcaccecbdbbcbcaddeaaebceadabaeabdbbdecebeeaeeebeadececdadedcedcbeddbccbcedddeeadeddcaaeebcbebcebcacceabddaaedbdadbdeaadebdecdcddecbaddebeccbabdebcdabacaddeeaaabbecccaccdbedbacadebaceccdbdaaebddbbdcbccebbdedceecdadddbebbaaabbcdebdaedaabbeabcaaebbadbebaeadedceaacbccbadabbeecaadabddcaadabcbcbbcdccebedebcaadcabebcbdabdebdbcdaccbbbabaeabcccaaebabddaeeeadbcdcdbdacebedecbedcaccadcccacacddbeacacdadaaabadbcdedcaeceaabdadcabaaedcaccbececeddabdcceccececedecceccccacbbebdbdecdcbbdeeaaebddcccdcedacddaceccadedecadbdebbcabeedcbcbcddeebebcddcedcbeabdebdeeabcddbdbbeaaaaddedddcdcddddbacdeeadaeabebbdcecaaecaadebedabaccedaacebddddadbeaeaaebeeebcdccbeedcdcbebdabcdcbecceeddceddaaedcdeacebdadccdebdedaacddbdebbecbcdeaadecdabdcdedddaaeedddeaeeedcdbdabadcadccebdadcbdbccbecbdccdbdeeaceaaaeedbcabdddbacbadbeacabeaaadbaebdcaadbbbcaaeadedddeddcbdecbeadbebdcdebcbccdbecbacabaeddbebbbdbdaeabaccaccbedeebdbaadabcaeeecdadedaaeeedbaecaeddebbcdceebddaddeaaebabbcdbadcdbddedbcdcaaeeddbcaceeacebbdddbcaccdbedabadaedbcabadadcdedceedcdaccedccaabceccbdbabcbdabadeecdbdbcadceadebcadededecabdeebbeacdbbcddcdbcacebcdedcedadebaceeacadbdaceabbcbaaaabdcacbceedbebccdbdaebbebaddbbeeaedbdcdaebebbddddddadacbeabceebbcbabaddbdccebbcaadcbeebeccacbeadddacccaedbacdaedabbbbcccbacecccaddaaeaeedddbbedeceebadddbdbadaeeeddeceeeacdedcbbacecdbeaceecebeaaaeaeedebcddddbdaccecdaadbdebeaebacbcbccccacbbdcbacebcdebcddeaaaecaaabeecbaccaaaaedcddabcbabccaddcdbeecbacccdcebaceeacedbeaaddcadceaeacbcabbadaaccbabedeaaadaebedbacaaeecbaadbdddcddbcbaacabeddbdcbaeedcedbccbbaadaaecddacaeabebebcedececbababaeaecebabacdbddddedcadaecedcdbddbaadaedecbbbadddacbddeeabcceedbbceabeacacaaeaeebadcbcdcccaadbeeedacaecbcbddabecedcedaccadbbabadaddceebcacdcbebeacaebeaceabecaabcebdeecceadaabdeecdbdbedebcbbddbaccdabaabdbccdcecababceddeaacecabbdceebccebcccaacdbdeedddbccabdeedeceacdacedbbddeeecbbbeedabbbdeebeeaadeddbdbababeebbabadccdbdebdbaabaaaabacebdaaeeeadbacadabcaeaececcceccdbbaabceabdbbaabdcddcdddeeacbdecdaeadadcabbdcddbccbceabbddbbddceadcacdbbaaaabbdabedadccdacabbdeebcceabdedcbcacbecbabdeadcedabbbcabaccebebbabaabaaadbccdeceadeaeaecdadbbeccaedeccaddbbbccdeddababacbdaacbbbacadeedeecbbdbbeecbeecebcbeaddbabdceeacdcbbbbccaeecadebbcbcbddcadaaabeaebecbccccabecdccecdadcceadbacabdbaebabceddcecededdbdadbabddacbccddeddebeadddcaacdddeebcdbbcecbacbcecccadabedeeadceaddabcedbdeabcbbbdeecabececabbcbabbbecedddeaceacdcbedbaccdcebceacabeeadbddbdcaeebccddeacdaaaabcdaeebedecdbcdbbdddeddcecbaeaebbbedbacbcbdcbbcceddacedcaecbbadacbbaccbacedebbecaacddcbbecbcbeacaeeeceedbecebdccecdbcecddabcaceabaeecacbdacebabeccdacadeedabeeeddecdaaaacabceaddcabbbbdabbebaaaedbbecaaebbbceabaabbacedbcbbcaeccacecbedaebddaaaebbcacbbacbdeaddceeceeaebcabceeeddadecaebccbceeacaebcecdaeebabadabeebacbaabebddcebeadedbacaecbcccddecbeaadabdeecddeacddbdaecccebcdcaceabaadbcbddcecaeabaaedeabdbceabecebcdcbeaeabcebbeeccadbcbecbcdeaabeabeacdbecbdcbccdaaaabeeaedcdbcecabcbeceddbbaeddadeeeacbeeaaededaabeeaacdadcbdecaeacbccedbdbadccbbdabedaebedbccdacaebedaeaaeacedaddeebdabcceddbbbddeedccdebbebddcaacccabbdbadcbabeeededbdcdaeaedadabaabcdeccebeddaaeeaccbbeadcbdbecacadabdddcedebabaacdaeaaacecbecadccccdebeaeeebaecaccdbdbdeacbcaaebaaccaeeccebdeedddbeecbbdaabaecebddcabceaccaeaabdbdedeeccbddabeabbabebbbdeaccddeecccbededdbddcebcbeacdccddcbcbedeaeededeaddeaabcebebeeedeedcecbeaaaabcbceebacdcaabcadeceaddaeccddcacdcaacaeebedeeeadcddbdceaabdaadbabceabcdddaaaddabbedbbadbccabbbbddbccedaeeacdaacbabbdcdbdedbdeeaccbaeedaebdaeaecdabddaecdbbebdcddcbdeedbabaaaacaaaecabeeedbddcdabeebedbbdcbabeacabcbcadecadbcedaceedaaccebedddaacbcedbabaeeebeeebeebebadddaecdadcaedebacdeddedcaeabdaabbceaabecdadecaaeaacbddaececbdeacedcdacbabeecdaaebcadbdbaccdaedbbaddaaddaccbcadabbcacceddedeababdbdacacdeeaadcbbcbbbdbddecbdbebeeebecebccbccebdcbedbccceeaaeadbcccbacaabcbbbeccccdbcdceccececbacbaadadceceeebbaedccdebaeeaacdbbdadaaadadceeedbdbecadadcaaccabdaddeceecbeabdcdacbabeceaeceddacaaeadbbdeaeccbaebecccebccedabbcbbacdecebebeabdddccedbdedddccdccadebabecbbaadbeecccbddbdbdcceddbdcebddcbeebebcdabebbecdeaaebaeabbaaeadaaaeedbadcecaacedaccebaaceebaaeeadaacacadccaabcdbbbbaaeceadddcaebaedeccebcdcbaebddadecaeebeeaeeaecbcbcbdbbecbbdbeedababdbcbeaaeadbcedabbedbbccdedcdeabbeaccadacebdadaebbcbcabeeaabbaaddedccabbeedbaeacdbdcbeaaeaecbabdacabdabdceeaaaccedacecdaeaaabdecedbcdbbeadeeccacedcddaaddbdbabdccaadddcdccabeaceedaddabeedbedaccdcebcdabcbcbecaebccdeeccededccdebaaabcaaebaddeebacebceaebcbbeccceebdeddaddadbcccbeedadceacbcadaddeadcccbcecccaadeadcceccabaaeaacdbecaaeeeeacdbbccbdcbddecbccaddacdcdbcaedadcdcddcedbcaaebbcadbcadbaeabddbdedcecabbdbcbcebceabdadbedebddabebabdbeaacbdcebcebbdaccaccdecabcabcaabacbcdaadeadabedaadcbcdddcbdccccbaedccceddeececdcbcdaaedeecaaecabdddbdabdbcaacedaadabebcddbeaeebdeaaabdddaaaaedbddeaacbcdacaeaacdbaaacdbcbecdcadccabdeaaabaedeedeeeccceebbaaeacbcbebeebedbdccddecbeabcdaebeceeccdeecebdbbdbaeccbdeebdddeacccabcdebeedbeeabaccbecececabddadcacdeecacadbacbbeabdeaabcacdebadaddacaedebcaabecaeccbeebccbdcbbcccebbeddeabcacdaaeecaeaceacddcbecadcddedbbaacbaddbcdbbaebbbcddacdebabbccacaaedebdcaaeaaedadcedddddcdceebcadabbdbeebedabaeeabedebdedaceecaaaeebdaaebbdecbcbeccbceecadccebecbdabbeaaedbdadcbcacbeaaacaeedbbdbaedecbaacccbaadadbbdcabcbababacbadbbdbebeecebcbcdcaccaacdebaddecdadbecadedccdceaaeadaebedabededaaaeeeddcccaacaadabcddceaeeadeadaacbedabdcddadccdeaecdeebbcddaddbaabbceebcdeacdabaabebadabddbdabecbceaacddadacbbeacaacdeedebeeaabeaebeccbdeecadabcaaecbbadbbcccabcaaaccebbeddeccedbeececbabbccbbbbccddceddcdaaddccbbdabbceceabedabbdecabbbbdadceeacdacddcabaddadcaecdbbaaebebbdebcadecdbbdebdabedbdcbeebcadededacdbdcbceaeddbcedebcdabeedaedbcdacaacbcacbadaeaaccaedbaacaabebababcbacdeceedcbaeeeebbcedeedeacadcaaaebbadceceecadcbdeacbdedaeeaaeeccbabeceddcbdbcdaabbacbbbaaabcaceeacdcceecabcbeccabaadeaacbbdbebdaaebedddbeadcecdddedbadedceddddcddbabbcbedacabadbcbcdcbaeebeeababddcebadabcabdaaeceabdbaedaabadaeaaabdddccbbddddabebaaddbcdbdddbcbaddbaddcbceecdbacebabbcabcbdacecadcceaebeccceabbddaeaacbdbcaeddeceeeeededbabadeecaaceccaaeaedcbbbdcddcbaabcebbbaccaaecaedadddcbdbdbbcadbeddccbbdeeedbeeedbddcedcaebbdebccccaababccabbdceadebddbbbbedbbedecabcabdaecaaaeaacaeabbccdeaeaacdededbaebecdcdbcadbbeacaeadaddbdcdbbeebcdeceacbdeebaaabaaeeaacaeedbccebecccbeadbdccbaabcbbbeabdceacbbbbabaaeacedddbaadeedbdcacecdcdbaacbcdaacebacbdccdcccbaeceeaecaacbaececcdddcaaceebccbddbccdecbcbbcbbbedadadddcbdbbebdcdecbdaaaeeddadcabdeabdcdcaeacbaecacecabddaabaccadeaeeabdabccdabdbcaddadcdbbdaebdbdcecabedabaedabbbadaadbbcbcabacaececbdabcbaeaaddaaeedccbdaeaaabebccdabbabcedceaaaadbadeeedaeebddeeaaedcecddeeacdeceadccbbcdacbeddcecbeaccaaaccebdbadcdcacdaadaebbaaecbcbbddcedeccbcccaddeddabbdabeebdebabdceeecddeeabedecacdbdcdadecaaadbedbebbbedbdbbadddcdbeebaaebbbaabcebbccceedeeceaeacadcdabecccabeeedeacaabddbcbeababbadcaabebbdcbeedddbdabbcebadebcaaccbddebaadcbaacdebbbbccbacacbbddedeebceaeeebedbbedcebbdccadecbbbdddccacaadbeeacbbedeabebbabeabaecdbeaaacceddcebbbdecdbcebeccbabcabeababeededdddadabebbbeeecaaccdebbacbadecebcbcbbabbbbceebcbdeeaedcbecaceededccbeceaeeebebdbbdeaebabccecdbeaeacdcdaedacdaeceeccabeaedcebcacccaaeaaebeebccdddbbaaeadbcaadcbadeebbbabecaddedecaedecccabbceacdeaaeaacbcebadeaeecaabeaaedeaabaedbccbcacdaeebacaccbedbeecdbabeaabccbcdbccbbdabbdbbeaedeecdeeacacddbdaaeacecaebcadacebebaadaacdaacdeeaccdbbcedcbadcdacddeadaeadcbbeebaacbdbcbabeadeabaaacbacbcdaacaaaeebdabdacbaeccdadcbcedccdddaebaedddeecbbcddecdbbabcbbbdabeedcdbccaddabdcdadddecbceddceabbdcdaeeacacaedbbeccccbdbeedcadeedadeadbecaaceeaaeeacdaecdaebecedacaeebaeecdcedbcbecacadaabbbaeeabdddbbeaceccdacaaddddbaddeadabbccdaadabbeabadbbcdbbeaaadddcbbcccabcaceaecbccaacdbceeccbbaabaccebdabbadecddcdccaabddecbaeeaaedcdbeadeceddeebacacaecbbddddaaadedecbadaaaedbaccbdedaeaadaaaadcdacdecccdcbbeacebcdeceddaccddcdadacadeecaccdbdebdbdedbceeeceedacbbdaaaedbceeacbbdaeddcaddddcadcdcccadceceedbcaececbcccbabbcbacdeaccaccaeeecceebbbacecacdccadaeaaebaaabdedaaaacaeebdccebcabddbcabeacebaeaebedcaadabaaccdadcacbebdecccedaebccadcedaaadbecbeddaedacabcceabcddcabacddceaabebcabdcacaaedddedbbcdaecacdecececadedcaddcabdaaaacdbbdbbababdcababeaececcbccdeecebdaebbadeeacdbceeebcbcdaecbdeadcebbccabbbbcbecbecdddbecdceecdedcedecabcceddcbebabdedeccabaaeddeccdaddcededbececbddeacbdbeecebaeadcedddeaaddabdcbeeceedcbecaceccbccaceadedebaadebedbbcaebdaccdbcdeecaeaababbaedebddcbaedcbaebbeacaeeaecabdeeaedbbdceeaedeebaedcadadacdebdddddcaaddeccceaabcadddeedcbebbcdcecebeedbdaeecebcdedbddddbbdecdeeabcebdecccadeabadbaddceaaeebdccecbbccbcbedabccadbaacaeedaceaeaeeddeeaceabdbecedacbaebabdabbcacacadddcbdebedcdcddcebdadceebbeaebceeabdddabebbdbaeabacedcbbeaebcececbdddeaaebddbddebbbcbeecadbdacacabdabdadbddacadeabdddbcbbbdeabadbbeddabdcbadddeebaecdebdeaacddcdedbeaecceaddaadcbeedbcbcbdcadeedaccbbaadbaaecddabcacebcaccbedabbceaecdaebbbdceebaaaededbcaecedddedededbcdabeaeededeedcceedeeabbbebdcebcebbbceaccbccdaaddedcdecacebbbbbbcabebbacdbbceeebcedecdbdabddadddedcadedbcbdaadabdaccbadabcedebddcdeeecebaeebebaebebebacadaceedbddcaddbabacacdccdcdadaacbeedbccaaacdbcccdaeeeeddedadebdcabbeaabdeeebcbdbbdabcddccebcccdccabebadcdbedeebcdadeadeecdcddecedcccaccaedaedbebbcdaedcccaeaadeeccbaceecabbaacbadbaeadddebccdebabeabbcececebaaaadbacddcdcacebdacabdadbddababbeeabdcacdcbdacedddeeaebcbdcdaaddcceeececcceecbaeccbadcadedbebeaacaecbcecdbcdebbebdeabbaaababbbbedbebeabbeebadaabeababaecdcbecbbddedddbeaebcbcdcdcdbdbbdddacaabadcabdceeaadbdbebdbcadeaceebbedeeaaaeaccaceacaaeadcaedccdaaedabbedaababaaaeddecdddbbeaaecaceaecececaeddcdcdeaeeedcedbccadbcedaeebddbaeeadeeadddbccdbaaecdddedcbadbbbbeccbacddccbeadbbacaeceeacbbdaddbccdaaecdaecbebcdabdededccdccbdbeecdeddbcdccbddededebeaecebceeecebacaeeadacbebdedcabcdddeeedaedcccdccbaeadecbbcebebeacccaaebcdaaeccecebbcddbabbbcbadcecadaddecdcebaaceaebccaeeedddbddedbcdeeceeaddcddbaeebebddaacaaeecbbddecbbccacccdbcaaabbbceadaeeeeabcdabcbbdcebbdebabdceaaeecaedebaaebcdebcbacdbedabbcbcbaccadabeaacbebcbcdaeedaeecabbecccdbaddeccdcbaeeecdcebbaccdbbdaccecdcebdabcbcbbaedaebdbbeacddaacbcbdcaeaadbdddccedbcedbdcdbaadabdcdedcabbdaccbdccdabcbdcbbebbeaebaacecaadbcbbbecacacedaeaeceecabbdcacceebaabdeaababbaecddaeadbdccdabbbcceaccabbbbdaebccedaabbaeabccbaeacbdcaeacdaabadceeaaaddeecabccadeeabaadcbbccddabecdbabbababaebbbaaccedbddeacccabceeedeeecdaebdebecabbdbaaacebebcaeacabedbebcecbebcbaadeeadaeececbceedecbcbdceeddadeababadcdbdbddbcbdcedacbddbdebbecdcbddabcaddaababdeeabbacdedabbceebabadbcdabeedeeeacceddaaccbadabcaccedbabbaaccdedabcbbbcdcdbebeccdabcaebcdabdbdcbaaccccdcccdceccdcaebdacbeaeddcbebeaeabedcdadceaccbbaebedaddedabeddceaeabaacdeddbabcadcdecdedacabdbbcdcddbdcdcbceddedeadebdabdbaeeabacecbbceeeeacdaddbcaeaeabeadaaaadbbbdccbadacdcdceddddecacdeddeadaeecdbddadcddacaababcbdcebeddaaddaeeeadeeeeceeacddbbcdbeacaedbdbebecbdeaccdacadbdaacdeabeedbaadbacabdebbeacdbbebabbacadcedcccdbcaecaddbdcccaebcaededbaebedceabdbeaccdedcadbdcbedcccadeeedcaceeeaecdeaadcebcddbbacdbcacbceabdaabbaacbcedbdcaecacaeaeceebdaeedecbbeaccccadcbadeeaddbedcaeedadbbedbededbedeacedeaaeeccebcbdeadacaaaadcbceaeddcbdacacdcbcdbbadeeceaedccdeaabdbcdeaaeedacdadcdacbeadcedaeaabebdedaeecedeebaabaeeeeabedadbdebabecdeacdddcebbdcaddaeaddcddeebceaecddeacebecddbcdedddebdaebbbdebdedeebcaaebbdebcddddaedaaacaceababdaccbecceccaebccaabeebdbcbbdeddedebaabcacaddbecaeceacbddcbcedeedebeeaeaedaeebdeadebbeedaecacccbaabadeadcbdedaaebbabdddbaeadeddeacbdcbecdabdbeccadcabedeeedadedcedccbcceceeeebcacbedecccbcabcbabbddbacabadcaeadecadccadcccdadeaeeecabbccaebaeedaedaeecdeaedaedaacbbabbaeecddceaaabbacdcdeaadebddcacaceccedbceabbcbbbceedcceadbbadabbabacceeababcaadbbcbbcebbdcedcbbbecadeebcedcedebcabdbccbdcbdcccebdcdadccaeaadabeebcabbcedaccccecccacabddddecedcaeeeeabddbbaccaceadbbccdaacedabbbadecdebccabcabbeccabccabcceebcbbeacabaddacabdbccbaaaabeedcdbcddbabaedbeacddbbacdaadbaaeaecbacdaedddcceddecbddcddedabcdaebdaddccbbadaccdcaddbcdcebacdaaccdaeebaebcaddaaccdedbbcddceabedddceedabbcbaedcdccbabbdbdbcadaadbeadbbddeddddcadceaaabaebbebbcccacdcbbeadeedbcebcbdcddaaabbadeaaeccedcaaabcbbedaaaeddaeddaddcdaebcacbddcdddaeddbcaeacedcabcaeeabddbbacdcbdeebcbabadaacaaddbbdeedcdaeabddbaceeacdbeeeeedaccaceecbaceecaeeaceaddaecdaaebbacbdaebccccecaaadecbaaabbbbebdbbceeaecccacbbecabbbdeeabcacdaaacebeedaacebccdeacbebeedbeaacbaebbaeededbdeeaebbabecdeaabeccbacbdeceabdacbbbdcdedbacebbdcaaaedbbcaaeeadceececaacdecbbbcaabbeedecbdeadecddcbbeeadcbaaeaebabebbadccebcaccbcdbbecaeecbeedaedbbdabdceccedccaaddddadebeacdacdebdcaaecabdaeaaabdbadaaedbecedcbcebacdebaceaddcdaecbcaebeedcaadcedccdeabcdeedcedcdeaaeaacaaacdadeaddbcbccbeacaaeaaddeceabedacadeadcbecbacdcbbbcadcbcaedbbebeabdebbbbdceaddcdccdeaedbaebbccbaadeebdaeaabbacabbadcbbcbeebaeabaedddaebdbdcdcaaaceacddcdebdecdbabadecdedcbecaaeacaedeeecceabeeadaaecccabeaeccbbeedeaccbbbbebceecdddadbbcdecaaecddccbcaacabdaebcbceadbdeecbdadabcaddcbeacebedababddbbdbabbabaabedceacecabeacbeabeabeaebbdcdaaedeedbecdcaccdacdaedabdcccecbbcdbceddbcedaabddebbecbacecabbaedeedaaaacabccbeaadecebaccbccdcdebbbaebddecbeaabddcceedaaaccceadeecddbccddbeeacbdddceedccebdeaeccbddbecbddebdaeeacaadbbcaaaabbcddcacdbacbdebddbaebbacadadcccceebaacdceebedbcdcbdbaeecceaeedcdddccaedbdaadbededeeabddddedbedaeecdacadaebcadbabeabddbbddaabeddecacbcebcbbcddcbaeccddadbbeaceaecddbbeecbdbcaadacdacdbcabeebddbbbebabeedddabbcaadbbacdcbacbbccbbececadabecdedecbacebcacabbbdaddcceddcacdbcdadbbeeabbebcbcadbdadabaadebcbabbddccbbbeaaeceebdceaecbaaacbeaaabaccabecaecdbbadbebbeabdedaebcddaedadbddadadceecdbcebacbedbdccccedbedeaedeeadaaeacdeccbedcebacedababdabdbbedebccaebdceedaaeebeeccddecdbdbceccbbcddddaabacdbbedcaabacabccdeebedceceaccececccdaeaebbbabceaecbdbcddacabccadbdeabedbceeedecaedbbaacceceebcaccdeeeddbadbecadebabbcedceadddedcedbbbdebceedeccaadbbdaededddbdcccdbdeeceaebbeaddbbaabedddadebccbaacaeaababdcaabddbcdbaacdbdacbaadbabccddcaaddcbeceabeabcebebeadcaceadddcdadcbdadbccbeecbbeeeaccddddeacbcbedecacbbcceeededdcdabaadbeeccabeeeddbeecaaaedbabdbdbdcabdbcedadddbbecceaaeecaaaedddcbbcceecddacddacdbabdaddbccbbecdebebdbaedcdababaddddedceaadddcbdcaeeeacbbadeebccaebebaeeeeabcbdbadaebdaeadeacdbaacceedeedcccebedbcceabaacbeaeccdaadcbbeaeeaccbdaddeeeebdbdedacaadecedcbbdbabcbdcebecdcdcaabaedddaddecadcbbeeecbbdcbecbaaaaebbbcddedcdaacecaecedbddbeecaaecebecaccaabecddceacaaebcbdccacbecadeeeccdaddeebaecdccecadadbbceaeadddeedabccebecabaacedddbdabcdecbdaedcbdaeeadbcdbebebabbcbbccabeebaddbebcabccdeaeeedddbeeacdeaacedcddebdcaadaacbabecbcccaabeeeabcebacabbbcbceaedcbadcbcbcdbbecbddeacaeadadcaabbebedbdaddddceadddacebeadcbbaecbeaaaabceacaaaebcadbbdbceacceccaddceecaeeeebbebbeabecbdaeccacaeaccbddbdeaecedcbcedcadebdbbbcacbadcecdeeacecdccecbbaadbecaeececeeececbebcbedceddddccbdedbaedcdeeacdcdbdbcabbbebeaecdebbddeebabeeccebbcaeeeacdebdbeadcebbebbdceabacceedcbdbbcdebcebeceddaaceadcedadbcedccbdcabcdeacecbddacedcbcaaeacaecbbbbaddbcaeceaedeeeaadedcaeabdaaddbddedccbeaceaeaebddaacaceecdabdcebbebedbaacbebadaddbeeddbacebcaabbdbdececeeceebdebbabddaaababdbeaddecdcdcdcdadddeadcecdadbecadcbeddeadeaeccebadbdadbdcebaaabdbadeebdcbaadebbcbcdeaeadcadaccbdcceecdddeabbdbedeaecbedcedbbecedbebeddabccdabeeeaeeaaeacbbeaacaceeaacdeebeadcebccbebceabbdcbedbcdbaacbacedeedbeeecbbaddedadcaddeddebabebcdbeaceebbdbabdaadeedaaabcebbecbbbacaabdcabcebecbbcbdbcbbbadaaabedadcdaedbbacdcacabebaabacdbbbbedeebeedcaceecabbbebcdccacbaddcbaaaeadbcbcebeacbceeaaeacbaecdcadabeabcaeddaadeaebbeccbdcccbaaddbedbcabdbacebebdaadbbacaacdecccebeedababdaceeaacbdbabbacbadbeadaaeaaabbccdcbadbebcddaecbedccbddceeedadabbeadeceaabeabeceabacbdeaeacceaeccbcabbcaacbcdbaaeebaccebaadaedcabcaceacceeabcacbcacddadccebebbaeaadbdbeecdbdedbbeceaecaeccbccbbaaeedebdeececebaadcebbaccdbbbcbdeaaeadbbbecaaaccdbebeccecaabccabebbeceeeaaceadbaedbeaccebabcedebdddcadbdeaeedeaaedcbeeaeedccaaeeacbaaaaaecbaaabbccaacecaaaeaddcabcecbaaacecdddcbbeddeeeeedcaababcaacadbceebbbecbbdbbbdabbedbddceccaaaccdeaeebceaecddeaacbedcbddbebaaabaddbacdbececbebbdeadeeeeeaaaccceeabebbcbadbbabadbadadabbdbebdabbabecebaecdecdecbddaacadaddaabbcaaecaddcdcebbabbeacdcbcedeeadbbcdbbeceabeedeccbdcdaeaabebabdddcaecabdcacdedccaceaaeedcdceaddecccbceacdedeedbacdecdbaeacaecbadcbaaaddcedcbbeddecdcacbdcedbccbbccdeeddbabdcddacbeacdcaeacedadcdcdbbebbdabaaabdaccbceddcaeaeaedbdeeceacccacdaedbcddedbeeaadadeddbbdecaaebbeedeeecccaedddaceceeaebdbddecdccddebdbdeabcdbaaebdabacabcabeeedabdbbacecbdabbdbccedbeccebadabcdcedbddecddbddecabbeeddacbdeaddcdceabbdedabecadeabbdacabdbebeeeddeeacacbbadcbbcaabbacadbecacbbaecaabcbacabdebccdebacdddbececadeedaadbceeeddeacdabecacedabadebaebdcaedbcbabbcabebadbbbdddaaaebdeeddddbcacacecdcbddebbbdddabcbabbaaebbcaadadbbeccdddeaddcedabcdeacbecdcadbedbcdddbbbdbdcebdbedceeadaeacdeccccedcecbeeaaccabcabdeaddbcceddabdbcccbbbedccedcdceccecbbdeabcedaaabddbcacbabddcdbbebaadebecbedacdeacccbaedeabdbcdeeabbdabedbcacdbaeabbbeaedcbedbbccbaeedbeddccaadabeeababbeaeedadaebdaabdcaacacbaeeecdaabebbaddddbbbbeceadbdcddeadcbcaedaebdaccdcbbaeacdabdbcacaeedcedccccbaccadaacbdedbecacebcdcbedeaebdededdccdbabedcdcbeecadbbebdcccaacbddbacdccebbeddbcbecbdbabcbdebccdebcdceebcdbaaabecdebdaaecbdccdcbbbecebaeababedeacaacdeaebcdacbedbedeaabccbebdeaccdcbeabbbcbcbcccadcceeeccaaadeeaabbdacceaeddbaadeeecddcdbdceadddedeacdbaebcbdbdecaccecdedeeaedbcbebababebeedadcdddbcaeabcddbacaddeccbbbddddcaebcbdcccabceadbaaaebeeddbbacbaeacdaebbaadcbbdedacbabbbacccbdaabcaacadbadccdbeceaacaebaaecaaedabdbeeebebbddddabdddbbaccacabebdaaaeacbaddcbeedabdcbdcbdcaaaeeebedccbeacdccbbaeedecebcdcedadbeaebeceadecbaaccedcdddbaeedaeeebceeebbedebeabdbbdcbdadeecedcdbeabdeaaebbbdceecedebeeebadbebbbcdcbccbdbdbccdacbdcecabbeebbcdeccecaddbbdebedbeecccdbebcebeaeadebedaaaadebbbdbadaacdaebdcadbeeebcaddbaedecbcebebaebcbcaaadcaeedbdcdccdbdcadbbcadadeaabadaebbeeceaacadeaaceeadecccddaabbacacbacbdeeddabaadaeacddeedebdbcaabecadbecadcaecdbeebabedceecaaebaadacaaeebbdbccceabaaeaebcceadaaaebeeddcdeecdcbbecabcdcbaadadcebdeeddcababeddedaaadadeaebbbdabecccbeabcebaacdeabbdbdeeebbeeebaacebaecaaeedbaeaeeabcaabacbabdaddbbbedebcbbcacadebecbdacdcbceccddadbabbedcddbacdedceddceaacdcbabcdabeaaeddebbaedccbbecbbcdecacedbeeeecbdbecadaeaebdbcaaedbcbabeacadabededccebebecdbdccadaababbedcecedbaadbcceeadddabccabeceaebdaeadbccbcebdcecdeaddcbeceeddeaaeabbaceaececeddbecedddaecabecebaecdabeabecbdadcbbdacbdecdbceeddaaacaacceaeebeeeddcacdedbcbdcccaacddddaaeaecebbacabdebceeceeddacbbadedcebadbabceabdceadececaabccdadabaeaccbaaeaccaaebdbbdcaeeaaabcaccaeecacedcecbccbdccbacdaaedaeaaecdecabddbdddeadbbddbdbdbddecedcedbbdaccaeaeecdcabbbeaddcdcebaedcaabeecccdbcdeebcddaaadedacbeddeeecaceaedeacdddabddabaddcecbabdcbdcdeebacecccdcdceccbbadeaaadecdddccbccabeaccbcddacebcbcccdaeaabedeacaaaeceeddedbbdedbddbeeadbeacaccdcaedeabdddceccbbdcbbdaeedaddbddcebcccdbbdedcadceaaacdedeccbabceeaaacabaabbbedabbecebacecdbbddbcddcdabdbeceeabcdeddeadeebebeabacdcbddaeeccdaceadebdadaddebcedcbbebbccebbddcaaeceabcbdbaceddeddcaaeeabcbecccceebcabdaedaeddbcaeaceddacbcaeacebebaeecbcdeedbcbbdeeadbcadabebccbcdbdbadabbaaeabbcadcccdacecbceeedcaabcdbdbdaddabeadaadccccbbecbbdaeddeaaadcaceeecbbebacbdaabaecbabeddeaceaebbacdadcbddeccadedbabcddaaeceeeaadaddccedcdcadedddccbdadadbddcdddddbeaadeebbadcdabdebaecadaceacdaebccdcacdbcacbdeaadbbdedceacdbcbaebdabcdeedcabdccbbddddaabbebebebbedeaaaedeebdedbcaadcdebdacbccaaeeedbdacdbbbcdcbeeaeedbdebaebbcaaaaadedcaecedddddeabceaecadeedabceabbcedecaebcedaeaabeedebecbcadccccbeedbdaaeccdadbecdccabccabbcaccdeeeecabeeedbeceaceabacceeabdedebbdecaeddaccbdddcbdcaadccdecbbebcdcbdbeccbccadbccbeabccdeebbdcdaebeecaeabbbcdeedbaeadcdaedeeddbcacbbaaccdedcaaebeacceeabdebdbebacaddcbeecacbaeceeabadddccdeaaedaccddceacadcebbccdbbaeeeededdedebceedadcdebdecadaaaadbbabebdbeadbcbedcacccaccccbbbaabbddbadbeaebbceabdddbdedeeabaabdbcebbecaeabdbdddccebcacaeddebccbbeabeaaabcdcdeadacdecdaacacedeecbeddcaaccabccabeaadbdbaaeacacccbecdaaddeddbccddebcbeddbaeeeabdbebcabbababedabcebaeebdbaeeecaccebcbeaacabbcaddceeddadddeaaaddebdbbbbdebeebeddbeeecaebabaadacaaabceceadeabacebcddeadddbccddadbeebabaaccacecdebdcaaebaaddaebadaeeecdceeabbbdacbdcccdbebadcecdedeacdecdccdadadbbbdeabdeebebacbddaedaddeadcacdcccaacdebdeeccdedcbecddbecaeedccbcddacbeccdaaacbbebadedbecddabccbbcebddbcdcdabdbbceeebedcccbadeaadcbdeddadccaeaedbcceeedbcebabddedcbdabedeaedaabdceccbdbbdcbdcaccbcdbaeeeadeaadececabbeeddcaacddbbcaccadddcaabbebddbaabcccbebbebecdaacadeeedaecbebbbcddceebcbdeaacbcbcacdabacbcecedbbccbcbdadbcecebabdbbadaaeddbaddaaaceabaccacecaeeaaeebeaadecdbbcbcceebdcbeeccaaabebacdcecdeeddbbecaaedcbccabecbabdaaebbdcaeeccadeddacccecadddcddacabddeebdadeeddabcbaabceebebaceeeaabaaebdbdebeaacedcaeddcaddabdcbeeacaabddcdeaddccdaaceaaacaadbdabccdbaecabbbebcdbbaeabbbaebacddeabddaebadbcacbcccadeecbdeccccdceccedabaedaedcaeeaebedceacdcecdbaabdacaeadddbdacaabbaaacbdddebcdededeaabaaacbecacbdabccabaeccbaebdeaaaaccdcdbcdbccecabcecedbdededdddcdebcdaeceedcaadecebaebcaddbededadcbdedcdadddcdebdbcaedbddcdcbdaeedebedbddbcbaadbceeacecacccabaaceddbeadedcbeabbdeeeebacceacbacccbaebdddcddaebceaaadeeebbcdcbeeeadaedabacceeabedeeabbeeaaadadccddbbacbbdddabcaecbcadebcdeeeabcedadadaecbabceeabcaaacbeeeeaeabddccecadcdbdecbbdceeaddabbcbccbcecdcabdadddbaabceeaaaeeeaddbdcbbcadbaecaadabceeebecaaebecedecbeebbabcbcaccdeaabdaeeebbbdbdcbcceababacbcdceabbeaeeaabcdbdbcaebcdeebaedcdaecbcacdadcebdeadcdaedbdcdebcdcaebebdebadcebadccadceeeacdcccaeeebbbdedcbaedcccabedacbccdcdbdaedebaddbdbedbdabbccacdbadbbcbdbbcdcebbebeaabcdcecbddcdeddbccdecdbcdbbadbddceebdcbddeaabdbbebebdedecedcdaedadedecbdccbbabdbeeaaddcaecbedcbedcaeddcebbbceaacbbddccaebdaaeaacbdbcedeecadeadbeddabebbaecebaabdcabdaadbaaeecdcdedadbdcdcccbcabceabaacdbdbceabdacceeaaceabbcddaebebbeaecbcaeeeaeddacceaedeeabacdaecbccbecbdecedbbcdcbcadeadcaeedacddadaecdbdccdcdebedecbacaceebbcbbeddddecaddabecbbadaeecbadcebdeabcabcbbaacbcdccbeeeacadccaacadadbedbcbdeaabcceaabdbcdbcbedceceadbbddaadcecacdecbcdabbdaedabacebcbbddeaddccabcdbdcedeeeacddcebabceccbdbddcacdaaadbaeceaecebebcaddecaddccccecacacddcbdddcdceaaeeecdebceeeabdcccbaabbeadccbbbcdeadeebcbcbaeceedededbdcaccbccbbeecabebcdaabcdcadaeaeabdbbbddbddddcdabedcdacdcdccdcaebceabbbcdedbdbdadbbcdbbebebebeeeedccacbedbecdecbcdceedaacdcbdbccebddebdeccdedbecaeeaeaecaddeacbddbeaccdcacebaccbdaaeedbebbdebcaebceedcccaabccddccaebcaaeddcdaabbbdcbeddedddaddcecdecbccaebabddcdacaabecdaddabcadbaeebebeeacbceddacaadaacbdabceedbebcacdbceadcaeebebbaeacebcedcacdbbcdaebeadaacabceaeebdddcbdaedeeecbadcbcccccbaecaabadeeeebaacbaedbbbebecacedddeacededacddddeaeeebbaaeceaceebcdcaadcdaedbbccdaacecdddecbadceaeeaeadabbebaebccaabdaebeecdbbccebceaceaccecbabdebeaebadaddecbbcdddedeaaeebeacecabeedeaecabeceacdcaaaeaebecaeebcdebadeabbaadddcedccaedecbeccceacecdaecbdcebdcaccbaabbebdbaecbdcdebebbedabdebdccebbcadaeeccdbebaabebdeecdeaaeccaaedbdccddabbebacecdbebbeccccbadbdaeebadadbddedbceabbdcccdbbdddcdbabbebcaeddaacbcdedbcaceecdbeacebabedaabcadcdadbbbeccdcbeabdebedbceeeddddbebdcbbbecccbbbbacaddceceeeaebbdddcaccaadbdcdeaaececdbbabebeeddacccdabcabdcdeeccaebcaaedbcadcabbdcaeadbdacdbddbabcacdaddcdceaabaceaddbdcacaddeebabcbbeacdbddcecddadebbcedbeeaaaaedceadebedecdbdadbcbbceabadeaedadabdabdcbaeedbabdbcadcdecebabccaddecadebccddaedbdbeababddbdceedecbceebcbedbcbecedeaacbeeaeecacaeaeedeacbbbecedaaabdbcccbbebbdebbebccceecbddaacbcbdecadaedccdbdbaadebcbdacbcaacecacbecdbcbacaaebadbadecceebebaedddeabcbcccedabbcbcdbabeccaddbcceababaaecdabeddbebeaebdaaccdcbaceaaabeedaddbadceaacbabebcdaedbddcceabaeeccaaccaddbcecedeeeabdbdcacdbebaeaeecbbadecadadcacebcdadcbcddcbbbaecabadededaacadaedecccdbdeadedbccbedcebedecdabdabeeaabcbceaebeeaceaabbebcddaccacdcbeddaecebbbccaeaaedabaeedaacadabbdccbecbccabbbceaebdcdbdbcceeaddceadbeedecdcbdbacdbedaedcddbeaaacaebbecebbdadcecbcacaacebaaebeacebcbbeeeaddaebdaaacacaadadbcbbaadcaadcecedbecbbbacedbeaeeebccdeedaacbeeedbacbdbebeeceabddddcabdaaaeaabccbeadaacdcdbdbcdeeecebcbdbdbdddadcbbaeddcabbabcddccebaebbdeebdcccbaaaebadbaedbebcebeaeadeaeeaaaddccccacebdcabadddcaaebdeddadbcdecbaaedaaddbbddeddeaebdbcaacddbbcbecbebeddbaadbabccebbcdeacddbccaebbdcbabcdabdeccdeeaaadeceadabbddcacbcbdcbdcbadaccaabdbdcceadeacbcbacabdabeccbecdcadecadedabcaaadaaadcbeaceabedddcebdeedbaadbecceaddacbecadbebdebecaaabdebacedcbbcbdcbdbcbeddbaacadbbdebadadcddbcadacbdbadaebbaeeabdbcadcedaceccccaccabceddbedcaceeaebdabbbabbdadadbbdcdadecedbcadecbebcecdabcddbbcabdbcaddbabbbcacbdebaabbbccddbebdecbdccdcbbacbbeaaebeadedcabedcceeccbabbeddebcaeaebbebbbcddeedbacaedcdeeeabcbecdbdeaeeaaaabdcdcdaddddbbdaddacedcdeddbcdbeaacbcbdbceabedbbacdaacbadeccccebeadcdacbedcdcbccaaeaeebcaaebbdaeacaaedaccedeaacbbedcdceeebaadedaacebbecaadabacdbeebacbbccbbcdedcadbadecceabddaabcdcbabcddedbbdbcddbbebcaaaadecbaeaaccbceaadcacdeedeebecebaceedeecaddccdbeceaaaaabedababbdeccccabacdbdaeeddbceeaabaaedddcccbcadabeeeeaebacbbceddbdccaaddbceedbeedcdeddabebceccaaecaacbcdadeecaeeabdbdccbdbdbeebdacecceeebeeabceeaaaedcccabbaebacecebbdecbcbbadecbecdbaacaedbbbeebbeceebeeeedccaebbdbbeceaabeabcecedeedeabcbbebdecabadcdabcabcbbbeeccbdbebdcdecdcaaaebcacdbdacaaacaaddbdeaddbdcacdbecacddcebebabaabcdabebdbbddcaacddcbddedacbabbcbeebaccbbeacadeacbeacebbaaaaeceedcacedccadccaabcbcdeecabedaadbdaedaadeabbeaacbccbaacbecaeebbcebbdebdceedddbabcbeccdedaedbebcebecaaedccdbddeabeadbddedbddbeeabaadacaebbecbaddbabdeabddbddbaecadbbeddeebcbdedbcdbaaececcbbccbceecdcbabdaeaaabcbccdcedbeacebedeececddcededdbddccceacbacebddedeadcbbdebaccbccacedeeeeaecbedeacecaeccbdebeeebedeadbaebcbdddecacbbeddddcdcaecebcbccccdebcdedecddadadbcaeeddecbbddabccdddbdccabecacebacebadceadcbbdabcccecbcbbdedadbddbbabdeadabeebdeacdedceaeccbbebcdbbcabddcbdecccdacadbceadeabbdacddabbeddceccbaaadacaebaecdcbacccaedbaacdbecddbbacececaedeacccaeebbbdccbcbeabdeceaadaedabbabeaadeccdccceacaaacbcebeabcaebbabacdbadabcadaebaedcaabbeabcbcceccdeccbbcbbecaadedabaadcdccdddaeceeabaaacdbcadecdbcaeacbbbbbabcaeacddcacaddedebdebedbadbcaaabbbaccbbeeadcbbdbaeaaaedbaeeeccddeeedadbbbadabbdbebbeecdbbdabaaaddeedcacdbbcccbdeeadebbcdddcdbbddbaccebceecccaebbcbcbeacaabeaedbedacddceeeeecbecceddbabbebdcadbbbcdaacdebcecbbbdbbeabdaddcbbbbacdecedaadaadabadacbaebedbeadddadaaecbaccdadeeeaddbccdbceabeebecbcebeadabbacdebeeeaeeaaccdadccebadbaeccadbeebdacdeeabecddbcaceceebbaabceaaebdacbdaaceeccdddadaabecedcedaedaecbbdecbaddeeaaedadbdabceacdcbdaebaeeaebeedcbcebccddbceeabeabccdcadeddccabdabeadeabbdeaebbcdbadbaabbeedbdaeceeadeeebdaeebabbbddcbedbcecbebacdeeddbddaaaaabecbbeebccddbdcedabdedbadeeedbebbaebaccdddccbebcbdcebecdccadedbeecddecadacadbdbcdcaeedeadaebcbaabdddecbcdeddcedbeeaebcbcacbbbbccacecbeeadbaaccbabcaaaaebbcaccdcdeccaeaedceeabeeeaeeacacbccaeaccddccdecebacbaeeeebebeddeabddbabcebcedbdacebadbbbccdccedbddceeecebcbacbcbaeebbaaaccacbaabeaabbccaabebbebcbccecbbbccaccdadbebbebaedacadbdcceebdaaebddaabccbeccdbbdddbbcdadceccbaddbcaedcecdbbabcbcdbbaacbcedccbbcbadbbaeaaeebadbcacebdddbcdadcbdbbcbbaeeabecabacedadccabcdaaedcbcebeeaeecbbdeacacaababcaaedbebdacddaeaecbdcaebdaddcbcddbacbbcccabeacbeebeccddeaedeaedbdaccdcebdbcbacbadacdbaaaecaabececcdbdcababedaedacbeaaceacdecbdacdadcdadcdecdeadbbbcebabacdbceabbaebedcbbdbccdbabeebbbaccbcadbdcdbabebcceeabbdeacadebbdbedbaccaabaaacdddbacdcecedacebaaaebacabbebecccdbccedcadcccedccddadbdbeacbbeedeceddeadcbcbbebbcadccabcbccbbcbacebdbabccccbaddeadcaabeecdaadeaedecedbbbbadececcceecaaacbdddbebdceeecbddadbacebaacadbccadbaaaaeebdeedbdbbecaabccdeaccddbbdebdbabbabcccdabcdadcaadcbacaddbdeeebebeaddebdcbdaddcccccccbaebeebbbbdeedccdddcedcbabdaccdcbcbccecacddbacbcabbacbcdaeacaaeeedaeeedadcdcacacaeaecdddaecadbdcbdeeaabdbaddbbdeacbcbbedcebeeabeabceaebeabbeadeeacaddaeecbddbebceecbeedbcebcedadcbbdcecebcadbeebcdbddbecaecebbdacbadacdecddadacdcbbeabcadededabceecdadbbabacceabbcecbacbaecdbbcbbecdacbecbcbcddaabebebadddeabcdabdabbebdadbecacebaeeccbddbbebaddadcdbaebcdebdbedaeeaeedcadaabddbbedacbaabacbcadceecacbabcdbeabdeacbdabeaabbdeaadecccecddccaaebebadbcbdddeeecacdecbdeadbedecbbeacadedddecbddaabcbdadebcaeacccddeeddbdbabbcabbdecdddbcdddaceaabddacdccacecacdeaabededcddeeecbedceaaacdcecaaaeecbbedccbbbbcccaadeebeecaedadcceedebdabeedbbddeeadcdebadebbbaeaedcddebcdcdbddaabeaedbeeccdaeadeccadbedecacaacbbbcbdddeceadacaecacccaacbdcccbbcbabeeeaadecddeedcdaccdcdcaedeabebdeedeccdcaaddccbcaeeddcaacaeadccebcdabcbdcbaebaaaddbcccedcaaceaccbcdabcdadecbdaeeeaeeabaeabbdbbdbdceadceaeaddbdeeecdaceedaadcbddacebdeecabddcddaddccdbabcabeaedebecdbbacbeeccdababaacbdcbdaddebabcdcedebceaadebeddecaabceaccaecddabedbdddbccdccaadbbbcdebbbbabdbceaacaeabdacabacbaaaeabdadbccccacdedeceebecdaaaebbaebccccdabcabbbddccbbcaecbddaabbcbbaaeadbbcbcdeadaccedcbbdddbdddacddaedbceeaaeecbcdbacddbdceddedebebbbbddcdbeeeddeaddabeacabbeddaeeddeaabaaebdcaabcbbcddcccbcacbababaaaccdadbecedddcddeeaaeaadcaeabdaccbebbbcaceebeabaacddebccdbaeaabcdddbdaeacaceeaaaabdcbcebdbeceeebecaccceabddbddaceebecbaecdeaeddaacaacadacabdebdebeeaabaaaebbccbabbbababeaacdbaabaaceaebbecceabbebaaacdadbcececababdadadabdeedcaedbeceedaecbddceeeddbdcbdacebbdbeadaaeaddceeeceddadccbeccaaccdceadcbbbedddacaabdbbadbbceecbbacdbeabcaedceeddeadccbcdecdcbaabdcaebadceeddecbccececdabbaebdceabddabbeaceccaddaebaeceedeaebadeddaecccdddcaccccbaaddcadbbbdaedbabacaeceacaddbabcacdcbebeaacabdbaeadcbbdeeebeadcdeccccceeaeceeecabcaebcbdeeaddcabbbbddbaeabecddcdaeadeeaccbdbddcccbaccededdaabecadcbbaeaaebdecdbcddebacabcabeecabeccbadbcccddcbeaebbaabcaecbbdcdbcdcdbcddeeeccbdbcdcccbcadcbdaceecdecedaaacdadaaadbbdeddcdbcdbadedeabcedbdaaebccaadcbebdcaadeddcbabdedecdbeccdcbacaaaceebaeeccdedeeabaaddaacddecdbedddbcaeebcaacaedebadbdbcdbdebdeeaabdaebeeaeaeaeccdecdcdcbcedbadeddbdbadbdcadbcccbeaaecdabccbedccbacdcccdaecabcabceaeebaebaeeacceedcbcdabaadbecabbceeaadaacabdaebcdcacdcccacdacdccbbebeedcddbadcbbeecacdadccadebaedcabbddcbbceadbdbaadecdbabbadaadbcaebaecddcbdaceccbdeeaebacaddceddcdeecaccaccdabccbedaebcacdddacbdaababaeeecabccdedbdecddeaaacdbecdcbaeabeeceeceebbbdaabaddbaeaabdcaedaeeacbbcbbcbbdccbbccbeceebaccdabdaccadcdaabbdeeddbaccabdbdbaeeddcccbecaeadadadaebcdbccaeddbaddbebbbbdeeeaccebeecebbabcccccccaebbadadecadcdabbddadcaeddcabbddeccbdecaecbaedcadedbbdcbecdbadcbeebbdcccabedaeaecaeedecdbbcccbaaecbdddbadccabcdddeebebaecdddaceaeeccdeabdbddccbeeddecbebbacbdecbacbdcbdbaebbadcebebdcdaaaaebeeeebcaabaeadabdbedabaaabdeeeccaeacbdeebbcdacedbbebdcedacdaebdaecbcabbecddbebcbedbaeddebebdaacdddabadaddabbdbaeaecabbabaebcbcebbcdbcadccaaeebcccbaaceaeceeedcaedacaaaaadceedbceeeecaebceaeedeccecbacdbccacadcbbdcddecdbaceabdccdaababcacdbdbcabcddeebdaceaaccaebbbcdbaebceddeccdadeecdaaccdceedacceacacddebdcdcceccacaabdaedaaccebdadacdcabbdcedaacabcbdeeebcaabcdddcdbcddbaabcbcbcbeeeebebcedadeaaeeaeabbbaebaeddeabccbdaecedcbacdbecdcbbccbaadcecdebdbaaadaaedeecddbebacbebadccbaeebbdedbcdebbcdcbeeadebbeaceeeeeeceebdbdaddbecceabdddbabdcccabaddaebbdebdbaeabeaaaebdbabaabecbceaddaddbbdcebdbdbdadbdadeeeccbedcebaddbebbddceccdbdaccbddaabddbeddacdbbdbebeeddbecccdbddeeeabbaeddecdaecdbacacaaaedbecadcebaeaebbbcdbddaaebcecacbccbccabcaabbddeeccbdedcdeceeacadacbaaabedccadbeeaceecbceeaedeceebbccdccdddebbdbecddcdbabddeecbdeabccdadbabeddeaddeccbbaadbabaddaabaabbbaeedbddabacaabaabedebabdbcbbbccedeadaedceaebedaeecdabeeccdabdbdaddbeddceaaeaddbecbdecbceaacebbbcdedcbceadbddaaccddaebbeabddebbaedbbbedccbebbcceeeccbcecdedaeeeadccdeceeababaacbbeddbacbcbabaedacacdaddadaddbdebecceeabadbbaedbbccdbcedeecedbabdedddcdaededbddeeadbcccceeeacbdceddbccbaddaddaaedbadcbaaadbcddaccecbeadeaeebbdbbebaeccbbebdeecacadcaacacabadecddbdacbdcdeeedecddbeeddedbddebaccebaebecddbbeebabedbbaadeabbdbcdaccedcabaeeebbbcbdcacbabdacaebeceacaeacbdcadbedcbeddaaaeebacbccbeaaabadeaedaceeddddceabcbbeecaaebadededceacabcebedededacedcdceeddabacdcebeabececeddbeebbebdddddbeabaaacbddddeabdbcdecacccaadacdddeabedecddcedaacadbbdaaccadacbbddddebbabcacebedecedbececaebdbdddcdecaeccebeadbddbcebaaeacecccadeabbdbdbebeedddbbacaeaeaaadbbdccecaadeadabdabeeebbedaaedeabaabaaebebacceabaceabdddaecdbeecbbddacacdadcaeedcdceeecdadcbddaddeaddbcdccdcacdabceeaeacdcceeacdbaecbebebbcddacdbbadeeadabadddecedebcddcadaceedebbacddbcdacebedaabadeddbbeebedcedadcbdcabbecebbccecccabcbadacebeeabdadbcbecbbceaeeecaebbbbcaebeebaaacbbedabadeeacbcbcbccaeadcdbdbbbbaacbacebbdacbabdcebcaedabdaeaddaccdecaeddebabcbcdabccbbbbbcabbdccbaabdaebebdedebdbaaaceabcaebdbcdbdbacccadeabbbadcacbdedcececcdbcbecbcbbccbdabcbaccbacdbeccbaaedaadcbdcccbbbdcbeeddcdecaddbbdbeedbdcdcaacbebbadeabbaeeacbddebbeabcaecbcdccdebaddcbbaeeecbceccbbcddaececececeaadaaecbdedcdbebdcccbdbebbdaebeaaacccecdbcddeabbcdaddabadadabaaadebbaacddaebebeecdededebdcbabacbdcbaaddcceccbaabbbcbcdaeaaeccbaddbababeebdedbdbbbcbdecdeeebaddabadbcaabcbecaacaebaeadddbbaadcaaebdaacedeeaadeddeecdaedcadcaeecadababdcdbdddeedcdbedbbdaaaaceeeebbbdbdebeddbeebceebbbdcedabdedeecbdebabcaadcecccaceebdeaebaddebacbcbdaaecbdeabcedcbabdbbeedaebcdbcdcbeaceeacdacbadebddbcceeccbbaddcbabdcbeedbbebadaebddecdbeaeabeaceedacaebadabadaabdeccccdbbadcabeabbcbacddbbbaccebbbecceebceadcdbcdbbbeeddabeeeebaaacbeceedddbeceeeccdaaaedddaceaebaceaaaeedbdceedccebbcaabaccbbebbbebcbacaecedceadbdbaccbaaaadcedbabdadeabbccecdaddeccdaeaaccecedebbbaeeddecacbacecbeeaaeecabcdceecdbacaebbdceeadadebbbebadbdcbbbcaedecceaecdebeebacbaabcedecdddebbcbbcbcaebeaeadbdbaebaddedcdcbdbcdedbbdddadccecedaaaeaeaaddacbacebebedaaeececcaeceeebcbacbabcdcdecccbebaddacdeeddebbeeebccaadabbebdbeecaadeeeeabbbabcceabeacdebbcadcaaaeeacbdeeeaedbdaeecbcbbebbbbbbbbaddadbcacdbeadacbbdbabbcbcbccadbdbbddeedadcbaaeebbebdcaaaaedaeaebbaaadcacddaedbbcaaaabeadadbacaccebeddbcdacbcddabccddabcdcdcdeaabecabbbeaabcbecbdbdccbacdeeadddbdaaedbdebccdabcaccadbadcdcdcebdccdaadceeecbadcdccacbdbcecdccdcbaebeccacedbbccdcbdecaadeaacdabdcbacbccadbeddacaebaeaaaaccdbeabeaaedbabeeadecbcdaacdedddcaabceceeaeabdaecbebceddbeeebdeaedcdaacababbddddaebbbeacbacdbbbebbbecbebdbaecaaabaebcdeedcddcdbdcdaeaddddbbbbecebcdcccdaeedadbbadbaedaddddbeabddabdddddacdeaaccadbcdaeddcdceaaeaebcaeaaabbacdbecabbeacdedaccaaeebbbacddccabeceabddbabcceeeaccbbdbddedbcdaecdaebaabbddcebeaabbacddccaededddadbeaabcaedeacccdbcceedbececaedccbccebcadddbbdaaeaedadcbaccdbbbcdaaddedbdcddeecbacadaabcbdceeddcacbceabadbdceadaaeccabcadadacacaccceaacddbecbbbbcacaaaddceebadbdeaccddceacdaaebedaccbeeedcdaeaeacacddaacdeebadbbadacedeebbadcdceeadabeccaccdbcbaddccbeeeebdecbeeaabaecbaadedddaecbadadbcbaabcedacbeebbedebedbdccdddceadeabacadeedddaaedeabddddbbccacbecdccdbcccddddeeaceabcceababcbccbdaaebacabbbaddeddcecbeaabaadedbeedbcdeaedaebeedaacadecbbbcbbcaaeececebccaeccaccddbcecdeccababaeebdeaabcaeeaeeddcbeadbddeecceaaabecdbbeecccaabdbadabcaeceeccbaaaabbebedbedeabddebdecbcaaeaabbadedbeeadedbaecaaeedebceddbdbbcccebeacaeddaaeabbabbebbeaacbcbdbbcdedcabddecadabbcdeedeccaccecbabdcabccadddadaadcebddeabaddeaaaccbbdcdadebbdcadbcededbaacdabdbbdedbdceebdcaeacbdbeecadcccbbedbcecccddeeecccccbbddabcdacceeceaccceaddeaadecadabaceeaebeaeecebedeebecdbdcebacccdcbecceabddccedadbbadcbbabaabdebebdebbdeeadaedcabebeddbbacdcecdaebbdbadeddabcdbbccdebabcdebabcebdccaadaadcbcaebeeeeaebbaaaaabcaeaccecdeecaadcccdbcdaaecdacbdedddcdcdbadadbeacddcdcdaaeedbaabeabedecacdccbdababacdaccbcaddebecaacddbeadaedbdebcbebdabcbcababaccebedbbdcbbeebbacebaaccebeebcebcddbdddeebbeeddaebdeaddbddcbaaccccacddbbbabecbbbecbadccbcebceabcceaaabdaaadcbebabcaaadaaeabebeaecdcbdbadedbccddaacabacbeeaececcebbbedccebacadeddaaadadcbeeaeadddaceeddcaacdcebdecebacceeaabdbeebccdaccbcddcaeaaeaacaeeaacdacabdcaddedcdabdcebcdeacccbebdaeacecabaedacbececbdbcceccbaebecaadaccacdbcecceaeacebeadabebebadaeeccdeebaaaaceaebccdbbcacdadbecedcdadeaabccdbeeaeeabbeaaebaedbdacebcaaccbdabceaddbeaebbbdddaecacacacccaadcbcececeaeaeaacccdedaccdacbbcbbccabbadcbddddaededcacaabbacbadcaddaacacdadebbbbabebbdcbccbcaaeecbbeadcbeedbdeddcaccddcacedbcdeceeabdcdddeebcceeebedeebbbcebbddcbdbedbcdbebbcaccbddbacbbcaeceadbebeddbccccaaeecaaabcdeddcbdedbbeabcebbbdbebeecaaadedabbedccccabcbbdabbceeddedeabccdaddcbaececdeacbbabaadddebebdcdaddcacadcacaddcacaebcaadeabeeaaaceceacdaaacddadebdcdeaebeacdbbccadbabebddbcaaeacdaebcdbaacaabadaecddcaaababbdadcaeeeddaadacbbebceeedddeebeddbcdebddecaacbaaaebbebcbddaeeedbaacdbacadbecabeecabdeacaaedbbebbeccedececabeeeeaedbabeaccbecccebcaabaadadabcbbeecadccaebdceccebbcdcebbabccdddcbbddddaadadeedecabbaceedcbcaecabbcddeeeebebbdbdbbbadebccacebaeeccaeebdbddaeeebdbecdbcaddbbaeccaccaebecbaebacadadaccbacbddcdedccccdeceaadadecbcaadeebecbbeabcbeadeebdababcdebbcedabeacccbdbbadccbdabbabadcccaaaeaccbaacaedcccbeaecebeeadbbadccbcecdbaedccbbecacebbbcedcecbaceaebbcaccddcaddaebcccedadcedeabbceacbeceacadddccabbedbeddcccabddebeeebccbdbcbbeccbabeedcbedcecdcaaceceabcbbdddcaeaaeddebbdebcbdebbbceaceaacedaadaaedeabbaaaccdbcceaeecbbeccabbabdbececeabadbbbacbebdeeaaebaaedbeeadaecbeedbcbcbbceebdcaabdaeaabacadeecddddbcbeaedaeccbabbbccaaeadaaaaadbebcdbeebccdbabbbeddaaccdacaecebcedcbdbececeecbeddeebaaacebbcdacbecabacbceadebeaaaedabedeeadaaebeaabecadcdecbebbeddacdaeebbbeeaabbcdacbdbeaceebddcbbddecdebaeaaadedbdedadadccaabbeccdbedaabbdecabcbbaccecccaebbeeabecceebaabdddedcccebceacdddacdcceabdbaeaceeabeccdaceebabcbecaccdbdadccbdeecbbcdabdabeabddebccadbdcbccbdadecacbdacebbdbabaeebdcabecbcbbbeaeaeadbdaddabcbbbecabbaaacbdebabaeaeddbeaacaeddbdebedcddcdcbcaecdecdcbdbbcecbdaeaecebdecacadeaaeebaabdbecccdeeccdadadcbdeabdbcaddcabdbccdeadbdeedcbecebdabacaebddceaadbcaaaedbdbebcacecaddeddbcdbaddceaeaeeaeeccdebcbedbeeedecdcecdbabcdcdbacbbbedadbcdedeadedddaceaebecbcddddeebaedebddeeeceddebaecdbaeedeececaaddbeeedbeddadcaeecdccebccbcbceabeeebcdcebedebccaebbcdbeaeeedeadecbadccbcadcbddeeaeddadddbccdeeaaaebecadbcaceaabeebbdeadacbbdeaeacdacdbeaceadabedbedbdbbaacaacadeccedeaeeaeabedabcdaddbbadedaedbecbddbecaaaeadeecddebcedecacedbabddaeaadceacbcccddddcedcecabebecbcedaadabdbedbdaabedbaaeeacadddeeadaeaadbaebabecddbabeededcddccaecebedcaedcbbbccaeaedaaacebbecbedbcecbaedbdeddbcbbbcdbbcedcaadaabbaaacabacaadbcabdedacaaeaecaddcebadbeacaecbdddbeabceddbebdecaaabedddaccecebdbdbccaaaeaaceadaedeecbbaacecdececaeaecbcabdcdaebeebcbbedbdbeadcccadcbdabaddbbcddaceebebabdebeebbecceaccedbecebaaadeaacbdcaeacceedeebbaeadadeddccddbebecbdeeccdeddedaddddcaedccddedbcccdaddebbccdbadbdddedcaeecddabbecebcdcaaeaadebcebebaabdeeabbcadaaeededdaadbcdbbaaaaecebacbdadbdbaadaeaaddbcdceebcabcdddcbdceebcbcdcbdccbcebcaabcdbaddeacaacdbeecdeeecbdadbddaeaccdecbeecbdcdeeeeabcedacdecedaaecddadbebaedbcecabdddabebaecbcadcabeeaabbaadedacdcbdcbdaadadacaaedccebadccbeebabbeebdaacddacbcacaccdcdabbddaccecaeceaedeabaadbddacdbbdceeeadbaacdcdeaeebaaddbbbacbeaebbbcdceaabeecaabbedeaecbbaaaabebcbcddecadddcedeacbbdaceeabecbeecebbadaedebabcdccddcbdddbdcebbcdcedcbcdeaddbdbeccdcaaceaeeecbdbadceadeadbaebbbaeadeeedabcccddedccbabaadbdacabadacddeeabbdbcaccdbccbcedaccbdedaddccbcdebbedceaebedbdcbddebcdcbdebbdaccdecdccbdeeaacdacccdadcaadbcbbecbcdcbddaabeecddeeecabedbdbeccabcaeddcbddcecbeebcdebdccbcbabbabbcdadababbcaedcbabdcbebdcbdabdebbaeedeeddadbccebdacdaedbdbbdaccebedbbcbddeabcbddcadcededddcaebeddbdbcbaedcccdcbebeddaddbdbdacecbbaccccbeccdecbccbcbbdcdebebebaccecaacbbbdccadbedacbdaceadbcbbcecabaeccaacedacbbceceabddacdbedabbebddbddedaedacaeecbdbeeccbbadbebaeaeabebcaaccbadbeaeeccccbcadcccbcbbbcbdadbcbacaaacbdbdaecebeeedbcabbdeebebcaeaecdecccedaebdecddcedbabcddceeddddddcaeeaceeadbbabbadadbaedeebbcbbbaeadacbcecbdecbdddceaedbdbccadbcaddaaadaabbcbcdddcddacdbedddeeaccddceeedbbceeedadccdbebebbadbdecdcddbcddceeecbdecdabeadaabadecdcaacaddecccedbeadbccaaedacaadebbbcacaedddbbadaedeceddbadacccdbcedadacccbcabadaabbcadccbbcaeccdedeceeadebedacbeccdebabbabbbeddcebabcaceaedebccabcedcdadedcadcedcbaaeccebccbbddbacaabdbbddcbedddeebdcbcdbbecbbecdeabedabbcbddaddebcbdbceabdacddbbeabdbcebaabcedccbebbbcedecbacddccbaeecececddabacaadabcbbcbcabbdeeebbedaceceeaddadccadeccdcedecdaceaabebecebdcbbebcaeeededbcdeaeddbbdcdadabceecbbceebcceadacbedadadbdccabdeccaddadceeacaddaabbbbeacabceceaeecbacdacaeaeacacdcedddabecedbdccbebabcbeaeadeddecbddddbdbdcbeabeecdeaddbeaeceeabaeebebcbccacddbeaebbecbdadebeaceedeebdbbcaaedcbaeedacdceeecdeddeadbedeaedcdcdccbecbebeeedbabbedadcccdbddebebabdabeadbbbaedceadebcbcadabadebdadeeeacbebaebabedcbbdddebdeacedeecdaebecbeaeedeaaecaaaadeeccacaabdaadedebcdabeeceebbedceaceeeeacadaeeeeeddeaddcdcbddbddcddcccbbccaebcabaedbbdabcddebbbeaecdbccaeacecbadbacccdeebccdddbbddabcadbeedddbacadcaedddebcacecbdabbaadbbcaddadddadbcedbeecbddedcbadeaaacbcacbacbcdabcaaaddabbeaebbadebccbdbdabdcdbbdcedcdebbbcadebcaadbaaccbeabcadceedcacbadbdabedbaccccdddebabcdcdbdcaadaaacbdcbedbecbabbccccecdcbdecbccedabbbcbcdaaddabdadcebddcaceabaccebaeacebeddaccabcaebdaaecbbcbcabedecdccabdbeaeacaedebceeaaccaabbadeacabaabaddbaedabbdecedebaecceaaeceecedebecbbdccadcaeedbebbacddbbbdaceacabeacedbdccbaaabcdcaaeeddadccdbdbadeabbbecdbadaccaaadbeadacdcccdebbdaabbcbcceabccbdabadbacaeeccedecbcdadbcabdeaadadeaeedecdecebceaebadcaeacddbdaccdcbedbceddcaadbbdbbbccecaaebedddeccbcecdbbebecedccdeeaccaccaaabbcbaddcdeddbedbebedbdcbccadecccdeccbbecbebcbdeaacebbbecaccdeaeadccbbeeddceacbbabbeaceddcbadaacdbdccdebeebccecbccbcdbebaacdabaebadecacbaecbccbeedebeebdaccdbedbbeaecdcbadcacadaaaeddadceacbdeebbebeacbbedbbecddcedcedddebdadadceabbdacddbaabcdbdaedbacdeddebcbacdaacaccdbedcdadeaaddcaebaecaedcbaebdcdbaabeaecddadcceedbaeccaaaeedeecdcaeeeadebacddacdcaaaabedbccebddebdadbdcbdddabceebcebececceccaeaeddebcaecdbecacbdbecdbeacecaeccdbdcdbacbadeeecdaedeecaeebececbeddeacaecdaabcddbaacdacddadcdddaedddeceadddececeaeeddedabeadcebeadaadeeebbbabacaaeaebbdaeeabadbcedcecbaecdecbdbeecabbdedecabeaaececbbceebdeebaeddcbabeeecaadcdbcadcecadceecbebcebbbbaabecedcccddeeabedbdeddaaadaadbcacdabdddaedcaebadecedabbdddebdcaccebbdedeccbbeabcecccabacbccbeccebbeeceebaeaaaaaeababddeeeaecbecbcbaaedeaeaccacebdeceacaeedbaecbccaacdeacacebaadcbaaddebacddaaacebeaeccdeececcdcbeeddaccacdadacacbcacbeaaabcdedacbdedccecdeddaceacaeabecbcbdadccedebeabebcaecbccebacccdaadebccddbbbeacecdebaebcacabedccabcbebdbbcedebcdbdadcdbebeedecbadeececabeaebdcaaceebbaceceaededabbeacdbcddceabeaacaaeadcecbccceeebcacbdebceabcdedebccdcbcccadccdadddbccadabaabbbdbdceacdbebeeccaccceaebabdcbbaeaaabdbbbabdbcddddbdddddcaacccacceebbceaccaddcdddabcbbaeccbbcdceddabcecbdcebbdcebebbdebeccbdaccdeecebcccedccdebbbbecabadbabaeeeedceeaabeebeebbdcdacdaeddabbebebdbcebcebcdcceaeecccdbedebadedabdedcbbbdddbebbceececdaebcbcebaaaacdaacbeeecedabbeceecbcdedebebbadddbaedadaaababbacbbebdeddacbddabaabbdbeadbbbccdeeeabeedecbbddeedebccecebcaeebecdcdabbecbebceabacbaeaaccddcdaeadceeaaadadbdeabddbccacaeedeaeabaedbadaaadadaacbeddbcececaaddaaeaacddddbdeeaebaccababddecabbdcaddbeaeaaaadaadcacecadcdbbeaedececbeadadcdeecccadbdabdeaacbaeecebbeaeacccaceedecaaeeddaaddccbbaecadaecedbbcccbbebdccbdceceebebccbeadeaaaedacbcbedaaddcedeabdbaddccabeadebdaacacbdaebaebbecbbbdbdccdbdedbeaeeddcdaeceacddbacbbbadabbdcbcbaeeecaadabddaabdedbcbbbdddbaeeeabbdbcbbedbcaebcdbcedcbacddbbcbcaabceaddaadeeabdeadedcdaddccadbddbedbdbddcbcadaeedbdcbadcecdabaabeeabcbdaacdecbdadabaacdceaaaabbaeaedabbaaeecdbbeceaddddebddeecaeddacdedceedcacadbbcceddbabdbdbaecdaaeecbbebbcacbadbdcddceecadadccdadadebeabedcbbeebdedeeabedccebbbdaabedbcebcdbdcedceaccdcbbbbbbaaebcdaececaacccaccebadbeabdecdbcaeacdcaecbceaecddcbeadebbdcbdbaaacbddcdadcdaadecabacdaadcceaddcddeaaaceaeceddddadaecaeaacaddaecceacddeeddabdabadeeaaaddcccaedaacebcddabceadddbaaceedbceeaaeabaeeabdadbbaadaedebaeccbabcacdaadcddbebbdedaeeeeabedebaeabebcdcbcdedaaaeecbdaabeceaebaecdbaaceadcdadaeebbebbabdabecbeeceeecaabceaceaadaaabdbbdadcadedecbbedeeadbaaecedcdbcbdcdedcacdedcecbddeaebedbdbbeabbeebdcbaaeeaebecdcabbcaddabbabedbadecdebebebeacabbeeeabcbcebeabaeeddbadaebcbecdcceacabdcbededabbeabeadcddddaecbdaecccddcbdaaabcdbccedcaeebdbdbaabccebbebbebdbdccacaccabbaecbdedddebeceaddeebbdcbedcaeaaeedbbcddedcbbeeabebccabcbedebacccaaebbadbedccececdcbadcbceebbbbcbddadceedeabecdebdcbaaeececbdcbbeccbcacecbbaabcceedceeddcebdeeeccbaecbcdbccceadbaceaaaadebbeeedeaddbcacebdaabacbebaabeedaaecbeddcaacbbaeccccceaaaeabcdaeaabcecacdbadcaebeeaecdbaddbaeaacddeacbbadbecdebababcbdcecececbdedcceccdccaeabcbabbbbcbcabcdaeeebccacadcbdcaacaabbdaeedaecebdeddcabcddedbbeecdceccdadbecabcadbbbccbedaaeaecededeaccdbdbccacdccdaaadadaccbbaddeaabedddeacdbbadbaddcdcecaddeddebdddbadddceaabdedbbddbacddaecdeaccecedbedbcdbdececdebdcaddcbdcdcebcccaadeceecadcbadcdcacdaaacaabeebbccbabbbdebcededbcadcaabcacbaeededbeaecaceedcceebbcddcbdaccbddbaaabcbaebebbdcaebaecbbcdceeaadaedcbcbebbcdbabdbbbdbcdcbdcbdccaaeecdddcaebddaababdaeeecadeceeddeadcaeaacecceaaadaaaaebaaeaecaeaeeabebdbbdbcadbeacbacadddccdedbcdacbbeddcaddaeadaabaeccccabdbcdbcccdbcaebdbbbabcebddebcebcccabdacdeccedcacbbcccaabadbbbbdcaaeadcbaeebdeaeaccddacbeabaadedcddebcedbdecdadaeeacaaacdddbecadbeabbebbbaadecebadccdbebccaceccabeeeccacadbcdabaaaecabcaedbdabccbaeebabdcbacadaacdbcbbccdeedcabcadbbbdcccacdcebbeabccbcccecbeabbeddeecdbadacdcabdccdcbcaaddcbcabbdbdbeebabeaaccdcecbaeaeaededacebdbdebbccecbddabeacdbddbaaabbcdbcddeecacbbdabbbedcdeebbdaaaaaacbbbcaeedcbcddcdedceedddcdaaccdbdabcdeeeecbecccaecdaebeeaaceeecdedacddacacbeabaecbbcbdaaeaccedacaeaadcceccaebcabbddcacdeabbeeaddbddacaaaeceeeccbbbbbdcabbbdbddbaeeadbeacaadcdbbdbececedaedbcadedccbcbcbddaeebadeaeaccadbaebbacbdedaaccbcbacbaeeabcccbbcbabedeeeaecbcabdccbadcaddeadbebcdaceabbeecdeaecbbabcdbadbbbecdbdeabdcdaadaebaeccdaaaccdccacecbdadbdbdbdaceeaaebdedecbcdeacbbbadcdcddebeaeebabbdacddcdbaabdaeaeeeececdccdbcaedadadebdaebcddcdecebaadeebeedbccbdabbdccadabeeeaceeceeccebddbcadaaaedebdedcbeeebadacdbebdcecdcdbaccdbeebaaaaeeedbddbedbbceeabaadbddecebdaccbebdcccedabddadcbdaceddddaceccaccdcabeccebebcccbbeabbecabdeebcaebcaeddaacbeadedcbdecaaaecabbcabceabdbccdaebcadabdaedbeddddbeecabaecdcabdbeccbaecdcddeedeeeedecdddaeecaedcddcddccaeadddbdaebdecbdbabeecebdacaabeeebbbbcbaadbbcebdedeacaebacaaecaeeecdeedbeebdacbcbcebbbeecbbaabebcceaeccdecdeaabaacdccdedcecedebeeebbbceadbbcaeeeaebadebcacbdeaeaaeeeecdeabdddddcddaeddedacbcbeadaedaadacbcbebdabdecdebabcdcaeecbbaaccdbcccececaececcbcedddeceaedecaacbcebdddabcaceeedcdebbcbcacbcaedaedbdcedaecadabeebcedcccbebbbaddbddcaacbaeeeadedcaebaaeddedaceaaacdaeeaeccecdcddcabdcaabbecdadccdbdbbceaabccdeacbcdeabadbeccebdbaccaaddcecadaceaedbbabccbcebaccbceadecbecbebaabdeccccbdedebbcdacaebeababceeecddcacbcbaacbcabedaadaeeadcdbbaaceadaeecabcebabccebaddeacdabdcccabcecaedecbdbcebcbcbccaacaaeddaaacdecbcbdabdaecadcacbbacbbdaeedeebbeeaedbadcaeeabaadbacbdcecddbaacbeebbcdeceddcecdabdcdaebcaddabdbdcaedeeabecbcdacddeeaddaaeacaabcaceaedaccbbebeecbcaacbcbeadbcdededacecddececddcaedcdbbeebcbbcbeabecddcedcaaececbbcceaedbcebdbceebecacccadacaaeceeeccacdbcbebcceebacdeedbbcbdaabdacbbdcacacdeebcbabcbdbaecededabbbbecbbaeaadcbaceecadecdececeadacaecaabbddeaddeeaeeaeceeabbddbdeebbcecdedbcedecaedddcbdeeebacaebccacbeeaaeeeccbdbbdbcbbceecccceabeebaebebbbdcbdcebdbeebddddaabebdadadaedabcedecccacccbbaceeecbaeaebdcdcbeebdcceddcabcacabebdbcebddaedaadbedbceecadadbacdcdcaeaccedadebdbdbaeddcedececcbcecadadddccceebababbabaebbcaedeecccbadadbeadbbaecbceecddbcccabebddeebdeecceebddbccaeccbecbbacbdeededcabceeddcecaebdcdaadabebeeaadabeedecbbabeaebaacacdcabaccceadadecebbddabcebecdbdeceddbedaedcadbdceccdeceecebedcabebeddcdaddeecccadbdebaebddbbbbebecbdaacabccbddbaaeaaddadcdbdacaaecabaeceeaebacbdcbbdeedcaaacdbdacbeecbdbcaaadedecaaedaecdbebbacebbebeccddbeadaedebaaadbdeedeebbadbdabddbbddedbecbccabaabdacbcdeadcbebedcdaabdbbcbcdbccecdacaccacdeedeaecaadaddbecaeadaebdebdcbceedededbeeccadbceacddcadcbcabeaeaadbeeacdedcaadeaaaaebadaccacdaadeacbeecbabdadaebbceddbdeccdaecdddcdacedeabceaadaacbceecaecbebdbdaeaaeddbedbbebdeaeeeeebbbcbbededebbecedaebbbadaaaaecaedddcbebdcebaceaaddedbceadaddbbdceccccdccdcaadeedaaaebbdcccacabcdbaebaddadecaaadadcddddecabbacbbcdbeaadbcadacbaaeeeadaddbeddbbcdedbecbecbbeedbadedbbbeadeeeaababdaeaceaeeacdaaedbaeeaeecedacddaedcacebeeaebcacdbaddbcebdbcdbeedbcceeaaeedacadedecacdedcdcddeebaabcbdbbccabdeeddaeabecadeabeddedaceceaccbebdcceebebdcecddcecedbaaccccdcdadcccccabdccdcdcbababeeaabecdeaaebabcbcbecedaebbcebeeaaeaeeaaaddebcdccbacacbbbbedbcbadeaadadaeeaabbeddaadbabadecacdcdaacbcadabcceaddcdcdcccddcbddcebbdaedcabeadedccadbdcdbdaecddeadbbbcbaecadebbdcbcbebbcdaceeaacadbeedbadecdbaaaeccbbcccaaebabebbbbeaaacbcbadaebcdbddededceaecaecbabaacbaddddbabebdaaeadadadceadceceaccbdbbeaaaedeeebccdcccbebcebbbcbabcccdcebacbcdacdcdacedebeaeedddcdbeebcaabcecacbbcecaecddcdadadbdaccbdbbbaebaebabdaedbbacabbedcbeaedcdcddedcddaeabdabaebebbacecccbeedabaebecceeabcecaeabceaedeaabdeadbabadeccabbaeadccaebcbcabbeedeaaeabbddcbbbacceebdaedeecebceccebaeabbeabbdcdeacaeaecabbbdcdccbecdaeabeedcccdbcdcedbebdcdbeabecdbebdcccadbbadcadbddcddadeeacebedacaeeaabebcededcbdaacaabaeccdeedecaadaceeeeeacbaaebdddbcaedbeeecbeaeecdeddaabadbebdbabdceecdccabbdcdbcadbbbcccabedbccdcacaabbcaadcadbcdaabceeabbdedcbdaadaacabddaaaeeedbacacceecabcaebdaceeabeeadaeadeeadaddabbeacbeebcbbaacbbabdbadaecebdddeacecaeeddcbbaecabaadcceacececbacabbbdccabebadacacbbcdebaedddbcdeaababdddeacbbadabaecadbcedceaedaecbaedecbbdedaedededcddcddbaeecaaebaaaecedcbcbcdbdedbeabecbdaecabababcacdeaddaaeccaebcdbabddaecebcddeacedaaceaecacedecebeeeceebdbcceadbbaebdddecbbceabddbcbbabdadeeaabaaddcbcddacbcbdacdbdbeabcccbbedadbdeecccbcabcbddddebbeedaadabddaedabdbbcbcdbeddedbaaddcbddacdbaedeedcacaaaeabbbedacbbadaaebeabeabeeeeccebebddedaadaceadbbeddbcbaaedbccecbebcccdcdbedeaddeeadbacdaaecbebaaaedcebdbecaabbaddececbbccaaebddeccaccdcacbeecbeabaaeabcbcaccececebbaaebabbedccbcdabedcceaeadecaaeebdcdeaddcdcadebceadaedeedecaebbdeccbbbdcebecadcedcccdacdeaabbbabbeaaedeabeacaddacbabcadcbeddbaeeebecaabdecadebdbbbaddbbeccceacbadbabbebbcdbadacebbdaccbcabcdabbbbceeedebabbdbddaaebabbedcdebbcadabdacddcbdeeeacecbcbbebbededdabbdbbdddabcbbcccecaaadbdcbdabbaccadabddecececcbadaddedaecdbddbcaedcacaddabadedbacaeaecbbbadbbccdddbdbbcdaceedbbebbadbbcaadadedeeabcbeceeecdceadccbbdcdbceeaaeebdeadbcdcbccceceeecabecbdcccacadacadecececececeeedbadccbceacdedbacaedecdbbabeddcdedeeacadebadeeeaacedabbeaaaadcecdbccdaeddaecadceeedbbeaaaceedbcacbccccabdeeedcacadceaeadbdbdcdbceeeeceadbcadaebbcbbeabbaddededbeceabdeecdeeaccadadedcbaadedeabedaccabdaaebbcbebbbbededcebcceaedcaecbeaacadbcdcecddecabdadceccbcedeecdacdbdbecddaadbbddcaeddbadddabceabcedddaedcabeddbbdeddbbbacbeaeceeeccbdeddbaeebbbdaaeabdaddaeeacdccabaddbbddcbbbdcaabbbaedbcbadbabeacbadddbababccbbbecadcdddacbedeaaebaccceaecbceeaeccddbbaeacebcecaececebbbdedebccbceccdecbaecabeaadcaedbcceebaaeaaebceccaeabacdbbbebbaccebacabddaeadadaeabbccbdaaedebdceeacaaddaacbbcdaeabbdadbacacaeddcdbcdeaedadccddcceaeaaeaaeaadcbcbbeeeecdabaecaabbcaacdccbaadcaceaaeacbbddccabdbcbcbeeedbcedadaebeedaebcdccabbecaccdbdcddaeddebbbebbaadacaccdbeadacaadcdbcacbcdedcddddccaadebdabaaecdbabdccdbbdcdeaccaebbdcdbaeeadbadaaeceeeabbdbebcccaeebaeadcecedcdcdadeccdbddbeeaceeadcebdacecaedcebccdabaabadeabdeeccbedceaabbbdbeebadcecaebdacbadbdaecdeccddddebedaedabebdddaabedaaddedecedacadcecaacbadeaddedbaabdbcabdcebabdabbcdaeeeeeecaedacbebaaadacccaebddeeedebbcbeecaebdbcabcbacadcddacaabcbccdaeeabecaacdddbdedecddbbcccbdaccebeddcdbecdacaebaabcbddecadeaceedcdccdacabacadbedabccddeddbabedbadcadedccccbeaeaecaeabccbeadedcedcbeaabadadaabdddaeaabbeacaabaddbaeeabaaabecdcecccecbbbbceacebbbcbadbebcbcedcebecbabdcbadddcbbaebeaddaeeabababdaaeaccdabecedcaebeabaceddbeabcbdabbdcaebbeebaecacacdeecdebddeccaeaddbdaeaaecbbdadadbaeacbdcbbadddedccdecacecddaedbaedcaebeeaddaabcdabcbcceeeecdecadabddadcccaeebeeeabecadbdedceeaaeeccaacbaedcebedeededcdbbeccdddcdbaadbddeaeceeecddabcdeedbecdabacdecbdaedcbabbdcacebccdecadbceacedbabcdabadcbadbcadbccadabcbeddddaccbbcaebcdeecdcaeebbadbeaabedeeaaeacceddcaeaecacbbbedcbbabcddbedcecdaebbeccecdeddedeaaebdbbabcabeceaeedadbdbeccbbacbcaeedbbbbbecbebbcbcaccceaaacabccccbaebcaeabcdcceeeababcbacbaeaebceedcbbcdbdaadbccbeaaeedeedeeaebadabebddcdaaeaececcaaabecebddeabeacddacdeaeaedabbdbabdcedbddaaadcddacabeaeaacbbbbaceaebedbdddbbbaaecbeeedeecbaadebeccaceeaaebcebdcacadcecececcdabddadedeeeadbedbabadcceacbcbadcdaeeebebccababdcecbaeddccbcdeebaacbcbcddcdebccdccdedaebbaebaeabdeaabeacabddadbdecedadbcabbbbcdbeeebbeecaacbaacccecceabccbaceeaebdcdecebecebcdcdadcaebcbdecdbcdbdedbedddabbaacdcdbdadeccbebabceebdaedabbcdcbedebbcabcecacaddaddaaaeddaceebacaccddceccdbbbeacdebecbdadebbaabbeecaeabedbedcadedebcdbdcaccacddebbebceddeeeeedbecebcebdebcacecacdbeebdaeeddbccceccdeabceeaebdaaacbdcdcaabcceddeeaccbaaceaebadbdbebeaadabebbcacddcabaeebeddddcaaacdcbdaeeddebabbaaaadcceddcacbaebeddccdcacedacbebecbdcbddeaedaadbbaacceebaeabeaadbddabbbccbcddddeabdadaaeecabecedebabaabdaddebadbceceaeaddaacaabaadeddaeeeecabeddddeccdccbaedebbcdcdebcdaecaebcbcdbcdaeeaabbeaeebdaeddcbbeaeeeaccdeaaeeebdcceedabcebaddababeabacbdcceeebeccccdabcbbedadebeeabaeccedacadcaaedcabdbbaeabababccccedaacacedeccbebeeaccaedcaaadeedabdbccadcaccdcacebccddeaedeaeebaaaaeaedddadceaecbabacecdeaddbccbdcebbbaaabecaeddbbbbbdbebacaceedcbcceeacdebadedcdbecabaebbdacbeccaeddadcbddbbdcaececebdaedbccccedbeabdcababaaccbbcbaaaccedecdbbebdcbddebdaeacdbecaabeaaacbbdabbabebeddcacbcecaceddcabbedbedeecabcbcaabeddceaccdeedcccbaebadedcebccdedeeaadcddacaaabaebbcdddeedcedabaedbcacdaecebecaceabddabeddebbbcbeedbcdddbcccedaabcecbadeeeebedcedeceeacecdaeaaabcecaedcacdabebdcbbaaddaebeadaaeabacadcbebbbeacaacabacbccdbaadddbecdcdbdcedaeeaedecedeaebdadedaedddedeabeeabbbabcbbdccabeceaaadabcdcdbbededebdbcaaedbbadeddaaedaebbacbdbbaceaddaeaebebcacdbeabaaebddcbecbdccacedacccddccbdcecacbbcccdbaedabddddccdbbdabbbaeebdbadaddecdccdebdabdebbcccdecbcacddaeadaabbaceccdbcbcdcedcdacecdadcbdaecaddeddeaaddaabdbbcaecbeeebbdeeccaabcdcaeacabadddbcdcabccdadaabbebbddcdeaeedbdcacdeeedbccaddddbcdcbdecbebeacabeacdacaaadeebaabcebeeaadcbcaacbeeceeecdcdbabedabadbebbecbccbbabdbbdbbdecabcddcdbdbbbbeedeeebdeabcdededadbccbdbcddeabaddebbdcadcdbeddeedbcdaebadbeaeeccecacaecaceceadbddcdccaebbcecbedcaeaeddeeeddcbeedabbccddecbcddbdcceaadccabaddcbeecedcabaaceececcceaedcacdecedebbddedebabdaceceebaaabbaaeaacdaccddedaebdadabbeebcdeebdbeabecabdaaadecbddeecacddaeabecbacebbcadcaedaceababbbdaeeadeddaabeaceccedacbbacbbeabedccbccbeebbcecaaebaebecbcababdaddeeaebeeacdddecddecbaabbebacbeacbdbeeceeeaeaaabedecdbdcbdcbcaebebdaeecddeaeacabacbcbdeaadddedbaccecaddcbcaadadddcbdbbbaccbdddddbbcddbaacbcbaedeecbcacbaabddbabaccabdcebccccbcabaadbcdeadaebadbbcdbbebcdccacdccaebbcebdcedcdadabeccbecdbdccbaaadcbeddeabaacedcedeecacadcdadbbcaeabeeaddaceebcacdddcaceedcdbebebedbbbdbdcedaecccadbdcacaebeedbcbaeabcecedecaebebdccdbedccaabeabeeececbdcaeabcbaedeaacbddabaaababaebaecdbbaddeceeebccedaeeddbdcceecddaeadcacbddcbacbedeedcadecaddcdceccbbbadcbdddadaedbbaeebebacbdbdeecadaceebccddcedeceedcdacabacbdcebcbcadceebcedcadbeacaecceadccedaabddaaadeabaeddeeddccbaaeeaddeadeaeeebaddaacbcecbacdbbbbdceabeecbcbecadbeeddcaaecbbacaddccacacaeedbbbeaabbdbbeacdcaecbacacaaeaacaeddbebaccbbadbababbcdbbaecebaceecddaccabdebcabcbdbbeddedaedacccbdccecbcbbdceacbcbbdbabdcbadbaeaccdeacaeeecebbaacbbeacedccdbcdebcbbacaeabeaadabeeeacbeceedbbbcdbceaacaeaccdacecdcbadcebcceccbecbcdaedbceebcbddbeceeabbaeecaaeadadceabedcdbeacaeddcadbedeadceabeeebbecebaceeddaccdadbcebdadaeaabcaeeccacddeaddbabbdeaccecbeadabcebababdabbcddecdddaacbeebddaeddebbbbcceecdbddedaceddedbdbbaebbdeeacdbebdceadacacbecacecccbdcabbdddbbdebdbdcddaeadebabccebcbdcdbddaaddddaacbebccddbaaacdbbabcedbebaaaeaedecedcacedadcddbebdadbeedeeeebbcbabaadbceaadbacebcebadcbebddadebbcedcdeaedebccbadeedcccbabecdebbbcacddbbeaaccbebaecadbedeebeedcbcaeddbcdcddaedbbaacbbbaeeeabaebeaeecbdbcdcdcdcdbebbcaababcaeaddadacabddaedeeddcecdbeccdabbbbeeabecbbeaececbecaeabddacabaedaecccbabeddbabedebddcaedeaecdedabeeccbadedcdbadcbaabdaacceecdeebccadddeaebeadcceeeecbceabeebbebbacdaeeabbebaedbeecedeaadceeacccecbcbbbcddabbccbeedeadecbeebcaaaadbecdbdbeaeddebecadaaaabbedcdeabbbadbdbabdeaaebbcebedbdaaaddbebabbbedeedcbbabdaccbaeabacaedbaababbaecedbacccdcddbebdcbbeaeaedcdabddadeedaeabddceacaaadbedbaabdabdccdcbbedbeccdeacbddeaabcbdeeaedceeacdebedaedbadabdacddbabaacaabcbbcbccdceeabeeeaeceabcbdbbddedcccdcddbbaaddddbebdeeccacabbedcaebcaaceaccbcabaeccbbbeeeaceecbbdabddbcaacadaecdcbcdeaeebcbadbeaebecbebdeccbdbbdbbbaccbebccedeadeeadeccdcdcecbcbebbbbddcddaabbcdadbcdecddaaaeadaacedddcbbaaeedecaabcbbcceaeeaadadacaabcabedaccdcbdeadcdccbdcacdcdceedcbeddcaebddddaecbceddccbebaeeaecdeeacdceaceecabddaaeaebeabaecdcdcabcdcaebcacdbdedaccbbbdcbabddbeeebebdaeaadecdbccceedceaaebdecadaadeaeeabadaadecccdaedcebaddebdaabebecddbbadaccbcccaabeebbabdcecbecddbaecbddbdccdeddeddeaccdebabdabaebedceabadbaddbdbdcabdeecddeabcccedbeabccecabacddbdadabeecbceceacadbcccccebeacbebdecdeebaddeddbaaebaaeaeebddaeeacceacdbccdadaccbcedbdcebaaeaeacddbbbaaaaeacbabcebdaacdbaaeaeedbbcdccacadbbacbecebabbcecdadddacbacbccbeeeadbbecceabdcacabedcbdcaeddedeaeedaacaeebcbceaeecabdcdcbdcededddcadbbddacdccebeeaedddbebebbbcbdedceeccceaaedaedcddecbeaebeecdaacddecadccacadeddbedaddeeccbceceecececdabecebaaccececebceaedeccdcabadeabcadbeaebdacbeabaaeeabeedaaaaebdbbcaadbbdcdecedcecbdabdddebcbcbdaadbeacdccdbdaddecbddeeabbdcdedbeadedbeecadbeaacababebecdcbdcbcedbadebabbeaeaecedeaccacaededddeddcddebdeaeeccabceebaabcacedbceabacadeeedaededbaddebecedbaeaeeaabedbbceeaedadccebeeebabbbbdedcaebdeabbadeececaddbeceadddbebadecdaebcdccbdedbcddebcbabaaabbbabeccdaccceedceebccbeadaaacadbbcceacdbdedacdadaaaaacdacebceeeddeeccaeaddcedddcedbeeeaacbeebbabdbdeacbbdddeeaeacebecbeacadadccbababedeedcadaabcaebcbeeecddbebaabcadadacabdbacedcdecedadacaecdbcebbcdabeeabeeaecbbebccbeedbabdbaacbeddeddbdabaddabbeaadceacccdebddabbbbaaceaecdcededcebddbcadcccecabeacdaabacbdbaebdaccadeebedebdcadcccaddbdabdabdabdddaaceadeebdcdbbbdadcacdcbeadbeeacadeaeacbdcadbdcdccdbaaccebebaebebbacecabbacadbdbbbbeddcaabcbcdbdcadddcaeebbedbdcebacddebbebdadbccceebbadcdeedabccbcecadbdcdedecbbeccecddecadebbcacaebeecdddaeccaaaeccbdededbaddbdeccbcbaccecacacbaebaebcbcecbdeddcacaceceebcbdbebdaaaadccdcbbbedbccddceddcdbdabaaeadedcbccbbdbaccacdedaddeccaddadddbaecdceaebbbdacdedcadebbcbdbeaceadabbecdedaacaedbecdebdaadccabeaeebadcaeeecbdacbddebacdaabebdcdecdbddccacbbdddcdeaceeeeeabdbdcbabaecbcebbdeaabcbacbaaaddeaadaeceacecadacedbebeadaaeadecabaececeeddeccbaaeceddecaadccdeadebeddabacbebecebbcbdadcccadcbedbbbcbbdadbabdecbbceaecbbdabddccdccbabcdaceaacbbeedcbceebcdbdadecdbdeaeeddbcabadeebdeaaeddbadaeddaeeacadeacaaaeecdeecbabcbbcdcbabbcbdcacaeddbdbcaabaecbbacdebccdbccecedaadbaabaeeababecaeaabdccdebcededaabcabbdbcacabdbbebeecdabeeeeaadecacdacdbbacbcdaedbdcbeaddcbdbdcabecdedbeddecbeebbadcbbaceccebdebedbaabbbeebebdcaacbecedcdbebcaacaeebeccddccaeacebadedeaedeaaadbcdeecbbaebeebeaedaaceabecaabbbedbabbbdeadcbdedadeeaccddaddadadddbebacabcacabcdeaeaebbabdecabbdbeddddbdadaedbddaeddeddeaceeccbaceaeabddbecacbbedbeccaaeaadaaebbaedbdbcebeeabddedeaccbecbecababcccaecabadeabdbedeeaebeaebecadeddddcbaeceedaeeddcedbeabaeacceccabacdaedcbaaedccabccedeccecceabbeaddccebedbaebdedecdebcccbabdbdedeadbcbcedddecbcedbaddeedddeadeedeabadabbeeaacdcddccacddabadadeeccdeaddcccecdbdbdbccacacbbeccdaecdbedabddcaeebdbebededeaebbccddceacdbdaaebdcccbdeacaebedeceedbaedddbcaecdddeadeedbdcbcddbecbdccdedaecedadccaeedcddcdabaeddddeaaeabbaccaedeaeaeccaddabcceeedebacdeaeddccedbbadcddbdaeedadeeebdbdccbcaebecbeedbdbdeabdddbeeebecaebcbcbdbcccedeadbaddbbbedaceedbdecdeabcdeeddaeaddbabacedbcbcbbeeddddddccceecbeadaacadddbeabdbcacaadbbdcedceadbdaacbaaeaaeaabebcdccaceeccbcdeabbddaccaaaddecebdddeedbaedcacaacebeecddcdddecacdbdabccaadbeedebcddeababdcdeeacddbebbeedeaecdbdbebdcaeececbeddaeeaebedeaecababddeacbdcbccdeecdcaebedcbeeddababbcecdbdaabdeccecbbeecaabdeabbabcdddacdeccbbcdaccdaeacdddcbaebddababeccaedcbdadeaeecbbbbccbadebbeaaceadbeeedabdeadcdabacbaddeacbdbcbabcabeeaeaeaeaabcaacdaccdadacbebeacedaddeedacdcccbababeeebebaaccdaccacdeecabbcedccceaeebdbcaecaebcecebcdbbaddbdedeaaaccbcbbacaaacdaacadabcbedbceadaadaabaacadeaaabeddabdacabcaabaeaeddbbbbdedeeaceeaebcadeccaaaeccaeaeecaabbecbadaeaeabddeaddeadeaabeaaadbbaccecddcaadcdaaebddacaecbabbbaeaaddeeaecadacbbcaebbdddecbdbcbcaabdcbbaddddebbdebadeceaabcdbbbdaaebbbeedceacecdbaadacabeeeddddddeccbddcbdedcceecbaddbedcdadbbabcbbddeaededdccecabaecdeddacccabbbbeddcddedecebaedeaccbaeaecebbadedcaeaccaabbdadcecacbdaceabdcbbccdceeddccebeedcebeebdbadbdbacaecdadaddccadaacaeaeaecbaccadaeeddadddcdaadbbcaedcddbbeccbcbabdcdeeeaabeabdbbccdaecbbdceaabdedcacdccdacceccbcdbadabcdaedadeeecadcdaaecbccdabcdddebdacbbdaacadbacbecbceadacddbecedccbadddaceabcdccbdaeeebcbbacdaaaaedabdbdaaedddeeeebacdebaccdeecedcabddcdeeaadbeddcbcbeceeebccabadeaabdcaaededdedbbcebcbccaaecebbdcdcbcadacdebbeaddddedecbedabedaaaceedadcbeadeadccddbddddcbcededccaadaedecccdabcbbecaaabadebbeaadcdaaaadeddbabbaecebaddebabaeacadccbddcdbcbeebbecdceeacdabdaacabcedaccabbadbdebabaddebadeaeddbcdecaaabbdeedaceccaceebccdbcbceeabbcbebeaddaceedbdaaceeacaedcdaebdeebcebadeeabcecadcbbdbceadceaececdacbedaaccdecaaaecdcececacbaedcecdbbdbbbdebeecdeeabcbbbababcccebecadddbeaaaacaeedceeeabcbcdabacaabedcddedcdaaccbeecaddecbbbeccceccdcabdbbaadaceacabcceddabaddbebdcbdbeacceeeebbaccadbcdbebbedeedceecacdacbbecbbebcedccceceecebaeabbddbaebcaebaeaeebeecbaeedcbeeccedbdddeadaabbcadacedaabeaacddeecebdcaedddbdaadecabedbdaaadddddacacdebeababddeacdebebebadaddbcdbcdbcbdccbcddadbeebdbeebbcdcaaeeddecbcaccadabcceabeabbeaeabbdddcebedbabcdcceeeceedadccbcadebbaacdcdbbecacbdeaedeccaeeddadebdeadbacdbdcdbddaceaabdadeeabdaaebdabbcadcacbacdbcbdcabcadabbeabbececdabeedaecaeebbdaebbaebaddddbabcbebbdeccdeecdeeeceabccddbbbebbbdabcebedaabcabcdceedcacdddcdcedcecadaddcdbeadecbaebbcceaabceeadccdbcdcadcdbaaeeccdbbabeacdbaeccccaaddecdaccaedaeddcbdcaacbccbdaedbbdcbbdaaeaebedbebbaeeacccecbdbaedabbdedcaddceedaebeccbabecdaddcddcdcadebcdbccdaebbadbbebbcdaccbaeecbccecacdadecbdbbbbbbddaabbedacbcbaeebddbdbaccddeeebaaaebdbaabcbceddaadbabddbcbdcbbcebedeeecadbbebacbcecaacabdbbdcedaabdcbadabeceaacccaddbaaeccddeabeadedabbbdeabbcbeaebdedcabaebaeaedeaeccdecbbdccbeeacdaaaccaebaaecbabedacadedeebbebddeacbaaabbbbaadecebdedeebaeddecbbbacbaabbcedbddccbbeabaeacecedddcdcdeebbdaddebddcaeedeabedcabeaebbacdbdbcebacaebadadcbaabdadecbcaedcbdcbceaebacedecbabbedbdedbaeaddeddbcaacaabbebaecdddceddbbeccaeccedcceeadebdcedbddbeecdabcdbaeaeacdedacedeededdadebacdeacdbcebedbedadaccbbcdaecceaecebdcdecaececebdcaaddaecadddedddcddcbbcdedbbbdaacddacbedbabedabddbbddbeabcdbcbaddbbecbdddadeccaeddbbbeadeeacaeddeecdaabdbaddebcccaeaacdbacdedbaecbcecbcdabcbbceaacccddcceadcaeedbecccbaeebcbbbdaaaeaacdbaaacedaabbdbbedcbcbcbcbadeacbbeaadcdbaaccadcdcdedebcaecebddaceaddeccbdcbbaddceabdeaaaabcbabbcddeabcbebadaaeadccbdebadecaeabacaebdebeaddbdabdceaceddddeaaeeccacbececbcbacaadedecaaadeaaeeeceddebaabbadcbbecdbbedcdaecbacaebdebbaadeceaeaceebddeabdaeaeadcbaaacbeaecaebedccdabbcacdaabcddcabdadddbdbcbddadbabcebeaabbdecbaeeedcaeedeadecaeaeadaebbcaaecbdccedbaabbbcdaabcdccdcbcaeebbedacbacaeaaabaebcaeccbcaaccacedaabbecceeeeeeeeddecebdceabecaceccbeadebebcdedbdddaeecdcbeaecbdbedddbdbbddbccaeaaabeadbacbeddeaecbbdaeabcaabddadcabccbbebaceaeecbdbddadbeebbccadcedeecebdaeeabaddabbddeeedcbcedcacedbedbaaedeaceeeeeabaebebddcdbcecddceaaecdbbaedeaebedcedabedaabbcbbcaebbeeeccdcabaceeecebabdddeedccebcdcdcdcaeecebadcaecadebeadaeecaddaebebcbcddecacbadcdbdaebeeebbcacdbdcebeeeebeadbdacbbeebecbdbaceecbbcecddddcaabbcbaabdcabccabaddebaeaebcbcadccdacdecccbaecacceddcacdccaddbcaeeacccceeaecbebacecacbbeadaaebbebbcecaebabeeedbabcbedcbdbeaebeeddbeebdeaddbbdbbeeaabacbdabecdaceecebdabcddabdcdcceeeaaccdceccbdcdbcdeddcececbdbcdcbccebcaccceabaeeeddebcbadeddedddaaddbeacccabedbedadaaecdccaeabbaecbaacbccbecbbecbaaebeeeacdaacdeaadbccacedcbdccbeabcdaaecaaaaacebaeaabbcbcaddacbeadcbeccacacebeceabedadddcabbaccbdcceecbceaadecbbbebebadadbadaadeacaceddebaabdaccdeaeddaecceebdecaaaebcddeaedbadebaeceacaceadbbeebbebeecbeaabdecdeeabebccaaccdebaeadbdbdcacbedcbdaadbccbdebadbdacdcedaacaddbbdcccdebcecceddcbcaceaccedbbbcacbcebcbbcadceacecbbeeacbabcbbaaaadeaaecbbababaadbbbacacdaecacaeddccdeeaacebaedbadcbbbbdebbeebbdeabaaedceebbcbaddceccccdcabebaacdaaaeeeacecbacaeaacddaceeedceebeedecbdebebedbcddcecccaaadeecacabebbbebcccbedbbcaeaccaadcabeaccadcbaaddeebebecccdaccebbadbcbbdaabeacbadeecbdbbbebdbdaedaedcbeccdaebdebcdeabbccdeccccceeebcebdacadacdcceeccaacbcedeacdadddceedeadaebbdccaddeadabaacbadbcabbcededdaabacdadbbabcebbecaaabeecbecaeaeeebcabebbdcddeacabccebdbcbcbecbebebeccecaeebcdacbaebccbbedeacaaccaeddbbdbcabbcaebcabecdcabbdacddacabaaaacebdbdaabecebbebeabcabddaecceabaadeddcabdabadaeebadcaaccbeddbdaacddcadacdeaecbacaeaebcbdabbdcaedbdbdeddbacdbccacadacdbaedaecdedaaaddddabcedbddebcdadddbabbddccdccadbbecaabdbcdcbbebeacbdccaadacabcacbddcbceaccbdadaeeecacebbbbadbcbcddebcebcdacdaabcddcebaeadcdbceededaecdceeaededbbebababceededeabcdecbddabcaacaaeacceaebbddcdccaabebaedbecdaebddabddbddcbdccdedaeacbedebbbdccadabaedcabddaeeaebaabdbeceedadacebbdbcccceeabddedbbecacbecbbdacbcdeacdbeaaebaceacedbdbbaaeadbdcdcaecbdbecaebbcadedbbcaebebcacddbbccebdacbaceecacceaeeecdcbceedcbeebeedeebdecaeeaaebcbceecdcddeeaeebceaccbdeddbdaabadbeaccaceedbdecaecdebdcbaeddabbbdcddccbacedacbcdbecedeccecbeecaccbdcccdcdacebbbdbdbdbbeaabceebbaaadbbddbcaaaacadbbecdbdbbdbeeaaedecabedaaecabaaaeddcbacddaaddedcdccdbcaadcaebaeedeaebbeabededdadeceeddbdbecdeecadeacecaeaabadaeabceccbaedddeaacbacdbedbbeedaecdaddedbbbceebbbeccbdecaeabebdadadeedadceacbbaaedadadeacbdbddacdcbaaaeeeabdecbcdeeadadbcebbdaaadeebdeacabbdaeaacaacdacacddceeddecedaadcbaacadebccbcaaeebedaecaebacdcbabbedaaedcbdbcdbabaacaeaccdeeebbecdedcdcdeecbdaaabbadadbbbcdcbbcbcacadcabcdadacdcacebbbababbbcabdbacbeadedbcdccebaecadbbdabedeedadbaacebeceebaaaacecbdbaeebbdabbbcedeccbcccceedadabdbacbcdaeaedadeeddbbdadcaecbacebdabaedcaedaaedeccebaddabaeadaaddeedbcabbedbeecdcaabbadbcaccdabddabcdbabbeaeaaaeddcbcbacbbeddaeebcdbddbbbecdceeccaaabbedecedbccbedccbadccceeeeaabeebbaebdbbdbcdedbbaaabadecebddabaacaceebdeddddedbcdebaadddcdeecbedaacdbbeaccaededcbcceadabeeacdabbcddeeebabbcecdedeeddbceabebcbcabebdcacebaaccedccbdacccaecededaebccabcdcbadcebdebdbbcbdbaeeebbdeacceedeaadeaeecebdcaabcabaabceceaabeaedeecdeebeedcdcbaaadcdbabcdadcbeadccabcaeceaaecadacddcbbdbaceecbbaeaddbdbddcacacadecebbaebbaecddebdaadaeeaedadacddbdeaaceaaeccbdeecaaccaacbdbdbdcdbcbabaadaacdcdbaecdbcbebadeaabebdccbebbccaabbddbbdadaedcbceaababcdabcecbcccbcaaccadaedcdbedbdbedcabebcddecdeaceeaaddcbbaededabeebdabcdeebeedadedeeecceedceeecdccaaeadecddeeeecabadabccebbacceeddecbddeeaadcbdbbbeccebadacbacedeecacacebabbacddadcaaabeabdadeceacbcecbdcceaeadbcdcdadedbdeeaceabedaacabaeddbaeaceddcdaebdeeaecebebadbbacdaceceeebceddadbaceddbbcacbbbceddeadcbaecbbeaeccaebadaebacbebdcdcceadaacedecccdacddeabbacbdebcebceeeaadbeeeabbccdaabbccebcbceebadcdaccabcdebbdbaddbeddbaabeabbceddcedcabccdaedecaacadbcdbccbdedaeacdeadddadcbebaedececebbaaceddbdcbdcceddeeeecbcebbbcbbbcacebeecacddaaeecceddcbbcbadcaabdaceadddcbbdaadaadeadeeaeaddbbbaaddceecebdcccdaaabdedcecabebaadebacedbaadecabbcdacdddbcebcbcdbbbdabdbcaaecdbccadedbcebddebddeadebeeaaccaedcbecdbcdbbaebeccaeaadcebdcbdcddcaebdeeebdccaebecddcebceebadbeadcbdcadbddddcbccedbbcebdbeaddaeecccdebecbeadaaecabecedbdeabebcbecbceddecacbddcbdadbcdcaabccdbaeaeadeeacbacabbadbedbcacadcacbcebbbbedaeacddbbaaabbbedbebbbdabedbdbbeeddbbcdecbdaaabaeeccaaedcbadcccaaeaaabdabaaaadddbdacdddbaeceacdcadeacbedcdbabdbadbcdedbbaaadcddadccebbcabdbeebaddacecaacdeddebdabacebdbecbbdcddccbbdbcbabcbbdbcdaebeecbdacbadbedecabaacdbbeedabbadeccbddbebdabdddeceeabdcccbbbdcebceaecbeeabecdeeeadebaeccbeadeadcaaeacdcccebceeaccedbabacacaeabdbdbeabbecadccabdcbbccbacadddeebddcdaccaaabcabcebebbdaddaccececcccacabcdbbbedbbaebaebcadbbbbaadcbdbdebedcccaebcebdaededeacbbdcbbbaaceedddeabcbcadcbdacbcbdbdcadbbaceedaededccdebbbbceedbebdcecdaceacddbecdcbbedbdbbabcbdaedcecbbedadcacdacecbbcaceedecacbecaeeaebebddcdbbdccdeebeddabeeddadebbebbdecdbeadeeaaeebebbbaaccedadebceccaccbcedecbeadcaeccabbcceecdcedaddbebeeceaadcecbcaceaddeadaeddaaeeddcecdbbdcabaddadabaabaebbaeebbeedbdaeecaabededcbbaadeeeccbeebebbabcccacabdaecebeebbeddeedbadedbaaccbcbbacbbbaeaaebeaeadebdedccccbeaaaeebdccdbcbedbedeccceabbebbddcadadbcbdbeebebddaccecdaebaddbebadecaeeeeaabbdbbcbdaddbddebbbaeadbbcbdecbbebcdebbdcaddccdaeccabedbadceebdedbdddbacdeaaabbdccaacadbbbccbdedbcebbaddaaebdcbbaacabcabceddabbabaecbdcbcdabebdeecacdecbadeaabbadaecbbbdddcddadcccbacebbddcbccdcaacdbccacaadacccbedbbdccbecabbcadccbbbaaecededebcdaeccbaebedaaebedabacbdbbdecaeebaebbdaabedbcebbcdabbcaedaadceddcbabceadbecceacaadeabceeaceecacddbeedcbcaebdabbeeabccacecbecdcecaeecedbcdabecbececccddbbcbeacdcaedbadadccddaeedcccdaaaedcaacddbddcbcaeadbadabccdadecedbbabdcbcbebaddbeceebeebaebeeebbebdadaabbdecbccccbdccebaeeeccbdadadbdacdaacacddaccdaecacdeecdbcbadaaddeedaacdedeadcabaecdcdcaecabbbdeccebcbcdadededcdbbdadbbdadbaacabeebeccecbcedccccebebadddcedeadebcccbcceaedadebabababebbbcabbbcdaebbccdabcacadcbdacdbcdceeaccbcabbbeedeedebededdeebacaeacdabbedddacceabdcaeaacdcceaaaeabbcddbecadeeebbebcacccdecbddddadacbaeadecdadebaaeacbcdbedcdadebebcaaecbaeddeabaceedcacadabbbecbdccaecddbdcbbaedabbaacbdeecdedcdbeaaaddebdceddebacccbdbbebbacaaacdcadbaecccdaebbdaaeeceebcdceaecceadbedeeeebbabdaabbadebabaacadcaaaacecadccdacabcededdbcdedcbcbadbaebddacaadbbbbebcdcababaacaccbbbedebbcbadadbacedeadeabaaccebccdbedecbbaecadcbbaddccaabcedbaedbcbbbcbabcedecbedbaebeacceeeeeaeaecdecabdebdaeaaaccaacddebaaaaeecccdbbacecaabaacdbeabdaddcecbeddbacddbeeaaccadabbedadadeecaeedccedbbaeabbaecddceaddbababebbebcacdcaeeddadccacecbedbaebabdcdaecbcadecbdaaacceaacaeddeededaddebbcddeacddceadaedbcebeebcccccbdbabdbbacdcbebaaddeaedeedceececaaeeddacebebcaeccdeddabddceaecceebeccceacbedccecdeddacbadeabecedeabebbecbdccdeecadabadabadeaabcdabebbeecaebbdbebecdcbddcdcaaacbaccdcdeecebcebcbabaecdebaeacbaacbbddaacbceedddaebceabacaccaecbccdbaaedcdedeedbcdcdcacedceabeaaaaadddbbdbaeacddadebaabdcadcddeebaceeebeaebeceaebacaaaacdacbdcbeebbdcecadeddccbedcbeaddabadeeecbbbaedaeabedadadadcebebaeddcbcdcadebdeecbdacdaeeebeebacaeeedadcbdcddecbeadccecaabebcaebdcdebcccadaedbaaceacbdccecbaeaacaeebdecbeddddaededcbcbacbabdeadacccdabcaeaedadddbbeacdcdaeabdcecadcedeedacddccebdbdaaaceabdedcadecaecdadaeacdbeeadacaacdadbcdacccdcbaceebddeeddcbaacbcabbbdccecdeaeabcaebeedbbcaacedbcdeedecdabbaaceaadbdcabdcbdceccecdacbcaeceaeaebbdecddedeecceebacdedbcadcdaaeeaccbabeaaceececedbabcebaaebbbdcaabcceacbcadbdaddddcbaadbdcdeeeebdcabbeceedaebdecdacccbabbeddcaceedbcaeedceebccaadbacddebccacdcaccedddbebaadcaadbcccdbdadaebcdbadedabcacdcbdadcbbdcbdeadcababacbdeadcaacdadacacbeeddcdecedbddccdebcabddaeebcecdedabcedcbbccbbbeaaabeedccbebbaecbcdcabeabceeadecabdbededacdbdbbbadbddadbddcbedeacbeaaebddeababbdcacebeceacecbccdabdbeababbcbabebceeecacebaaeaabcdeebddeaeececebbcbcaeedeeeebbbdbdebacebedcdbceeedabcdecaebadedadeacceedabddaaeaacbdcccaaddeaeccaaaddeddbecacedaaabaedacbebcbbccadbbcdeaccdecbbdaaebccaabedacecadbcbccebdcdccbbdcbabcaaeabacbddabeccbeeaccdbbcadeeeaaeebbbbedcdcceabaabbcbcbdbdaedadcdabccbbbabecabecbbceacbccceaceaaebeaddececbcaddeaeddadccadbadabcdcacebadaeeadecebacdebbceacbccabadecdebadaaddbbbeeeabbbdaeecaacbcbaabccaabcaecadaceaeabbebdbaddecdbaabcacddecadceabbabeecbdaadddacbeeecdbcebeabbdaeebbaeecdadddcbeaeebccedabcdddeebdcaedaaadaeceebcdddbdadedcaaaecdeaaaeaebeeeadabdceddcdaddddceaeecbbcccdbbbbaadbeaeeaaabdbdbbdebddebcebabebadbbdcbaadeebceccbcdceeccabeeabdcadecabbaecdabaacbbeeceebaabcaceebabeceeeacdebadbeccecbbcebabeaeaacdabeddcaaedbaaabaddadddaacdbececddabaadcccebbaabacbeceabceedcdebbacceaaabeaeaedbcdcacddcbbdbbdadeddebeacaabaaaeecddcadabddaceeddbacceaeccbdccebdeaedeaecdeceeacbacbbcdeacdddbebedaacbacdbdcccdebaabcbcbdebdaacacdcddaabeacdeeeebdaaedbacaecedcebacaaabacebcdaeceacaeaaaaebbbaeaaebddcdecdbeacadaadbbbdeadbdaadbdbceacbdbdaedbabbdabebddedabcbeddcebaddcedbeaaacdacbcebbeddabccbccaeaadaccdecbadabcdbedaceeaaeccecbaecaaeabdaeedccecdcabeadbbadcccdaeecdbecaaacaccaceebdccbeeddbccddcaecbeedaeedaeecbacabdcdddbebeddacdccebaaeaebbcbcbedbceedcecaeecdbdcbaedadbbbcaacddbddccacbeccdeabdcaaeddbdcbdadeaabaeedbebebbbeebacecabaadacdaeeeaedacadcaadaeeeecebdedcbddedbcdbeebdececaceececdbaccbacceebdecbdeebacecbcbbceaabbbadbadcdbacaecabaeabdbcbcacbedeeccaecdceaaabcedcebaaebdeeabaaaaebcacbcedeebccaaaebedabbeeadbaeedbbcbcabacecbcebebceddaedbadbeedaaacebacacdeceeaaebcbadddaecbeabeebbdeeacebcedeacceceabecdcabcceaedcedddeecbebdceeacbbbcbbeebddccdbdbcdcdbdbdceabdebbecdedbddbeebcbcedabceeeeeadeabcceabedaacecdcccbdeaaedbccdccaaeedaeceececcddecbbddaeebcbcddeadebdddebcbeaaabbbedadbeaaedccecedeaedadddedadbebddaecbeaecdebdebdddcebcaecdbdaaecebaaccbceddeddacacdbbacbbcabacadddeceecdbdcbceedddbeabdccebbbaedadacebdcdaecbdbaddaacbcbdcdedbdeedbabdacacdcdbbacaeecacdabbdbabddeecbcaaebaaebddaebcdcabcceeaceedcdaeeceebeececeadbaecbcdcccebbdabbcbaabadadbaeebcadddbcbacdddbceeccedaecdadbacabddaeecccbbeeeadcabbdeaeeebaadebdabdecccdbbddcacbeadeeaacdbacbedbaedeacecaceebaddaabedbdbddadcadeaadabeaadacbdcdbeddaadcdddddadbceecedeebacabceedccbdcdbbbddcbacbbceaecccecceacbebcddaddedeebeecabdbeaeebddbdbcbcceedbeecbaeeeaabebeabaeebbaeadddbbbcedaddccecabdacdadeadeeccedbceecbdcdccecededcacbebbbaebecabdeedbbddeeaabbbdeddbabaaddeedbeeaddabdddeaaeadbaadbecebceceeabbeadcedbebdeedbcadbcadabbdccebbcbecceecaebedaabcbdaacbeababeeedadaeccedbbdbbddaeeaebbecbcaebcddbaeaacbceacedbbbbaedeeeeadcadeaddaccbccaeccdcbabaeaacaaaabbbebedebcaddddbbedbaadbcddbbcdddbbdccadebebecaededabcbebceebbbacacdbbbdaaaabbddaccebdabdccadaecbaacedcabaedbaacaebcaaddaaacdaeddbbeaaaaaecddcdaaeebeceabeeeadedacebddcadaaedaeddcecaececbdcbbdabdaccacbeadeebcdecedebdcabccadcadaadcdbcbdedeadcedbebeeecdedbcebbebaeaabddbbeecbecdbababddbeabbeaacbabbbeccbebcacaeeaebbdeabddbbaaecdccabcaeaccdcbdabbcdcddbecaccbddadedabbaebedaebbdadbeeeecdcaaadeaebaaddaedbbcdacdbeddaedbedcbdbeededacbdededaaacdeceaaababaddeadacdebdcabbaabeaabcabaaacbdaacbcbcccedddaebdedeaaacdaaccdcdabcbbdadceebcabdbbebabeedeaaebeeabdbebbebdecbdcabaddeadbedbdcbeddeaeeecebbecbebdcebacedaabebbaadbceeeebaeacacceadeddbecbcaadccebcadcacaaddebccecbcecdeacdbdccdeedabeaccdabdabecdbbbaabaaeacaddcaabaebeacbdadbccdcdebdecedabbaaddaacacbcddceeaaaaddbcccdbacbbbcddcabdcdbbdeadabbcccccaecbaeebdbabdaedcecabeebceaceedabbbceaacdaaacbbdabbaaeabdeaeebebbdccceabbeeacabebcbbebbceebddceacaceacbadecacbeedaeceaadeaacccbbdbedbdecaebbdaececaecacadaadbbcdceeccceccebddbadebbdddaddbedbdccecedbddaeabeaebaadbdeebbebbebeabdbadaaacdcbbbadbaaabdeadbbecadccbbdcaeaebdabedceccdeaabcaacaeedbdeabbcabcbcdbecaeedbeeeeabebccbeadaeeecdeaebabbdacabdddcdabcdeacbaddecbcebdadccbdabcabeeebabebeccdaaeebcebcbcdaabcbbbebabdadddadcbabadeaacbdeaabbbbddaedbbbbcbecabdbcbcabccdbbdccbeceeecaddcbdbeacabeaacdaebdecbddbeddbeeeeccebdebbddbdccacceceacdaaeebaddbbabeacdbdccdbdeadcaabaccbaebcdaedcbcdadececaadecdababedaacbebadaebbdaeaeecbebceeecddedcbebebdceaddecdceaadcedbaedacccbabdbadcceaeeabaabaddecdccbaabdedceccdddebdebdaedaaaccdccdebceabadeabcdaaedbeaebedacecedbbeacaddcccbbdbccabaaeabeacdcceebbdbaaceaaeeaddbcaeeabbabadcacbadaaebacbbeacadaccbbacaeecceebedbbdddebaebcebacabccaaabdeeddeceeaadbbdccbaedbbcbaabdddecacdcebbaabcaebcbeeaeecbeaaaaebccddaeeaaecbcbabeddddbbaccdedbdeddadcbdcbaeadabacbedeccaeccccabbdeaaceabbbcabacaadcaeebbadedddebbaddbabadabaabeaadeadedaadcbaadbbccebbbdaebcddcaecbbabbddedcdedeeaeeeccbbeccbbaccaccbbcaabdaccbabeeedbdcedbedccbbcbaededcbbebceacbdbadcbbbbbcecacebecbbcaacbeacdcebebaeaecaabddaaadcacbdecdbccdcacddedeabacdeccacecaabcbabeeccbcdbcaeebadaccaadceadbdeadecbdacceaaabadbedeabecbbebacbbbbbcaaadaddaadbeeeacdacccbbaadeceddccacaaaecbadbedacddbbcaecaddaaaaecbbeceadabcecbdcecedbddbdaacabedeeebbcbdcecbbceaceccadbdcabcccccedaeeabaaecbdecadddcccceebdbcaebbbacadddedbebebaccdbdcdadeeabcbbaaaecbcdbdcaeabaedcadccbbbabbccdddebacddaaccdecaabacdebdbccdcbdebeebbdecaceddaeeabedcacbcacaeecbddaecedeaceeebcbeceeebeedeabbabeddbeaabdaebdedbaabcbabcdbbabbceeabbcbebabacebcdaaebdcbbebdeaedccccdacacaebecadeebebbdccccbaaeccaadbbaaaddacdeeacdedeecdceadccaaadcdbaccdddebbdadedabeeaebebaddcdebcdbebcedbdcdcccaaeaeaabbecaacdcccdbabedbcceeddaeecbebebbaedbccbadcadcaeeebbbdebdadaecaeddaeaecdadeaeabdceaddcdeeeeebeaaedccabecbebaaacededeaaadcaeacdbaeeeaaaccaabcddeebacadddadadbebadeddeebaabdccebbbdadbebdadbccecbecdcccaeecbbedbddacdadadbddeeeaabeaaebdadbebdcaabbccceeeabbadabaedaacbaedeccbdbeacdbccebccedceaaddadbbbcdcacadaadbcdcadaaccbbcccbeccebdddcbdaeedbcaacedbdacbdbecdeebaceccbabcabdcbcebddacbebdbdddbcdbaeaadddcedbdeeadcbbdcbcbaeaeadbedbbeabdbdcdbececabeabbbcabececbeaaacaedacadbdcbcdcdbbaeceaaccaedbcacacabdbaebeacebceaedabaedcebaebdceceedccbddcacdecdbebecdbcdcbebbbcdacdcdabedadebecbeabecccbcccaaadeeedbccaaaadbadaaaecaeceeebadddaebbaebaabcdeeddbecedbbaecacadcbdabcbcbcabeaadcabbdbeedcbcbccbabbaecdcaccaabdaacbecacceeadcdccbbebabadaeaebacbbeacbbacaeabdddedcdbcadbcedceaeebceabeebeddcaadbeaabbbaeaeabebabaccebeceebebdbaeeaceecdbababcbcdcdceeadeeeebdacdaeabcadeeacbebeadabbeeacedbeebabcecadecececeaaaacbaeedbedbabeaadcabccaebeccbdaaeedcdeedceeeaadbecdbacbeedbacabcbcddcadacecceaedecceeeceaccddddcaaeecabdcabcedddabbeebdcdeececcadcdbdedeacdbdbddcadebecbcaabeacdcecbeddedddddbabccdbdbaddbddbebcadeedbbaeaeeedaabadaddbacdaacceddaaedabbcacdacedaadecaeecbabbcabbdccaeebbdedcecadbabeebadbeeebbddbdcabecadcdccebceebcedabceadaeaeeebebcbddcbceaaaebebbaabddeecbebbdcabcdccbddaebaeaaebaadedacaccecdaaecaaccdacddecbbdceaeabecbbddbbaccdeeadbddccaaadabcceeabceaabebcddacbccdaddaeddcddcaeadbccbabbcdebeebdbbedbcdacdacadbcddeedaccebdaaaabbecabcaeabeebcbecbacabccededbeddcbcbbeadcdaeeecebccdadbdeabcadadaadbccaeabbcdaaabcebeaabaaaadbdebabaabcebacaecbaebabecceebadcdeaccabcdedccccecacdbdcceeecdbbacbedbeaedbadcabbedaccbddbeeecdddabdddebdadaacbadcccabeeeccceebdbcdccbacababcdceaddecbeceddadecebeacdeccabcbccbeeacedcccbddadabebcdaeaabddcdebacecbabcabaddeeceaebeaeeaadcbcedadccbacedbdddaeeccdcdebcdedbeddebbbdcdaceceaebdebccedcacdecbbccabaaaacbcbebaaaccdddabbaddbdeeacdaecaabeedabcbdebdacbdcebbcbededdabbeaeddecedcabbbddbacdeacadecdbeeeaadedbacccbabaadeeeeaadaebbcbeabecdbbabeebbacaacacdbdaadeaeeabcddcedbcaeeedaebaabcebacacecbddaeaaaedbbbaaaabebbebaadedbcdadedacddaaaeaabaeabcdbbeaabdbeadccedbabaadeaddcdddadbcdaeacdbacbaeddadcccdacadcacccadeaceedaddccbabedadcadeabeeaccacabeecedcdcaeaadecbcbebbcbcaaaadaaeaaedacaabdeaeabdbadeebbceaaeebadcbcaebebcbdbaccbbabdddbccceedabeadccbbbbdacddbeccebaadaaecacaebdddcbaedeeddadcdbbbdcaabbbbcdecaaecadbeebcbebacddacbbcbcaadbdeeacaaaccbddbbbcbdbcecebbecbdbebaedccaaedddedcbbaebddbecebaadeebacaedeaecddcdbcbbeccaedddcdbceebdeaeedeedadcbbcccedccbceebcbcddbececccddcdaecedbcbccebcbbeaebacebeaabcaabdcdcaaebebbaabbdcdecdababeaccaecaacccddacbadebcdbdbaeddcbebcebacadeebadcbacbcecdbcccddcadbbeabbaaeccdbbadedeeecdbcbbecdacdecaddbdcaaceebeecceecacdbcbcdbbdabeeeddecbeadeabcbbecdaeebcbdcbdceaaaaccdadeeeeddbdbcdeaeebeacccceadcaeeaceebaebcedacbcdcdeaceebcaebbdcceacceebddacaadcecadcbdedddcdacedadebbaabbbbdebaeeacdbdcebbbcbabdcabbacdbadeacdddeeecabeedbdcedbcadccddbbeaeccbabeeeadebdaccaabbdaddbdeabdccddeeddcbccadacbaadbbcddabdacedccdecdbecdcedaebbbcbddcacbddcccdbcedcedabedeadcacbcddceaaabaadecebccaccdaaeadaeecdbaaeabadbdbdecbaddaedccbeeabbddbbabaebccaeccebcceaecccccabdddababebacdccccebddacabeacedccbcaeccbacaedcedbddadbedbeeebbadbdbbdbcacdddbabbeceaaadebeccabdbdbdeccdddbbaeaabbbaccbedadaaaccbbedeedbcdcceddccbcacbecccceaedacdbacaaceddeceaecbddacdeceaeedbebededbcdebeadeecdcadbbaeeeeccebcdbaabedaaeabdaddebeaaecacecccbdddacbcddeccbeeebdaadcaaedeceaaaadacaaaaeebdbdbbdccccebceadababdcdbeedddaabebbabccebebbadaabbbcadccbaeeabcdadeaacecbadbeedcaededccccdbddcbcbdecebcdecaeebedbaaceadbaebabbbbcbbacedaeadaacdcabceaeeedecaebaeaeeadbeeebbdbbcecaaadbcacedcecaadacceeaeaabdebdbdedaeaacbcbdaceacedadadabbecaecceebbbaaddecaaacacdedcdeaaccbabedbdedeaaacaecdebaaceeccaaaeeaccacddeeedddabebeceeeecadbeaaeccbdecdddeabbcaccbbcaceecedabedbecabcdadecbadcbecbccacbbaeadaccdcbdadabbbcaeddbcebeebdbddaeecdeaecdcbecabbbcbcaaceeaaaddbaaecceaadaccaecceaaebdcddbeadaeaedeaccddbacbbdcadcdaeabdcbdccebccdaacadededabadaeeaccdbcbdcaacaebecdddbbddbdcebeaaaaabbbcbdcbbebcbbceaaeaeddbceaaecbeacdaeebaadbaeabdcbedeeccabcdbdacaddebccbedceecddaadcebadabbdbedaebdeabeadcaabbdccbacedaebadeabaebaadecadadcaeaabecbcaccdeeaabbabcaeacabacebbeecdbdbcedeceaaeeabebdccedddcbcadcdbbbabbebbccbcadeaadedaecadbcbdceaeddeaebbbacdcbbdecebeddacccbdccdadddbcccbaceebcdadbdeaebddecbddbdbdecbcbbbbeabdcebbddacacaebadaeccdcbbbceeaecabbecdadadeeabacbaacdcecabceabdbebdeeabeaeececeaceeabaabbddaebbabdadeaedecedbacedcbcacbceedacbaaaabedbadbbcbddcacedcaeeddaadaaeadabccdbaddabedbccbeaaceceebeccbeebeaeebceeedecedaeadddbdebacadceaaddbbbcbadebaabccbdbcbdbaedceebeaaceadaedddcbbbcecaeabbabedaeedbdbdeedddeebcccecccaebaccccacaadddddcacdeaaeacdbececbcebaacbcabaaeabebdacaacbcaabbbddaedbdebdbccdbddceecaceccbbaccccaebccbcbcdeeeebdccebebddcccedaeabddabbdeedcdbbbcbcaadbeebbdeabebceebcddaeddeeaeddcadeecaeeedbdedaeeecadeaebbccaccaacebdaecacbeeabadbbddcdeeabecceaeeddabdacecbacbccccecbcebdbeadaebeecbbbacbbdedccedececaddeebbdadbbbcaacbeeabaeeccaeedcadeeceeacaebbccdbadabedacacbdbacbeeddbbabcdebeceeabbbbdbdeeecbdcceabcadeeaabeeeabeccbcbdcbbedcbaeccbedccdbccaaddeebcbddaabbedccddddcecaedbecbaabdeeecaedeaddbddabcbdcddcabbcabadbabdaeccabdbaabbdaccecddeeaebcbaebbacaeeaaeecbbeedeaaaeededcecebaaddaaabadaadaaebdcbadebedcdcecaaebbeaccbbdeaaeaebccbadeabebabaeabddededadacdadebddcdaeeebecaacdbabcbdbedaebaecadbacabdeedabbbaabeabbaeaabceaebedaddeccccabdaddcbaceadbdbaeaecbcecdbdcecbddbcbabbdccbdebaebedddedabdadadaedebeaebadaadceacbbbceadceedbacacdcbeceaebcaadddaddbdaedebabcbccbacadccdbbdbdeddcdeaeaadbebaaeaaaaccabcddeceeaaeaeedcbdbeaabaeaddeddcebcaedecbcaabedcadeabdebadccaebbbadeceaccababaabbdbebbeaecececbceaaddbbddcdedeacacdbebaaadbdbebbdecceacbcecadeeaeaeabaabdbdeedabedecbcddbdecebbeedbdaadddbdbdccaaceddcbceaebadbcddabebebeddeacdbccbdbbbdbedecdcbdddbdacccbedaacbddddaababbedbcbebbdcbbadddababddcbecaaeecdadbdcabcbdeededddaedebddddeccdbdbeabeeaacbdedddeeebddaedceeddddeddaeabeaabcadabecdeccadecdedeaccccdbdaaaeabeabcbbbeeddbcdbbdacbccddddddedeacdbdcaaacdcdabdeeaecabbbcddbccaccdeadeeccaadadecedaeecbdccbcebddacdaddceaeecbdbdedbbedaebbcdddacabcccedeaddbeebaeedadadceeecbeedcbcbdcaddbabddcabcbbeedddcbdacaabcadeadcdeeeadabaabcbebbcadbaadebdabccacbdebbdadedceceadbbdeaeebadebedbebabdbdbecdedceddccdaacadcaedacdbacdcdcaddbaedbaadabdbbdeadcaccadeeaedabbadcbeabaeaabccdbcadddaebeeaeacabdbbbabcacabdcdcaddccebcabedcaecbebaccbabcddcceebaadbaecadabedceceaacedbacddcaeaebccaccadbccadadaaaddccebeebbdeececeececbcadeeeddbcadcaeddbdbedcababadbacddcddabbabacbeecaeaeeaeabcceaedebcecdcbacacbcbdcedbadeebbecbbcadccbcabeedeedecabddbacebddcaadccbbbbbceedaeeeaeecaddaabcadabdadaaadeecadaecddaacccdbbbbbacddeddbdaeecdbcbbebcaddcdadcbbeeaadabaddbeeedabeaabacdedbaceeddeedbccddeabcaaeecedeeebddadaedbcadeccedaaeedceaaadabcdebeacaebbecdbbecbadbcbcccdcedeebedeeabbdbeeaeceeadacedcabeececbcedbeddccceeddbbcedbceaecdadadaddbcdbbddebaaaedecdcccaddacdbccabddeebcbebbebcdadbdecbdcecadeaccebdbbbadeabcdbbacdedeaaeabaeacbcedeeebdaaccdeedecbcbececcebdebcbaabaedebeedcbdbbcabbccdcdccacdcddecbaaabbadcebbeddbccdbdaacaaddebdbdaaccabeeacccccdcaccaeddeaacbccbabeabededbededdeccccbaeaddcadcadaedadbaabdcadadabdaecbeabeeccddaaddecaabdebbeaeccebdaceeecacecedcdcbcceaecdcdbcbbddeebaebbdaeddadebcbbdeaedacaebbbddbdbabdeddedbbacbdebbeabadcbdbeeebbbdbebadebdbaedddcccdccbedacadbbecbcbabebbbddadeddcebecdeeebbacdbbcdbbdeedceddeaaabbbbeeaddcacaeccddcaabcddcccdeeeecbbcdabbcdddeceaceadbaacdeaedaeaecddaddaddcaddaadbaadbccecdaedbeebececbdbecbcdabddedaccbacccbabecbebdbcbacddaabaaebceacaaeaeadbcddaeedaeaccbedcebbedcaddbcebaabbcabaaeebedebeddebbcdabecdecebdeedcbdecdbbaddbbcdebbbaecdcdabaebeadcabcedeabbcecaaceeeabeeadeddabcdaebcacedceeecebaeedabaaeebaecaeaddcbdabbcbbeedecbdcbadeccbcceddeecaadccdbdeaacccebedabdbddebbcacdeddeeebeabddacabeeaaceceeecbcbbbadabbcdeaaabeedaeecaeddaeaedceebeebcdeccecbbdccbcabbebeddcdabeaccbcbbedccabbdaeebccebacdcdcdcbebcebecbcdbdadeaaeccdedbebebaaeeadcaedbecbacedebacacbbcecbccacbadeacccddbacdbbadacdaeaeadbddacdeecccadccdbdcbccebdabdddaebcedacbaebdedaeeaebabaddbcbbacabceeeaebedaaadedcbbadeeedcbcccbcdccdcebebbdbbeabddbbbeebceebedcbaaddacebeaeebabbedeeadaacbaccaeebacaecaecdcbdbbbcbcdabedecebbcebacbdabddbadbbbeccdcabdddcbaaadecdcddacaaaeabebedceedcbdbcddacacdeeadeeecebcacababbeadbecdebbcbaebebbdaebdaecccaabecbdeaedddddabdcbcbcdeddbbcabacdbdeebeadbebbccacdbbcdcdaeebdebadaebebddcdbdecaabddaabcaddabbbeadcaaeddbacdbbcdbcdaacdcdcaebddbdcdccccabdbcbedbaceaabaccdddeeebdcabbccbbeedaeaeeedbaaeabbedcceaedaedecbbadccbaedeaeaeacddddddeadcacaccbeeabcbeebccdccdecacaabbdbaeebcacdeaedbbedaadddccadadeccdcaebadabaaddbeebbaeaeadebbecbccebecdcbdacdaeebcdcdbeaaebbcecdeeabbdccabecddaeeebaaceabaaacadccaeddeaeabaddddaaaceacbaaecdaadbbbeeccbeeccaaedddcaecbbdaecaacdedccdcddeecccdeabbbeabeccaebbbdbecacbeedaabdbdabdddcadbaabcedcadacededceebceccaceadadaecebdedbbacdbeeceeabbdbcacdceadecdacbaabdcacdedaeedcbadabbdcdcabbdeececdeebdcbeadcdbcabaaabebdcebbdceaebbdebcebeaababcabccbebbdbeceeeeeebdbcaebadbcdddacdadeeccdebdbedbbceddabddceabdbeacbaaeabcecedccdaabcedaaceeaeecbdcdccadbbabaacdabbbcdbcaccddaedbebeeaebeecbedeceeeddceaaacbbbddeccacabecbdddaadadddebedadaaceaddaddbaadeeaedddbbcbdbdcccaccccddbcecdcaddeedeedaeabccecbdeacabbdaadaaccdbdaeebbeeceaeecdeecdaedabceaeeaeddbdededeabbedcddbacbbaacebdbceccccdbcecceaddcedeeeebccedadcaedbcebbbedeaacebebbadbcbdeebbaccdcdaeaadddacbceaaaedabdeabeecebbcabdeddaadceecabdcceeedbcceabdecaeeecadecbddeadbbeaaadeaccbacddeeedeccadabcaceeeeedeaeccabbadcbbbdecebbbabbeebdceeecacebdcbdadeadaaaddadeeeeadebbbabdcbdcabdaecabadbdedaeecabddbaeabacdeeaebcaddddddbacacaaeaaaeacebcbbcaaabbdbbebeeddabdccbcbcbbeedaacaabbaddeaccddbaabbdccedececeabbebcdbdeacbddeadabdeeeedccebdeeccbeaecbaddabdbceeeaccaaecaebeaccbeededabbcdaabaebdbcbbecdaaaeccecdaedbbacddeeceadbcaaaddabaccdbedaeceeecadabbebddbdabaeaacadeedaaacdccbebaedcabdcdcabcbabecddcbbcadbecbdbbccbadbcadcccaedaecbacacbadcebaaaaadceeceeccdceabcbeeccbdcaededecdcbbcebcbbabcbabdcecabeccaeceaabdbedddceeabecceaadedadbdeeeabdbccdcbeceebaebadbcbdbceacbaeeebbacbdcababceddeedcdbcccecdadbbdacbacabeccecdaacddcbdcaebbabceceedbecdcbceeebbeaedbadceceacddcccbbebeeceecaeedabebdaceccbcdecabdccdacbbbacacaabcddddbaceddadcaabcaaaddddeedbdcbdcbdcdbdcbdaaaadbbccdbdeedceaeacaecebcceabceeddabbeedbdaacebaeddccdabbaeeaaadedbccaaaccdaeeacdadcbbecacdcacbdeabdaebbccdeaabaaaceaccadaabccccbaecbebbeedeaeededbebeeedbcebddddcaccbeaacdaadcbbdddcaeaddbabebbdaabeaedbecebacbdcabcbddbbeaeebdacacaebdbdbacdddedceabeaeeaebbdadcdebdeaaccbacadeddcbcedaeeddbbedbaadeebaeacecebccddaaedaaebeabccbdceeadaebeeeceebebbbebeebebadedddaaaeabddecbacaeceebbbcabaadcdcecdeedcbbeccbddcbbadbbaaecbeaccaebbcccbcddcaabdcaeebbcdbaedabdbaabdcbeddcbcbabcedcacdabdaaddcebddcadacaaaaaddadecdaedcedcdeabdaccabdbeeecedddcbeeaadcdcbcdbcaecdaeeaabdebcaaaeacacdbdcebceecdacdddaeadbdbacdbccbbdbcaabcbeeeedcecebbcbadecaecabaedbadebababeccacadababdbaaceaabcadbcecadbececaacbaeabdcecceddcbaabcebadbedebdccbeecbaeeebebaccdabaedabeaecbceabccbbbbdcbadbeccaeddecabccdabbacbecbbdacaeeaedbdcacdaeeabddedeaccdbececcccaebdbbdecacccceaceaabcacbeacbcdeaeaaacdbaccdababbacdeebebdddbdaeaddcbeabbaabcdbdcaddcbdbcaabbceecbaeebadbbbbddedcadbedbbeeabbedbbdebabbdcacdceebbededaceaadaceeabbebdabaaebccebaedcacdaacdbcdcdcedddcdbdcebdcbcacecabaadaddbaedbeebeeedeeeddbdbcebbaedeaccabeeecbebceaacebcebeaaeddaedcabcaddeaccadababcedeaabddccdebebcbddabbdbacabccbdacebcebdecebbabcdbcbeceaceeabadeaeeaaaaedaedcbaababacdddabababaaceecdccaacbcadadedadaacdaedbbeccbdcdddedbeaeddcdbabeeeeeeadbaadeacbcaeadbabebcaaaddeadaccabbdababcaadadbececcdbcbbdbbceecedcaacebeaaddecacdbdeecdaccbbbdaceedbaeaccdabbbbdebeeeadbcceabebeadeedbeeaedcaecbaaecadbbccaeaaaecdcaecbbdbbdecdbdccdcddecbcedabedbacaebbcdbcbeadaaceaaccbdeabcbecacacdabeeabbddadacaaaadbbbaabbcabbaddeeabddcecdbceccbddaaebdbceeccbcbcdaebcdeabdaecaeaaedaeececdcccaedcdeaaecbaaeaecbeccbedbdadeeebbadcccbddecbcebbddccddacddcacbbeabaedbdabbedeadbdcbdbdcadbeabeaacdcadaaaedbacbdaabbeeaabdebddbeddcdebadbcabaeecccedcbdaabdabcedcacbaedbaeddcabcbaacbdaeeebceddaccabacdddacbadaaadcbabdbddbbecddecadeececbaacabecdcbeabdaedbaccdebcadecaacaaaecdecccadddcbddaccadcbcabbaabbeaacdbcaeecadcccdccecebbbedebbabcddbddbebeadcaadedcadbeeadcabdddcebecddadbebecebecacecdaadceccdcdaadbbabbcdccccdabaeaecaeadabbcdbeeabeeedeedbdbbbdedbbaecebcabcecdbedaedececbeaeecabbddbbbccdceeeccbccbebdcadceaeadeddcdcdabdaaaaeedddbdebcacebcddaabaebabeaedebbaedadabdacdeaabebeedccbeaaabccebacbceabebeabeeceeacbdceabeaccbbdbeeccbaabcdccbecaddececddaddbaabaaedcbbebdacedbcebcdbbccecdccaadedadcecbdecabcecbceaeaabcaadebacaeeaceaaddabbbbeccacdaddeecdbbceceeddcbbdcdacebcdcaeacdcecbddbcccdbbdcdebdccccecdebdaccbbbbecbaaacebdadebceebaadaaceeaddbdaebedadaacbcbeccdccabbebcaaeacacbeedcbebddcccaebdddeacdaccaccbcdacbeaeaaedddbdbabaebcbebdaadddbccebbcbeeaccacdbceeebdeeedaceaacadcbabddeeadcbebaaeeacebaccacaaccaaadddaebabbbedaaacaabeccaaaaadbaceaceedccaeadbaddbeeecaeddabeeaebaaaadedadacacaeebbdcaedabcbdabbbabacddcdecccddbddbebbcebbaccabbaddcaaddbcdeebbeecabcabdcedcbeeaeeadceaacaecbaadcdddddceaccadcdcaeadbdedaeeaacbaebaabececaabbeccacceeccdccecdaabdebececbccaabcdeaecbcdbabdebdbaeaeddaecebbdebecaccdbaecbbddaedbdcabbbedaeebbceccabaedcbdcbabbacbcdaedddaddaaceaddbbdcddeaabccdddbeceeaaaaeabacbdcedddcddbeecdcaeeadaabcebeececbedeeaaaddbbdcaaecdedaaedbdbbbbbdecaeacaaaabaccbcebaaebbbcdceeadaeaddccbccbadabaabdcadacbbeddabbcaceebaebbeeececbdabcbbdecdbaacbcaccdedebbaecabdcaadeedcdaecacecbbeeaeeaaebedabcaaadadcaabcbaecbbcbddbeabeacecdeebcdabdaedeabeaaddddbedbdacbcedacdabbabbbbbadcebccbbceecdbdadbadbabbacadbbeebacadbbebeecbcabecebeaadddcebebdaedeeeadccaeabcabaeecaeaaeeacedeaeccabcaacedcbdddbccecacaccbbbccabceacebddbbceeaacadcceebcabdbcadbbdcddadbbeceabaabbaebdaeaecdbcabacebccbacabddbabbabeddedacecdcabaedadbebabccaecdccedeebddecbdceaeccadcbcaacbebbeabababeebebbeaaeababaedcbdbdcbccaaabebeadeeddbcbabadcdbeececcbbbacaedacceaebcacccedcdbccbedccdcdecacdcbbddaeeabeecaecbaebddcecdacbbaabcaacceaabdeeccaabdaabcdeecbbcdcdebdbedcecaacadeabdeaadeceadbbcdeddbeddedecccbbdceabdceaceccbedbdecdedbecaaadddcabeeabbabaceededecbaadcbeeaebabaacaceeabbccebddbabbbeebbcedeedccbedbdeeedacbacaededceaaeabacabaadadebebaabaaaaecdaadbdecadaebcaadeabbeeaeddceeedbdabbdeddeabaceaecaacadcccaacdcdaaebadabaceadeaedeecdaceacaacdcababddddddacbabedbaaddebdcdeaaedaaabadeeeadcbdecadbddcabeaddacdaacbadddeaeeecddececbebccadcacedddedeeeaaaebdbbebddcbbcecbeaecbbeaeecbebbacebedbacccdebabbdeddbdbbbddcedababebcbcbeaeebdcbbdcaecaddbdbabaecbbaaccdaeaeacbdacbdaadbadddcaaeadaecacacdeeebebcccbcaeeabadcaadbcbaeeaedabbdacebdbdaadceeeebddeddaaaeaedadbbbabacedaaddaadebecceaacccccccbeaccbeddeededeeaabeedebcccaadcaeeddbeeecddecbbeceddadcaaaaeebeccbbcecbcedabdbbbccedeebaaabccaaacddcbddbbaeeededbbdddabeebeccbabdbdadabeeccdbecbdccbcbddeceebdeccbedebceccddddcdcabdcbdcedcdceabcccddcceabbddcdcdabdaebcaecedbcbdaecbabaceacadcdedbdaebdeeaceeebacdbdebabbcbbcebbdccceacacacaaccbcecbeabedeecaedeecebaadcdceeadcacbecbeecadedabdbcaddebcdaebbdbeaacbcaceeeeaaaecaeecedbedcdaebbeaaedbbbbdeacbdeaabcabcbebdacddbbeabbcedaacdcdaecccabebaacaebdbdababbddebacbecacccbaebbbacdaddedcbcdaeccabebbceacaaedcbcbaadaabebaceededebacbeddeadbacabcdbadabccebecebbbedcdbecdbebaaedebdecbdbecccecceddabaaabbacdaebbababecbbebabcacceaeadbeddcbdbdcedddddcbbaadedabcbbceaebbdbccbbeaabbeceddcbddebddacceeabdbcbadbeebcededdaadcdcebcdcdbebbbebadeecbdeeaeeecdbdbeaebbdecbdebeeccbbaedeadbebbbbabbcccbcaccabedcecabbaeaaeceedceededeaceadbccebddadaecedaecdeebaddbeedbcdaedcabdebdabcbacebdeedaaccaaaaebcaddbdbcbacbacbeaeebeeddcbbaeddeedcceaccebdbdbbbebddacebadbdbdcceeddeaabeaededaecbdedbabbaecbcbdbbccccbddaacadebdcebbdbcadddaccaeceddcabdddbcedeeddcededaadebebcadedcecaacacdcbeccedceabadcccabbddcbdebcdbbdebbebcadcedecbceebdddecaadcedadabaccaeebcdeebdabcbdecdbcbaedabbedadabbeeeccedacccecbdbcaadeaddeeeeebececebdbeeebababedbbeddcebddcccecbeddedaccdbbcbeedbceacdbacdccdabdbbadcccadbccdcdeddaceebededcabacdddeacabebaabbaacbceacacdcbeecbeccabbdaccccdebdbdeeadbcabbbeeaabcccdbcadcadbdecadebdceeeedadccedcdbbccbdebbbcbcdaacaeeabbdbddecbdccedcadcdecddeabceebdaacdebdebaaaaadbdddaabdaebcdcbabbdadecbabddaadadacecbaebabecadbcccdabacacdacedeecbbdaacaddecddacaececdcaeebddcdaaeecbdcebbcdeabcaadddececaabbcedeeeddebcccebecebbaeaeacabddabebabeabdddcbbbdecaddddcabececaceaaadaadbedcceeaacedbedccabdebcaecdcadccaeaeaaeedeedbeecdcddeacbdacaedecabaeddababbceceeabbaddaaeaceeabbdcebadbddaeaaccecadeedadbccdeacebcccaaadcaeaddedeebeacbbecbeaceabbeebbdecdecbddaaedaaecdcbadbadadabdcadbaacedbebdacdcaddbbddeaccadbbeadceddccceeaacbbedccdeaadabcededddbceaceaedbeaaaeccbbacbbeababeddacedaabbaddbabdeaaceeeeeaaaeeecadaadebacabedaedeccaaedaadabeaeebdcccbedaadaccdadedeebaaeabaddaecdaccdbeebdaedceaadebecaeeadebbeacecddddbeecacadacecbebdedcacbaabdaededcddcaabacacbcaeadbaeabdedecdddadbdcbcbaebcceeebaeedcebacdcaaeaabbacbbbbbeabaeeccbddeeabeedeaebbbbcbdeeabbadaeaddacadddbbdaddecacdaadaceebbebdabcdebbbeddbbeedcdaebdcdaadbabacaababcdadeddceabeacdbededeedaeecdedaabdcdaeaeaddaebecacceaeadabaddcabbabedabcedebbbaeacbedeadeccadebbeadbaceacccbcaacbddaecbeddbdebbdbdadbccdbeaecbbcaaededacdcceebdbedcdecaeaacbaeaacededdaabeeaacabeeccaabebddbbaceceebbecacdbdcaadecaccbbddaacddcabaabaadccaaebdcaabdeaaadacddbaadbdaeddadadcabddeccbbabaaebbecaaebbdaeacaaaacddabbcbbebbcedcaccceebeabdcecbedcceddddecdcacadbaccdacccbcdcdbdbddededabeaebbdccdecbddbdedebeecbaecebccdaaadbdbcddadeeeeeddabeebebcdeebdcedebeaadbbbebaccecccdedecdcbaccbaebdaabeecdadbccbccbedadeeaeaaebdcebcbdeecabcaedcddcedecbedcbbaaacbdaedaacabeabceceacbeeeebaebccabeeacdaadabbaadbcdaeeadebccadbaeeacdbdcedadcbaccbacbedceecebccbaacadbbebbbacbbadddeaeeabcbcedccdebdeaabbeecebeebedbddccbbddcaecebeabcaaddbebedecddbacdedaedcacadbcedbdadcccbedcbabbcceecabdcbacaceabdabecaceaeccebadcbdaebdaacbeaadddaaeadecaebeeddaabbecaaecbbdbaeacdebeeeeaeaecddccbbaabecbbaecdcabdddebecaaadddeeccedaacabadeddddaddcbbeeeedcceaabdaebecaecbaebeebbdebbabeadbbccbaeeecbaddaadaccecbeccaeedbdeecbdedaaeadecdbaadeadcddabcedaacbeccccceaeebcceeaebaedabeecdddddaecbedabdbceeccadbbcecbaadbacbcabdbdbddeeaaccccbdeeacddecebebdcddacceeaceeebecbdadbbccaeecaeeacaaddcaabddaaebbbddeccadcbbbabedddbeccdbeaeecabeaeedddcabaabdacadbddccdbbeceedbbbbadbedcdceedbbbbeadccaeecabbbbababcacbedacaceeddecdeaecceaaecedcadeeacdeeddcdadaeddbeccddebaedbdeeabeeccbecbabedcaacebabbcebacdebeacdeadcdddabecabdbaddcabbbebcddecedddacacbabecdaabedbbbcaedabccbecacbddcdbabbadaaeecbccdebdceacdcaabaeebaaedaceecadddacbabacbbcddbcaddbdacdbedbdcaedcbddbeacdcceaadedeabbeabeeadaaaccdcdcbdbdddcaecaeaddbbecbccadcdbebcbbaeeaceeaecdbacedebdaedcabaedddddcbbbedeaebacccebaeabebbbcceaacacdcdabbcababbedadddbbccbeccabdeabbecdcbaadabaabebbcdbecedeaaaadeadbececabaecedcaaaaeabbcdcaadcdeecccdaecbcbacedeadeaeaddbddecacebedbbcccddbaedaccabecedbbddacababacaeaecbeccedbbddebbceabbaaeedddaceaeebbaceadeccabdcaacabdeceaccabdabeaaebbbcebecedddbacdeaddbbdadbcebebdbceeebcbcebccaadcbdacbcdecabbaaeeacedaccdaacbbabdcedeaddaedbbedeeccdccbbedacdaaaebcebacddacdceceabdbbcbbdcceceadbdaaeeecbcccbbeeaaddedeabdcaedcbabebdcbabedaaeadcbcadacddeedcbcdacedcdbcdcdbcadaadaacdaacdebccabeeabddeabdbdcbddbeaaccdddcadcaeebebbbbadebbccadecdbabcbeaabdbcecaadacadbcadaebdbdbeedbccbeaedbdabadeaecdabccbebecabdccbbceaccededabeeedbdbebedaadaadeeacbdcbcccccdaabbcdedbdbdcabacaeacebadcacbaacbdbebaadcaeeabbebdededbceadeedbaecdbbaeebeebaebeeadbeaddaacadecbaccecabbcdaedbbccedaecebdbbbdcebcccdeedeceeaeecaeeaeaabcebcdcdaabaeeebaebceeabbdabeddeedcceddaceaedcadbacbaadeccddddbccbbebaeebbaeddacbdcecebddebccbceecadecbbaeddebaaabcdaeddccbbbaabcdddeebacbceeddeaaddcdadaebebddeabbcacabcabcbabcdcecbabdcbbccdeaabceecaabdbddccbdaabddeededcdcccbaaebcbceecdccbddcedebbbccedcbbeeaabccaadacdeeabdbcbbcaeececadecbabbcbaebbbaaacddedbbaebeeaaceecbeadceeccbbcbabbdadaeecabdcbdadeebbbbcdbbdbaeaeddbdbeabdcddaddbdbecbdeddaabbaabebedbceaeebaddeeeaedcabbbedadbeaeaecdccecadabebaddeaddeeddeedabcbbccdebccccbaaccbadcbeacaeaecbedbcdbbccceacbedbbbeacadbeccbdcddbbbdeababbddbabcbeaeedeecddbeccbbdcdbccccbdbecbbebcdbcedeeabcacdeaccdbededdbbdbcbcdebaebabcaebcaabbdbadceecebadaccaaecadccebcbeeebadbdaacebbbeddebeebaccacddddecedbecdeedeeadbeddbaaeabcaaeacdacedcdbaadedaeabdcebabebdeebacdaaabcebbadaeabedebbaeeaebeecbdedeaceecbdcabddddeeccdedcdedbecabeabbeddecccdedaaddeebedeeaabdceeeededdebaacbdccddedcbcdabbbbacdaaedbdbaadcadccdbddcbaceebcaaacaecdddabdcbaabaeaebaaeaaaaeeebcbdbcaebabbedccbacccddcebdabbeddddcaebebdaaaaacedddabeecbdceaeedaccaaadaddaceadadeadeecdddeceedbacabdabeaeaacbcbaabbaabceeabaceedddbeeabbddaebcdbccaebbdabbeaceddabbbbddbacadbdeacccccbbddddaeddcccbdccbedaaabaecdaaaeaaabccdebacdebebdbebabbabbbecccbcbdcbeddcccbbdacdedeedeecbeacdebabacaaceceedcebbbcdaacbaaadbdeacbecdaceacbaccbcaccbccaeeabcceacdcaccdcabdcbacdbecbbdcaabdeccedcacbdeecbdbeaabbeacceadeabceedeabaecddbecdcbbeddddecaaaaecbbcdbdabadaeddcccaaececaabbaedadbcdecbabdacaddbcddeeccbceeacdacebcbedeebbdcabadccbdabdbacdeddceaddcacabebeceddedeabceccdabbceebaaebcaebcbdccdaabaeedaaaadedbdecbbdacbdcabbceaeeccbbbdebceacabddeedadedceadaeacadaabeabccecdeedeacddadacddabccceadbcccaeaddcecdcdaedccceadddbeceebcdcaecdbcebaacadcabbbbadbcdeebccccccebebaebdcbdddedeecaeeaabbeeecbbeeaeceabeedadaaacedadceedccdabbeeeeebddbeeabeeecdabddacbaeaecbcbecbceebadcaadddddbdabbdcbcdaddcacbcaaaaeaeceedcdaecacdddeaabbdcbaacbebccbeabbdcccaeabacecddabaabacebadebdedabedcadbbaddaccdebcebeaccaedabbdbecbaebaaedaccecbdcecdaededcabddccacaccbdabbaebbeaabcacacdcacbbbcdebcaeaaabdacececeedaedabeeebdacccbbccdbedbdbebeaabaccbeabcbebdeddaacbaaebacddebcbadaacaecceccabdcddbcbdcdbedacdedcabbcaeceaedccbbcabdeedaaeebbbedacdcedcebcacbcedccddeadbbbabebedcdcabebadebbcaacbaaadddcbcaebddbcebcabddbdddddaeccbddedeedbcbedebeacbacddccaeeadcadddbecdcbdacedcecaacbeeecccccaceaccbbbaabcbbbacaddddbeeacdabdadeeadecacdeccadeabbadaedaabdcaadbacaccdcbaeebdbdaacdbedaedbcebaebbebdbcdebaaceedaeeeceeededddaaacbdadddbddebeaeceeadcebadedcebbcccdbcdeadbcbddaecbbbccacbcdebeebadcedacebeeddaeebadeeebebedcbcaadbadceccedeeddedbdaebbcdbedebceebadabdccdaecedcbdecacadceaeddbbaddbdddcbdebcceebcaaeeccacaedebbedaaabacbccaabbdceccbdaaacdecddeebdbccbacacaaeebbcbaabddbcdddbaaecbecaebbeecdcecaeeacaeeeabcdaccacddbccebcceeacecbbbbbedbdaeaeebbcedebcbdbcdccbaabcccbeeaebeaddbabdebeddcccbbdbeedabbbcaedbebecbabcadddcedbcdddcabcdebcebeaaaedadaddecbacededbcaeeecbceeddcdbebadeccbbdaaebbcbecaaceebadcbdabdccbbaabceeddedaabddaabcbdbbbadbeaecdcddeeddabacadddadcdeeccbdbddccaccaecddaeabbeecddebdbbaaebcaddbdabaededbdabcedbeebcaadaaacbccdbbebebabdeaadccccbbebbeeacdedaeadeecbdebeccdcccbcdaeabaccaddbbebbdadadbdebbdedebbbdebeccbcdbcebcbcecddcabbaddedcdaedcacdcebaddbbcedaecbedebbdecdaabdbddcceebcdbcadceeeebaecbdcdaeaaaacdbdcacaceeeadbedbdecadacecccdcaeaadaecebbcdeaacbddaaebbddcbbdaacaaccceccaabddaabdbecaaedbdedcaacbccedbcdeecaebabaababddcddbbbacbebccedaaaabdeabbccbabccceaecaecdbeacceebaecbcbaacdadccaeaabcbeceaadacadddbccbecaadcededebacdebadbbdbcebeddedbedbeeacababbddddaaabcbebdbbdbddecaadbededccecaaabebbccbaecebdedaebdededcbbccdbcdbecbeccddcddecbdcedcadabebdeedecdedeadbdadadedaedbceaebdbebeeeddadbcbbccdbccedcdbbedbcbddedaceaaceaedcdabceccdaacdaeabeaedebccadceaeceaccdbeaceaeecabaaaddabaddeddedcaacbebccececceecaaebebabdeecabcbeddabcddecdbbddadecedecebcbddcaecbcdcaecacaccbbdebdaaabaaaedecadeebddacecdbdcbeadddbbceabbabbedbdcbbbacbbecdabbdbeeccceaeeecbccaddbcbbbccbbeadbbeadebaedadcebbccdddecddbcdeceaeecdecaaebacbbdeaeaaaaceeabadbaddbacdddcccdcabbcbbabaeeabbeecdadcccccccdbcdcdaaadeecdcaebbbbedecadcedeabbcecabbcdddcebeedabededbcbbbdadadcaeaaaeaedaaacccaaeedbaaaddadceaaeebdeacaaabdcbdcccaacadcacbdeebaebaaedbedaabaacbcccdadedaebcbcdeabeccecddaaccacacceebeddeecdcceddbabeecdddbddadccbbdcbadaeeeabadcacebddcdaacdcaccabdbcbdeabdeebaabdbbecccbeeddadddadeeabeaacdcdecccaebceeebbbbeabcabedbedacaaedaeabddcbbbbccceabeadbdebeeecedadbddebdbcabcdaeadbeabdebccbaaaedbbcdeecbbacbaaeeaebdeabeaebdcbbacbbebaebeecbbbacaacccdcceccaecedaadaeddcaaaaeedbebcddeebbbbeecbdceebcbdabdddaadceddebaedaddbaaadaeadbdedaddeceeeebeacabbddbcadbaccabecbbddcaadccceadaabbcbededcdedcdebaadadaebaadbbbbacdbbbcbccadbdccaabcdeebeabbcbceaccebbecdeebedadedeeebabbabedbaaaddaecaceaaacebaebddbedebdaecccbacdabbaeeabeacaeeeccbabaadadddadcdabceeceadceeacbeeaeddecdeabdeaebebacbedeccabedceccdcedaadecabaaddadabbaadaabaeaabadeeaebcdcedddbadaedbcecdbdeadbcbcaacaedcaccebdacbedcdbbbdcdecdcbadebcecebbaedcccdcababdcdacecddceabddaacaceccbbbaceeeedcdebceedaadabddaddbbbdcdecdbccedbcabbbbceccedcebedbbebcaecbddeddaaeeeaeeaaebaddccbbeecddccacbaedcbbbcccabcdeebedbeeaadacacadcbddedbcdacbabcadbcaccadecebeecbdaebbdcbedccabeeabdaadbbabbcbdacbdecdeeecdcdbebecdcebdddecccbedcebeabddcdbeecaeecbadcbbbbddeceeeececeaeeddacceeadcbbdaeebedabdebcbaeabcdcecddccacabaacecebeaeaccbcebbbcaabdebaebeaeeebadadebcbecaddbbaadeaacaaebaaacdcccbbbaacdccabdcadbaebeecdecccadcdeecddeeaeeaddbedbdbbdabbaeadebddaaaedeabebedbebdcececcdacaacecaddabaeccedbebdccadacccdcdbcaeeababaaedecacbebecebadccabcbeeaabaeabbcbecadbaceccedaacaaadabbeecceeadcaadcebdbcbcceacacdacecacacadbabcbbbceadbbdcbddaecccdaeaacaceaaddcdccabddaddedeaabbaaabbeaccdbbbbccbbccbeddcbaecebaccddbebadcedceaabbbecdccdebcdccaedbdaecbecbaeecdaccbbbcccaaedeadcddcdbaaccecceadacdacbeddbbaeddbcaddbacdacbdceabcaedcccbacadcacccaaaaebeeeeabeabdaddadeadadacdccdadedecbcaadddcecabbcaaeeadeecbcbecdbbbcddaecdccdedeeebddbedbabdecaecacebcaeeceaaaacbeaacaebaeabebbbededddcaebcabcdbdeacccccbebdaedbeaeadceedbddccbdcdeedececdbbaacdecabecbccaddebdcbceacbeebeecacdedaddbaaabebedacedcdeaedaebcdddbeeeaeaedaecbcabccbebddaeeccadedaccbeccebbcbbaadbedcdbeaacacedbccaaebaacebbedaecdbeccecadebdababdccacbecbdddabbdabaccecbdccdbeedcdebcdbcbddaaccedabcbdcaedacaedcedaeaeedccccdbadaecdeaceeebaeaabacddccbdaeaedaabaaecbddebdeedbadacbacedececcdccdccddbeddbdddbabdeeecdadbcabaacaccbeaecabedebaedccaccdccbacedaceceeddbabedbdacebdceaceabeedaadbeaaeddedeceeedbcbbdbbcabdcddcaedbdadceecabccaaeaedaeeebabeaaceebaabdbcddabeedecaceecacdeeeacaebdeedabdbaaaeecbbaaceeddadeeecaabebbabceadbdaebcadbcdbcdcbeaeecdccdeadccddacedabacedecdaadeaaeaccabceceecaeaeeabddeededacbdbbacdadbaacdaaeeeebaaebcabbccdbeaaebebbdeabebabeaacdbedddeacecaccadecbecedaadcaeedaaabbecdddadacabbecadbbeabcbbdebaeceedddceaaddeaeeaeedebbecadbdaaedccdeacbeedebcbabcbcddbbbbbbdbededcbbbedcedbcecadbcdaddbdabaeceadbaddcdeaccdcbacbbedbedeadceecaeddcdbadbebcdcedeeaeeeeacabeeacbccbabdbaddcbeabcecddccddeaabeeaeecbeacaceddedabbccdbbbabdaeaaddbceddbbccaaaaaabeeebcacdecdedceaebbcdbedbbdccdacdccaabccaaccddcecaaabbbcbcdababcabdadaccbdbacaccaaaceacaccedbbcaebcdeaaeaccccdbcacebedcaceccdcdbdeaabaecbdbbaaacacbbcbccbcebdebceedcdbeaebabdcdccdeecbeceebdedddcbecddcdebcbababdacdbeaeedbebeebccadeedcebbbcebebbcdaeccdcdacbbdbeeabcccecbeecbcbdecbdeaadeabeccaabadbcccadbecbedebebccceccccdcaacdaeaebdcdabcbbbdceacaadcdaaeebaecabbeecaebcabdecaabdeaaaeccedbddcebdcbdbeedbedbcceacedcecbbddeaadceebbaccabaaedceedcbacdccaabaeaedeceadddcccbedecdedcddcbeadcbaacacacadeabbebeacaabbeedbdbeacedcbaecaaeadbebdbcaedbedebddaabedabbebbabbdbcdeedaacbdeeeedaecbedbabebdcadaceecbeaebabaadadbdcadbaabaddbcbdbeeecdbcddddcedbabacbdeaeacdddeccbbcceaccaccbeceddcecdedbdabdeebdbcabeeadbeceadccadbacbbabedcbdebbcbaaeecbceccaecaecdeaebcaadcaacaaeaebcacdaddbcaeaeebbaecdcedaddceaadcdadeebcaddaedcbddabdabaadbbaaaadabddbbebcbddbdabbdcbbcaabdceedaceabebececaccbadceeedebaceadabacdddedddbbdbecccadedcdbbaeabadeabedbdbdabdacccacabbbebbeccaeadceeedbeaddbbeedcebcdaaeeabbdadebdbddbdcaebabbbabebcecbcabcbecbccaeacedbbaebbcadddbacdeeebbeeadbaaecdbceeddccdeccabbaeaaadbcaeaececcdeceeeeedbaaccdacabbaeecadebebabcdeeedcbbbbccdabedcdbcadddcaebdaacaecbbeaeccaaecabbbaacceabdcbbdedebcbdccbcababacceecaeccdbccebbcdabcabbdabaeeaeaccdceccbaecddebabbccbabbbbccbabebebdbcddaceebbdbcbbdcccbacbcebdcdeacbdacdcaadabceadeddbebebaeaacccedecbbddcbbeeeedbddeebdccbecbccbdeceeddecedcbceceaeecccaaaaebaddbddaeaeddeebebedababcedaabdebcddcbdccaabdbdcdeecabaabedaaaddabbbbbbcddbcbbbebbdabccceebeedcbcabecccacdbccbeabcceaebadbdbdaabacbeaecbeaeddcdadcecdbccdccdabebbbccbbeabeeaabacdccadadddddaaeeaedebedcaccbdccaaacdebaeedddcaddcabdcbcbabceccdbebdcedceedbddddaadacbedeacecceedbbddedcbccabecdedbddccbecedadceeebecdbbebeddcdaaaecedbbeddcdbdcedbebebbdddbecedecadbdddcbeececabbaadcabdacbeadddbbdbbceecdbbccdbaccebadbcaaaaebccbcdaeecdbeacacaebccababdbcbbaebbeadbabbdbeaeccabbdcbaaddcbedcbccadbbaaabaecbbbbcaeddcabcecbdcebbdcedcdbcedabaececeadacaaecdceeeacbaadcaeeaceabdbeccabdbbcccdccdaaeabeedaeabcaeabaebabecbdaaedbcaceaabbbbdcaeababacaaccedceababbbedbaedeabaccbccddcdacceeedebaaaaddcadaecbcbbedcadcebdbebddeecebccceeaedcedbbaaebaaceeedbcddedcdddccecedabcbaebeabaebbddadaecdcadbacdbceeeeeaaedeecbcdbdeacdbbeabdcdbeeabeecdaedabaddadbcaaccaedabaeeeedbeceabbccbcbabdebbbeeeeabaabedadcccbbadabeeebccbcaceebdcdbbdadbaebbdeebddabeaacdaeaaddcaaedeadebdacddbcabcadbaceabdeadcedabaeacabcabcdddabbedadedebcdcadcadadebcdaccdbeeebccccedbacddaeeeaadcaecbdcceeeaaedaabedddebbceecbbadeadeceaacbabccddeadbeaacbeccabcdbecceeeacebbeeddcdaaedbddcdcebedccddbaaabadeceaedcbcbdadeebccacabaacccdbbabaeeceeacaabbddcbceccbbecaebbebeeabbbdaeadaacdebadcebadeddaaddcbdabaeeeebdddbdceeedcecacdceecbcdbbdbcadcabedecacdeeaeacaebbebeaceedeaccdbcadeadcdaadeccbbdbbdeebdcdadcbcbdadcebcbccaeaccbbddadcabcbbbdcbdccbcececdbbaaaceadeeaaadbdbacbaddebbdadaeecdeaeadadacdbbeadaadedabcacddcedddcbccdceedeeadbccedcaabaedcbbacdecadebbbabdbdcdeebbbdbceaddebdebcddeeebdbddeeeebbaeccecedbbcebbeddebddbbcaaeacabadabbeccecdeecbcbeabdcbddbcbdaacbbadbeaccdebdbccaedbaabeabdbcaaccabeacccbadcdedebeaeadeeedaecbaceebbbcaccaaadcddecbccecccbadcbdebdeaccdaddcddbcecabdaeddaaadeecdebeaaccadeaabbaeaeaccaaeaacbaaeaeebaedddceaeccedeedddceaaceddaaccecdbddbabbeccbcddcaddaccdcdcceebabdeaedbeecdcecaececededeecaaaeabcebdedecbebdecdcebebbceccdbaabdebdaceeaaeabbabdbcedbedeabccedebceeeeebccbebddbdecbbbedaababaecbdbeecccbcacecabbeeedaeccbbdecedbdbdceeabdbdebeaddeaddccdceceaccacabdcadbaceadddcbbddbcecedabcbbacceccaabdbceebddebeebbcbdbeeebdaacdabaecabbcdbaaaacccadcdeecaadeeaaeecbeaeebeebcedaedbaeaaceadecabcadedbcebcacadcaabedcecbcbdadbbaaaebbaecdeaddedbcbbbbabeccdeaadcbdacadcbccdccedaaaddbbbabdeecdddbeeddeebbdcbdbdeeaaadaaacddababebbeeedceebbebaedcccdbbddacaedcaabceabbedbdcddeccddabebbbaddeeeabebaddadacccabeeccbecaeaabbedeabbcdaabeceedcadadebbaacaabcbbcdeddaccbbccdebbdeeeabdebebbabbdbdeadebbeaaeacbeabdbbecceceecbccaedbdbbbecacaacbecccbeeccabeccdbaabaadadeaeabeadacadcacaaeabaecedaebeeeadbeeaeedecadbeeabebacceeebaeecdcbadbecdbaaaaeaecdecbbabccebddebaaeddbbddcebeaccaeaacabebeeabeacdbbecbaadeeacadbacecbadecdeebcdcabbcabccbeadaebeddbddaeeacebdbbcdaaacaacbbdeacededbeaeeaddecaccbeeecdaaabaeaeeedddaccbeacdddeabbeedcbbccbecdecdbdbedbebbccbeadcccddbeecadbbceccaccaadeaeecbcbbbcccecadbaaeccedaedaddcabddebdcddecbcedecdcaeddeceecedcaacbceebcdcbdedeadbaddaedaaecbeaaccbebebcedeeebaeecbecbdddebaedcdaebebbecdcbaaaaeadcbedcbacadcadbcdcacaecdaeccddbdedaaabdacbbcebbdeaabaaebaaeadbebdeeceadaaaaadacccbaeeeedcaebcdebaeaccaccbaabaebdeccacbdabbadadcadbcdeaaaeccabccbaaacdcdbaaccbbebcdacbbacdaabddddbbdcacecbbcaaabeeadccdadedccddbcddcbaaaedeabdddcbdedadaedbbedecdddcbedbceceeebcbebccedeeacdadadadadedeabdaadbdccccdacdaaeebadabbddccabbedbeaeadaacbeacababcebeaabaacaaaccbcedabbeebebbeedabaeeebbcaaabcdeeebabaeccdbaeaccdcceeedcbbabaeaedeceadeadabbdcededdcedaacecccdcebaecccedeaaceadceeebbbdadadbdecccacccbbdcebcccabeddecbdebacadeacaaabecccebaaabeaaccdbaebbbdbcaceddceecaedaaabdaeebcdcebdeaeebadebaccdcecabdecccebdebbbabcabacbbcdeedeceddbceeabbcdedeababebadbdbdecbceaceddcbacecebebdadbbeeebaeaabddeccdbacdebdaaeeaddeededacdeaeccacaccabbaaaaeeeddeeecbcdcaddeadaeaaeadbbbcbbbaaabaeaedeabbeedcdbdbcdcbbbecaeebaececdecdadeeccaaddccdeaecebabcedeceacebebdcbbabeeecdebebedcccceaaceaebecdbaeababdaecabcceacdcebbcdeeeceeadbceddbaddababdddbaeddcaddaedeaeeedeaadebaecbccabaededadbadcccbaadcdecebceabccdccacebccdceaabebebedceacebeecbadbbeaacbddeaabebcbacecedadecbaaeaaceeeebadddedcbdabecbbeeeaeecbccbaabceddcbcaaceaebdbcdbeeececcbcabbbcdbdbabbeabaaadcecbadecdddaceaabbeaedeadebddeebeeadebddadaeacecdcebbebaadeceeccdcbcdbbebeadbcaccbcbbceadedaeabebcecacaaeabcbacbadbdcdbeeeadcaceaaedaaeaccbdacbbcbdaddebecadcbddeeedceaaccebdcceacbbdabbcebbdceaccccabcebacadcabeedaddcdbbbbeabceadabdbceeecbdbcceadabcdabdaadadbdeaddeaadcbdbadcdeebdceeaceaebcbbedbbbceedddbddddbcbddacbaeedbaeedcadbbbddaebbacddddcdcdeeaaebaedddddcdbebaedaabddcecbddebecdedecdbadeeeddbdaccaebcecebcabcbbdcadcbeaaeaeabaceccbaeaeaabdbdaeecdaddbecedeedbbdedcdcaedcdaaeedcbadbeebdbcddbdceeecbaacaeeeaebcdbdbabadbaedccadbaddbaedcceaaecdbcacadbaaebceddaedabacebdddddbabcaaabcdaedeccaecbdeedcdccebacabebcecdebebcadabdbbecaedbeddcccebacdbdeedbdaeaadbbacbacdeeeeaaeaeacdaabceddeccaeccbaaedbadbdccebabdcaebaadaccbcbbcbbddbabbcbbadbccaebbdcaadecacbacdebeaeebcbabeaedcaadaeadcdebedeadebaaaddcdbdbacedbdeedebabdecacceaeaeabdcaabdcedcaecaedebbcbabaecccbdadcbadacbaddededabebdbdddcbecaaabaeedbaddabdecccdcedbacdbdeeabbcebebaecacaaaedadddeeacedbcbacecdddadaadedaebeeecbacdadddeabddececeeccebadbbdcabebcdecdeedabcbebabbcbcddccbacaaaceecdaaaebbaccdaaedaaedaaeebcdeebcdbaaebccecacccdbdbaadbdbacddabecebeacbebcbcdbcbaedccabbbdbceecdbddcdecceaaabcecedbdadedeacbeecbebdeaeadcccbcbccbbaadadeddeedcdbaabdaebababeceaebeaedccbadeabbdedacaeeddcedebbacbdaaabcdeadbcbbabdedbcebceecdcbcbeeebdbaeeeabeddabeabbaedebbdbcddadbdcdaaebebebdccdeeeacbcadaccbbdabbcbdaaeadecbbeeeeeeaececcabcedcecaaddeaacdadbedcdadbeeabeaaadecdccdeccdebcabbcdaeadeabcaedcaeeaaaaabccecdabaedadaecdbedebedaccbdbbacacbbecadddadacbaeadcbddbeeebabbcddcbaecdedbdeabceebbcddedabeecaeeeabdbbbaadcdacbaababcdbebaeebadedaeacaeaaaccaaccabdbbebadabeababaeecdbeceabebbacaebddaceaaeeaebaaeaccacbeadccdadbbbdaecedbdddedbceedaeadddbbceeceabeedecbbadcdcccbcaecceedabedbcbadceedaedccbcdcabbeaccdeccebbcdcdaaeeeacbbddeceaabcbeabaabacbddecabdaeabcbedeecbecdbaedeecceaaadcdebcecdbaaabbcdecbecbaededbeebaaaccbaeeaebceaecdbaeccbccaaddbdddccdeeaedbedcbdabbaddbbaaabbeedebbdaddeaeeceaaebbabaecaecaebccadccadaeeddecbaaebaecbdedadbcbcdaaceeaeecccdeeecdeddcdcbddcecebcbdacdddbeddbebadacedcdbadeddcaccdbcbcdceeecdccccdccecbcbdbbeeebaabbaedebdaaabbdbccceedbccbcabaeadacdebeecaadbcdbbbbedddaaabededbdebabecedbbababcdcebdbdbbedeaadbdebedebcacbdcdceabcacecbccbbdeeccddeebacbdcdbdeecaadcdcabebcbccbaddadcaecebeadecbeebeccaaeaecbdecacdcadcadbcacebdbcdcadebbeabccacccebdbdcaccbbeeadedbecedeadbbeaceebecbbccdddbbaecbebbeaecccbcbdeacbaacedbbebcedddcabbccaecacdbbadcecbdeabcdaebedceeeaddbcccaadecebbecbadadeccebaaedaebcecbbbcdeaebbdedcbdebaeccbdcbdccbacabedcbdddccccbeadcdbacbdbaabadbabdcdccacbdbccecbbeeceaaacacaecddbedbaaedccebcccbbbeaaaabbccccccddcaceebaaaeaaeadcddbebbdcdcadeaeabddccaecbcddbacadbadcaaacaacaeebbdeceddabcaddbeabbcdbeacbcbeebbcdadedecaebaacebeebdeaedabdedbbeeccaabbdcbcbaacbbabddcbbadccdcbbebcaabcbeebccddadcdaeebadaaaadcaebdccdebcbbcbaeddbadabdecadbcaebaacadbbdceccdedeebbeccdbddeaaceedbbcaaeaeedcceaaedcdeaedcdacdaddeccbaadbddcbbaadcdaecbbedacdaaddcdebcdbadbbabcaceabdacbaaabecbacaccccdaabbdbbdbcbccdbeebaddddababcdddcecebbbaddedccceebabcedeeecbeecdaacbbbddcbdeacaeebdbbbaeebaccbacaadcceccbaccdcddcaeecdbcecdcaaeaabcaabecaebaceeaaaeedcdbdaabbaadcbdcbbcaccdeaedbecadaeecaebebeedaaaacccaedadabbbebcdbdbdbeecbeabceececebdbbaadecaaeddbdddbadaeadbbeaecddadabebbcaceccbcbaddcadabebacdaeceaeeaedbdbeadebdedbdeadcdebacbbebbbdcdaecdbbedeecdccdedcbbaccadcbcbdcccbdabaeedcbacdcebddbeaedaadbdddacacadcdeebaddcedcadacacedbbedddedcbdcbaecbaecbddbadecbcbddbdeebaececdceadeeaabcdeebebecbaccccceaadbdbdaacdcabadcbbbcbedcdbcdcebaccbaaccdeeadeeabbbdcdaccaddeebccddaccbbdccbeaeeebddbaecbcddaeacccdcaabdcdcadcbbabccdbbbaccebebaabdadeabccaabbeededbcecbcaaedcbebcdccaacddaaabcedcbcbadebcbbbedabdadaadadcbdccaccacdeddddcbcccdbcedcaebbadecbeabbbbeceddaabbbceabbecbcabbdebcedcacbcbadbbadeaaeecaabaebceacbcaadacbecbccbbadcebbeedceaeecebcacdbddceabbbdbedeecabbdeedcebdcddeddccebaacaccedbaebdccbccbdedcbaccdedcdcdececbbceebdbeebdceeaadeccadbebddcbebdaacaeaebdcecacbadacdbcaebbadcddadddbabdadaaadcbbbebdabbbebdabcadbdaeeaaacaeaedeadbceeecebbacbeaeacadddecadaedebbeceabeccccebedabbccbbbdecbebbeebbbdceaabbdbebddaaebeddcdaaeedaaaccddbbeebcabdcebcbcddccbcedadecddcaaaddbaedeabdabdbceeacecaceadcbbbeaebedadeeddbcbbbcbaecdacbccdbceedecadcbcaedbbdcdeccbdedcbcaeeaebdccdacdabebcacebbebdeacdbbeacacddcccabbebacabbabbecdabbaaddcceebebeadabcecddedbcbbecbeebebebaceceebacccdaddeaaabadabacedeeebabcccbabdcaeceeacecbbccbdcebccecbdabdbbccbeaeeddebddcebdbecdddddbddeaedebbadcecbbdcaebbaeabcdcbdaedcddeaaaaebaccaeacbcbdadedacaebeadcaedbdadabbceaeabeadddaabebccbceabaedaaddacaabcbbdcaccaeabadaaceadeedcbadedaddbcedcdbcadbcaebdadbddadbbbecebcebbbaabeabcbecdccbbacddeeedaceeecaccadeebcdeaceacdcbbaecdabacabdceaabdbccadebddaabbdeaccdacecddbabdeeddebebebadedceeeabecdedbcbbceabdbaaedebedaacdacabcbdbeedbeabadabdeacbbcaabeaeaddbaccabcbdbedaadcccedcbaddcaabadeaacedccbbdcddaecedabeecbddedeceadcbcdceedbdcbcaccbddeaabecaadaaaadaedbedebcceeeddbeacabbdcedddcdcdcbdcbecadeedccedbcbbeadccccacddcaecdcbeabeadcbccaccdadbcedeaadaccbcbdeebcadaadeacebbaecceaeeeaaeebdecdeeedecbeeeddbbdbdbdeceaedaedbadededdeeeebbcaedaebddbebabedacdcdeccaebbccdbdbbebcdebabbcadebceddbebdabdcaddcebcaaadebdbdedceeebdcbccecbbccabccbbdcccaeedcadebadbcdcaabcdbdedacbbeecdddadaecdabdbdcacaedeedccdcddebeddbddbcccbeceeddccbdddecdadcdaecdaedcbaebaecbedabbbceeaaebceeaabaababcbdceadccedaddacccbcaacacccacababbcaeeeaebdaaecaccbacbcedbcebeddbeaaaabbbaceeebacdaeecdbdaacdcbcaadcebbecdbdacaeabaadcbebecabcbebceadaaabeaeedccedddeeeecadcdaababcdbecdcbabaceeabdedebdbebaabaebdaabedceaeaebebecedcbdeeadcbbcacecdebdedccbccdecaecccdacbeddabbeaaebdcabccdbadabdbaaaadabebbdccaecaaeaedaacbabbecaaeedcdbedbbdecedaeaebbcbbedbcdbaacacbeddecaedcbceddebddcabeedcdcbdedecddcedbeabeaeacdaaedcabbcccabedadddadedcddacbdaedccbbabbabeebaeeaebacdabcbdaeadaeeedeeaccdddedbcbeecdbeddebbbceddeeddedddbaceabeaceeccdbbbabeadceddcaabdcacabbccacedcbceebedacbdbcddddbeadceedcecdceedbcdbdecbbaeddabeadebbeaeedcdcadbeeabbedabedbaabeabdaeedcdecdccdddabaeeeccbccadcdbecacdeeebceaaababdbddccaededabedebaecaccbbddaebacbcabcdbedcbebbcdbdcadbbbcdeacbcadbdabebcaeeceaebbeeeaddeedbbdecccdbbcebcadbdddebaecadccbeeabcabcadcddbbbdbdbbdbbdceceacdbcdeccbcabdcbeeabbecadbeedaadbdaeccaeeeebdcdbedebecebcaceaabeeaedcccbcaaebecdbcabaacaedddecadbbabddbdebebacaaeaaaccecbbebceeebaecbadeaeecedbeceedccabbaeceeceedebbbbdcacadbdebbbadaeccbcedcdacedbddeacecbeebacaabdcdcbbeebdedceacededcdabdbbabeddbabbeddacacedbabcdbbebababadeddbdcddddbeaadceecddcdbaeeaaabdddaadbdbecbeacbdbeacbbcadecdabcadcbbcbcaceeabdaaaddbadedeabbaaeaccbadabcacabddbedbdececdcbbdeddeacbeaeaaeecccdedaccccabccbbabcebdeddbdeaececeacebdaabdadbbbdbdbaccdadbebeadcdaeebbadecaadeaacabdddeeacdcbabeebcdcaeeecccacbbabaaecdadcdaebbcebaabeedbeaaeecbbcbebccededadbdbaecddcaeeedabeadbcecdabedbaacabeaccbdabbbcedeaddbebbbaaeceddebbadbaaccecbaaddabecaeeeecdeedebacbccccaacbeabaeedceaeeaeadcddbcbdceddacbeddedcaebeaeeaccddddaabcabbcbbecbeedbdebcdadcedcaeaeabdeeadddcaebcbceeaebadbcccdedebeccaedbcdcebbdebcaadebeabecbeaedcbccdcbadbbdcdcacccaaddbbadbcdcdecdaedeccbdcdccabdacaebceeacdcbabbdeeeddbeacedbcdbacaecbcdcbdaeacebdaceeaccdeabcebadaedddecaaeddbbbeeabdececbcddecdccddceaecbcdbdaaddeedbacbaeccabbaaececbeababebccbdabeeeeddcecbbcedaaddeebdcdeebdbbecbbbdbaededadeeebeccbbcdbbabcacebaaabeadeaaeeaddebccdaddbdceedaeaccabaedbabbcdbacdbaccaccbdddedddabedeacddabcabddecbdecbbddabcdacadeaededecabaacaddcaedadaccecdabbedadaccbddadcaacceabcdcabbadbcedbacdeeccbeaecedadeedabadbeaddeeadeabededdceaeecbabdeacacbcabadbecaccaebdcedeaadeabeecdcbcbbddedbcddbacbaaebeeacecdabaabbbdabeabcdedacbbceaacdcbaeeecaeebedcddddeecdaabccbddbcbaacedacebebddccebbecddbeccaeecabacddaadbbdaeebeacecebdbdbbdceeedacacdabaebecbbaaeccddcaeebeddedaecbabbeeacdedaeaeeeacdcbdceceeeecdaeccadeabbdaccddccadaddcbeaaeeadaaabadeababbebaccbdddeaabcabddababbdebecabdcdceccbbcbdaecdaedeecaedaddaadebcceddbedeabcabacddabbaaebdbebedebdceaaecedbdabedadaaaddbeecebcceecdbbdebceabbbebeadeabcecbebebaabcbdeaceeebeabacbdaddbdceecdaceaedbcaaceabdeaceeedabbacbcaccdeeaaedadededdbdcbccabdabbbbecaecbaedbbdbcedbcbacbdbcabcdcdbceeccaaeccabccbadcdaddbcecbaececedcbddcecdaedaaeeadabbccbaaecddadcbeebebebdcaedddaacadddedacbcaaeadeedbedceabcbecdcddabdbacdaccbadacbdeedebbbcccdabbedcdabcdcbbaecadacceeaedaeccedecdebaaddddaebbaaabcaecdabcacccadaedcacecadedeeaaeacadceaeadaedbcdbacecabbddacdaeccabdbaeeacadbedbaabdcdbedcbadaedeacabaedabddcbccbdcdacdcdabcedaabeadbacdaadacbaaeeacaedbccecabbdbaedaadcaccccbdbdbbbedadddcbdddecbbbeacddebbcabbecabbaabdbeeceecebcecdecabcddbdccecaadccdbeaceaeebbcabcddedbcdebcdaacdaabbbeadbbdbdbdccbbeebaeccbdcbcdabccabcbbecebadccbbdcedadcaedadecdceccdecaecdcdebbddebeddeabcdccccaaeccebadbecabceaeedabbcdcabacabaebadaadaabbcccbaedeacabdaeeededeccaebacbcabcaedaeaedeceddcabcbdcebdbcccdeeedabdcbbdaadabebebccaedcaacecadbedddeccecabddedcacaccabddcdddadddbcacaecbedcbcdddcedadbedecbccdcdcabeeecdedbbaccecddddcbdadaaaceccbbddbaeaddadacabbbbadbeadaaddbabceadddeadaaedcabdecabaccbdaaededdbeedcbdcdadccdadedebdedacdcdebccabcdbaceacbabebbddcacbecedceeecddbccdcaaacdddbadeadcdbdeebbccbabaabdbbbecadceaecabbdbdbddeadcecbeebcbaceaddbebddcabdedeeebecabbcdbcbbeceaddacbbddcbbdecbcdcaccdcaabacaadbeebadbdaaebbedbaadedbbaaacbceacaeadbcccddbaeabbbdceacccebedbdabadcdabbecddaeaacddaaceedddeebddadaaedbaebdbbedadeaadbdaadbbeaedcdddccaecabbecbdadbbccadedcdabdebcbbebddddbdbdcdeacbcddeadcabbaaedeaaecaeadcbcebeccadeaaaadcbecdbcebababdedabbabadbacccaddbbdbdaebdacacebddbaadcdbeeeabdcebaadebdaeabbddeacddadebeaaedcbdabbbdeeccbccbcbabdcbbececccebbedddeadccbadadcedeeebdcdcbdabbeaccaaedaeecebdedcdcdaaaaccbdddadbcdeaccddeecccdcdcbaaebeccbdaddececaceccabdadbecceebabdecebbaebabdeadcdadcdccadeabaaccecaeaabdcdeddcadcaaeaedbeebacaeeeabaaebadaeacabccbdcdacaebbaebedeedeabaecbbbbacbcdcccccacdccbeadadcbaeedebadbddbcaedaadeeacaccbebbbdabcbaeccbaabcbdabcaabdadecbecccaddeeaeaabcbeaabcabaebcecdebeadbbeccbcceceadacdedcebbebdbcebaebabdaacedaeacbbaccadeebdbadaacaecbcaeaceddacccaaabebeeccedcbbbdccbcdaecabdccaaeaeeaececbceaddbeaeccceaecadbdeccbabbdababdebeaeadeccaabbececdcdedcceebabbbacdaacabcaaeaeacddaabaebedecbebcbeabdebcccabcdccdcaacbedcaaeedacaaebcebbdedcbeabbedcaacaeccbeeceebabbcadaacaedcbcbdcaacdecbbaeebebeccbbcbeeeeddccdaacaaedbacbbdadcaedacadabcaebbadddedbdbadddbbecaabbaebcdbedaacaddccaedeaccccddeceeabbdbbbbcdcadccedddacecbdbeaadedcaedaecbbddcbcdbdbdebdeeabbcbcaeeceeeaedbdacaaedbebccdbdacdbedaeeedabbaceeedbddacbabbeadbbdbdcadaadaedeadabcdbcdbeddabccbcecbebaacbcaddaddeaabaeacdeeadcdeaedaddddcaccaacdaddddaeaadacaeabcdcddaadbbcbedcdbdddcdcbcdcaebccaaeddcbccddadcbbababadaeeaaceddaddbbdeabdcddeaceebdbeaedabdcddccabbcdddbbebdabaedcddbaaebdcbdecccbdbedeacbceaeacacecacdbdadaceceaecbcbabceddbddbbabceaeaccbbeabbeddabccbbaccabeeeabeddaabbcbadcddeeababeaaeebceabaacccdbddbcbdaeeedacebbbabcabdbedaaeeabebddcaaadededebdabcedccdedcecacbbebbbdacaddaaceadadbadddbbbacdeddcedbdababadadedbbaabadedecbaccbaebdebaeeacdbacedadebeceacbbdebbebcdddccaccecebadadcddbebdbacdbddbceeaadcadedebadaabbbbdeedbecbbaebacdcdeecbdbdacdabebaeaebacddcedaceccbecdbccbbcddaacbbebcdedcbedbccdcadceddaecbdaececdceccecdbaadcbcebcceabaddaeccdacceaedddddacacdbdbeedbccbcaebaeebaadbcccdbbdccdceaabaedcaddaaeeedcaeedeaebaaadaedabcbadabcdceeeeaecaaebdeaacdeddddcbaaabeebbdabedeabadeeedcdaddceceacdceabaecddeadedddabbebccbbecacbddadcbacebabecddcdeecdbaecddbcdccacdaaeadcdaeeebdadecacebdaedabcbbbeccdaccaedcdcbeeebaddccabadcabdeacbdcecbdcbeebdecccdbaaaeceddbbacbeabadbdebccebedaaaccdebaaddbabebedaaebcbccabbbdcbeccaadbaebdcbbbdeecbcdeceaecadecdddddbccdaeeadeddcebcaaecdecddedabacddecacebceaedebacdeecbbcccaadcacacdaacdcdbddbdabaedcaeecdebddccbaababbbedbeeccdadcacbdeebeeeaccccabaaabcbdcededaadbdcbaebedecdcbdcbbcbccbeeaceeaebccccedceeaecbabcdddbdbdccaeedcbbbadbcaaddddbbcbccedeaebabeacadcdbbacdcebaabbbaedbbabbabececcaeacdeaededaebdbbddeabdddcdbbeebcaceecccababcbcddbaaabbdbbbeeebcdaaabcebeadceaedbdcabcdeacaeabebebdbdeddcaeebeedcadcdebaebbbdadeacbcecdadcedecdaceccebedebedaecedccabceeccedbeadaabbbaacdbbbdccedabcaaacabeeceeedbeaedbccaaccaaddcacdaededcaabcccbedaaddcaedddebbaccacbddcbdeacdccbdbadebbabaebecdaabdabddcdadccbabbdaebadaeeaecdeedeceabbcbcebceeccbdeababaebdeceacaceeacccdbcbacdeecbddbcadbbdeabaedadddddabedcacaaebdbabbcebedeaddbcebacddacdcaeaaeaadbbbaacbceddccaaaaabdbcecacadbabcccdcebdeabdebccaeabbbaceecaeeeddaeeaccbeeaedaeceeceaaeaadcdbdeaddbbeeecacdeccaeeebddcccadeadadecabecdadedbccdcbaaddaadbbaadadecbbbbadbedccdbecccbeedcaedacaddeebdaddbacdaebadbcaddcaceaebadedbecbaebecdebbbeeaaabaededcbbaecadbacadeabbbbabbeeccbbbadbaadadaebacbdcdbcaaacabadeadcddaabcdcbaaecbaaceaacceeeaebbccadcdbbcaadaeaeccaadededaadccebebeeaacebacbbaccecbbcdaacadcddebabbeecacabbcdbeebabbbdecbbccdcecaaaaaadaabdbacccedbabdadabadcdedcbedabcccbcdbcbdcbbdcabedcabcacdcbdbabacbccddcadecbeecdedaaccbceceabceecbbdacebcbeeecaecaddaecabebbcaaddabadacaabaeadaaedcbbeadddedcacdbbbedeaaddeaaababdceddceaedeabdebbceddcdcadeecaebbdbecbbcdbaeccacabbceaceeabaaebaccadaaedeaabebdeaccdaacdcebddbdbbbaaccccaceeeeeadadeadeeccdbcbaaebeadaebabaeeebdecdbcedaeebadadbcecabbeceebaccdbbccebcdbadddaadcaccabbebcbeeddabbacbaebebabebaccaedcadebaeacdcecdbddcebccadcabaaadceceddaeeabeebcabbdbddcdadbaacadaddddcdbdbbaeebccdabddcdbbcebeaeacdabcacaaabcdbccacacdebaadcebcedcabebdeacababbeddabacabcbbcedcdbbedceabcdecadccbaacadceabeaaedbbddcebeacbbebddcaeacbcedddcccabdcdaadaecccdeadeccbabaccdcdccaaeacdbdcddbcbdbcedcabbabcdadabcdbeeaeeebdecaaaaaecabdadcbcdcbbdbcddeedaaaecbaebaddbcaddebceebbdbdecaecbbbddbcbbeadbdcaacbdbdaebcacebcaadbaedacdcaacdedbeeacabbdabebccadebbcdbaeeabbcbbaacbbeadeadddaabeadcedbcacdaebcbbbcbcabcbcddcbcccabdececcaebdbcdaaceaeccdcacacbcdcebeabeacdeacdbcecdaccbbbcaedbbaeacdbecabecebaebebbcbddadaebebbdecdcabcabeaeebdabeebededebecbaababdedcaeccbdcebbcdcaadacaccbeadcbeacbabdcceaecbedbeacedaadcbebeadeebabadcdcbaedcdbbaaddabeecbdbaeeceaabaaadabcacedacdacdcedcdcacacadaedabadacdedcbacaacdabdaeabbaebedbecbddbdadddaedbdedeadccdcdbacbdeeaabdbadacbdaeecddcdcdbaeabebcddaceacaccccddceecbabcbabedbdbadebdbcbaadcdaeaddecddebaaeabdecbdcdccabddaceaedbacabeebebcadebbcabebdbaeccceddedabdbaaebbcbdabaecbeaadeebacccecbdbabebccbdaceeeeadeaddcaddbebcabdeecbaeddbeedadadbabbacdbeaacdbeaebbaeccbcdaabaddccdcaeecbbaaabecdedeaadbabddbccebabdebacadadbeeacadbeaeededacddcadaeacaecdedeadcbaabaadbaabeabbcacaecbccbdaedbccbdeaebcbabcccacbbcdeededaaacdccdeeddcdedcabecabdcdececbdcddbbbabddbaadeabaeabdbcbbeeedadacacdbaacebccccadadedcccdebbbdabddeeeedbbddecedbebcbddaadabeadeeacddaeebaecabccdbededbdeaeeadbbbbbdccddaebbdbbcbcbabbabbaddcdbbbaededbadbadadecbebcddacedcaedbbddbedbccaccabedbebbddacaaaeacdebcededdebbcceaeebaabbcbdbbeedcbccaddabcbccbbdceedbcdebbdeceaaaddbdeccebcdddbcbecadbddbaccacaabdecaaabbcdebdeeebadacccaacbababacacbbbbabbdbbecaacacbceaaddcedbbbbacddaeadbbcccdaabadabbaeaadcedcceddbeaeebcbbeeccbcbabeabaddcadaebcbbbbcecabacbacecededeabbedccabcdbecdcdebeabacdcedebdcadeeceeeacbbebbebbdbceadcaabcaaebaeacedcaccaadddeadeeedcecbacbddcaebececddeaebbbdceddcbeabdeeabbdbacbdbbbdcdbaeaebadabaccedeceeacbacaacebadbadecdabceaeaeabbcbcdbbabbaecddcebcbbaeccdcceadccbaeaeaaaaacdeeacaaedcececcebdacddeebacccaabaccdceeedbcdedcdecdcadbbceccbdeeaedecdedeadbeaedbddcdbebcaabcaceaccaebadabacdebdbbdccbddaaadecbeeddbbbbaeccabbdeaacbdbbaeaaedaeaeedbdaeeaebbaebeccddeabaeabcccebddaecbccaacbcaadacadebedccbbeddeedcbebcddddadebaeddcdeedeebbbbbbebcddcacaddcdaeadbcedecaaacbabbeaeedceeddaebcdeeabbdcecbbebcebaacbeccedccacccabbaaaccaadecedbacbdddaecadeedeeaebddeeddacaaadbedeebcadcdddebadedeecacdabcdecedabacbaeeeedccacdcaccaeaaedeebbeaaebedaddbeaccdabdbadcdabbedbcdedddceeeccadcccdbbdceddaaeabbbbdbebeadaaeaaaebdeabbbceceecbbccececaddcbeaddecabebddaabebbedcccebeededaedbcadebaaccabebaaeaeedabbaccaadaedaeecbebedccdebdeedebbbbedbedbeaaedccdceaececacaabaedbbbbcceccbcaecddbaeabbcecbddeaaeaabedabbaadbececcdadbcdebaeabedcebebacbdeeebbbaacadeddccbacbbbddacddbaecaaaebaaaebdacaddabbddcddbeddeaeaeebdbcccedadbedeedccbbbecadeebcbaddadcddabadeeaedbedacaeeaacbbdbeaedebcadabcbaadaabbadceadeeacceeebeeeeabaabcaddcaebeeabbdaaaaddebcedbcedecdcacebadddcecabdbeaeebbebedecaabebaddeaaddceacebbeccbdddebadcddddbdebdabcceaddddadabbcecadddbceedbdcdaeeabeccbcddceadbcaeddbaaedbdacecdacddbdbdbdaaddadacdcaaeecdbecbdaebdbcdcdacdddabbaebccccbdbccbcddedeeddabdceaecccddbcbabdbaebacbcdedaeecddacaceaccddcddacdacacdecaaeaadeebeeccbcdaccdcbcacdcccbaeedbaeaddeadedcacbdecedcdceaeecebacebccbeaededeadecddacceeadccdaedbaeebaddcdccdddcebeeecbdebccaadbebbebadecadaaeacebcdbcecdcebbaebeaceacdbcbdaeeabebdcbbdbebcdaceecddbdbaccdccccdbacdcabdaecabecacceddaccaaeebbadcecbeaceeccbebcdaddedccaeacbeabdabeaeadcbadbddcdcadddaeecbeceecabaeabacdaaaabecacaaaaaeebbbeacbeebabaadbdebeaddedccdabcbaecdecdebadaedeaacadbedaaadecbdcaebaacbdaedbcacbbbaadbaabbdaaeeaedacebdceedbdceeeabeaedadaedcecacbbabbdebdcceceedbaddbbdbdddcedecceeacbbbdcbbebdcaacbadddeadabaaeacebcccadcaebaacaedeeacdbabccdcbeddcadebdbbccddacecbbeadcebbedccabeebaabbddbabebeedcebccbeadabddcddbbaebaceaacadbebbbabdebebddcccacdcaddbaebaebccaaeadddcebaceddaebdadadaedeabdaaebcbbbdcdcdebdcceacadecceaeeaeceaeaccbdcccbdeedaabcbccbdaebaeacdbbcedebedeeadbcaeabcdcceedceedeebdaecabcbcbeebabbaaceedebcdddcbcecabcbaddbeeecebbcdedeeedccccaaeedcacdbdaadceccbaeaaabbedbbbdcdaebadedaecabddbdebddaebabacbbaabadbaeabebccebcbbdcddcabdcebcaddebedcebbcdbcaddaccbbcacaeaebabbccbdcbbcceabecddedbcbeccbecacebbbaddbcdeabbabddeeabdbbacabdaaccbedacebccdcaccedecbbdbccbccdbdbaacdaedcddaacdbdbbeeadccbdebcbbeadaacabcdddcdbcdbbcacadbcadaabccbbedddbbaeaaeaaaadcdecbedbcbddbecebcaeddbddbeebdbadebddbeceeaebaacbacbecdcedcbeacdbbddbabaecabbcadcabbcedbeebeabbceeadacbeabceabaddcdceedaaddeaabeabddeddecdcabbeeaaacdbdbbadedcdecccdebaaceabadbbdbeeecddcbadacbbdcbccaaeaaaedbddeabcbbadcdcddcbbcaeecddaaaeddddaacdcdcbdbedbbccbcaeeccaaebaabdedaedcbedebbbeccbdacdaadabadbcebeedbdceaabadcdabdcbaedcbddbdbacebbbaedcaebbdbebeadeccebadcbaadaceaddbaeaecacdbbcadabeecbdbcbdecbdeadbddcaedccebebadaeacdcbbeaeeadeacdcdddeabdbcdbecdedabeeeadeddddaaaacebeceebabaacdbccabccaebaecaebcacbcccccebaceddaaeebadecdcebcbbddedbdddadcddbcccbdecdeedbeaaeeadbcdbdcdaecbbcbdaeccabbbeaabebeecbdaeadecebdaaecddeddeceebaacdeacbcdccbbddcdeddedddabbeebaccaabeceaabcaeaaddbbdbeadeedebbeeebdaaedceecaeeeecdacdcdabdbcaccecddcbaaadabdebaaacdbeccabccabcaebbeedeccbccdbedcebbddbacddceedeedeeabbaeadedbcbebddddcaaeeddbcceddedaaddcdaacaecaecbdacdbdbaebeaadaddeababedaeecdbbdcceddbeddebcdbcdbeceaeeeeaeabcaebccebdeacddbbccccabdeeebeedabceccddddaabdeeceddeeeeddabbbbeceeccdbcbbececcebbbeddaebccbbecadacecaceecabbbcdaedbbcbbabecbabbdcaaeeeadadbbcdcaacbdbdceeebcebcdddcdbbccdcecaadadebaeedabccacacebeebbeaabecececebeccacdceedadddcbabbeaeabcbecbecdceadbdbaeabbebdedadbcbbeabbcdddbbaabdaadeacdbeebaecaeeadceceabedadbbbccaadebbacdaaceceaeebbeeceaecbeaacdaccddcdebaceedeaeeadebebecddccbeaabccacaadebacebcdecbbaecbaecaeadcabcedceecbddcbabadeccedddbcdcdbcdddbaabacabdedcaacceebceaeddcbacacceeadeddecbacebcbaedeaedcceeaceececdcceecaebaadcbebcedacdbebececabeebddaaaddbdbcceccbcebbcedadeccbcddcedaeaebdddcbdbdcacdedbcbedbbbbaedabcbeedeeabacbcdeaeaeccabaccbddacbbebeddaeaeaebeabbedbbedabdebadacaacddeabeddddebdaaadaacdcecccddccccddebcccedcaeadcebbdbcdcccecaaeccaecdcddacdaacebaaeececacdaadcadcbecceabcbaccaaedbeddacdbcbebceabdbdabbcaeadecebeabcdeeeadaaaddcedcecaedceaacedacdaacdbebbacedbacdabcadbcdcdabeeaddbdabcdaccabecceababedbdbacdbacbaaaeeccdcebededdaddebddecdddeabcdeaaadcecacaabecdcbadbcabebceeceabcadbaadddaeabaabdcbbdecdebedececbdeacbcbbdcabeaabdacebebbcdaebeadaedbceeabeeabdacdcceddcdcbeecacadcbbeaaccabbdcbdcabcdaccdbadebbbdbbcbaaebaaaccbcbeceedbbabbcbbbcbdebcadcccedcdcadcddebddbabacbebabecbbedddebdcdbcaccdbbbcbdeeddedbbdbbcebabbbdceeddcababedcadedaedcaeebbeaecbebeaccbcdebdcadcebdbeedcdebaddaebddbbcdaccdcabeabbbacbcacdcbaacdeeadaeeddcbecebcebeeaccaebcdaacccdbdaedecbcdccceceebedbccedaeebecbdecadccbecaecbacddceebaabcabcbeeadcdbeddeeadeadeebeaaacaeaaddededdcbcbdaaadaaedeabcadabedaacccbdabdbcedeccebeddaecdaecdabaabecdcaddeeabccbdccdebcacbadecedabbbdbcbccacddceeddaddadeedceebabeeaebeeceecddebaceabbceabdbcdcdccabaedcbeceabebdcddcbaeddebdadaadccdebdacdcbcdcbdddedbdcdbceaccbacbddebecedacdbcdebbcedbbdccaccaaaacdebaccaccbcbcaeddaedaaaabbeeadccaaadccdcbaedabbadaeabcccebcccccceebcaecacececeaebbedcceccbedbbacdeeeaabcdbdccbcbecbeaccecdebeedcdaebbdcecccedbcdedaadcbdcaabcbadacababbeedcbceebeedcbaeaccdbacbebacdeabbdccbaacdddcbbcebdaedcdccabbeebbbdcddbeeecccceabdcdaddaacecaddbbaedeebcceddeeaeebbaeececdaaaacdedbdaddebabbbeedbbdbeeaecbacedccddeeedddcadaeaeddaaddbceaaaebcaabaabbaebcdacbabaeedacadeaceedeebaabbcdcabdacbdeebedbbdccabcdceadcbadeceedcabadababadbbbabddbcdcdecadbebdabbdaeadccacabbcbdeaaccebaaaaacabeeddbddcceaebabdadaabeebcbbdddadcdbbbdddbabaebcabcdaeeeadedaaeeebbbededeeeeabeddbecbbbeaddeaeaeadcbcaeedbbdccebceabdbbbcdadbeacecbebeadddedcdcdbdacebbdabeeaeaccccaebabdeccbacbccbbdbcbbdeeaeccddecaeaedcdbeadbeecddeabbdcdaeadebdacdbdbdaaebcedbebcbebeddedbacddebaceeaaceddcedeacbbdcabbbebdabdaddceebbbaccadadadaaaebbcbddbabaaceccdbcaacddacebeaeebaceaceeeeeecdcaebbeeeaaacbeeeaddadaaccbebbcebacbedbdaacccadbbdbbedaebabdacebceaddbbbbcdbedadcabdebdecbbcdcecddccddadaedbbecdcadbecbdbacecdbdbaadeacaeacdaaceadebcaebdbaeabaacbdaeaccdaeebbadbaddcecbebeaaecababdcdeddddcbadbaaccdcdeebecbddedadacbceeedadeacaabdebcedeceecabdaaedbbdecaaeebeaadcbacbedeceacabbaccaaacccbbaaaeacdedbacadcebcdbccbdacaaedcdbaccdbcaeacdacbdbbebeabbcdbcabbcdcebeaaacdeccbcbcaaebbadbbedbcacdaeaddbdaebcaebcdcabcecebdcccdbbeadeadcbbaaebaddedcacabdaaeaecacbcddadecabbbbdadacacebddcacdbbaabedabcabecabbbbcdbbbcccdcbeabeaeaccaaebceedeadcaabdabbbdaceaaabbaeadcddcddeeedadcdeadecddeaaacabcbabbdaaabcadbbdaebccbcacccacddebadeaedcabaaebddaddbceeceeccecdbaaabcbaedcdeacedaceaaadceedcbcccbaababdbeabccaebebddbddddddaccededaeacdedeedbbccaaabecdeaaaebacbebbedbeddcddadeadbcbdabddcaecaabbaacdbcdddbadaeaeebeaceddcaacbbcaceebadcaeaaddaddedbcadaddbabbccceaacbbddccadeddeaebababcdcacccabacedcebaceebcebcecdbecbedeaaaebedaebbcacdacdacbbbcebcbacebecdaabadbebedebacaccdddababdabbadedacccecacbbddacbdaabaececcbdeadddbeeaccaaedcceedaacbbadeaaddcabcaeeeeeceabdbcaaebdecdcccbebedbcdcaeddeeecadecdcbedacaebabbdcceddccacbbecaeaabceeadaddaedbaabacbcdaeaabcacbdeaeecebdbabbededaaddeceddedceebcabcdbbacdbbcabdebcdbccacbceaaceadebdcabacebeaeaaadccaabeddbebaeceaabccbeeebcbdceccdbbcbbaedaccaeedcaddaabaeaededcceabddaebedeaeacdacbbdecccaabbbddbeedcacdaedaaaaaebedbbecdacbaaebddacdcdaeebcaecdccbbcaebbacacdbcbabecdaccabdebbebaceebedaecbbdccdabaeaccddebedaeaccddebdedabaecceebcaebaadeeaceecbaabedbacecabdbcaccebdbbaadeebbbeeedaeaebecebcdbaaecbddabbdceaaabadaaebcdacaebcacbaddbcdccceeebbceeeeddcbaddcddddebeecbaeeaadadadbcaeceeebdbbeeaaddbcaecbaacacceecdecbceebddbdddbedcbacedbebaeabaedaddcbaaddaeddecebdaabbbdcedebeedaeeddaadbbaaaecbcaabecbcadaeebeacabcdbacadaebaebbebdeaabddcceadbcddcaccaceabababdabebccabcbebeaddccdddbcebeecddcbdebaaecdcdabebecbcdbebeedbedabdbeccaabcdebabcdccebdaebecececccdaacdadbcdcacebddbbdbadccdeaaadaadbaaeaaeecaaaceaebcbaeaecedbbbceaaecdbbaccaddeedabdaddbbdecaddbcdcecddaadebdbbcbaacdbcebaeecbccedaaddddeddbccdcebacbeeaeeaecddebaccccbbebaedcdeaacdcdceeaddcadaeaaabccddcaaacacdeaccbebdaaebbaddbeeccaeeabbeeabdadecbabdbbbbcbcdbdabccbcccdbeadabcbcbbaceddaddcddbdbacedaaceadcbdcbdcdcbabdbbdedcdecaacaddaebbccddbdbdeecebdcbecadccbcbcabdbbbcbbceddddbabbbaeecdeaccccdbddbacabaaecebadcebecdeacbceeebbdadecbeedbcdaecdacbebdcccbebbbbdbadebaedabcadacaddbcadebabdccdbbaaaccdbdcabaaadeceaadacaadbeeddbcedebbaaeaaeadabddeacbcaaeeaaecccaeecdeececdbcabdcbadbaaaadddaeeaaedeebcbecdcbebabdedaddbedecaebdccbacdeeabaeddedabadaebcecadaccdebcdedeeaddabebdcacabdebbcbaaddedeeabeddcbcdaecadecbaebaecddaccaecbbebeddeaaacaacdbecbdcbabcccdbedaeeacebaabbaaecdcabdceeecbcecedacecaceebdbccacddcccceebcaabaabceccabdedddcacddeeaccdcdeceaabcdccaacbbaeaadcabdbaadbceebbaacdcaaedaeaeebbcaaadacaebceaedcccaaeddbccdedebdebdeebbeecadcadeebabbcbeabeacecbaaedbdeecdbbecbbbedabdbcbddeddeecdecaabaeadcabaeeeeeaeabdccebceadaebcebbcbbaaabadbbceeaeeebdededbddbbebcdeabddeeaececdbedecadceadcdeedacbbddcdebedbadccabdcbccbdccebcdbeccadbedbdcacdbbedacddccaecaddbecababaacbeadeaeedcbecceccededcccbbabdbcbddbcecabdeeeeedeeabadddeeeccaeabbebaeceedbeeabdccadceadddddddbddcddbaceceeeeacbeacbeebaaadddabecaadecaeaabcdeadbccacdebaeacdbdccbeccccbebaeceacbeeacbceeaedaceccbdebcbeddcaabeaabcaeddbecbccaebedceeeddaedecadaedebaabdbadbdecdaeabaeadedbadcabaaadaeecedeadcdabadbeabaadedcccddaedbeaaeaceaedddbbedeebbeeaaecdbedabbdacdbeacccedaabeecdbacecdcccdcdeaaddbedbecbccbbdeddeccecedaaccdbbbeebbcbbbcaaaeabdcbeedbeabddacebaccdedbacddeceabbebdadeeadadadcaeaabeebccdeedacbaeaaebbaadbbebedaeaaebadaecbaeaccddcedcccbebababccccecabdcecddeeaabbadaddbeacedbcdcdbabaeebcbaccebabddababcdbdaacaddddbcedadbecebaedbaedeecaeecddbacdcaaebebaceeaebebceececadaddeaedddeccdccbdcabecebbbdcacecaaaaecbbbebdebedcaeecddcebcecabbcbebcaddccbcabdbedcddbdbcabcdcabedebdebdebabbaeaacdaacedcdedcccdecdbebeecbdbedeabedbabecdaedaaeadbeeaaecbbdeedbeeedaaaeddcbaadbdaaaeebeddebdcbecaedabdbbaedceaeaeccdbbbdceebbacaeabcddeeccdcdabbbdbcecddccaaceddbbddcadcceecbdaddddcbbdbcbaaceebabeeaeddcdedaacbbdcadebbbccbacdbaaaabacedcbcecbbacbddcdecdddedbdacdebadbaaaacceadbdcdbeecddcacdbcbeaacaacdeebcdeabeedbddeaddecdebadddeeebbeaaebbbdeceedeeebaeeebeeeadacbbcecdebdecadddcadebdcbbcadbcceaaaecaebabbddabcabaaddbdaeedbedceaaaebbbedcadbbddaaedebcebaccdecdbbddddeebcbabbdcddbeccbadecaedcaadeceddceeebaadaccaaabaccabbcaedaacbdbccbebacbaabebdabebbbbebdbcabdcebbeccdaabccccbeaaddeccbbbabcbebcaebaccaaadeadcdecaecbedacbbeadbcdcddedaebdbdeddeabbbccbaecadcabbdcacbbaddedaddbabaaaedabbdbceadededecbacbdbccbaebbaecbcbeceeeaacbabbbdcabecdecbbabadecbdbbbbcededbbcaacbabbbcacbabbbcdaeecbcdadecdeecbcdaedabeaabebbacdebbaecaacdcbaebeaedbceacbcecebbaadbecabbaeadedbdaebbdabdcedabdbbabbeadadcecdcbeeabcaadcaacbdecbeceeebcaaeaeceddbaeabadccebddedbabdbdacdbbadcbacddcaddbdebadccecabdaeceadacaaacbddacdbcecacbdedbacbbedabeeeeabbbadebdbbbcecebeddddeadcacebcdabbedbabdccddaaebdbdcaeaedceedecacebbecabcaeedbdbadebecddebcedcbdbbbaeadaaccccbabdedacebcdceabaadebcacaddededdebcaddecdcacaebcdaeeebdaadedabbbcccabbedaaadabacaeedaebdaacaddadeabdbadaedecccccdeaededebcdbdeaebcaebcbeabeebeddeeecdabbadaeaacdabdacadbeaeeaaeacbdcdbbddbacecaaeceaaaecdeabadedebddcdcbbceeeeaebeabaceebbcbedcebbebbcaababbdacdbbbeeeabedbacdbaeceedacaacccacabaebeeacadecdccaeedabdaddacdadaecaaddddcacebccbccbaeebceddbddcbaeeeebcabadbecceccbbaadecabceaddaebccebabbeeeacedeabeadeeccdcacaddbdabddbacdcceeedeeacabeeeeccecdcacbbceadaddeaecedddadeabdabbaacaedeabdadcbdbacddcdecdceecbcdebcbeeabbcbbacdbcddbdbbeeeadeaaeeecdcacbbccbbcdaeccecceeeeaabeeceedbdcceeedabbddbbdebabeeeebbebaebacbaabbadcdadddcebddaeeeaabbabbcecabcaebacdacbdccddedbeecbbdbaadcabcaccedabcecbbcaeddeabcdaaaeacbccaaeedcddccbaabacbddeeaeecbaabccceeadebcddcecccaecacbdeabdbbacabebaacbabadadebcbbeadadcbddcdddeebdaadbcbbcbdcaacaebdeeedcaaeebaeaccebdcdeedcccabacdaadbdadbdccdaacbbbcabcdcbeadecabecedcbedededcbabecbdbaecedadbaecebcdcebeeaedaeddeeaeeddacddadeadaadcccadabceaddebadaeebdaabdccaeeebdaccecdcdaebcbddccebdbcddcedbeeceadacccbdbbebddcdedbaccbdeeeccebbdbddeadbbaebaecdedcbbdbaeeebecbddbcbbdadadaddbdbecdccedeaaaceaacbbcbeadaecedddacdecbadbebdeaaceceedecbececaebdbdadcbbddaacbbebebdbdedeaabaebcddceaccceaacbeedcebddceeeedeadebbaaccbacaebccaadbcbedbaaaddbedccbeaedaecbdeacaeededcaeceeeeabdeaaadadebbebaceedcadeaddaebccbdcedacebeaeceabbccbcaebcdcbdcbccaebacccbadaedcaeaaeaabdbdedbaeacadabdadecacdcecacaadacadeaaaebcdeaabbbcacbdbdcabbeabaeccabeebdbbaadddadccaaaceabadaabdeabcbebabebbdbeddeeecbadbdceeabceeabcbeaeabcbecabcecbddccedccbbeacbdeddbbcbaaedcdbdaecaacebcedecdddddecdcdbdddbeaeebebecbacbedccddeababebdcacacebabebaebcbceacdceaaaadbcdecbbbdadbecbdeddeecddaebceaebccaaecdbbababccdbeaeddeadbdbbbcbadddaeaeabcbdaddaeebdaaebcecdbbadcebbdaababaeecaccadcdbcdbbcdbbdadedcdceeabbccecaacdacabdbdeedaaccadeaedbbebccdaeecedebeaceccebceddbdcdadcadacdbddbaddbababcdecebcdebbeceebabeddccbbdeedeeaececddcaeceabdeddaababeeaeabeabaacabcdedeedabdeadadeaecbdacaceaeeceecdaedcceacecbbdbbedeeabbecaddaabbeeacbdeecdbabadbadcdccccadddbebdabacaabadccaeaadbaeecabaacececdebadcadeaabbacbdddcdabbddbceaaeccadbbeeddccbcbabcdceddaeaeacabdaddaddccbcabcbddcecebeadbddabadabcabdbaccbedbbebeadbedecbdcdbbdbebbbbedcbabccacbccddaadaacdeeebedcdedbaeddceeedebdbceecbccbdacdcadeeeceedebbecdaebcaebbcceeceaadddaacbbdbecdbbcdeabeaebeddbbdddaaadbdeaedbccbbaecccaeadbccbbbabbeaacdbbbddebdbabcbbbabcdcaddeeebebbeeecaecdbeeedbebababceeaacebbbcacabbcccbbbaccdadaaddcdbabbecbcdabcabacaadbccdbecebddbdaaebcbdbabcbaaddbabdebbceacbadadebccecebaceaccaaedbcbbbbbeccddeaabbaceaeadbecaaaedbbcbccceebdebdbbbbbadaabbacdcbbceaacedbdcbebbcaacececaeecbbdcebbecaeadccaeaaccdaaaaecdcaabcaddbebacddccbdddceceaadcbcaaebdaedecddbecacabaaeedcaaccbdcdcebdaeceaabbdcacbdaaccbecbdcabebaacbbccadaeceacadcdaddcaeadaccecaaacecbabdbbcbcccdaacbdacecaeededbcdedcdeebcdeeabeaacbcbeadeacaabbbaecbabaadadeacddecdccddaaaddecdaebaadceeccccecccdaaeddecaccdbaeabebdacdadcbecdbbdcdaeccbdbeebbaddeeaaebcbdaeeebbaeabeededaecaadeaebecaddeaadbbceedabaeeddaadaccbaabeeabcdbaeeabbcccbdbabadeabcdcbbcdebacadddebaceeebebbacaeeacdabbeabadcceedbcbcdebabddccedbdbaaaaaecccdcaeeeeddabeebcecdcdbcadccbcaeaccedaedadaaccadbddebeaecddbbccddadababdeeeecbcddbdceddeebdcebdadaecceabbcabdcdbcaaabbdccabbbdabbdddbdeabedadbbbdebadcaaceecadcdaeedabcaacdeabbdcdabbbaddbebbeeaeecbcabedadebdabccaddaaadcdaededeaecbcdebaabdbabceaebdbaadaedebaaecdbedbdabacbbccacdecababbccaaeadaeaaddcbaedcdeccddbcbedeeaaacbccbadacbaeeabcedcadbacacceeecceebacdcddebedeaeeadaaedbebcaabeabbbbcaedbdaebdadadccbadbbacdbeebaeccdccaedabeebeacbeeceeadcbebdeecedaeeaeebeeaaecddbcedcbdbeecaaddeadbccdbebdcbddedddebcecebaccceaadddeadadebdadaeccaebbccbeacabdacdbcbbdcbeacaaebbabdedbedbbdbedbbcddbdbdebebedcebeecdbeddeacacbebccdabcdcbdeacedeaebdcabaadaebacbbedbbdbbeecbeddbbaeeabecbacdedcdaeccbaccdaececbcbbecadbdcedeaaebcbaacadeebbbdacdadbbeeabecaceebedccadebaeaeeeaadedcaebddcccabbaeabcaaddbbecadcbaddaaeaedadaaadbaacaaedbbdadadededbcabbbbdcaecceedbdbccebdceadceccacaaccaceeadbdaeeeeadadacbcacecaebcbeaabeaaaccbeedeacecedadeecaedebdaddeddeeedaeaebbcabecdeeecadcabcecabacaabadabcebbbdcaeaccddabecbeacdeaddaeacaeedebcccdbacdabaccdbdbabaecbacbdedebbddebdcddadeacadaacbcdbbcadccaabbdadbcbaecaccdabbeccadaaddacdabdcccddbbcdbeeadeabaedeaceebcadedecbcdcbeceecacbedaaeccdbbbceaabedeabeecebcaededbbcdbbcdbbcbdeaacececbedddbbebdbceaebcdbaebccaaedaeeddeddadaccebdbceaaebbacbcbedecacbcedebcdaaeecddbcdcbbedbdecaaddeaabecaeeeccbedbeabcbaaedcecccdcbcdbdaebacecacecccbaddcacdbbecdebaecbdbbcbaacaedcdedcdbbcadcadccceebbcbcbbdaebdaccadebcaedbdadcbcbddecebaeecedbabeaeaadaacabcccdeedcabedbcccaebcdbceecabdeecdaedbdbebaedabcaabcbaeebecadcdddabaebebddbbcedbccdbbdacabadcddbeaebcbbadcbaaabbebeabaccebdbaaabaaccdbeeeebcabacaaeaaaacaccdcdcbadeaeaaadabebbbaeaaeaccbacdbeebeeccedebbaeccacdbbbceadeaddcaccebadbdabcddabaacdaecbdcdaabdbbbaeccddacbcaaaebdbcaeeedeaeababdeccdbdbbeaaedbdebadddbbaadadbaeaaaaaedacaadbceebebaddeecedbabecebadaadebdccbdbedaccbcebdadcecaceccedadeeeccaeeedacedceedbbcabaaadccdbaaebebdaeccddecabceaaddbaaaeceabbaaddbbbaadbedcacebedaabdccedadcaebabdbaeedbcedaadbbcbdacbbeeadcababbdbadecedabaaabeccbbdebbdaeebacdbebacaeeceebcadccedebbeaaeeebbabedcdcbcaecbcaddeceebaaeeecdceacedddbbbaeceecaddcddccedbeaeacdcabaebbcbddbccbebaeaaecbecabbcbaaeedaeacbbaebbcadadecabbedcdccdbadbabababbdaddbccaeabccbdbddaecbddadeabeacbadcccacbaccbeabacbdcaaadacbeacbbbbceeeaeadebdbcdcbedcbcdacdeaeadceddecdbadddedcedbecdabbcaceeeeaccecbceeaccccdedbccbdaddbbecbdbcbdbecccdaebbeadcbdedbabbeaddbeeeecdcaeaeccbdadacbdebceeaaddcceaadbaaadebccceecbaaadeaddbdcbdbeebcccaaecbdeedbecbedeaecedbbebadecbeeeedbeedbcaccaecedccaacbcddaddbddedececbeccccedbdcbedcecbebddbccdcbbcdaeecaaaeecaaedcadabbaeccbeacbeebeedabcadbaebcdeeddabeabeeeecdedcdedcddcccdadeedbdeaabbddabaddecbaebadabdaacaaeadabbeeeecdabacabdaeebedcaedadbdeaadbbdcebbeddecccaaedcabaacecabbeeeaccbbebceddabbaacbacacbcbcabcdeeadebdaaccabcbabeacbeacacecceccdeedcacaeaaeaadaabdeccebcccdccdbacbccebbbacaccccdaeaeeaeeddadceaedccbccaeeedccdbdcdbcedadaaedeecbecebdebbdeaabeabddcadbddcdbedebcdedddecdbeaebbadecccbbeebbbdddaaaaccbbacbbbcebccaeecbcecaaeabcdeeabbbcebdabaaebdcecbddccbebdacceebcceabbbaadbaeceaeeeedbddacbedeadcdbaccbaebcbbeeaeebadebcdadedbcbabbdeaaccecdadeeaabcebecaacdccdadaabbbeadccbaacbeadcceaadeadbedcdaeaacecbeedbbebdeacdebaaeeceadeabccecaabdaecaedcdeeaaadedededeabacdeadccbdbdaabdcacebbcaadedcadeacdaacadccbcacbabaddebaeeebeeddbbeddbdebceaeaeacbbbaccaebeeceabaccdeddbcccedaddccdeddbebcbcceacadbaddacbbacdbcecbcaeabdaebaabadcccebbcadbcdbcecaacbbbadeccdeccdabbcbacbaedabbbaabbabaeabeeeabeeddabccbebdddcbbbeaeeaddecdcdacdbbdeecececdcebaaeeedceeccaaccadccdbddecaceececbcddcccbadceeccedbebdeecdcdedacebaccccaabecabbbadcbcebbdcedabddcaacbdeaeabbacecadcaccbbdacebeddccadebdeabdcceaeaaeaebcdabcbeacbabbaceabaabbaabeddbadedcddbaebbecdaeabedaceeddacbcacdbcebdcbacaedddbadcdbecddccdebdaaedeebeeeddedaaedaceaccdbaddcaebeaedeacabeaceacebdebaacadaaaadbbbccdadabcebebeeaabceaacabaebccaccdcdecedbaeebededcbaeebccbccbdbebebacdcadaabbddbdaedbaaabaaedbddabbadceacbbdeaaddbbcbeacdcbdabbbbbdcbcaaaebadeacacddeacbcedecdecedccadbccbceedcceadebedbeedcbdbabbeacaecbbbacceccabdeaebebdcbdbbcdcdbdcdbcbacdbdacaadbdcaaededeabdbabbcebeabccdacdaaaaeebabeabedbadcdedddbedddedacdbaecdddcbdbadcdbbdecbdcdbbebaaeaebabaedaebdbacbacbcbabecdadacebccbbbeddbdaaddadeaeeedebebdbebaaebdeeedaaccccdccceecabaaadbddcecbbdbbaeeabbbadcedeeedbadceaececaecedddbecbceaaecaebdcbbddabdabcdbdcbccdaecaeccecddbcacedaccedeeaeeadddddbceaadacdddddeccbdcaaeaceabbdbeeccecbdbbebdedaacdcddebcacdbecdccebbdaaacacddddedaddebeaaaceddaccaeadeeedbadacceacebebbbedbadeeddcadaeeedeedaadeaeebacbbcacbaaeccbbbeeaccbdeebcababbbbedbdcabedcbabcdaeccaadadbbacbebbdbdbcbdbaeaacaabdbdbdedbabcdceecedddabcbebeacdbbeeaaedaecdacbecececebbcaccecdecdceedcadaeebbcdeecadeedceececebacdcdacdbaeccddebdbcbcceabdebebdcbeadbcceaaabcededdaaeeaceebbbdacbedebaccbdddaebdbebbbebbecdbddddcbedcedcdadbaccecaaddbdcaeeadbccacccaeaeaadbebececdecddaccccceeeddecceedbbcbcbcccbdadcdbeaecebcabbcaaeddcabdbdcabeaccacadeacdaeebecdbcaebebbcdebdaddbecdaecebccbeecdcabdcbbbbecaaabdebacddebabeeabeaeddbcacbacbccecdabaeeedabedaddbcededbbabbaddbbceceaceddcadbababdbeacdbaeccaceabcbeeeeeaaecbeebaabdadbedcccddeabbbecdeededbabcddcaaedddcdbdddacedccbecdcddcbcaebdccabecaeedcbdbecdeeaeeccbdbacdeceedadbddaaaccadadeedebdbbccddddedacdabcbadbcaeebaaeabbddbdbedeedebccddeaadeedcbcedcdeebdabcddcbcbdbdecbcddbbdebebbadeebccacccbacaeadebaaaaaeeebebeebedcecebdeeececcebbbcaecdbdacbbbbaeeaedeaaeaacecaddcdeccbbedeadedebacecdeceeaacddccdbcacbbbcbebbcdbddcaeaaeebbecbbdbccabbaecaedaccaeaaeddacbcacbcceaedcdbcdaaaebaebcdbbdcbbdccacaaccbcbeeedccbdbedadeebcedacccabccdecbceacadeacebbdeceaaebceadceccacaaccedcacdedbccaedbabcddbdcecebbbeeaeceaecaccedeedeaededeccceadcaccdaaadcadabcccacbdadaaddcabadbaebebdecdacedecdccaeadcececddebdccbbdeaebdcddccacbdbabeccaabcdacebdceebebdecceaedcdbaeceaaeecabaabebeebecaeecbadadacbcbeeabcdabeccddacdabbcbcacbadecaddbeddddeabbccbdadebabedcebeebcbdbdcedaadecbbadabcccbdecedaeaeaececaddbdbbdbeacbbeebbbeccccebbbdeaccdbeaecbedeabaebddcbdaccceabccccdeacacabdedeeebaeceaaedaadcdcadcaddcbbeddadcbaadabcecaebdbedcddbcdadddcdaecdaadbdabdabdaebcbbbbdeacecabaebebeaadbeaccccedbdaeaabbcaaaaaaaedbbbbedbbaeebeaebcccdaecbdbdbeaebbecebbdaaeabccabdccddaabbbdbabdbcbadbbbcedbdaebacacbbeaabacececaeaaebcaaabcedeacbacedddebdadeacadecdeddabbdbcabaddcbecceaeedccedeceadbbcbdccbbcedabbeebbaeebeebdecaaeebbccecddbceedbbaabbecadccbadcaedbdaaddebadeddadbcaccbbcbbabdbabbdcaccbeeeecaaaeeaccbacbadadacceabebbdcabdbaaabeaddcdceebaccabbdabadbeaeedebabbeeeacaaeaceaacbaeecdbaccbaddeddbbcbaacbeaebcdaecaadebbbbcebabcbdacdcaeeedbaaacdddbcbbdabcdcaccceecdcdccceeddddcbeeeaadbeeebaabdeebddcabdebebddbbdbaceaabdaeedcaadcacbaddebecbabbebaadabdaaaddcdeecbcecdbbeedddabaeedbbaebbacadbccacaccaebcbbeaeecbecccebbdbaedaaeeaeccaabebbbcdeadddedbcdbdbeeedaddbbdcbedaedcbaddebcccdededaadebeccacddeaebdedeacedecadeeeacbbacbcdddbdddccccceaedaabecbccdeabecebabdeeacbdbaacacdaeaeeaecbbbdbdcbebebbccbbecdeeeabdceaadceebdabdbbcabddbdecdebedebdceaedcebbeccacebeceaeaadcedeeebcceccddaeddbbbcbeebaeeedeabaacddcbcceabbbdbcacdbeebcaecdaebdcbcacdbdcadcaaaeabaccaacddddeebedbebeaccbaededeacbeabcbddbbcbabcccadeadaaccaaddabdbddcdcddbcabdececabdadebccaaccacacaabccecacedeabdeaeceacaaabadacebbdcdcceccdebcaabceeceebdcaeaddaabaacaaaacedccbabbcabbebdceddcceaaaecadeddbdedccbcdcdcbacebccceaedacaebeeeecdbaaebecdcddebecadcabbddaabdbeebceecdaedaebeecdbabcceddaeedeceabecddaeacddebacebcaeeedcdabadeaecabceeceacaceebcaddabcdeccbacebcdbdbebcacdabbbaeeecaceeeacaadcecbedceabaadeccedbbaaeedcadeddadccaeacedeceadaacaeaabbecbeccdbadddaaccdbaeeeeebedcccbbdbcadedadeddbaacbebbacbebbbaeeaacdbdaedaecbaeeedddeabbaebddbbbcacdaeaaddddceecbceeabdebdcdccecdabddbeabebcaedbcdbcacccebddaacceceaeccbcdebaccbceaedbedaccabdbaedaeeacbeeeebeccabccbacdbeecdadeccbdabaabcdadaeddcdedabacabbecdeeaeacddbdecaccdcaccdbcebdccbbcabebacdddcbdcaaddadbaebdbcadbddeecdbdbcacdbabbcaecdcbbbbeadcbdbcdbbbbabcdcceeacdcadbdeddcbaeebdbaaeaeceacedccbbcbabeaebadadbaedceeabadeeeebccbdddbdceaaededbdcaabadbaacdaacadaddabaccabaacbeedbbadbbdeaeebbccbcbdaddbcbdceeddedbbbaaeaedbeebaeeaeedebcdacdbadddedcbbebabdecdebaeacaecacbadeebebdecedbebbaeaabcbbabaeaddddbcecdaececadadadcdcddadeecedaaaecbdcddcbbceaeadeeaeaeadbadadccacccabbdabababcbdcbdcbaccbddebebedadebddddaaeccacdabbbccbdbaaeedbbcbebcbeaecccedbdabccebedbcbedbbaacccaadecacadeeadeeccadabcbbcedcdeccbaeaedbbeaeaaeaebcdabbadceccebcebabdaaddadcadacbcdeadeccaddcbbeeeadeabecaceeeacdcceebdccaaedcbdecebcaeabcddcacbcbbdaecacaddaccdbdbbbedcbedadeaeaeadadbcdaeabeaddeedcadadaecabbabdeaaaddecbacadabcedbaccdaccbecbcdaeadeebbdebadabedbebbcdcdedcddbbaaedadeebbdeecbbbddcacedeccbedddcaeedaedadcdcebebbedadadbdecebeaaedcabaeeeccbaccdbbccdedceccecbacabeceaebddabacabcaeeaeabddecadcbdeacdeddadcadcadcbcedcbbcaedeabecbeaaaacdcaccbccedcebdadaaeacbabcabdadeeeeeeecdbecbcaadceaabeccacdbeeebdbcdbdaeaddadabebcbcbdbadeedeaeaaecbababcaaebaedebecceeccebdbbaebdeaebdadadedcedccabaaabccdcebbecbbccbbccbabddddbdedddaabbdcadadccecddacdeebdedcbcdadebddcabacebeccebdaacaddebaeeebabedbbbadcdeccecbbdaabbdcdebcdebacaeeacdbdacedcbabeeaecbebabcccdebdcddddddacedabcccaaedbaddadcbaaccbabbcecaecabdaacbeaecdadbecaeaebebaabddcabeebdadbebbccedaecbbcedcbebcbebacedbbaddebdaadebeeabbddabdaecabbcacadeaeabdecaddebadaaccecdddebedeecabbebcadbbebadecbbabaecddaadebccdddbadaeeeecedcdbbcaebcdaeeeeaaabddedaaeddebccccaabaacdeeaecdbeccbccebbabaecaaccbbdadbbeaaaceeecdddcccaedeccddbedeccbadebebedbacbaaebabacabbaabcddcbbecbeddcdbaeaccabccbaacdcdbecbcbbadadceecccbeacccadabceeadedbbbbbbacebeecadeebededddcecccddacdacbdeecddaeabebeeeeacbcabeeccedbdbaedabccdacadacaecedeebebdbddcaaaabbbcacaecadbebccbbaecaeededddbdacbcaedcbbbcdccecebcbdeabbcbecdccecedbaceebddadcbbbedeecabeaeeabbebdbdaabddbbeeabebbdbcbdcbebcaacacbcdcbeebdbcddccccabdaaaaddedcbcaeeedddbaeadbaceebcdbceeebaeedddebeacbbbdccaeebedbbbaeebaddebdbddabadccedbcdccbbbeeaadcabcaadeecaeaecbeceebaecebabbebadbccaaeeaedcebebdaddcecaaababecdcedcaaadbbbcccdabacddaeaeeaddabddddeeabbeceaeabdeaacadecdabbcaeceedbaedeadcecceabeecddbdebcebebdeedbcaedadcedbbdebeccbbbbcadbadaadcbedccdbadaedebdcaabdeeaebdebbedeacacbccebebaecceabddecaedaeeabaddbdbbddeedcecdeedaccecddbeadacbeadbeccaeccdaeecbcdeedceceebcebaaabbbcacbaabdbcaedbccddbdaabbbabebeccdbccadddbceaeeeddbaeaabebbcebaaeacbaaacaaecadeeaaedadddcacdbcddcaabbcdeaeedcdecbcbedbecdedbacbaedceedacaaedaaccecdabcdcebcecbaacbecabcccdabdaadabddecbbeeadebaaebbebedabeadcbdceaebabbdddcbeceecbcdadaddbbbcebadadcecaecaadaedcdeddbaaadbcadcaadacdeacccdecbaeccbaacbcccededbdecceaecceaaecbadddcdaeabbccbeebdedeedbeadecaeaaecbacbbcdaecbbbdcdddeaeecbbccdbbdeeceadbadeaaebeecddbeccabcbedbcdeadadeedbacdaeabedddcbacecadababdaebdcadabdacbdebbbcbadccaaeabbddcdceaabdacebbebaedbbddbecceecebabdbbddcacdcaeeddddcaeccaaedbbebdccdbcccddeddbbeebbedecaacedcbcbaacabdadeebabdbdecdaeeddbbdcceedeeecddddaacbdbccccaaadaacabceeaeaebdbbddcbabeaeeaccbcaaccbcceaabbbdabcbdcabdbaebdbaadcccaaeedaebacacaddccdaccbdeaceaeabdcbdeddaccbdebdcdbaaedadaaeacebaaaebdabedaacdbadbcdadedbecebcbcbbccddadadaddddbbecbdeaaaedeabccbadedbeddaaececaddeeaeebddbaebcdbaeaedbeadddebbecddadbccedeedebaddcacdaebbcbeddecccdbdcececebbdbdadebdbcaebcdcdbcdbceaceadceebeabaceaaebabdaadceeebedcbebdeccccdddbcdbcecadebecebbdeacadbdacbabdbccddccdddaeadbececaccdacaeedcacdbbedcceedabdacebccedbeaeecadcddeadebdcbcbbdceebacaacaccabaecdaacaccbedbeacdedeedacbdecedecbbbebcaaeebacbceadabeceeaaabcaccedcebdbbcbeaebccbbbbeeadcecedeceeeabedeceadcdccddebabddcdcaedcdaaabbabebebecaeaedccebcdbeedcbeceabadcdacacdeecdbbcbaebcbedbaebeebbabbbbbabccccbcccdddedecededbeaaadaecdedbeeddabaddceebdbeaedbceedabceeeccabaacedeeadabbaeddbadeeacbaaeadebcaecdeeccebdbbadebadddedcacbdbeabedcdcdacaceeabdeecbbeecccbcabeacbedccebebbedbdbcebeeaacebdceceaeaedebbcbaddaaadabadaebbdbccbbeccdadabcaedadbbaeacaeacebacddecdcacebcbdbbcbcbdcccedebedbbdadcceabecccbaabdbbddecaddebaeecbdbaeeeddedddebdddbbdcabbccceedecececccadceadaeeebcdacceebeddeadabbabceddcddbecbbabacbdeecdbcddaeeadabaeececcbbaacdcaebdedcabedebbbeaceeededaddecaadcccedebbeadcbdecbbdcadaeeaabdccedccebbebaeeaaaedbcaaebbadcaeebccaededebbdeceecdeaabbeaaaabaeeabccdbebaeacebabcbbdcaebbcdbdbdaaeabaeebccdebcbaaaedbacceddacaeeadbadcbdebdcceeccadaccbceeeccaeabdecddccdcdddabcdaeddcdcedecdccadaaeaeecbebabcdcadebaceabcecebdbcddcdebbccaaadbbddecccecadbcaeadccadbcbdbbbeeebeadcdccdecceebaedabccbeddeeeadadebeaaadaddbdddbebbccacabeaedeebeeadddcbadcaebdcbcdacedaddcbeddebbedaabdadbbdaeebdbdcecbcaaeababbdcaddbaadbdadddeccdbabbbabccbabdaebeabeebbacdeadcbaeacbaedadcddcadbeedaaedcabddaadbbbbcaebeabbcdbbcecbdaedceaeaeceaacbcaeccdadecabcdaeddbdbbceacdcedaaeaeececdcdbabecdaecdceaededdeebdcbebdbaeacbacedbceebacbedeaedebcaebbbddbdebdeabeccbdacdacedeadccdebbeacedebcdabceaaaacdcaccbcdaebaceceaabddcddebabdddbddebbbcaaccbebbcdadcacdccaabccedcddaecdcddccbebeadbedadbdebbaebeedcddeabacadabbbeabbdedbeaceadeabdccadedecbcbbbcdbcaaddeaebeeddbeeddbddebbaeeeeebbedbbcccbdbeaaecdeccdaaadbaeebcbbedacdaaccbabeeabbbbedadcceaecbbeadcbdbedccbcaaeccddabdcaebaaacacaceabdacdbecbabbceacaccbddbdbbabccbdabecbdeacbbadcaabeecbbeacbeacdaadacaeabbedadebbcdcabbcdcbcabebaeabebcbdeedabcbdbcdbdbdebabdeacddbcdecbdcaadbebbbaacdeebbcacbcbedecbeeebcabaaedcaeeccccbddedcbeabcecccaadeddbecabeeabbbbeedacaaadddcedabdbdadbbbedbaedebadebbcaaaaacdcaedaebcdebddcaadeaeeacaaddaaedbcceabadaeebecbcababedcccbaecabdacccddbbabbaeaceecacbdbeaaeecebedcdcbdccabeceeccccebdbbceebeadcdeccbccbeacbbcdaaeabebcdcaaeeaabdeacdebdccedcecbaacdbaddabcbdaaabceeebdbbadabaedbdbebcbaaccedcaaddaceddcdbbeecddeacccabeebbabdddeacdeaacdacbaccbcbaabaecabeeedcccbaaceccbcbadbccdcacebabddeddbacaabcebbbabdebcbcadcbdbbcacdcebcecbecccadedecebceaaabcdeddedebbeebcdbaebdccbdaebddaacbbddebdcaeeeeaaabbcacdbebeaeddecbcccecbcddaadedceededdabdedeeacdaaadedadccaddbcccebecccdabdaedceaeeecadeaecccaebdeabbaabcdaccbeeaddbecbeeebadabacacbcccbdcecddddcdddbcddebabeecbbdbeeedddebeaaddbaceceaaaccabcbeadadcdccceccacdbdaddbbbedaccdadeeebcedcaedaadaeedadbacaddebcadaaaeabbbebebeaeadbcacdaadaaadeceaeebbbabdabecbdbbcacbdcbdebbbaaaadebdcebbcedcaadeacbcddbcecbdccbcaaecbbeaacddcebacbcbcecacadbbcbcdbbdcecadcdcbcabebacecdcabdbdccabcadbeacbedeebdccdaaacbbddeaccdcdaddaddadcbadbdadeadbcceacbeaecbaabdedcdecbdbbcadeebbccbcabcdaeabedeabecceabaaddadcacedebbacdbeacbecbeeaedacebeccdbdbadabeabbcedacbbeaeeaddeadecbadeaceedaacedeaaedaaeaeeebcebacbaaddedbcaccedccdedeeaebadedbeebccbbdadcccaaddbbcdbeaeabdedbabcddbbbbdedbacccaebbdceceedcceaceeccccdbaeadedaddedeaddadbababbecddcacaeabdcbdaadcebdceeceabecbaceebaaddebecccebbececcbcceebdccbacaaadeddeadabbdadbbdbdbeecdcedbcadbeeaceddbaeaaaedaabadadebccdccddedebdcbbabbbbbbcdcdbdbdbceecdaeedeceaaaddeacabbabeaacaadeaaadebbbecdaabebcadecbbeaaceeabdbceebeaacaeadccbcdcdcededacadcaebdaedceebceddedcebdbcdacbcdcbebaececddebbdabbdddbeaeeacaeccdaddddbeccecaebebdddaebcbcddadcabaeedceaddceecadabaaaebbceccbabbaaeebcaacccaeceacbaacadccadddacccdecbaeddcbedcacabeebceacceceaaeceabdabceddccbbadddacabbccacaadedcbedcaedcdaadeaceeadaebadcacceeabdccaabcdebeebeacecedabbbdddeacdbceecededeceadbbbaaddadeeabeceedacaaaccceccccebdccbbcabbdecdbbaaddeadebaebeedeebebdcbdedccbadeadccecadebdaebdadabdbdbdcedcabbbbceaaccccceeeccebdeadbbeebaacecbaadadcadabcacdbdcdeacddcbbeabbeadcaacaddbebacecaeaaecbeadddcecceebeddcbeebceedeaacdaceabdcebaeebecbbaeecbbeeadbcabceedbdabbbaaeaacddddcccaedbcbbdecdaadbdccdccbadadeddabcdeabcaabdaeaaeabbbabeaecaebdbedeaaeeddaaaaebdbededacbdccecededaaaeaabbedccbabbacdeadcdbaebdaceebdcdacbedebbdebdabacccecdceedeedabecbaccbaedbbdeeaeaacebcdcbdcadebacccedcabbbdaedabcedbccbeeadcaaeeeececdadedebbdaecadbbcdeecbdcaabeabedeeedddcdebacabecbeacabaacceeebcacbcdedbebecabbeacdcddbdeadaeaccdbeebeeeeaaeeeabcbeedabddedcecbaecedcebbbebbabbabaaaebbbadaedeeeeaaebcdddacecababadcadaceccbceecccadaadacbcccaeddcdccedecadcdbcaabecceaecdabaedaaadbbbeeeebbcbbacdcbcecaadeaabebcdaeaeddbeecebbeaadeaedaaebaadcedceddabceabceaceaddccebbaceddcebcdacedbebdeccbdeedbcaaeebecdbaabdecbcdcadccdddeaceaccaaabedbcedcacccecdebdabeebcbdbceddecaecebaaeddaacaaaabaccecaabaedcdcaeadecaceadbdbadeebdbdcbeeedadcaddcbbaeddababcdaeaedbcddabebcdddedacdaeedaacdadeababcecbbddceaebaaadedccbeeddceadecdbeaeeecccdadbabccdedbabcadaddabecdcbcbbdddbdebbbebceddacbceebbedbbeadbabbacadcbeecaaeddcbeccbccedcdebbcacaeeececbbdeccdaddaeeedcecebcbdaeededddacbeebbbeeaccdaecddedbdaabbcecbbcbedbcacaceedacbbdecacabaabddddbbbceeebdcdbeceeaeacdaadbbbadcebacaebabaabccbeeeecedececaeaaaacebabaebcddddbebdebebccbdbbbbbcccdbbaabbddbadbcecdaebddcacdbcebebecceacebcbbbeeecdecccccdcbcdbcbbabadeacaedaeadebccaabedbdbdbabdbacdceaebebeaebeeecbceacdcabcdcbceeacbaadbabcebeacbbbbcaaeecbeeceaecbeabaebceedcaaebeecdbceacbebbedbddaeadbcceaeebcacdbedaaeeccaddbbcaceaaebcdebebdbecdabdeadebedeeedbcddecaddacdebabdceaebabebdabddacbbccacebdddcebdbbabadceedebcdddcbadeebeaeecacebedceeeaabedceeadaadcbbdcdaaaadcababaaadddeeabcdbabcccaabaecaabeeabcddcbdcddeedcdaabebeaebbccaecadbbbabebdbdeadcabddbddceaededdaacabeaabedbabdeccaabbeaccbdcdecbdaeecdccccdebdabaebccaceebaeccccbcddbacabcbcdbcbcacdaebebbcdcaedeedaaabddaccebbdbacbeceedebdcdbabdcdcdbbaeeaadeaeecbebabaaeedbacbbabdebaaaaccdecceabcceebdedbebdcdadcaabbbcecaddeeddaaedbaaababcbeeeaebcdceaabbeaecbbcadeadadcaaddcbdcbdacadadebebbaaeaabaebdbccebabbcbeebeededbdacdbcbbbbdddbeacaedbbeeddecadbbbebccebbddaceeccecbbcaeacdcbaccecadbdccaaadcaddaacbaeaedadaaeceedeebaaacacedcdbbdacdeaeedbaaacdebccceddcabccccadbceebbdedeedbcbbddbbeeeceaaecaddbeaceebbcbbbacdacbdbbbebedabbaddaeaaabacadaccedbaeebbdbdacabbbecddabdaeecaeacacceadbdcdecbdbbcecaceeacddadeaeddedbeabddaddadddbaccbdbbebddbeecdbdcaeaaddeadcebaedbdededbcebccbbccbdeecabaedbadedadaccabdbdeebeabbbaaccabdbbaaedceccbbabdcdadeeaceebecebbbddbdabcdebeaaadacbabedbdcbcdbaaabdcaabdccaacdbdbceabebabdecdacdbeadeebeeaccecabdeaaeeabdadbadabdbdcddeadedddeccaebeeddccaadcbccbcdaecbecceaaeddbdabaabddbcceddbbcadbdadeccddbbceaccdbdcebedbceddaebeecebdbaebeadabdacdeabcdacaeddabdaebdbabcbcaedcbbceeadbadeecaadbbaadabddaccddcaacedeecdeabecbccbcccdcddaebddcdccbadaabcebaeceeacdebeaebccaccddcccdaedabacdabacbcabcedeccecdeebcddcebaddeebaacabdaabbdddddadeeaaecdabacbadbabdcdaaaabeadcbbbcadeeececbbacdbedbbbcbeabceaeacacecaebaacacabaceeaeddaaaddeaacabadbcdaaabcbbeebcdadcbbcbbaaaedcdaeadeaabaecaebbdbdecccbacadceaacaeadcdaaebeabaccbecdcdeebecbaeccaeeedecacaaabebdadeebeaececcaabeedcbbcaccecbebeacdabdebdedbbccecbecccecacdeeacceaeceaedaacccbbabbadaaedbaeaaeadcebdcbebedecddbbaeddabcaddbcbcaecadceabdabacddbaeadbdaecdcdeecdaccecbdbbeeebdacdebccdaaceecddcccbaebbbaaccbabbabaabbbbccbdabcaaaebeebabbcbdbdeeeceddeacaacbaaeadbdedeebeedcedbdbccacdaabbceddcbeeaeecdabbeecacbedbaebdacebaeabebbbddbdcaaaeaedbbbaccdbebeededebecedcacdbddbedcbeddbbdeddcebcecddabeccdcedceaacdcdecdaeadbebcaedcaaaeaecacdaeddceebbdacedcdabaeeeeacaccceaacadaedbcccbaceeaededddaaaccaaeddccaedabdabaaadacdcdcecccdbeacaaebedbbeabcdecdeceadecaddbadbccaacaaabcaeeaeadeadaeadedbbebbadddacabdabeeeeccdaeeaaabcededbddeddeabdcbbadebabcecadeabbcaccccbddcaddceacbaeaaeedecdaeeeaaabcdbcdeeeaccbabbaecadeaddcbdebdcdebcaebbdbabcceceaeaaeadadcebcbdecbcadacaeabaddebadebcdddebdeaaadbcbbcbdcaaccbeaddeddbaeccacbeaabaddedeceeaeacaebdbbabdabedddebccaebacacaaddecacadebacaddeabddbecdaaaeddededdeaacdeecbbaeaaeebcacabbebbeebceecbbbaadaeeedaabdceeeaaebbeaddabccccccbaedcaeaeeedecaceabecbdeeeadcacdcdccadcadbdbeaebebacabbaebbabddaedddebaeabceaceeabacaddebabbcbbdaedeaccbceabdebaebbbbeacadadcddbeaebadabcdeeeaabbceccdebbaaebeaabadcecdcbeaaabdecddcaaeeededaaeeebacadaaccbaebdceadbcdacdebbbbadbabaebebcedabdbabcdaceaaadbbaeacdccedbebbdecedabbbbbbaaccbbabaeeaedaaeececdeabbadcddbdacdccbeecadaeebbbbaedeedcdacaeceaccdbbddbadaedbeeaadeeecabbbecaecbbededccaecceacccebdddcabedbbacbcedbcacaebdaeaecacebcdeecbacaacccccdceedaaccccbdddeceeebcedacaaacaabdaabeceeaeaddceedcccbcdaddcddacdbcddcbeaebebbabeebdaedbededbabaaccebbcceabcbeceedcdecaebbaedacbabecbdedceadccbdbcbdcbdebeacdbecaddacbbaabeeacddecabcdadcdadeddedadabdbaaabcceaaaeeeeddbbecbecdbccadbacbcedccaeddaddbdbbdcdecaeabcebdecadccaccbecbcaeceabbbcdabbaebeabeacacebabacaddcdabbbaaaeecbecaceaadedeeedcaacedddbbdbabedacbeecbaadbeaebbbbcbcacabdedacebebeaabeedbadecadcaecdccedbededbbdbbeaaebdccdaaadedbebbdcabdcddcabcbbbacdbcaebbeadbaacceebbeebdbbcbbdcdedbdeadeddaeddbeedbaebdedcebbcaaeebeaaadbdbccacbbddeeddbeebdccbbcdbdaedaeadccaabbcdebddcaeeacaeccdeaaaddbdedabbeedabedabacebabeceecbcebcceececdbaeddbeaabbdebbabeaedeecacdaeeedabbeacadeeacccaeeaeedceceaabdcccbbaeeddcddaabbccaaecddccacddeebeaeacececdedaeabadeddbccebeccbcababdacaadcacccdcccbeaeecadcbbcdcdcccadcbeeebadedbeabdcbbeddbaaccdbbbcabecdbaeaceddddebceeeddbcaabecedaacededbebaadecdcdececebddbdbeeedaacdcadabbecebcaadbcedeeadbcaadabbbbcbaebaddeeaecbadbdbeaaeeeecbdbcbacaecceededeccdaaacabeaedcdddbaceddaacddcedabbccaadbedaacadaccdaadacbceeacadedcdbedbaaebbeaecbebceaddacbddaedcaeabdeadbbcbecceccbddaedccaeddcaacabdeceabeeddbdebbeeedccebeccdcecdeeaccaeacbebcdbdbbcdbbdbbadcdcaeeeddcabcbdaceccbccabdbdeebadcdaabdbcbcdeaacdccbedcdbdcedbddbbeebabcecdbbbebdacdebcebeeededbbbabcdecedacaedabaabcedcaaecadccbedaeadeccabcdeacdcbdadeaccbbccdaecbeacadacedeaaedecedddebbaaaaebeeeeaabeebeabebaeecdcdebdebecdedabadebccaddadaacceadebdbbeaaaecdcdaeebdbdadcddecbcbcdbedececdabdeaeaccaecdbebdabacbcaedcedceccccadbaccedceeeadabeccacdbddccdeeaeaaeebedbaedaaadeaeccebdbbddbedbdbccacdebdcdecaaaaceceeadaceaaeeccaeaacdccadbdeddecacecedbbdbdbaceaadacbaebcbccddadbebbadcdcccddececbbadbeabbeebcdeeecaacaabacabeaedbbcbdbdcdedddceeacacaedaebdacdbbcaedaabdcdbbdcacbcdbaabebbaeedaddbcceaeadabecbdccccbaaecbaeacdbeaacbaedbcdbedbeaacaaaccadeaeeaeeeabeaacdcababdeadabecdccbbabadacabbedbbaaacabbdaadaeeecedabeabdeebaeacaabcbbcbaacdbabcbceadbdbbdccbabacaeedcbdbececbebbccabbbcdebccebcbbebcedacbdecedeebacbdcecaedcbacdaedeedcecbbedecdddbeddbdadeadbacebdcabbcbceecadddebdedcbcebbdcebabbbabecdeebecdccbedeebedddabebebcbbaecdeecebbbcedcdeeeeeeeaecceadeaedebeabadcccdddecdecacbbdecbbccdaabddcdaaeaddcabeeacabdeaecadeaaadeeaddcdddecddbcdedbcacbddddcccebbdbdcccacababcecbdcbecbccabddcabacdaecdabedbebadbceecaaadcceacdadeddcedecbedceacaadcacdecaaadbdcceacccadbcccdbdcdededcaaedabdecdeeedaebbababcabaeccccdaeeebadeceabeebebdedebdeeedaabbddeecebaebcdbcabadbeeeeadeeedcebceaacaadbdeebadaedeeebecbeeecddccecbbedccdbdbbdcbdacbdcbdcacddacbbbaccadcededaaabbeeabecebeabcaaeaaaeaabddaedaddaababbdebccdecccaeebdbadedabcacaabdccdeddceaadacccaccddeabecaddaedbabdaeacaaaaecadcebadcecedebeecbcbeababeaeceedbaebdbbecdddaddebeccebaceecaeddcaaaaeaacebdddcebdecacbeccabbdbdbbdeceaaaecddbdbddceeedeebbedebebdbabaaccededabacbaedbbedbdcbdbabcbeabcccadaccabdaabdabeaaacbbccbebdebbacddceccadecbcaeeaeabcdcebacadacdbbccabacedbdbeebcdbaeeaebbdaeaecebbedecaebddcbedbbedbaceadcceeddbbbadacdbabedaceabdcecbcaaaaadedbebedecadbedabbadaebebabcadeaebdbabdeddbabeecacacccabbebbadeabebbcdaebecbcecdeabcdeebdcdabcdcbdcdbabddabcdaecedccddeeaaaebaeadbaddcdbaedcecdbabbeaababccbedabcdccdbebeecaabbeecebdbdeabacbadbcdcbbeddddacddeeddbddaabccccaaaceedcdaaabecccbdaecdbacbeaabedcaebaeeeecadccaacaadaaaaddabaaabceddaccbedbdcbbbdbedecabbceadacaaccbaabaacbbadedbdbcaaccabcacecadaacbbceccbcedccbcddbbccdaabcdddceebeacadebdaabaedababcaabeabebeaeeaebcaabcbddbbcaaaebcdeaeebcebcbcdcdceaadeeaddcdecabbadbaabdbeddaaaceddbaceaebdbebdaaccdacbdcecdbdcbceebdeacaaaacabbdbdeaebedcceadacbcaaabdbdddcedcdcddcabaadaabbcccaceceacebddaebcbcebbcdeedbeddabbdaddccdebecadddbbbadbeddaabadbdbaaabaaceeccebdecddcbcccedacebedcdbcbcebaddadbaedcebdeaeddaaaadecdeacecdededdebbeeddadcecddeebdadaaabedadceaadebbdeaedcdedbebdbbebcbdabcddbeaeeccccebeacccbdedcbdcaebbecebeabedcededdadaaceacedbdcebbbeaeedcdbaabaedccdbedecbdbbceaebbcabbdabcadcdececccadacaabebbbebacbedbadadecddbaabcbedabbbcbebdbccddadbddbaebcbebaaceaacdccaaeaecbbbaabcceddedcddecebadbbaaeabcacedaaeaeaeccbebcebbdddbdabdcdaadcdbadbbbadcbeaaeddeaecbdbecaadbededccbdbddecdcbddaaddeeedcdbbaabacadebebaaebeaabacceadadbcbaececcbeddeaebbabaeccbdebaecddedcecedecccbdeabaacdabdccbbadbaadceddededcbbceaadbcbbbeadcedcaeceadeddddbbbccdecabeadeddbbdceaddeaaedaaceebcdedaecbcbeeabbeeeecedcceabddadbcadaaabebdeebbebaddbedbaadcdaccccdbadbcedbcadabeaaeadccabacbdbaabebadcdadbdcbadaaabccabebdacdddabdadaabaccceaacdcceceddeedaeaeccedcaebededdecbebddccbabbbaabdbcbcebacabbadebcabcbddcecceabcacaaacdeceacdcecbdcccbeeacadccaabceeaebccaacbceccedcbcaccbebdaedacebeaadcdbbbadbbedcbcbabeebbbeeccceacababedddecbdcceacaccbdbeeeebbcbcabcbaeccccaaaabceaeceeeaaebdbbadabdceaeccddddccbdeaeddbaaeccaabeecadbadaaddaddabdbcabedbcebdcaebbcebacdbedcdbddacbabccaeeddcbdccddbacebaaaaeadbbdabccccacacebddaedadddbadcbbdbcceaeeaeaecbaabdbcceccdedecbbcdbaadbaeaebbdcaadddeacbbdcecbdcacebabbeddcabeeadedeadcaceacdebdeacecaaddccbdaeaaecbdeabdedabeaabbdecebbebbcdeeeacedeadcebcbabdeeeeeeacadabbbdbcedaaacdbcbadbacadaadededcdaddacdaaeebdbdcccadbbbeabdddecdebaaeeecdbbdabedecebdacccaadcbdddcdcebeddbbaeecdedbedcabeadbcbeaacecacddbddadceeedbcbdcbcebbbcbdabdcbdadccabaeebdddbcadbdabbcbbcbabacedddebaabacaecaaeabdbebcbaadcbbcbddceccdbaaecbdaaaabcdbabceeadcebadbccbabcedcaecbebcdbabecdbeaedaccdaeabbdbdeddbdadcacdcdeaddecaebdedcbceeccceebdadbeacdcbddcbeabbaeceacbacaadbebcdbeeaddaaccaebcbcecddbeebdbedaccbebeeecbebedceacdccaaebaebbddcdcaebbdbbaeceecabdecaaadebbddbcbdebcacecccaabbeeccccdabbacebcccabccbbacceceabcecacecdeebabcbcbbaabeaaeabebdadbacceedeeeebdedbecccbdcacdccdabcdbedccedddabeaaebddddebeadccbedcbedeceeeeadaeacadbacdbdaecacedbccddeebccbdaedbadbedcdadbeeecdcbedacbcabeedbaeadbcdbddbbbbdabaacadaababbdeedcccbcdbbcebaccdccbcbbebabcddabeabbdedbebceeccdabbabebadaccebcceedbddddbbaeddeacbaeaaeaaeddbcaabddabccecbadcadaaedbedabedadcdaacdeaceccecbdbcddaabeacddcbaabeeacbccccbeeeadcbdeebadcdacdeeabeeabaccdacbeeebccceacdaecebeccdeedacecddbdeeaebacaeaceeadcdaebbeddcdeaeaddcaebedecacddadaaacacebbabccabcebcedaaecbeecdedadeeaedcadddbdabbacbcdeddeaabbbaccbeeaaaececcbbdeeeeeaeddebceadcdddbcddabdedacbabebabdcececcbbdbcdddbdbccbdedaebcaddadbcecdcdcdbdedaeaeadddaeabdbedabacbccaddbeaaabecdecedccccacacecaccbaaccdaeabcdbcbcdbdabbbbaddbcbdaaaacebbabeaccbbaaaaceebcddbbdddabcbebcbbedaeebdeecdbacddcecabcddccedcdaeddbdccbabaeccdcaebdaeaacaedbedabcbbbcdedbadebccdcbbbbbbebdddaabaeccbecbbccaaacaebdebddaddcaedadbacdaeadeaececaceadcddedccbadeaccddabceaadeadacebbbdeeabbbeadaacbdeacebacdcbbccdbedcdbaddaccdaaddecebadedaaeccecbcbedaedbcbaedeebcabdbdebbeaebdacedbcdceacadedbedbeaebdecbcddbaaebeadcdacdaeeecdcacdeeecaaebecebeadcebbeaadebdceacaaacbcedcdbbeaaedebcbbbbebbcdddcecdddeadcdccaedebaeabdbbceceaeacabbddaeededdcddebbadceedbabbaebebebabbeaeaecbbddbbecdbbbbaaaadaabeaaebcabdcaabdaaaaebdbdbbbadadacbedabcedccabeaebeccbdadedbccbbdcdcdcbadddebbcdbeacdbdabcadbaadeabaabedcdaecaadbaaaaaddccacbececeabcbcbeaaadaceebddaecebdcaedbaeeddaebaacbaebeddbeaaadcecddebeadddabdaeddbecdbbebddddedddaceecdcdecdebdbaddcbaabbaaeeebbedceadabaddaaeddcbddecbebeacdededebeaacbabeaaacdaceeaabbcdbacbabdadeadbebccbcaaedcddbeedcbeecbdebabdbdcedceecebaccbdeacbabeccdeddaddadadcccdddacaacddacccbceacabdcaebacdbbdcddcecdebaeaaadeadadeacaecdeebdaeabeaabcbebcacdcdbdebaadeadbbcdbeedadbabacadecebedbdadaddceeedbdabdaedbaadeaaeecaccaceebcbaeadbaedaccaadcedaeddabbbbcbadeccaedeaaadbdebbcedacbedbeadccdceadbdecbbeeccaacceddbacbebbdabdebcbcebceccdcbebdbebbcbaacecbdbcaaecabbdbbdacdecbbbeddedabecdebcdadacddecdaebcaddedabebabcbadbaabbdecdbdceacbdbedacbadaaaadedcabeabadebddcdaebecabcccecdbcebeedeebecbbedabaacbcdadcdedeacdaddabbcaaecdecdebbdcabbdccddcdceaeeddbaaabbdedebeccbeeedebddceeabdaadaeddddeaebdbecdbcadddaeadddbaaebaceccdbbdddbcabdecddccdcebcddceaeebdcbabbbcdecbdbbbadaacdbecedbbcbacedbecbbacddcebcdacecddaecedeeebacbbeccaebbcedccbcdeaadaceceabaeebaabbdccdcdbeeabbdbceebedecadbdcbedcabdacaaceceebadadaebecdaddbbaabdedeedceaeccaddaeaecdbedcbeabeeabdcebbccdabcdecaebcdededceaccdeedebcceaeeebcdeddbcdecaeecbcaacebbdaaaaeaacbbdecddedcdabdddabeddaedcecaebebaaedeecbadbdaacbecbcdbdeebaddccbadeddcaadabaeddaeedabddaecdeccbabedddcbcaabbdbbeccbbbcdebabdcecaedddbcaadcccaacaedbadbbbbaeaedbeaeebbbcdcbbdebddcabbbcddcbceaadaebbbeceddbdeadddcaeedcbddacaabddbeacdbdcaadeececcececabcdbaeecdbebdcddbacdeaddbeebadcecdeacddbebceddabeceaaeeeabceaaaabbbdcccbdebbccccbdebcabeabcbceadcadecedcbabebeebcbbacabedabcabeacbbaddeccceebebaececccddddccbdaccbecdcaabcdacaedbbaaecbcbddbaadacecdadedaccacbdbaccebddaecbecdacccdbbbcdaeabbceaedcccbdecbaabdddbdccbdcedbcaabdcecceeacbbecaececacebdcbdaecdbacedcdabcaeccebbdaedaaaceedcaadbebcdbbacbabadeaecbdbeaeaebbacadcbcdcbadddeeeddbebbacdebdaacdeaeeeccbdccecdddceccdebdacadecddcabcbacbdccbddeeaedeadaceedcaeaaadccecaacbadbcaebaaadaabbcdbbaaadddcebacaeaaeddcaccbbdcccdcadaeabcdadeaeaeeaeedbebaeaececeebaecbdbbabdaecbcdcdedecbbbccdecddccebbdbdaebaecaebbdedcdbecccddbcbaaabdeecbbeedaebcccccbabbbbedbcccdcbcedadbcdeacdbdaccbababddcaebabcebaabcedadcebcbbbaaecdaebdbaabdebaaabbeeeebdbdeccaecbdeeecabdbceecaddeddbedaadaaedcdabacdbbbcddcdddceaabcbdebddbeacbeabedacbebdbceeabbdbdcbddadabbeccdadeeeddcaeeeaacedaacecbaeacddeeddceaaddbdceacbbacbbdaacaaddbbecaaadcccdcbebabeeecdccbdeeaadedaedbebebdaddecaeaadddcadcadebaeeceeebeecccadcaeaecbedbbccdebdeebeeeaecbbbbebecddacaeaadededceddcbdeacadcecdbddacdeaecbcececbacabacbdbbedbeedcacccecebdebaebacceddbaeccbbbccbabeccabdeedaacdcbdbabaabddcaecbaaabaecbabddebbdbbeceeeeabbadbbddcebbdaacbbabadaaabeccedbbbedcccabcaaaacaddabdabbbacbabcabdaeaeabbeedcbbbeaedadddcbadabdbaaeadbbedabdaacebdebadeedbdbedcbdcbbbcddcbdaedcedbdcceabbacadcebecddbbcddcaeeacddbabcecdebdeeebeacbbddddcdceeaebcbbeccaacbebccbabbaaccbbedaabcadeeabaceabbcadadcdcedeccabbdbdedabedaabdbdadddaeeeeebeaedebbeacebaaddeddecaeccaedcccacabacaddbbcdeeeaccbdbcecddcdadddebdcdadadbbdcaaeacddaeccdcbecccbbbbdeccceeacdcbdddceaeddeacaaaedeecdacedabacadebeeccceabdeddedcdbdddddeaaeaadcbaaaebbeaabbbabeceecdccbacadeedcaeecbcaedbaeadecedacebccaaecaaabceacadcbaeaaccaabdeebbbcccebcaddadebebdceedcbdbabdceabecddbadcedcdcbeecbddbcdecbdabcacecebadaddbdeceedeabadbbabedcedcbbebbededdcaadacdedabedccecadaedacabdebddebcdbacadcadcbdcdcedbbbdccaadeaedebeccecbeedabbdedbaccbaeaaddedcccdbbaabedaaddceaddedaacddadddbbeabeecccadaecaabecebaceceaeccebedabccceeacbbeadddaccedcacacbbbebedecbceeecacaddadacccceeeccaabaadcaccdcaddaebbebacebcdbeddaaebddddbbbccadabdcbdecddbbbedbeebebabeececeedabeedaaadeaceabcbadaaaadccedbaeacabaeeebcabdccacecabecbddcecabcaaebeaaaeebadcedbcecbcaccbecaaccaabbcdeadacdebcadddacddabdbebeaacaeabaecdaedaadccedebbcdbdccebdeebadddcedaddbeaedadbbecedcbdbabbdcadeaabcebabacbbaddececbeadbadbbcddcccaddacbbbecededbacabdedabcdeeeacadaaeaaacdacdaebdcbbbcedabeecbcbeeeaedabecceddadebeaebcdbdaabcaaaeaddeadcaadaddddccddeabbadeadbcaddbcbcadbaaeaebaceeabbccbdceaeebbcceaedeececaaabacbabaeadedcbeabaeeceababeaaccedbcbacdcbbecbbbbbbdbcdeeedebbbcbceaacdcecebaacaacbaeeddccaeedadddadeddbdecbedbeaedcccdbbecdcbedaddedcdbddadcceaeabbdebabbbabcabdaddcdaeeaebdedbceccdedbdddabecebcbeeaeacdabdeecadadeddcaacbaaadabdeeecdccecabaddddcebddedccaeeedddabdaecaededaebccbbaeaebcbecdcbeacbaebecdcecdcebedcbbcbadaccdabbdedbbacdabcdaacbabedaabeebcedaddeceeceeadbaebdbadeeedacdbccecaeeddcaaadaccaabceaacbaecccbbdebaeeebcdebcababecbbdabbecbbeaeeaedbbbaccbeaecebccdddcbdeaebdbbcbeecadcdaeabbaadeccadaeeabcbacbdebdbcdcedcdbcaaceedecbabcbeeeacacacbbabddcacccaebdccedadbaabbbceecdbdcedcecbcbdaabebdbdaddedcaadebbccaecededdabbbcaeeacdabacaadcdaddabaeeabbdaebcecbeaaadcbadbdcdebceabbbbbacdabcdecbecedeabdcbdcdeaebcddcbabdccddeccbdecbadbbcbbaaadccedeaeebddbbaebadbaeedbedecebacbecceecaabeceadbbaabcdddaeebcdaecbbbcddcddbaebdacbbdeeedeeadbcccbacdbecbbdcaeabaabaecedeadabbacedadebaaaacadbecbbeecbdbedcedcbbceeecbcbadcbdcaebcedbaedddaebbaddbaecadacdbaadcbdceabcdbacabccabdaccedbbeabdabadcbdbaacecdcedebacbcaabecabaabcacbcbeebbaeeccdcbabadbdcddedccbeeeddbdceaaecccdccccadebebcbbdebcdbcadebadecabdddcadbedcdbbbcbbcdcdddabcbabcedbedcddceacaacadbccaecdbdaabeaccbecbdabcdddcdabccabceeaddcddabcbcbdacadaadaccdbeabdcbaebcacdbdaadadcbedaeeaedacadddcdcbbddaeacdeccecbbedddcdaedeebddcebbddabbabbcdedbccaaebddebbdddcdeedacacccaeebebeccdebcaaacccdeebcdbbaeadeaacdcddbcceecabedbaedebebabaadceaabedbcdbeabeadadbeceebddccadeaaecceedeecadeacccaaeabecaaebabbccadcddcadeeaaeacdaedabacdccbbabdbdebaecedccdeaacebaaaeadabcaeacacaeeaddcbcbcbcbeebbcbbacbabbcbbabadceeaadcecdeeacaadcbdeeaeaadceadebddcebabeeddcaebbcbdacedcdeabaaeedbdceeebcccddbabbcdbeebbbdbbeaddaadcedaaaedaebddbbcacaadcccceadcacadcbbaadbaedcddbbcbdbeceebedebdbbecbdadccacbadcebaeccbcdbabdaeaacccaaddbcaedaecaedbeaeeecdbeaccedebcddadcebabebebbeeeacebdbccbbabcbaddcbaebdbdabcdbacccdddadaaecebdceccebedecbeabdecdcdddadadccdaeedbecebcddddaabbceceebdcecebdabdebdbaddecdcddbdbebbeccddbabaccbadebaebadeecdbabaaebdaccaddeeabdacdaecbdabcddabcdeeabbddaaceadcbeaeeaacacebceddcdedeadcabacbcdcbdcaceacaccbdcaecbeceecddebcbadaaacecacebeceddabcdceeccadebacbbdabdddbaddcaeeedeaebbcecaaecedababedcccdceaacdbaedcaeaadbbbebedcabeedcaececccdeceebacdeaabdeddbbbdbbbeeeaadcccddbabcdbcacebddcdcccaecbeabeebabdebedeeeebdcaaabbccbcdcdedaedceddcbdccbcaedddceadbedccdbeeaebeedecbdeebabbeaeccaddaededabecaccbedeaaecdeceaadddedeaccbaeecbccadaacedbaaeddbddaaeebcbbbdaecdadebbbedbcdebbcabacaccabcacbcaadbcbdbadacabaebcbebaeeabaeaaadaeaceacbeacdeadacbacbbccbcedecaccbcaaccbbaebdebabbcddebaebccbbabcedcaedecddbddadcebebeaaeeaacdecbeebedceeeaadeceaacddeebcbeaadcbacaeaeebcdebddcabdeacebdcbcdcabbdcdeecbcaabedccbeacacdacbcadcaacaaebeebbecaedcddaccbbecbaddddbadcbabededadacdceeccacecadacacdacaebbbbbdcbecccdddaddcecceecbeceebcebebbbcaabdbedddbeaedeaccbabeedceacaaebadbdacebbdbbdedbbeecbaedbbcbbdeeeebcabcbbeccddabbbddaddcdededddedeccbedcebabedadaaceabbbdebbeeebbcaececcdbdacedbcdadecbedadcdacaebbaeeeaceebbeeeceaecaddabbaecebeaeaaddddedcdedebbcedcebeaaabbebbeeaccccebcaadecaeaababbeaaebdbdecebdcdabbeaaedcdccbdadccbadccebcedbccebddabdebaaaaddebbaecdaaecabaacbeabbcdbbcabaeacdebebcbcbbbccebdddaeecbbdcaaceacbbbbecbeddcebebaaeabdcbdecaeedbadcbddcaabdeadbadcbdccdcbadaebaecbdcbcdacabdecbdecabaaecebbadadcbabcebddadddeabdaaaccadbdabddcabcbecddacaedcbcbbaacdbcebbeecdaaebdbbccdcebeecdbeaeaddbaabcacdbebaaabdebccbdcdaddaadaaaceabcccbdaddeaacaddedcedeaddacccddaecceebbcdeebaaaeeceaaeecaeddeaacbbccedcbceeeacebccbbedaebdceacbbbcbeaddedaaabcbdcbdcdbeacaaebbbbdaaeeecaaddabddbdeeeccaebbbcdccebdbbabaecbacaedbedbdcaaebddccedecccccebeebbaddaadaaaaeadaeadedebcbdcaabbecbebbbbceebbeaaebaecdeacacceaacdedededccaebeeadedbdccddddddceeceebbaeeaaaecbbeeabbbcccebecdcbbccbcddebbccbeeebeeddbadabdeaabbadddcdaddddbeebbedecdebddbdccbdccddecccecbcabbebabbabbbbcdcbdebbbebeacccbdadaecbcccdedacbcedbdceeacdbadacedcdadbeceaaeeecdccaaddbcccacecebcaeccdaceedbdbccddbabdbbcdccbcccebcecdadcdbbabebdaecedadabbeeaccaeeeedbacbdbbcadaacdceecebecdccccadcbdbcdebbdceadcecdebbdeadccedbdcdacddabaeebadebbabbbcadcaeadbadaabbdcaabaccedbbadcecaebdeeadadabaecebdbdccdeabeeededebabcdcbccceceaaecdbbabeddcdedddaebeeeaeedeeddcbbcbdddcdbbeecbbcacaecbbbcaebcabbeebadcadacbbbdaeddedbebdbaadbdaceabbadcecaabbbaeebdeddeacddeccbededcddcdccccedcdeaaaaddbececcaddedaceeaecdbedaebcedcabcaeceebabadadbcecdbacceabecdebcedbadeaddabbbbeaddbebebeeecacbddbaceeccddbbcccaaacecabaccdcabeaaebcecacaacdceeddcbbbeabaabeecdaedbadbedddcddecbdccecdeabdabdeababebcbecbcdebcbcddbecbcaaeccedaddeeebecaeeecbbcdaeddbedeabdadbcdddadcedddedbbaddbaeccedbabdcebbdbdeabebabdeccbedebbbeddedddacddecbaeabeabddbbacdeccddcddaacdebaaecdcbdbbaaecebdcbbdedbbddbbeacbdcddbdeebdbededbdadcbddecbbdbbacccbbdacaaecabbbcdeceadcbbcecadccbbccbddbecaecbecbcbbeaadeabddcbaeacdeebdbaabbbebbbbeddabadcacaeadbeabdbebdadbacbaaabeabedebbbaddcaaacedacbcbeabdcccadcccbaccdcdddbbdeabddccbeeecceabdedcebbebcccedbaaeaeaedeadcaaaeccabcdbecaaabaeaeeedccacaeadcaaeaabaeeeccdcadeebedabaeeeedbcebbadbeceeddacbcdcadcceaeaedbabddedecdeaecedccabdadeddcdeddcbbaebedcebacaaeeaadbcdaecbeacdeeabaacacbaecbaaeddedaaeeacbacdeeabdddeabecdbceeebdebaaebabddcdadceeccbbeaeaaadbbdcdababbdedaebbcddeaeacaeeddddecebdccbaebeababeeeeddcdaebbbeddeeabbdedddcabeebedbbacdeddedeebdcbbcceaceaabeebeadeaabcebcaedebbdeacbaaccaaecccddabddebebaadcaadadccbbeebdcbcbaddbeddcbbdcbcaaadaeceecdacbdaddbcaedeabaaedbbaabcdeeddaeecbbccabbeebcaaecdccdbeaaeaddbabedbecdabbacecbcccaeaabbddaabceaeddedebbeecabeaceedaccbbbbbdaaeacdabbebeabeeceadcdbbacaeadaaebcaeeaaebdcabdbddcdaceaabdbaacbeeaaaebbcdeaaedacaecadbcebabdbaccabddcebecbcddaddaacacebcdcccebbeebebaedbbadddcbbcceaeaddbddcaabadbeadbddcadcdaaadecaeaeeedbdbbbdeababbbbedcdadbdbaaceedcedccbacbdbbdcecbabdceaaeabbaaecaddbaeacabbcdedcdaebabcccdbcacceacdadcbebecebdeaabbccadbcdcdeeccbbaecacaebecdecadcceccdcbeaebadcdecbababcabedaadddabdaeeeebbccbebedcabacaabdcabceacabebcdccdabbbccdcdedabedaedbabacebbebedddcecbbdbdbdaddbbebcedabbbadabbdedddadbdabcbbdedecaababcadebdeccbecaceeaecdbddacaeccbebcccdddacbacddeeaebdadcadcdbdeedcdeedebccabdadcdacdcdaacadabadabbbccaeeecdcbacaaacedebabaabaaeecabcadcecddeedbcbeeccaaccaaaacbbabeeacdbdeacebaedbcdcdabbabbeaabbdaedbcdeabdbecacbeeedbbeacbaeadccddeeabedcaaddcdebebebdddeabcbcedebeeaacbcedbabeeaaceeccdcaaedbdcdaacedbacabdbedecbddbebdbaccbacbdccadcceceeeeacebbccdadcaecbeabcaacabeacdecebcadeaceceecabecbbabbcaebadbeebadebceeaddebccbcbddcebedeeaaabdcbbccccdbbbbccbedbeababdcadaeddcbbcddacbcaebdadbedbdbbabdeadddcdccedebbdebcdbaedeceeaededdedcacbbbeacbebbcaeabeebcdddaebdaccbdaeeabbddccceeeadeebcdbacebcdabeddcedaecdabbbcebbecdecebdceeaebebebdebcbeebeaedbbceddebaabcbdaaabcdadebedeeacbabbcadedaabbbbedeadaedaacbaeebadbdbebecdaeadbaddccdceeddcaaddbbcccddcdbbecdaebacdabaeedbdbcddeaceccdbeaedcbbccbadeaacddbbaedaaecedebcebadedccdccdacebcaedcbcacebddbcdcaaeebeaebbcebcacdabdcceabdaaadaddeaeeddccbecbeeecdcdeeeeaccecddbcaceabdbedeccaaacaacdccaeedaeaddeedacdbccbddebdbdeeacceedcdaaacadaaeddebcdaadddaccbbdaccabbbbabaaacccdbdebebbbebbcdeccaedbebeabcebeeadacdbdbbadddebacdadaebceecacbdcedeebcbecaeedaaacededdabedecccdaedccaebceecacddddbbcdebdbdecbbbeacaceebcdcbcabbbcbcdbcbbbaeaabcdcaaebdcecdcbeebeeeaecdaeddadcbcebcbdeedccaecdeebacacbcaaecdbacacebedaacecdcadddedabbdccbaebebbeeaebbebaabaadcaaccabdbeecccaaeebbcdeabbedcdaeecedededabececacbeccbcdaccdcdccaebbabbcaecbdbdadbdbbcaedcbdeccdcbbdeecdcadacedccbcedaadeedeeaedaadabdaccedcedcaabaaadddbaaaedabeecadeebcadbeccbeedcdecdcedbaacbacbbcdcadebedcdbacadbdaeaceedabaccbabacdcecbcadabaaaabccccbadddacdcbacaeaceccbdebabcecbaacedacdabbddddddcbceccdbebebbbeebdbdcabcaebceebdcbacecaeedadddaccbcdeeacbcecaebaeedacbbdbeaeaebabaaadccddbcccaedbcddbccdecbaabcdcecdeebecebacdbeeadebccecaacaccdbdaebdbaccebdcedaebacbdbdcbadcaaceabbaadadebdbddcbbcebbcdcacccaecccbdcbbdacabcbcbebeebaeabceceeeebcecccabbdbbacdbdaadcadccbcdbdadeccdabbedeebdeabbacdbbeebbbadcdcbbeedaccebbceeaddedecccbcdabbabeebebebbeacecebabacddebbdbeabadccbabedbccbcabbadeacccadadcbedbeceaadecaeaabdcbcbddbccaceaedaabbaccbbaceaceeaededeeecbbeecddebddabbcaaedcdabebacddeadadcbebaedcedcddbbcbbdcdeaccebccacbbaaadddaaecebaeeacbcaecdacceabccbcacbbedebebcedeebeabccdbadbeaacbeadacdcddbadeaaecbcdbbacbddceedaedcaadeaedeeeebcaeaabddaabdbebababadcdebdcedbeaacadabcedacceddabbadecedbbaadabdaeddecbdddbcdddbcbecedebdeebadceddcdeccbaadcdeeddbbddcedcecddadadaeeaedbeecddeeedacdbcbaebdbaebbceaaaceaceceadacceebeccbbbacdbbbeaebdbeeaaebddbeeabbcbddadccdbcdcecaacbeeddaddbddcdbeddeddaccbdaecebdeacccbdeeacbaebccbeaaadebabaaaecdabbebdcaebbbbcbeccebadcdbccdaabdaabcdebbeecdedbbedaaaacdaaaddeedeccacaceedbbbabdcaecaaebcabbdbbbbcecbbaebdeaededbaddabeddeeedbeaaaeaebdecdbbaddedddcabdebcbcbadcabaaacdbeadadeecabecbceebebdeeecadecaeecceadbdbbeceedbeaebececaaceaaacecbeccdbdddbdbaedeccdebaccedddcddeccbaeebcbbbbddabdbedbaeecacdaedabbdbbeeccdebabdacedddcdbebdaecdecedebbeadeacdbaabbeecbdbdebacddaccbcccdadbccdeddeabceaedceadebaabcbecebaceeeedaaddceadeabdcbcabaaaabcaddcbadbeabaecaaeeeaaaaebaecccacdcccbaccbdecbbabdeeebabacaadbdeddeaacadddbbbdddaecdaceeaeddadabdddbeceeccacbddcacecbdecdecdbbadadaccceacdaeaadbbceebbcabacbaceaacecaadddcecdecdcedbaaeadddcebdbdbdaedcdabbcbadcadeadaebbbbcbebdbbbbaedaeecaababdbcddaccaaacbabbbbadabcedebccdbebcabcebceaccebeacccceeabdbccddebbcbeebdabacbeeebcbaebaacdcbdcdcbcecbaeccbdcecdedbbbabedcdccacaceceabadccbeebddcedbacdcddeebdcdbecddbbacbaebcdbcababdeeecbbdcedeceedcebdbebddcbaeabadabedadebcbdcaccdeeebeddaaabebaaaeabcacacbedadbddcbacdedeceaeedbdcdddbbcddebeabbacbeccacceebbccacdcbbdbcbdacccddebdbbacbbabdcabceeaaeeacaceeabccaacbceebeacbbcdbeeaedeecbeadbaaecddbdeaecceaedcedacbaccbbbcaeaadbdaddedaddbccdacdcccdbacbcebcbaacadcddcabddeaaeeecbdadaedeeaadabdcbdcdddcedeabacbdecbcbabaeacdadabaeebdbcacaeaaaaeacbbaecebceceeccbeecbecbdbcaacbbcadeaeeadeabbbdaccabbeeacdebecdabdbccbcaceecaddadeccecdcdbababadebcabdbcbbacebbabcbededcbdadbecbedecdaabeabadaeacbcdeedccdabeabbadadbdcddeedeaceaedabacbaadeadcebacdaecdbeccccacbabdeaadabeaeeebbdbceeeddbedcaeeecadaebbecaabccedbaaeadccbeddeabaedebcdbbadeaecadedddbacddecbcedddabbcebebcbbdcbeabadbaebbcbaeeccabacdacaaecdcbddeccabbddaeebeecadaceceaaaccbbadaaecdaeeceeebaeaaebcebbbcecbdddaeccbacdaeeaebdabbebabeddaddbdacedeacbcbbbeeecdacddbcdbaceedeadedbceaddcacedadbbbbbdcbadbabbdbddaaaccecdacbacebeebdccbcaabbbccddcdedcacbdcaebecadcaeacdebadcbababbccdaeebbeaeccbabdaeecadaeeecedecbddbebeebecdedbcbcadaedeadcedecadabbdbdbaaecebadddbeedccecbdbaeeadcdbabbaaaebacdccbdaadbccbaeeeeededeacecdceecddaaacecdbdacaaedceeabbceeddcadabeabeeeeaddaebccbaeeccbbecaeeeaadbdbbdbebccebccebaecbacbebbcaccbcadacbbaebecbcecadbeaaecbdeacdbbbccbcadecbbeeeacaceaacccbbaebddcebbaeababeebabccdacedcbaabecbdacddaacecebcaacdaeeedeedbbbabeecaeccedeedbbebacaeecdbedadadcecceecccaabaaccaebeeddaceeadcadabdbacaebdadeaebdabccadbcacceeadebcecebdeddccacaceecadccedddbdcdabbabcbdabedcdbcedcdaebcbedaababeacadcbdeeadbacabaadecddbddebdbebbcaeccbbebbcceeccebadbbaaaddbbbbbbeeceaaaadcbcbddebbbeddbbcedadaebdeeecceebededbcceeedbadbcddedcbceebdecddaccdbbeabebededbadebdbabcccbddecbcbdcbbebabbdddccabbeedcbabbccdaeeceadecdbdddabbaaaaababaabeecdceecdcaedecebabcddbcababccebbddcbaaebecececdeeeadbadaaccdeeeadedacecebededececaceedbecdabaddbcacddccddabbcddeacdacdacdecdbeeccaeaceccaaabccedeceaccdbebccccdbbdeaeeaceeebaeaaebaacabbddaeeadddeaceeeaebeeeedebdeedcbaedbbdbaaeebaaddcaaceddaadbdeadbbebbbceddccdebaaeacbadebadaeacbccaedbeeccccdbebdadbbdbeacdeeceeeebdecabacecabebebadeeeacceacabebbdeadcbdbbaaeccdddcabddadcdedadbdbcbcbedceaabcaedabaebbbbecaccaceabdabdeeedaabeeeaacccdccdeeaebdedecaccaeaadddabadeacccbebdcadabbdabedeccdadecaabecaddaaecacdcdacbbbddddabddcdabcaaebaeecdacaecbabbcabbdebdbcbbcedddddbebebbdeeaaaeeebbeecabcbbcabaeecdebedaeacdeeaceeccbdecdababedabccacceaddcddbbedabedceaeaedaaeebabdbecdaebddedaaaeabadcacdbdaceabcdccddeddeddbdbeaceebeccceaccaacccceceeedabbedebbeeecadcdcaddadabecbdeccccdbabbeeaaaabcbebbcbbbaabeebbeacacebebbcbddacebdbbcaaebecececaeecedaeaecaacbbdbbacceeeaaecbcebecbbcdcaedcdcdccaabcaeacbeeaccbcaebeebdebaeedeebeccbbabbacdbaecaebbccebeaaaadeccbbeedbabaeabdaaddccaababdcecddaabebcbaeeddbdaecaebeaddadbaebeaabdbcdaacebdadccdababccedadedadbcaadeccccdeeedeebbebbaeadddddbddaeeabaebbdaeeecbbbcdcedeabcbeedbeaedebcbecdddbecbaebbccdcaecaddaebeecbeacbcaeeceaecccdeaceacaccdeaaaadeadccebabebcebcbeacaecacaececceacbbadcdedabdacacdedaeaaecababddaddbdecadbcccddaebbbcdcebabeecbdacbbabaececbceebadeedcceccbeadcaedaeddcbababacaaaecdbebdbceccdeacbceeeceabbbcaedacbaceecaacbdbdbdeaadeedaaeeaacacedeeeaecdbedcedbaeccabcdccbbabebcdbaebaedcbdddbecabaebebbbeabebbcbddebbddecbcaeaaddcaedbeabeeeacbcccaecdbebbbabcedebeaeeebdedeccdceccabddbbebecbeaeeededdceababeaecadbaaddebdeddcadedcbecbaabbbaebacacbebcaaecdeacdddaeabaedadaceabbacadddbdbdaeeaeeeabbdbdeabededddbcabaebbbcbedbdbaeedadabdcccaaccaaadeedaaabbdbdcadcbbddcdbeceedcbdabccdddabaebacdbeadcdebbdeeaecdeaeceabdcceacebcccedebbabcdaaddceadbacaaacdcbebaddcbdeccceacdddcadeaedbaacaceaacedbeecbbcacebebcadbacbacdeaecedaabebaccdbeeebbeacddadedeeabdadaedddedddcecbdbbcccddbccbdedbabdebbbcdabeeedebcecccacacaaacececdbedaeadcddbaeeaaaeccdeebcbbdacdadbdcdeadaecceceacabdbbbdebcecacedaecebabcdbaacadcacaabceccadaaccaccacedabcedabdeecebcdadeddaadaebbacedcabeedbccacccdabcbdeecdecbecceeadbadebdeebabaecdbbaacebeccaacbabbdbaacbbeebacdccbcbbaabebbcdeeeebdbbebeebaabeabbdcdaaccababcdcaadcbcecaeacceaacdaabdcdbcecbcdddaeedbddbeaebdacaeadbcdccebedaadecaeacbbeceddaacaaeecbdcbcadabbcdeaddbceebcbceadeccdbdbdbdcaeaaebaebceaacebacaabdeaccaaebbddeeecbbabebccadbcecbecebcaecceeeaedebecdeadcabdbaaeedbcabbcddacaedebeabaaecdeccbbcdcabdaddbbddccadabbceabdbeeebcdecbbaeebccbbecdebeaaceaaeebccededbacababeaaabaaddaeaeeceaeabbaebaabcaaaacedebeadabeadceecabeedabdecbdcbdedcdaaedbddeedeaddeaceaabcabbceeacbddaceadbadceceddcabdebedddaeaccceaeddeeabdeedbadbeeaeddcaccbddbaccaecddbeebdcaecadabaaacabadceeedcecceddadadabadbceededadabeacaebbacbcdcbcddbeaaccecaddcaadcbdecddaabbaadbbebcadebcdccedeacaaeccaeaecceaeccdccbebedbbbbbaaaeaeacdbcedeeaadebadbeadacbddaabacecaecbacdecdbbeaebecaeeacedeedeabebbcebbdbcaaeceaeceeaddebceebdeabcccedaaadbcadbececeeaadcddabecdeccbeaeabcddedbceacbceecdecdadcbcbcabeabacbedbaeccdaecdbabecbceeebddedceacdaaaceeddbedeebeeeadecabecccbedddabceabdcecbedceeccaeddaaadcbeaaebdcceebcbbeeccbdebedebdbeecdecbcedaeadbbcbdeedcabeadebeadeeeedeacacebaddacebdbecedacdbbeeccdbceadaebdbadeedddbaebdacabedcbababcbccecdbbbbdaedadeabeebcddeedbbadecabdcccedcdaeccebcbeecebedebdebabdccebbcdbababaceabcddacacedbcdbaddbdbccdedecacadccebcbbeeedababdbcebedebdbbdcedacbcebaeaabebbbdeaecdbdbdecccebeadcdccbeaccaabbddaccdeddadadbbcabacddebaeadbcdbcceccccbbbddbadeebedebcbdaccedbeacecaccaaecbaadbbbbdbbebedcaebecbceaaaaacaceabeeeedcdaaaaeaadedcdbcaaedbdadccdacecacddaaeecdceabcddcceaebacdaeabcbbcdbabeaabadabacadcaeaeecbcdeeddcecaacaebbeacbdddeebbacddccdbaadeddbcdeacedceeceebeaeedcbbbdcbddcbdaeacaceceabaadbaedaeedacaaddebaebaeabdaedbaddabaedcbeadedbdecadadedbcdbaeecbeceaddcccbedeecdcdcddbaecbeabdcbdaacbaecebbddaacbadebecabadacbbbdbbcaededecaaabcaddedbebaaaebcdcdedaaeedbcdabedbaebaaebeddeeebbccedbbcecacaaedcadeeaeaccceaeddaccbdbaaedddecedbeedcdbecccbbaceccaaaddcaedcebdeebbcbdbdeccdabeabddebadddbedddcbdbabaddbdcbdccbcebceeddebeaccebeacabccaccaccacbcbedeedaabaadcedcccaaccebbeabddeacadaacaedcbcbaedadcbcddabcdaeabddebaecddabcacaeaadedeedbccbacecbedabbaececbcabbaaeaaaecdaeadcbbebcdeacbaaaacaeedcaedcbeeebcecacaaebaebaeabadbeaeeededbdbbcdabbadbacbcbbbbcaebceaaacbcadebccedabecbacaddbcddaabaccadecdaeaeedeccabdebacdcbaeadcddbadaabedcddbcedebdcadacdeebbbeabcdaaceaccbdedeaddbbacabbcceaebcbdedebaebedcedcdddceeadbcaaeaaabbcaccebebdbbecbecbcadcebdbdceadedcaccdceabeabecbedeccedbbcbaabdcabcaacdabaaddebcaabeadaaeabccecbaccbccccbeabeaeedeeebaaddbadeebdbdebebdcbadcbeeeaabebcadebaecababbbecabbacadcccdcdedbcabbedcebdebeedcdcedbcdaeadaeceeeeeadadbbbcbbecedababbebadabacdcedbabdbedededaecddbedeeccaeaadaeaecdaecbadeedbdeeaddacbcacddaadbaeacabddaeabcebceabeeeeebcdecbdccdabceabecaeddaabaccdeabcaceceabdeecebecacdacbacaeadecaceecaeabaddabcbadabcdccaedbeacbbcedeacbcdabbeeaeacbccbcabccbeecacedbeeaeeaeadccbadeccbbebbedcdebedaaaaabeebbaaacaedcadccbaaadbabddceceecbcdaaeecadbcbaebdacbcaaeebccebebcceadbeeacacbddaeadecaebeacaeaaeacbedbcdaccebeebbebdaacadeecdaaebdbebccecccdeeeddbdecbbbeccbdacdcecaeaaeddbbbccacecceaedceceddaceaeaabdaccbdcdcccdbaccbacdddcddccedadcbcaaedabcacbcbbeceeaabdacebbcabeeebdbddaadeaecbabdcebcbedbacdbbebbbbedbeeabaaedddaeadadcbcceaadebddedcaddcaacaeddacddbdecaaceeadbaabccaaabcedacacbdbaecdaeabacebddbecdaebbebdaadbbbeadadaccbabeeabdeddacaedbcccbbecdcaecdabbcacedbdbaecbedbaaeebeddecdccadebaacecceaaebddbadbeacedcacbcdbbbdcaebdbbedaddeedbeaeeadaecebeaaadbcaecdbaeeacbbbbeeddbaaedbadcccaacbbcaaceeacbcabeeebebedeaaedaebddeaeaedbdadebcbbccaeeeacadcebcaebbeaeeccbadebaeacebdbeebcaeccaebdbdbeeaddededdbdddbccedcecccbccbaeebaceaedeccbbebceacbdaaebbbeebebabbaeabbbacaebdbddebdcbebdbbeedbdcdccaedaceabeeccbacdadabbceccdbdadbeabcacecadabedbadaeeaaaddedeaaeadcaadbadcdadebedddceeeddccadaaceedabbbaabcaceedcaacaddcedbccebdaddddceccccededcceaadcbbbdcbdabdbeaacbdddddbcadebdaecdeaebdaeaadaaaabddbbeecdcbeeeaabbcddceabeeaaabeecbaaeacddbebabdcacedbcddcdddeacceaeebeedddbaeceaacbbaaecbcbedcddcbebcebcebdcaceeaaeccbceeaeddacadddbbbdcdcaeddabcdbaeebdceeabbeabaecdebacccdadaecadddabbebbeaaaeabbdebdbecceacaebecadcdaeceeedbdeaabacadeaeaeeedbebebeaccbdbdedbeebbdecbddddabecadbceaedbbcdcabadbdaabdaacebaadadbeadccaacebdeaebcddecdaeabbbcceecaeddbdbcaaebeacacccbdeeecabbeddcccdadcdaccbadcaecbdaacaddbcebaadcdcabcdcdeacaacbdbabaceaebbaddcbcbabdabbaeeedcebbdaaebeeecbeebeccebcbdeedaacadddcdeedbabaeabbeacbcabcaccbabbebceaadcaadecebddedacbadeacdccecdebcaabbbecbabbbddbaddaeddabdbaceabdebecadedaaaaccedeadabcecaddebcacebecedabccccdedabaeddbdcdcbcecdbaaceebdccecedacccdbcdeccbaacabedabeeeeeccbbbabcaebaddadaabadbcaaccdbaaccdedbbbddceeadebaededcecbebcecbdbdabaeecccbdaddeecacacdbbadeebcbdbabcbcadccbecebccbeaadcebbccadcbdbdbebcbdaeeeaeeabbdccbbaaccebbebdddaaaebcaabaeeaeceaabddcbadbdadbebaccedbdecaeeedaddabcbeabacaebbaeeabdecbdeadaeecaebbebadcabcaddadcbbebacbeddcaedcebbdeeaeeecdeaaeecaeaaadadababcecbcbbcbdbbaddadcbdbcedccbbeadbeddaaeebbdbacddaaadbdeecdecbadbbbebdbaccbaaeadcdbdaacdbbdeddecacdbbdbdcbcecebbebebdacceacacccbebecddadabbdcececddcebbdbecbbaaecbdcecbceedecdbbdbabddbbeabbebdbeeacccdecbbbdceacbedbbebaaacabbadbadeeeaacadededdcaeecebebacdadeabbababccabceeedaaaceaabdedaceddbabacbbcdaaccbcaddbcaddccebaccdccbadbaeeccbceacbbccbaebaaebbbaaedcdbbdaebdcbbeebdaeebbabcbcddbdeeeecabbedeeaabaedebbecbedaccacecacdeecdaaaebbaecabbdbccadcaadddabbdbdbeeceaccdcabdcacaccaeddbadecccbebeedddcadecebbdbeccaaebbbbbdacdadbbadecdbacaeddedcebcabcecebcdddaccbebcbcdcdcdadbeecaedeecdccdcdccbcbbdeabaeceacedebdacbacbcdeebeaceecdecbdeacebeaedacdedeaadeebedddbcbadbdceadbbbacabcbbdcccedebeceddcebddcddaeacdedabcdcdbadbccacbbadccdaacddcbeddabcdccdededaeeedcecebebcecadeabdcbcadbccddeeabdadbdedeceababebdcdabddcaeeecbdaddaabaddedcdbccebbddedaabecdbdabbebcddddbdebeeebdcbdabecacdedaedddddababecccbebcacbbecaeedaedbccdebaabbabdbbbebeaaecdcadaabaababcbdacadeeedbdbbddbcbadaaacaeaaeadccaacdbbcbcbccbcdeeeaaeacacdeccaedbcbbeeaeadbdbedcceccaeebecddbaeaeeaaabeacecaddbdbdecebbbbcccaaaabceabcbaaeddabdccedcedaedddabbdbcddcedceaeeaacddecacbcadaeeedcacccaceeececbaacadddacdbbadbebabaaecebcebaaddceadeebebbcadebbebdcdcbbdedccaacbedbbaaaabbadeebbecddaddababdaabdcadabbbeeacbaeaaacbaecebebaebcaddbccaabaeabecdaabcbabceedcccbbeedccacbcdccdeaaeceabeeaeaaaccaeadeabceaabaebaeeaacbccdddbdbcdbcbdaacbdebaedbbbaddacbddcdbceaeabbacbcdbbadcaeaeadedaadaabebdcaeabbbaddaadbaaeccbaeddccacbadeecabddaaacdbddceaabbadbbdeaecdcaedaecadbeccdcdbedbaedadcaadacdcdeaccbdddaddaadcdaadbeddbdaadddaaacbbcaaabcdebaaabaebabebcbbdaeedcbccedbdedbeeacebaaccdcddcecbcabadecbcadbabbebabccdbebcdebbbdeaabbedccaedcedcdeaceccabaeeaeababdcacdabeceadeacaadbdaebcebbdbebedeacddecaacdcadadedcbbcbdadacdceecdcccbccbbaecaeedcaedcabaeedecdbddeeccabbdbceeeebbaeeacbcaabbbbcebebedbebbdccccbaebceececbeddcbcdeaacdedececbdbcbcdcdedeadddcebdbbcdcdbedcbedbacbdedceaecdbbcbaddeeabebabeabbaceaddeacacdaceeaeaaaabebebcedacaebaeaaceacdbbdacabeaeebeaccdabdaccadadacddeaceebccedebccaeabedbacddabcadaeececedaccaedebeeaebacebeceacdddcbeeedaacecdceccdccddeacbecabddcecaeabadadacdaaadaccddddedbaebbbdbababcebdeeaabacaabdceacbdabeebacdeaecedbcccedebdcdcacccdbbeeecebdcabadeddbeaaaeeeebddacbbeceadedbabdbecdacedebabcdacebebdddcbecaaeaacbbdbdaecabbcaedcaaecbadecceebbbdcecdbbbabeacabbabdcddceeabddbadeababdccceadaceeaeaceaadddeadeedebbaceeddeeceaaacaeabbcaccdadcdacceebcbccaacbbecdbbacdeadccbaddcdcdceebdacbececbbebcdaaebcddaabdcebaeaadeceedabbbccecbdececbcbeaaaadbbbcbdedddbbcddbaeececeddebbddccdebdcbbcedbbcdeeebaecadaabdadcdcdcabacbbeacddcaeeabecbacdcbbacddabbedcbecccebbaceaeedaccddeeadbbcbdddeadebcbeaeabaeaeaadbaaddccacdbddcabddaabdebdadabeedbacddadddcecceedbdbadaebdabbcdaeddcccacbabcabccdcaeecbbbbcceeeebdbbddecdabdbbaeebbdddabceecdbabacdadbaddbbbddcbabbbecedadebebeabcecabcceadbdeabbeabdbaeecdcdbeedbbdadbabbebeecacbdecdaacddabeeddeddbecdbbcaeecacdbddabcecadacbccccbeeacaeccadeeacdacbcbacaecaeebdccedcaadcbcaceecbadcbeceeccbbcdbbdabcacbcabbabaabceeaebadbaaddaeeadeaecccdbdccccaecceaaecaecdcceeebbbcebbeacdbaddbcbceeaabecedcbaeaabcabdeeddabdaadecccdcecdbeabdccceeaebebbaecbbbbaabadbbeabcdadedebcbdecbcaeebdbabcddcdbeeccccedcaaabedebbeecceccdebedbbddaadaaabaeddbbdebeacedeebdaceabbaccaeedaadadccacaccddacdadceaecebeeaaccedebbdabcbeeaaadaeeedbbacbbadebcbaadeceeddceddbdabaebaedcbcbdcebadbebddccadadabdaddccbadaeedebbadbcdaeadebdeabdcdebdaecaaddaebadeaccbeabbbbbdaedddcbccbbdaccaadcdaaecceeaebddddccdeabbcbdbbdccdcdaacbeebbccedbccaecaababbaeeddabdddccbbcaadbcebdcbddbaeddcccdaacdeccbadcddadeedaccceeddbeacadbdddecebdaeabbdedccceccaadaebadbaccebbcbcbeeaaebbbccbeacadbacacbaadeecbcbcbbadbcedcbcdbdacdbcbeabdbddadbdedddaeacaeececbdbdededbccbcecbbaabedabdddaaaecdbacceadacaddebebbecbddbbecdcdaedeccbecaabadcedaaeabbcbadeaddbcedecbaabcddaceadebeacaeeceedeadbdaadaeebeadddccddcdabadbeecaababacacdbaddcbecdabdcabadddabdccadaadbdadbadccdeeabbeceeeedbdeaceebccaeecdbebbebddcececdbeabdecadbdaccbedbcddadbcbecddadaaedabaccadeadecbcceaccaebddaeeebbdbdcccececccbababceeecacaacedeabdbedccdbadbaedaaecebeadecededbedcaeeadbdcbbaceebecebdddcdbdebddbaceeacddeeabdebbeecbbeebddcbcdaeeeacceebdbbbbeccbdedabbaaaebbbcebaccbddbdeaceadadccdbdcabeedbdcacdbdabecabddeaadadecdebbbdcaabceaecbcccaecbdcccccdceaabbcbbeeadabbdbeaddbeecbeabdbdbcdcacbabbcdddceaeaadeaaeebcedbcbacdceccacecaacccacbdcdcbcaaaebacacdcddceddcceaedeebdaecabbcbdaccdcbeaddccdbebecdeaddaaaabbadcececbdebddabbbecacbbdaaeeddaadaadcdadaeccbbcbcadbbdbadaaeeacabdcebabacedeccbceecacaeacdedeabccbccbaccbcaeceedbccdeebbdbdedabaaadceaabcabdabbccebbcaaaaceadddebdedaeadbcecacdcabddccadbabeecdddbcbaceaeddcdecabbebcdeaaacccedbabdbadebcdbabcacdbabadaddeccdcbbddeaddccebbaceaacdebcdbdbacaadbdeadedacebbbabacdbdebedaccbdbcbccdacdcaaadacbdaeedecdadcdddbbebbcddbcdbceebcbcccccceaeddcabdedeeccbbecdddeaeadabeeaaedacceaacbaacdeeeedbdacadddceedaaeddcbabcceeeeceaacdbaaedcededbceaecbeabeddbccbcdbaadbeacdebeecdbaaacabeccdbadbdbacebbcdadccccbdbbacdddddecbcbdddddedaabaeeedabbbdebcadbcccdcbeedbcddebecbecdbacecdcadaeeebcebdcadceaccdbaebccaebcbcabcdeabcaeaeeeeabbedeeacddbacabccbccedbbceaeddbaeecdabdebebeadaacbbaeacaedceaaaaccecacacacdbbdaeeccebbceedadcdaddeeccacbbaebabbcebcccbbbbbdbaedabbdeebaacdddbaceccdbacadbeeadeeebceceddbbbceddbdcaeecbecccbbbebcaaecebadbeaddbaabeebbdcbaadeacbdbcbecaaabadcaeacebcbedadeceaaacaedeaeeeeacdbabedabcaacbaeadcccbbcddbbceaddddddcdaceeacbaceebaedadeabaaaadaccceabbaeecdbdcededdaaecddeacecbcaacdedacdecdeedbebadccabadcabcdadccbaeabbddaeabdbecbdeececabcbbdedeecbceebdaccddcddecaacaecbaaabbdbaaeeeedabeaecbbddbeeabdbadcbeebaebadcebcbeedeecaaaedceecdeebeabaeacdabbdbbcbacdcdaabbaedbaceeccaeeebeebdeaeeebeeeddacbebaaaaeddaeecabaeacbccddebbccaacdccccdcdbeaeabadeababadbdcbeddcdadaeaaaaeacaccabddaaacdbabbcdebbecbdbbeedadcbecaddeaccadceecadcadddadabacabaceabceaebaacbcbadcebbbbbddbbddeabbaaacebbddaadaaedbecdbcbbaeceaddbbcabdbdabdadcaecdaebeaecdbbbdacbaeaeacdcccddacbadcecebcceaedcaaeeaeecaedacadacbdcbbbcaaeacabcbeabbaaaabddbcecbeeeeaabcabaaacabdcacaaddeeaabddbbeddebcaededdecdeddbadaabeecadddbcacdbebabebaeebbccbaaeedcaebaeecdcabeaaadbaeabceeeedbadcdcaaceaaedbebcbabbacacdceeededeccabceecdbebabeaccaaacddeceaebcbbbaadcbdeccbedbedcccbebbbebbdacebadcaaacadbabcacedbbebebdeecdbdbbccbcdccebbbccedcdebcbdebaeeacbdebaeeaceccaaaeacaacbdbcdddcaaddbbdbbedaadbcacbccdedebceedddcbdabcddedbeebeaeaaeceedaedbabbbcebbdceeeebdceebeaacbccccceeecebbaccebbeebccccaabbbacbdaccaeecbdbccdebaeeeeeeeedcbccecddeceececbbbcaaacddceddabcaccebaddbddadbcbaebcdbeeeaacceebcdebdacaddeeeaabeddceaedadddcedebdecaeeadabbcdaecdcceecabdbaceebcbbebddddbadcdebdeebcdddaaaeecdcececdebaddccdeecaacaaabdcccdcbeedbdddbbeddbbbdbeaebddeeddceddebdddbecebbbbccbbcddbcbaeccedadbabccdebcedbabaaaeebdadddcbdbdedaadeecbedabaadabbcdadecddbaecbdaeabaadddccaabaebdbbddebdcdedbddbabbcccabccecccbdbacebadbdaecbbdeddcbaacdadbceacddcbacbddaedebabceaacedbaadeaeebadeeccaadbcbedbaeccaceeeaddacbebedacabbcedbdbeabedcddbeaeacdeaccdcadccaacaebeeedcddceeaadbdabbdebeeaaaaedabccbdadecbcdaabbaecbccecbcdbacecdadbdddaaaabcdbaecceeeadbbabedccaadbecbceaabecddccedbbadeddacddcbbdaceaecabdadcedbebaebedcbbacabbbddecadcdcedbeaebdecceebbeaedaceccbbdcaadeacaeeaacaaeddbeabcbdabacceaabceebabeceaaaeadebccaddbaedbabcedcdeacdededeabbecbcebdbbdaeaedeeedcddebdabaeabebbcaaadacbcaeedddbcaccadcedcebebaccaacebeabcdaaabcdebcadcbbbaacbbaceeeadaabaeedaeabbdeeedacbeeddecbddbceabddcadacecdcddabaaebbceeeacaeaacaadceedbabedbeebbcbbadaeecaadacadcabeaedaddbdcaaeaacbbeebedaeeeeeccecdcacbacceaadbdbacabbddcdababaecddeaadbddadaceadbabccebaccddabecdabedcebdeaeebcbcbaeccdaebcedbdbdeadadeeaacbabebeccdacddeacadbeadebedeeaababbddebbeeabdcabdadaabdddeabdaeeaabcadbaeaaaebacbbeadaceecddccbeabbeecccaaaedababcadedbccaaccbbedadcddddcebccdbecbbdedaebdccddadedbcaccabbaacceaabbadaaebdeceaeaacdacdbbbbbedebcaededcabccdaeccbddbbdeceeeecdbeeeadaecadaaaeaabecdeedebdacdbbebadecabbbeaddadbebddeedbcdecacbcaedebabbdadeabcacdecbeddaabdddeaacabeeebdcccbbacbcbaeabbeaecdcadeaccaabaacacdeaedeecbbaccaddbaedbabdbadeebeaacbcaedaadbbadabeeebdedaaaaadddcbdecbdaecceeccdcccbecbeddadaabcaabebabbecbbabddabaccdcacbcacedadbbccdbdcdabdcbcabbeabddccecaabbdaddeabdcbbacbaabbecdcecdcccddaabbabcaedaabeacaecadcdaaceceaebbcdeeaaadeebeddccacabedebebbbdbceeeeeeabeddbeacaeebeaebddaddbcedecaebdbecdceeeceaabebbedbbaeaeeabdbccbccdaeabacaadeabecaecccededeaccbcacacbbaebcdedacaceebebadecddebccaeeaeaacadabdbdedebaabcaadcbedebbaabeeceaabbcdeeaacbdaabaebedaebadcaaceaeabdaccccbdbcdbedeeacbecacdaecaaeecedebacdaeeabeedadeaacbeaeaceeaabdeeacadedacdabeacceadbdcecebcdabdbaaacabbdbbeaaaeaebccbcebcacacccddaecdadcdbbbedbceebecaaccaaaecaaeeddbccdeadbbbccdacaecbedabcbceebadbdddbddbaadadcceabcbbdecdbcaeaeacdacadbeeecacbddbdbadaebbbededdeaaddaecdbdcdbcbedbbceaabdcacacacbeabacdaaaceaadaccadaeaccadbecabdddedbeaddcaddbacbbdaaeaadececebabbbbdeebacbceacdecacaadcecadeceeddbdcaebabaaabbbcaeabedadaeebdbdeebddceebdacbbeedeaebbedaccadaaedddbdabeccacbbdabeeaedddbdeaececeabddaebccbbbacececcbbbecbbdaabcdeabaeeeccececacdceebcddeadedabbdbabdccbaacccecbcdedbeedcdbacdadaedaabdedcabadedaecdeccddddeabbeddabcdceaacaebabebbbdebacbbaeacdcedceccedcdbcceddcccdebbeddeedcabebeaebeecaeeabccecdbebedbcbbcbdaabbddddadacdeceddbabacbadbcadbdaaaeeeeaeebbbceceaeddbbeadeababbddeecccaaddbddcccecceddadaecbadbbbeeeaacdeeacbadcceadccececadbdcdbabcdaebdaebebcdeeecceadbcceaeaccdaecdecabeabadbcedacacbdcacdedeacbaaceadebbbcdcbdeeddddebdaabaecaebaeaebbedabaebacbeaeaddddcedacaeaeccdaecedbadcaebbbebbdcbebcbacaebcacadaddcacbadcdddedceacbabacddaeacadcdacacdadaadbacbdabaaddeccbcddbddaebbadcceccdbdebaeceaeccbeaccabdedcdbbbbaabebbbddbddecbdddebceceaceecbcbbdbceaabccceabadabdadccecdbbaebaeebdacdddaecdcddeeecebaeadadebcdcaeaeeabdabbdcdcdcbadcaacadcadaeedbaeababeebbeaebcdccccdcddcebdaebeedccedbaacbeaabedbebdeaaccbcbceeaeacabcedecaeabaeeadaadbdaebebcadecdbbcbaceacdecacededaaaccbaccebcccabbdaecaabadbeabedebeeaddabcbacbcdecbadddabdababbdeaeedcebadabdacaecbbbedabdbeabeabceeedebcacccdecdacbdcbbcadddadcbdcbbdbbadbacdbaaedccaacbecdeddaedcdecdbbeeecaebaeebedaddbeadbebeeacacebabdebadbedbaabbdbdecbaceecdcebbacbbcbaaeecbabeedaedabdbeedaeeadcbadddedbeadcebaebdbcdedcbbbdcedcbeadceddddccdacdbcbecbecbceeadebddbbddaccdaebeddabccacaedccabeaaabccaaceddbaeddcbbeebeebebaacdebabdceccedaaaadaaddbcdcbdeabeabcdccecceaaaeecebaeedacdddcecebaecbbeaedcbeeebecbdbababacccebcbedaacdcdedecedbdacabeaddccbebecddbcddbdceccacedeeeaeebedadcdeeccadabcdbedccbeaccdbdedebeccccbaddccccabebbbabaeaebdbdcbbdebbccbeaddaabdadbacbcaacbcebcaaaadaebbcbcebccdcbbebdcabdcbcaebecdecebbceeeabdeacedabbbcaddacdecbdbccdbccdbdcdbdbbcaeceeecabeddebbaecbcbaaceadbccadceddddddccdacebcdbdacdedabceceacdddadaebcbbebebddccbcbbeeecbadeecdeccabaaceaadbebeededbcdabeedaaaeeceddeeaaccccaccaeecebaabdaabadbbdbbbddeadcdbcdbeedddeeeacceebaececcdecdcabeddddddcbcdbcaebdbdebdabbecbdabeddabaadbaededeaaaecdaaaeaaeaeeceaaaebbbaadebabacbddebaeddaebcbeabdebbddedeccbcdecbccddbdedaaecbbaebcdaaccbeadebaeaeecbbcbeeeabdaacebbddeabebbaaaadadcdaaddddececeeedabdddeedecedebcbbeccbaedbaeaaaddccbaacabbdbcadcdbacdeeadabeacbbeceddbeabecbdeccdccdecbeceadeddaaebdaceecacbbdbacecaedccbbacbacdcaeaaaacacedeadabbaaaceabcacdbebadbbaacabcabaebcabdcadbdaaebbdeadedaadbeeaeabbceacaeebeddeababdceedcbebacdabceebabaccedbbbebdccbdedeecaeeddbcabbbbbcabdddbdeedbecbdedcebebcbecdcacaeddcdabcaddcdbdcdadbdeedebabaabedbbeaaebecaceceecdbcebaddacbedededabeaeeccdeccceebeedbaeddcbbbaeeecaacccbaeaeacaaaadbcececdcdcdcbdbbbaeddcaaeacdabaaeaebcbddadabcbbbaeccabbbaacebabeeeaedbacdaaccbeaeadeaedceedddbeebacbcebebbdecebcdbecddaecceebceaebcccaccbdbdcddcaaddcebabcdacbeaeeeaaeacbebceadddbbabedeadddddedeadccacbabeeeeeebceeddcabdddbeebaedbeccdaeedcdbdeedbadceadeaaeceaccacedecedcabeadecdedeeceacccdeecdeaebdbdaabdedbaacecdebceceaadcccbbeabecddddaebacaaabebaabcdadcbcbbbcedcceeeadebaedeeaceadddabdcccccdddaedadebdebcaeacaeedbaedaadedacdaacbbbeebabceedacbdedbaeabcaceeabadbcdbeedaceecdbdceecacadaeaebddaedbabbedabebbcceaceadadaedaadddaecdbddeeacececdcdbabbeccaaaebbcbabcbaaaeacceabbcbbbeaddebeaddbceeeecbeaecdebededbaccbeecdbdadaecdaacaabddcbcadeeaecdedbbddcaddaaaceadbcaaddaeebaebcbddadedaacccdbbeaeeadeebedeabebdbaaeabdebcbbbcaebccedcdeedcabaacebdcbcddabdceebcbebebcdcabadaeeecbbccbbdbadecdbccddcbecdbeabbaeccccdcdecedcdeaebbbabdbdaaaaddaeddcdaabaaedadddabedccddceecddbcddaebaaaabddcccceadcaeaadecdadbeaecbebbdbecceeddbcbcdacdbedddbdccabeceecaadbdeceecceaeaddebebbcccebbdebecacbdcabddaebbddecaccdbddbdecdcbcadeccbcdcecdbdeabcbeccdebdeededbeaadecbedcbcadcbecbacbeeedaeddeabddeecedbedcaccdbcdebaeacccacebbcabaeabaadcccabbbbaaebbebadbdcdabacdebddcbaeddeddeacdaabbdabadddceedabbceaeeeabbcbbdcdececaedeabdcadaabccacdcddcdcdabacdabeaeedabadaedebabbedaadbbadaaadeebbbcecaaaaeddcaeacbdebddaaeaeceaeebcabecaceeeecbadbcbebadaaecaedcccbeebdddccccadeedaecacbdbcbdeaccdababbccbcbbbbaacaaccacceaecbaccccaebbdbdabbccdaeabecddcacaaadadebdecabdaedeaaadcbebcbadbcddecdbdcdbacddeabebeecbaeeacaeebaaebbbccaeaecbcbbaeccecbeebcceabdbddacadaadabbacadbdcdadbcbadddbebabbddbddddeabcabeddcccbbadecdaaeeacececaacccaddecbcbeaccaeeabbdbeccaaebdddaedacbdeaabbcbdabddacdcdadcadaeaedceaeceacabaeebaebeabdddaaeedcdcbabedacbaddedeaeccceabcdcbbbaeebdeeaebaabadcdecbddabcaeedbabdceacadcacdebecddeeadbbaddeaaedccaceeacedeabbbddbdeccdbeedaecdeaeaeabbdadacbdadbedcacacebcaeccaacbaacdccbcbceaedbacdcedebbaceddbbedeadaeabaecdcacbbecebcdddadaeddacaaeeedbcdcdadbdadcbcbebdaabaddebacabdeecaacbdebcabdbeacececeeeeaccdcdcacdebaaeacdabacbacbebbcebacbdecbdacebecbbcbdabdbbeeaeadeccdbebcbaccadbedbedacbbccdaceaacaedbaebcecdcbeeabccdeeebadcaaacbeeebbebedecdacbeeddeabdaeddddbdeceaeabaadbdecdcaaecebdbbedcceebacebdeabcbcaeebcababbadecebeecdeaaeadaadacdaeebebeedbabddaebbeebccaabdabdcdedacbaedadacddcbbaecbbaaedbcddedaceabdedacecebdedddadcabaaeadbacbeaadbaecbcabadacdbaacebaecadecadbdabbbcadcededeadaaaadbebaebbebdebdaceaedcaaaccaabcbeabbeabbdddcadcdcdddcbdcbddcedccdaaceaabbaadcebceabeabcdbabbebeeaacaddbeeecabcdecabddddeddcbcbabcccdadacadcbdcbebdcabddeaaaadeecbdabdbcaebbcbeedebdcdbceabcbbeddcedacdcceeaecedbddbbdaccecaaacecacebacaeedbcadcadcbeaaddccccdcddedbdbbcedacccdabccbddcbbdecbcbbbaabeeeeaeaeacdedaeeaaeebbdceaacabdbaecadcaeccebaeabceddbbeadaadeedabdddebddcdcabaebaeadeaecbbcbdddaedcdaaceadbabebcabbdaedaadcecbbaeedebccacaaacdeededaebdcadaecddbeeaedaeeacceedeadbdeaacdcceeaadeccadcdeaeeababcddbceabddebbbeabddadcebabcedebabadcecaeaaaecbbaebeaedceeaaeaadabaabbbedcbdeceaaebcddadcaebcbdbaaecdbcdecccdacbaebadedaddbcddebdaaeeadcdeceaeeedaacacbdbacbbebaabdaebdbbcdaadcdeecebedcceecabcecdeaceeeabbaedeeaaddababdbbabdceacaebabddcabcbbdbdbbbaadaaeaadedddcaccebecddceabcbaaeebaedacedbaecdbdebdcbedcccabceabcebaadbcbcdccbaecbadeaaddcdceacdeeeceaeecdddbbdbaaaeedeedabeabbbabbcbceeeacebcceecceadccceedddddceacbecebdbbebebbebaacebccbbadecaeaacaeaddcdadbcdeacabebebeeacccebcaeaccbbebadcebbbcdeacbccbbeabcdcbbdcdacaeeadaabbebbeeccbedebaaeabbeeecdedcebdbbdaaccaeacbeadbbaddbbeacceccadbebcbdcacbebceddbdeceedaccbdddcedabdbcacededcdedcddbdaaeecaadebdabbdeabdebbccecbebccdeedaecbedeececacbabdbedcdecccdbcbcaaaaecbdbebbaebdbaebccaecaadddabdbdbddbbcbacddedaebccdccbbadeecceeadeddceddabdbacbccbeceaacedbcecaabcaecebceabadadcaddbecdbcbebbebeeceadeacaccbcacceceaedbdceeabbcbbaddecbddccedadcaeddddbaebcceeaabbbcaaddcbbeeacdaaceaccdeaaedeeeaddadddaaaeaabbceabeebeacbcceeeeadcceabacaadcbbcebcdeacbabcbcbcaedbecebbcccdebadeedddeebeebcedabdcaeccacddedccdecbdbeceaceeedbdecacbcabdeabadbceababacdbbadaeddcecbcbcbccebdaecdcaeabbbaebbecaecdacaaeaaaeddccecccacdabbbcbacdadaebeecadacbddaceebcdaddcaabcdddadcedcaeaeeadbbcebcbaabbadababbdaabcaaccabdecaeaaceaadbedabddcdadbebabbcdadcbabbeedaaaccdccaaecbadbbbdbdeedacccdabaebdcecdcadaecaedcaebebadcbcacddaaaadcdbabecabddaaacccaeaebbbaaabddacaecaecaeaaabedbcbeaccdeecaeaeabbdeceaceeecdcacbecacbebedbecadbcdccaabccdcebacbdbbaabeeaceeaacadbadaddbcdbecbcaacbbaeaedceeeaacdceecabdcaaebecdacbddadbbdeaadabdaabedbcdebbdbaecbbbdbbcbebddeaccbccddbaebccdcceabeccbeceeabdaabcedebbeacdcbaccbcdeaebcddabadeabbedeedeebbacdeaacabaeaedebdaebcedeecbdadeeabedbbcababbaeacccdbadebabdbadbcbadedbeedcaccbaeecacaedebaebddedadaeaddeaaaacedbabdccbadaeeeadecbbeaddedbddeeaeccbabaadeaaeeabcddaeaebbedbbbeccdbaadbeebcccbbbeaecbbdabbeedbedeacbdbcceddadaccbecbacceacadaadadacbedccdacccccceabbdbcadbccdcdcebcdecbedaaaeededaabbbebbacdccdbabcaadbabaedddabeaadabbddbaedbebedcbbdaddbdeacdacdacccbdaeccccabceccaecaccdbcedcceeddbcabaacdaccebaeaceaaadaeeecedaacdbacadaccaaddccdcebbdcdaaeaaabaabdcdbceddcbcacabaeabeebebeedeeaceacddebeccdcabeabbcadeaaedbddcebeadcccaecdbcabbdadccecebbececbacaeaddecabcacdaeaabbbcccabcdeabdeaeddaaebdcabdeadbcdaaadaedbeacbaeebdbbceeadcbabcbdbbbcebcacbebcdcbebcacceaaedeceecdaaaaedaddaecbaddcdeabbbdedaebebbccaccdcaeeaabedbcacdaceebabaabdeedbaeeacbabcebadeebbeeebeacabcdbcddeaaaeecdcddbcecebbdbabaeeecaaaaabbdaadcbdecedbdcabecadaeddaeaabaaedbadeecebaaadcbdecdeceeecaececadcdedadcceddaababdaacebbeeaacebdededcacbddbdcadeacbacdeeccadabeabcdaebeebcedaadbadeeebcbbdbcaccdcbcaacaabbdbdbcbaeaecededeaabbbacecbdbbcadadecdeaaeabaececadadebeaacbebbcbabeaebcdcaeebadcbcaabacbacceeecaaeaebdcbdabbaedecababaacacbabadcbbdecdcccccadbdabcdbebcbcbdadccbaadcbacbdcacecacbadbabebccdaaaeaaabcaeccabddedeaabacbbcdaeebdebdbadecaeaddeacbedeabcdadbccdbdedccdccaabcaadaaeebccbbccebcbaaadacecedcbbeabaaccecbecebdabebaedaedbcbcddeddceabeddeddaacebbbdbdbeceaedbbcadceaebbbcebaeedaedbbdebabbddcaddeeaedaabebeeccedeebaceaaceadebdeaceebcbccaaaeeeaaadcbaccebdbeaeaacbccdccbaeadacccebdacdebbdcccaddeeadbaceaddebbcbccbdabbbdbcdeaabaedeeaddbcdadaaeaadaadcecdaeabecdceaaccbdcbdedbaaddedddaaaccbebbbedbdecceeabcbeadaabdbceddadcadddcdaccccbcbdcceccbcabbaebeceeaaddbabebdceeceaadbecbecedeccebdaaabdcadadbdebdccdedcdeeaeadacecabdaccbaccdbacddceebdbebdddebcbdcadaedabacbbebccbbdcaeaadecdedadbdbddbbebbedcdccbeaececaaecdcbdbbdceedabddeaecdedaebbeccbdcbccadcbbbcadedcbbeecdacbacbaedebabbeacbdabbdacbaadeeacabbdacaccebeaaebbecdabeabddadcdbddbbeaceebdaeebbebcbddccadddaeeaabcdbecdceabbbaabbaecbbcdbeddeddaaebaaabacbcddeeccdccaaaedcececcbbccedabadedbceccdeaeeccabbeeabddeadeebcecbbaaeeacebccdbabbeeedeedcaaaaaeaceaeddbedbaebbcecebdaaabcaedddddcbaebcacdeccbeaddbdaccbcadbcbedbecbabbbadaceddbddbdcaaacabadaeabaaeecbecbabebdceaeededdbdeadacbebacddceecadabebdacabbecbcababebbbdcdeabaeddbbcdccccabcccdbecdcadbadeceeeabebdaaaababcadbeaccecbbcaadcdbeaaaabcbcdeeecddcdadeeabbebddcceaadacadddaaddeaebaadcacbeceadbbcbaadccbbbeacbdbcedcddeabdbbdbbabeacbedaaaeadcdbbcbcabeebaedbecdebbdcbeceaeeeeacacacaeaddeacaaabaebcbbdcabebddcbdeeadeccebbbdaeccabeeccbceaccceabbebcacdbbceaebabededaabaeacbdcdbceecebdecaadbaebddbcbbcdccabdcebdceceaadbeaecedeccdabacdcdbbabbedbbbbcaaddacadeeececddcecadddacebeecabcecadebbcacedbceacbaabacddacedcbcaaebbbccaebccbdaebcdddedcaabceadbbbacebecbcdecadcccebcdedceeaccccaeecdeaaebeaabdbbceddccedddcedceecbdedcdcbbceddccbaeddeddccbecdedcdadeabbebdacebceadbebbccadbaeceeeedeaacbecaebeddadebeccedcceaebeeddeaaeadbcaacedebacbebacdccbebbebeebeeaabccaadeceeeaaaaabeaeccddbabcdccbaebaeeacaaecbcdbcbdcabacbceacddceebeaadbbddaabdddbeeecdeaeeeecaeddcaeaeeceecccceccaabcdcdbebdcacaeabbbccbcbaecdeebccdbddeeabbedecdecccccbbbbccbadaacacbaabdebcbdbcccbabdbacbceeedbddcbcedbaeccdabbaebedcecbbacedcbdebadbbbadedaccaddeadecabdeeeccabaeeecedceedeedbbeecbadeabcdbcdecbbdedbeeaeeecaedcebacebeebecdecbebaeaedccdadaededbecdaeccbcebeddcbceacadaddbbaccdbebcacadbcddebebbaaadebbbdadbebecaebaaeeaebaeeecbcecbbeabdedbdaceededdcbbadeaacbacddacccbcebccebaacaeeaddbaabbebbcaddbcceaecddeaddcbadebaceddbccbaaabbcbbdcabebbdabcdabeaaeddccccabcdadeebcbddbecaedccbaacdacbdbbddaebbacbddedebccddbebccbcaebbdaacececbecceedbcbeadebdbeceeaacbaccccdeaedbedbedadacdddbaedededbbedcbaadacaeeaeadaeeacebebdaccddceccbeceecdcccaeddadaaecbcacecadbaaeecdccceeaedaeadcbcabacedacaeaccbdbcdddbbdaadcadcccaeeddceeeddbbcceadbccabaeabaaaceaeadcaebbbdeedaebbbdbcebcbebdacddedbddcabdebbedeacbcadeadcedccecdaabdebcaabbecbedecbdcdeedaaddeabbdadbdbbdebdcbcaaadebbbdadacadcbecdecdceddabebbeeeeedcaaacaacdcaeeedeacaabcdccaedecdeedcedbbbedddcbbcaecabcdcebdaccacdbacbadcbacbecbbadeddebcbdabaaebdceabbbeebbeeebcceeaadbccbdcabccccadbdacadbecdbbbdaaceadbdcbdcecbabbedbbabbecbbaecddddbedbaeeeaaaaadaaadeccbcaadcdbbddbcdebaaeecdedbaeaeacdbccebeececbaceceddddeddcecddcadaebddbcdadbabaabdbaadcbbacbdabbecddaabbddccbdbeccdbccdadbddccaccbaabbcecbbbbaecabceedbeebbeaccaebacebebadcccddcbadbcdacbacbdaaeaedaabeacaebdeceaaeadbadeeddcabceddbaeddaabdcaabedeeeaeeaceaccadcbdbcebbcdaedadbcddabcbeebebccdcbdcacbebecddeebdabbaabeaabcebbbdabcbedaeecacbbcddbdccbdbbadaaabacbababbeeabcdedadedabeceecaebeeebacccccbeecebdcebcadaeaadabdacededcaadabeebccaeeeceedabdaecbaeddebacdaaabcbbabbabcecaecbccbbdedeceadccdebcebebcbbedeebbccdacaecdbdaacbdbbecedcebebedadcbbdaebbdaebbccbebaadeecaebdbcbbabaaedccabbaaebebbacbeebddcddbcabbbdbdbadccedbbddcdddeabddaeeabbdaaedcbebbcbeceeeddbdccadcdadbaddbdecedbbdceceacdadacdbecbccbaddbedeeceebbcdbcecbecabeaccedceaadcdddabedcaeadeeacbcddacaaadddabbbdadcbeeadeeadcbaacaaacceaecbbbeeceecadcbddddbdddacebedadbeecbeaeceabdaacdcbdcdabcdabdbdbcdbacadbddbdeccaabcbbeadeedcbcacdcbcccbbccaaaccdbcaacabdbdddcbdbecddaaedbcaabececdaceaaeabcbebdeeebcdeeabcdbeecdadbeeaccdddecbdcebdaedcdeceddcbcacacdccbecddcaadddcdcdebdcbdcedcaedcbbeecdddbaacdbaebadcebabdaecebdecdbcbeeecbeeaadcbdbccddbcbebceeaebadeddbcddeeeaaaaceebbebaecceedaddeccddbbecdbeedacbddbccddaeabbbdccceeedeaeeadbcababcdaddbeecdbbabbaeadcdddeaedcaeecbaadedcdadceccbbecdcedcdeeecbeaecadabaccbdedcbcaeaecdaadbebbcecbbabeedcbdbdbbdeaaebcaccacdbeedabecddeebeceeaaaccbddebdbcdabaccbbebdaabceeabcdaacebaebadaaeecdbdddcbbbcacbdaaaecbededcaebeebeccdaceceebccabecbccdadbacebcdcaeddecbbbebbacbceaeadaeebcddbabeccaacbaebdcaabbcacbbcecdaebedbebeaabbccceeeaedccbcdcdddaadaecaddbdecbadbacbbaabeebddbcdcaedddabdcabbaacdecaceadcddbacdeeedeebabcacaaadceecaececabbaaccecdacacddcbdebbeceabceceaccebabaebaadbbebabddadaddcdcbaeddbbebbccabaaddeeebabcbdacacccaccedcadabeeecceaadcbacaadbdcecadcedcdbaaabbadccddeacaaddcbebcbcdcdaccdcaccdcbbceedebadcccdbcdaecdecbbaaccabbcacaecddeedeccadcadcbbbebcbbcdecceeacecbdaaabecacecebecbcaccbccacedcdcecbbdbdabeadbcedebdeedecdcadcacddcabecabaabadaacdcabbcbddbcabbbeaeecdcecabbbbbbccdadbbaaabdddbabacbbddbccadeaaabdabdabebeeedacdcaddbeadabadcbbccddbaeebcbdbbebadeeadaaadeecdedaacdedadabaabbbbadbbbebdcaeccbcbaddbddadebadeaedbeeebacadabcddcdaaadbacbbadacbdcbceeaaaeeebacadbaabbadbcacdceddeaebbdbabebeeedbbbcdcccccaeddbeabcebcdcbcecaedebaabccecacaaeddcccdeececedadbaddbceddedbaaeabcedcaccebaecabbdbcedecabedeedeebdaaaebcdeacadaedebbcbbebdeedbeeaaecdbaecaecbadecadababcbcdebabadbabbabdbbdddcadaecaecbebbddbeaaedbaeabacbbbedbaccbeaedbaeaacaeaccdbeaedebcaeedebaecdadbaaddaeebcbbddddcccbdcaecedbbbabeadbcbaadddbadcdeebececccbccddcceccbdecbedaadbddedbabbcbdbdeccddbcdceaccedceddaaddeaebdccecdeabbacabebdbccbccbceaaaaceaedcbedaedabaabcedababcebabebdaeaeeacedddabbaeecbbaadeaedcccaebdadabdebcaacecdeeebcbeddceadaedcaeecdcdabecacceedbbbdbdacacbeacedebdaacbdabbcbeccccbebeccbaacccebadbdaabeeebccbdacaedabdeccdcbeaebbbbcccabebbdcddebaaaeebbebcaedcccecbdebbecbabaedcaccbebcbdaaebdebccedddbaeebabdcebcbdebabebbeadcedcabbddaededdbedcdaacadbadbaacacddacbccecbdedaceacaeaaecbdabaceabbededaaacadacedaacdeccedbececbeebdedccaddeacdceeabaadbdedcbcadaeecebdabaddaddebedeeaaccaeeccbbcabbaabecbecaebddbedeacccdaceeccdbedabccdacbabdabaedeacaedeacaabaeedcdcecedeaccaedabbadaadbedeeaacebcceadebcbaddecdebaabaccaceacacbdbaabbecdcacdddeccaeeaceceebcdeacccabeebdbacdabcdacbacbbdbcaddebbedbebeeaecdedceeaaceaeeaaabeabddbabdeceababbaeabedceaeaccedccabcdecbcaeaecddacaedebaeacbaaceddeacaabdacaeebcbcccadabdeebbccdbeebdadaceeceaecdeabbaaabbbbdddbdbedccaecbdedeeedceaeaaeadddcecceedabcaecbcdcbbdaebdbcceececeedececcbbabecddbadedcabbcaaeaceaacdcaebaeddeecbbedeaeddacebcdeaebebcccedaebceacbdcdbbacdeecdadabaecdddbcbbbcdddededdaecdceeadbbaebddeeecbdbbddaacdcabbbbedbbcaddadbddaaecbedeaceaccbecacdcbecccddeeaeaabcbedcbcaebeeecbdacbbcbebbdcbacccedcedbeebdeeaebcdcdbdcdecababaaabbabaeecccabeabeeebaeebcacecdbebeacadcdaccccbcaccabbbbabedcbbdacaaceebeeebcbaeeaecbeeebcdedaeedccacdbacadeedbbabdebeabdbeeacabbdcdaeecbdbbeacbdaeaaedbdcaddccdabcddbcebdbbaaccdecacdcddceacaeaddadacdaccacadceacdeadccbabcaabeaebecbcadebbadadeceebddaaddceadebeddcbeacddcbaedbcbaecbbdcededcedaaadbceeaeeaedaecaceebbdccccacacecbcdabbeacaaceeddbcedadaccbabdbccbeadeadbabaaaaeedaebdadddbbcbcbadebdabebddecacbcdbdedeabdecccdeedadbecbdcecedeeaddbedaaeceddadecdaecccdaeabbbaaecaaabbeadbbabbbeeaeadcbbadeaccacbcdbbbedddaadbbedaabccdecabeeadeaccbebddaaddececcceeaaebeaccbcbbccbacedaaeadebecdaceceebcaecbcaedcceddbbbccaaabccebcacbdadccbdadadaaadddddaaacadbcceedaebaaeacedebbebdcdcecdeceedeaceeaabaaeeedabeeaaebcaeccdccabdbaabddccaaabaadaeabcebeddbbdcecaadbdbcdcacbeeabebebcacbdbdaaaedbbcdbddbeecccadaacecacadeebebaeaceedbdeccbbeccbcbbabeeabaecaeebdbbbadecadabbcbcacdbbcbbedddddbedbeeecdcbadbbeaeabeeeabeabbebbdababeebddddcabecdadabccbbdccbdeaaaaedbbdeccdecabbccabaccbeddaeaaddbaedebabadaaebcebdaadcacaadbaebcbbdcebcaccedeeeccdeeaabbaebdcaaceababbeadcdbeddededbdeacddbdcbacecaadbdbebeedcdaaeeaaacaeedaeedabbcdadaccdacedbebeddcbaadeeabedebaeabdcdaebbeabcabcabdcdaaacabebaceeaadebbcebcbaabdccadcdccbbdaccdaaedbebdedccdadeeaedddecdeebddbceaecbdadcdbdcbacbaccbbaaeaaecdbbbbdaaadeecaeaecbbedcdbeecaccaabdbcbaeebadceeecbaceeaebaaacbcdbdbecdbdbebacbeebbdbdbbcaeadcdeedadeddebebeedccacaacecceabceeeabbcddbabddccadcedebebbddeedbcaadeaecebaaddeccaceaaaeeeddbacabddaadcbbbbcdaaacdbebcbeadbbeacebbbeadaaababeccddbcabbabcabdabedccbadcbaeaaacddddcbedaededbcecdaecbddeabedabbcacbcebceccceccceaeecacbddcebbebaedadaaadeebbbbdebceebdeeeebbeebbadeacdbccaedecdbabedcbdbdcebdbcecbbccabdcecadadbaadddaebccdaaeebbbbbcddbedbeddcdaddaebaecdedeabdadeaccaeeadbeeacbacedbedeedcecedabbcedadaebcabeabaabecdbedaabbaeadabcacceeeaecdbccbcabcdbbcaaaaabacceedccdeeedccbeddcedbaeeabaceabbaebacbadcebdcdcdbeeebaeecccceacaaaeccccdabecccdaccbcdbeeaabaadaaecdabaeecacbbccabebeaeeddacdebdceccdababecccdeaddccacceaedcbcdccecdebbeeccacebeabedddbedddeebbecdbdcbaeacebbeceaaaccbdbeccaedeacaeccdcebbadecdbcbababbcbdaedeebabaeccdeababdcddcedbbcdaddbdeceaabebbacddadacdbebacecedecbcdcbdcbaeaccdbceebedaecaacbdcdadceadbbbeeaeacccaaebeeaedbacaccdcbaacadacbbdbdeeddcdceebaaddcddededadccddbdddebaccaeccdcadaaadbeddeaedaabcdceadadbddeddbacccedcabddddddeaebebcbadecbbbdecceccbacebdeebbcbbebbeeebcadcecbbbcdeddebbcaeadcabedbddeebeaecacbdaaacaabdeedbaaedcbecaccecdedeebdbacadbeaeabbcedaedaccecccacebebcabeadaabebcaaeaaedcdbbaaaddccbeaacacddcbdeaacccacadbceeecbdbccacebedcebaeeaabccabccaeceeabbdadbcceccbbaeecdbbeaaedcdcacdadadccddcacbcdddceacdbedddebdcdbbceedcbdacebdccbeeacbadbcddcdcccaabbebbdceeebabcbddaddbdbccacbddaeaebeabbddcbaddecdebdaceddaebdbdeebcbdbdebbdcbbaabaddaddeccccbececaebbdaaeeebeebbabdaaeaebadbcaddeadaccaddaaaeaeadbebeaeaaebbeeecaddbcbaaceabadacbccbeacbdeebbcdbccbcdebdbbeebdebecdcedbccaaaacdcccbdbcbacdbbaebdcadcbddbdeedeaaedbdbdaaccecaaeaadcaeeeaabcbbdbdadceaeccdbdbdadbdeddeaadcadbeebaedecaedccbcdeedbcbeaaddcbddbeabccadaacbbcbbcededdecedeacbbdbdaabbeeddceacbbbcbdceeaedbdbebaaacbaaeaebadbedccddecbdceeaedbbdeaaadcdaceeeddeaabebbebabaadbeacbecddbdcecdceabbadcbabaacbcbdbdceaaebaecbbdbcddcdbededaeaaddccbacbbbacdbcbcedadbaddbccecebbedabedcbaddbbbcbdaaacdbaebecadaebadbbeadaeceddaceaddedabedaddbdcdeebeaaeaeedebedbceebbdddaebdbedbcbbdcabebbebdeeddbdcdccbbcddcbcadbddbddbcbcedaaebcdbaddabbaadadedbbeaceeaaecaeacbcaeaacceccedcbcdadacbdacacccdbcebceacbeabccbccbdcddcaccbceaabadeecacbbbeecdadcdccccccdaedcadbcedbabcdcbbcbdbdcbcbecaacbddedaadaeaceadaacaeabedcbbabadbbaacedbbcccdcaacbbcaebebabaaaececdcbeaecacbbccaaaaaeebcbbbeebceabaadcceeddeeeacbaccbcbaccbdbebcddabcbaeeaadcecaadbaeaadcdbbcaabadddddcedcaeacaeebbabadbddcdccbadacbedcacdebebeaecadcedaedaaeeabddeccceaceddbdcaceaddcbbbbeacbcaabaebcbbeaebdecaacaebaacbcdaceabccbccabaaecdbeccddededbaaaeaadcebebbccccacdedbedcbedcbddbbdadabdebabcaeacaaeceebaabecaabaaaadaeddbcebdbdadebcecbedeccedacabeeebdecaacdceedeacaddbaabcaacbacdededbbbcebaeacdeeeebcaebbdecddecaccbeeeeabbcdaecacddebccaccbcedcdcdeeccceeccbdbdcaeadcedebddbecdccedbaaedadbaebeaeeacbeaceaadbdcecccbcdbaccacaddbedacbeeedcdddeeddcceaaaddeadabcedeacebebcdcbdbeecbddacbbacaeceecaddaacdbceaaaedaacadebdddbbdcdbaedaabcdccceedbdccabcbddcaceebcdcadcebdcadbecbcdcdddebbbdedebedcaaabcbadbacabacaaacddbabecdbcddcaabeacaadbedadbabceedccaebdbdbddbbcebcadedadaeceabcadcaaeedbadeddceadbedbacbbaeacacccdcdeeecdebcebaaebdbceaaecaeaabbdeacecaaadaeaddcabcbcbaeccccabeeadcacaecdececcdcaceceedbadceedeadeabeeedaecaeabaaebcdeacebcddaeeecccceabeebedbcdbbcecbbbdedacbeeccdeabadaddabeacccbdbbddbcbceeebbdccabeddabbadaeaeacaadeddaadcdbbebebceeeeabceeadaaadceeacbdcddbddbcbbedeceaeeeeeccedcacbacbeeacaeedbdcdabbaadaacaabcddeaacbcddbaabcabddccbabadacbeeebcdbaeabacaaedcdcbebcbddeddaaeddabcdbaeeddabacebdcdcbbcededdadecbdceeccbabcddbdacedbcccdeebbebbbdccdebadacedbdaaaceaeecdbaebbadcacebbcbbcbcbbbbbdbbbbcaddaeacaacedadeacaccdbeacbedcaacaaaacecbedcdadbdeecebbeadcecddabadbbdcbabddecdadddcddaabddaeccaedceababbedacebcccbdabbadaecdbabcccdaaacaadecaedddaacdddaeeebacbbaabceeccabcbdedaadcaabdbedcaebbdcbddbcedeceacebadcbbebedccdbdaeaebbcebbedceaacbaccaecceeedccaccaadccaddaadcadeaadaaaaeaecacddeeeeaadedeaeaecdebadedebaaccdedcedadedeacadcebcabdaceccebcaeabceebeeebecdbabbacaabecdbdadeebbabbebdadcebbaceaceedceddacaeabaccdbcbedeeabeadbaabaaecebadbdcdcbabedbbabacaeedcaaadededbacbceaceedbdeaceeaeabcabcdbaaaabdaacacaadbccaedcadcbabeabceeaadebbedbdabbcabcaaebddebbdebaacdedadbbacbdddaacccccbbdbdbaaccdaeadcddeddabeebaedebeccaebacbbdeacddeeccaccdbcddeedbedecbaeadbdacaaebbbdbecececccedbbbadababaaadbaeedaadabececeaadadedaeecdddbdddacabaceebbaaacaedccdcaeaacaedcedeaacbecececdbdeedbdacbedeccbbdbbabeadeebbcebbcadecdecbccaedacececbaceedacaebdcdbdbaaebcdebcdbaecedddeeecaabbceedddaabeccddcaaedbbaabcddbedaeaadeabdaacebebdeaaadebedeabedbceedaecdcebdbacebeabdeaedccbdcddaaccbdebeaaeceabadeccecccdbdeecdadadcbdcdeebdecccedabbbdeeccbedbcacbabdddaeaaabceabeebeacbeccbcbcddadecaedbcbbadcadbbabbbceebeedabcebdaadcaedbacaacedbeebddeeeccbabaecbdaccaeacccdbadccadeccdacebdadaaeaacecdcebdaeeecddaeeaabcaecddaedbaacbceecbebbecdededcccdccdaedaaaebeccaabaaaeebcbddccadbdaecedaebadddceeccacbbacbdacacbaabdcdcbbdcaabbddeeeddaacaebbbaecdbccdedbbecdabddacadaccdecbcdabbaccacceaeedadadcbebecddadeaacdeaabededebecabaecebdabeaaaaceceeeedbdbdccddebcbbcaceabacbabedeabbebceedebdbbbbcbacdeceaccebdacadebcaabbdddcebbecdabedeedecabccaccbacbdcdcdbedbcdcbddbdacdedcbabdacddbcebedbeceeeecaaacdebbadbebbcacddcbbeceeaaadbdccbaebddbddddceabadeeaddbbceeeebaabdbaeaadcdbdeedbcaeeaeccddcaeebcebaeccdebddbcdbacbeecbaaebedcacaddadeceecbbcbaacacdcddbcacbbeabcabbeeeebabcdbecbebaeabedaaaeccabebbccbdbcdccdbdcadcbeaecbcdadedcbeeceabdaedabdbbabedeeaedebbcadbaaddeebeacbebeaecadaabecdcbcdbcebecccacaabdbccbcedaeabedaedacaddeddaceaeaebceccddadabbcdbdaaabcbbcabbaccdddcdeeeadeaabbcbdbaeedacacaabeeadaebbebddddbbdcdcabadadaecedeaeccebdcbddaceebdcdcbeadbeabaceddeadaaeaccddcceddcbabeaccbceccdbbabcbbebbecaedeebeeddabecbacadcdbcdddbcdebacaaebeeadeecedbedaabdbacaaebbdadeebbcbccaabaadacceebbaadacabdaccaebcabdabddeddeadebacebcdacbcaaddbcdcadbdabaebcedcddbececadcaadcbddeeccdaddbcecabcbccdbeacadbbcbbacccbeabedaabedecbeacdeccbabdaeadabcbdcbaaddeaadadeedbaccddcadcbcacbaaddacecdeaaebdabbbcddbeaaaabdcbcdedcabddeeedbdccbbcaaeedeeccdbbcdeddabbdbbdddaaacddccdbdcbdeabedebdaabddeececdceacaabccdcbeecaccaeceebbeecdbbbdbdddceadddbccebddaebeaecdbabcaaeccddaecccddaccbcdddaedbadccacebdcbecdacebdecdacabdccebcddaadbdcadaaebddaadadcbcbdcbdcedcacbadccabbaababdbecdebceaacdcbececedcdebbbccceeecebbdabcbbcebbcddebadadebadebebcccbeecaeaeebdabeaeeeecabacdbaddbaedbbcbccadececadbbdbcbeaecabcdddbddbaeadcaecadeedcaecabadcdcbcaabcebceecddeceeeacdadbbcacdbaddedaaaccedddcbcbbebddecbdebddaeedeeabcbeccdccaddceaaaedabbacedbcbdcacabdaaecdedaceabbcbbddaeeaeaccbedbacabecaecaebcecccaceceaabddcdebeddaacaaadecabaabeccceaceedcdecddbaebdddcebcbbaeaebcbbceacaaebdacdecabeaedbdabacbaebdddeccabaaaedbcdecdecdaccdbaeddacddeabbaacbcacedabbcaeaeebbbeedadaacbceaaaacddceeaeadbddebceddcbadbbdeddceacbadaccadbebddccadbebcccaedcaeebdbadaceabccedeaecaeecbbdbaadbdedeaeddcaabdddadbeecdcdbbbbdbeaaccdddbccbddacebaacdeaadbbbcabeedbabbbcabbeecdeebbdeabeaccaabecdddeeeedbebeadadccadaaedadbcbacdbbceaacbecabccabcdbdcdbcdddacebedeabecbdadadcabdacbeadceaadbddddcadcbdabcddeedbccaecdcceaaedbbbaabdbcaacedecbdedeaaceeebdcaabcdadcdedcbbbadcabdabdbcabbacaebcccccdbdbcbecadcbecdecbdbbacbcbaebbdebaadeabbaebcadadeceeaeaeebaadbdeededdebccdbcbeaecccceeacbcddabaddcaeadabdbbdbbbeaebedaceabcedaaadbbbeaeeaecbacebcaebbcbebbacabddacdcdeeedabddaaccecabbbbacebdeebaecbdcbbbceccaddceaeaecdbbcedaaacbdebecdbaacbedadaceeccadbdbacaacdcacadddcaeaaaecdcbbcbacdcccabccbacdedaddaeadbecbcbaececaebdddedaddbebbbcbeecaceeeabeacecbbcadabdcdcecacccebeabdacebaecdddeddecccabcbbcbdcaaaeddeddcddbebedbabccdddbabbcbbbcbcebbddeadebaddadcdebceaabedadbdaddcedcdeaebcacebdccedbbecaeacabaabedddbbcacabeecdbbebbceddecbaeccbcdcebaacdbceaeedaaceaabaedcebcadaaebdcccbaaacaecdabeeabddcacaedeeeacbeacbebcddcbaeccabdeabdadeecbebaddedadadccdddbdebedebddecbaeebedeabaddacbcecabeddebeeebcddcceeabbeeeaebaeabdecabdeddeaaaadecbccebedbdecbbccbeddeacddbcdeebaababeceadadacdcbebcddededddedcdbcbacdccbaebabeddcdeeeaeedacbedbdbbbbeebcaedaaaedadaedccdceedeabddecbdcbbadcaaedbddaaaeaaebeaacbceaadccccdddccbaccbcaddadddcabecddbcdceaeaecdbdcedcaaddbdbdaeddaeaebbceedccbcaddcedebdcbccbacdbebeecadccbdaeccacedaabdbedeadcbedbcbecacccbaabdcbcabbbbbbadedadddeecddebbeeeceeaaecabcaeeeecbcedaecdaecaabedaceccdecaccaeeebdbaaedeeaccdaeabbcecbdcedccccdebebbbdbcacabbddbeaeeeaaccedbcbbbcbbbcdaadcccebcadabaaadbbeabdcbaadebadaddecbcbcdeadcacabbcdceacacebcbddedecdbeadbbdaeacabeeebecaeecdcceabaddaccecaeedbccaaaabcdbdbadeabdcebbeebaebecaceadadcaabaaeabcddabcdccdaaaeccccdaeceebdcecaadaadddcbbabeddabbbcaeaaeedcbdeaecbededacdcacdbbeadedbaecdbdcdacacdaceadbacdcaddddbddbadecdcddbbcbabbabcdcbeeabbabcdeecdadaebdbeddbddbdcccdcaeabbecaceebeddbddcadcbbeaaeaeaabccdddaccbcabbeaccbeeeaaaaaecacdaaabdcbdeaceaacadddbaceaacacbddbbaebbdeaecbaecbbbcbebaaebdcdadecaddcaebabbabcbdceecdbaaeeddabbdcbdababbcbaecacbcdeaadaedabaebedecebebdabdeebeeebbaecaeaabedceaaaccbabaeebebccdddeabaebbdddbbbddbdebcbdbcedeacdaaaecadccbecceccbdcdbdccacdbaaeabcbeccebcdebdacbeeececdadaecadaabbbacaeacacdcbaadbcbbdbcceeceacccabeacccccaeeeeddbaddbcaacbaeccecaaacbecdaedbbadcdbcedcaceedecdeacedaddeccacdaccabaaedbcbebebedaccadaecaccdbbcdbedbadcbecaeaadbdddaccbbaceeeadabeaedebeebcbadedcbacababaaededbecacbdeecaacacdeeeeecabdbccccabccadacabeaaddcecabcdcbababcebcebbbcabeaededbddcddbaeadbdabadadacdaeccaebdabadbbeaecdddcacbdcbaaeaababbcedbdbeaadedaccdcdeecbdbcbebbddbceacbcaadbacddaaddaecaebeebaecddbdedccbeeabaddbbbebabaacebcabdabeadecbeeabcedbeeacaadcaaaabadbddeeadebeaabaddddadbbacbedeeceadaaccdcaecdddadceebdbcddbcdbedeaadaecccaaebbdddaeeeeaaeccadbdabaeeacbedecadbeebaccecbceacbdcccacaedbaeedabedaeeaedbdcbbbbebacddceeabddbbccebedcbcaeacceeadededebdbbedcdbbcdcdddcbaeccacbadbaaacbcbabaabbdbeacacbacdaabacdcbabccecbebcbbaaeacbdbcacdadbabdecdeceddeaadacddabdbdebcdebddadbaebbebbaeccbebaeeddecdebceceddccbabdbbbcadedaaedabccdceccadecccadaedaeabdedcadcadccacbbadbadebadedecdcdbaaeaabedbcecebcdcdecedbedbbbaaaebcbbcbcceedebadddaeaceaeacbdeccdabedcaeadbbcdaadbcbcbcbcddbeecdbdecadeeeeaacbccacaedbeeddeabaeebdecdebbdbcdaadedbbdabeceeadbbddcceebadddacbecabeadddcdabecdbcdccaececaacbdddbeccededbbbebdcecbdaebdadbacaccbeedcaeebdedcecbeaddbdacddeadacecdedeacadeebbecdcaeeabaeacdeaedaabdbcbdcadadacdbbecacccbadbeecdaedbceecdceabbdaeaddbdaeceebaeaabcdcdcaabbdabecadaeabbecbecaaedacedcddcbceccbedcddaeeeddbcecaadbaacbecadaedcaebcdcbdccdecadabebdcddcbededdceddeeeaaaceacdadbeeecdaeeecacccaaaaaacbaaebebdbdcebdadddddbccddcadcaaccbcbceeecbbacabeebaceecacecaccdeaabccaaccddbbcdaeedcbbcbdddaabcebebcdebcdebcbceceddcddaeeecbbdcdebbddcdbaddbddcdddbbcdcbdbaeceaebbecdeacdaccdeceedccdbcdbbaeecabccadcbacceacecbebeebcaebeabbaadadbaeaeabacddedccdbdabcddacaebbbdaaecdcdaaddbbbbbecbddaecadabdceaccbddcdeadceaacceecdadaebbbdeedeaeeeedaebcdcbcbadcccbcbeedacccecbcbbeeaeeedbeeecacacdaeaeebacadbddedbcceacaedbadebdeadbaeacdddabcbdabbbadaaeabecabceaeabbacbdcdccbdeeeddcedbdbbdebbceabacaaeadeaebecebbacbdcbbedeaacdceebecbacbeeedcbaceabbbbcbeabddcadaecbbcebbdbedcbecacbbbcdbebaecbcedbaabbedcbcaddabeebbabadebebddcdaaecbacaacbcdacedcacdbacdbdcadcbdabeceaeeccdeaaecadadeababcbcbebedadbabdaedabeeebabcabbedbdcebcbacbadeacbcabeceebdadbeaecbceadccedeacabcdeaedceeaabbacdadaeebaebdcbcebbebcbdceaacdaddbebaaebabadbbbdadddccdbebceebdacbdceddebbbecbdbcbadbbeddecabccdadbebddebaadaadebabeeaabeccacbceacebadbbdaddaabdccdacecedbededcecbcecabcebcddceaadcbaabccbecccdacbeecabecdccdedbadabbaeaabcedcaadbeccdaddcebbbecbdeddaaaabadcedbdaccaadadcbaaedbbedbcccecbaeabcbcedeceabbbcdbadecbcebcdddbdecbdbdbabbdbcddeddbeeddadbcaeceabeaaecbabedadacacbedacdcceceeebbeadeddccdaadbdabbecbeebaedbbdeaedcaaadacbdebaeadceebcecbdeddbcacaabaeddbdaccdeeabcceebeabcabdedbbbbbbcbdeedcdcbbcaeebbaccddcdaecebacccaaadbdabbceedeeabbbdbcecaedaeedddedaabcdbdaaadcadcbecbdbcccaccecaecdcdaeeaedcddacaadccebbbbaaedbadbdeaceddaabbabbcaaeececcddabdeebcccbdcdceacacbdecabaacccccaaddcacadabeaebbcbaeceeccddadbdeeacdeaaebeddadcbbeeacdacedaebbeecedbdeaaedbbccdcdddccdeecaacbbbbabdedaacddedbeeddbeddccebdbcdacecbbcaaeeaadaaadaccceddecdaaacdadadedbbccdbdecaaadddabcdbdbaaeacaeeeeaddcccddbabeedbbcacacaccaaaabddcdbcccddeaeceaeecebdcadbedeebdaaeebabbbacbeadacacaacbebdaeedaeadacacbaccdeaedbaabececededdabeedddeabbaaaacedcdceaaedcbccaadbadccebddbbebeadeabaacbbdbddcecacbcaaaecaacdbcebcbbeeacabbbcbbeeebbebecadbbaaddbdabcbeceaccbcadccbeedddcacadacacbcbcdeebdeaceadedbabdaeedebceeddcadcecedcadcabcceaabcaacbdbabedbadadeadeacbeebcdaddecbdcdbbdecacacaceeaddcdddbbdbecacceeadbabbbedebabbcbadadceaadcdadaeceeabaedebcbccddcbadcdecebbbcdaecdaebddaebecabcedebcabaedebcecdaecdbceabcaebaebbddbcabccaaedcaeebddddadcccccbdcebeacbdaaecacdceadebbcabbcccdcbcdccaeaccbbbceaabbccbdcbeedcecaeaaeeeddbcccacbbebedaeceabcacedbbbbabaebdbcddecbdeebcceedcdbebabdceedcdccbbadcdebbcbcabaaecabcbbbababaabdeebbacceeabdaedccbdbaedababaedaaaaadcadbdececbceeccbaeedbbaceaaabbbbbcddcdbcbeadababeeecacbccacadabcaecdccbdbcddebbaeececbadebdbbbeedbcdabebdebcabeccaecacbbcadcbbcebbdcdacedcddeadeeacbcaadcddabddbbebdabecdddecceddedddadbebaaecaaccbacaaeacdeaecbcaebcbbccdadbccbbbcbcbbcaccdcebbddbeebeadacacaaededcbbacaceabbdbcbabcdcbdabaebeebecebbbcaacdcedebcdbadadecdacdbaaabddeeaabecebadbccdaceccabddabcaaedabecebeabcbaebcbbdbedecbdcebbededdbcaabbabecdadaeeebcbcdaaddeccbdbdddeaebcbdadaebbebaaccdeeccbdadecedabebecdeebeadeccdabddcaadedeacdbeaddcecdaadcacceedbebbcddadbabeccbabaaebaaddeaaaebcadccdcbcaaacbceabdebbaeddaddceeaaebaadcdcaaccecadcbeaaedadcddccadddbbcbaddcbdbebaddcaccddabdbbdbaaababcbbbdbdbdcdbbbdddeebeaadbeedcbeccbdddeeecdbeeeecccedeeadecceeaebbcaebcacaedebdbedbccbdaaedaddaaaccddccbabeaaccccebacdbcdaaaaaceaabddcedacceceebadecdebbebaddadaebecbaeeceadcaebabaebddcadaaaadcccdabbceacedeaaabbeacacedebdabceababaceaeeabbcacaeaacedadcddebbabcbabeebcaebaacdbdceccebcdcadbdedcbecbeaeebcbaedbceeeaedbccedebabdbdbdcbbabdbcabdebecedcbdbadacbecbaccdbdcccebdbcecdaeadadaedbbececacdedaadbbddadcbebcddacccacabdeeeecdceacacdbeddcaaaecccabacceeecbdcdbbbeccddaddcccddbeceeededaeebbccaabccddceceeaeddccdabdeaaaaabddcdccddbddebdecaaecddeadcbaaccabededaecadeaddebbadcdceddddaedcebddbdcdacdebccedaeaeecaaaecaedcbdbeadbabdeaeeebccdeadeadbabcdcaddecbcabacaaadcdccceccccaeaeccbebcdabdabaccaccedaaabeacaeebedbaacddcbedaeedaedabbbbdaceccceddbccaebddebecdbeedddcdaadceeaabbbabdeddadaadbbdccabdebceeadeeebcaaeacbabecdabdcacadbecceaddbbcacbcacecababacaabdbcdbbceadecccacaecaecaadaceebabaeaedaeeabbadceeeacaaeaaeaeccbaabaabcacebdecebbcdaaacaecddbcbcbdaeaaeaadbdddadeaacccadaebebcadddbedcdbeaebaceedbcacebadaaccdadadeeeadebaeaecddcebeeedddedbabeccdaceabdbabeebddabebceecdcdaacbecdbcebbeaaecceddabaaaeeecccbebddcadaeeabdebebaaebbdbeccdeaacbdbeedbdbbddeccdbcecdbbeaeaceeabbecedbddedccdcabaaaabdbcdceaeeadcabadaacddaccdcdddbcdbddddbadbdeedaaeebacbeacbbedddbcbecbdeacdaeacebccaccecaabedccbeeecbdbebbbdadaccbccdcdbcbbaddddbccdbddeebbbecebeacdcedbeababbdbbbecbedaacddcdbbecabedaecdbeacabecaabccaaecaeeaaddbddedccdbbdbdbaebedeeeeedacbbccdccbcbddcdeaedcbaceeaccddaedcdcadcdecebdcbaddbcddbbcdddceadddbdcdadedcbdabaeeabbadbeacecadadddacbbbaaedacabbccaedbdaecabececddecabbecdcaadcdaeacdbdaedbbdcbcbebbedcedeecbccccaeeddacebdbccbecccdaeccecbeaeeaabbabaeceeccbddbacebabcebbbccbeeecbceaccddeabedebbaaeaeeaceadddeccaccdbaadaeccabaedaaebdebcecccaeadbaecdacdaaededacddddbbdebbcdddacdeeddbbccaeddaedbaeeeeeeddebbdeeeaeeaaceaedeaceecbaeccdbaeedccccadeaeacbdbeccdccdaeebcbceededcabcceededaaacbadbcaeeacdebcbaabaebcabcabdabaaadbcdcaacaabdcbaddddcccdddcdbeceeccbdbaeceacbceccbcecbeeedebbebccbdbeadbbddcceaedcdcbbaacaabeeaabeaebaaacbeadedcebbeacbdeecdedecbacacbbdabbbcedcabcccaadbeccbbceaeddaecadccdbdbdabacddbeddceaadaedacbceecdcbaaceecbbcaedecacababedaedbdbbcbdaecddbadbdbbddaeeaaabbbcccecbdbaabdcdbdedebedecbcccdbeaabbdbbecececcedebebbddaaeabbeedecedcbaebddcabaadeebdcadcecaceadbcadcdcbebdcdaddebdccedbdeaeddaaedeedececaabdacaddcbbbcabddedbcadacbebaedaaeeeaeebddbccbdbeeecbeddecadacaaeeaacedcaecacbdccdeaadeddaeeeabeacebccdaacdbbdacdccebdddcccaedccbeadacceeababbbcebbbcbeabaaccaedebdcddeaabaedebddcdcedadbdcceeabbaabbbcaddceadcabbbaadadaccdaddbeebdaaadceacacecccdecbdcbaacacbbdecbebbebbecbadceacaedeacbaaeebdbddaacacabccccdddeeddaeeecbcbdeeadceecbcaebececeeeacbdbddeacdcebebbcebbdcbdedebdbbbaaeadccabeaabdadeecacdbabcdccaaddaaabdddccbebeababbebbeadbcaecaacededbcbcaacdbebaacabccdcbdeabeceaabaaaaeacadcadcecadceebaedecbdaaecaaebeeebebedabcddbbeadbacbbadcbddbbdddcbaeeacedcdccacacacdadabdeeeeabedebaceebadeeecbdceddcababbacdeecadbeccbcbaaceaaadaecdcdcdddcbdccdeadccacacddcebaaccbeebccbaeedccebdabeeeeddbdebceedbacdaacdcbdacaedaeaddcacdcedacaadaaaeadaddeaceaecdcecabdcbddeecdbdddacddddcebddbbbcccdadbeeccededcedccacedcbdcccdbbaccdcbcceecdedecaeeaceaccaeacadaedcedbeacddabdaedbabeebedeabaeeedbdcbeeebcbcbcbccbcebbdccbccadecdbbcadecdecdbbaadcbbaaeededdeabcdbdabacbaaebbcebcadeeedadbaaadbaedceddaabbaceacaccaabaaebcbdabcadacbecdcbeceeecedbcdacbbdcdbbecaedddaceaeadaccdeabddbedaedadbecaccaecbebcbdbccaebcbeaaedebabaccdedbaecbbeecbadcabecaaabbdeddcaadbcbdeacaeababddcccedcbacdeceeeedbdceaecebcaabedccaccbcbbadddbaabcddacecbcadbddaccedbabecdccedcdaaaecabcadcbcebabdacadbcaecbcceedecacecdecabeeaebcebccbbedadbccdecbdcccebcbdbabcebeaecdbaeceecceaabeddceaccabcedaaeaacadaeeeeacbedcabeddcecaabeddbbdddeabedbccbeddcccedbacbdcdcbdeecbbdcdeaceeaedeaaceaeebcbaddccdbdbedebabbbddeebececcbabeedbbcaaaeadeedebdbbeadebbccaaadadeccaabceedabacccbadcebedcdbbdebeccbddcdbdeaaaabbedbbccdcecaecacedeeeeaaaaebaedaebcccbbbccaebeacbcdaabcdecabadeabaddbdacbeecbdabddabeeedcdabccbaddddddeeababaaacacdacaddeddebacddeacbceeaebdeebeceaabbdbcccebbcbbcdaededbdcdbcebdbedcccedbadeadbebbaaaccaebedcbecebbaddcddddddaebdcccbebccaaacebdbbbadddecbdbecaacebaeecceaadeeaebaceecccacbcdcdddeeadaeedeecedcadabaceeabdccaaebccbedeecaccbbbcbddadbacdaebdeadabdaacdeebdcddcecbbadacebebeedadeadddeeceedddadcbcabeeebceddcabdacdadeedbdbbabdadcaacbbcddbeaeecbaccedebbccadcdccbddeeceabecaabcaceecdebecabbedbddbaccbacaabbcacccdcadedbacbccbceabaacbabddddccecbbeeddcbccecbbcdcbbddaaadeebeecdcecaddebcaabbcbcecdedcaccdceaddacdccddaccdddaaaceeadebaeaccebedabeebaadeaebddaadbdbedccbadeacbadeadebcbeaedbdeaaaceeaceeaccdebcbaebbebacbcedbbcbaacdabbdcccbecbbedeeeebaceebbcbcecabecabaadaebbecddddadaacdedbaaacccdeedbddadadebcdebecceceacbcabedcdedcddbdcabaabebdbecbeabbdcccddadedddadecebbdeaabecdbabbcadcbaebedbbeceacddeeeaabdecbdeabaebebaedccdcbecdacbaeaddaabbddbabbbbdaedbcecbdecdaaaebedcacbeaabbaccadebeadbdbbbdeaaccccedebbdbeeaceeadcaadacadbbeacdbadcecebcbabeeccabaedcadbdeeedbebcbceedeedbdacdcadacadbbcdeedadaceeaecaebbaddeadbadcaaaecdeeaceeddacdeabdebadcccbebdebccabcaecddacbecedbbddceecaeedccbcbeebebabdaabceedaceedddacccacdeaabcbdaabaeadbabebdeaedecadcddebebcdbeabcabadcbcaeaecbccebcaeadaeacbcadaabeeedbdedadbccbabbdaceedadacedbdaebadcbcddbbaececeddbddbbaaaedaccaccaadbdbecedddabedaabebddebddcdccecbeddddbaaaccecdaadccacbddaedcbebeaddccaddcebdddbdabbdaabddddbadeebbabbeecdaeeadaadadccbebdcdbabeecdebcdebabbbbcabdabbbdecbaedbdcacaaabdccaeaeeccceceedbdcddabceccaeaaaabdaaccccbbeaebadcdaddccdccbdccdbdcdadbdcadceeaaabadbadddedecddbbedccbeebdebccadaccccdedaedddebeecceaacaaccadcdceddacceccdbeccabdecabdcdbbaaabdbbdcbdecacebbaededbaeeabaebddecdadbdaadedabaebcaabcebaadaaaedddebcaceacbccadddebcdebcadedbbeecbccebdeaaacadadbbbdebaacdaaabdbebbceadebcaccbddddacbcdcaddaabbbeeeaabedbabdbccacabcbaedeabeddbbbbeabcebaadeacecbeacaacdeeeaecbbaceeadbaceaeabaccbabaecdabecaedcdceecbadbecceaceebbcbcdbedbeebadbdccebddeccbccaabcaaaccbeaabaeaeebcbdabbbbeccacebcceaaeebabacbdcdbcacbacecdaccbaaecceaccecbacdaccbcbccadbaccbaeaddedbdccccccdedbddebdaedabdcaebbbddcadadcdaabdbabaabbcebbaecbeccaeecdeeacedeacbcdbdebeddaeeecddebbaaebeecaeaeaeebeeedecadacaeababebebbadbbddbceeddaccddbdccdbaedecccdaebdebabaddbcddaadbaeabadecbdeabcebabebcdccdebccaaedeaadeeeecbcccdaebdacaaedacaeedbceccdaebdeaadcbbeeecbabbdcbacebdabeadcbedbbddcaaadedacccaddaebedddccacebbdeaecdeaaababacbdbacbccadebdbacbccdecdacdbdedeeeeabbcebecebbbeaccbadeedbdabddbecaaabcddbddbbcbdabdbcdaaedcbceadbceddcccecdcebdcadcaccbacbdcebbadcaeaebbbdabcceaecdddcecdcabaeaededdadadcaabbcbddaeaabdeadcaabaabddeddabcbecccaceaaabaecdacbcebeabaabedcdcaaccccbdcdabdedceadebecdebbbebaaabacceebdcdadccbaeddbaebcacadebeceecbaaaadebaacadaecacbcdddbcaadaabebbccaecdecbdecddacdbccdbdaaedbaecbdbcbbccdeebeecdacbbdcadddebadebaadddecacedcededcbecbaaeeadbeaeeabaceaaedbecadbdddcecaddaacdaaedbdeddabeedcdccddbcdacabcccadadcbcbcecbcadcccadcdbbaeeccabdaadbccadccaeddadbcccceabcebbbaedbbcabbccaaceeecbbaadbbaaecdecabcbadbdaedaeaaecababacadcaabbdbeedecddbbacaeaabbcdaaabbcadaceccdacacceacaaabbcdbbcdcdaeedbcebdbbdeaadadbeecabccecdcbbaddecdbdbdcebecdabcabeceeccddcadaeabdadcbbcddcdedaceeacabcdbdcadbdbbeedebdedeebadeaccaacaaeedcebdbebecddbcdcddaedcabdeaccabedaeebbadaabcbdccdbaeacbccbbabedddaaceeedabdacadedacdcadcbeacaadebebccabedbbbedadceddbaeeccacabacddcaabdbbcddbbbeacadedbadbddcccbecaddddeaacbbbaebdcebdbebcaeacaacacacbddecdcdbbedbacbebbbceadeecdeaeabdabeccbcadaaaebbdcceabbcaaaabceceaeadadabcddececbaebaaacdcaeaaecaacabbccabebddaadeeaebbcebbaedaadcdaabcaadacebeabcabebacdecdeaacedcbddccebaebedabebecebdebbecacedbbbbabebacbcaeacccdedaebdacaaeeacbeaaebcecbcaeacbbadbceadebeacbbcbcabecaebcaaecaaeabcecdedbedacbcbebbbccedaeaaeacdababccddebbbddcedababcdceabdadbedebacaeebeebdeaddaccdcccddcdaacdaebaaaaaecdbccebacbcdecdeccecaccadbceaeecaecdccebcebceeaeceadddadccddadeeeaaacadaacbceacaededbcebeccadcbcaedcebcdccdacaedecbadabdabceeceaabcdbbedecedbacaecacbadcdbcaebdddcebcacaddebabdccddadbdeaedeaaccecddbeeedcecbeaccacbcbdaaeadddbbabeebaabcacccbaebdebbaaecdedeadbabadbebeeeabcdabacaadcdcbcebebeccbbebcaadabccbbbcaebdbbeabababdbcbdcdddbcbeadaebeececdacbeddbabbcdbcbdcdbbdddddcdedcbddeebeaecaccecbadcbbededbedeecbddacbcdaebaaedcdeadadddbcebeecddebdebaacaeeadaebbeaaeebdbbaadababbebbacdcdbbcddabceeebabdedcadaaccdddcbbbbaecaececaceddaecebbacacaecabcbcaceecbbaedabcbbaabcbceebdbacbebebedeecccccbeeaeecbeaabeeccaeaeadbaaadbdecaababddcabbcdceadcdadbceedddbddbadaaeadddaeebbbaccccaadcaccaddddbecdaddaaeccecdacdaedbcbacaaeecbdecdaecedcecddcaedbbcaeadceaddabaabedceebddacbbceeeecdabedabeeddcccdabecbcebdababcdbdebbdeeceaedadeebaececedcadcdabdabaaadcdcdabdddaaacbacedbeabccaedcbdcadeeaabcbaaaacdabacdcbdbaeaacddcdbceabdbecadadcceecedecdedeeececccbceadbebabbdaccdedaabdeacddebdacdebeadeecdaacbaaedcddedeeaceeebedaaeabacabbbeaeeaacbddcadcedacadbbeabbceebddecadaddadebecbecbcbeecbacdeebbeceababebcabbdaabdcbeadddbbcaaebaccdccddabcdcddadecdeedcddbbabcbaddbedacccacaacacdcddbeeaabebcbecaacccbbecbbeacecebbabbbaaeaccaaebaeceaebaedbbceaccecaebbbaabdaeedabeecdbadbbbadeccbbcaaccaceccabddadaaaaadbdcaaacbecabddcdcceeeaedababaddadacbdaadbbaaabcdcaedacceedaaadebececdaacadebcccbedcacabcabecdeadadeabbbdeadabeacbdccbedcebbabbaacdeeeabbceedddcbedccdcbaacdebcddbdeabcccbcdaaaaacdababbeccddebeeccbedbabcdebaebccedbaaebcdecbbeeeaacebebbadcadebddebacabeecdccdddbecbcebedbacdbddaebeaabdbcaeeacbadebcbaaecdbbceeabecccbaeacaeedebdabdcdbddcbaccbadeddabcebbaabaabdedbbcaacdabeacbbccccbeddccbabbdecbccdaadacadeccdabebaeaeabbaabcdcbabdebcebecbdececebccdeaaacdaacceceaabaeecdcabeabcaddadecaacddaeddbdacaeebabedadeabeadbabccbccbcebcbcbbeedbbbdccbacbeebdecacddaabebecceabdbedddeaebdbdbeadbaaaddbdaaaabdabdecedcbebaebeecebeebeeebaaddaacaadcdaccddededeeeabecacbabeeabaeeaecdcbdeadbcaaaecbeabeecbaadecadaddbabdaebcbaaaddcedadbeeeaceebbeebbcccbaebcbebeaddcaecdebbcecbddddecdddadbdceeeccbbaaeacabcccbdacceaaecbaccbadeebcbcbcacccdcedcbaaaaadcdbccccdeeadcaabaabdcbbdabaadcdceaacebedbbdbabcedcceebbdacdbcadcdcaeeeeddeabcedcabbccedccbecaabedecbbacecddabaacceaeecbccedcdecbeacadcedddbcdccdcbabeadbcbecdcbccbbdcbdbdaebaacbddaabdcddaedcebbbeeedbadacecbedeaeddaabdeddaccddbabeedceabbdbbccdecacdeceaadaeecaaddcbcaecbadedcacddeeadcdadbdcbeeaecedabaadcceeeddbbceabcbeddaaabeaccbbbcbedeeadaebccccccebcedddedeadacbcccaaedcdbcccdeccececebeebcbcccdaacedebdccabbeddbaeadbcabdbbbcddbedaadabcbebcddacaccbedcedbcddeabbcadeecbceadccdbbacbcdcdddbadcbabdeabadbbaddecddbceddbdbddbeeaecdbeddeddbddcbeadceebbdddcedaacebdeecbbdbebddcdbabdacbbcbabaaacedeebbaecbcceeececccbbdeaaebcceeccbdedcccbaacccacccdedbbbcaccbaecbaaacaecbeaaabdaadcdbadcdebedbaeccaadecacbaadcbcccebbeedbaaabcaeeacbccceccadceccccadbaddadbddbaecdacdabeeadbdbacbdbedacbbbeaaadcccdcebeddbcdbdbcbdaecdbebcaccbabddeacadedebaccebbcdabcecddcaaeecadbecdcaaddddbedecebbdedaaeccaabcdaddecbebedbcacaebedbabdbaaddbebdbacbbbbeaebebdacddeecdbcddcecceecdcabcceeeedeccaaecedeabcdaebacededcdcbebaeabcaacdadbaadcedbdbdecccdddabceccaaadebdeecaccbeeeebdbaebaaeeddeacaddaacbceaecdcadcdecdbacdcdeecddbbbaaeeaccdddbcadeddbaaaadcccdadaddeabaacbdcbcbaecbddeeddcededdcaabbbbaecccabdadaeabcdeecbecadccdebecededeebcdbbcdebddbaacbbbbdcabebccabdbbbebeacedcdacdecbbaedcddaaeddcdacceaacbaaceeaaadeeaaeedcbdedecddcdaecaebcbbabddcbbbdceaccabdbccbeaebeccedeaabcaceedadccadadeadeaadaeabbedebeadecadeebdecdbabadacdbaceadbcacaceacadebadedbbdddbcaddcbcdedacdcdabaceeeecbdcedeadbcecbaadbdcaceaddecbeeacdedbebeababedabdcaeabecdaceecccabbddeaccabaedeebdceeccbcbedccebebacbbcadcbdaaeaecccebabeccbbcceadeebebbaabadaebdaaddaddbdebccabebdbedcdccabaebababbcacebacdcbdeaabaedbedebabcaeabdabdacabdbeeeedebaebceaddddcbbeccbbeaebcbdcababcdeccadadcbaabbccbddcabbbcaebedaccbedbeadaedeeeebaaacbccdeccdcbeacddecedccedebadbddacbeeacccddeebcecbaedaabdedadabaecbebdaabaebdceaeddccdababdaadaddbaeaceddebbaaabbcbebbdebddcedadcaceebcadbdedbddbabbaddeeaaaedcbecaecddeeabaabdaaeadecaedbcdcaedcaacdcacddcababacabaadaebbadecbeebdbdeaddaeeeddadaabcdbacccdbdccedbdaeddeeecbbccdbcdbcbaebacbcdecdbebbcacedeededcdbebadedabdbdcbdccaaecbabbaceaeadeabdbeedcbeacbcebbcbababbbecacebddaacebccadbddabeddacbeccdeaceadccccddecdaabbdbaacdadecdddeddbeeebdececdecadcabebdacadbdbbdadbaeececdbbbbcaeccdaebbdebbbedbccadaecdcadedaacbcdcddacabacccabaadccdcccbdcecbdacdbcbacbbedcbdadcdeeebcdbedbcccccbeaeecdbcdccdcabacbadbcddbcdcddbadecaadbaebeaeedddadcadedeebcbbebedbdecbacbccddcdbdaaebccabcbccaddbbabbcdcaadcddcebbbcecddadcbbcbcdbdeaadadddbbaccbdacebeedcbbbcecccebeecbbddebbebacbabebacbdabdedacaeecebdeacbbedcedbbbacbdabacaeabecaceccaceadcdddabadcceaacadcacdbdaabaabaedbdeacdececddabbccebdbcaeacbdbacdcddaccbdabadedbacecceaebcccaabebdaeeedbbeeaedcbddecdcebcdbcbccadbcbccbbbceecadaabddbcdcdeebceeadeebdbbbebbceecddbbdabbcdbadddbceeedccbeecbeeecbdbebbadddbdaabddebbededceeacaaebabcbeadaaecadeaeaedbedbcabeecaddebcceadddeedbedcbabeddaacbddbeacceceeaaeacedbabbccdebdbecbdeaeedadeccbbdbacddabbcccabeadebdeddcbcbaaceceabeccaecddceeadeeaadddacceeeadaccdaaecacddacbbadbaeebceccdcaaedeebbdaeabdbacbceccededebebaabcdbbcedaebacbccacccdcadbbceacdbcccddbecaabdedcadaacbeaddbebdacaaacadbddddabdcecbabddbdbecbecccaadabaebdbbdddaaebcddceaabaedbcbbcaaaaadabadabcddcacedabcdedcbdebbddbadbebbbaeeeebdbdecdbcacedbabdebaeccbdcdaebceebbbbccecabdaaaeddedddcdaedadebebadeeaebaceacccccccacceabbdaddcdddebaebadecebbdecccebdaebbceddebbaebbeadadaeccaadadedeaeaddbeddbcebeabcbeacbbecbcddecddeacecaecaddeaeeebabcddbebecebcacbdeeecddaacebdeeadebebbebacddcdcbeccbecdcbbbadacedaddbaccaceeabdccadaceecbeaadabccdddbedaccebbbbdbddbddcaebcedcddbcbdaeecbaeabeaaddbcabbbacdeccedbcadaeabeecdcbeaddbdbebaaebcababeddecccedaaeceeedbcebceecedaabbebaeeadbeccbedcadaccdabcccabaccceadbdeadcccaeadadbecdbaabadccacbbdcacaeceacbcecabdddaaadbaeacacbedaabaecdcbbdbdcdceaebdcbacbcdeaaeeddeebaaaecbccabeedcadbebbcccaadeeeeaebedaceaedeccacbdaceeadcedbdbaeaeebcaaddebeccaaaebbdcacdebebebcbedaaecbebddaeddaabacaedcadabceeddedebdecebaaaaaacaaededaabbbbcdddedbaececabadeebbbaadecceacececbaacbbeebbdbceeebcdadacacabeaccdcddeddcbeedecaceceaebbcaddbaecdeeaddcedcddbcbdccedbabbeaaddabcdbcaeaacdaccddbadbcecebdbedabdaeaaeeeadeaaadceecdcadeebddacbddedebbdbdbceeadbbbcddecddeabbbcdbbacdddeaecccecddbbbbccaccabbcadbeacceaaeaedcaacceeedcdbcbbbaeedcaadeaecebdddcabceceaadcbcdddbeedccbcccbdebaceebdeeeebebcaedebbcacddaaeeacabadedabdcbbbdebecceeaccabdedaaccaecabcbbcbbbeacccbcaddabddbcddbdbbbcaedcccbadaebecabceccbbeaddcaeaababacbbdbaebdbdbaccdeecaacbccaecbacabdbbadacdaecbacbbbabddebaaaecbabcbdebcbccdabcdecabcabbcecceadabdeadbbddecccccbabbadebdbbcabbedcceeeeadeacdedcabcddceeaedadbcacaabdcdaccbbecbeebaaabbdcedbedeedcbedcbecaeabacbabbeabbabbccecdcbabbbbcecbcadbedccaedcacdabdbcebcddcecbdebcadebbabccaeaaadbabbcdeceecbeeceabbecaceeabededbcbcbdbedcbacaeacededbaabaadcebdeeaacdccdbcdbeeedcdcebddecededccbbadeabadaadabdeedaecbaabbbbaaedbbecdacedabdaeddebddacbccebdbddaededdbaeeeeaedcddaeadbcbbecdbccdbedadcaddddbcbbbaedcebbeadcbeeadeabbebaebdadedacbbeaeabdceeaacedeaaebeaabdeddedcadeaaaebbacbdcccacccddcdabdddbdaaecaababbceecbcacddeaaaeebecaeececdadadbeecabeecbbeaabebcadacbcedbcbbbbbcecaddbcdcabbabeaeeadbceaaeacabbabaecdaedabaceabecddccdabdadaeeebaddccceadcbccbadceabedcebcecddcdddbaebadedcbebcbdbaeedabcaebaadecdbcbbcdcabbebdbeedabadbbdaadcbedabcbbedbedaccddbccebbeddadbdddbcceecaacbeebbaececbaebcbeedcdeeddddadddbcdbeddbccddbcaaedccdaecaacbbdeaacaadbbddececdcdbececbaaeeaebaacabeeadacdbeccbababebddababadbecbaceecdcdeaccccdddaaadccecbddacdedbddacccecbcdeabbacbbdbcabbbddcbbbdeeaeceabbeaaebceaeccaeacbebdcebadbdccbabcebdaeabaaecddcccdebbebdceaebaaddbacaedbbcdeedbbeabbabcbadedccaabbaaacdaceeeaeadbabebccdabbbadaacacebeaaecdbcebadaaebccabbeceaeacbdbdcdabcddeaeadbcaaceebceaeceacadebcebdceecbebcdccccabadbecbedbeddabcbcbceedaeadabacbbacbdeabceabcdadbabcadeeaadadbabaabddababceadaeacbdcecddedaebbaacbbbdeccebeccdedbbccbdbcbbaeeebaaceaecddedcaabcabcedbeebabceebabedbbbcaceecbdbddaaadedbbbdeeebadeeceabaabcdabbabdabbbdecbcacacabdddebacddeddedcdcecaddccbbbdbddcdeccbddcdadcbcdacaaddeddaeedcaadaabcdcbabbeadbeddeaacebdedbacdedebcdaacdcdadabcdcaebebcdcabceaaddbcacdabddaabeceadceedbbdbbdadedbeedeecbddcabadcceccddaebeceeeabedcedbeccbbaecdceecbcbdabdedbaadbeaccebedababdbabcdcbcacabcdbbdababcddaeeabcdcdbbaadcdadbacdebbaeaeecbbdddbadabbcdbeebcddebbeccadebacadbeebeddbeabbcdebeadbebeceeaeedccaececbedaadabdaacdecddaceccbeeabcdeeaabdababeaabaebbdacbdcaccdceaeadaadebeabcbbebeeccccecaacaccebedeadbcdebbadbaebeacebcdddddeecbeebcacbdcaeedbceeaabacbeababebbdebeeabedbaacbdccecbbdacebbcebbdcdbcabdbdeabdccaedcbedbcdeebcbabaeadccedccadeaadbdbabdbebbddbecdaeddeedbeabbecbdbebbdaedcaccbddbabdacdbbeeeacbedaedebaebddacaaeeedadbdcaddceccecaddceabebdbeebdcbabccdbaccdceaeedcaadacbabebeddcceabdcadbbcbaedcbcbceaadeeeadacacbaccbcbccbeebeacaaceebdedcbbacceabbaebdccaaacbbabedebcedaabecdccaaebbebccaeadeebdbbbdedeabecdedadabbcdeacbaacbdcaeddbeaecdeeaedeabbddecdcceccabeaeadecddaaebebbaeeeeebecbeabebdaebddccecdbaebbabaebbedddcebdceecccababcbaebbbceaaeceeccdccecedaaddaaaebccdecbbeaecdbeaeeabdbccbcdadccacacddeadedeedaeeebbccdecbcbaaabadeacdbacceeededddeadbceaedeeecdacbcdeedabcacdcaccecbdbdabebbcacedadcdcdbcbbcbabcbbbeacebccbabddaaedccbbecbbaeecabedccadcbcacadaacdaaebddaadbdcbccceabbccaecedcbdddbeaacdbebabdacdbebebedeedaaedaabbdaaabcdaaaaeeadecebecaaadaccabdddaccbeaaeeecdeadeaadebbbadadcababaceabdadbaebcaeeccecdbdbbaadeeedcdddbabdbebceaabdaaedbeaeecdecbcabadaddbbdceacbbbbcebebadaeacbcedeccbeceebddbbaeceebcccbaedadaebaebbbecddabccdcbbedcebacaaeaacddaceeadaccaececbddaedaabceadcbccbeedbbbdedebccaaacabdeabeeaeebebaaedababedacbeecaeeaaebeababdaabaccccabecddbcbdecdcbccccabcecbbeaeebceccabbcecebdeeaadbdcdacbcbbedaeaddbcccaadbdbdbbaeacaedeababceedadaccccddbacbcddcabaedcbcdcbeaacbcbceacdbeeceabedabddceaeadbcdaeceebdeccbbeacdeeedbdbebdeeededebabdebdbadabdecaeebceacbbbedebddbabcbdbabeadbbcaeeceaaacbdbacaabbbcabcbeebdcdcdbecebcebaccebabcbddeacacecdaacdbdcbcedbbaecddbbadddaebcebabbebcaedcbaabceadaceaedadbecebbbbaeabbcecaaddbcdddcbabbecebbcecaededbcdcbbebedadbdaeebbbcdeadeebbdbcdacdcebbaeabcbedcbbdaeeaebaedceccdaeaaddeedbaaacdddabdeaceeacbcbaacdbebdbbeeebeeccdaaceccacbdeeddcdeadaecacbeecdacbcedbcbdeabeedcaebdcebebdbaeebabdcaabcbeabedeecbeccecedeabcbececcecebceadcadbecdaebeeccabeeababbeccaccdcebecacdcdddcabdbcabbcdadebdbdddeccaacbcecabcbebdaecaccbadbeeebbedadbdabecccbbccdddbedccebccdeeababbdacbcaabeccebaabbdeebeeabeeaaceebedabcacaadadeeeeedcdadabbeadcddecddecabadbcaebbecaeeaeeecaceaedddedcdcaceedeacbbdbaccaaddacabeaebdeedeedbaecdaeecdacebbebacbaecddadbddcbbbcabdadcbbddabaacccaedadbbecddbcceaccdeecdbdcdedaadbcdccecdbbdbbecccaececccebdbeceebabbdceadaecabaeeeabcbddeeaaabaccadcbaedadedebabddbbdceaabecdeadccaeebcaecccabeabadbbbcaedaeecdaabbbeccdbceceedcdcacdbdaadaecccadacdcacdebeabbdcbdbcbdacbdaaeadabadecdadaababaccccdeaadaaacedaaedbeccccbacccadbeebdbceadbeccebcaaebdabcdaaadaddadeaacbdcebdbbadaccecdcdadacdbdbeccadeadbacebacbbdcacdcdbbacabaccceaadbbaedabddcdaadbbebabeedddbedcbdeeabbaeeacdecadaebcadaabeaebecceabcdccbaaccdabaedddcebecbacaebeedddcecbbdabaadceebbdabcebeceaacebcbbdacbdddeaadbdaacbcebedaabdbcaaaddddcccabeeedaacbbeacceeedccebecbeecbaabcdeabdcacbaaadceebcbeecabdceddcabedcdbaeacbeddabbdddcdddadcaeabdebcbaceddeeebbeddecadbccbaedbccebaceebedebdedabbaddaebadadcdbceaedbeccddaebadaaccabbdeacaebcbdacdbeddcdbeadeabcdebdbcbadaccababcaabaeeeeaddebdbdadbadabbdbcaadaedccadcedcbeceaccbeeeeeacdaaddedddaeebcebabceabbaacacacdcaaeaabaedebaebcbdcddabeecbdcdcadbeaeeaadddcdacdcbebceaedccddbbaaabcdadccedbbdcbbccaacdcbbaeebcedeedbedaaebcdbbccdeeccdbecdccbccbcdbeeebdabbeeceeceacdebcedaabebaccabadececbbdcebaadbccaddceeeddbddcbadeacccbebcdabebabcbcecdbdbddaaedbdacbbecbccbebbcecaadccbccacedeedbcebcbcaeaaeecdcddbbcbddeeacbcdcbeebcecbcbebccbdeedabaaeceadecdcbaeebcbddbaeccddacbaadadbaeabdeccdbeeedabbbadbceebebadacaaedaebaceaedddedcabaaebdacbddecdedddceccaaaacbacbcbdaaeadaecedcedcabcbadaeaebaeaaedaadddbdceaecddccecdaeaabbcbccddedbedaadbadabddbcbccccdabaadabbdcbbebbdebeabecbddbddddcaaabccdbccabbecccebceaaaeacdaacecdedcaccbebcddacddacbebddeabccabaaddabbbddcbacccbcaeabdbdcdcaaadebeccbeccebbbddebdbadcdbadbbbbcdbbbcedaecceccdadbecdcedbedabededbeedadedcebacdeebeeaaddaadabaadeeacdcbecceeecbdbebcddcdaadeaaccbedebdabcdeeebacedccaddebcbdbdddcbcddcabacdcdaaceeeeeaeeddcbdbeeeddebecdeddbdaecaececcedaecbadcbeacedcbecdcaeebcceaaddecbcebadacaceebacdcacbbddaabaceabbecdadabedabaacedcdceeeeecedeaebedaaddecdbcedbacdabcdbaeccdeccdeabdbebadadabddbcdcbaeededbbabcccbbccabbceeeececddbbdbcaddccaacdcecbdbdbdedaeeabbbbbcdaadadacaaeaaeddeaadeecadadaaaadbedabcbaaedaacedbcbbceaaaaedccaaaaadbeecadbcebadcbbbadbbbbedbbaabeabddeebbedeeeaeecccebdbaddeabdcdbbdcebaebceebcadcbedbabaceaadbadddaebccadcbbbeeeadeedcebdbcccadceebbbbbdbdeacdbedaaeeecabaecadadbdedabeaacdbeabdbdabacbebabaedaacecaccddaecbcbdceabdaacadabbaaceabadabdabbebeaebaedacbbebbbcebcacbeeddbeacaeabbdbabdeabedbdbcecccbbaeaacacacbdccadebaebdcbdedbdbcbeabcedcdbaadddcacddcbbbdebbaebdaaecbabdadcecaecbebdedcaedbedadbcdedbaddecededaddaecaaedadcaedadcbbdeccadabeabcdbeadaeccaabbebcacbaebacbddacbbbacbacaacaaabaedcdccaaccddeaeccbdacaadbbecadeaebbbcdbecdaaebcccaddcdeccabdeacdaebcaacecadeaceabdcebadccaeabbcddceceaecbaaeeabbeebacbbebbdbacaadaebcbbddeaadbbebbdbcddeedaadebbaeeacaacecdcceaabaacabccedbbcaadddccecbeaaaabbcdcbcdcbdecacaecabbcadcaacceecbaeebbacebeaceaaeacdcedeeaebececcacacdbdaaabcadacbacbeecddeebcdddabeabbdbeebdddacbeabbadceddbbdacedbcacdbabaceaddbeeceddceaecadddeaedeabceddeaabdbedebeeabbdecbcaacdedbbbbcdaedbcecaddbaecdeaddacbcddacbdaaececcccadaddcddbcbccaaabaeababcbbbacdaeedecacbbedddacbedabbdbddbdbcdacaadbcaededdeaaeabbedacaddcbaeddeebabbbaddacdecaaedccaebacbbecbebeebdbacaddebcbcccebbebbdbaeedabacaedbcdcaeddbeddcecaccaecbbaabeddeaacecbdaceeaeacaabbabecabebeecadaecedcccabdeebbdccabceceabbccbbcbceabbabbedceacededcaacbbcbaaeddeedcdedeeaaaaebaedaabbacbcedeaceaabedecdabecceedacddecbbebcaccaeaaceeaebabddadeedacdaaacbdbdaeaaadeccacabbbeabcdaebaacecbdecbcbcecbbbcdbebdbeedaeecaabdbcbeaaadcedbacbbdcabcbbbbbcddaeadeaccdabddaaadddaadebbadbccecacaaddcabdaebeaaabaaabcbecddddcdcededcbbcabdeebdcacebbcbeabcaaababaebcaddbadacaabcaedaeebecebddceebddecbcddbceccededcbeadadbbabddcacadeccaebbedbdabbbecebbebaedcbdaeddaceeceaaabacdcdeeebbdeedadcbaeedcbddbbebaabeddedcecdddcedeccccecbeeebdcaeeeacbdccbaecaaddddeedebeeeccaddcbacccdedaedabbdeecdbecebccccbeeaaebdebeaacdcebeabcdadcbaeeaadecdceeacebceebddeabebabceebdaebddebcaaedadebadedeecdaeacdcdeabaedbacdcdcecebbeabcaedbacbdcebaedaadbabbbbcededdbeaaadceabdedaceacceaddedcadabecdbdaeabaabcbaacdbdcbeabbbbcdbcbedcdcbabdbebdcebdebddbbdadebeebbdaeacccebbddecdeaeccbebadecbdaacbbacbbeeceebaeecdceaddadbdecdcbbbbacebdbdebbeebedcbcdbcabbcabdedeebdcdeaebeddaecaeabccccbcdeddccaaaddbddaabdeadbdeaadbdddbacedebbaccbabddbaadcbeaaeabdebeedaadbccdceebaebebcaacbededbaeceadaceedbecccadedcbebdcddddabdedddacbebdeabcecacacbebabddbbcccdddeabadedaebeedaddceccbdcaabdacbaadbacabbcdaceaeadbebbbecbaaaacccbdccddaccddcbebecbaddcddcbcdccbdcaddbeaabdeaabbadcbeabbacadcdcebebdeceabecedcbaadddaeadaccedeedabeadebbdaaeacddeeacedeeaccacaaaeaeebdbbbadbebbadbbdbeaedaeadebaccbdbeaddaedaceccababbcadacebcebacbdcacbddbdaeeccabaebdcdbcabdbbbcdebbccbcaeaecdedaddaedececdbdedaabbeacbadcadcacebaadbebbcceddaedbabeeaaabacbddebcecccbcebdecceacdbdacaecaadbabeebeacddabeabdeaacddbcccdadcbedbbcdebdebceeaeaacddaeebaabaaaebcaccccddbdeedebdddcedaeeadecbccddadebbaababadbcbbeaaddeccbbaeeabeddbacacdbddcbbacaeccaaeaadbbdceeddaaedaedcccbaceecbbbcbddadcdccccdbbcdbadbceaaeccbbeadebddcbbbaddcbebadbadabadbdedaacbcdabaabaeecdccbeccbbcdbadddbdcaebcabcaebbabeccdccacdaaabdcdcaedcecddbdaaaeadbabbeaecebaedbdcedaeaeaedaadbbabcbaedbdaaeebcccbceecdcbddecadcdbaebdecabebbdaaadbaeaeecadbcbbdaeaceecdbebaebdeeeeccabaaeadaccbddaedddcddbcabacabecbabaedbcaeddbccbeaebbebedcaeadeedccdadaeadcededcddaecdecbceedceeedadbacedeabcececeadcdecbabadacdbbbebdaedcebdbcdccdaaceebddbcecdadbdaebdabacdddcddebdeaebcedadeddabedeebbebeaeedadcadccddaecbecdedccedacbdacbbbecdaeccbadbdcabbcbccdbcaeddccdcdecdcebeaabbaaeccbbabdeabddbcccaceadacddeccedccdddbdeadaeeaccaeacdcacbeabcecbebbddcdcdccacdabebcbeacecabbeeabbbcbeaebcecdaebebbdbbdaabacaeceacdcbacbcebddcbccddcbcdebacabacadcddecbcbabbebacbdeaaeeecdcebbbadddebdbbecdecaecdcdceedbbbecabbdedcdccaaaeabcddaceedacedcbedddbcbecdaacaeecbbecdbbdcccccdbdaaceadcdcbadcdabedaecedacbbdacedbadcceebcabebadecbbcbdeeddecccbeebbccedacbacdcbbaadcbdbbbadbecededbabdddeddedcaacabbebbbbdbdaedcceabcdbbdebdebbbacccadeceaecdebdaeedbdbdddedbcbabbcadaaeebabecabddddaedabeaeadbecadecdbbdaecacceceebceccbcbeecdcdabbdacaedcecabdeededbbdcecbdceacddedcdaadbdedadeaaebaecebbaebeceacbaadbcbcacdcacadcdaaaeacdcdabdedeedaeceddcadecedaddcdcbbbbadbacdbbaccbedbaebbadbdadaeeacbadbbdacdeadcbebddaeccdbdddedacadeeadcedaabedbccbddaededccdeabcccdccdceedcebbebabbdbcecbdebaeaddccadcedbaeeabcdccedaaeaebcacdbedacacaaceeadaadeccbadaccbadeedccdabcedaccdaaababdababbaaaeaabbceaebcebbeededaabeedccaeabaabcebdcbbebaeddbccabcbcbacdebaeaeaddaadebebbbddbaddcadaaacbcaebbabbaaaabbbceaacaccdeecaecdeedebaabcacaeebeaecbeecbeaaabcbdcbaecebabdabacebbeadcabbadadceebcecdaabdcdadccaeddaeadadbaeabaeccabebaaaaabeacecdaebeaceabcebbecbbcecdeaceecebbbdaebdcadaabbcbddeadcadaadbeeaebccddccbdcdbbdceabacbdddbdbeecdcbeebedbaabaaacdebbbbbeeccceaeecbcdddbcaadebbbacadcbedaeacdcbcdbeeddabecdaaceeeedacaaddccdbceeaabacebceedadacbcacaeebcdddceaaebbadcbcbaceadbabdbbdaeaeaccbacccabecbccadeddedbddebcdcdbcbbbecdcabccceeeaddabcbaecbebeceedeccabaebaeedbcbdababdadadcccaebbeaaebdaeddadaabcabaecebecdaaecabebdaeeddebcbbcddedcbbccceacebbdabebdeadaddaecbbeebeccbcbeaeeaebcedccbabcbabbdcececccdbcaacbbeaeadccdcabcbbccbbecabbeaaeaaddceeacceccbbeeaeedeedcdbaeadaedaccaecdacdcbebbdbecedeacebdcddbbeeaaaebbdbebbeabcbabdedadbccaadcebbbdebbcadaedcaebbeaaebacbedbdeccabadbaebedcdddeabcdbeaaaacbeebbabeeabbeddebbcbbdeeeadbcbdcceeeaedbdcdadebabeaaddbbeecadcacbcaceeadcdeabdebebdcbbadcccdebabcdeaccbddebdadebbeabdeaadecbdbadebbaeadeedbdbcabbdedccaabecdbccabdabdcdadedaddebcacbbdcaabdbaeeeacdcadbceaedddcceeecacceebeddcdcbbacbbeadaeeeadbdaaecddccbcdaccaccbadbdeebacdbaabceacaeeddbcbacdbeaaeedadcceedcbecdbacabbbcdcdcedddadacbdaccbbabceaadaaeececeadaeebbebcbaeddbabaecebbeceaaccbacdceaeabdaecbabecccacacdcaadedadaddecaaedbabadedaecddacabccabbbcdcdbeaaaabdbdcdbcabbcabbebcdbbceccedbbdeeeedabaadbbbcbddbeceedbabacebdddedbedebbedabdcdabbeebdaeaddcececebebcceeaadedaaaebdcdaaaeedceedbaaceaeadbbdceeeeabdddcbaeaabebdceecdaaadeaaadbaeebdcaabcdeaedccedbacdaebdebbaeddbaaccccdedcddbcdddbaddeadbaacaebeddcdbbdbaedcccbbebeeedadebccbbdcacaaccabbbeadeecbcbddbbbcbabdadccaabecaeecbdeedddbbcceaecddeddceebeaccdceecdddddadeeaebccccedbeaeaaaacaaeaeabbedbddeddebbaacddccdcdedebedacbbdcacccadcbceccdaedabdcbcbdeccabcabadcabbbcadebbcdadccdabadcbabdabdccbbcdaccedcabbbdceabecbbbbcebdcacecdebbbdbccaadbceeaeecdecddddbaacaaacedeedbdaaaebbddbcebbdcadcecebcbdddcbbbececdcdcabbaedcdeccbacedbbddeaddbadbedcdddadbbacaccaaaadedaedabbdeacccebdcecbbbdbdddceabbeaabbdcdcdeddcbeeabacaacbbbceaebbdaceaacbceedceedebbabbceebbbceaadbacabcbcbdbbeedbacedceabceebbaedbbddccbdeacbdedbadaecdddeeddbbdaaaedcabdaecebbabbebcadcaacaeeecdbeecdbbdedeecbcbbcbdbaeacdddedabebedaadccdceebbcddccdbbececeaebdeebbcaecccbadedbdbccecdaacebeebdddeadbbcbadbcaeccbcabccbadaceaeceedaeaeebdeadadeebabcdecbcdcabacbeebbbabbeacdcddacbdbebecdbbcabbeaaaeacecbeabebcadbbacedeaacabbdaacccabbeebabaabadbeddeaceccbebeabeddddaedecdaabdedcccdebeaeabdccbceeddcdcedeabacaaaadbceeccbeeeccebabcbceddbbcebeceddbbabaadacadedbdadbaecdeceaeeecdbcceaabecbcaecedbacadcadbdeebbbeaddedbdeeaddbbeeedadeeddabcbacddaeddaabadacedadacaacccaeddbdbbddaadbedbdeebbbdbbeabcdbcbdaddeaebcbaedbabecabedcbdabdadecccaecbccaeedeeeceadccdebeadaccccdaabbccbbbabecddbbadcaaeacdcacceacbaceddddebdedecacaeebdacacbaededbddbacddbcbdddcbbcaadaebcbbceaccebccebcbecdcbebdddcdadebeeebcecdeddeeecadaebdbeecebcdcbdecbaccecebddeebabdaeaabaebeadcaaaecccebaacdecbceebceccdebccbebbeeaceddddbbdacebcddecddedddeddaaacebacaacadcdebbdaadcaaeabaabcaaeecbaeebabdcebbbceedaeabbdaeecdbbdceabcedcdabacddbdbaaaaeddebebadaeacdabeccbabaacabedceeeeaaaeeacdbdbaaaebbacdedcbedacbbadeabceaeadcedaaddbbaeaccdceaaddeaececdcebdaabbeedaaeadcabaabaebbdbceabddcedbdcbcebabeeaaabbcdaaccacbbbbcaadecaeeeaccadcbbeeddaaebedadbbdaccdcecedaeedcbaadccbdadbeccdeaeacaabbadadebcbceaabcecbcbaadddcaccccccaebbadbdbbdaaedacbeabccbadddacaaccddabbaebadddebdaeebeeecaeeadbcbbeceebeadbcedabcaadedaecdbeccdcbdcdbebbcaaadddcaabdcaeecdadedadebbdddbaddeebdbbdccaedbcdbeeadaecbcaaddaeaddddaeadaabedbadadaedaebbacebcbdadbeeedaaddbdcbdbeaadbabbaccbcaebaeccbcacabbcdabeeddabdbdaedccdcbbbaeeccdcabecadabdccddbadeaebedcdadaaeaebbbecededeacaabdeacdebdaaaccdedabbabeceeddadcbbacaacdaaaaaddecabbdbdebacbecedeedeccdcbcbceaacccbcbbeedbacaedebedbcaeeacecbaccdcdcedeeaedadbaaedddacbeddbccbddbabbbbbdeeecdacabcbbeaeacebeeaeaceddbdbbeabbbeaaceccaddedeeebccdaecaabbacceabcadababacadadddcaacbbccceebbaccdbdebdeceabbaccaababbbadccadbbcaecebbaaccdcddadaedcecbcbaecdccdabbbccceacdaebedccdedccdcedbdbdacbbcdddcbbedcbddaeadeaaacabedadedaaddbeaebbadbacaeeebcadaaaeccacddacedddbcacabadcadabcccdcbcceedaeccadcaaceecbeeccbebacdaeeadbbaedebdadebedccedcaecbaceaeabbceaeaaaaeaeeecebabbbcabcdaaadbcabebecdcbcccbddacbacedebbaccbccebbeeebcabdaebcbbebccabacabcecaeceddbcdcabaabababdebecadbcbdaeeeecabdcaebcbcbaacabccadaacbbedcbaebcaccbaeccdcbaaceecddaddabebedcebedbbcadccbaceddecacaadacdabaaebbedbdbbcdcaeceaccaddbeaacbbcbcdeadbedceaaceddacbeeeebedabbdcbacaeeeacdebaeeacdbbeebbaceddceaececabdbcdccecdbacccbdaddcebebbcebeaeadedcddcbdbeebdabbeaedbdebeaaccebdddbdaecdcddaecedbaeaccccecbacaadbdbeaaaaeadbaabdecbbacabddeadeeadadaacdcaeedaeecadaceabdcebcbaeceacaeaabaabbbcddbddbbceddedbcccbbdcbbaeaeebcaddcbdbabeedbdcdcbddaecabacbdbcdaababeacbbbecaabecbdaddabcdbbcedabecebebabaccadadaeecbebaabadeeebebedeabdadabbbabdceaeaddebebccccbcdcabbabceacdeeecccbabdacacbbcaeadaacebaadabdcbeddbacedaabedbacedbcaedabeaaadeddecdcebdebedadbccedebbdbccddcedecbbbccabaaabdeaccbbadeceeaabccbecaddbbadadbbcacaedebddaeccbcbbdccccddcdbdbebbdaebcbcdeaaceaaebebcacddcddccbbbbcbddecbccccbdadbebdbacacabbecbbdcacdadbbdededbeaadbcbeddcbdeadbeeabacbaaadadcacccddddeaabdcabbdabedbbbcdadabcbbbcaebdeebeedcdcccbebbeeebaebbaadddcbbbaecceabcdaecddbeedcaebecbbbadebdeaeedccaeaddabaabeaededdbdaebcceebecaabbedabaeebbbdedcadceebbeaceaacbaecabcddbdabebdacaaabbcdbcaeaecadcebccdcdeeaedcbaccdebbabdbcaddabddcdddadcbaebbbdbdceebaaeaacaadedcadadeccabedcbbbbbbdeecbaaeecacdecececbdbbabcbacbbbadcdbdacdaaeadccabdedeebecaabecbdcccdbaeedddabbaeacbaeeccbabaebeadeccbcddadddececdaeccdcaacaebcebbccdbaddebeeccacdebdcddbedecbeabbbdbcaeaeddaebdaabcabacaadddcbbdbbdacaabcccbbdbedecbcebabccadeeddaabcabaeaaceecaaabccaaccbcecdccbddcddbbcbddebaecbeceddeeebbaecdbbeeacabbadaadbaceeddbaeedbcebeacdcacabebecbceeacdebdbaadbaaadeabedceadcaacdbdcdeaddaadccadedadcaceeaababcdaadccbabdcbbecbaddceebabdbccbacbdaedacbacdccbedccdddbceaacddaebebeecbcbcabaeaecdbabdddeccaeabbccddacdcbedbbbdbaccdeedbdaaabdddddcdcddcadacbdcdcdcdcadddbdddeacdacdacebcdeebcdeeeebeeaeddabdcaecaebbadcbadcdecaebdcabcaebadacbdeddbabbdedeeeedbddecdcbcbbeccbcdebbebacccccaaadbcaeddcccededcaadabcdbebdbeebaaceeccdaebcedaaeedaebbbeedebbabeebebeccebecaabaedabdacdeeaddcbbdacebadcacadbbccbeccabcdaccdddeddadeaaadcbdeeccdaaabdbedbccebeececbaaeaebccbbdbaaceebddbdbbeeadbbaabdcdddbdebbcbacecdcadbaaeaeacceeecacadececdedddbceacecdcecacccdedbabeccdcdedeedbcebceeadbcaacdbeeabbcddcacaebbcccccececaaebaccedbbaadccedccabaaeccbecccdabaeceaeeccedccdbaaeaddebbaaddddebdcbbbddcadaedbbbedeaebcbacacabcddbbdedcdecbedecdaebebecbeeacaaebeadacebcbaaacaddabebadebcbaccdabbebbdaceddabeddbccaeeeaadaeeddecacedeaacadddcbcceccdbbacdbadccbadcbcbabceacdceeeadecabbdcceaaeeeaebedadaeacceaadcaacdccdecaaccaecbcdbdaddcdecdacaeabacccccdceebdaaeeaecaceccbdabeedbbbcbbaeaeabbbeebeeaeaadcadcaaaeeddebdaebcaebcddecceaacecddaebacdbddcededeaebdabdccadbcdaeecdacaecedacaddeabbbedaacaceaedbaeebcedccdedececcebaacbcaeabedacbdebaeaccaaceeaeacaaabddaddeaedbebdacdccebabceababeedaddcbebecabdeabeececeacebacdceebedacbdebeaeeaddbeaddbacbaadaaaecddebcacecceaaddcccdadeaedeebebbeaaadecceaabaaaadaebecccdaeddbedcbaaedcccecbeccccaaceedacebcdaeaddeceacddeceddbaeaeddbddbeeceeacdbeeddedadcdddbaecaebdbdcadeacadaacdbddbadbdcdaddedeedecebedccacbedabebbbadeceebdbddaabbdeeaabbaeebcbacacbdcccbddaedbedbbbbbedbdcdbdddacddbebeeaccbaabbdaebcabaeccaddedebedccebdaabdbccdaeceecccabdabaabedbeaddceabdaceacacdebeddddcadeadadaedaaacebcabebabeedcaacabeedeaacdabeeabcacecccbbadbcbadbbaaacdebdbbccbaadcababaacabdcaecaabcdcecdabceaabeaeaddcdbcacbaccedaeeecbebdeebacbaeececdccdcaecadaadbedacddceedbacecbeccdadabddeedddadceebcdadabaceddcbcaedecbecdceabaedeaddbeddbabcdbaacaacccdcebaceaabebbbbbdaacbaaecbeeedabadaecdbcacbdecbdbbaceedbcdabceabdbcaabddddbedcadacdbcacaacbcdecdacdaadeecadcacdbbedeeeeceedebedeacbabeebeabedcadbceaacdcbacdeecaedebabaeecbeaacebbdaabaceaebbdecdccccaadcecaeadbeaebeebadecabadecbdcaaadecdbdcdcedebddaeeebcdaeabecceccdeeecbeddabececdbcaacacbeebbecbcadaecaadabecccbeebcabbebaddbacceabceccaecdebaaccbeecaeddadaeebbbbaacacdbccbacdaabccdbeabaaebabadabbbccddbbbaadedcabedbcbcaddbadcaceeedebcebbbcdcacabbbdbcbdcacdcdcbbbeadeabccbdaacdcceddadbabaabcbdbeedceacedeaceedcddbbcbcedeeebabcaddacaeaccbcdebdeeddaebccacbcccdddddedeaebaeedecbbecadcadebdbabeebadbabaddcecceeadccdbaadabecaeebabbebdedbcdedebabaddeadbccaeedcaacecaccabecddabdddbceadadaacebacbdbaceccecbbabddcdbedecaeadcbddcdecdaddbccaacdebceecccddcddeaceabebccccebcbcdbcdaedeeadbbaadeccecddbaddcbcabbbbeeecbbaebcdbeadeecadabebecbedaebbedeadbeaadccabedbeabdeceaeadcbecbaaadeacebcadeeebccdcccaacdeecdceadacbcccbcebdcaecebbaebdecdddceebdaececaeaacddbbdbdecccbecaedaadaceadcddedebeccbadbabbabcbdbddcabcaceedebdbcbacddeccaabedbdbddaadbcaadddbadebcededcecbeeaedaabddcaaedbbacaddeccceddcaeebcdedaeaeaabbccbbccdddcbcaacacdcbbdeeacaeccaaaedacbbceddcdbdcaceebacdeebeeecebecdcdbdaacecebeedecedaecacdacbadcdbdaadecccbeedaceeecacacdbbddcbaeaeaaeadaeaadcedbacccabeeebbeeddceebbddedbcabacbedecdebacaabdaecacbdacadcbbabdbbabbbdabdbabbabadbcdbbbbcadebeeccaebcdcecaaadabeecdabbaabdddaabccbaacbdcadecaeacaccbbbedbcabcaaeebabcdeccbbdcdcadebbeceedccacbabdcdcbbabbdbdbccebccaccecdbdacedddacaaaeeeccdcbaeebbabbbddddbcccdaecdabebebcbeaebbeeaccdbabecebdcddecbaaaeeeadaeeadceeeaeeeeaabcedeecabebdabcbcadcbbdedddbabacbaddcbbddcadcbeeaeeadacaacdaaccaabbeccaaebdddbbeadccbeabecbeddaebeadbcbbebeedbebaeabaaaadccbadbaadcdcdebedbebcbeaeaaacedceddcbeacabdadcdebcaeaedccddcdbaaccddcebaddddabccbdabadeaddadaebadeaeceeaacabdcadaceedebcbbbcbdabaaabaeaebacabbccdabeecebaecccdaabbadbaeebdbbeaeecbcdbebbaaecbdcccaedebdbaadecabeadbddaeabbcaedbecacdbccbebeaabcbddededdeaacebdaaeaeabdbbeaeacacbcbdcabcecbccccecebdbbcdaccdbedcadcbaeebadbdebebdbceeecccacddbeeccddcccdbcaeacbcabbaebcbcaacedeedaacbbebbcaababeaeacbeabdcadaedbccacacddaebaaaaceaecebcdbbceeaedccecaeaacdbaaaaabeddcaaececbbbdaacbcceaccceabcbdbdbbabceadeabbaedcebdddcdbddacebddecdeecdbaaacacccbbeadaebabbeaecdeeeedaadeaaeccacbbeaedbddedcbdeaeadaabebbbbedabaccdcdcbcdbccadddbbbdebecebecedecedcebdedadadaebacacddaecaddbeecaedcabcaadbcbcadbbcaabeedbbcbebbdaabaddcaceedcbccddccedbecaeaadbdceeaaacebdcbaaeacbbaaabcccaaebebbedaeeabbeaadcaaaeceaaaaebbaadbabbdecceebbecbadbacbbaddcadecccaaecebcbecabddadaaabaedcbdaeabcdcecccaaeaeddbaccbaacccaddcacebeeeeeababadceedeeeaadeeddadddccebeeaecceecbedbbbeebeceeaebcbacaeebbbdcdcabeadcbecdedceaabedaeadbebdccaeaaeeccaedeeabbbaecccbcaeaacececcabbbdbecdaeacaeeebcaabadbeaaedbadcddcdcdbcbcacedacdeeabecaeeeeecaddbaaeaccedaeebaccdaeabbeadbabdddedcdcddabcbabddcceebbbdbdedcdddbccdcacbbadbaaacbedebddbeaebeabaecdcdcbcdcdeececbdbeaeeddeccabbadeeadabcbdabeacddbccedaaeddccaaadedadaddedbeadcecdceeedcbebeaebbbdcdebbdeeddcbeebeddaceedabbaaacccaddcbeaaaecccbbccbabcedcdbcaedbdbccabadaceebbbddedeabcdcdbaaaabeeeebdbceddaeaeaceeacccbbedcccedabebcabdabbadcbdbeddeeaaccabbccbbdeecbdceebcaadcbdabbaccbededccebebacddadceedddacebeddcbecccacadaaaabddeacebbccabcadddcddbbadaebeddedeaceceedcabddbadaabbeedddcdeebbadaaeecedbbbcdacdaecacccebeddcbaabecebeddbaaaeadbebedcdddaceececacbcaaacdbedcdeeaabbdcaaccbeaeedbebdbccdbdccadadbedddbdcbbcebabebdcaedeedaabcecaeebeacddbbaeddadabdbdcccdcdbadeaadbedadeededbdccdbdbcabbacbccadcaecddcbaabcdcdeeddbbaaaabedaceacabeadcaaedcebdddcceaddacacecacabaaebccbccabeaccebcebebcecadbceacbccebdadcdbabdaaddacdeedcdbbdcccbbbbbbbecaabebbbeceeecaeaedaadbbdaeccbecacacdedaaececcbdeeadddcdbbeaeeecadcaaeecbaaebbdccacebeceecbcaeabbcbabacacbbaeadbbbedcdbdebbcaddcbcaebaecbaeeceeeccccaecdeeacacbbdebcdabcacecbcabadeeeddddadbaaddcabbebedabcedeacbbadeeacabeedddadeccdcacaecbedddeeaeeadabaacbdeadcadededcaddbbdbceedccbaaecbbceccccdbaecacddebaeacebecbcbbcaecadccedcaceabadbabaaaccadccdadeebeabaeccbabcccaabbbdbadeabcedddeaaedabecadabeebeaacccbabacdacdcbbaadadddccadeecddcbbbbcccdecdbbbabbebcdaccebcdacbeadbcaaabebdaeeaedbddabadaebebbceaecacccbebcddeadbcddaeacabbbcaacaeaedccaccbdebacacddeceabeeedeebaddebdddbabdebcaacacabbbadaedbecdeaecedccaebeaaeebaaaddeeceeebabedabcdceecdbaabceaedcaeceddedcbeecdbacebbaaedebaeabaedadcddbbbdddddddcdbaecccbdddbccdaecaddedabedaaabddacacaeaceedcacccaaecddeeadcdadbcaaaadecdcabebadaeadcaacdcdcdcdaceaaeeeaccbeeadeccecebccdebcabaeccbecabddddbaeaecddeddbcebaaebccebbcdceeaeacecccedbdebcaccebeadedddbdceedbdcdbccbbbebdaddbeecabebbcccbbedbcedbcabdaceadbbcdbbebdaadadeeccbdcdedbcbbadebdbcedeacededbaaabdbcaeddabaeaecadadeaecbeeebcddbdbeeccedcaacaddabeecebadbdbbcabdabbbbdebbdbcdbcaabdcaececedbecdeeaaaacadbdeecbdcdccccadcaeeecdbaaeabddedbbacaccaeeeebbabdcaeaddddeddaecdcaeedabaeccdadbbdcebdceedccdddaaccecbabadbeeeaddcadbcddaeaeadeaadecadaabecacaecbdaeecdbbedaeeeeccddeedbbadccacacbdabaabaaeeddbbbeaaebecbdceeceecbddacbdeecbcddbedbaaccdeacaadadbeecbadcaedebddebcbecceeeebccccdcddeaacaabbbbdacbebdbaeeacddbdacbaeabcdeeeaecededcddeccdcdacdaebebecabbddeedbabbceeabdcaecdebbebdbaedcdbeaccdccacbeebaccccabeeeaedaccaceadacbaaceaaacddabbbbbbaadeeedecceabcababedbebbaccecbbbbeccddbebbbbbddabdeabacaeacbbadaebbdcacbeabedcccaddebbbbbecaeddcbaeecbdccabbcbbabecedbcdcabdeaedbbcababbaeccabbadccbeceaccddceaecbddbabecaedaeaebeeaecbdcbadccddaabcbecadabcebbdaaaebaceeecbbcbeaccdcdacdcddbbbbcdbadabeedbbbecedeadedcbddadbecebcdeecbeabadbbeddabddecbaddacaceebecccaccdbdccaacbedbbcdecacaedaadeacddbcbceaccdcbadabceaaecaaddceebbbdabdaebdaecdeabacdedcdbabbccbdbdaeeaaaacdbcceadabdccddadccebcecdeaadcdabddadaedecdcbbbdddbcdbceabbddebcbaabddeabebcebdebcccbcaaecccddedceaecaccebbbbaaecedbddcaaeeaeeaebebdeccabbacbcacaacecacdacccaceddbceccbdbecbedbadcccadbbceeeccdbaabdebeeeeacacbaaceabedcbeabedbdcaddcbdeaacaaddbebaeabceadaaadaecceeabdeeeaebbacbabccdbcdbcadceeabbecabcabdbccabcbdcceebddaaeeeadcdadbbecebccdedabaeaaaccaedabcceebcdcaaaacdbedadeddbdccbbecedbececccbecabeaabdbceeedeabbedeacbbeddccabdbbdbeebbceaadeabaaeaacabaaeddedcddececbbbaecadabccbcecebceaebcdababdceabcddecedadaceeaacaebbedbcdccdabaecbecdececdbdacccbcadccabeddcecbeddbdcddeddadadccaeccadaceeeadecebdbaaedbdaedeccbdabbdadbdccadbbdedaebadadacdccaebedcebccccbebbbdddabcceebecccaccebbcadddcebbddaaddcebdddcbdabdcaacdbadaeccddedcedebeebedeebecdaaeddcadacaceaccabaaaebdbdbbcbdcacbdcadcdceabaebedeeecbdeaebeadeeeadeddebacadbdadddebeebdcacbdcbdcebbbeaebebabccddbcdccbccbedbceeebabcadcedbbddceecacdadabecdcadbaacecbaebddbdaeaadadacabcbeaeacaeeebccebbcebabebdedebdaeddadeaacccdabedbbaebcebeddabeeccddcbccacecbdddeaadaebeebddeceaacbbdebaadcbeddcdcdaecedccdbbbacaeeddadbdceeedcdabaaeeeabaaedccdadbacddababbbbddacebbdaccbadddbbadaddedccaadbcaaaaebbaabcbcedadcaebaedcbeceaacacabbabcbaceddacacedaadebdbccbbbdacecedadbeceacdccccddedcddcddeacbdadeadbcdacedadeececeabdbcdeecdbcbcddeadbbedaecbbdbbadbbdbcedbcbdeacbccaeebbedcaccadacbdedabaacaaccbabbbbbbeaacbdbadacabbedbcbebeaecedbeaccccbbceceecdeadcbcadaeecdaecbddddcbcdddcdccaadaeeadebccbabcabdaecbadbdddaebcaddcdbeeeaeaaaddbaaaeebbbecadaeaceeeebaaaaddedacadabcaacddebebcaedabdcdeeaecebcbecaeebdcaaddceedcceccccceddaebdaadabbbcbacdaacecdbadeadcceccccecaededacedbaaeacbbaebdeddcdcacbcddebabecbdceadbbcaadaacbebccbabcabeeeebbebacecdecbbdcbdacdaaecbccddadbbeadedeaadabacaebeabdeabedeeacdddbaabcbadecaaddecccdcebccedcdcdaaeeaaaceeacbabcabdebabebcaddbddeebbcabbdadaecbeeeedcacbcecdccbabccdaaddceaabaeabaebddbcadebcadcbbbddbeaeababdbddaaecbaadacbdbeebbcaaddbeecbeaaaacecadecdebdceccbdedbecaccbdadebadbcbcecbbaebccccbdabaeebacdbecdaeddeabecabedbbbeaeedbdcdedbbcaaacacdeecdeeabaeecedcabbbaccabcdeeebadadddcdedbcbbadcdbbacddbadcccebcecdddddabaabedabeeeeccaebbcdcaabdccdddabbaabdeeedbbeabdddacdedecdacaebbceaeacdcebdabbbeecdcecbeacecbaabcddaebdadccabbeecdddedcadecbaaebccdbaedbeebccbdeacecaccddeecebeadbaeececdebbbbccdacebecbdcdacaabdcdabcaccaebbbcdbacacebcdaccbcccdbbaececdccdacdebcdbdeadebacdddeedcdebbaeccddebdadbdadcbcaceddbdebaeabeddaaeeaecbedbcccdaedceebbbccedbebbadaecaeadebdbbcdabaccababbdaccecedaeacadabbacdabccdddaeecbdaeaaebcbbaeaabcedadcecbcaadddcdaddcddbebbcebebcceeceacabcadaddddcecdbadebacbbdddcaadbedcdaddacdbaddeadbdbebeabaadeecdaeacbadadebddeddadabcccedbbbdebdbaebabbcababbceccbdcbacbcacdeddbbebddbdbaebbadecddebaaeeedabdbeacceeedebcbdaeebceaceecbdccabbaeaceeccbcbcebbbedccaeaacceddeebbcbabebcebecebbdbbbddedaeebdcdccadccadeaaecaeecddbebacbdecededededceecdaebeedcaeddddddcbcdaceaabcbbbccbddabdceaaccdabcebdbecdcacaeedadabdccedaecbaadcccebcabedcedcbaaabeebddbdbeeccedededaccaacaecaeceadccdeedadeedaadedecadbacddcadccccbbcabeebaeaaebcceeabbddedadbbbaaebccddbbbabedbbbdaabcabaddbecaedaabbbeeeddcecaaedececadabbbdcbdbaaceebabdcbeeadddabacbabdbcddebdcaedcccabaedcbccdeebcbedbcbdbcabeaabecaeabcbdaeadbcaecbcdbbaccddedaeaadcdeabdeaeadedeabbcbedcbdaadddcddcbaaeeadcadecdadececbdaeedaddccadccdbcceceeadecbddedadaaaaebebcdcacedcaccadddccebcccdcacdeeebdceeacdbceceadaacedbeceeecbeeaeaddccbebdbeaeececbdebdcdbcdbcbeadeadbbeedacbedbaebccecebebcecddecaecaebddcdadbedaaebbececcaeecabdddeaabdeebaacaacbcccdbcdaeaeedddcebbdeebceebbbbeaadecebaacddacaceacdbddceadcccedcaaadccaddbbbebbddecbbdeddedeadedabaadadaebceecbdcbbddaeddcabaeadadedbaaabddbbabddcbcdbccadeaddbbbbedeeacdccebbaaeadebedabebdbebdbccdeeacadcccdaeccdbadcabaaadbeebaaddeeeebebeabbaedadbedbdcbdecadcbedaaecceadeccbeaaddceecddeeaabedbdddceddbdaebcbcdaaecedaeaabdaaadbaacebaeeacddeeebedddcbaababeedaadccaacaebcbedebaeccccdeaaeeebeabdbcbdabaebbcddcbbcbcabdabbacdeaceaadeacbdacadceabbdaedabaddeddcbdceebaadbbbccaddbcbdedeaadbcecbbbbdeccdeaedabcbecdaacdbedcaedabebdbacbebeedddbbbbdeabecdeaccbaeabececdcedcddaeeceeebeceedbecadabccebdbbbcdbeebbdecaceedaedbdaeeddecdebcbeebdaccaebcdcacbbceaedbadeabebecaeeaeabcbaebedbdebcbdbacdebeaaabbceacbaaacccdcedcdbbeeaaebbcdbbaeaeecaedaedccebbcbacdbceceeccabdabeeabadbeecdeedccaedaeacdcbcccbddceebdabeacceeedaeaaeadcdcdbbccbdddcdadbaadcadeeebbdccdcaabaadccdccadebcdadabbdcdeacebabdcbdacdcbeeeceeeeebeeeecbabddcbddacddbbaaddbccaeeaabdeaaceaeecedbccdaeeebceadecbdbeccadbdbdddbdddbdabeeedccbeabeeddaacbdceacdeaabadccaeddaeaddeeeacaabccdcdadbadcbeadbedeacaabddeadabcaaeccebdadeabceeeeceabbdcdaccdabbdabbeedecdbaebbbdeadebeeaceaeccaeaaedcaaecacdeecbbaacdcaacecddaaaabeccbebdacddcdcbedbbebeebaceeaaabacbcaedadebceaadbeaacccbbbdcbaedbcdecabaeeeaaaeeebbccccecedbcecdaeaaadedeaabeebcdccdaeceecebaceabcbddcaaacebececaebbabadcdcbaebaececeaedbccdcdcceccdbcaaecddcdcaebbecedecbbabdbbccdbbbdaacaebdcebbddbccbccbeebddadabbddddeebecdacdcaddbabdaadabdcccebecdaaaadeaacecabedeedbeddcecaadadabeaedcbccbcbbdbcacedeacacaaecdaebddcbdbacdbeeaabcbddecebebdcacbbdabeddbadaeeccccdcabdbbbdcdbacaaeceeeedbbcccebebbbbaadacdedcedccebecdcadadceabbdadedcecebcebeabddbabddcdebbdebcdbbbdceaebdcedadaadcebcecddccccecaeecdaacedeceeaacdacbbbccddabdeaceaaeaccbcebeedbaabeceddcdabedbbcbeebcaadaaddeecbcbbbbaecabccbacddbeaeebeabbbbeeabcabcabbeaeeceeaccbededacddedecaabeaddebcceaabcbabdbbbdccceacccebbbecbcdaaacbdbbdccaacbdeabbcdaedbacdeebdcceddeaaeeebeebcacdbdceaadcddbceaddaaebddcbeeacdaaebdeddacdbadacdaadeacaadabcebeeaabceccbddecbeccaedcaddaeccccadaccabacdeedbcabddccdedecddceebaebacacedcceadeddcbeacecdbccbbeadcaecccdadcebdbaaedcdcadbcdcdcadeeccbacdcedabeceaddbadcebdddaedbaacbdcabddecedcbabddeaedabeaebdecdbcddbbadeddbecabbcecabaeccdccaaebcedadebaabaccdceedcabeeeeacaacbadebaaabcaeccbabdabcccbcbcdddeedbedabadabadaabadacceccbeeecebcacdaddcbeeeeececdedddddcabebcdcdaaaecddeaeeedaeebccaaeeedecdcdddaeebeabaecbaebbcabebedddebeadcabdcbaaeeabeddbadccedacbaabdbececccbcaabaaebcbececaddbecabcbbdbdadcaedecbdddbdcccaeeceecabcebebecdeccbbebadddbdbcdcbddcadadaaaebcaeaededbbabbacbedcbbdeccdcaadbceadebaaeccbaebbdadddbbecaeadcadbcabedeccebbdaeaebdcebdcedcbbacadebcacdebcaeaababbedcceaadbbdcabdecebeabbaaccbecadcdbcecdacddbecaedaddbbbacaaeeabecaabbaaedccbcbdcbeeabbbdcbbccdbeadeecbaaacaeeacedcbdccddddbbadabeebaebeabadbedaedacecaeedeeccbaabecaaaedbaccdbeaaaaaacaaeebadcbacdbacbcdadacddedeebcdcaaaabddcadccceccdbeabcaacaeadaebbadcbabbcbcbdaabbabeceecdccccdabdaaaedcebabebecbdbeeaaabbbdedaeacabeaacadbbecedbddbeeeeceadbbeebaecdedccebadaceaeaaeeddadebbaabeadbdcadbedabbeacaabbbcddabdaacdeaeddedcccdbccbcecaaeaabeebdccbbbddcbadbebdbbedaaabadcccddecaacabecebcadedacdceccabbcceedebacecacdbbabaccacbaccbdaceeecdaadabbdcdedaeebeaddacabbdbcaeaecdbbaacbcdeeaaedcbcecabaeaaccddbcbdbbbeeadacbcccdecbcccbabadbaaeeacadebcdbceabdeceaabbadcbbeebdeceaeeccacaccadbbabbacdbdeecdbebbacebeaecbecbbdabeaeabccdbcabeadbabedbbdccbcccdcebdacecdeadbeaaddcedbceedbaccaaaceddbbdbaedebadacaebccdcdbeeedaabacabcecdbdbabdadcddabddaccebabcaacecebbabadcaebecccebddedaddccedaaecaadaabadddcaaebbcdeacbeabbabebacbaccbcdaccecddacaecbdcdccbbddebbbabdebbdddccabcacbedcdcbcbebcaacaccdaccaeadbdbbbdbadacdbaebebcccbcdcaeccceeccdaaddabedeebcaddddbdbcccbecdadbaeacbdeedebcaebcbacbadeadadebeaacdbdceccdaddcebadeaaccebabbcceadabaacebbdebaeeaddacadbecddeaaacadccebcdbbcebbbaaedaedaabdbecbdedcaececddcaebceebeebeacdaaedecccaaaeaeebbbcdaecdbedabaacdecadaeedadcaedbeacdecbbdcbccdbedcddbbcbadbbabeeaabddcddcbecbcaeabeddbedbdbbaebadcebbbeedccecebecebabaceadaebbededadaadacdeabbcaddedcaeccaeeaedbdbecccbccbccbcbcbdeaeeebeeeddcabbadbcbaaaccacdadebabedbdecbaabaeadaacaedebebcedeaededadbdeecaaeeeecebadceecdaaddbedbeeeccaedcdeeedaaebeaceebcbbbbddaceeecddbaebeecdedddadbbddeecadaedcaecbbedeadddabdaabacebeddaedbbdcdcddaabdecbbddedbdecbbedbdbbedcbaaeaedceaedbacabbeccddcdcceaababaaecbecdbcbbbebbdeabbcdbabdbbadeedeeaababdcadeebdceaabbaaaeccdcdededeeebbcbabaebcbaeddebabbcdcdccaaebcaeebabdbeaedbbabaadcedddadaaacdbacbaaecbeccbcbeccdedabebbaaddeeddccadbaeeabbacadeeeebdbecbccceeacbabcaedaebbadccebbedaaaabaddceacddaebeeeceeceaddebcabebebcbbeaacaacddbaeebadabedbdcbadadcbacbccdaeecacededceeaabbccededadaeabbecbcbebebdceaacdeeedabcdeaaeeeddadcacbbcaecbcdeccadeaecbcdaaaaebaaeaeacbebccbacbecdbcddceeeeaaddbabcbddbbdbdccccaddebcadabdbbaebbdacbdbcabcabdabacaeebaecedbdbbcbdcccdecbcdeeadacabcdddecadbdacdcaaddebcadecbceabdcebceaecbaadddceeeeacccceebeaabcebbeecdaeaccddcbdadadcdbbbeacdcbbeecdaadecabdcccebbecedaacabceebeaaeddcbbcdbdcaecaeedbadbddbdedbddcbdebbaedabcadaaaaddaebedcdbbaacbbadddeecabccdbebdaabebcdebeccabbbabdadeccaddaebdbcacaaeedaeccebdeacbaddeacaeadebddeebaccdaeeebecacadadadabcdeedebcbbbadaabbebaeecdadcedeecbcbbebdcddceedcdaabedaceccdbccccecbdbabebcacdacdceaaacecbbcddebcaecbadecccabeacbdedeaebdaccbbceebcebdcbdabadbbceeecaababeeeccaedaaebaeddbdbcdbddebbecacbadbabacddeccecdeeedcceadecaaccabceedaedacdeeadcedbbaedadaadadbcdecaecbdbacbdcecabcedaecaedcccecceccbacebaeeebbbdbeadeaebbaaeddcecebbabcdaaccaddaebdadbeebebdeaebaddcdebceecbbeddedeccbeeaacacadebcaaccabebabcebeddabbbbbdedcbbcccaaddbdebeecedbacdaacbdadabeedbbecebdbedccaadeccdeabdacbbeeccaccdeccdbcaadceeadadcaedddaaceccdadeeabeecbeccadbbaeccadebbddccdeaadbebdadcacecabebcacddeaaebdecadbadaaebeeddeecdededbebdeeacdcaebcccbdbcaadaaceecddceacadceccacdbaadadbaaadebeececcbceaacdecbadcebdceababcbdebdceeabcbeadbebcdeeecbbedeeceabccdaecdbeadebcdbdacccacdeedebdbdbaecaecdcbebabacdbceeeeadeeacdcdceadeccbbabcabbebcdbaadeedccadceaebddeaddaeecdcccecdecdbaecbbcdeecbbdedeaabccadecbdbebacdeaecaabbdbaeaeebceeadddcbcebcceeadddbbcdecbeedabbdbbeadaedabcbaaccedcaddcecebbdebedaabaddbaecaeaadceeecbacaeabebabdebbbaebbdccadcbdebeaaebdddbccadeaaebcaaccebdcaebbddcaddecbcddaadaaddeeeeaddabcdccddcaadecaaceceabaabadaeccadcbdaaaabcedbaabcabcccbadeaadbcecccbbeaccddcabbbbdebdadaaebdbaebaeaedaebecaadbededcdcdbcbcabaadabaebbdbaeceebdccaacaacedbbabadedbbaecbeccbbeadacacdbbbabccdedeccbaecbbaeacaeaaebdbaedcaecdccdebaeaaaedcbaeceeabacbedeeaeeeadbccbbddcdedaaeedcddcbedebececddaedcddbdaeaeeacdcecdabcbdcaeabadcbebaaaaeacbcdabcaddbeeeccdbdcabeccedecedacddbecdbeaeacdeadabeddbbadbcbddbbcddaeceedbbeebaecdbbadebecaabaedccccbbaecbbdcbceeeabeccaabaacacdbeecadadeedbbaecbedecabacbceebcbcddbddbaedabdbadcdbaeadeedbceeaddcceaaaeddcddccbccbcacaadbacecaeccceaeebcccdbaccccaeddeccdebeedbccbaaebecbdedbcadabccbdbeacbdebaeecbceecbaeadaeebcdaedbaeaedbbbabeeebbddededeadaceacbbdddcbbcebcebeadbddbecedbbdadbcceeeaebeeacbebdbcaeeaeaadbccceecdbbeddcdadbbdccebcababcceaccbdceabeabadbadbcabadaeebcdbacadedabcedaceadececceabecbcaecbceeeeddbddbababbcbdbbceedaadeaaecdbccbeabcdccedbecbdacdcaeacdecbbcaeeddbdbbecdeadabaacecabccbbbadceddaadbbaaabecdcbaeeaacaeebdaceeccbbccbedebcddceecedcebecacececdaeaaecbbeeeeababedcaabaaaaeebdebaccaaeebdecddbdbbdedaaeebaeabbdebaeddcdddbceecadcebddbadabeaedacbaadcabedcbddeebdeebeddccbcadbceacaddcccaeeebbcbedeeeaecaeecbadaddbeddcdceaaccedadeaeecbdcbecddccbbbeacdaebaebddaeaedcecddceedeeecaedbddeedbaddaacccbbebeaebbaecbdeddeeaeadabbdbeedacddcbdceceadbbacecddabbceacecaaababaaccddcccbcdcbcdadcccdcbdbecabeccbebebccadebbdeeccceaeacecebbbcaeaeeeeaeeeaaeabeedbaecbdeeebbdabdceeacedccaacddbbdaceaeddaddceacaccadcdcabdacceecbdadbebdbddeebeceecbabcbaedeceedecacedeacdddadbebaeeebbaddecebdaaacbaebaadbccbceabbeadbdadedecdddbbedceaeaaacaeaddbceaaecbaeddeccdddbdcbebaaacecdbbcaacecccebbccddaddbdaacbdcbcddddcbeeaadaceaeaaeeaabaaceaddddcaeedbedcedbdaceecdbeedccbacbaaababddaaecaeddabeaccabdcbdcadbcccaadadecdbdcdababbaacadaeeddedecbecdbedeabeadaeedbbcbbcbbbcdacecacdadccaaedeebedaedbdcbcbdabeacededebceeeaddadbdbdbadcedabaaecceadddebbedecaddebadbddebccbcaadecaadbbcbbadeabbedcbaebedcdccecddcbcabecbbdaadaeaebbdecebcacdddaeadcdcdecddadcadadecceeaedbabcccbacacbcabdaedcdbbaecebbaebddaeadddcecedceaaaebaaddecaaaaabcdbebaabcaaeecdbeedbbddaeeebedceeececacaedaacebabadeaddccaddeeaeddccaeeacbaccabacdcbdadccbdebcbabcdebaaccacdeeceaceadcddcecdeaecccdbcaeeeacdcdabdaebaeedbdabcaebcbceeeedccdaddbeadecbcbadcaddbbadeeadacaeadbabecdbaedeccabcddeaccaeaceedddbdaceacdccdbecadccadabcdecdaeaaddebbcdabdcebbddbcecbacaadbcecadeeacdeaabbdedecadaabbbeedceedcbdcbcdbcdcceacebdcbaacadccadbbdbbceadcdbccebacdeaeaacaaadebaedceeddccaecbeeecdbdbdbabebedecddcbedaeeeaebbabaaacbcaebeedbebbbbcbcbeeaddcdcdcdceabcbbcccbcecdabcdadecbeddcadcadbdbbdaccbeeccadecceddeaccadecabedddcaeaabcbeacddbeedbcebdbcebcbeeaeccaadeeaeeedacaeaababdcabcdecbdeaccebeceebbcbccdaebebaaecddeaedbaecbbbaccadeeedadcdaccabcbcbeadcaadecbcccaeeabdaadacbaecaecccdbbadcdabdadccbdddcaeedcebcedaedaeebdbbbcabbdeabacdccbddceccbcaedaebedbadbebbeccdbdaeeebccaeaaaceebdbbddeacbddacadedbcecbebececddeabbcabaebddbbeaacedbbeebbadebdcedeeacbbbdddddcadbcaaecddeadccbdeaccbcdcbaebcdbadccdabcdbdaacbeddaddeeaadaaacbdcaecddaaaeaaabceaeeebdcccdcabddeadebbbaecabdbebeeaecbeebecbcbeecacedcbbeabcabebadacacddbecdadacabadbdbbabeeccedebaecadddbdbdbdaaecccaccddabbebeebbcecececbbddcbacbdeebeaaeddcaabdddceaebacaeababaaababdccbaaebdbadcdabdedebcbcaebdbbabdebaaddbeaebbbbcbbcdceddccccceccabbcdabaddcbbabdebcdecabddcbdebdaaadddcaaccbdddebedabeacdcabebcbbdeacaaadeeeedecdccabdbbcbdacdcbcacbacacedbaaaeaaaeaedebedddebaaeceabdddaeebcacaaedbbaccbddbeabcaeecbebcaecdededeecbdaeaadbceddecaaeebedcedcaaddeacddbbbbaadddebbcecadbdaaddcdbdcdddbbaceeabcbbbeedeecbcbaecaeabcebbabccddbcaddeddcddbeeaecbeeadaebadcadcdbeaeadecbbbdeebcababaaccaecdaeacbaebdbbceddccebcecaccdbeeeacbccbbaeddcaceabeeccedbcdcdaeaadbdbbeebceadacaabdbadadcbdbbdeabacacebeeddaebcabbbdaeaacebdeedcceeaeedecacbbceeaaabacbbedabcdaaadabbbbbaebbaaccbaacabdbbdbbaecdbedeecbabcacdcddeeabbacadcbcdccebbeabdbaeabeadabdcdddacaeeddccbacbbacecbcdcadeaabcceaccdaaeabcdcaccaacccbbbdaeecaebdddceeabbdedadccedaddebdddcadcaecbceacdcdbdaaaadadcdcbdacdbeebddaaaadcecaeddbeaccecddcdbedbcabdacacacdceeccdeebddcaddecaddeeedecdaeabaddceceecdaadeadbbecdeaabadddeeebacedddabeaceddacbbaeacddbedcccbbeadadcdecbdcdadaebbcbeedbcaceceabbdadcbacbbabeccbdecccdbabdeaeaecebaadaccdccebbabaecebecedeaeecdbdccaaecacacaacceacbaabeedaacbdabbbbbceecdacaeedeccbaebcabcdcedabcbbbbebaaceaadcaaedddcaeeaabbbaaeebeacaedeeccebebeccccaeeecdabedccadabcdadbaedbadbddbaaacbdbaaaeaaaedbbbbeaaccbacbeeaccccdbcddabebabbddcedeabebbaecddbbadbdcbdeccebbbcaddaacacbbdcaaeaebbeecdbdabdabcbadbddcdadbccdababdbcacbecbedbcaabaacabadcebecedebbbbcdbadaabcecdcabcdeecaacbdcdbeebbbadebaebabeaabcddadeecdcdcbbeabcddaedbbbccbbcaaeaabdacabbabaeadcdbdbdccabeaabacdedbcaaadebbaabecceadceddbeeacdedebebbbabeceeaadddddeeaceacbecbddbeeadbabdbeddeabcbcccdbbdacbbdbcebdaceecdbbcaadbacbbdddeddabedddcebadeacdcebbbacddcaabadbcbebacacccceebeebcacdcdaeaaacebbcbaedeccdabbdeebacabbdbedabcccdbceebadadcbaabbdbacedceaebbcdaedeebbedecbecdecccbedbbebeecdddaeaebeaebacedcacaaddcedabcebaaaececaceeabddcdeacbedcaaaaadebbeeccbccbdbccdaaabdcdedbebacdbbbbaccddacacdeeaddbbadebcccacacaacceacabadbbeeddbabeacabbaeceebcddddbaecdaddbbaaadbdeddecbbecaeebceedebebebdadedbeeeaaddceeeeadcaadcbebdbcbbccbccacddbbddccddceebdeedebbbaeaddcecedeaccdcdaacacebcbbecaacbadeaadbbbcbcdecaddbdedadeeddcacedabdbbcacbbcacecdbdcbbdceecceedbdecbdeeeedabeadcbdcbbdaebadabbacebbabecaadaaaedcbdedcaaabebdbbbbcdebeddecbaaaaebadcddbaaddececdbcaaeebddcdebaacdeddbddccdecaaaeadcedaedbbdedcebdccddbadcaecaacdceaabdeddaaebceeacabdddbbcaacacbdcebccbcdcbabeebeabadecbeabcdbebdbdcaacdaadcabbddeacdbdaacbebacabdceccdeeacceaedcecdebddcbaadcdbeacdaeaedbeabadaedbeddbadbacdbeacabaecacacaeddbcbebdbebdcedadbdaacbdbaddcebdbccaebaeadcdcdcaccccacaddaeccabdcbdbcebbaccadabedaeeccdbdbcccbceebdceaaaaceddadcbddcaaccbeabdbeeaebaaccbeaabddbecccaebacccdcaacedecedcebabeadcbbceedcbbaedbedebbbaedeabadacabddcccbdceeaaabbbebccededdcbaacacbdabadebaadcddadacdbecabacecdcdaacdceececcdaaebbcdbdaeedeadbaccedceddeaaaecdcbdbaecdeabacdedaedebdaacbbbcbdcecadebadedadcebebbcbedaacbacddbdcebbdcdabbeecbddcbedeedcdecabbeaeadddccdccaacebbedbbcacbdebdebcecdcbaabebcaddccddacadbdacecbcdeaacacbacbbceceedbebcebcebacecadacaeeddadbcbddaeaeddbeabccdadbdcccdbacbbbaeadbcaedbcadcdadcdaacceddbbabcbadebaebecedbdcccaabdbdbbccebbbddcbabcbaeceeeddedadcdcbeabaecbcedcbbedecabdbedddccaabdcdaaaeecebaeaaddbbdadcebabaabbacbadaceceeecbdcdeadbbdcbbcbeaeaeecbeaadbbcdddaacecdebeaeecceccccbecdebaabebaaedbebaebbdaecaadbedabdebabbcdacbdbcdacedaeedecbaabbddebcdcbebaadddcbaecacabbceecadbcbaebecceddedeeeadedacecaacbcccedbeaddbcbdbeaeedeadaebbddabeebccabcdeacbcecacaeabbceacedcdebbacdecbaebadebceaacecebbdaeecbbebabedacccdddaccebaedaadadcbcadaabddcbaaadabbcdbcbaaeedddeaeadeceecbdaaebbeddaacbdebdecdcddaececcdcdabbcdebeadeacacbdbcdddbbcbdeedebccccbbcbedaeaaededcbbdbbabababdabcdccceccbbdcebddbebaadbcdcbeadcebdcaabaececbdccdcedabecacabebebdebdaccbabcbcdbcdedeceeacdcbeccbbdaddeaaaacacadceeaccabedbaaecacdbecbcaadeadaedebbadaccddbbbcdececeededcdbaeeeeabbcebdacceceeceadccaacadddadcebddecdcbcadddbccecebbebaadacbdabcadbcdaebacddbaedeececdceaedbedccadcabbddbbdedcaadadaaadbbebabdaedaeceadcddbdbdbeaeeeceaeeeebdbdaeadeaddcdedcabadccaedeeebddaeaddbddddccbaaeeeddaeceaccecdaeeccdedcdbcbbbbcbbaadbeeeaecdcbcdecbabbdcdabcbdceaecbebdbabdeeaeadccbbcbbebceacdbeedaacdddaceebeeaaddcecdedbccedbeddbacdaeddadebbdcbaedcbdbdbcecdbbcaabecbbaaedcbeaedaebccbbccdcbdcadedbbdebabbbdbcadbadebbdbaedaebbdeceececcbcdeaaceddeedadbcecaedecdeadeaaccaebccbddaebdbebadbcdbebddaaaeebbeadacbaccddeeaceecedbcdededbcddabacaddbbeaeacbdceedadbdbdaabaebeebadebaccebcbedbdcbedbeadeaecdccddcbbbceddebeaebaddbddaabcbaecaccbaabdaceaccdccbabebbecbbabecedebdcabacbceaacdadacbeadcabadebbcbbbaccaacaeabaedeaeadebebedadedadbeaccbcedecdbeeddbcbaebabdeadcbdbabedcbdedeecceabcbcdabeaddacccccacbebeaabeabdedcaaabecdabadbbbdaeebadbbddbbdceebbbeaabcbbcadabcdeacebaeccdddbecbedccadadedadbaededeaaeedbaeedbeecebacadcbeebcbdaaeeeeceebdccadcdcaacdbbccebdeacbbdbcceccbcdaeebabeceacbebadadcadccadebadaabccdecdadbceebddecaddbdcdcdcdddecbabccddddcbccbbccaaddbdebceaabcbaaaadabceebdaebaebaebdbbbdbddecccbabddbcdebccdbaaedbbeecdbccdddcbbccadbcaedcddabbbbaccbedeccdadcabdcaaabbebdaeabaaeaddbeaabcccdaabecedcdecbaaebdbbaceaceeeadccdcbacbbedddcaabdabaaaccecceeddaeeabecedebcccaeabdbccebbddbcecbaadeaceabdbcbbcbcdadbecdaaceeacacedeedcaaabbdebbdddbceaeacedaadbdadbbbcbaaccdebaaeecbbeacdbcadabecacbbadcbebdbeecddecdecccceadeadaebbcbcabdbcedeebbcabeddddeddecaceecdaaacccebeacbcbbeecacdbdacebaeeaecbeabacecaeacadcdabaababceeaaacaddececdbcadddbabeaeedeeacacbbbccbbcaecbcaecaadceededabcaaccbbaddcacdbccebbabdbececbedaddbdddeeaddcccaabbaadbbcdcabcadcbacdedbeceebbecbbecceedeaabbaacedeedcecaccaacbacbebabebaeaacbdeadcedaaeebbdcaebaaceeadaacaadcbbaaebdaeddabbdaeeaaeacabdeaceabbebcaeadbdebbdeaecbbacdcaabedbbabcebeabaeeeccacaceceeedebadeccbeeccaadbecacceaaceeddeadbbbabdedecbabdeecbdbcbbbabbbaedaaeadcaecaebcaaccadcccacdbcdaddedcdabaeccdbecadcebadadeabddbbedeadacbeedbaacedacbddbdaceeacceabcecddeaddbdcebcaebbadbbbaaecebbaadcbaaedeeaaeceabecaabddaadcbcecdcebcdedbaeccbdabbdaaabbdabddcbcaeadbababadccccdbbdaaaabbcbecddddabbcbcbbadedceedceabacddcaabdedebaacedbebaeedaaaebbadadcebeadaadbeeedcdbededabdcadacecdbeeadecbbdecacadaaeabcbdcdaedbecbdeaaddecacbbceaddcdecccaeddabaecbaccacbcdaceedbbedcdeccdbdabebebcebaaadcbecabdeaaacbedabceddedcbbcbddbedaaabdedbbcaaabcbebcbaddbedbeaadaedcdeeebcaecedbeddeececcccdddadabeacdcbbdaedddebbadcccaceabbbddeaaccabeceacebcabbeacecceabcaabbeedaceeeaeddbedebdbacadaaaddcceeacbacedbedddcbaadccdaeeaacdaecbbaadcccbbbbeeaedcddbbbdcbedeebbcdbaecebddecaecbedaebedebdcaeabceeaadccbdeaddcacedcddcdcbdebbcabadbdcdbeaacccabcbbacbbedddebccccaacedccadaabdeddbeddaecdeadabcaacedccdbcabbdbdecacaddcdececcebeaceccaaacaaaccdccecacdebeebcddedcddaabaeadadaaacdbdbdbbedeecaadcbcddaeebebeeaeecdedacccdeaebcadbcdaabbdeebcdeddcddacebdccbeeaddbcdaeaeaceaebaadaddadcbedecbacabedaabdabcccbddcdceedabbddbeaaaeedabdebcbdeaddbecbaaeaadaacaddbadaccadbcbdaecceddeccacccacbbccbedaccebecbebedeeceebedbeccbacbabceddecceeaadecbacadbcdbbdbdcbcbadddcdcebaebadaccaaedbededbbebebaedddbddaeeaeabcdadcedeebdeeeecdcbdceebceecadeeeaeeaadcddbacabaebabceecadadacbdcdddedccebecdbbddcaebeaacabbeeaabedcaabaaedddbdbccbebcdcddedceadbdecaccbadcdcdbadaadbacbabcbddaadcbaddbdddcbaedabdedaddebcacddcabdecdbbbdccbceccedbeaacbcddeededebdeeaecadaccbbebbbebedcccabeecccaddddbaeacdeedbaceaddabcccdcedebeebeabbceaebdecaaedccbacaaebdaabbcedacbddbaeaececebbbebaaaccbbccbdabdaaacdebbcdbebcddddbadaeccbcccaeccbccdcaccdbddbbebaeabebdebebdeeeeacccecddbeabddbaeacdcbddadacabbdaebeaeebccbdbedcabceadcccacbbbebcddeecbabaeaeeccddaadcccbdaacacddcccabeceecdbcdbecbbdbcbecbebcdddecabcceaeaaacceeedcecbdcbebbcddbcebddadedbbcceaabccdddbeabcdaebbebebbaabdcaebedbbbcaaaebdeacaebecddeeecdcbabbbdebcdaecabeaebdebddcebcceececaddcbeaaababbaacdbbdbbcabcaecaeabdbbacacbcdaccddeaaabcceeacbbcbeabbcbacdabaceddcaccbdccceaecbaaaaedbcaaadeaecedeeaedbbeaadcdcaecaaeabceeeedbcbeaceadabebcabdbebbaadbdeecececdedecaaddecabdcaadeedddeeebebaeabdccbddadeccddcdcdcdbedadabacbdabaddceeddebaceacccdabdbcddebaadeacebcdacbaedcdbbddcdccbdeedbebcacbcbadbabcbeceabdccecedeeeaebaebababacadddcbdddbbecbeccddeceabbbceeaeaacecaeadeaedaceececdedabcdcaacceeebbbedbcdbebbaddbdcedaeccaeeabbdadecedeecdbbadaaeecdccaedccdccebcbcecceabecbdadabacaadccdeaceaeeeeebcbedebbaabdcdcaebccaeeeeadacaeebddaeaebcbaaeceadcbebbdcaddcecadaecdcdbccdaedcdccebeaabcddadcbcaecdeeabdbacbbcaddbeabacadeccacbbecddadacbdbdbcbbbcbaeadecabcecbdcbbbdabeecccbecccddbcbdaabdedecdacadceaecbabeaababbaadcebeeedacedbbdacdaecacbebeeaaddcdbaaebacccaabadcaebcbdbbcdceacaacbbacdebbaccadddebdcccdccddeeebccccdcebadaccbebadaeaeadeaeaecebacaebceacadedaaebdcbddadeaedeceacaadceaceeeaddbedaabaedeaecdaedcbbdcdaeeadcdadeccceebdbbecbacddcececeabcbecadecaecbcccbceabeacbeedecadedacbaddeaabdacadcebddaadaebdccbeaaaededdeacadedbdbcadddedbccaaecaddcadcccbddebdbccccaeacdaddeebbdaabaaeedbceddecbbbaabbeceedabddcbdddddbaeeadceccadeaeecedbeeaedaaeebecdbdbcbbacdbeaaeceaeccbbbcdddabbcbadeabadbaccacdddcddbecdcdbececebebbdddedccdcacbcccaeaaacbedcaaecebdebccbbccbcadbceaccdadacdbceedbacacabadaddeeabcbeedcbdeabedeeebedbcecaaddcbebaccdaceebacadaabdcbabdeaacbaecdadadaeabaedaddadccdacbcbdecedebbcabeebaaedbccdedbbacbeaabebedaadaadceabdcaedebabebdcccadcdbdecdeaabbbbdcbdbddcacbabecedcaadecdcbcacceecddbcdbdeeedeaabecdacdccceeacdabaeecdbebccdacdabeaaeaecabdaacddbdbdbbeeaebccaaacbeecbdddebdbabbdeeddcdebeedbcdcaeadadaedabecdacceaacbaeedaccabddbbbbccebbceaaddbddadebcaddabbdbacecaaddddbcebcdddeaaebedaecabaecaacceecacadddeeedabbbcbecbaceaeadbadaebcbacedaecaddbeeebdebedbcebdabdcbcacaccdaaccbacacaeeabdbbdcacdcbddbcbaececdbeaedadbadcbadeccadcdcadbcbdeeaeaedebcdceabdbceecbacaabccbddbebadbabcddebdcbedaebacbacccaabecadeecebedadbabebededbebabaabaacbceacdabcddaaaadeeeccaddbaeccbcbeacdeadeaebbceecdcadcdddbdecedbbcebeeebccabccaebbcececbbeabeeddadedeacbbaabebddcbcaeaecebbdcdcebabcacaeecabcbeededcaebcceceebbdcadccebcababbbaaacaadecacbddcbbbebbecaadbabcbdcbeedcbeeeeccaecdbbbadabaeaededabbeadedebdececdcdddbdcbaebbbdaaadbdbeaeccebabebcbbcadebedbcebcabacbaeaebbeedccaddeaaaaddbcecebeebabceeadaeaceaebbdbacbbacabebaaddebeeeccbdbdbaebadbcaeaddccbbebbbadededdbeeeeeaccebdeeddcbbbadedbdeddcccddcabcacedccdeebedbeccedcaceeaecdcccadececeabeceebacebdaeebecacbbcbabdedecabeacbedcdbeddbecdbaededeabcdabebacacbccccabeacacbecddbacebbbaedbaedacedecccdbbeacdedbaeaabbddecbeaddadcbadcedccedccadedeeeabcccceecbcceabedacddaecadddcddbdbeaaadeeebacabaadbbbbccccbbcaecbbacccdeaaeecbcadbcdadccbcbacaaeaeeebbeedadbcecacdabcdeadbdaeededcccabaecbcbaeaceaaabceaddebdcadadedaaccaddaaabcccceaddbdcddeebebdebeacbeddceaaaeddbeeabdcccedecbdcdeaacadcaecbecdadbcebcbbeabdcaacaacebbcdaecabecaaacdcdbcebaaeeaccebbdeceadbdbceabadacdbcdeaccaeacbceacaeecaaeaceecdddeaeadbaaecbbccacddccdecdddccaedaecdccbdadbddceabdbcbadbebacbdcbabdcbebccccaeebebcdaeedcaacddadeacbbdbbaadacdebbdeedacdeccebdbacdccbecadeeabaeeedcecceaeaeaddbbdaaacdadededddcacadeaaeaddeacddeeeeaceddebeadbbceaeaceaeacbabaababacedbcecdcaedbbbbccddcdadeaceaaadbaebbddbecccaccbcedabdceedcbeaacdbebabbbbbbaddacdccdccbdcdedbdccbdbbbeebcacceddaecabdbcddaceccaababaceeebbcbcceaaceabcaeaabebedacaabeedecdaceccddcdadbaabbeaeddeebbdabcaabaedceeabdcdeddceddcdadeceebeecedcacccabcdbeadbbaabdaadccebcaacdbcbadedcbcaaecbacccacbcddcccdabaccabdcebdabcecbbbceaabdaadaeaeddaedeeaeecedbbdeadcceedeecaceacbcbeeebcabdbdedcecbaaeccadaeaabbaccecaabcbbadbecebaaacaaedbabdbebecdbaecdeadccdaeebccbeaceebaadaeceaeeecbbedbeaaecdecdadceabcaeadcaaddebabdcadedceddaabecbccaaabcbbeaecbddebcecdadbeedbdbeeaeebacdeebdeedeaceadbbeaeecedebabedabcbebbbbbdabbecabcbaddcdaeacecabdbacadaaedaabcaeccebdddbedbdededbbecaddcddbcbeddcdbebebcbccdeddaddaaebcdaebeeccbeecebadceddedbdedcaebceeaeeccdadbdacaabebaaeaeabbcccabbccdbacacbedbbbabcbdbdcaaceccacacddddbbbeeacedbaebddedaeeaadeaaebbeaacaeaabdebcaaaaaaeeebaacaddcbebbaaaebdcccebdadcedecdcbbdbabaebcebedabcbbaedcdbcecaddedecbebdaaedbaaeeccdabbdcdddeddddabcdaaecdbaacddedddcedeeabbaceaecccbeeaebedcaecabcbcceebdddbecebcbbeaabebcacccebcbaddeddaecebacbeadebccaaccedcbedccaabceebcedbacbbadabaeaebedbdcdcbccbccdaadcbedabaeaacbbedcddebbcebababeaadcdacecccdeeeebcddeeebbddbbdcccbdbbcabacbacdadeebbaddbdaecceabdbaeaadddceaceadbedeadedbaecedacbcaacebbdbdddebdaecbdebdadccaeecbecadbeadbecebcddecbcaccbdbcadbedaacbeabedbdbdbdebcbabddedaeaeabbeebbbadaddabbdbbbcccadebecbebcccccceebdcecaaadbdbdddaabadbcbaaeadddacbeecbdbdadedabccbcdcecceedadecdaaebceccdaedaacbcadbdaebccbbabdddedabcabdeddebbccceaadeceeccdddaabedcbdddbaecaaecddeedeaabdadaedbddbcbdaececbddcebdacdacbaeddacbccddccabbddececbcaeecacdadcbddddeaaedbccbdbeaeadebabdcacbccdaeddeebabdcdddadcbdddabcbcaeebdeaccdeeabcecddadaabdabcedabbebddceaebdabbcdeddeddadeecddebecabaeaceceddbcacaccbcbaccbeddbdddabbadabebeaabebecdaeeaaabcccbbbddeaebbdcbaaaecaadbeceedceccddccddcdccadbabcadedeaadeceeccebacbabeeaebddecabaebcbebdacbcdddaaebbccaebecebbebeaeeddddccdbcaeddecbdedcecdacdbbaedebeceeeecdecbbccbebeabaeaeececaaadbebceeeeadacbcdabdbeeabebdbaabdeacbbecccaedbbaeaecaaaaceaeddeedeaaebaddbbccacbaceacecaabaaecbeaedcabaeabdbbcceaadabdcdabaedceeebcaececcedbdbaaeeeaebebbcbddacdddadddadccadbbdecdccedebabbdccdccaaccacacbecceaaaaacbcccaaebdebeccdbaabbecaecaaeddcadbecbddcebabdbedcdacdecacdaecdecdccdddebecbbceecdeaebcdabbabeaabbccbdabdcaaceeecebaccedaaadcadaceaebacdeacedbbecddcdcbdeddeaedbdaceeaeababdecbaeedcbbcecdacaebeaddbccbacccacddacdadebeacdbddaebcedacbadecedcaaddeababebeceadccecacbbcbdcccbbcaddbaebbcbbcbaaeddadaddcdbdeabcbebbdeceebbbeabaddbddcdddcbbdcccababaebbcdcdccaadaecdaebbbbbcddabaebbbccdbcacedddcedceecdacababbbbbdacbadadbabdeeacaaeebecedcedcebdadaebabbeeaacebccaddcaacaedeecbcadebeaebabcbcdacddcbaccecbcbcaabdaaadddbeadaedcabaacceaccebbddcdebaecccacbadeaebccdbcadbdcdddcacbbaeddeccddabbcddedeeecaaedecbedbdddabadcbebaaccbdecbdbcecccccbaebebacbbbdaceecacddbcaaecceaceacaadbdacbbceecabedeeeecabeddedcbacdeababacecadedeecbdcebecdbabddaceaabcbcaeccebdbbeecbadabbaebcceadddadccbabaeddcaacdeabadaabecdaededbaecdcedeebbadcbcabcdeddccbecaccbbbdeebedddddeeadccacccddbcccbbdebaebdcbbdaadaaadaadbbeccceeeeeddabebaaadcaabbcebccddbcdddecaccbcbddadeadeccadaeabbecadaecadebebdbeedbcbadecabbeedcdeadcdcddeddddaccbaecccdbbddacbbbddedbbcdbcebcbacebeccbaedadbbeaddbecadcbebbeceaddececcbeceebdcbdcaeeddebcdcbdedebacecadccdbacceedccaadbabbbdeedabdddeeacbacbcbbcbcdabeaeadabcebaaecbecddebadbcabaebcaacccceebdbcbbadebdbebdbaaaacacabdacdeabaeaceeaededeaecdedbabcabaeaaacbedcbebbcecdacebedcaebadaecdcdcdadacecbecbcdeaebaecccdeedebaeeebdedececdcdcddeaeeddedbcedbeeecdccacdaeabdbeaeaceecdddeccccadeebdaabeadebdcceaeacabeebcdeaccabbcaddcdeebbdeddeddacabcbbbdcaecaccadbbadbdbbdedcdbbbbccabdccbdaeaeeedebdcedaaeddbcebedeccbecdadebdcdcdceaaedcdcdeaddcbebdacbdbbecceaeaeeabbacabcaebcabeabddccacbdacddcaeddaeccccaeeddadaaebaabddddaeeebddbccebbbeaedcdbceccadedcccabbbebabacebabcdbebeeaebbabaacdbaeedeccdebcddeddbbbebbacccbbcacbecbdaadadcebebdecbebdaaaaacaedcdeaccdeeacaaceacdeacccdbdaadadcecbdaeeecaeabbddbcdcbbaaacbcaadcceabdaedbdeceaeebcabeebebdbabbecadcecaaddebcccdbaacacbdbbabceccdbaeeacdecadbebbecbdcbbebbedbcccdeeddbccbbaceacedbdacebedaecbeeadeeaebedcbaaeccdbaeaddeadaaeadceaebbeededceaaddbbeedcdeedcdbadbbcccaeadccabebcbeaecbebbdbbbeaaddabdeecadbbbbcdadedbcebccedbdeebaccbecaddadeacdeddcebeeceecdbbdaaacceeebbdcdaaecacbeaeadeebddcbdacbbbcceddeecdceecedbdcbccdadbcbabbecabeaddcacbdbdbddeddedbdcdedcadbccceeebdbbbecebcdaeecaeebcecbcebbcccccbdacbabadccaceeaeaadbebdbdbdaccacbdadaedcccddecaebceabaddeecebebeadbcaabaeccbbdccaabaaeeddbdbeaaccbebbeebeeddcabeeddeaedceecbbbcbbabcdddbbcecbecbbaebbddabedbcbcedecdeadcbdcabbdaedbacecccacbeeccbcbdcdaeceddeebccdaccabbedbbceeebdeeeabdaeacaaeecbecdbacbabeceacbcebbbadebdcbaeebceabaceedeedccdbdeecbacdedbaeebecddaeddcbcebbaedcbebccabedaacabbddeaadbdadadddebebbaeebbcddddcaccbbeccadcbcddaeebaecdebcbdcdbbebcbdbacdabcbdeeabbeedbadbadeccbeaacddccdcebcaebbcaedccbbdbddbddbeccbeebcbcaebcddbdeeeeedacdbecccaaaabdcadaabebbbabbadcbaabaeebdeeacaebcbdcdabbeecddddaeedeacbcebdadbcdaacdaddeacbeadecbcbbebbbbebaaeabbccececbadcaabccebceebddddeacbaecbcbaeedecdebbabeeacaedabeaacbeaeacbdadcbeeeaeccbbebdeeecedcbeeabeadaaeaadadbacbeeebaaeccbdcacdcebebdaadecbbeaaeddcbebaabbeceddbbeccebabaceeedcdaeabdabedcaaddabdcbbabaecebdaaadeaaecacdacbccebbbcbdaacabbbbbceacddaabdaeaaebdbaabbdacbeaddcdbeecaeacbdbeaeeeacaedaadbeabcdcaeecebbeaabaadebdcabedcadbccebdadaaaddbcaedbbecebdcaaedaaadeadcbaacdecaebccaeeebcedcdbabdeaedcecddbdeabaadcebbddaccbdadccbbbceaaeaccdbcdbbaccdcddbacabeccbecdacdaaaddabcdaedbeacbcbacedecbddddccaadbcdbceaaccedcaccabbadeaadbaaeaedccdeabdbaaebecaeedbcdbcebcebaadbdeabceeecaccbebbdcddededbbabcbaeebecedcebdaabeceecbddecaaaadeedcaaaeceacebbdabbdceecddcbccbeedcbcddaeebbdcdbedbcbbddcdbbbbceebedbaadceeaecadccaeeacdcadeeedaeadbccaebbcceaebaccaabbeacaaeacbbbebdddcacbbeeeeaccdcebcebbadcebddedbebedcebcdcbeacbaebcadbbbdbdddaabdabdadbbdbadaaaadcabbaaababeebcedddddbebdaedebabcbaccadbdadbdbedabbdcdeeeaeacebacacabbbcccbcbdececbabdcaeeaaccebcbaeaadadbdecbeecbbaabeacecbbcaadacbbcabaeeaeabebccbcbadbededaadaaebabdccddeaeeabccaacbddbbbebbaacdcedcbaeeddbecccdcbcbdacbacaccecdaebaadadbcdcbccdbbbcedcaebdecabceeddcbbaccdccadbcbeebbaabdbacaddceeacbadbcbabacdbaceaeaccaddeecabbbdaeaedcbcdabdbbdcbcedbdecaaebacaeccbabadeccebdebabdadeaacabacbcbdbbeeacdcaeaeadccabeccbabeeacdaabddccedbeddcbaabaaecedbbbecbcbdbcdeaaeeacbcccabaddbccbdeeabbbdccdccbaccedcccceebecceeeacdaecedecbedbabccbcaebcabbdbcbbbbbedccdbceaeaddeaacbadabaecdeeeabcadbcbecbacbebacedecadcadaaadcdcadeeabaeacdccadceabeadbadeedcacbecccbdebcbaddaaceccddcdadbbadbebcdebeebaddaccaecdcbddedaadbabceaeaaabdbadbcaabbacdbeacaccbceccdccebedaccbbabdbebddbecacaacaaadeaccddeadebbabebacbedbcbeeebcdcebbaababdcedbdbeaedbebbcdbeebbdadabbcdccdeabceeabadedbbacbedddaceccabbbbebdaaabddedabddbeceabaddeecaeacbcebbabaaecadeaabdeeeaabbaeebbdbbaccaebaadeababddceedbaddeebdccbaeaadbdaedbeadebdacacaebddbddedecbbebcaedcdecdcbebbbceaadcebeebbdcacedbabccccebccddcebaeebeadebebcaccdbccacaedaacddbdbcecaaecdebcedccbccaeedcebbdcecaeabeedebedccccbaccbebacbcdededbcbaebbceedecdbeeeaabebacedecbbcaccecebbaceedbceacebddabcacbdddbdabdebcdedcaebcaaeececadeebbbbdcbebbeadbdbdcdbdabedbebcdbcaadbbdaecaebcdbbaeeceeeabdeddbcaaecabbbcecddebebcdedaaeabbccebedddddacdcaecccbbdbbaaceeebceaeaedceacbcaeacbeadacbebbcaecdbdddeedccaddcededbedaebdacdeccbbdecaacbbcaeecebcdbdeadbdcabaadcbdeceadddaaecbcdbeaddddeaddbeccbcedbaebdbeacebeabbeebdecbbdeaddebccecdeedeaccedacdecabbcedaeecaadbccabaadccddddebdaeceacddaabcadceeacdcdadcbddcdececabecddbbdccbacadbaeeccbdeacdedccbaabdcaaebeaaaebcbbcccbeeceacabcdddadeaeebbeebeadabacebcbbddeaaadccdbccbedcbcecdaebbdedcebbceeabdeaccaaeaebbbdddaebbeacbeddedcddcbbddbedeceedeaacedaeceaddacbbecbcadacdceebeaeaaabcaddbcdedebabdaacdbbeaeacacdeeecbbceebaccbebeaacaebcbbacabadccebeccecdaeeaadadbdadbacddccaedcabccbdbecebacecadbcbcccbecdaadaeeacbbaedcbabaaabadcebcebceeacebdabbdcedaabeccbabdeacbbeacddbecdcadebbbbcebecabdeacadaadbcecebabbebcbdbddabdbabdcddcdeabbdbceebabeecaebddbaaadaecaeeadbcbdeebcbbbbeccdcdebcdedcebabecdcbebaabcecbccbcbceccabdbcccdbeeaeaebcbdaeddbdbadebacdddebaddbcececcaccbbdeaadeddaceaddebebbbdbdbaaddaaacdcbebedabdcdcdabedbbbabeabbbcaecdaabbecddccadaabeababebecdeeabeeababcaaccaccddbcdbacaebdbeaccbeddededebcaabdcaadbebeacccedcddbcebdddadbcbbbbedcaaebcceceeceebcaddeecdbadadbecaecbaddbedbbcedbbbedbcbcaddabacdedbdbbcabeddeaecbedcadebceaddcaeadcaccebbcdbaabbddccbbaddbcdecabdedacbebdbcadedbebbaeaacaedebeceaeaadabebdececedbbbaeecbceadbddaabcbbaaaabececacececacedbbabdbdcdbaaecedecaddbdbdcbebdeaebbeacaccdbcaeaeaaecbcddccdbdceccacdddbadbcebcacabedeaadbabdbbebecdaadbbceadddadaabbaaeacbbcaeddbbcaadebeedbbeddccacaecbedadcccaccdceaeaaebecdaddebcbbdbdeaabedcbcaabddeabdbaeaeccbdedbdcddbacdebeaadcabbaddcebbbedbccbddabedbbbacddddccedbdabdeedbdabedbbdcdacedcdcebcbbeccbbaeedcdcdddbbddbdbcbeeadeecbbacbcaaededecddeceebcacbbeabccabdcabecbccbdedebacaaebdeaeebbdceecceacaaeaaaecabddcbadeedeaaeeeebbdecdbcdeececbecedcdddccaaeebbaddcbeeccdaeaaeccbdccddcbbbdcdebdbcdcadcdbabcddacedabddabbacddaabddccaaabacdbecbaaecaacddceccdaeaceaaeadaaedabbbbbaaccaedcdedeaacecdcebadcedddeaccacdcdbacdaaedddeeaacbedcaaccaecaacedbcdaecbdcceaadabcddbecbeeaebacccaddacdaeadcaadbebaccaceaabebabacbccedabcebdadaadddaccecbbcbeedaabdcabeabceabeadabddadbcddbacacacedeeaddcddcbcacbdcbdcceededcaadbedcceaeeceeccbaeecacbbcbaecadddebcacedcddbbabbbbadbdababeeecbdedbdaaaccbbccbccacbbedddacdeabbedeeadddabeceeaeddeeebabdadbcbcaebeababcceabcdedbcbaecbeaadcaeabadbdbcadbccaaabaacbcbbcbbbadaceabadbdccebbdceadaeedecdeabaeaaacccbebeceeaaacebdebecebedbeecebeadbabacaedcaeeeadcdbeaeacccdebaaebeaceacadeaccabbceedeebedceedebcaaaeeeddeeeebdedecabaaeaaacadbaaaeebeebedaecabdaabeddcdecbeccabeacbdebbaabeacbecdecaecdeaeacbdaeaaddeeaaccbeaacdcabdedeccbbbbaddaeeacbebbbacecbbaeaadcaeaacedebdabbcdacaabbcadaaabeedbbeedcdcbccedaeaceeaadaccebdadbdcdccedececdebaedadebbdeaedecbdcdbebeaabaabdedaceaeeeeacdbdcbedebcbcbccbddebaddadadcdacbbdaecccabaeaeacccbdaabdcabbebbaddeacdbdecedcaaecaebebcacebaaedbcbdcbbcbcacbddecabadbebbbbdeedebdbbdceeeebbcacadddbecccddeaccddcbdbbedacbbdeabbdaddecdbaacbdaaccbbdcbabaaebcccbbacdadcceaaddbabceabebcabebeccaddacacbbbbeadceeacdeededdcdaeaebbeceaacceeadeecbdabbeceacddcbebaceebcbabdcceeceebabccddcdcacddaacdcbeccaddeedceeaaeadccacccbcdbdedeedebaebeabeaaaabebedeeeeabeaeaaadcdabbbabbdaccbdeddebabeebbcbcebbeaabacdddbbecacbbcdbddcbeaabcdaacdbceeebadbcdcccdedbbaacabbddbdcbbdcadabcbbdeaaabbadbcbbbebaaceaacdcacddaedcdcceebaecacecdbcddbbababeddaddccebeedeeabaccbcaceeeaddecbecbccdcadeeaabdceaddcdcbeeceacbadcedacbeaeadeeceeaddeddeebadcbdcbeebddbdabacdebccbdcdbcbcbccdbbebcdbcaeeccebbebdaebcacbeedabbcdbaacbdabecbedeeeddabbbeedddebcbaaddaeaadeadedcacacadcebbbdebdeacaabdcdbddaeeaeccadacdbbdededeaabcbbcdabdabaaaeaaceacdaedbcedbdeaebaaebaebeecdddeecbedbbabecbdaedececccebdcaeeebabbbdbababeedecbeaecebbebebdcbabbcdbcbcdacdaaecccddcebebaecacadadccccdaadbaabddbabbbbebcbdcdbdeaabcacdbbecbaeacabbbcbdecebbaecacaadedacdecbdaccbbcceaaeadbccebcadadcbbedeacdeaccbabeaeecddacbacddcceccebeebeedbabaeebabbabbbdbabdacbecceebeccacdebbbeaadcaeebecacceccbeebcaedadcddcdbeeaeebbadbaecacaaeeeccaceacadbbcccbabbaaddddcaaadbeecadcdceeccaabadadaddeabcbcceeabccdededddaceadbeeaaedacaaaecbbeeccacaecbcbbcacdaeacedbbbbbddbcecbabcbbbccacddeebaeaceaaecabaaedabcbabbeeeadeddbddbbebbbacddedddcdabcddaccbabbbddedddadedacdceacaabbeaccabaedddccadebddcdadeaaebadcecaeceeceeaddbecbcabbeccabaeebdebddacceddbdbbbccbdbdaabbddddcbdbdaaaacaccecbeccccceeaedecbcebcdcbccbbdecadecadbeccedbceeceecceccdeebabbeaaaeadabcaebeaadebddeeccbcdaadadbddbccadbcdebddbbaacbdbdccccdcedabbbeabcabbcbeababaccbbcbcebcacccddcbceccdcbcadedcbadeddaaddaceaeaabccaceaccdaeebbdbddbdeecedeabeddedccbcbcbecbdeabccdecebcdbebbacdbeeadeaabdaecaebeececbebcceeeacaabaebebeaecceebaeabbbcabeaedbadadbabeebddbdabcaeeacabbcbadededacbecdcbdacbcdeadecbbaceccbbadcabedcebbdcedebabadcaaeabddbbbdeadecbbccebdaeabccedadecaacebdbcaaeecacdeecbabecaadbecbeeccaecbdeaedadebedeeaeaaabebbbebbedcabdcdccdebcdacacbcbddbeeebadaaaeceddeecccceececdcadceeaeccbaadaeeeccdbeccacdecbdedeecedcabbcccabecedebbaadedebbcaddaccbeeaedeebbaecedbcbabaadbdbdaecedeedbeaecaebbeacdbbbabaaeaecaeabddcbcbdadaebdabbdeabcccddcccacaedbaebcebeecceabeebbaececeacbedbacccbbccccacadcaeaaceabddbaccebbbbcaaaaabdeceaccceecabaaaadeaebbeeaadacabdacabbcdaecadcedccdbeceeccdbbbbcdaceecdceeacabeaddcaeaedcbcbeebebedcdcbbcaddbcbdacdbecedbecbddcddabbcbceceaceaaedbedebdaebbbdeeddabaeceeadbeacbbceadeacababeeaddeabcedebabbbaabadaeadaccaecbdeeacbbebdcaedbdaacdccacbaebdaaeebeaccdaabccacedaeeeebadebbbadceaaaaecacdaebccaddcbbacaecbbbdaceedccdbceccedaceeacbaaadccbacedaaedbeaeeaecdedcbededcbbcdccaecdbddaebbcbbaebabadbbeebadacbdbadedceeddbdeeabcbcebddaebdabcaebdebcbaceeadcaaacdadebbcdeebbccaddbeacebabcdbeedbacceabcddaacbacbcdbdebcbceacadcbebacbcdedeaadcbddaedecdceebdbaeeabceebecdaeaabebccabdebceacaebbcaeebbecbadeebdcdbeabdacaabaeacdeeddbbadcdebaccaccdbedeebcbbbdcbdcbbccdbcacdeabaeaeaebbebcaaeceeebecebebeadcbedecdeddadeadeaacbbdceaadedeeedabdeedeedcceeeabdedddbaeadaaaaceeccccdaabdbebaadaeabdaccceeddadaeacdedaebdacbcddabacacdacecccbbaadeaeaccbdbaceacbbaedcbcbabddcdbeaabdddadddaacbebddbeabdedbadbcadaeadecbeedecbebccdbbeeedbceaebeaebaebcababbcdedcdbebdebaadbdaacccdabdeabcedebcdbadbbbadbdababccbbbaccaeacabddcaceaadceddbbdacccaceceeabbcdbdbdeccaddbccaeeadaacdbbdaedbecadabaceedadcaccbaedbaabddaedabbeeeaccbadebebadaaeaeecabddcccaaccbbeceeccdaeeaaddaaeaaacbacadedabdabddeaabcdddedeeabadeacebccedbbebcdedeaeeaeaceeaeeddcbccaecdabdcedaaecddecdacdbaddeddaeebdccabeceabbebeaeeaebbeeabdedaddcacbccecbadeeeacedbabbbeeedcccbdcbaddaeabcdddbddebcebccaeedbdecdeeaebedccbaabeadebddbdaecdbbcaecaedaaceedcbbdccbeabadcebeceddcaabadabbddbccdeaddddcdeadeadcdddbaacadaacbbcebaccecdddacdcbbedebdacdaebdebaeeebddcebcbbcdddcceeddeccccbedddedaacedbcdcbedbdedbdadccbacbddcbcaceadceeeceddbbbaebdadaccacaeacbdaeecccbabcacbdbcbaeececddddbdbeddbdcdbcceacdedcdbbabcdebabddbebccdcccdcdbeceaabbdaddbcbcabaccdbddedbcbabbeccdddaedeaacdbcaabaecbaeeeebecdedcecadbabcdbbdcaebaddaccbeaaedcaccaecdbdaedabbbceacdddaaeedecceaabadeaecacbcaaecbceeddcbccccecbeaeebadedeacbbbdadedbadabbbcbecededceadbcedebadbaaeedaadbcdbbadadaaacccdccdaeacbebcbdccbceccaddbeedbeadcadcdaeebcbcccbbcadabdddacdbcdecedaedaabcbccbbcabbdacedadbcbeedabbadbddabeaebcbaecbadbddcbeeecceaeceadabadebdabebbbdedbadeadeabaedddabdbdadacbcbbdcdaccddebaddebbecacadcbdaaceeeeeaecaaacdecedeaceccaebcabeecbcdacebdeaabddebcdbcabececaccddbaabddbaaeacddcdedcaecaebacdadbadecbdeaeaedacebdcdbbccbbccbbcedabcacedbdbbdcdcceedcadcddebedbcecddeeeebdadbbddaccceccaeccbaaaeeeaededaabaeaecbbbaaeeacbbebaecdbbbcccacdceadcebcdeccdccbaeedbbbbcbbedcbbedbeebdeebbbeaecdcdcaeebeabeeeaaaeabeeeebeedcbdddbaccdbbebbcdbdceccbeeaadaaebcbbccdecbccaacccbcadddceecaccadabaaacdbacddadebebdcebbdedcbdbccbdacbeccebebaedaadbaceacaebcaddabadbcbadaceebddcbbdbbdcabcaceedebeacdadecaccdbdbacabdecaacbcddbaebeeebecabbacedbddddcbceeeededebdedcebcaacbeaabebceebcbceddddaccacabbacaebebdbbacacbadccdaebdaeadaccaccdedeeeddaedcdbdeebaacbddbddededbcddebaeedbbbdebaeaaaeddaeaaaeaeededccbbabddbabcaaacacacddaedcceadcbecbcedeaedcebeedddcadedbeacaeabecdbeeacbebddbbababacdccadceceeeacedecacbdaecadadaadecbeddedbaaccaadbebdcccddcedceabdebebcaaccadbacbbabebacbbdbaddaacebeedebdddaedaaeececbccddacbaabaadabbeebedbcaaaaeecbedacdedddcbaaeeeddbeacabbedbceebccceadbcaaabecbdadbbccaeeaeaccdcdbbdbdeaaeeddbbdcedcccedddeeabeacdbbacadaccebabcabedeacddebdaceddabdeadabbdbadadeebebdeeecbeaacbcabcdbdecabeeeccabbeaaccbcedcdedeeacacddacadddadecdbbcdcbbeaddbbceaecbcdcebbbbaaecbacbcceaeebdddcdcceacdcccaeeaedcccdbaabaadcebaadebcbbeebcdbddcdaebbdbcdbcaebdcdecdedbcabbdadeecebbceddbbbbeddbabcaebeddcaddcadccaeadaddabceeeddbbdcbcbbaabacdebbadddaabdbbbebbcbbaccecddcdeaabecacbdbdcedbedeabcabdcdceaeebbcdddbabdeaedacbcdcaaabcaabddbcadddeadeebdbadeedcccacdadaccadeebcabbdcebebdeeebcdeebbedbacdecedddbeeceacbbbbeeedbbcebddedaecdedcbcbacaeeacabdcbeccaedadbaaecebeeebadbeaecebdeabaaccdabbdbababceeeeaeacebceeabaddaeeeeeadbbdedbdbedcdbadcccaaeaabdcebbddddbcbcbecdbebcdeaeceeceebeeedcdcecbdacdbabdddcdaebbdadaecaaaaebaaceaceccaceddbedadbdeacaeadecddbbbebedbdddcebddedeadbaccaaacbadbccbacaadecdddcebacdacbcecacceadadabadcbccdceceedeeeacbababdccabacbbdaeeeeaceeccedcdeccaaaadbbeaccbaddbdeebcecdcaceecbecbddeecdbccdcceaaaecdeddbbbedcacdbdaaddbadcedbbcbaedecbcabedcecaecccdabedbdeebbceaaebaedcbdabeadbaceaedaebdccebbdccdeabbebdedaacdddaaeecedcdeadecacdddbdbceaabadcdecbecebbcbababbebaeacbdaeacddacccbbbbdcaaeddcbacecbcedbdbaaecabbecbbbebbdccacbeaeccabadddbbecaceabbaccdbddccadbddcedabedcedebcedbbbbbaddbbaecbdeeddccaeceddbceddebaccbcaecbecbdeeddeadabecbbeedcaceaaaecdbedbaabdebcceececdaaccaeaddcccdbaaccbeadaedccededabcddbbcccddbddcbddebbbdcebeadbbededcdcadeeeccbccbcedbbdcabcdaaeeecaeebcbabacbcccdaaaebbeedbeadedddeddaebcbbbcbdcddeadecccdbebdbaedeecadcdaaeecbbcacaebcaeeacddbeedbceeadcdcaaaabdadeceedeeaaccccdcebddcdcadecaccaeccebdddabddceccadabbdacceceaeeebdddcaeedddddaaaabaeddcdddcaaeceaecaabcdebcbcdbbedeacbedaaacbeaeeaaeeddecbcedcdcaeaceceddbeaaddcaaaecdcdccbeaccecbaeeedbadaeacbdedccaacceabedabddbeeccaeaaeebbdbbabeaebedabbbececacbeddeedcdbebdbdddbdacebbbbeabaaeabeddeddbaeacebbabeceeecdabaeadaadeaecbcdabbddbccacaadadcaeebdacebeaabeacbdbaacccdeeaecdecadcbadcaebdeadbcdcaeaeedcecbceedcaebbddeccabbedaceeaaaaabdebadbacbabececdbcadcdedcbdbedbdddbebddcecaecbecdadddbcdceedeabdcccabacdbeccbdcacdbaacbceedabcedeeabeeeaecbdbdbdedaceadaeeebdeabaacacdaadacaddbeebaddeddadcceeaecadbbccceaaddddebaaecedbeeaaaaacaacddccbddcdebbbdcecdbeeddbceaecdbeaeceebababaacbddeaaeedaaadacdabaecebcdcaabbaabcdcaaaedbbeddbadcdbbecdecbeadcccecbeebecacdbadbaeeecdccaeebeeeebadceaacdbbecdbaaccbcedddedddaccebbbaacbbdebbbaabdcaaceddbbeecdbbdaccdabaebaeeceeddeacdeeebbcdaecdccbeeeabeeeaccebecdeeecadbabdaadeedcbceaecadbcedccbcceecdbcaaabeccbeacdbbacccaaedcebaaedcceccbdeabeeeabbedacdbeaebcecbddaacdbacacaaccbdbedbcdcebddecadebaedeeaacbbbbcadeedcadeedbeaacceeabccccccdbccbdedbedddbdcbcdbaebdeebaebcacedccebaacaabcbdebddeceabedcccdaebccaaceddddeddacdeabccdbdeaadbcebcaacbababddaaedeebdddeebbaabbacbaadbcbebcabdeaacaeabcccccdbbbecebcbdcabcecccdbbdeccdaedacadeadeabedbcdcbebbcceaaecbaddcaedaaaebeacdededcbebdcedabdaaeacaceaeedadedbdceddedbacceedeebeebdbbebeacdbdeddecaebcddbbeccadcdbdadecbdcbbdbcbedceddadecbdcadcaccddeccaeabdedaeecbebdabcdeceebcdabccedecedbbcaeabdcdacdedebbecdddadbdeebcbcecccaadcebbccbbddeceaacaddedbadacedbaeaededadcaadabdceecddabddbaadadcdacadabeacbceacbdcdacbcecbbadebedaccaeabbacceebebbececbcdacddbabededcbbcecbccceedcbaaccbbedaabcaddadbebbaeaeaabbbacaaeccaeadeddbdadabddcdddceccabeadabedddeedcecbdaeeacadabdabecdeeddbddebedeaccedbeccdaaacccdbacaabdaadbcedbbcaaadcbebddbebddbeecaddbeddedeaddeddeacddbeacddeabddeedbadbeccdbacaddcdcaddeabbdeaaeaceeaeacbddcbadbcbcccaeecceecaccbeddabdcdeaebcccdbabaacabcdbcabaaeaebdbddbceaebcabeccbbdabbedaecbecaddcaeaaaebcddaeedccaaaebbbcddcacadebdbeccdddbaddadaddacbddaacdaaeceebdaaeebcaadbbeebdbdaabddeabbaacaeaaadddebbdedccebbdedddcaaeaadaabbbcdaacabeddddacaebbcbaaccddbccadaedaddbdabeccdadbcecedcacbcdcaddbedcdbbebedcabdcddeeaeabcecccccaedcbabedaeceacdbcdaedbceceedccbddbedaacbcbaeaccdeacaebececbbcdecdacedcabbaabbaaadaaaeacababceaccdeccdcdaadeeceaaecceebebacdcccaeecaaaeabcdbcebdbdcdeabaaabeabbcecadcedbdbcacaeecceaeaacbbddabbbdcecbaababaeacabccbcdbdaacaacbdddacabeebcdbadaeebcbdccbaaecbacbbcccbddabadcedbbbdaeabbecaddbdccaddcebaaaebbeccbcebbcbacddbecbbcabcabbabeeadccbdbdcccaecdedddacdcaecdbebddcddbebcddaaebbdbabeadadabcacdccbdacbbaeeccbbccbadbadacacebccbccbceecdccbddeaacbaaadcbccbbbcbedeabacaaabcdbebeedaebbdecbdcdeadadbaaaeccceedaadeedcabbadeebadaeccdabececccbbdbabdbcbdedbaeeebcdbaedbdcebcebbaaccebccbdeeebaccdedcadacbeedccbebebadeadaecdedeedaaceeacbeabdaebbeacdedaacdbcaddcaeecbcbbdeaadabcdbcdceadbabaabdbcbdebdcbdbecaedeeabddcbdeddaccddaabedbbcaededaccdbcbccbcadbbbdebaaeebadbacebeacddeaaddcecedacbccebcbebbcddeedccebaddbcebeaabcbcbdcecdccbcecbbecaaceeecddddcbbceebcaaaaacbeebdacdbeedabeebedcbdbebdebedabccebcecaeeedbdedadedacbacdbceecaccaccadbdcabacbcabcaecaadecedcaababdbeebdadcdccceaeaaeaccbbaabcedcdbaaebbcaaeebeabbadbeaddeddedaaabbeaacbddecaaaedddcceacaddddadbbebcdbdbaadebeacdacebeceecdcadceaaaabecebeeddccccbbbaacdaddddcdccacadbbdaaeeedaadbdbcdaeabacbabcadaaaabbdceebeeecaebbddebecaccaadedcebadccdeadeebadeeeabdddeaeccbbcbeccbeebbdabbdabdadceaeeacbbaeccccbbbaeeecadddcaebeecddcebbbaceabeadddcceaaeacebbbcbdeabaabaecbebbecbcbddecddadedbdcaccaeebeabdcdbedcbddabebdbdbbceebbacbccbeddaadcaedadebeacddbbdbedaecaccbdaddebddcaebaeeabdabcdcdbeebeedddbddbceacccacbaccaccbedeedcbaaddaecbbaddcbacadcabbeabedaeeedbabcddbccbcdabebcdededdeccaabaabcbbeaaaaaaadedcaaedbcbecceecacacdacbbddedaaddacceeaeccbcaddabcbccdaaaeebaceebbaacbdadcaeaeeedabbebccceebabdaccedebabaacddbceacbdccddbdebedeedccebcacbdbcddeddddcaccdadeebdadbdacabbcdcdecdccbbdadccdedcabeebdecdeacdeedcbabeaccbbeceabbccdbeeedbccbaccddcbaaacebdcaccbdabeaaaddbdbbaeaebcdcddaccdcedceabacecdebabbbcbeabeaaeebbdcbdcacedeaedaedcabeeaeeaaeaabaaebbbebebbdabadedaddaebbadbaebbecdbadcdbbdddadebaecbabcaadedeeecacecbdabaedbbdcbddeecbdabecddbbbeeddbaadbdaacddbaabdeceaecbecccaadbbcdcdacecbdbcedabaadbcbebdcedbdaedbeebcddaceecbbdecaccbaddedbbcebeacbbaeeddebebdeccccdddedbaaeeceaddedcdabdaddaaecddebbddbaecddecaedbcebbebaababaeecaecaaabaabbecaabeaabadbdcedcdceabecdeadaeadadaaecdbcecbcbceeabeebabbdebacaeeacaeabeacbabeaedbecdbaccdeddcabcccddeeecbedbbceadbecbbaaaceacecbccdbeebceccacdeeeaaacdedaceeddaaecaeccebaebdaeaaecbbdacdcddcaeeabdbdcbedebaabbbbbebbcdcdcedecedccdebdceadacbeedcedebacdadebdbcdceacaaeeaaedeccdeadbdaadaadaeceeeeeedecebcbddabbccbdbedccbeeecdaacdedeeccbbdddcdccddcabaccaeceaeddecaeabdeebbbdddbaddddcebebeebadbdedecbedeacaebdabaebbdacaaecbceebaccadecbbdaabadabdbbebacbcaccccabeeeeabbeedcdebbecedebdeabbaddbaabddadbabacbbbadadadcbdcbbcadddbdaedecdedaecbcddaccdbbdbbccecadcabccceddccceeeddbccdbcbadacabcbdeaceadbaabbccdaccddeccabebedccacacdaccaacdbdabcccbdeadcabcbbdcbccdcaddaeeadbccddaadadcedecedebeeaadceadddecbbdbaadcdebeadbcaabcebacbaedecbdcaaebeaeadcaeeceaeaeacbbeeacaadbaaadacdccbdeecaabddbaddcbbbdbcbcebbcecdcaebcedadccddaacaecbccdbcbeeadcacbbecdadccceadcabbdddabbeccabcbbcbacaebbbdedccbacdbbdccecaadaaeaebedeedcebdcbbbccbdcabbbdbaedabcbcbecddacdacedacddaaceeeecedcdbcdbabecebccadebcbccdeeedaccaeedecebcbbbaddbbeccbdcdbcdaedbbbdcabeaaebaabeeccadcacbacecdadbaecbdeadebceaacebcbdaaeccbabdcadaacddaabaacdccadecedbbdaeebdeecdcdedcdedbebacbaecadacbcacbaccceabcbdbacdcaebbbccccceacebddedcebbdacdaebddbcadcbbdbcacadaabbabdebaeadcdcebaddccbcabbdddbcbebbbddeacdaadbdbaecdbbcacbeadabeaacdbeeabbebaddeaacaeecebeaecbdbeeaccedccabbacebaabadabcbbeddeaabebbdadcbebabdbabaccdbedbdbdabbcacabcedaeeedceebacbbcbcacecceacacbecbedbcacdbbbeeebbbcdadcacadedbddccdedebbabaaebecdabbbecbadacedabcacbcdedcbbdadbbebcdaaeeabaadbdeebebccdcbaedcbadebdcddbddaccaddcdaaeeebdbdcbcababeddceeaadaeccceecabdbccbeeaacbaeeedddcebaabddcbdcabbbdaaeacecbbbaebbaadaedabbaedcdccdedebcaaabedabdcccacbccdceaddeedecdaeaacceeabeecdcaeadededccdcdaaeaebaadadddecdecaadeeaddbdcbadeccbdbbbcdeebbddedbaecaedddeccceeecbdccbbecdbacddccdcaaaeebbadbcaeeecbabdbbebbabdcaaaabedcdcddabddabedebdbdecdeceebeebbacbbbbccbedeedccbddcecacacbaddaeecaecaabdaeeddcdccbcadebadcaeaacbcddaeecbbeceebebbdceaadbeeaedbbdabcbddcacdcedbdbebccececadbebaaabadeddcccbcebbbaeaaadbbedaaadcdcddaceabdaecbedadbdbeaddddcebdaacdddcebebbacaacdcdcaeaeeaccbeccdaabaceebcbeaccccbdacaeceacbdcceaacccdddddcbbbdbeaeaaeebcddccbbebabcaaadaaeaacebcaaecdaddabbbaeebadcbaabdecabedbdbbbcceeebacdceccbcdbebbdcaebaaddeadccbdecbaaccbacabbaddccaabaaeaddccccbdacacdacbbaaeadeeeabdcabccaacbdabccdaddacaebebbaceacdeeadeadaacaedabbaddeddcdeedebabbceeedebeebaeebeadcedbecdbbcedecedcccdadaddbbeadcbeabecebadddccdccebbbecbebbabbcebacebbcebdbebeacbedcddceadcaedcecedeeaeecbccbedaadcaacbaadadcebdcaaadbeabdeaeccdabaacaacaaedabceadaabeeaabedceacebdbceebdbdeecbbaaedabccbcecbdedacabecebaddddbaebebdacaaebddaeedaaeecccdbaeecaabedcdcbaaebcccceedabddadaaeeaadebabacbbdcbdaddbcbcedeccedccbddcaedeccaccadabddccdaaeeacbabdbbccedccdbaebaaddeddaccdaeaebeacdecdccabcbecdcecceabbebeedbabebbcacabdebabcddebeeedecaebddadedddcdbceadaddaebceecaeeecedccdaeddadecbbdcaebdecaeaaedccceddcdecdacaddbeedecacaeaceccdbeddeccccebaaedbdbcecdcebbdaddbdadaddbcadddbbcddaaccdbccbbbcadcddbbcdceadbddddebedcedecaddecaadeceaadacaebdcebaebcdbeadaebccbadcdadbdcbeddabecdbbcaeddeacaeabbacdbacedbcaddbcbcdcabbceedbeeaddaacedacbcbcbdcdaadaaccecebbdeaeccbdbdceadcedcdbbddbaeadcdbcbdebceebbdaebecacdbceaacabbebacaaadadcabbeddcbdbceaadaaebaedabdabbecdaccaaecbccdebddcadeedccaebdbddaaeaddcadbaccdcbbecbebaaaedcabaceceeaeecbbeaedceebcaecbdddeeaeabedebeddbadceecaddacbdcedabecababdcbbdeeaeaadcdbedaacbbeeeeedbdbdadabdadbcbceaeecacbabedacceebcdecdbedeedaadebdeedadbdabeeaaddadbabbdbbccebdaccbbbeceecbbbebebcdcdaeadcddcbbcddaeeceddaadeaddaeabdbaaceeaebeacdeebaaecebbddccaeeaacdcdcaaabcdaaceadaedededeeddceaebdbdbbeabcbcabcbccdbcdedbbdcaaadacbaddecedddcbeebdecbbccccbbdcdbbdcaccdceaccbeabbdcacadcdaceababdeccbeedaabbdacbacbcbebecaedddaabadcbbabaecceacababbebdcdbbbeebeaecaedaeaedeebbdaebccedcdbdeaeabebbdccccceabcabbecacaceedbeccaaccededccdccadceabaebcbcaadceabddadedebcbceabdaaecbeabbaddbddcdbcbabedbaddbcaaacadbdcaeebccdccbeeccbcbaecaeedbeaadeebdcecdeadddaeacadebaadaeddebeccdbccbccadddebededbadbcedbbaddbcaaacdcbaadbcdcccceebddabedcaabcbbaeaabbadaaebebdaabdecbdcebbceedebbbccccecabccadceceeddccbdedacbcededbedccdbddebdacaccbadcebdbecbcdcebeeaadaabebcbddeabeedbbbedcbcbedaadaeebbaaacacdcabbbaeeecbeddcacbdbcddbccabdcbdadbcebadaeecebdebddaadbdbadbdbeceabcccbbbcdebdeccaaceedeadaddcdccaeecbaebabdebabedbcedbaadcaaacebdeaabacdeeebedbacddddebaddabbabbeddbedbeaebcacbdcceaaccdbbdbabadecedeaeddddebbbeabbddcbdceccabcbacbdcdbaebcebbcadceecdbadaadecebacdecbedcebccdbdacdbbaaeacaeaeecadbabeecadaeaecdcaeccaacababdeebdeadeeeeaceebbccdecebaaabeccddbbcaebaaadaabbdcebccdbcebbcccecdecdbabedbeceaedccaddabcdabecaccdbbedcdddccebacedcebebabbdebddbdaeabeeaceddaabcbaaadcbbbbccdcccdbdecaccbdaacdcbebcbdeeddaecbcdecbbbbcdedeaeaccbaddccdaaaedacbeaaabadeaecbbdcdedcdccedabceecccbdbbecbedaacabaabdecbebaccdbddcebecdcaadeadbaaeeaddbedcaebbdccdbdaedacbaaddecadbcbeedcbaddebededacaadadbadbccbbdbbbcceeaceacaebbdbdacedeccccccbaeddbdbbcddddecadebaababecadbeceabdecdcbceacbdbcabdbdccbcceccaabeadeadddeeceaadeeebcdacaacadecddadcdbaaaddedcbcecdbceceaccdddbabeeccecdcdbbaabeaabcbbabbceeedcbbabdbdbcdbdabccaedcabacdddaaaaaadcacaaaaadddcdeabbdcbeeeaecbceeecebdcedabbdbdadeceaacbceebadbbacccaeebddeaabecccaedacbdededabaddceaddaeceeeeaeddbadadbbcedcdcdedcedaaaeddcdeecedadebbceaaaacadddedbbcecceceadaadaacaadabdebebbadaabbacbecceaadcbcacbdabccacaaaeacbcdaccceeebebbdcaaaaaeedbceedadbbbaabeaaacabaebbccaaebdcbaebbdcdbdabaeceadecebcabbddaceadcbebcddbeccaebcdbebccabeacddaadaabbddeaabedaeadceccceebbadbaaddcddedcbccbdbbbdabeedbbdbddcddaaeadcbacabdcaeaebadcdcbaacdbadacdaaeaacbcaccddbddbaecbaeabacbeababcdbecaabdbdabeaaabaabebddadccdbccedcbeaabddddcecebcedceaadcdceebbeabadcdcceabaceacecabbdaacbaeeaeeeebeedbdeaaceadccababbeedccdeddaebcbbdeddbbbdaebcccccccddaccbcbcabbbbbdcdedbabadedbbbadcbdeeacbeadebaecedcaeccbeebbdebceedddadbeabdbcadbaedccbddceceacdabdcebeeecbbdbddeecbbcebdbdcbcadeaeadacabcbbedcadbcdceacccaecaaeebedcecebddabaecaeaeedebdabcdcceddcddcaeccdbabeeccacecdaabadeaadeedcbabacbbbdbaacacdbcbacbcdcbeebbbeacbbedecdabacdcdbccbbdcbaedddbecbbbeeabdeaeecddbcbceadeaeeddcdaaceaecbcdebaebebccbcccaebeccedabbaadabeedceadebcadddeadcccddeeaeadcceacdabaccadaebbacdeeddcbaeaacbdbabdbcbedebabcdddbdaaddeccbaaaaebacebdbcbccedbeeedeeecbcdcddcedcbcddcebebccaecaebbacebcebebbdaecbebebdbeaececbbddbddbacebedddaedeabaacbcaccdbacdcbdeadeabaedbdcdaacbdaccebdcaebacecaadbabbcbdabdbdcedaaeeecdddebddbaaeeddacdebecaedacbebebbcedacbcbcbeaceacbbcdcdedeeadccabbeaebceecdcdccabbcbccdeccbeadbcdabbedbcccddaacecabdbbebaeaaeecbdcebacebdbdabddeabbcbbacbebaedbbbcaacadcbecadcdeacabaabddeddbdbdaebbaeeaddaecaeabadcabccbbcccadcccbabbacedbdaecbddccabdceaedbedcebccaedaacbeeeccaecdbaabebcacaadadbadebbcaebcbeaacbbcededacaaecdeabeacaecdcbabbedcdcbbbbdbddaaceebebebacaaacdcccdebbabeebcbadcdecbedebdeccdaadbeeecbcbdbadeaedbcdbbeeecaacebdadbbbbdaaaddeadaacaeebebdacdbdeacabccbebccdeeababedbddcaecdedaececceadecedddcdeadbbbbadcdacbdcaaadbddbceaeaadcbaeaaaaeabeddbdcaedeeeaabadaceebcbddebdcdaabddcbbeaaacbaedbeccbeabdedabcdaddabaaccbedceccbeadeaadabcbbbbeeabdbcdecceccabceaaecaeacacdeacdeeeebcaaabcbcabcaeaacdeccabedbeadbbdcbcaaadaebdaecdabdaecdceebbcbbadbcaabadbdcedeaabceeeebaeeeecabbbbaadcddaeacddecaaddeaededbaeeeabbcdcaaacbbeeaaebabaccbcdeadeeddceccbccabadcbecddbdcbcaedcaaaddceebbcbaacdcbabcbdaecddedcaacddbededadbacaeecdbcacaeeadeceadbacdddcdacbbededcebecbbcabcdbdaeddabdebbbdadbcaccbcbabdbbaedbacabddaeedccaeacaabdcdeebbaddccaddabbeebaccaaaedcdbcdecbcadbcedbcadebceacebbbbdeecbcadcabdacdbeeddacadbeeceeeaecddadacccebcbcccdbedcdccabaccdcacaddddaebddeadbeeadaaaceceedeeeaabcaadaacabcddeccaadbdebdecbdeebecabceccdacbcdeeccabdbcccdaddecdeaebeabbecdbabeaedbbccccbdadbdcdbdeebccecdcbcdcbaecabbacdbcccececedaabcbacccecddaebedcbabaeecbbbccaadbabdaaaaeecdedcdeadcaacbdbaecdcddbebddbdaabdedaaedecabeabdeeacbbacbbeaeeedbbdeceaedaebeddbdbcecdcbcadcbecebdedaedcdbacbeeeddbcabebccaccccdaeeaecacbaaaaaeaaaeceaeeebbebccacbccbbeaeaceccbddecbcaaabcebceddcdcbabddabbbbbcdcedbbeeccbccacecdcaeccacbabebdaabccaedddeedbaaadeaabecdeaecadcadcaebdddabdabdabbcdaddbddedcbebbddccbdeaaedebcdcaddecaacbaebbcaadbabedaebaedbceabaeddaeccdcceaeddadbabeaecaeedcbcaeddeeacbebababdbddaaaaecbbbdcdedcdeecbdddcbaeecdbdcbdeceacebadbcaaadbcceecedccebaabadaabcbcadbceeaabecaaddbaaaebaaededcabbbddeaeabdeeeeabcaacadeaaebbeaebcbdbdaeeadbbcceeedddcaebcbadccebadcdacabaacddaecebdababaaadaadeecbbadaddbbbcaacdeabaacabdaaabbbcaabeeeeaccdbbcbbcaabcbebddccbbdabaadedbaebcbcaedbdaceeeaaeddccedcccceaeeacdbcbcbecedcabbedbcaedcedebadadcaedeaaabcbbeacadcbdccbbadedeccccbbdcccbccbccbeebebbadbcddcebaaecbdbbaccbeaadededeecccdbaaccddecbacedbcacdddbdeaaeeecaeddccecebeabbaddecaddbbbdbbbcdbeaeebeabcdcdbdeadaedbecddddeddaaadbeabebbdabcdcdcabcaeebeeebbceeccedcaeeddeadcdecbbebdbcdeaaedcabdebdecceecddabcdcddcebebaadbadaccdcabbedaedaacccbcadaeebddacededceccedeccceeeecdcebcaccadbcbdccbadbddbccedcebeeabdbaebeddcbddbcceaeecedcbcacaaccedadbebddddeacbabddeadababdaeaebdadeaebbcdcebdcccdadddaacbadaeddcaedcbcbacddadbbbebbbeeaeeaebdbadabbeaaebaccdedbcceadbacdeceecebacacaccabeaabadacaaeccdaeaebacdaeddaaebacecccbcdeecbbebbcabeecebdddbcbbaabaaabddcdcccddbdadeaeadcdcecacbaecbdaebcdcdbbbbbdeecdbdeccdeccaaecccddcedaedacebaaddddcaddaeebeaececacaccaedaeadcedecaaedcddbcaeedbdcccdcedaceeebdaebebddcadaddecaddadadcdbaebddbcdabcabbebebebcbb dccdebecebdcaacdbeaa