babedbedddddabcebaccbdeddeccbecbcacadccddeeddcdeaeabccdbeadddebbdcadbddbccbebdbaeaacdbdcebeabdcbaadbaebcdaeccbcbdedbebaccbddabccabbbecaabcdaebcaddddbaaedcadbabebdcebdcebabcdceeeccadadcaccedddbceebcccacedbdeaadbdebeadedaeddbbaedabeaaebbdcbcdebaccbbcadaaadeeddcbacaadeccccdcbdcceaaceccebbdacadedadeeeacdecaeaacaeacdcaaacedcddddbdaccccbedaadbbdaedacdbcaceabbabdcbebbcbadbbaebdacbbbabdddecebebddcceabaeeaaecaebbaabddbbbbdebecdddcbbccadddbcceeeacdcadbbcaadadcabedbbeacbddbbbaeceedeccebacdbccecdcaaadaedbbadabeaedabacabaacdacccbbecbbdbdccdccddbbcccccaebdddababcadeadecbaecedadeacacdabeabbbbdbadeddcbdeeceaecdabcbbeccebbeadeaaebceaebbccdceddddcdababaaaaddcbedccadbcaddbecbadacdbcabebeddddadaebbdddcabadeacadabbaddcccceadceeeecdcacdadedbeeebecebaeeacecdbcbecaadedbbbebbcecceaddcaaceddeabdbadebaddaeedaacdaecccdeeeebcbdebeeabcecdaecabbdbeadacceddcedcddadaccaeeedcbdddeeebabbebbbacbccdceddedabebecaacbbebbbbdabcaebeaaebdebccddbbacecaaabaeadacecdabbcacabcdbcbcccbbbceccdbedcdebbbbcdcccdabadddaedaccacdccacdceecdeaadddccecddebeabdbbacecccbddedaceaadcddeaebdebceebddcaedddbdbddacbcceebebaacebcedebebdbecceeccbccbbccdddbdceaeeadaadbbddceceddebdbedcabdaaeccbecbccebcedbcaaecccaabebbccbecddaccbbbedbdbdacacaebecaceadadcccbedcebecdbebdebadadddedaeedbcddadbaedaddadadabadadaeeedcadbecbdedcacbdbacabebabaaabddeadbbcebdbecaeceebdbddbcdeabadebdbadcbadbcdbbadaaddceabccbceabbddacccabeebbaceabeebbceedbdabcbceaeeeddbcbcddcbcecccdaebadabbceeacdbebeeabcbadcddaddaebaabdbcbdadeebccbaacedadcbbcadbebccaebebdecdbedbedaeecabdebeadcbcbcdecebadbadbaaddaecdbcaeecaaabdacaccdedaecacbadcaebbcabdeeaedceabadaaabddabeddacaccaaaeeaacccdecbabbdbcbbbeddaabcdccdbaccdabbbdcedccdadcebcdceaebceeccbbcadabbcecadbdeeaeebaebcebdbedcedabbaeacbabaebcddcbcadeaaaedbadcbaceeebeedbddacaebaccdbdceaabbedcbdcdabdcdabddbadcdaeaaaceaaecbdbaedecddabedbcbecbabdaddbcbaecebbcaabeaccdccecacdacdebbbbcddecebaadeeacdbcbbecbaddbbbdceadbceecbceebbdbbabdaeedbdecacbdccedccedacbbbdccaccdabbacedabdccadedcbcaabddebbddbdecaaeecaeeceacecedbcecbeacabcaeeadabebbddbdeeeeddcedbedddeebabadbaddeeedcdedbadcccedcdbcaaedaeeccceabdaadccdddcaabeddbedbddbbaaaebbeabbcaacedebddabaeaeccaedaabbedbcaabdabcedcebadacbeeecacbdedebeacaccdbdaeeccabdebaadecececaedaaccbbeddeaccaeecabeeeddbcabdaabaebadeeaddacadadebcaeebaeeaebbabbbaedceddbbdabdadcdabadeebebceeacaeaeabcadeeedcebcdaabbdcddacecbeedecacaedebaceebdaccdaabccedbdaadbaabdbeabdbdaedcaccadaddecedaebbabdbbdbcedbadcacdccdceebeeaecacebbababeccbdbbcedeaaabeecabbedcacbeaceddeabeddadeeadaebeddadddbbeaebcbbaebecaacddcaadcedbcbbadadeccbeebebaccbdddebebedaaecabcecccecaaceccdabbeaaeaacedbcbeadeeeddbacabdecebcacabcddeabacdeeaccccacdbbabcdcdbbdbadaccaddcdeeddbcebcaaeaaceaaebabccadbbbdddbaacbdacecacaceacdbdebdecebabeaacbacbebbbbabadcbdccbaeededcaeaceaadbedcbaadcbeadabbceaceecbbccdaccadcbabaaecedcceaddabecebbabebeecbeeedddecdcadcddedeaacedeccbdccbdebadacbdcbdaaeaccbcacbeebabdaacccbccedbcaaadccaeceabbbdbdbcaecaedddcaabeeccaecccdaebacbbcdeaaaebcdbbcbeddeadecdecccabbebbdebebaedbeaeeededbbbeccedccdbacdbaadadbeaeeaadbbebabcdeebeaccdedcecbbdebbbdeecaabacbaadabbebbeddebdcaddadeedbbbaabccdbadebdaecadabbddbbebebbdadededceaaccadeeaabacdabaaceebeadaedbdcadaacaaecaadcbabbccecbebbdeabdecdeeabdecccbabccdeeabdbacdbeecdaaccbcedbdaeddaceeaedaacbbdeaccbcdecaeddedcbdcedcadceeaacdbbaedbecdbbaebacbdaebcedbcbaebbeebbadbbcddedeadaeaeddddbebdcedceadedeccaccdababbdeeebddebeeaddcbbaaaedbdaaceccbdeddeeebedddadbcbcedaabaaccebadaadadcbbbbecceceedcbedbbecceabcaabbddacbcbbcaaadebbbabeaeaaaeaebabdabaddeadeebcededccdebaeaceeddbaccccbeaceabbadaddacaccaceddaaadeeecdebcddbcdbcdcdabcdddcaeddeaaecbcddbecdacbebbacddaabaebabdbeeedadacedadcbacdbececdcdcaeebaeaebcbbeadcabadcdabcbeeccccbcbebaecaabaedeeaeaabbeeeccccecbbadbeddddcaaadbdbddcdcadecbcdadecbcccacbecdedcbadcdbedbadcdceeeaeeacbecdbabdbbbcebedeaabcdeabbdedaceabecdabbbdedbecabdeddceaebeadbbebcbbedeadbdaebaaaadcebdcdddaccbcbddeddadeceaceeabdeaeaaabdbabedcbaceeccedecedecddebecbababddcbbccdddbdbbdeeaddbbcaadaabbceeaecbdadbcbebbebcababccabaadcdeddbcabbbaebebbcbcdbbaabcdabadeaaeeddecebdebdbbabeaeacedddeaabeceddcdabbdabcbaebacaaaceacaeeacaedbadedebabbabebdecabbccaebadbeddaceddbeadededbdddedcaaaabaabbebedbcaeaeeaceddcbeceddbbddcdbdedcecbdacdedbaaacbaeeedeecaedbddddbebabebcdeadbeadbaededaabbbddaccecececcbbdadcbcdebcbbebddeedcaebbdedcbdbcdeaebcdaeceebcbecdabecbdecbddbcecbccbcdacaecceccbcecdcebdeabadacecbcedbceeabeecaebdbedeccbedcdedaacaecaadeedcccedaecaceadedcdceadbbddbeeadacadadddaedebbccbdbdbdccdbbbabaacabdccbdddedcddeaddbdecbabedbdecbebaabadaaaecceacadedbeeabddabacdaccbbccbabcaabebceeeeccebaaabcaebbedbddcdaadedbdcbdacebcadcbbbcdcbdedbdeecbddaedbeebdeccababcedcddaeecddebbdeedaacabacdeacdacabddaecabcdbdadcbadedeaeebadcdccebbcdcceecceebaaeabaabdcdadbdbecbdaecdbdabcababbedcbbbebcebebcbdaedccbdadcecaaaadabdeddddcaededdcdcdebcdcbececeaceaaaabcbedeaaadcbbeccddcdebbcdcebaecaadbdccaeadbeeacebddbbadbbeeebdbcdbeecaacbcdedcbecebdbcaeedccdbeeabbdaddccacbdacbcddaeadebcbeccacdddddceedcabacccddbdbcebbbbbccdbdbadeccaebeaacceadbcadbadccedeebdcaedeedadababacebabedeecabeedceecbbdeccdeddbddadeedccbaaddeabeaaecdaabdcabbdcbdbcacdadabcabeebdebaaadaabcdbbbacebaeacddbabeecbeeebeccebdcedddebeaeeadbcbbcaadacbebcaedacbcdbcaacaacabbdbedeedbbdcccbdbcdbbeeedadadcadbddaabbbdabeabdabdcdaebcceaeddcddddbdadedbbcdadaaeeabeedbaddaebcbdbeedceacccbbebcbbbbbcdbceeeaeeeeacdcbddaabbcebbbdbabdeaabecadccccedddbbbddacaeecdbbadcccaadebeadddabcedaacdaccaeaaeeedbacaaabacabecdbbcddbeecbbdaeebbaaaecbeadddbdadbbdcddbebaddecdeddabdbbbbbceebcdebaecbbdddaeddcaaadabedbdeadbacdeedbbabbaabcebdedabeeaabecccacceedcdabeaccdcedebcdebccabecebeeecbcdededcbceebacbbbbeeabeceaeedddedcccabcbeddbadacdabcbadeccacdcebcaeccbeaacdabdcaadcbbcddbebdbcaeeacccedeadcbbedbabecebeaeedbadaaaaeebeeebcbdcbadbbcabbddeeaebdecdcbcbbdbdbcbceeecaeeabcccaccebabdceeaadddbebcbedbccebcadbcbecaedcedddddcebbdacacdbaadcbdaeecbcdabddcedbeadeeecdbbcddcbbaddaaaabeeadedbaacdeeeebbedccdbedbdebcccbbaeeadbbaadcacdcecaaebddcaeaeadbdeebebccbddcabdbaadeecededdccdadbdbcceccededaaeecadbbabdeeeeabaaadccadbdaccedcccceaeecaceedebdbeaeacaeeabeedceeaacedbedebedbcebaebadaeedebbcaddbdeddeaacbedeaebbdacdcebabcdcdbacabbbedaeeacabbeecaadbdbecdedcaeeacabbccbeedbabebeaeceadbedeeaeabecdaacbcbaacdeddcadcebabeabcadbdddecbaeacbebbaeeaebadacbaaedaccbcacbcabcedacebadbebdaedcdecabcaddceddbadbcdcaddccabcaddedcbdecdedbbaeabedbdbeaaababedccdcdeeeceeacdcabebabdbeaebedaeebdadddeacddabcdaceddccbbdbeedabbdcedecdadcaccedebdaeaccbbbebbceabcdaeaeaeccdbcbaadbabdeeabdcddedacbcdadeedabceaddbdacedddcedededeaeadbcacbaddccabbaaaabaacbdeedbadeeeceacecdcbacecbaccbcdecbcacadcbbdbdebcedeadcbedbaaedaccebaddeadacebcdaceadbbcabcaccebbeedeabaeabbcddcebcdceebcbbacbcdbecaecaacebdacaeceacdeadecddbdedadcdccabbddeeabceeeecaceacabcbcbdcdbbbcabeacbecddaaaedbeccdacdcaabbeceeebbdddeedbcaebcadecbbbacddbaddcbcecbeaceadceacecbaacdeddadbabaeaabbaeaeaedbeaecdeecebacdacdabeebddddeeeadbcbabbeeaceebdacbadcbadebcccaeccdaebbdedcbbbcebaeadbaacbadebcaeccacdcabdceeaabdeabaaeaccdedcecdeeeadcadcddeecbcbdabebacdedcdcbbccbcacceacebacedaebdbdacbbeccccbdecabbdbecbcbbcaeaedacccadaabdecaeeedcabcdcceedddbacadaebbedbdbabecdaddebbbeacddeaccccaebaabacdaebccbecdacedacdbcecddcbbeaabcceabeeccadbdebdbcddbddeebdaeeababdeeeccabedcccdbebdeeccacaebabaaaadcecbeeecdbcdbcecccdcebadbebccbaccaedeadaecdedcbdcaeaacbbbddccbcceaeedcaadddbabddadabdabdbcacebaddabeaccebaeccadddeebedadabbbbcedcceabaebaabacdadaebebdcabdedeebbedaecbedaecdbeedaaabbaadaedebcebceedcdaeeadecbbabcedccddeecaebadecceacbecbbcadcccbaaebbbacaeceebabbcbaabbcdedecebebaacbdeabceeacbdedeaacedccaadeedcaabebbaeeeddacdbcdaaadaaedadabaaaeccdcaaabdebadcdbaaaccdcecebeccabacabbedaccbaeeacaeccaaadbebacbeecbcbdbbdccdadcacdeaadaadebebebdedaacaabccccddabeacabababacebcbdddbddccecaebddddcabeacdcdbcaecacdcbaebceadaccdcaadeddcceeaaeeecadedbaebcbdbbbdbcaeceabbaccabeeeeeaedbbaeaeeadabdabbaaecbaeeceadbadddbeecedcacacceceedbbabcaedeecbacedabbabdaabecbceabcddcaeabeadcdaebeabbcbcddeccbdbaeabdebecbaeebecaaeeebeedceeaebeeeaedadbabebacdebadaccabdbcdcbecdcdebaeadabdecbaabdbddaccceabeeacddcadbadacdbbecabcedadceddadaaceaeddeaeaaaeadacdacdecaecddadededaacdacaedcccbcebddcdceaabbcecabcdebabcadaddccaeabaddabcecbbbcbaeedddaabacccaadbaccdbbdcaeceddaaaadaecaecacbcabbdceaeccaaaadccaacdeaaeabbcedaceeeddccaeeaadebceedaabadbeabbabedbdebacbeccaddcaceadddbdbdeedbceddcacdcdadbecdecadcdddeececeebdbccbeacdbeeebceadbaecdcdadddedaddcedddebebadecbccdccdccdedbbccacaaecdadccedacaaddacccbcebddcddeedbccececccedabcbbeaaaadeaeadbcecdcceccbacdddacbbbddcecddaddcaaeeccebbbbaaaedbceacedbbeeddeeebdaebeeceeddacdebdeaedebddbddedcdcbddeadaacdcbaaeacacbadebdbedcadabcbbadcdddbdeecadeddecbcabbcdabdbabacdbececaacddaabceedbbaededeacbccbbedacbcbabbdcecbcbaddbbbccedbbeeeebcdbaaaacdceeaedeacaebabcaccbebaadbcedcececdcccabedbceaeddccdbcbdedecbebdcdeadcbecaedacaddedabeeddbeecaeddeceaebeaadeabceebcbdccbecaddddddacdbeabeeccbdbaadecccadcbbbdbaedcedacdebccecadcbddbebbccbebbbabaeeeddddcbaabbeebbaecaccacdaebedddabdbbabbbdebdcbdeaeaaacaedeacdbdebacbdcccbcbaddcdbabdebbaceabcbcddbddbbccdeadcdddeccbcaebdaecbcedaecaabaccddecacdebccecdabeebaaaebeabacabacccbbccebbbbabbeebcaecedbdbdbbdcaabbbcadcecdabdccccedddbbbaadeaabdbdecbbbdeccaedaadadedadaedaddbcdeddeaadcebabdbddcaeabdbddbceabdeaccacdacdaccaaadcbbccdacbeeacabddccbeabbeeaabbdebeeaacdbdccbecdeccdbbcadacddcbeadcbedeabebbbeaccdddeecbdaccceadacbaaeebceecbbbdbcedaabcbaeabdbdbdadbcddaaaecdaebacedbaeaadcdbddaababeeeadeeaaeeebabdeabeddbdceedabaebddbaeecabdadeddedaaabbaacbaaddbdeadeabeeadccebdcbbebccecebebcadbbbedabbcdeeebbbccaeebbedeaeddbdedaaeacedaadabaacddcbcaadeebbbcbaddcdbdaaaadeaeaddabbecbccbaeeaaaebaebcaeeddcebecbcbabddcebbabeedcbeddbaaccdecdcdecebedccceebaeeecbadbbeedaebdedbecbabaeecbaacbbccadbdeecbbceacecaebbaaeeebbaacbbacaacdeacbcebdbdabeeceaceccdbccbebacbcbdcaadddcbcaeddcbeaeaccccbccebdddebaeebccaaecbcbbbcaceaaeccbadabacddceceaadbeaaacbddeecbeadeeaaaecceaebeabebbdcdeeccadaebcbaadddbbbeadbeeedebaedeaabebeddeababadeeabacaabcdccaaeaeaddebabccebccbeabdbaacedceecddbaaaabcaeabcbaddeeccbeeceeeaebdaddbacddcbaccdbadbddbdbbdbecadcecaaeecabeabcccbbdcbacaeabeceebadaeddeeceecbebebaedcbadecabcbbdcdeabcabaaabbacaaccbcbeecddcaeadccaadccbadbdcbbcaebeaedebccbbdcdaedebaaaacecaccacbeedcedbeeddeadddbebedededeeabcdaaeddcccebedacebcabeebcbbdcecbaadccddedaceeaebeeabbacecaebedacdeabcebabbadabdeadecddaddbeedbedcccaaceeceeaebbddbaeedebaedbdebbeadaeaedabcbbcbaaeacdecdcdcdccdbccebadbebdcbaaeadebabedbdbbcacbcddcdabdaeadadebbcaebddabdbebddedbdeaaccedabcbadcdadcadeabeadcccdecaebacaabaabaaecadbcbbcebabdecacbdbdeaecbceddadecdedcdaecadabbbdcbabddbecaeabccccdcabcebabbceacbbdecdbeabaeabdebcabbbbedaaeaeabdededdadedbeaabdbcecceccbeaabceddbbbbeacbbbebebddbeaddaabbededbaebcdbbddadeacbbbbedadbadeecbeccaaeecdbaddbabeeceaeaadceedebcabedbaedaccdcadaaeceebcaddadecadabcacceadaecbadaaebcbeddbbcbbadccebaaddbcddccbcbacaebbcaeabeceaccecbeaadadeecbedbbbebcbaeaedcdacbabccaccdcedeaacaceadcbeadbdbbeaaaeddabecbdddbcacbbaabdbadbcdabeaaeecaededeeedcbbbaadcaedcdbcdbdbbdaceebbeaccabcaaaeaecbbeeceeddbeebbbeecbcbaebdbedeedbcddcddacbdaddadadeeeeeeddabcdebaeacbcbdadacbaccbabeaddbcbaeabdebacaacbceceaabeeddbbeaabdcdcdcecbcdabeacaaddbbccdbadecbdbeceebbbbbbdadcbbcaedbbdebbbeeccbeccbcedccecadedceaadeaeaaaeccbadeadedbacadbabecdadbddddebeedbceaecdadaabbdddcaecbadbcbdaaedaaaaaabcaaeecbecccbbbbdbdaacdcaadcbdedeadadeebcacadddbcadddedcaeacdaedaccaeecaacddbaeabbaabbaceeaecccebccacdbadaceccccddadbecbaddadedccccaadeddcbceceabcdeccacdeabdccbbedcdddbaaddaecdbbaeaebbdaccebadeebdabcdcbbcbeecaacdbdcbdebcdcaceaabecbaabeeeddaaadbdbeebcabeaabbdebbcddddbebceeebddcacbaeeeacaabbdbedebabbdcececbddddeadccceadddaaedcdceaababcbaedabacbacaacbbbdecaebdcabcccdcebadbacbeecceeceaeedbcdaeaaaedbcacadcccbecaeccbaaeddbebbabcadbbcccbddbbdbbbddbaabdddaaeaaecbcbbdcbeacabcadaeecbabbbdaadccccdbdcbadadcacceeddeaccbbcebebbddccdedbaccacdebedeabccbabebcadbcdddeaaecceabdeeecadadbdaacecaeaebaaeccaedccdddcaaaddcdadbcbccabddacccedddbdaaebdcaedcbaadeeeaaecaccbabededaaccbdbaaedacdeaeabadabeaecadedcceadadbbcadcadcadebbbaecaaddecceadbbebeeaaaedbaacececdcbecbaecdbacddadedbeceeecadaceaeceaeeaaccacedaabbbddcebecdebedcbdadcdadcbbddddabcaaedaccbbbabccccbdadaebeaaebcddeadbabaeeadebabebbdeecbcebedcacadccdcbbdcdbcccebceececaabdaeeceaadaebdabdbbcdccdbdaccbaedddeedaadbcedceadccdddbcaeecabebbacbcddcddacbdcbdaeeedccddbdbeadcbeeeddecccceaddcbabceaceabedbaeeceddeddcdaeedccceeecceceddaeadbaebaddacedeaaedaaceccbbcdeaabdddabebcaedaddbcdaecbdbbeaceacccbaecdacdbcddecbedcdbdedadbadeaddedecbbcdcdedbaebeedeabbadbacdebeeaabbebecbceabacacebccbebabbdcddcdaabacbbeddbcaddaaceadcbdbabbceeecdacdaacaabddceadaddbeabadeebbdeaedebcdbededeccbdbcdccceadeaaacbbdbeccbdacdcdedcebadeeeddadeedaeacebabecbbacabddcdaaaeadcecaecdcedebeaaaeaabcdadabdaaebebdebebeeeddbabdaaecabdaadbbadeebababedeedcaaededcdccaebdbadcddebceedabebbacbebeabaeeecacbbbbeebaaebdcebcccbabdeeabaabbbbcecdddeacdaaebbeeebcdcadeddcbbdeabbddecacccadcadabbbeaadcadedeabdddadddaabcdeacbcececedaeacbdbabdcbaddedbbbeaedebbbbdececbebcbadbaaceacedeccdbbdbaacccbaeeedcaddeeebcdaaaaebadcdecaaeeeaecbbcbdecbbaadabdbaabaebcedbcccabdcdbbbcdceebbbbeeebdaaddabeeeeecdcdcdedbeebcbecdacdacdddcebcaecdebadeddbddbdecaeaabeeaccbeebacaacbeaabdaecbedabdedceadeeadcbbcabaaaddbaebbebbdebcbdceedbcbedeadceecceedcbbbecdcaebdcebbbcddaadaeeabccbeccabbdceaacabdedaeaabcceadabebaebbaceaaedeecaaaaeccdabbcdbeddbacaabadcbacdcdeaddabbbeeeeaebcdbeaeeabbbbdadbddeadcecbaadbcebaacdaacccdbeebeecceadccebddcbecaeecaebadcdbedcedbabebbaadbdcdaceedddeabcadacdcbeeababdacdadcbadaebecaeebededcabeccebcdbbbaedbaceccdebbbddeaeeecdecbeadabebbaaddeadcbacadcacaddeceadadeaccdadcecbcecaddaaacadedcaeeeebeacddaabbacaeabeaaeecbaccbbeecdcaaaedcacabbabbeeacaadcdbcacedceadedcadbabbaecbecceaceabebebedbeecbcacbdbecceeaeaabaccaabcdddcccbaeabedcadaaaaebaacdaccdbcaaaadeacadaebddcebaaedabdbeccdaadeccaeacecacbccdacdccebcdbaabbeabeacabaabdaedbbcebaeddaecddcacedededacabbcecbbcbebcdabeeebcaecdbccdaebbcbdaaebcbeccbadbdaedddeaebcbeeeeaaedaaccdbacdcdecbbddcaccedededdecbaaeebcdeabbbbbbebadedbcebbcbccacddbeadeeecaabeceabdbdccdaceadaedabaabbbecbcedcaacdbbeeeecccbcdedcccdddadcadcaddaabceedbbcbbbeddecaacbaacccededccdbccebbaaacecceceeebcdaeaacabbcaeeadcaeecadbdbbdaccedeccbbeaedacdccadbacebadecaedcadbdaacbaeccbabdbeccacccccbceeddcaebcabaabbbaeeaadcaaaadbbadcccecaadaebddbcadbbdbedcebdeddbdadcabaadadcddcadbaabacaddecdebcedeceecaceddbaddacecaacdadeeeedcadadaaadabecdedebadbabbeccdbddaaabacceadcddcebdcadccbedaddbeccbbdacbacbcbcbbdbdbeaccdededadacdbbcacdcaddaedcadacccaceaababeebdddaeeacabeccbcadadecbebbbccaacadecdbbdbcbbdadbdaecbcdccaaceaebbddccebcebeeaeceaaeeaedecdcebbddddcedebcacaaabdcdbedaccddbecdbbbaddaaddcccbbdbedcacadbaaaecebaadedaaaadeadaebbadbdecbcbbccacebeecadbbdeadbabccbbaddbcbdcaecceeadcbadccbeccedacbbcabeedbacacbaaddcacdbbccddecccdcedebbebdebbdbedbaaebeebacdcebecacecceaecaadabeccddbdccebacbabcbbadbcdaabadbeeabcebbeaecccedcebbbceabdbcdccdcdcccbadcecbcdecbbdbaebedacadebecbdcddbcebeaeccacccbdeaecdeecedccbbeaabacdddabecaaaebdddddbacbbbeaddaacdbecdedcbedebbaeeeeedcbcbbbdbccdebbbceecbcdceaeadedbcbbecbbeceecbceeeacedacddbbdeacdaabedeedbdcaebcbeadbddcaaebbeeeeedccacaedbabcbacbbddbbcdbddcaeebbdccbbabedacdedbaaacaceebecaadaebccaeaedededacbedbeabcaccddcdddcebcbdeceebecaabdcbcdbddecdaeeaadcbecbcddcabacbcbbabdadeeabedcaceaadcebbeecccedcecccabebdadbebbbeeebcadbcacccacceecdedcbceeadceddbdbdaadeeacaebcaccaacbebabbebbeccddacababbeacabcbecbcdaceedbbdddceccbeaceceeacddebabaccdcccadeeadbeebcbadccaeeaeddabdebcadbcbecedaceadbdbbddcaaecdbdcececbeedbeacbeeeaaccccecbcbccdedeaceeedcaabdebdadcdcaaadeedceecbbeeebceeccacbdcdcbebcbddabdbadcacebdcbcbceccebccdaedeeeeaeabdceaaacbeeccbcbbdeeeddbbeddcaaebacbbeacedeabaacaabebcbdcdacdeeeebaaadaadbceebbabbebcddbdcbcddbdbecabdccadcddddbbccbbdeeebbdadcceccbdecacbdbadabbacdadbcbeaeeeebdcddabeebceaebaaeaaaaebcadaaaaecccecbcaeaeaaccbaaaeaabeeebbbcebaaacdbeaeacbbaaeebcedadebedcedbdedaecdbcccbdbcebbbcdcadbabdaeabcadabcbcbebccbbddcdbeadebdcbbbeddedbcbacddaceaecdbdbebacbbceaaebeaaebceadbbbaebdcddbadadcddeaedeadcbebaddcceaeedcebebebdacbbaadaababebeaeccbcacacbddbaccaaabccaabaccebaceedcaddeaebddacaabcdeeabbadedaadaddbdbdebcbdcbecdbbdaecabcaeeddbdcaaaeeacadbacbddadcdeaabbeeccadacbddcedbebeebbccecbbedadeeddbcdadbdaaaacdbbecccebaabbcebcdbceacdddcbdebbcecdbcbadedbecbaddcadaecdebbedbabaeeebeecbbaebaaadeabbaecaacccbdddeadaaebededbdedddeebedbaddbdeccabeedacbaccdadddaaeecdddecaecadeaaccbbeeceebabeecbcdaeceadebbccaeccaddceccddebddebcaecddabceedbdacbdddcbcdadeeaceddaebecedabacededcbedeebcbdcbadaaadbebecbdcdcbcaacaacabeeacabcceaebaabdeeecbecaeadcbeeaeaeaaacaebdaaeabccdaccbdedbebbdccccbcaecdbbdcedbeebacaccbbbebbedcbaeaaabeccadaebcdecdabeceeceabaeebbbceacbddbacdbddeaadaacbcdebeddeeabecaabcdececedebabcceecbadaecddbacbeeebbdecdcdaddcdaceceeebdcbabddbccebadcecaddbbeedccccbbcdaddaccaccaeeebecebbccdecbaeebbdbccaaaabcdaaaedccbacaecbcccbabcbadeebdcbdaeadbaabeedcbeecaebcdadcabebbbdcbaedcbaadaebececeebbccbdbbcaadbcedcbebecaadeedddeabcaccdcdacddeadbdaabecdcdddbecddbbbeadebaadcecebdecdcabcceadadadbaaceccaabacdddccdeeaadcdeeeddeaaccdebcceadcebadcbdcbddddeabadbbaeaaacdacdaedaaaddaedbcbbeddbabddbcdccdbbebccacccebeebcdcbdabdbdebbdcbcaadababcaceceedaaccbbdbadbbdeecdbebcbbaabdacbcbeaaeaaabbbeeedeaeccabcbaebeeaddcbbddacaadcddbebbdebbcebddeceadeccbecabecccbaddeacdbedcadbaebeacdcbdccacbbabacdbcdceabdedbbddebeabbadecadddcbabccdabbdebeddbaebdccbeecbbcccaeecaadadaecbcceaabadbdbcddaccbdabedcceacadaadaebdaededcbdecdeceaeeeceabcbddcaeadccaadcdececcdebcbccbebbaaddaaaeecdadddcceceaadabbccbcbecddecccddbeceeceaeebdbeacebbcdbdbecccdbbcdeaabcebddedcccbabdddddbaeabbadeaeddcecabdcbcdadcacaaccaeebdddededecbadceacecbcebbbaeeacbbaebababbabcebdcecabcbedabbbcdcecdebbaeabedeceddbcededaccdebbcbdabecababbbcaedabaabaeacdedebacdabcabdddbccaebabcaecddcabbcabdbaddeaeabecadbcebcbadeaeacebeabedbceabcbaaadbaeaedbaacdcabcdeadabecdaedeaecedaabcbecdbdbcbceeccabccadbebbabcccababdecadeeebcceeccbbbdebbbacabdaaebaecaceecacadeccbedbaacbbebecdebbccdcacaeecbbebababeaedabceedadaadaecdaeaaeabadecebeabacccbbadeacacecdddbdbacbeeeebccdbedcbbcbeccaaebeccdacecadcdbcecedaeaecccbdcaaccaedbbdadabececceeaccaadcbecaadeceeecdbedaeaccaddadcdeeebaebaacdcbcebbcbbecbdbbccdddecaeddadeebabeedabacececbcabaddcbcedaedbbaaccbdadcaeabebebccaaebbcdbdabacceeebbeeacbabbeaeedcebeabbcebebbedccbeecedaebadbddddaddeeeccbeaaeeabdcaeeabcebedebeeecadaabcebbbdbaabbaaccbedaeabadcaabeaadbeecdeabaddddaabdcccdbebcbaebeebbbcebcaaeaaecbaadaccbeeabdeacbdbcacbebedddadeeaeaedaacecaccabbaceabacbbbaccaadaeeccdacabbababdedcdbedeaedeabadedcabdcbabdccbbcecdedbeaeccaecacaabecabeeeacdebbdedcabdadceaceacddbcddbcbedeecccbabdeabaebcebebddcbebadbcdeebcdbdbaebdcbaedcaaddbcdeedebdbdedabcbabacdebcabbeabececeaeedabaecbaabcaecacdaecbdddaaedcdecebbaeabdaaedccedddadceadbdbcceadacaebaebadccbecbebdebeeabdbdeeabecdcdeacedddcebceebcabdbabecbeaededaadccdbdedcdbcbacbebcaaccacbdcddbbbcdecceeceebaadebabcbcbbdacdeaacecbbebaccaecebddbecddeabdddedccaacccaeadbbdceaeecbeeaabbdedcbddcdbecbcdddbddbaeeecedaeedceeaadadccebdadaedecbdedaebebdabecdcbebcedcebceacadbbddbbbabaeaadeedacaabaaaececcdceadccaceaeddacdaddecbaaecdbeedccbbcacedaddabebaaabcdedbeaadbaeccebeebabdbeaaccdcbdaedcacadeeabcceacebbbbeceecceecbebaddaebaedbddbecdcabeecddcceedceaddbbceaeeaddedebdbdcbaadccaaaecaacdedaaebdadabbcadedccdbeaebcbacacdecdacbebbbdbccaeccececceebacbcbcabceeccbcabadaeaeaababecceaaeccdccacecbaaeabaeaaceacaeedbcceaadecaadedbebeabdcbcdbababcdeccdbadbaccdecaebbedcacaebcbdccdaedccadcbacdaeccbbecceebeeaeeeaeebbddcbbdbedbcdacaaaacddbbdabeaeeaabdbdccccaabacaddeeecdbcdabecddcacaccecedaaaeeabebccabebebdcdebdbdeeeadcdebbabbbdadacddaaaccdcabaeadcdaeacbecbcaadecbdababedbedabecceabbacaedebcbaedadaeaedcacdcadecbcdceceeddacdebbdcaebccdeabbecdbccaeddebccccadecdddeeeecdddddcaecebdccacceddcbdccbdcebedcbbaceccebabdaadabcdcbadececcaeedcabaaacbcdbeddeedecbcaebebabbadaecdcebebcccaddcaaabcbabcddcceecaeaebedadcaabebcadabeeeeadccedabdccecdacdeaedcabdcaebadaaaddacbeacecdadcbccacdbcbdccbbbaeadaeacecebaebeaaacadbddbadababcecbabaadcddccabbcecadccacaedcbeaccbdddeceecabdabddbbdbdeadebbbbeabcbdeeaebcdbaddcaeacebddcdbdcdeeecdabbcabeedbacbbedaccbeddeedaeeeeaaeebeeaccdebbbbadbdaddcaaccbdcbcecdcbeeacdbaddbcddcebddcbabbadcccceabbdedcdbbcdbcdcaddadbcbccdeeddacadedbddeaecbadaeceacdaeceadbdbeaaeabcaeceaccaaccbaeabecebaceaebaabcaddbceabccbcdbcadcaeeeceeecbbcdaecaaebcdacecdddbcaeeacacbbaaeeacebcbaebbcbbeebddbddcabbcaaccebaeeceacddaeaaacaccabbeaededadddcbedccaaeedebaaccadddcdebbebdbedddcdadddaeeadababaaedbadcecebdcddebacbeaedcbcecdbeddbdedecacdedabdcaaaeaaebedebceedcebaddbbedbbcbdaeccbeddbbadeecebdedcbcaedebabdcadceeedeaabaeddcbacebcddcedddeabbebcdecdabadcbeacceeeaacacdcbbdccecacceaaaaacedecddbaddedceedecabddbeabcbbdcecbadeedeccebcacaccccbdaccecbdecaccacedbbcddaedebaeddeceddceccceabcdddacbabbdbdcbccadeccaaadaabceeddcdbdbcadcbbdddcacaeebceeacbcedcebbbdeecdededaebcaecceecdecccceedaedccbabbbecdbbaddbeddbbceeebbdeedceeeacddeccacdcaceccccdbeadebabbbccdbbcedddebeaaadbacdaebceccebeabdccdbadedbdbdcdebbcebdecbbedcadcaddbaadcdcceccbebececdcedeedabcedddadbabadedcbeeceebadbbedddbbebaecdcbceacaebbebbeaacddbbcddcaabddaceabccebcbbcaadeccdaedbbabdaacbdcbbadbcaccebceeccccbedabdaebbeabadbdacbbbaeedcdcdccdaeabbeddddaaaacecedeaaeccbecbcdcacdadcedeadceedcdecbbaabbeeecdeecababeddebcabeaceeadebcacdebdbecacaceebaacccdbebdecbacddecabbcadcbecabdbadceaccbdcadaedecdcebbcbdeacccbbbcbcdadddbcdedbccbeeccadcbbdedcdabecbdbccecebcaacccdeaedddbacdcecddacddedcdeeeedbadbdbcdebccacdabacdbecaceaaeadedaccdadedbaaecbedecbecebecaaddeecbdadcacacebaaabbdeccebaaeedeecdcecedcaaceaaaeddaeaceacbaeccccdeeedddbabcbadbddddeecaddeecdbdbdcacbccbaabeadcaaaabeeecdeedcbebaddccacceaceeccddcbbbdecddbbdedbcccaeddedabbddbbcadaddeddeebebbebdadecbbbeedddcbcebbbaadccdcaabdddebeecdbbaacabcedacccdadccdbedcbbdabbedabbbccdabacbadadababdaebecdcaccbcaeaaedcaacdadebebaebebcdcbddecadcadcbeacbbdedeadacadadcdedbdabdcdebcdacdbdbeaaecceaaedbbccceeaeccabbccebdeeacebaabdabbebebaebedbbcbacdcecbdcaecbeaaccbbcceddbcdbbcceeedebebedbdbbedddaddcbacdcdbbdddabccabeaaccaeacaddeebaddbbacbacbbbecbbeebbdacbbeebeaeceeebadbccccaeccaeacabbcabaaeeaacebbcdadedabbcadaaeeaccbadcdeebeeccccbbdbebebdeedcbacdedaebeabbebaaaeebabbdaaaadbebadeccddecbabbddeaccbccadddababbcbaaabbccbcecaebcccaadaeeedbdbaabdbaabecbdacbcbddaebacecbadbcdeeaadadbdcdcaededcbcdcecdabcedbceaaebacebbbdadacaaedbbbbeecdbeedcbdddaaccedddddddddaacaaececbcebadedaadcdbbcabeedbaaeedbdbceddacbbbbccedbeaadcdadbecbcddaacbeccebaeadddcaccbbddebbdeaebbbabacdbabbabdbdaaaddeabdbbdeccdacedbcbaacbcababadccdeacecccebaacaeebedbbceceecabbeecaceadaccbeaadebabbcbeecadabbedcbcedcecabebdabaecbaeccebaedbebcceeeabcbbeaebaddaaccbeebaaddaecddbeedaeccbabeabbbdaeebcddccabacdaaadabbaeacdbabaabeddbcbaebaeeebcbddcbadbaaeeabbaaeccbeabeeecdbdceacaddebaedcbdaabaaddddaaebcacecbdabebbcabdeeaceebaccebedababdbcedaeebceaeaaccadceebebcaedbcaceadcccdbbbaabbebccbbbcccdbaedcabaceaceaaccbdeebbcdadbdcbccbeaeabaceacbbbeceaaeabcacacceadbeebdbcdbabbabacceecaacedadbdeabbdabeacacddddeacbecbccacabebabbdeeceaebedcebaabbecececcaebedcdaacdcdbebdebedbbedbbaeccadcbadaeacdbadbdeeaeddbcbdebacbaecabaeedbeeeceedaecddbdeeabbdbcdbeaecdbbbbccaaebdaccaebbbcbdcdecbecaabbabcdadbbaceaccababeecadbbceceaacdcdabebeedccbeecaeaebecaacecbaadcecbacccdeabdbcebaaccacacbbccdceddeabdcdbccbbecbadaeaaadbbbeedecddccbbceabbaddabaceaebeddceddcadbbcccadbeaaeeeaaaabeadddcdaaaabdabeebddaeedabdeddbcadabccbcebbeaceedabdcddaaebbcbeeecceaaccaccecaceeaaaaddedddeebbddedeeeeccedceeecddaccdeeecebbbabdcecaeaceceeaabeadccbabeabbcedcbaadbaacbeaeacabcaebbdacbbcbabdedccdbeadebabeeeeeecbbaabdcadacaddbccbebbcedbeaebcbcbdbcbdababdebecedcbddceecbdeabeaeaaaccaeddeaddbbdcceddccaddbcebeaedaddebcbbcedcecbeacdaeaecedbedadacaebdcbedcacbcadbabbcadaceaacdbcedecedbaceadeddaebbdccdbdeceddaaacbbadadcaeaadbcbabeaecbedccdaebbdaccddcdcaeedbcacbcedbaeacacebecdedacaccbecbabaadeaeecbaeccaecceaeeccdedadeccabcbbcedebcbdaccdbdacebeeccdedebccdcbacaebcaebdadacaabbcdaecdaebccddbbbbeebaedeabcacccccbaadabdddbadacaccaeebbabceeebeccdccededbacbebeabeceeedcbaeccdadaadeabdccbcdcbdeeadccbcdbcacebeeadacddcadecdcccaccdcdbceaabeccacceaebdbdecdcdaaacbdbdebecacacebebdcbbecbcbddabcedeaecbebdbeccbcdbecededcebdbbcbbddcebabdddbaadabdcebddbcebcabcacbaabdabaaabebbceebebbecedaddaeababaeebaaebdccbecebeebcdadccdecdcceecbdcbcbecedbddaebadccaadecdbbdecddcccbccdcbabaabbcbacaaebaabedeeeabadebddccccadbccbecabcabcaecabebdcaeaabcaabecceecdcbeddabdccbdaaecdaadbeabbadeaadeecaeabeaeaeedaebeacbccaaebaeeecadddbeaaddecbabecaaaaedbcadddcbcbbdaadeabeaecabeaebbebabacaeadddaaabdecebbeabcaeeaedacaebcdeeaccacceccebdedcbebbcdbbecbddeaeedacdcaacdadeaedcdeaabababdeedecddddadcebabacbeedabcceabdbcebedaecbedddccdaadadbacbedcceeebeabccdbdcdbdcedadcbaaedbeecaaecacdeddbdecbcbedcbecadbadbadaecbdadcaadccbeabcccedaceedadebdaeabdbbabbededaecedccbbdecbbbaebacbaaecdeedbcebbddcceabbbddcddbdedcadebcececeabeccacebcabacabeabeceaccdcbcddcbebebaabbdebedaadadaedecdecdaaaaaacadebccddeedadebebcebbbecdbebbdabeddedeebdbdedeebbebcedbaadcdeeaedaadebaaabbaebcaceeaecdbdedccdabddaaeccdcccacddaedeedbcbcdabaaecddedccbbdcddeddccbcdcbbbbdedcdeaeacbbacaaaabbaacdebbdbbbeddceacabeccbbcdedadbeababcdaedcecaacacdddedadbbbeaedeaadeaacbcebeacabacecdbeaabdcddaeacbedddbedcadeaebacdecaddccdecbeeccbabbdcddcadeacabcabdceeaccaaebdaecdbeccbbeadecadeedeeebaccabbecdcbcbceadceedabeaedecdbcccceebbdceacbbacbccbeeccceddecacbebdabddeacccadcaabccabededaeccebcdecdddbcbbcdcebddcedbcdaaeedaadcaccacaccaeeecdbdbcecbadaeacaabccbceacebdcaaacbccdaedddeaecabcaadddadebbaecdcbdaebaddcacabaabcbcbbeebbeecccaabbcdbbcabbacdbcebbbbdacbcceaaeedacacccdbebdcadbedbecacdbacdabaeecdcaeeaccecdeceadaaceebdaadaceebcebbedeabdbbecebbceeacbbaccdbdeaacbcebcaeacadacadbcacbebbbcabccaacbecaccdbbebdceeaabedcaadbbbaadabacebccadabdcaabbcadccebaeadbabdeccabeacbbcebbaeacdeccdddcdeddaddcbdabbebcebbadeceacacdcbbcdbbedeebcbbbbdecedadeadeaaadcebddabcedababaddceeccbebbcaddabbdbabdcbeabcedabadbcbacbbdcceecaabecabbedbadeeadbddebaccdcddbeadedbbadaadbcdabaabaebdaeadaacbdcebdbcabdadcadaadbcdebdccabcecbdaaeeceedeaeecdedcbdaaadcdbbeeeaabedbbecceaceddcdcddbaecbecaecbabdacaebdedcdddebdeabedceabeeedeaaebedeebcdeadbcabadbcabdaeddbcdaecddeaaacedcabebebebaeacbdbddbaccacaccecbdadadbdabbaadebbbdabecbbbaadacbcddeaacbededaddcbdacaeedbdaaccbacebbabacbaabeadbeecbdbaabededcdeccaeeadebeabdaedeeeeedadaeaacaadebcbbdeaeedcccdedebeeeaecaeadaaeccbeddbabaedabbeadecbdeddadbdebedbddaadbbedebbcbdeaddddadbadddbdcedeadaebbcdbaeababaccdddbbacbeaebaddadaaccadeeeaccebddeeaacbbeeccaebcaacccbcabdbccdaeeadbebaaedabacebdccbebacbbcdddaadddbbbacaaebdeecdaaaaaccbaeaacbaacaddeeebcceeececccdedececbdabccbebdaaadedcdcbcdeabcddaeacaedabccaedbdacbaaaddbeecacecccacbceddaecaaacaaddaadaaebcaccdccbaecabeaadcedbbacddeddccedabdedadaaaebbdcbbacbdcdaeeeeaaecceddcdcaadeeadcedcbdccababccabbbeebedcbaeedeabdcbdbdcdaededbcbcecdcbbcceeddbcdebccecdeaeeeaaaacdadedbdecedbbddceadadcedadebcbececdeabadaadddaeaedccaedeecdacdebeaeaaccdaaabcbaeebbdeabdceabdeaeabdebdabdebaeccedaeaaedccdeedabacacabecabadcaceadbbcaeeabeabbaecebbaaaecdabdbcdaddaecbbbbececbabeedacdcaabaddeeddacebaacccadcecbadbdebcedbdbdcdebebecaaebcbdbedabacddcaaadcbbdcdaadcdcbbdcdbcdeaaaddaddebcedabadaabceeddecaebdddcdcebedbccedbbccbedbebacbebcadeccacbbbebdeecbecbbdcbdcbbcddbadcdbbaaaebbadbcbcecbddaeabcabbcdabbdeaccbebcbaebcededcaaddcabebdaedeadecbeddcbacddeaeebcbadecddbaaeaadaabecdceeeacbceadceddbcdecaebbceacdecdaaccaeceedcdedabaaecccbaaaddbbaddcabadeadcdaddcadbeacaedcadbdcbcedddaedecadddbcddecbeeabeabbbbceceabddbaaaeadecedbeeceecbaccaddacabbebcacaabbbbadbdcecabaeaeebcdcbbbbcbdedeeebdceacdcdcdbbdbcbabdcdebecacdebabaccadebaedcaabebdadcecbbcdacbbdeecacaaaabbddaadaadeebcbbbcbeadeadcdeddaabeeaacbcbacaadbeecadaacaaadbebababbccbadebbebebcbdeecbbbdadacecbcdbaaaaadaedebbaceadcdaccbbaeebeeecbeceeabebcedbccbbbdddcdeecbdcdaccbcbcbebaedddbecadcbcceecbecbdebaddbccedcdddbccbdbaccadcbdeddedddeedeadbbcbbdecbeccddcdbeaeceeaaecdeeccdeebcedebcbdddcdcbbbcccdddedddedecaaaddcabbbdabbdeaaceedadaaabeedabdccdabbedceeeedadecbecabbadeacceadaddccbdbedadaccaaecbaacbabbebcabeccbdbebecceecaadbdeddecccecdcdebbbbdeacbaedeaccbceacbcedadaaadbbdaccdaaaecbaedaeeadaabedeeebdadccbebdddeaaddccceecedbdedccdbabdcddebaceacadebbdaeadadcadcbceddaddccdedadedbeddcdaadbbdcdcdddacceebccadbaaaecdeadcdecacbcabacbadbeaccbdbbecbcdaebbacbdedbbcebccdddcddacdecdbbbdcccaebedcdaedebcebdcdaeaeedceaddadccaebaaabecdbbddedeeecbaceeaaebaeacddddccacdcacadacddcbeeacdbbdddaccbddeaecbeaeddaaeeeaedadbbcbbaaeedeeeebdddadbeccbaccccbcccbdeabcbaaebaeaaccabcdadedccabcabadeaaaaaeadeeebaeeeadbcbbbdaeeceddbaeecadbabdaadcbdeadcdaedbddaebbaeeedebeeadeecccaadbeeabcdabdaaedbdccdaddbeebeedbbedaccdebddabcadedcedbeaeaebdeaabdecbdebadabbdabbbacadcabdeebccaccbaaddddcbececebaabbacddcaeaeddccbeedaaecdabcbcdcceaabcabedccaeaecaebbacecbddebeaadceadbceacbaedacaaaebadaadbcbadecaebddadccebcedcbadbebdeedbecccedabbdadcaadadcbcababdacbbdcedbabdecdbbcbadadbbebcbbcebaceabddeaecbbabcbcebccdedebcdeeaeacccbdceabdcdadaceecdaeaacabcddbbbaebdeabeccbeaaaaeaeeabdbcdedbedeacdcdedbeeddddbedabddadcddcedeadbcabcccccdedabaccbececcbeeaccccaeadceacbccdaccabdacebceabedeebaeaadeebeabbdadbadbadebacbecbbcaacdbcecbcdbcbcecacdacabdcceecaacdbaecdbbbaebbaaaddbeababecaeaadbbbeabcddcddecdabcedaabbeaabebaadbdeebbcbbebebbabbdeecaaabcaabbbbaedbdbddabcdaaaecddcaebaeedcddcdbcdbecddbabdccdaeecbecedddaaecdebeebaceabcdbdbcbbeadeabeadcedeccbacbbaacabdaddaeaaaaddedadaacedbbaeeceaedbaddbaeeddecbdebacbedaebbeccecbcaacabdedcaeddeaddcaaebadcebddcccbdbdeebedeecaaebbebbaeccbeaecbcceccbddedccbcbbcbedeeebcdbabdadccacaccdcbaaedcaceabdddeecedcacdbdcacabcbeadaeacbcdbbaaadebcebabcdbdeabecbeaedcaabaacbbeacdbcbeecbeabddbbcaccedadcabcbaddabbcaadeeccbdceabcabeeabbbdaebaeaecbaebbeaddcaeeaaecdaecadcedeaeaddaddbccdceacbeceeaccddcceadacecdcaeeecbdbebbecbceebcadadadbdcdecdedddbcadbcacdadadccdabbcaaabdccbaebbbdbdebacbcecccaccacebbabceacebeaaadccdbeaacbdeaaecacbebbccaaaeceeaaedbababdcabedcaeccdbbdbbdbbdadcaedabdbececebcaacddcabceaaaaecbcbbeedaaccdcdbdabbbdedaaecaebcdddeeabbeeabbbecaeebbebdeceadabeabebeceeeaaeadeebbdecedaceaccdcacebdadcaccbbaccedadaecdbbcececdbccdbbbabbdbbdaabcadaaadabecabeacebacccdcadbdbcadabeaadbbabadbbeabbddcbdaaecbdcdaccbbeededebceebdedbceebcdadcccccdbdabeedecdabcaaeabdcbaceebadbeceaedabeeeebbbaaaabeeaccbbcdbbbcaccccbbddbedbbddabadacdebdadeccbbaaceeabdaeedabeeaccaedeacbebaddebaebdcbcbdaeccadeccceabbbceacbaebbcaababacbcbcbbddacbcaeceeedeedddcdcccddbbcbbddaeeacbbabdcbdaebbdeedbacabbdecabcabeeddabcadcbcddbedeaccdeacdaedadadeaccecaecbbdcdbabbeadcccedcddaaeaedacbeaedcbbeccaecbbbcddeccddadbbaedaabecedcceccecaeeedadcaacecddbceaeacebeedacdcabbeabbcebacabeeacdcbedadaaeeadedabebaccbeebdccedcdbbeeeacabcabdebdaeecaeeeaadbeeebedbceeaaadeceebdbcdcceadbbaacacedabadabecbdabdcbdcaeedbdbacdccbeccdaddaceecbecbbbaeddedabddcabbabcedebcdcdebdbebccabbdaceeecbdddeabaeceadceccdaeddadabcbebabaaadbbcbcbeeeedcaadacbaecbacedacbdaeeadadaabcacbeedbaababdebcaaabeededbedbcaaaeecbbbbedeaeaccebbcabceabdbbbddeebbdddccdaaccebbbeaededcbeebcadadeaebbcdbadbccaccaeeaeadeddbcedbcddbcdcbcedabcedabcaadeccccaecdaecaeccbbcadbdceeecaaeccbcacbeadbcabcadecaacedcddbdadacabbadcdacbaaabbdadbaacadcdbbbdeebbbaeabbddcbddadcaebeabaabaabaeddbeadadbcaebadcbcabaabbbeccbaaaaabaecadbddeeddaaaaecdeabbdcdacadcdbaadaacecedbdbaaadebabaaddecebcccbedddceaaeabacaeddbaeaacbcceebadddbcbaebccdbbccbcddbaeadddccdeceecbaebccabcecaabdcbdbbdcbdcdebbcbcdcdaaceeaededabaecaabacabbabbcebebbdbccbbcccbdbbbeaabcecaaecacedcebabcdbabdebbdedeadbbcbeabaceedaacdecadacabadecdcabebbccadbcecedacadbbdabbceaaacaecaccbbabddecdeebcbeecdeabbeaeaebabadbcacbabcbaccceadadbcecaacabaddeebeaadcecbcccbedceccebeaeacbdaadecdbdcdcaaeebddebbaadabdcacecbddcabdabcdbebbeebbcccdcbdbaebcbbbbabbeaeeaaeebecbccaadaceebcdaeaeabeecbbeebdcedbbaddeaaebddeccbdaadeaceadcaeecacbbbaecceedcdaceceabeceabaeecbcddedceaaacbcebdcddcddbadaebdbdeadcecdbbbbdaeddecedeadecdcaddaacdadbaaabdeadbbadcdeaedbceaeccceccabcebecddeadedebcecdbabbbdcdaedcedcebaadacedcbdebdcaddadcdecaddadabcceaacccbebcedbedbccddbdbbdacaeceeadabdcacdedcbaeebacccdddeddecdcdaabeaadcabcabdaabdebabddcbdbdadbdcccaddbdbacbbdabeebeebebdaebcececbccdeddbeabbdeddcacbeedaacecdeeeddcddaccceacbbdbecccccdbebedcaccbddaecaceeadbaecbccabedbbddaedaceabbcdccdaababaceabbdedcedcbdadceddeebadeaaebedcaebeedbdcaebdcdaaddadecbaacedaeaabebeeacaaeccbbaacadabcccedcccdabaaceccebdbcacdebcceadababadbccdeccbcdebddbaddbeebebeddbdeaacbaeddbabdaecdadbbbeeabadbbabcabdedbdcadacaceddbedbbabddcaeceaddbeeabaacbcddbcdaacddeadacaebccaebdbadddeabbceddceeeeeaaecbccbddbeeeadaccbabeaaddecdccedacdacadcaadcdedeacabaeeabecbbabacbddaccbcbcccbdbaecedcacedbcadddabcdbbabadbabbdeeaeabbdbabacbdceecacbeacedddddecdcadbddcbaaccadebbbdaabbbbbcbdadcaddacecbdabbaaadeedeabbbcbdbcdeaeddcdbebbebacdbdaaaeaaeadddbdedeeeadbceeccacddadcebcadbccdaaacaccddbbedbdabddddaaececebdacceddacdcebbdcebceacadbbacceeedabaaeeccedeaabbbdcecaceeabaebcbbadccdedcbdedcdbbdbccbcdcaeecbdeabacceedcddaddbeabdbbeaaeeaccecbdeceadcabbcdbcecaeebbcddeabedaadaabddddacdebbcadebaeebbbdacddbebbcbaeeccecbcbbaebdcadabaaabeeeddadccbdaddbacadcbeceeadebeeeeaecceabbbcbdbdbaeababcdcdeedeaabdcdceccbcecaacaaaaceabbababcbeacebcbceeadbdddaebabaddacdadccdccbaeedbacbebebbbcccbeeacaaeeedbdebbeaeaabebbbaeebdaabdbbdadcdecdacacacbdcdaadccaedbcdbadaccaabbbbbeeeacaaacaebdddadbebbceaececbdaecdaebadaedbaebdbcbceadacabdddbaccceeeddedadbbeceeaededcebddeedeecdadddcedbcdddddcdaeaddabcebeaddeeecbdecbdcacbbcbcbcbcabbbeeedcccedbbceadcbababcccabeabdcbdcaacddcebedeacddaabddbaacbeaabbbacbdadcbecacbcdbcaeeacedbeeeadcbbdbbdbaebcbdeaddccaacabebcadddebeecabceecaeedbeebdaaecdabdabbcdaaabcedbddadadeddcbecaecedbcaaddaedcdbbbeaceacccdecedceddcbebbaabadeebdbccceecadeaaeeeececbacbddbddecaadcbebbbdbadcccdeadbeacbaebdacccadceccedcbcebcdabbadbebececadbcceedbaacaecedceaddcdbcbcbcabdbddbbdccebabcdebdabeedcedbaabadaedecdaadebbaedeaecabbccbcbecaceeeaedcbadccdeabdaabbbcaaceeebcdbeaebebaedeacaadeaedcababdedbaadddddbbdceddbbbddeaeeddbebbccacaeeaebcbdbedaeeadbcbddbadeeddbadccabceeabdadccedbdbeabddcceaebdecbaceeebeaedbaaeebadabdcdeccdeedbaebceabebeccbcbdbdbcaceccacbbeeabeacdbddceaebbedecaedbaeddbbeddcdcebcdcdcbcebcdbeeccebcacebbebadcbccbdeeadbabeeecaabcdaeeeabadcebacaeabebbdbccaebbbeaceaddbcbbadbecccdbeeadccdebebbbccadcbaebcacdcdabaaebabadcaebbcdbcbacbbcebebdbacecbcceadeaaebaabcacdceeddccbebcedcecbeebeaeaedbcebebaedabeddebdcdcebbbddadeedadeeacbcebededcccdcebeeacbdeaabceebaaddebedbedbdcceeaedbadcaeecdadeaedeaaadacebdeccbeceebeacaddbeedeaddcdaabdcddeebedaaeadbbeaadababbcbaabbbdddebeddacbdacbbcddabadceaceadcdabdcbcebddeddcccbeaedcbcaddbddbcaddccbbcddebddcedadbbabcbbccdaeecbebdaabbaddecddebcadcbbbddaebdbedebbeabbdaeedeadadbabcccdaadebdcdeababcabbcdbcebceeddbbcacbacabccdbeaeaaccbbaadcdbacdeebccedaedabeebaaabbcbaeddcdeccbcdaebcbbccdaabceabeaeabebdcddaedcaebccbebacbdccdaaebbdadadebdaecceeadeaccbddcdccdeaaadeaaedbcacadebdcacdebacccebacbbedbeddebddcbbeedeeeccdcdebcbbdeabdeaadacbebacdeebecbbacedcaeedbeebedbbbecccabbbaddcadcdbadaaecbcccebeaaacadcbbccaeaecddcecdadeebcacccaaadccdccbbcdbcabddddacacbcabcadddcdeaedeabbebdddeddbaebecccebcbebabddbcdebccebcbcaabadceeadcddddcbeaadececdaadbdeabadaedaeedbceddbbaccadaeaacebecebadeceeeaddbdbaeebbceeabdcbbabeccbccdacaadaedddedbadecaeedeeebeeebcbcebaecdeccebeaecadcbbebcaeeeaaecdbacaaaebbdbeccdbadcacbdacabcbbdacabdecdaedbceacccedeacdebdbdaeaacdbedaaadceecebdecacacabbdcaecededeceddccbadbcbdcadeecabdcdddcdbaadcbcdeeebdedbaacdedeceaedceadbeaddebbccbdddeddbebdbbecebcdadedecbcabbdbebbabdddabeaaadeaaeacbabbbdedaabbaaeacddbceceaaceeeceaecaddcceeaddbcddbcadcdbcaaebccdeaebbedddadbcbadaebdaadcdcbddcacedbdeeaedddddebdebaaadaaaccabaeabcdabeadcccabedbbeebdccbcedcaddddabcbeabacbdadacdcdeddbbdebbdeaabbeebbbabebcbbdbccecbeabeacbcdedaeeedbaddcecabadeacdbdbbecaeccabbdecccababcbadddaebbcbbbdecbceabcebaeecebddebebbdbdbdebaacddeddedaabbceabeccbccebececdcecdccccbcacdbbbdcabaddaddddbdbeccedbacaceabaedbddebabadeaccbcadcbcabdabeaababcabaeabcadddbeaddadedadedcdadbbaacaadcdbabdbbdbdabcddccacbeebcbdcbaaacbedcdabdecebddebdcadaccaaabeeaccdeedaeabcdacddeeeadaaaaabaccdeeddedbddadaadbaebeadaabcacbbadddedcccbacdddeabdecdddaedecdacaeeeacbbbcaecedcacedbaacbbbaddabadaccddbccdbdcddaccebbaceccbcbcdccdccbcadcbdcadeccdabcedaaaaddcbcdccbaadeacbeaeaddecedaedccceadbbdabadaceaaddbeaacabcedeccacebcbaeabbaabceacbdddbbebdddbadeedcdbcacdaabaacacaabdaaeadddaaedcaceecdeddaddecbdbeabecccacbdbcaeebeceacbaddbabecbbddaabdeeeadcddddbcabcedabaaadcbeeaeeedecddecabbcaadaacabadabaabadbdddeaccccbdcebddddaebdeeccecaabbdecadeecadccacbbaebaeeecccdeaadaeddddacddaddbacdbaadcaaaaabbcccdccdacdbddeedcadbcdecdbbeaeacebdcdcebdaeebaaedaadbdeccccdbbdccbdcabebacaaabeeeeadbcaedaeedacaacbaebdabcacbcadcdccdacccdedadaabbddbabcaadaadeeaecabdccbaddedabebebdbeabeacbadcdebaeaeaeddcdbbeaeecbbbccececccdcaebddddbabeaadaebabdeaddcadddadddddbedaceaeddecbbbeaaecbdddedaeebeceededcbddaeedecbbdbeacedcbcbadbbccdacdbabbdbcdbbccadaccabeaeedaaaddebceeeccaadcdcdbeeadeabdeccdecaabcbaaccbcbbceceeddacabdbecdddceddecdccbeaacaacdbecebbbccdebaeadaebeabdcbaeeadbaadedbddbcbeedabaccdbcbcbbbbababcacbadbcdecabedacacadaeeecacbdadedcaecaeeaceaacaaeeddcabebdbbaeacbdcdddebaabbcceaeebeadbccddbbaecddbceadadccaabadbbaabaabebaadbbeeeaeeecaadbbcdccddcadbdcbddbaaacaeaaadaebadbdcecdacbbeabdeabbbcdaddcddcbdedbdabdebaadccaacbeaaebeacaacdcedeaabdecadeecbeedbbbadcedbeacbcccbebadeeadeedecbcdeacbaabaccdeaeadeecdcbdadebdaeecbcadaaddecbcacdeecebcbbaabcdeecccebaeaabcabdcebbdcddaaedaeddbdaddacbeecadbbcabecacdaebedbceacaaeacceadbdaaaebbddbdeebbdccdabbebddcbdbaccedddbaecaaacaeccbbbceaedddaabdebeadeedcccaeaaccbbdbdcdbecbcedddaaaadbcbeadaebeaedeceaceaeaededebeaadaeabcbdeedacceaaedccecaecbdceaaeebeaacaaeedcdceeaeeaabbdddbaaedacaecdcedbeeeaccadeecbaaaaceebdcabceecacceacbdddabcbaeacaceebcaecdddcbdcddcdebeabdeaccecadadaacbdccececeedcacaabadeabcbadeaadebdabeccebaaaeeecdbedaabadcbbaaeaccddcebdaddedaaaeecbbeddccecacaeeeedccdcdbcaaadaabbceccbeacdcacadbdecabadcbcedbaaecbcabddadbeaedbbdddecdeaedcadcbbbbbbabbbadacedacecdbeadbcacdcecccccccaeaaabdebcaadabbacbdedddedeecddaeaeacaacebeadbdeaecdaacccccaeeaeaeddbdccecdcaddbaccdabccdebbaddcebdedaeaadedebcddeeacdddadadabaccdcdceadbcebdddcbebcdbdcdaeecbeaceeeebccbcbeebbeacdcddbeaeabbbaabaaebedbaedcaaeceecbdccbdddedaeadaeeeacedbadeeecbdbcedebecdaebebdeeddddacdaeccedddcbaeaceecebcaedbdeedaccbacacaacaaacbaecccbbacaceeabaeceadccbcbcbcbdceddeddaceaebdcceeeaeccebaebddbabdeccaabaadedbaccaddabbdcdababeaeabbeadaaecdbdcedeecaeacdabaeeededdaebcbededbecbeecdecbccaabdeeaddacbdbaccdaecebebabbcbaacdcdbcdbaccaabecabbbcbbbeecddbaddeeabceeecddebcaedccabccbdabebbbbdcebdbeeaadbdeedddebecccaeaabbebaaaabcacddaedacdeaaecaedcededeedddecdeeedccdeccadbadebbaeaacdcbdbcbbecdebbbcbcbebbaaccdaedaeacbcedeaaeeaaabcbadcabbadbbeaecaaccdbcecbbcdcbcaebacecadbdcadbaaddbeacbddcdaddccaaccbecbdcabaadeacebbecebecaeaaaaccdebdebbaeedccbadccdcdbccececabedddadbeabebdbaebabedacbbdebdaebcabdbebcbbbeeaaaaabbdcdcbcbbdbaddebabcdaadacebdbbcebbdadcbeabeaeacbacdeecbccbddacddceddecacedacbbbbcdeaddadecedebaaedabadadbcccdbaedcccbddaaeacadcedaeeecbdcdbabcacdacacdeeccceeeaaeceaaaddaabababbdcedacbebdaabbbdbdbdedccaebeccadeadeccdabadedecbddabdaccaeeaddadeccaebbbdbcedccaadadbdaeeebbeddaebddaabddcdcebdbacbbcbcbcdeeabbacebbeaecdcbebecbbeceaadddaecddbddbddaabaceadbcabeebcbcebeceeecbcccbbcddccaceceecddedccbaaceaadbcaedaedecdbbbbaeaaabbddaedacaeacacccbabaedcaebbedddbddecaeaddbebaddaaacbcddeaacadcdbdaacdedeacaeddacccecccdcbedaabdcdbacbdedaaeeedccccdccbeabcadcdeaabaaddeedaacddbebecbdbdbcadbceacceebeeceaacbdabccaeecdbdacedeaadabceeabeeabbdaabbeaeadadabbceacaaedabcebcecdccacbeaabaaadabeccbcaadbeebaddbadcdadddbedbbbbbaabdceeccbbaceeccdadeccddcbedebeebcbdedbaaaeebbdabdcbceaeddcdeaeccdcdeebbeacdcdaceeccceecaaacbdbdabebacbcdcabaebcadaedddcbecbdebaebbebcdaaaaadcbacbeddececaecaeccbdcaabdbcbdbeedccedddceeeceddddcbbdbecccbabcdbdaeaecbcdedebebabaebebaaebbabdbeeeaacbdbbdabadabadbbdeaaeeceddbcdebddbababbaacacacddabcdacecdceccdbdbaeccdedebdbeaeadeddbdcbbdeabebcbdbbeecdcddbaaccdddecebeadadacdcbcdaddecdccabedbebbaaddaddcecadbbbccdbebcedcccbadecaabdbbaaaadcddacdbbcbeeacbeadabacdcccdbbcecaabddbbadbacacddaeaeccaabcacabccddccbcacdbbdeddacccbebedccadcbdddbaaadcceebcedcbbabeceddcddabacbdaabdbaedcedceeeddeeddadadebceabbecaaccdaebdcadcacbdacbbcaaaaacebecaaeeebbbaedadedccedddaeadbebeadaccdacdbecdeebdedcdebacabcadbebcbcddaabbdebadeabeaeddbbcccccbdbaaebadaccadbdcaedacecbccbedbecadbeacbaccecdbaaceacdaddabeeceaddacbaccccbdeceadcdbcccaabeadadedeeccdcdbbedabddaeebdcdbeabdddabddaeaadbeddeeedbabebcaeceadecacadadbaacdbbbaaaeccaaeebcaedecedecbbbecdadddabaddeadeeeedbbcddddecbbedcdeeeeccbdadcaabcbdcebedcccabcedbedbdeeaebeccbdabcbbdcaebccdeaabedbbdbeeeeddeccbedccecddabcebbaccbbbeeddcbddabcacebddacaeeddddecceedeedbebbebcbcccabdddcdbeeeaeabeadeaddecdeaeabbebacbbdbccaebcecabeebbcdabbadabdcaebdbebcebbdabeeececbacbcccbdcdadedcdbaecedeaedcddcabccdbdeccaeeeeaadadacaaddadcccaeaeaedbebdebebbacacdedebcabeabbeeadbdbebacebeabcdaebecebcdacdbdbbeeacadbbbbbaddebddcacdaddadcabababacdbaaecebbbebdbbdbebdeedbcbbbeeabedbbaeeccbbbeeccdcdeeabbeeabedddbbddbadbdbecbbeabcdcbdcabaedaaadbbeabbabedcedddbbddcddaedeacbeddabebaeedbdaaaadbbacdacdeabcaebebcedaabbdcddbbcabeadacbebbeaacabedbcccaaeecbddceebdebdcbdadcdbbaaeacecbbbbbcbbedddabeebaacbdeabaebcacbcdedaaabbecabecbaceaedeebdbcdbedaacbbaaedeeeecebebeddaabddccbedbbcecbcecdebecbccbdecaaebdcacebaababbbabdbbdcadcaacaecddeacabdcabaaadeebbeabeccdbabdbecbdcbaeabcdbbcecaaacceaaaecbbabebaeeabecabdbeecdaadcdbdcecadaabeccbaeaecdeedcdbceabebeeddcecdcabdcdaabaceaeaaacccddbbaadceecbcbbdcbcaedabdbecdbdabdebadebbdbbdeaeeecaaabbaacaebcadcebeddecccbcdabccbedbdaeabdaecacaabbbccecdcebebcbebbbaacdebbbecaaecaaeaacdcdddaaaedaeebddccebdecaaebcaaecdcadbccaabecabdbcddaccdbebecebbbaeaaabebeedebbcaaecbeaceadbcdaddebbccedcacabebbbbebdccdaacbacbcbceacebdabbcdeecadbcccdeeaadcebadccdabdcceccccedacabeddaedadebcdecdccebadbdcbdbdacaecbdbacccdaadbbdbcadabdbadabeabadedbeecedbcbaeddceacaddadbdadecaacdbcedadbecebddeadcedbeddaecdadcedeacdbbccaaadacededbbebbbaddbecbedeabdbccaebdcdaeddbcbbbdddaecdcbbbbdcebdbcbacbbdaddeacaebdbdebcccabbaddbbeaaebabeacaeeaddcaaaceccaceaacabddabccbaacbceaebdabedccaadbceaaddaaacdacddeaeedbadbeeaaceaaeaecdcebeabeebedecdcbedbeceecddbbccdeddaccaeaacbdcadbacbacdeddbdccbedeceaaaaccaaacacedeecdebddbebceaccecbbacbeeceeedbccbcecccdcdaedcbbccbddbbbeeeeedddaaaaaaddaecdbeacbccddcabbedddcadcbbcdaebbdedaeaddeecebbbeedbadccbdaaedccdbaabecbdcabceadbecbbcacaaeeedcaaebacbaeadcacdcbccceeabebdccdbccbabbaedddacbccdeaaceeaabbbceeedbbabdbbadedbcdcbdcbbadabccbabcdacbaceeeecbddaecacedaddcdbbbbddcdbacddcbcddaebdadbbcededcacdacadbabbddcbccabcbdcddeacbdaeaaedbbdcaedcedededdbaeadaccbcbcebadaddabeabaadaeacdbcebebabdcabdaeceedceeaeeeedaeebaceecadbaedcceedbbdddcbdbbabdaaaddebccdacbbdddddbeebaededadabcdcbddebadadbcecbbcadeadadbebbbaaaaecaedbecdeeeacdaecabeabeabeedcaeeacedaaacbccbddbadeaacebdeebdcaaccdbeccbeeeaacbababaeceaaeeebabcdedeaadaedceceebbcbdcacbcdcdceecceadeddebddacbcbddcbaebcccececabceabebdedddacbdecbeaeecdcbcccaedaadeddeddbabedadaadbeacacccdcaaababbbcaabddabdaceeaecbbadbbbbbbbcadceadbbcadcecbbbbdccbadcebbbcebcdbdbacacbbabdbdeddddbadbbbbaecdcdcabcbeaecdbcddcbcbebedecbeeacadedcbeeceabcaeeacdaebddaabebadaddcedcbbacecabecdbacaaeebdcadecccaddbcbedbeccabdcdcdbbaaaaebcdccccecbdacacabcbbeddadeacadcacbbdcedaebbdaebaabcbccabaedddcddcbeaceaaadbdbdcddaebacbaedebdaeceadaadebacbebeaabcdccdccbceedecdaacabcbacddedacdabcebbaadbdbcadabecadababbeeeccdcebcdeecaceecaccebdbcbddeacedbcdcaadcaebbbedaddceeeeaebaeeeaccdebbecdccdeeccabeeabdebaaceecddeaaceeadbbadebbecabcaeaacbdcaddcacddbcadcbcecddacabcebbedeebededccccdbceceebaddbcdbedbdcebcdacebdccbaebdebddecdeecdacaabccdbbadacccadcbbcdabeedbdecedbdcbdeadeebdaaecbdcceabaebedabceadacdbbcedcacdedaddedbbceacbadccdddcbddbebceebdaaabbbdeceaaabbdecdeeedadeabaaebcadaaaaebacdbcbceddbcebbeddcbcaaadcaaadecdbabdcebaadedddcbdeeecdeeebeeeadddbbeacaacedbbabaccdbaeeecdbadeceaeecbcdcabeebbedbcbbdededbdcbeecbcbadadbdcadaebaadabbabaabdaecbebbabedcceaaebeaeebaacbceeadddceabbebdbbbdbdacaeeceeabcbeeceedbdadaaaddaeddeedcdebecabaddadbcaceaeddacadaadebbdddcbaaacbdedecaaaaaeecbbdcdeedcececeebdacbbbebdeeeecaabedaaddaddaabdebddebaebdececaaceadcdeaaacedaebceddabddaabeeecbbacaaaacdddeaaeddabecbcbbddaaaabbaebeaeaeaddadceaacbbcacabccdadddddddbbedaadaadabacadceeddeebeadbddcebdededabcdadaacddaeadcbbdaccabacdbbbebddcbeebabacebceebebadadacddaaaedaaacaaecaeeddceadebbaecccebdadaeeaacccdebdcebcbcdbcabbcacabebceeceabeaaecdccabceabcccbbcbddcdecedaeccdbcaeeabedbabdddccbceaedebdddeebadaedebbabbeaabecddaaddbcdcccacebbaebcedcdadceeddecaaaeecabecacdacedbdacdbeeebdcdecbbdccebcedbabaeadaaeebbbeeedadaaeaaecabddedaecbecbcbeadcabcdedcadbceaadedaceeaebdbeeeadacddeceaecaabeceadeeebbbcdddebecbcdccdededaeaaceaececbcbccbbebddccadddbbbdecebbbcaccbddbccacdebabacecbedaabbebddedebbecddbcdeaedecddadaeaaeeceeadeadcdedaddeeecbabbdccddedadddeddbdcebcbcbadeeadcdeaacedecccaaebccbbddbddebdcaeaacedabebccadbadbddacbbadaadecdeaaaeccaadbaceaaacadbaacacbeacedcccdabeadabbabceebebcabcccdcbcbcaeaeacbabcdaaeebbcbcddeadacedaeebcbcdaebdbbddaedaaabebebeeaeccebbdebebabcbebbcdaabdadeaaebbddaceaebcbedebcebccedbcbaaaaeaebcabbbdcaaeebaedbdceaddaadcebecbbaebbeeeeadbaebedbcacddbbacdbdbcdbdcbcbdeadedeacdeaaecbceaabeebbbbdeccdcadaecabbbdebececcdbbeacddeecbecdebccaabdeeddadcacadddaebeddedeaecddcdbccabcccbdbabdaeceeddbeaabdbaceebcdadeaabeceecbbaebacecddedbcdcdbbeceaaddaaabcdcacdabddedcecddbeeadeacaccdcbdebecebcbbdccaccaecaeacabacaacceeededabeedababbdcdccadbcabdadeebdeacdaeadcdccedadeedddbaaaecdedeabdbabacbcedbeeccdaebccacaebcdebbbbaaabbeeedcecadaddbcdcecedadacdceeaabdecbbadeedecaaeacebaacbdbbaebccabadeddcdaccdccadbcadbebedecdaeaaeaaeabcaccdbbaededcccaaebedededcaceccbecbabbcaeecdaadeccdaaedcdbacbbdeccedeacecddcbecdabcabaacdbecbcadbdedcccccebeeadaeedabdaabaaaeebcbaeccdeeeeeaabccaecbccebdddebcceeeccedebcadaeccaaddbccbceeccbebdadddeaeaccbdbcdceabeeaddbcddeaaabadaabbaadbaecacbccabaacccabedacaedccaeccaedcabebbadeedcaaacbecaaccbdccccadedbecaadecaecbadeeacbebcbedcbeebdebcdbaabdeeedeccdcaaeadebdaaeedbaedaabebbdcbebdaedbeadbedccaccedaacdcaabdbdeaaaeeadbcaedbddbeaacdbaacaaaaaadeadeeebbcecaaaabbeaacadeeabdbecbcdcdbbceececddbaabcacebbdedaedbcceedeeeadebcdbcadadadbddcedcaeeecebbbbbcaeadacceecaddbebdbbcbeaecdcbbcdaaddabbcddecadaaeeaacccedcbcadeaeabacaaeeebbeeabbecdaebbabbdbbaeeecabbccebbdecbbaeadbccddaedebebbcbceecdceddcbdbbbddedebaacdceaacecbeeaeedcdeacddaadaadaecdeccacbcaaaabbdddaedabeebaeacacdedccdbeecaedcdebdbddadadabbbccadbdcceeeccedeabbaeebabaadecadbdbdebcedcbeeeeadeddecceacabdbbecebcdaeddecbcbdddddcdeddcededaadaecbbedaaececebaccaedcbdcababbbcbcaeeadbbadceeaaacdeaeacebdddecdaebeabdeaeecaaaeabecdaacaeabacacbcbbeadbdeedbecabbbeeaaebeedaddceeadadbeaacdeccbcacbdcdbbcadddabdbbaeaaceabdcadadeededacbabbeddebaebcdcaaabcddcabedbaedaceacadccaaadcdadadbcdceceeabbecadbdbeeaddcacecdbabcdabcacddccaddeedecdccdaacceddeeaaccddaadaebcedecccceccaacbdebbbeaadcbaebaccacceeceabbacededdbeaaccaabaeedbeabaccabbcbadeccabaaaeaadaddabbcdbdbabaceaadedcadceeeddadbccbacaadbbbeabccbcccebecdbbbedabcadacddedebdcbeedaeabbddcdbedcadeacdbdceccdaaeacdadccaaedcbbebceeabbeaceeebdaccbdbabacdddbeeddeedadcbcdeeabdcddbaacbaddddccecccceadddaecbabdaebcaceadcabdeadebdeecadccebbcedbcbedabbdbcadeebbeeccdeaadebcabcebceacbbdaddbccdccbadbdeebcccdaebdbdbeedbeedadaecdcaeacbedbbcbbeabeadecdcdbebabcbcaceceebdceeaedebdccccbacbbeeebcabecceadcaabdbcbeeeeadaccbbcceedbdabadcadbcceedadcbebadbebdcdbddaacbccadecdbecbecceaebbedcadabcccbcaacbedbbcdbdbbdddcdadbcacbaccacbedeacbcbaadeeecdabedadcbdacbaccacaebcbaadeeabadeecdcbdedaeeaaacbbddacdeeeaeebbdadbebdecaabcdccbeedddbddbaeadeeacdabcaaecabaccecaaeaebbdceaebcaeacabddbbecaddbcadedbdabeeabbdadcbaacabbcbebacbacaeaaaeddddbedbcabacbdbeacdbaccbbabbbebedaebeadceebadddcdcadbcdbdbbeccbbaabacedacaceedeeddeaaaaaeaaaecadaeeddddccdeaeddbceeaccecebaedabebcbbecbcdcaabdeebbeddedececcebecdceaebdadbdcadecdccdedaeacdadcddcebedbcaaebaddddebcdddeddbddbcdeebbcebddeaeaacedadaacdcebeadbdcccebeeacdacbbacedbbcdacaabccbcbeaddeadaeceecbbdeaddccacdabcdabadcacbbbbcadddcacbcbacbabccdcbebedbaeccebcaebbcaeadbbaebceacedccbbeeaeabbebedebdeccddcbabdbeccacbedcecdaabaddabcebabccdddbbededeedcbbeacbbdadacaabdddbaaddbceaddebdbabdedeadcacbebaaacbedeacceeacdbaaabdeccddcdeccbdbdeaeebbcdbdeabacdcdacdaaddbabacbebeedadcebeaecbeaceaabbccededadadcbaecdaeaabdabadeebeadabcceeaedabbcddcaaddeecaaccecdeeeabccdeacddabdeccaeecbbcbbcaeecbdeddbdbdbbbcaddcdeaccaacbcbcbecbbaecbadeaecbdababbcabdcabeacecaadcbadeccedcdebdeceeebbcdbebaecdbacdcdbbbbadddbeaebbacdeccdbdeddcddedeceaaaaabdeaeebecddaebccaeacdceecadeabcdaccacbddaebbebbadbdaadddaaebcdcaadcaabccebcdbdeacdbaedcabaabadbacbadeaccbeedeadedcaaabdcecdedadbeebceceebeadbbdcdaeaccccddbaaeaabbeeaceacebebdbaeccbdcedcebcaeedebdaaaadececabdeabdaababdbdaecdbdbadbcabcbeabccbbeaddbddbeebbcaedcccbdeebacbadbbcbbdedbbbabebedbdbccdaabaadbaaacdeebaaacdebcabbceaebbeacabcdddcdbeebbdeaeaabdadcadeabbadaecedcbbaedbadadbcdedeedddeaedaeebebeaecbcbeeadceaabedacaccddcaeabdeebdabdbcbabbaeabadeeddacbcdbdeddeeececbecbdebdbadbdbeeaeeecddddecdddcbcaaededdcbecaebcedbeaadcdbabbdaeaecbaaddebeebbddcdeeeeeaeadebbabcbcaceccdacbbcbadaebcceaddbedcbbeddcbecbbdccceeddeadcebbeedaeadbaabbcceccadbaeccacccdcadebcdedbaccbdabbaeadbdccbadebbcbcddedbcdbcdaeadecabbacabacdaceecbeeeaeeaddecaccaeecdbadddacebeceaebdbbbcbacdcadcebaaebbabdbddacbebeabdccdcaedaabdaeadaeacddbbabddbeaecabaeeeadbcbbbddbbecbecbcbaeaddedbeceedceaeebedaabcaebcabcdcbbbdbbbcbdccdcbbccacdccbadddeccbadcacccadedeacbcddbbbebdbaedcaceaaeedebaadbcbcdbbbdabbadbcddeeedcacdadbcdadcbbdcadeeeabcedebeecebadbabbeaedbdecaebcebdabcdaadcbadacaeabbaeedeccebaccdcdbcdbcedccddbddadcbabbaaceabdccddabeecedbdebdbcdaeebadbdadadeceadddbbbeacabedeeebbbbcaeaabdeadaddacadbcdcbcbeccbcbacaedeccdebceebddaaeddcbdcccdbebabadadadcbecbebbbbbecdbabcedbdbeecddeeabccbacabcbcdbedcebabbbaebaceebcbdcccceedcbbdaddbbeddbbeabeceecdcaeeccbdaaaedbcdaeaaceeebedbbaabbdcbbeeacdbcbeeccbaeadbaadbdaeabdeaaeccbecbdbedbeaeddeacebddabdeeaaeadeeccebbdcbcabadebdaddbbbdadaeadddadaecdccccdebeeacabdaeebaabcdbababdaaedcaddbcdcedbbbebdbadedeacebeceaedbeaedcaacbddbbdabebbeecbaccbacbdebecacdcbcdecbeabcabaebdaeaeaeddccebaabbbcaeeadeddeccddaddeacabdbeeeaabdeecbabcecaacaddabcdacebedcbadddbbbccdacacdebbbadadacedbcaabeaccbcebaebabadbcbbdcdcdbeeaecabddbbabccedcaaabeedbceadcdaedbdebeeacdbccdbacbbcdbccbeebebebedcaadedeabeaabdadeabeeacdcbbdacbcaabbeeedeebabeadacabadbaeadacabeeacdbcaddbcbddebbcbbebdcccbdebccbdbacdbbcbbeccddbeebecbdbceadcadcecbeadcbdcedcebdbecedecececebcebbaddabbdccbbaecdeeeecdddccceaaceccdbdaddacbdcbebacebaeeaaeaeeebbeeaddbaaeaacddaebcdcbcbcedceceaebcbabaacabcdabbadcbcccdaababbeaaabeebbcaeaaceebcacbaeacbdcdcbbaebedddbddbccbbabecebcebdecaacdbaaaceeebaaddacdadedaadacdbceedabaaebdcdcedbbdcbdcdcdbbaaccabccebeaecadaeaabdeddeebbbbaaecdebdbecbebbdddbceeedbbeadabbdeccaabbcddbacedebdbbbdedebdeebabdacaeebecddbdbbbdadceebdecedcddbeedddedbceaacbdcbcadabbebdccaadcadbcddeccbccddaabbeeceebaaecdceeddebedbdccbccbceedaeacebcadbcadbcadbdcbccceacacacadccdbcebdbbcaadddcbeedbbbdecdbccaaeadacdcbeacaabcaeeabeabccdaeecddbeceeadbbaaaadcaabaabbdeaaeaecdadcbbabeaebdeabbeabecccecaaeddaceedadcddebbaedaaabdcbaeedbcacaacacbdbdeebaaeabceecedecbcceaceecabebbaccbedbdcbdbdeeccdbaecbbdddaacaccedcebcbddccadaeddadeecedeaecdcbaeccddaecbbeaddddddeeddbdabbbedadcdbdaeeccaeacecceecddbcbebededebbccbbbdccddacacbdcaebceebcddebbebbabbabbebbbeabcbcedcdeabebcbdababecbacbbedaebaecdbdedaadbebecedcbcaaedbacededddbcbcddddeebaaecadbeedbbddadccbbbaaacbaacebcddccdedeeedcbdcaabaabadabddbdcaaadaedbebcecedbeccaadbcddcccdecbedddaacedcdaddaabceeacdbbadabccdadbedecdcdbbccabdeaaeabebedaabebccdcddbccdebabdbcbaabcebdbdaddadebebbdbecbcbcbeeddcebcdaaabecdedebbbaebdbdcedaebdaebdbdacdedbbaadeaadeeceeaeceddabcbccbebcaaecdcacbaacdeeadcacadccbdcdbcddaecadcbddaacccbcbecabeecadaecabbdaaacbecebcbbaaeadcabddbacbacdddcacddbdabbbbeeeeededdbcaccecdbabaccaadbabdaedccebdceeacbaacbdaebbedabaadaaecadebaacecbccdbeaeccbbcbadcedcabaedcdbdbacdcbeeedaadcecaabccbbdbaaecabacedbaaacdbcdbecddccbedbcbbabcabbceaabacacdbaddbdcbbeadebcaaabdcebbbdccbededeaadecacaddeaebaccbbbabbdcdddcacbbaeaacadcdebddaedcbbbbdbaaabedebaecbccecadaecaadeeccebdeaaecaacabbbbceaaadebbbbdeaabdedcadcccabeceeebcdedddcacbdceacadbbeebcbddabdeaaaecdcecbbeabccdecdacbbcdcccedaebaacbbcccdcddcabbeaeceddceebacdcacacbdabdecbcbbabdddbaebaddcceebcddcdacabbcecabbaaeacedbaceaedaccecdaeedbbccadeededdabedbcedbddaeecaceadabdccdeeebcebdaedcdeabaddadadbbdbeeadbadbbdabceedabcbaabbcbeebeacacabddadabedcdabebbaabbdddeeadbcdaebebccbbeeabaacecbeadcabcdaaceaeddadadabebecaaebdddaeeaecdadbdacbbbcdddadbcacaeecdaebaeecbdbcaebeabdecbaeddaecebaaadbcaabdeacdbebdaeeaacaeaebcccabbceeddddedadebebedbeeaeddedbdecbbacbbbacccbcbbeedeeacdaaadccdaabbeecabeccdcaabbcacccecbbceaeeadeddcedabdaebceeabcbdbeaacddbcdccbbedbceeeaaeceddbddbcacdeadbcbddebaceacdabcbadcdebaaadcbaedcbebedaceecdebeadcdebcbacdbccacdbcbcdbaebbebdeaebdadbadeeadddeaacedeeecabcaededdddaaaceadeedeedecbedaeabbeacecdcecdeddbbecddaaaaaabaaacedecbebcdbadcbbeecdbbbcadcdcaeaeabcadebeeabbabdbdadaadadeddbdeabccdaceccacbecbcacceecdecbbcadbcbaebabceebbeededabdcccbebdbbeadbbceacccabecbaccaedbeadecdcebccbeebddeaddcbbaaebeeaacbabdccdebddbcabedeecbbcaaedacddcbebdbcccebdededebbadeeeeacbbceaceeeabbdebedbddeabeaaccaeaeecdebaddebdaaebbabcabbbbbadacbaeabdbcedccacababadebebeaecabdeeacdaebddbcabbdcbbeecdcecaadeeabbeeabacabccaadcaeddbeaabebaaceeedadaecdcdbeecdddabeabebbbaadcbedbaaaaeaecbecbbbbdeeceebdbbbebecdeaadaaeaacebceebcdaebeccdbdbeecbcadbbeabecceabbdebcbeeebebbbcdbbbdacdadbcacbdabedaddbbbbbccaaaadbdccbcebaebabbbcacbdcbbbadcbdcdcdecbdbcdacdeaabbcecdbbccdeeebdcbceabaeadecbeecddedbdcdddeacdbabbebddaebebeadcbaececbddbaeebedbbeeadecebecebaeeeeeceebbecacaebcdbaebaeedebdbadaeaccebaadedcccbedbbbbcebaceacdecececbcbcbbdbdeedbadabbadeeeabdddcaaebaceabadeccbcddabeeedaeaacacaabecbbbbbbadadacdaaebccacdbebecdadecddccbdcdadcdeadadaebaadaeedeebeaddddeeebabeabbcadaaedacaaceedebbaaacecaebeeebadbdaabaedebddccdebabacaeeeeddcecabdedadbaeeadddaadaeaadbabdaccbacbceeabddbeaedcaebdcedeadaaecbbcdbaabdbabacaeebccaddbccdddabebbccbeaebcadadbaecccabbddbbbccccdaecbabcdebdbbacaacadedecddbaedbeaaccabebebedbaecbabcaadabbecccadcbdecdaabbdabccbaaecdbdcdeabedaccbebeebadceadacdcadeaaaedccbcbeadceedbaececdbbbbecbbdcbbeaccdcebdbaebcbbbdcabdcadbceabbebecebeecbcdeabcceddabacaeaccbbeaecebaaabebebcaabaadaaadcedcddbddbaaaacecdabcadddccddbededbbaeeaabeaedadaeeecbdbdeeebccaacabcbbacecacecaaebededdeedbdceccdeecdececdcdceeeddedbaaabebbbeaebddbbddacddebecaabbaceaebdedeaebabdebceacbbaadeabaeecaddebbceebdedbbadaacccdaaecbbcbadbacddbaccccdbeccdcedeeadebddebeccbaacbcbeaddcbdbbacdceeedecabdbbdecbaecdcbdadcbeccdbebedeeaaeadbcdeddccaaaaaeaceedbcdddcebeaccbecceddbedabdcdbcbbbcbbaeadddbeebacaaeedeedecdababdceacaeaeabbcbadbbbeedaebebbdbdbeebcacddedbeebddeaeaeaeaeeacbcbbbbddbbbdeaecaeaeedecdaceddeeedcccdadbeaaecceedeccaecbacbaadcaceebddbbbdebcbcddcacebeddbccdcceaeaaeccdababdcbbbadceeeeceaadabdbbeeeccccdabeedeaaeeceaaceeadbabaccbaceacbcdaaeabedcededaccabaeadebdddbddbabbdaccdbeeedceedaebcaceeebbdbcbeccdadcdeedecaaeddaaaeadabaedadebecccceeebddbacccabeeeedaccaededbdcaeacccdecdccdcaeedbbebaecbbacadbbddedcddecadbdadeeededabeccadceecacaaeedebebeecdddbbadaebbaacddedcddaeedaaddceeebaccddadbceaebbddaeadccaaedabceddbaedecaaddadcebaceeeecdabceccdeadbedabbbecebcaebeebbbeacabccdcbcebaedabccdacdacbabbbdaaebbaacebabddeabaabbbccdcacbbbebedcaeaccbecbabbabeeadaccdebeeeaddbcedbeeeebdeeabedcaeaeeedbdaedaebccadeeeebcdaacccacbcbebddddcdbbbdcdbceccebabecbbdcdacbaccacebdaccceabdeccbceecddbadbaccbbabccbbcdebdeaceccccdbababbebdebebdbabceacccdecaaeeabaecdceaecdabdbaeaccdcedccecacededbdadccbeeecdeceeeeecaccbceeaaeedbdeadecdeeceacbbaeaeecdabbcceaaeaabccecddbdceabcecccbbcbcceadabbaabebbaaaacbcbccebedbaacedbbdceeaddedabaeadacdbaecedaddebcbbbabdacedcddcceebdbcccdcdbedcbbcadabadbdbecbaabecdadddbbdeacdeedcdcecbecabaededadecbeccedeaeabeecababeeacacdeddaadbccceedbbebdbcaddbebcbeceeedcbcbdaceeaacacbdebaadababaaaaadbccdbdabeddebbabbbdcadadadeacbccedacadcbeaaacdaceabdeeeaadbcbcabeeaadbbeebabadadaddbceedeeabaeaabdaebdaebbbdedbebccdbbbebeccdaadebeaecdddeceaceccadddcabeecdeacdbbebbddeabdeabebabddddeacbadcacbbdbbccabecdcdcaaaddbdeeacdeeecdedbeaabecabdaebddcdaeadeddabbaacbeadceeaeaeceeaddbeaacccdcbcaebcbadebbeedcbdbeecdbcbbaeeaebadacbbaaaeececaeaacaadcdcebdcedadbcecebbbabebcdeebcbbbaaceacceddbddccbdacaabecceceeeacddaaeededbadabbeabdadaacdeaabeeceaaebbacdaecacbeebbddcdaaeebdbdadaadeecedcccbedcdabeebeeccdcabddbccdcebabaeebbeddcdcedddeedeabcabeadbadecbcaaeaabbcdedebddbeababdaecaeeadacacdecebbaaebecbeeeacadaccbceedddbdeaedbcedaeececbccaedbddadbdabcaddacecaeceaeaebebcaddcbcddbebadceaabdabeedcbedbaeddceaabcecaabeaeedeacaebcacdcdbdebbeeeeaadceceaedbedbebbcecbecdbdbcaabaebdacbdcbeebdeedceaabdeacbeedeeeddabcdddcacabecebcdceddbbcdbbdbdeaeacaedeedaaeeedccaabbbbcebddcaabcebeebdeaccebceddcbbcaebdcdadabedeacbedbdabdacaaceadeebcdedeeaebdeacbcebdeacbbbbaeceadeaeaadbbbeccbcbcddaacebbaadddeeebdddcceebbbdddaedddabaeabaccbcebaaaaebabaaabbecbeeebbcdbdbbddadcecadecadbddecacdddcabadcbacdeceebbcadcdaebbbaeeecabacdeccedcadcdaecacbdeeccaabcdccbaedacbbedebbccaecbacbccabceedebccdcdccaacbabcaebeeebecddadabacabadcbacbcdbdbadbaadaeddcadacadedeaaddeaeabcbeabacbbdbeccceeaebddccdcecccccebedcedabdbaddeddbbaeceabdbcccadedeadcaaedeaddebdacedcaceacdbadcddccbdeadccdbeebddadddacceabdccddcbbeaeeedcdddebaababccaeedabbdaececaeddecbcbccbbcbdaeedbcadcaacbdcbcbccacdbcedbcebbdacedbcacbcaebaaebacabababaadcbdaececaecceceabdbbecccbbacdbcebcdedbaeabcbddbeccddcdcbebbacaaacbdcbacbbcbebbdbbaadbbccdcdebdbebbabbdeccdcbbbddedcacadcaacceaceedeadcaabaccceaaaacadcbbaccccccbbbcdebabbcaebdebacabeecbadadbcedacdcaeaabddecacddacebdccabceebeeacbcbdaebaacbebbcacdaccbcdcbaddcbabcecbbdecdbaedeaeedbdcaddbbadcaebedadacbcbcbccbaaaeebaedabdaacdcebceaddddaaedcecbeccaabdeedaedebdacbbbebadbadecedecacdacbecbdcaedbbcedcdeeaaeecaadddddbbececdaeebccddccecadebaecbceedcedbbbaaeceeecececaeebcecddbaedebeadabcaaeaebdebdebaebdcdccebdbdeabdccaaddaddaacdcbdbdcaeeeccaebcacbbedadcaadccebaeecdeecadaaedbddbeddaaaecdcabeaecaeeceedddacadabcedebcaeedededcbccbbedddabcbddabddbaeddbdaadcbdbbabbccaacabaceceeedeeccddecddbbcceabaebbbbedececeedbebdbacadcdabcaeaacdaedebdaeaceceaedddccdbcdcdedadcccddddaaeeaaeddebabaddcccccddacedbcdbeebdbacccadcbcbddcbcbabddeaacaabdaceecbdcabdbebccdbdeababadcbaedaccdabbadabcdbebcebdcedbbaecedeeebaeaaaaeaaaeaceeebdadcecbaeccdaecbacdbceaedaaaebdddaebecddaeaccaedcacececdbaaddbdeeaacdbbecaaadeceaaecaabeebaeedaebdaaceaeddcadcaddeceaeddcdbbededadaaebaeaebdebeacdecaaeabecbcaebdadabeedcaacaddadcdbeaadebbddebebedaeddbededdcccaadeedbbadcebecaabadecabbcaeaaddadadcbeceeeeedddaacabaeaceecababbabdaedeaacebdaaadbacbbbacacdeaccaeebadaacebdaaabeddcabddcdddbeddbbebaacbbbccddeedebacebbecceaeabadacbbccdbdabcbbadddaeeaabdcadebddaeaccabcbdbbacccccdbbbbeecdcddcababdecdceabddeadcbaddaedadeeadabdccbbecacddbbedacecaccbcedebbeabecbabcbbdcecddeecaebeddddeecaaecbbeebadeebbecbdaadbcbbcbccdcecdbcceabadaccebdececbddaeacdecbabececdaabbddaacebaabcbccccadacedadcebaaaaccbeebebeacbedaedcceecadbbbdbbaeeaecbdabcedbdabebaccbccaeadeeabddcabaadacabbbebbdcdccdceacbabadbabbbaaccdacacdaedeacdecbcdbedeaaccedeacdededbdacceccdedabecbeecebaccbedaedaeddcebccecbebcbaebbecaedbabaeeccdabbebddceabdacbecebdebbcebcecbbcbdeddaadcebabebacecebcaeddbcedacabeebcebadeedaeacecaabeeaabbaeebaeceeeeadbbbecedcdaedbbaeabbdedeedeadaaccedbcbaabdaedcbebecddcebdbbdaccbcdedcccdccbabcedeecbebccaaedeabbcecdcbdeabcceabaedbbaabdeaaddeabdcbccaeccceebedabcbcbecddbcdccaeabaeaeaadaabaddbaabcbedcaeaeaedaababceeeadbcdeacaaebebadedcddebcbbddbecdbeccdbaaadabaeceeceadacccbebebaedcadcbdbadedcacbaaebcebbbbaacebcccaecedcaadeeebbeedddcccdbcddbbaadaadbbbeecbedaeeeeccdccbddedeacdaaeeaaebebceaceedddbbcceaceaeaeababdcbdbacebbceacbadcbdcdeceeedcacdcecedcdbceaeabeaeadcdebadbcbdeeeabdceaaceadebeacbddedecabdacbdbdbcdebccebeeaacbccdddeaecbadecebbabdeddacecdbdaabaabbeaedceacbeceadcdeacaccdaedadeeabedbabbcccedcccbbebeabbbdbaaddbbdabadcaeeedbbbbdedabeeebecdacceaaedeccdbdcbeeaaeebcadeeadcaeaaeabccbdaeedddbbecaddddecbdcaecacecbbeeabadeedddbdccedccacabacbebaccbebeeadebebecbccdbacccddeaeecbbeceadadcaeaddbbbccdaeaeaebbdeedacddaaeccbbbaaabbcceabddcdcceecdebeebabdcddbaaeacdbdceaaededbcdccaaabaaccbceeddadeddddeaaeeeccdeacabdbbdaddcbeddebcddcebacebeaabcedddbbcdddededcbacdbaccebdbcbaeebbdadcccbaceddcbbaacabbeeabeaaaedbeecedbbdccabeaadadcbdbbeacceadcabbebbbdedbcdbeabeebacaeebaaaceadaaaabeabdeeadcabdbabccdebdbcbccddcdadeedbeccdaebeecbccbceaedcecbccadddcceaccaaeccddedabbbbcbbcdecdbebadaaadededabbeedccdedccebceddeabcbddbdbdabdceabcdbccdcacebcccbbacebaddbcaebddddbbbcadaabdcdbdaaeeeadbacebbcdedeabeeaeedebcaabcaaeecacabaaddaaebccbbbeabcedbadacdebabaacbbbbdebabdeddbccbcccddbabcddeedeaebcaadcaaddedbedcaeebdbbaacddaeddccccbdddbcadbcbaaceabaecbacbdbeaabbdacdadbeebceaacbebdcbadbdeebcaeaaecaabdaabdabebbcbcbbbebdadddeabdeecbaeaddedccedaeddcbeadbdbedcdeaedcccabccacacdacebbceaecadcccaaabeceeebeadaadbbdaddddeeedcebbaadbeedcecdbcdbecebdceabdcbaadabccceecbaedaaeecebabeebbadeabdceedaaaeaaedcccbcaacecbaabdbebaaaaccecdcceabcbcadcacbbdeddcbcbcbbabcbcedccebbcaacadcdadadddddaccbecdcecadbeabcaaeebbbccebdeedabaecbedeeecaaeaabdaeaeacaadcdeabcbcbaabeedabedcebeeaaecbecedeaddeddccdccedaddbddaeebdcedbecdcdabaadaaadcecbaecadeacacdabedecbcceadddbdcaddcdbecdbceeacdedeacedcabbbdbdcccabdbeccaaeadceabbbddbbccacbbbacdacadaabbedadcaadaeddccdcaadaadedddbbabaeaeaeacabeeeeecdcdbdceedceaddebadccceebbcddeccdabaaccbabedbecbedbaeadaabacadddcdebbeebecaabdddcaddabddbbeeeedaabdcddcddadebceedbedeaddeebacdbacebedacebedcaaadcbbaeececabdceeeabceeeacdebaccdcddbacadbbcbedabbacebcadcdbeeddbbbbbacbcccedcddddcbdaceaaabdbcecdddbdeaabbeedbabcbeddeccdabeceaccddceadacaccccbedcaedaaebcdadcbabcdeeaecddbbbabeabedccbcbcbeeaebeedcdabddaebabaaabbdcecdedaebaeeaebaeaaaeadeaccdadacabcaecbacbdaababceacbeceaadedecddcaedebbabcebadbebcaaaebedebaceeaceccdceedadcdbcdaaedcddcedeedabedcdecebdaddcbcedcaecadecaaebccedbaacbceaecbecbdbdbcbcddabbdeaeeaedbcaecdccebbecbccdcddbddbbeabedabddbecaeadbacceeacaceccaaababeeebdaceeadcbbdcdceaebdcdebeddaedacbeceabdbcbbedeeeaebbecbeeadabaacdceadacbecabcebedbccdcaedbecdccbcedcaddddeedbeeeeddbedabeabacddcecbdaaeeaecddccebbccbaccbbcebbbadedecaaecedddaddeaadabbeebcaadbeeeebeceddbccedceecdcbcbdbebdddecaceeaeeabcbccadbcdcaddbcededbbedbeacdaaabdaedadeebbdaabaaeabacaceababcbaecdeeeebdddaeadbdcdcdbbadaaeaacbeacacaedbcdaaebbdbbddebcaaacedabcbbaecedacbecbadaccdacebddbbdceeaccceaaedbdecedebabedaccbbbbabeddebdeceaeeedaaabddeeceeacebbbdcaeaeccbbaedcaddaebbdeaeebceaaeddedeabdcdacdedeabeeeccebdaedeeeceadbeeaddedddbbadcdbadeabbedabbbcdaeabeacbdabcebdeabaccadebdabddedddaabcbddcebebeacadaeadddccddddbdbdeaacaaabadeaceaebcaccdecbcbacbdccadadecbeacecedcdaeccddddbbbedeecbabddaadadecabcdecbcdccacacccdececaedceaaacdecadadeedddeedabbeaaaabacbbcdcbdceadcacaeeadecbcdeebadabccddbdcadadeaeadbebaebdebbacabbbaaaaedadbbcdbceedebbaeccedccbdcdbcdaaaeedcedacccadacadeebdaaddacddecbeabadcbdacbeacddccdecdedaedcacaeeeaeadbbeadddecbcccbacdaedaecdeebcecddeddbbdbcbaebaedbbcdccdaeebdceaccdccadebccbcdedddbacedbaabeaececccbecdddeebeeaaadebeadaddcebcceebcbdddbaabbcebabcbdaeaceedadacbeabdaeecacbdaebbbeeecbecceabddcdcdccbddbcdecbbeaeeadddecaeceaececeedcbaaeddebbaabeaceaadddcdaadeacccbdadcdabdbccbcedcbceaeaaddbbdeabcbddeaccbaeddeebaeaaeabddcdccaaecdeaacecdbacbdabaedbbebbdbbbbdcccbdeaadabcebbeedaeeaadceecceeddaddaeaebccbacabdaaecceecbabebebacdaadecbbacceccbdbeaecdcbbbaccccbccbddcdeccaabdcdabacccbebbabeccbedeebbeececccbedbbddaebedabedaedcedccddeedccedebbabcccceadeadaaddebdcccbdeacdadeccaabcadecbacccddbaeaeeddbcecebddaebcdabecbacdeaebbeeddeebdaadebdcaccedeeadaccbbbabeccdeaecddceeebcacaebeebbabeadbacebbcaccdbdcaeedcbdbcbdbabdbcdabbaadaaebdccaedabccdcebdeebbeadadddeedaadbaebccdeeccdbcceadbbcdabdbeededbabbeedecdcbcecabacbbbbecbeeddaeceababdbedbdbeeeeaebabdaaadcbdadaddaecdeaeeaaacdaaabacbdcdacddbdbeedbedbddaebeceedbaabbcbbdccdbbbacacecdcacdbdebaeccadeeaadeacebbeeeddbacecbbabccaaabddcebbdabbdcdadbedbeceaedbacacacaaecbcadbbacaebecdecaeebebabddaedcacbbaadcabbcbceeccdaebbeedbedaeebbcdadadccbecdbcdabecbecbccbcdabbaedbcceabbeecbcaeedceacbcaceaadceedeadabebebebabccaaeabcccdddbdaaaddeabbbadedaaaddaecadabeabecddecdaacaeabbccbaaaabbbaecaaeccbbaeeebbdabeccdabeeddcdddbdbaecebaeccbbcdddeaaeaecbcbdedddacbeeecbeaaddcddaedbbecbdcdbacacdaabdedecebceacdcbbeaaeaeccbacdabdedbcdcdebecaabadbcaeaaabbebaeccbaaebadacedbbacecabaeabebedccebdeabdedbddcbaaadbaeeedddebaeebcbecaadbadaccaacddadceebeaccddcdcdceeacceaebdcbacbceebbcaacadcddeedecaeeadcbccaedeabeececcccbabaebeddbddddbcaadbebdcadcacadaaadbebaebaeadbdadbbddbeddeedcaecbbbadbaaabaaaabdddcaaecdbbebcaddeddcaebbbeacacccbedebecaeaecddecdcecdeeebcceaacbeeeccbabaedaaecedebacbebeddebdbbaeabaecdabaaabbedabadcddceedbdbadebbaddecaaebbaaccbeceeaebdcebaeabecedddbaacedadddcaabaadcabceebccbedccaccbeeaeabbaebdeedddccadbedecededaceabecbcdaebadcddecdeacaddaabdbbacbbdcdcebbceebbcedadcebdbececdeadabbcdcdcccebddabbabcddadbeabcecaaceddcebeeaaebaaaeaceedbccadcbebcdeaeadabdeeeebbaebaadcbebddbccaabaaddccdbcaaebbbbacbabdebeddcdbaccdedcdabcdeeadcaeabaaadbeedbdbcedacbebebebccbabedccaeabdcabdaeadcbbdbdabdabdddabcbaeddeceaeddeebdceadccbeddeeaadeaedcabcddcabeaebecedccbdbaddbbbcbecaabebeaaadccaaeaccdeaeaedcdcddbacabdcceacbedebdeaaedbacddddbeeadcebecaecabeacabcebdbdeecadbbbeceaadaeebbdcebdebcabacdbbdacacacceecbacceecebdbbcedcebcbeebaaaececcbbabccbacbabdaecdcedaccaaeadcaccaeaadabaeabcecaccbaacdaddaabbaaaededbdacbbecdbcaedecdcdcecceeedbeeebddeeebeedebacaacadeacddaaebeacddacbeeccaabddadecbccacdeadcaabbbddcccddbbeedebcddbaceabcddcdeccbcdceddccddbbceaccadabbecdbeaceaeedddbcdddaccaddebbedbceeebacbeddedcedebccbbeecbcaccbaedaeeabbaadcbcadaadedeccabdddacdaaeccccbccbcdbaabccbaceeccbeeedbcaccabadecbecccaebbcedddcddeecbaaeeabedcedaddbdeedcdcdeccceccdbdcabeeabeddcaeecaddcdcabbecbbadaeececaeaaedacedcdeaedcabcdeaccedbceebcebeeabcdaddacedceedaeddceeaeceeedabccadcbccdcadbcacaadecbbbcecdebcccbdbacbeecbdaabbbdcaedecddaecdbcecdadacbacdcacadabcedaeaacceeeebdadeccaaebeeaddaacddedadbabeabccbabeeccaabebbcecdcdbbcbeddbddaecceabebdaddcadadeadababbabccaccadbdccedcbbeecbaceededbecebabbbceaaeeaccbeaecacceadabcacabeaabcacddbeceaedbdebcecddccabcccdebeecccdbebcaabcaaccaddddddbbddcbeadabcdaaeabdcdedcddeecaecbbcbeccaddadebbbceadbccaacceeedbccabddacccdecacabeeadeabaadaceeeccecdabaacedceedcaeebbdbeebcacddcbccceadcdddbcdadecbbdaaadeebdbbabcadadeeebaadceeaebddacbcaeedccebbdddcdbdcabedbbcbeeacabaddaabbcdeaecbedcaaeebbcacacadbbbdebeeabcceaeeeaeacbcabceccaecdeedadaadddbacedeeebccaecaeaabddacccedccbaaccbceddcebdcbccbeecdcbbbdabeeebedecceeeabbecbabedbaebcaadbcecbebcbdccccacdebebaccecdddceaaebadacddbeaedabaebcaccdedaceecccdabceeccbebdabaabcacbacebeaeccadcdcbaececebdabedbdeadadabbceaecdcabaadeceeaccabecbedbabbdddaaddbbbaeddebceebeababcbcbddedeccceacaebdebecaddcdadecdbcdcdcdbdceceedbeeeeeeadaedcdbbaeeccacabacdacbdbabbbdbaeccabeaabddcdeabbbbeaeecdebbdebadddacdcaaccdacdceedaecbddecdbedacabddebbdbbaceadcbbaededaebecaebeeecabbcdbdaeaedebdaacaecdccbdceccbcddecddcedbcedecaaaeeacaeaccebeeeeeadeadbedabacedbebdeaaeecbddcbecebcecddcdcdccaceddbdbdbeddabcdbeceedaecabedcdadcceebadbcbbbcacdabbbcddebeedaabcceacbaabdedbaaabcabddbecbdddacccdeaecbdbdeaabbcbccddedbdbdedeaddabacbcdcddebbeedddcecdebabccbbbccdeedadaaacddbaccebcbbaeaedcdbdaabaaaccbedaddabdebaacabddccbcdabecbecebdeabeddbecbdeddeaceedeaddedcdebbcecdcdbebdeedacbdeadeaeaeddcaaacddbbedaaadecdccaeebbebabeebeccecbebcbebddbceedddcdcaeceecdaabbaaebebadecbdacabdbdcbebbbcdecdbdacdeddceebcaabbacaadbcacbddccbbcebbdedaeddaadcbebaceadbbabaddebcaadaeccceedaecdcebddbddacebcbbdabedadaaeabbceabebeeeaddaaeebbcbbdcebecbabaadeebdabadcadcccedbeddebeccebdccbabedadddbdaeddeacaaaedcabcacaaeaeaeecedbaebdeccaabaadeeeecedbedececcbbecbecbabeebeaecdaebebcdaebedccdaaebedbddcddcccbbededbedbedeccaccdcedeaadbbeededecebcdeaabdbabbedbaebcceaebdeeccbcaeeeddbdcbdbddeebcdcdcbbecacbdbcaddbdbaecbacadddceaebbcccdedcabceaadddededcbaccaaedebbbababbeaecbcbbecbebdddebaaceeececdbebadbabaeecdacbbbabbabdededceacacedaececceebedcdacceadddaaacbcaedcbaebdccdbbccbbdeeaebbbbadebdcdcaceadceecebbaebbdbeddbedbebceeeddeaeedeebcbbbadbbadbaebbabaadaebabcdbacdcadeeeccddabdeccadbaeacddbbdbdaebaedaeaaadabbaeeeaddcacdaabaebebdeebdeeddbeebabedaaadacdebbdcecadcbdebaeddbadcbecccdadadadacbcbabeccebeebdcddaedbecdddddaeeeaaaedbbabceaeedadcbeedbeeacbaedebcdadadddaeaeeacbdcaecddcbededcdbbeacebdaaeaeedceabcbabeaecedbbacaeceecbebdcadbddacbedcbacdbbebddddcbdadeaddeecdaeebdebddbdedceaddbedcaaacebebbebacccdcbddbadcbedbecccbdcebcabbadeeeededeaaaddbbacbecaacdbdbccabeecbbdbaebdbcbaddceaeacddebddabaeeeadbbcdedcabaabbadbacacbaddbdabddcddbeccebddacacbcdcbdbbecebedbcdbaeebabddbbeecdeabcdceadacccdacecdcbededcdbbabdedaecaecadebacabcbdecacabcebdceebacceeedceebcccadcceadcbdababcddddcacbbdebeaabcebbceeeddaeceecdbcbacdebabdeecacabebedbcceeaadbbdeaddcdcceddcbbcaaaddbccdeadcacbbabebaccaebabedbcceedbddbdbaebbbabceecbcccaddbedeceacbedaacebacceebecdaadbbbaebdaedbabecedaddbbbbdcaeceeeacdeebcacdbaeebabbaccaedbcbdcedecbddbabcaedccaeceecaebecdcdbaacbdbecdccaaeecebacdeaecbceadecacbddbdbeebacecdabacbaceebaddcaccabdccecaebcbceddecdedddabaedababbcaaacdeeededcedbbeeaeabccbbeaecebcbdbeaeadccccccbbeebebabcbecaaeedbcebabcceaccedaebeaadcbacaabcbcececdcdeceeaacebbdaccbbebececcbdbcaaacadaabcbaacddaeceadcbdbcacacecaaeaaedcbbbbcdddcdbddccabcdccbbeebdabcdcbccdbdbbabcabacaaeeaaeccbbdaecdbccbbcebcedeaabdeebcdbabdacbeabdbaececadbabdbacceadbcbabcaaceadebdbaadbcebbbdbbaeadcdcadeeddedcecccebedeaaaedcedcdaacddccebbcadddaebecbbeeacdbdbeebadebeabadaedbcccacdcccddebcedaeadcbadcdebbeaadcbdbbcdbbbaaaecdcacbcdaceeaedbdcededbacedadbcbcccdbbcaacadcaedaacadaeebecdcbabccadeccdcbdbcbcdcebaedcdbacaaecbcebddccebededadcbdaadeddbadaddabcacabebbaaedcbeedbedbcbeacadbcceaaeebbdcabadccdadebeacddaedcaabecdcedaecdaadccaabbbbaeeecabbddabccdcccbddceadabcaacdcedaceacebbaeebebebaedebbbcdcaeabaecbebacbdaaabdbbbdeecabadbeadeeeaccccbdbeaaadadcaebdcbcbbdccdadadeeadeedbbbdedddbeaceecebeecabbeabaacacaddcdbccbcbdbdadbeedcdebedadadedeadadbedcccdbaabeeeeeabcdeabaabaadabbddcbbddcebbbbdcaceecbbdeadeeebeccdbdebcebccccdaceeceaaabaccddbdabcacccbdbaaabdaaceaddcbdcdecedaebbcbccccbeecdaaecbadaaadccdbbacbadddabcbeccbccdeedaecabbcedbdadeadbeaeddcbbebabddeebdbcaccdebbcacbbcedecbdbdebbedeaabbabbadbdeeedbeebacadcbcbcaacbedbbbeeabeeecdcdeaacdebdecaecbedcabbadbadccbcbeababccccbdababdedeaadddccbbedbdabebadabeabebaaacbcadadbeeacaddeacddccdadcecdaaaababecaedbaccbdeceedbccebdbbbdbcddeacdddaeccbabbacbabeebeeaeadbabeeabedbbaeaeadceeeddabaebdacaecbebedbbcaabeddacebcdeeabcacccdedbeeaabbddadbdeeddbbcdabcaabbcaacbadbeeaeeedebaadabcaedeeabbebdccbabedaccecdbaedbeaebbbbedeccaeababbebecbadaaeadebebeeebbcbcabbbdadaaceeabceeadccdadecbbdaebebabcecdeadbaedbebcabdbaededcbeeeeebceaddbdaedeedebddcbdbcbcbddedbbcbcdadecababaadbeaedcddececbaecdcaeedeceedbcddccaeaccadbddacecaebbadbecbbadcdbeebccaaeaebddaabddddddabeaacecbbaeabbadebcccdbebeadcceecdddbaebbeacbdedcaacbeddeeccbbcbbcbcddbbcdbbaceedccdccacdbdbedbacaabccaccdbaaceceeeeeadcdbcecceebcabbcaeadccdaabecbdebabaeebbccaddcaaddeebbabbdbcebacbbacadeaaeebaaaeaebedbcbddaabdacdcbdcdbdceeaebabecbdecbabdedeedcbaeaddcababeeaaeacbceebecbceacbaaeeeececcaeadcdcadabbccebcbdbdccbdbeeaccaecaabddeadecbccbdbddcdaaeebbbbbcceabeccbdcaeaedaacdcbccccbdaeecdacbbcebcdbbcbbbcdebeaeadbeaccaeeedbdecbaabbecaeaadcedeeeeeeaccdebcbcbcdcdddbcdaebdaacaaeaeebebbbeeecdceeddcdcceaedaedeeeeadeaeccdcbbdccbebecbacbbeeaeceecaadedacebdaadaecbabadaceddabceabeccecabccbdebacdebcebbccdbbccdcaabbcdaccebbeadeeaeeabbdbccbbdeebcebaadbdbbaaadaaacbdbababbcdeceeeacebaaeceacbeceaedecadadebeebaeceebeaaebbaaaebcabaaaccbbdecbdeedaddeabcaaebadadbeededeadecdcbdbebacdccecdcaaaeabedaebedeadedddcaecedcdaaeedeedebbecccaededdcdbdebcecdaaccadcbeccaaddadcbaaebacacacaaacdcabceebbbbbecbbdaebceabdaeaabcccbaedbcbddaddbdcabaaedcadeeeadabbcaddabaeadeecdadabadcccaceebdcaecbaebbebbeeaedebcbdcbcdadbabaeebdeecaaaaeccebaeaaababeecdeccbdeaaedbaeacaacaedeeecaddcaeebdcbccaacccbecedaedbbaaadacbdacebadccebaecaacbaeeaeedcbceadccdaeececcdbceddaacbadbcdccaeeeeaabceededdbaadeecacadddccabcabceeebadddddcaaeeadeddacdbaeccdeaebbbeaabadbeeabbcededeccaaebceccbadbcebbddbbacddccbedddedcadaeeadcceddbcdddabddcbcceccdbbaddaeeaedbbdaabdebbcbceadedcaeeadabedbbcbebeebdccdbebdeccbabecaeeaaecceedeccdcbdebaaccedaaeaddbeaaececbeabdabebabaaccadbcabaabcaabddcaeababbdbcebdcaddbeeccbbdbaeabaebeddcdbdbddddeccccdecdaedbbaabcedabebdedeadaaaddaaabcaaadbdbadbcccbbceaedbceaabedebdeaabdeeeeceadabbcadabbdbcddddcbdbaeeceabeceaebdabbddcbaeddeecbaebecaeedaaaeceaabbabdacedbbebecacaccdaebbbecccaecdbccdcedeabcbebedbeadbcbccbaddbdeaeedbbacadbeecadabbaaaaeddaeeeedabbcebebcbecacbcabbeeadcdaacebabddaeddceebdbededabdaceddecdcccdeadabeabbeecebcdedbaabbcdbdaebaeceacdcbbebccbadbcbbaddccdeecaedebddbcaedacadedbccbeceaabdacabecadaaadeddaaaedacdabdedebcebbadbcbeaebdbaacdbbeceaacccadedecebaebdabbdccdadbaacecebecbcababaceceddaedadbaaacecdacdcbbbdeaecbdeaabacdabdbdbdddbcbcdebbebbcccbdeeedeeaaebbcdeebbdacecddcacceaecdbcaccaccbccaeeddbbcdcedbabacceaeceedceaeaedbcbceeedeacdcdccdaeeceeceddcdeceebccbadddeedeabdcaebdaeaadabcacdabbbaadddcdedecceedacaabdebeeebdccadacddeeddceacedbbcdddcecbbadbaaccbdccaacbdbaebbdadacdeecdabaadccbcaddcbbbedeceacdcbcdcaacddbcbbabaccdecbecbcbacadeedbceeaceeebacceddddddacceceedccbeebecdbbabbbcabedbabcbccbecacbddecaebbccebccbcddedcbbaabbaebbebcacbaecabaadecaacbcaebcdabedaebabedecccbcbcdbbaeabdabaaacebbdcbaaaaaeccbdadddcaceeabaaeaaaaddbbcdcbeeeabbaeaedeaedccaeaedceadcbdcddbddcedabdcaabcaceedcaddcbddddbceaeceaeceadbbaddcccaeecbdaddcaaebbdeacbbbdadaadacbdeaaadaebaaeeaacedeaaadeeadbdccceadacacacbecbbeccedbdbdeedbedddbadcedaeeabbabbebebccbbaddedebaaacabbbcdacdeddbacdbcedadaeddedcdccacdbacabedaadeddaeaddeaccecaabbbdeddeaddeacbbcddcacdbecaaecaedecbcacaabcddbaebdecccbbeececcaebeeedbbadabdcedadbdaedbbcecceacbbbecddebceebdcaedbebaddecadbaacbeaaaadbaedbcbbeddcebeeadaceaadcaeabdbcbadeeeeaeeebdbccbeebbddbbddccabaeabaebceebdebcaabdabccdecbdadccddccbabdeaebeaccbdebedbbecaeaadaebcdaeccaccddceeccdacaaceababceededadddaececbcadacbcddacdcbbeaebdbebeaddcabeececabeeececcacddedebeeaaaadebbaceeaccaaeddadcbdcedeacccebbeeddbaeddaaeebaccebadabacededbdcadacdbdedeaaaaeaabdabbccadbddecbedadedcdceeadeecbcedaacbbbbddddcadbebbbdcdbadcabdcbeebbbdabcaadeddaabadabdedebbccbeeeeadabceddacbbdaecabdaecaeedddebacaaacbdcebdbabdadadbceeeaebbbedadebcbbcdebabecdadcbeeabdbacaeaecdbbdaabdaeeedcacebaceccdebabaebcbabdddbccdbdeccdbedecaadabbaabccebadcacdacdbcdeedebabcaeaccadceddbeeeacadaaecbdbbadabddacaaebaabbebbaceacaccdcaddccaeeadeeeabbeebadaaeebcdebebdbaadebaedacbacaaedddbadcbebcaaaaeccdeabaaaebdbcccdaddacdbcaddbdedbecaedecbedaacedeeeaecbccbbaeebdeedbeeceedabcecceaeddebbcecaadbddcdebdabcbeddadbddcaeadbeabcadceddcedcecdbbeedacacbdbedbcdcddecaeedeacdecdadbabdbcaecdebbbbdddaeadbebeaeedacdaeecceabbbbabebcddaabaadbbdcaeedcccdbebcabedacaedacbccdcbaeceaecdceeeabebcecbbabddcbaecaceeaeaabaddedbcaebadeccadbcbaddcddbeceadaddaebadcbbabbdabbaeaeacddcabacdabcacbdaeaebcaaeeeedbddccccaaaaaeeceeeebdcaabeaeeadaaebeeeabadcdcabdcbdaacecebeccdcccbadddedebbcaeadbeddabcebdeadededbaddadedadbecabebceedadedabdddcecaabddcbdaaaadbdbdbdceacabeedaeeeccacadceadebeeebaadbdaeebdcddaececbeaccaacdcdeeabeadbadcdeccaaaceebcdaaaccdcbdeeaeecdcbccabdcdebcebdaaecaceeebcaeabcbadbdbbeaaaeabbddacceceadbbcbedadebdabacecbddcecedbccdaadbdebeecadaabcbdbeaebbceaccaddeceeadcdbbebcaaebdaaedbebdbdadcbedaddaaccbdbdadbebccecccebaacdbcbbacaccdebbebcaacbcbededbdeaccecbebcdececedbcdcdcdceccbaeaedeeeaccebcdaebacabeaaabdccdeeabbccbebbdbaaeaabbbebeadcdbaeaadcacdaaccbdddadbedeccdcededaddcccbddbbeedddebecbbcacacbaedbacaacceaddaadebaeadeadeddbcccdcebacabdaaadaaaadaaaddbdbaddbcababeeaedddbbdabbecbdbecaccbddcadacdedeeaeececdaccddccacbbddaccdcccadcecdadabcedbbdebbabbbadcbedacbccaababcbecaecadacecebababebdbcdcebebbecceeebbabeccbaccddcaadaeeceaddbdcdcaeaddaeaaecebdacedbabcbdadebbdbbbceaadeacdcccaebdccdecaedbddaaaaeabebecdacbabecbeaededddabececadecbddeabeebbdacaecbeaeccecaebeceeaddbbadbaabddeaadeaaadddbccbeabadeabeacacabeaaaaadaadddaacbebcadedabebeacabbeeebceeaeeccbadccabbdaddaabcdedeaacbcdbbceeebaaabaebaeedddddbbbabcaebdbbeaccaaaebeceabeaacebeabcaabddebddebeebcbcaeccacedcaeaabceecbeebcbbaaebecbbadbabdeeeabdbdedecaeeddbdbedadeeaacdbcedbeedcdaadcdcdcdbdeabbddbbdbbdedbecbbceedcadeeeaeeabdcabbcebcdaeddbddceaebdeccbebebcddcabecdbbecbbccbdeecddeadcaaebdcedcebbaaddcdcbaaaaacbbeacecbedbbedbbeeaeeeeeeacbdbedcaedcbabdbdaccdcabbcacdaabacaecacaeeaececcacceebebeeabaadddabcabceeadedaaccbdabcbcaabdecbbabbcaecadcbbbdccbddcbbaabaceaabccdbabeaaabaddedebcccdbcadcccbecebeadaddaedbdadedbabdebcedabeebbeaeceecdbaebabcacaaeddaeaaecacdcbedbbbcebecaabaeabcbbecbdcbecdeceaededbdaaadcecbdaabeeddacaedcceddceaeabbedaedaddacedabaccdecbbddaccbdbbbbbccdcddbbbeaeaaaccdbdababcbbedcbdeabceddadddcedeccccbbebcbbbaabaaecbcabcbedeadbdccdccecdcbdbededccddaedaedaabedceaeadcbedbcedccebddaddeacadbeccaedcbaebbdcaacccdacebbcbbecaadbbaedadebbbaabdcdcabbcdecaedeebbaabbeddbbbeddaceacaaedeeaaddbeedebabbaceebbdddecacabaccebadbbacbbbecbaeddacadebbeacdaddebbadaeeebbeacaadbecbaabaecddadbdcaedeeabadbbdccbdbbadeaaeddbbddeebecbaedbcdceecdbddcadcacbbbbcaeabbccbeabceddaabedbcacbeaaeaeabcdccdbadabedbebcddbcddbdbbadbacddaaaeaeadaccebbbdbcbdcdeecbeadceecadedaedadceeddeeeacdddaecaebcabaaccbdaabdbabdaaaeabdacabaeceddbacdcedededebecbccaeaeaaeaeccebcbcddbbbdbbaceccceececbccadeabcadadbebebbbbbbdddeebbdacdadeaabcbacadeabbbaacdaecadaacaacdedeeddecbbcadecdccccdedacadaebbcdcbcdbdecaccbbbceddacbeddaebcbecebbcedadeaedbaacbedbccebeeacdabebacceeeaeacacceadcccaeeabaeebdbcddaebeccdbebceaadcdabcacdeaeaeadccbecddedddaedeceaddcabdccccceadaddabebbdcaadaadaaddceccdaddddbadbaaebedbdceacacbcddbdeddcdaecddccbbaccdbadddebcbaedbdeddeedbebaacecabccbcdaabaebdaadcabbaabbcdcbcbabccebdadbaccdccadcaacddacebacbcdabcebccbcabeeecadcedecbcbbaaeddcecbaebbcaddddcdaacedceacccdadebacacbbebbdbcaaaaaacdcbaaeeeaacaeccbadcccecdcdcbbbaeceeccedeaddeedaddcabbcacadaeecdccdddceeddedeebbbbaaaeadacbbecdbaeccebaccebadbeebbeedbebbbdbbdecdedddacecebdbaaaddaeadabdceeacbdacbeceabebaceedecaeecabebdcaeccaabaacbbdacdaeddbddaddadaecbbbbcdaadbdaeeececaacabbdecccabedceebbeadebccceccadbbcadceddabdbcceedbcbcabdacbdabdbecbcdaeebeeabeaaddabcaececddabeebcdceedbcbeddeebdcaeabbaaebeeeeeaadadecaacabcdcaacdcddbdbaeaccdaabadbdacbeecdccdceaceacacdbccabacdbbcaabbebeddaaeddbebdcdacbaebdddebcedcccdddedbeadababdcdbabeaacabeadeaedcecdeeabdbbddcdaccdbbeeebdbcbeedaeaadcceceeaddbbdcceadaeabebacbcdacdecebdbdddeececbddaecaeabdcbcdcadceeccbccaecbcbedbcdacebcbcdeadaacedaacabbccecedeaeadacaaacecdcadebdeadabcbbcecededcbdeccdedddeedcecdadababebedadeebceebcaabdcbccbeaeaeabccbcaccddeaacdbaeddaeadceeecbbcebdddccebbcadebcceabbcbbaaabdaedaedbcadabbeadaabbedeaacdeaedaadebbdaeedcaaababbecaecedbeadacdecadbadedcddabeaebeebcceeceeecbaaececebccabdbdeeaccedcbedcbdedbbbbcdadccdbacdeecddbbdbbebeeeccccdcbbbbbbecedcbadeedcceabddadedddecebbceabebeebaecbddbebeceecbcacbaddcabdecdabdabadcaabdebbadbeeacbabdbbabaadeaadccdecbadcdbbcdcccadbeccedddceaebbecebcecededadcedcdceadbcaaebcaaaeebdeeaccaccbcbacdecaebabedbabeaecabaeeacdacdeaedcaaedbbeadaedcdcceeebbaceeebaaedeedcedddaeabaacebeaddceaecdcbcabaabcdededeceacebcbebbaccaeebbaabbbcadedabddcaaedcedaebcdacaaeeabeaeaedceaecadeeabbaaedeebedcadaaebeadccaebdadccceababdcdaaedbbdcababcabddbbacddbbeabccebaaceadeaeddbcaaddceabbcbbbedcecedbdceaedcaccbcedecedcdccdeccbbeaddedaeacedbddbdcdddebdadccebdacdcceebaccacdadbaabcceebcabbebdabbdaecdcdcaadcddbceeaceecebeedbaabebcceeebbcbeeaacadecceddcaececbaaaddbbccdceededbecdabdaccdaccdbcadbeaebbdadaeecbebabcdeddaaaaaedabbecdbbebbcdcdecbbcdbaeaabddcecbaaabecabdeacbdbcbbddeaebbaebadceccbcdecdabbdacbabdcdcdbcaebeadadceeeecbabbcebacdcdaacedbcaceeabdbacccdcceaebbcccdeecdcebcacebecebacbdadedcbbbbecdeceeacdabcdadbcdeabaecacacabecceabdadeccaeacceebeeecdccdccaeeadbeecaadeddeaaaebaaacdabbdaaccbabaeabbadecabbbdddbdcddbedadaccbbddccccbbdbbeedbaabaaceaabbbcaedecaedabeecddbabcacceceebdabbbcddeeecccecdcccdcddbbceedaeeeebdedbdbaddbeedbcedbdabacdacdaacedbdbecdeaaddacaaeeeadaeccabdeabcdbaebceceaebcecebdcaaebccddacbeacebdbabdcdbccaedcdeacebecdddddedddebdbdbadcabccbdbeceeddbbaacadebbeaeccbaacccaadaaceeedededededaaeaabbadacccaacdbddaaabceaadebbdeaadebdcebcaccdcceddebccbbcabbddaabedceecabdadcddcdabcaaeedeeedaeeeaecdbcdcdbbbecaedcbeedcccebbcabbccccecedbcebaebdaaeecbbdeeeeccebaaabdccaddcddadadbecdbbdbaeddcdceecbaccbcbcdcdcbcdbacebaceccbceebbadadbbeabbebdeaadaabbebbbcdcceddeaebcdcdbceaededdccebcaccebadddaccaecadecebddaabdedabbdeccbeededadbdbedadeaaedcdbedeccbaceabaaeebedbedeadbddaccbcbedbebbedccebdbbdbbedaeeeebddcbaaebaaaeecbeeeedaeeaeaedeaeabeeebaacdbebcbdbbcecadcacabaadacbcebcecaccbbcdcdbeaedeabccddaaeccdaebacedeedccdcbeabedaecbbeebaebaaaddabdeeebebacbcadcaaadbdcbcbbaccaeddeededdddbeebaaadcccaeadaeceedeabdaaacaecbebaeebedcceaaecbbcabedacbaaaebbbbdedcddbccdedacddadbebebacbeeadedbebbbebaededbabcdccdbeaaecdacdcbacddeeabecccbbdaeaadceeedcbebcabdcbdaceeaeecebbddeedcbdeabbabdedaccbbdadddddebdcaeeaccedeeaccbbaadbeadcecacdaebaccdddaebdaebcaacbadbcdccdcccedebbedeceadaeeaadbcbabbbccabdaeaadbccaeddbcadaebdcbbeddbbceeecbdbccaadabbcacbdbcdaccabedeeacbaeaceddeaeecacbaeddebeabaeabbaddcbcdeeceedabcededdbecbcababbadaadbeedbcebaabaadbccabccceeadedbbbecebcacbdcacaabacbeadbdedbccaaeacbdbecdacbcabcbabecebaadaeaaceecaeedcedcdeaabeceacccdeebabeedeaaeeabadbddedcdcccedcbaccababbbebaebccbbaeebcadebddedbbdbeaddaeebcabecaabbededabaceedeccddbaeebeebdcccebeaedaadcdedcdceabbaddcdaaeaccdccabaeadbcacdacbaaaebdecddedddadcaceeabbedcdeccebdddeadbeaceccebbabeaaabbacededbbbeebccadcbadecddeabcdeecaaaadeedbacbeaeedbcbbdddadeedeaceedbaedbaeebccbedbcadadcaebbdccaaaabaaceeecaddeeaaabeddeedccdaadecdbaaeacbebbebaebbbebdaebedbecbebaebdeaccaaadcccddadedcbdaabcaedbabbcdaaebeadbcebdeccdccbbbacedeccaeeebdceacdabbaecdbeadbadaabcbaeecccabbaeddacabceedcbeeacdcbeeeeddcedebbeecceddcdbeaadaecceceadddeeeeebcaaabcbacecbcabcbdbabeecbaebbeeaededbdbececcbeaadbcccbcacceccdddcccbeeebbdaabcbcabceeebadecaceedeebebaeddcceecebaeaddaacdacdaaecddcbebdadcdcacbbadeebaebaeeaedddababbcacbbaaeedaaedaccdcdecabdaeebeaeeaaabaacceeaadeecaacaadeeecabaaadaebddcbadaecacecbeedbcaedcdabedceccbeacdedaecbbbdedeaccdedaaeaddcaeceecbcbcaceabcabdacacedaaddcacaabbbccddaecdebbbbbbdeebeddedceaaccecdebcdcaaabaddceaebaeeebdebbdcaacdeccccabbeacbceabdeebddceddcaacdaccdaadeecdaeeedaebeeecaedaaccaeabeccbbdaedebcddddbdadcbddcacceadcdabaeddacececdbdadbaecbabeeeeccaebecbdedabbcacdacbcceacdbabcbacccdccdeeababeedcbacebbaadedcecbebcbcaebabbcbabceadadbbeabdcbccbeeceeabdbdeaebeddddebadbcbdcbedebeceaeddedabeceaebeaaedccededbabbaadecabcccedcebacdbcdccdadbbedaccbecacbbaaceeccceebacaeeeaacddaeddbedddceaceaeadadbbeceaccadccedaabebcbbebecbdccceddaeacdaabcbbeaaecdacedeaebedeeaadbaaecaeccaeedccdbeecabacabaaaacacabbededccbdcbaecbbcdbccbdabadbbceeaebddcbadcdbdddaeaeaaacddeddaaebbdabbadbabbcaecedacccdcdbebbedbbbcabaccbcaaddbebaeaedabbcbcaebebbabdeabbebbaadacdeaaeebdabedcbbeaaadedbbdccacadabdcedecedcddccadebdaedcabbddbdaecaaddaedcdbedaebbcaddecdebcddaceaeadbeebcecbabecaebeecaeacecdcdaecbeecaebacedbaacbaddcbddceacaccbbddacdebadaadcbbdbcaadecddbcadeaeeddedaedededdbcdbccabccaaecbcadbabeedabeebdeaeaeeadaceaeedcabedbdbecbbaecbecbccdccaadddaceebbbdaeadaceaaadadadbcbaeaabcbbceaadbbaabbebcbadddbdcedcbcccbebabbcccdeedceebadaabcbddbedeeaeebcbcddcceaecaeabacabcdccebcbcccdeecbacabbaebcadddcccaceeecbaedcacbabcbbadadcbdaecbdeaaddacbcbaceebcbbdbadcedcbdebabbddadcdedcaebaccadbcedbdebbdebdecaeadccbabbedaacadcaddedbadeaebadeebaeeaadbccabeacdcbdeadddaceaeccebaaabebeeaeeccacabbcbcdedccbcacdbadcebeaaaedecadcebaaadccebebcdddcdceeebecdeecdbcacbaddaaecabdadcedbacabccedadaaedcdeaecbdecaedbdaaaabcbedccdcaeeebdcccdcbcaeddddcedbecbdeabbdebdbabddbcccaabeacbcacdaeeedabdecdabebcdcbaccbaaaeaaacaecaebaacdccebaebcaabebacccdacbdcaebeeeadccaddbbdecabdebccbdcdbdaddceececcccbacacadbaabdacbacadbceeaceecacbaaebddccedebccbdbededacadaaaadbaddbdbabcdaaaedbdedeebccabcaabddbdbceadcebbdeebaeeaeecbdacabbeddccbcbdcbbbededddecbecceeadabaaaedabdabbdeadcebcbbbeaeaaaadbddceccaedddeeaedabadadebdeddeddbbdcccededebaddedeeabbabbebdbcdcddbcceaccebbcacbecdacecdededcabadddbdeccdbbaeccbacaceabbcbdeddbaaaecdebeedabcadbccbceaddebaadeedbeaadddaaabaaadcbcebbeeaceeaecaaeaaeccdaccabaeeaeadbaaecbecbeddacbddbecbaaebdedebaceedcdccdbddebebaceaccbeceecdacdadbceaadccebebaebaacbcabeedaaadbcbbbcbcdcaebdbbccceacbddbbddcbdceecedbbdccccbebadbabaceaccdedabbdccbbbdbbdcecbcebaebaaeebcacebbeceeddbcdbbdbebddacebecaaeaddddacbeaebedbecaadbebbbabecdbbddeeacebeaeeaceabdedcbbbacedbbbdbbdabdcdeadbeeeebebbaaabaaecebdbbeebbacaccccdddecaaabcaebeebecadbebecdeaaddcaecaeeeccebaadacbbbcaedacadeadaaecdcbadcacdeaaadaecbcbaecbaabeccddbceeeaebcbeacabbebaeadbceecadeadeadbbbcdacceeaccaccbdcaecdaadeaacbbdbaccecaabadbbcdebdbececcadcdcdebdcabdeedbccbeabaadbdabccbaeadacddcbeebaebaadcaadccadbdbbdedddadbcaeddeddbaecceaddeceedabeadcdbdbecaddcbbdccbedcdddecbacddbeaadeababaeaabdbdcaeaacbbaceedcedecccedbadbeadedcdedbebbcdadcdacebccdaeacbaadbedabdcaeccbccedddeaccecaacdddbcbdcbeeeaecddcbcbeebcbeaaadadbdcdedbbccedcedeabaaeababbbccaadbacbeabecadccdadbdcaceddcbdbadaacacbcadbebbadbebadacbcbdceccdcbddadcabbabdceeeacebebaebdbcacaadababcdaeaabcdececdeedcabcdaeedeacbadbeadcdbcaabacdcdbddceaaddeeedccdcbeeacbcdbecabccadbaaaadcaaaaadcaeddcacaacaabeecbbbacedcbdbaabccadcaaaebdaddeeeaddcacebacecdceeabdceabbaddbbecaddebeabbbaceaaceaedbacadabdcdaabdcaeccaeadaecceedccdcbcccddecacbdbaacabdbaceaebdaddebbaadbecdcaddeacdcdeeddcaeddcedacacaabdcecdbcadcabecdacaebbbddbedbdebcededbbcbccedcedaeabbbececbeddbaeaadebacdebabdaecbcdceeeaabdcddddeaceadebdaebdacdcbbbaabcbbbabbcadecbedaeebbcaaddaddbdbbddeaaaaddccaceceeceebcdeccceabbeedadecdbdcdedcccdaeabadbbcbdabeabacccceededddccaceaedbbaccccbbbdccdaccbaabdbcbddceabececdedadbaaadcbceeedbddeabaaacdddaeaaaabbabbdcdbdeddebcddbecebdceddacdcbedebeecadcbbcabacaacbaddbdcbccdcbdeeeabaedaeeaecdcaeedcccecccbdbcadecceadeaeeddcebecbcaeacecbedbbceedbebaaaceedddddcdcedcdecbaaaadcdadedeecadcdedadcbacddacbbdebebccaaeeeeeeadcdeebbecbbbacbbabbbbaedcdbeebdbcabedceadcdaadcbabcadbdbbebeadcdbccacecddbcbdcaaccbaedadedceadceeacaceebcebbbbeedeceeeebaabddaeadececedcdeceecdccbbaaadaaeeebeecbbacccedaadedbacdbaacdbccaecbbeedaaeddbbaebabddccbdbedcceedacebecdecdeaccdeceeabadeaaedeebaaccddbdbbabbeaccedccecbaaadebbeadedacedeededabceedebdddddececcadabeecedaddbacbcdebaecaedbeadbdacecaaacacaabbbbabddaedbaaeecdcebadbdaceaddaecdcbcbbebbcadcdbbcedcdccdcdaaceeccacbcdeabdeddbeaacacabcaacebadeadbeddaeeedaeedeecaaebcdcededeabeabcecaeeaecbbbecbabdbacaabaaaedcdaeaaaadabbaaadbdaeeeaaeaaebdceaeeaadaeddbeaeceaabaedbbaccceaaebacbedeaaeddecdacdaddcdcedadbdedebccecbebcdcdbdcdecebaceceddaabdddcbdbaaecacadeacbcccdcdbaebcaacddaadecaebecdbdaadacdbedaaedececcccbacdbeaaeaaacaaacbdeabccddacecdadbedecabccbbbdbaabddcabceeeaddbcadccdabaadcccededcadbadacbbdbdaccbbbeeaddbecccaecabdcdcdecbeaaedebecaebdaebbbcdacbddcdaedeebcbcceddbddaeedaacaacbebaacaccaaaecdedbcadbdcedbcdcbbceddedccbcbcaaedbccbebccbaabdbeabbaedbcddcbdbacbdbcecdcedcdaedcadaddceebbdbeacedcaeddedcaaacadeddcdeadcececeddaeeddbcaabedacabedcbdedaccaccaeeeddeaceeacbbeecabddbbcabcbdedbdeeeabeeebbbdbebacdbaabedcebebdaeaabdaabbadccebdaddedbbbceaaeadecaeaedbbbaddeedceedabbcaacdddcabadcadbcbcabebebeddbdeeddcaadddcaaecbbcabaebbdddbedcccaaaccdabedbabadebbacedaedbaedcaeadeeeecbbeceacaaaebceccecddbddbacddabccaacddccbcbedeeeedcbcccadacabbcaceaceadedecdbadebcbaadbbadcdceedddcbacdaeceaceababccbaacadccdceecceccdabeeecbcabadbdddbcaacdeedeccbcecdeaedcceaabcabacbbeaacbeabeaaeebabeeccbccabdabccddcdcdcbbcbeddeaeaacedaddcebbbeecbccceebbbaabccdcddceacdbccabcdbaeceacdbbabbecbedcbaaceaadebacacabedcadcbdbeaadbaeacebadbdecaadcbcdadeadaebdeaddbaabcceacbaccdddeaedacbeaeaacabacdbbeccbdeecabeedddcedbabadcecaacecbeedeaadadedabcdbccbaabdaabdbdabcaebbedadabcbaddebdbbcbedbdbbcadadeeaaaddaaeddbbedaebecadbbcadcaecbacbdeeaadeadaebadaaceccdbecddbdaecdecbeebabdddeadaeeecebbddabbabecbcbeddedcddeaabdbdbebdcadbceaeedbdacbcdddcaaeabdecebadacbcdbaaceeeddccdcaebebececaaadbadeeabdeabaddececadacaabbecebabebaacdaebebecbcebccbaaaaadccaaeaaebdaeaddddacbaceceaddebcbcebcdeaacaebbcaccadbdeadeecadadbbdbadedadabaabaeaebacbacbdabeaeacbcbbbacbbadeacbeabaacaecaaaabebaceeaaededaaeaebbeaaaeddeabcbaedddaaeeeeabceccceaedabebcebcecebbcbacccdaeebebdccceebcadbcebbbbaebabacacadacbdceebbdecccdbcabdebccbbcbceeeecebcdcddecebcbeecdccaebeacdecdbecceadadcaeedeaaeadeeebebbcbcdcaeacecaacbebbcedadbdbdadeeadaaacabecaaabccadbdaabacdadebdeaddbdddeaaeddbcdeeedecacababdddeecbeecbbbaacbcabedcacbaaecdadbddcecdbeceeeaeebdcbedebeaecadccbdaebeadddbcbcdaeacdadeacccddbbabdeedbcdbeebdeaaabccacdddceedaeeedacdadceabebdcddedcbeacadbeaabdcdaddaeebcabacbeaabeeacaccedcbbacebcdabdeacaecaadaccacaaaeccebcbcbadbedcecebcbedadebacdadecacadbeeacecdeddbecbeadaaecddcaecacebdcabeecddcdabedbcccdcccbacaebdadaecaeaaaaadaaeadccbbacdebccaabaddcecccaaedccebdeaccccdcabdadaceeeadaaceedaabbbdacabedbeedcedcddacecddaedbbbdacbbbcababedddbaceadcedbceeccabbdbccdebeeeccdadbcebeaaedaaacdcabacddeadedbbbdacacbaaaeaceeeeddcdaedbebebebcccddeecdabdeeeedcbebedadeecebdecbccaebccacdceabcddacaadbcbcedceeddbaddbedaceaaaaacbaccbdddaccadccdcedcabbdabeedbbabeeaeebbabcabcabdabaccceccbacbcdeeddbccebaecccbbdcaaaeccadbeddebeedbecdbecacaeeabbeeaddedebeebbdcacaabcedecdbabdbbadadbbabbabeccaddebdecadeaedddaccecbdbbbcaceaccedbbececdececcbbcddeedeabdeebccecdeaddecbdaedcddeddceedbecbbeababebabdcaaecaecdcbbddababaedbacbeededddbcbbcbaababbbddbbdeeebdadeaddaeaabbddabaaedbdecbbcccbadddecaecdcdcbdabccabdbcbddadaddcdeaacbbbddaadedbeabbcceebdbeedceadccbdbabecebaacddaaebadeccbddaccadbdbcbbadbdaecdbddadebcccacccebabeedcaadbaeebecccededdedbedeebeebcbaaedbdcadbddcedcabbdeeaccadeeeacdabbbbddbbabacbdccaabbbbcacebcaceebaecbcecdcbccddeebeecbeaaadeccdcabbbecaeabeecbdecadecacdedebdebeeccaedabccceaeabaabeaeaedcebcecdedabdcddabcacbdedadebccbebebaecdceaabebabaccceaebeacabcdbdebcdedeaabbbcdbadbeccacaecbcaebaddcdebcbbcebbbeddbaaebdeecdbecbebdaaebbceeccecbebbeabaecdcdadeaebeeaecdccddddaabeddabdebcaabbcaabdeddbdccdddbcbdecbdebedbebacbbdbcadebbcbbcebadaaaabbaccbdbddacaabaeadbeeebecebcceaebbaaecaddbaacecbabaeaadbccbdedeeddaeadcddeabdacaadcebbbeeadbcdbceaecdbebeeddbaeecbeaccdbbeccaadbbaaeadaacddbadceaccebcceceedcecadadbccbebdabaabeaeccbcdebcbeebababebcadaedebdbeeddcbedbdbcbeabdacadaebdabdabadcebdcebdaeeaacdcbeeaeeadebedbebcedeedebcccaeccbebbdaeedddeaaeddbcabeddeabcecbecadcaabdaeeedeaabadbddeeddeadbacdecaeeeddbeeeddbcbeddcdeedcdceadedbcaaacbcededadccddddcecbbdacdddabbbeeecceaaaabdaebbceeebcbddbbceadaccbbbeabcebccaabaedbeabebccdbacaebbdddaebabceeececcabeacecadcbbeccebbceaeecdddabbdcabcddaedecedacdccabbeeaabdbbebaaeeeaaabcceccccaadcbdeadadccaaedeecbdcddceaacbadcbbabdeaecebeccdeacaaceadbccadbcdececaebeacadddbaaadceedcdedccdacaaacddcebbabcdbeecabadcacabeebbdaaecdaeacdeacedddaabadbeaadbadecabececcebacabcbbaaecadbabbaccaabcaaddebdbcabdbabececdbdbbeccbeabdeccaaccceddccabbaababaeacbdebedecddbbddcceccadbbadaabcebeaccdacbdcacacaadeadcdacccacccbdaeadceaecabccbcacbddbddebcbceaadccecaabacaaebedcccbcabbeccabdecaabecaeeeeaeaeebeeeabbacebcdcdacecaccaabdcdbebecbcaaeaebebbadabbddbebaabccaadabaaeaccbacacebacdddecdadabdadbbcccbacecbdbedbcdbabcaaebeeadeeeecccdaebbeecabbadbddacceebaecebaeeaedeceacedabceeaceddbecdebbbdddeebadaddbeeececbdaebcdcdcbbbaccbeebadeeecaaabcbdaecdbbddaccadaceadcbcadebaedddbdeaeadbeeceeacdabeadeceddbbdbdbdadbdcbecdbceabecedbacdceabbccabcedabdaaddbbdcbceaeccbadccbcbaaeeeddaacadbddaedeaedaeeaeceddcacdccecdaddcdbabeededabeaeabbbebceacdecdaaaceedbdaaaadcecbacbedccbebcabdbeeebecbcbdaeeecdaacabccecdebdabaeaaaadeaedceadcbdccadbdebeedaddacccbceaaeddcedbdacddebdddeadaebabaacacbdeccdabcbedbeeaeacbcabcdcecdaedabcaebdaaaacbacbcaccecbdbdadaeedaaddbbbaacaedbacddebbaadecbdaceeedaabeeebacdcbbdabddaedaeeedbacbdeddbcabbecaceaadccdcceabbccebccddccdeeaeaaadaacecbcdebdaadddbccedbcbaecdccaabdcbcedabeaebbeeededcdbbbcdbcbdcbceebeabcedabbacebbbabcccbdcdcebbbdeabcceeeccdecbbadabaeecdcbaaebcedaababececcbbbdabdaadbdbbaecdadebbebedcabbdeaadaabcddedecaedeceadcaeaddaabcdcceadddaedaadcaeaaadbddbcceddcaebcbbadbecbeeddaeeadcdaeedcadebcecbbdacacdedcbaeedabbcaeeecbeaaeaddbaedeadcdcaabbadbcbebdadedabcabbbbacdacbabdadccaaedddebceaedeebbeeabbacbcacaaeeeaeaccaadcaeeebeaabbacdadcabcceccecabdcdbbcadceedeacebaecedbcadccaeeeebaebdcecedbebbcdaecaaeaaecaddeaedbdddceaedcdaeecbeebededaccbcbcdeaeabeededbecaceebecedeeeebdebcbedcecaabdbadaeccccebaebacdedebaddbdaedbadddaceccaebdeacbeadaeedbcbbdcaacbedcedcdabcdcacbaeebaaaacdeddcdbdacadeaddbecdcdededcdcdabaddaabadcdcedcaeacdeededebaabdbabdaecbceadecececdbbccaacccdeadcdaddecdedeceebadcaabeebcdabcccdcbecdbeabacabbaadabcaacdeedecdeaabbbbeabdecaeecedbdebacdbbeccaacaaadcdccedbedaeeabdcccdcbededeedadcaedebadcbcaeceabceebdececccabdcbbabedaccaeabaddccddadeacecaceebdaacacaecbbdbbcdebcceaaeaecddccedbeddbaeaeadbcddaaeebdebaccacbaccbbcdccbacbdacbcbeaeedbbabbababadecaeeddeedecdeddcbddcbacbceabbaebceeeadabcdeccededceaadbceabeaecbacceaadbddccdddebdeebaebdabeabeabddcdadedcbacddadcedaceceaabaaaaedddbbbbeeccacaecacacecedeeacbdedbacccbbdcebbdadabebbbacdbceceaaeeccdaaceebccabcbddbcbccecdecbaeedcacdacecabcbaadcbdadbcbadebabdcbedcedddbeddcccaacaecbddbbbabbdaeaeacaadedabdcddabedcbadecbdeddaadaedbcccadecdeadceddbbaecceaaeadeabdaeabcceceadbedddceaeecbbacdcaabbebccdeebcaebadaaeecbbeccbbebaccadbacbabcecbeabdecdaaaaadaaacccdabdbcedcbeeeecdbddbacccdbebadaadccbcbdbdbbddcdcbbbdceaabddcadaceecdeadbbcceabebeabbaaeecabbcaebeeabeadacaaaecdddcbdbedcbadcbebebaeebccabbbecdeecedacadedcaaccecdaecacdebecaceaeaddcacdcccdabdeecabadceeebccdeacabaeeebdcbcedecddcbbcdcabbcbdaacbddbecbcbbcaaacebdbaabdadaabaeabaabbeedaeacddbacdaebceedaddbabacbdabbdacaedcdbeaedabedeeeecbeebceaedabcadcbcebdeecacecccbaecccebadaaceebdbbaddacdbbacbeecedccadbdaedcadcedddcdabdeabebedeabcdedaaecceaabaabaadaabaabaaaeadbceedbddcbabeccccedeabcbbecaabdbeaeddcebddadbecebdedbdeeccbacebbabdbaaecdebcaabedbccdbdebdbcaaceccbebceeabceaaebbddaddeecccabdbacbeedbcaacaaadddbdabbaceedecccddbaabcaedbabbddcbccbadeebdcadcedcadaadcccdaebecbdcbdbaabcedbbdbeaacacabaddcdedbbbdadbbdcebdecacaeedecebccbbbddecccbeacaedcaecbdbaceadaedbaacadacccccbdccdbacbbdbdedbcecbbdeadeaeddcbaacbadcdcddbcecbcadcecedabbdcabaebaddcdceebcdaebdacedaebcbaecdeccabbdeecdbbcbbbabbadceceacdddaeddaaceaaddaebbbeaacbddeabdedaccedacbbcccedeeaadbcbeceaabecbaddcecbcdccdadcabcdbebcbaebacedbacbccbdebbcaabcecacbabbdabcbacdeebbdddbaebccecacdccbcbaccbeceacdcabecccdcdcdeceabcebabecbeecdeecbabdbaaeecbcddbcebedddbeedebcbdceabccceddecdddbdeedacaeacdbbabeebccebeecebaeecaeeadceaccdbaadeecabdbedeeedebdabccbaabdccddbeeecedcabaeeadaeabcdadacdaeeedcdccbcccaddeddbdadebedebcebbdcbccedbceaaeacdadeabcadeaeeabdebdaeaaaaadebebedacbacbacecbdeadeebeadbeeecacbcaebadedadbbebabaacecbbdedaadaadaeaedccebbccdbdbbecdcabcedaabebcdcedaedbcbaeaeedbbeedcaedbaceaeebceaedcabceaacaedebeeecddbbcbbaddacdcdbaeaddbaabaeadedceceedaebaaabcbaabdaccdcdcbcaebbcedbadbadaeccdaaceecbbecdbddeaeadabaebbabbadcbddedbacaacebeebadbdecedeadbadbebadcabcbcdacecbbdddaccddbcadddabdaeccbbebaccadcadecdcaecacdbdccccbcecbdcccabaaadccddbcdcbccebdabcdaacbbcdebeccbecadcedbccbdbcdebdbaecabbecaeabeacdbcbeaddeeaaddbdacdeedbcdeccdedcdcdaeaeecaeccadabddabacbbdaddbdbbededcbddacdbbeabbceebabbbceabdbcbdcbdcebcacacbaeacdaeccecabeceeabadcdadcabecebdcecebedbadcbaaccdbeadebeedeeedbacabcdeacaccedccbbbacdedeeeaeeaedcbcaedeadedeebcbeceebeaadcbaacebabcaedaeaebedaccbdececaccdbabedeedbbcadbdaeeceacaacdeecebdcaedecebeedbdbecbdacbaebaeaaacbeecedbbaebcacedacebdaabdaeeadcacabbbddcbedcbeedadaebaddcdddcaadabaadcdcdeebdbadadaeacabbeaadddddabddbcbebebeaceaccccaabdcdbdeceaedacbbaacbcbcdedebddbdadaedbcaaeeeceecabaacacaacabddcdbcaecbeeaadaaeddbaddabcaadeaaadaadeabeaaacaddeeaedabbebededeeadddccbbecdcacebbbcabddacadaeabbeaabcbceddbbabcbccaabedcdbacabeabccdbcdaebbaeeaaaeaadecaeddaebdbdaeebacecbaeaacccebcaeeccddcadacadbcadaebecbccacdbadccbbcceceeaadceeaedcadbcbabeadddbebcdadaaecdbeebeaeddccdceadeaaecacebdcddcbaecacebdaededdebbeeacccbcceeecbbeacbbebebeaddeaaeecadeddbcaebcccaecceaeebcdacbbaccacebbbddedeccaddedadebcebdbacceaecdccdeceeeebbecaebdbbebbcbbabeebaecdadebaeebdeedaceeaeaccabdebcaeeabcaeacbbeeacbadcceededdbcaecbaeadaccbbbdcedbbbadbceababbadecaadaeaccbadcddbdacecaeaebaebdcbcdcdabdccbabdcecebeaabceddbbddbaaecbcebcddbbaeedcbacbbbadcccbabddcbadddcaebababceabddeddcabdeccbcaccceebdcadacaccecabcdbddabadddcbdebcdadabeacebdddccbbbddeeaedaadadbbddeeaacdebbabcdeadaebeeeddcaaeccccdededdcdeeeaebedeacecceeabedbabecbddcdaaeeaaaeaedeaabcdcdeabecdbaeddeadcbbaeeddadaeabcaabaadbcecaaadeadacdeddeaaebbdceaaacbccabeeeeeaebdabdbabacacbaeadbaaccbbbddeadadacacddeaddeddbacaaecadbcedbdebdaadedaeddedadaeaceceaaaccdeebdecedbaaadaadddcbbadbabeacbbcbdadddadcaacaecdedecdcdaeccdbbbcdebbabaddbceeedbeeaadaaeeeeebbbbbddbadbceacdeaeddaecddabeaecabccaadbdabbddedccbcecbddbcdceaaebbabddecccaebaedaeaabaaccdeedadcaddcdedcdbeaecbaedcbaebdbaabbdbddecaedcecceacceeecbabeaceeeacdddcadbcaccebcedddbaadabacbdebabbadaadebbbdbddbcbeaccbcaadcedeaabcdbabdeeeecebcbcccbedcebbdbabaceedeabcbbbbddedeadcabecbbaeeadbeededeeaedceaeebaedeaccdeadceadbdbccbecdbdcaacaeedacdbccbedcdbcbebeabdabeabbbcebcdebcbcaadbbdbebcdeaaeccdaaddebcbadaaecedcdacacedcbebbccecaeaeceedeebccbaddeebabedebedebcdadceeabcbdddbcebeebeabbdbebdbebadbbdcacbddbbdcbeaccabeaddbebcabdbabddaedbcdadbcaebdabdbcdadcbcadeeabdedbbadecbadbedcabeaeccbacbcbbeaabdededbbdeccbbbaabaddbbcbcbdbbabdabdacabdaeadaaeeceedbdbcddeecdaeeeeecccdeeeacccbdebbbcdbbdaadeaeacacbbeacbcabaeccdaaeeaabaddeeaacceebbdbdcbecbdaaadccabbecbaedbeebbaebcdceebaceadebbedaeaaeddaeadebbcaebdaabbceaacbcdccbbacbdbaeeeecbcaddcdadeebdcbdeecaeceaecdceaddbabdbbbceeaeeeabdcddabbaadcbeabebadbeeabcdaabbcbbcaddcedabbdacbdedddbdddeedeadeccbcbaeadaccaeacddedeceadaddadcceaabaebcbbddcbebcdaaadaeeccdbdcbabaeecadabbedcebcdcbdceacedbbcbacbcaacbeebbaebbcbccbcdebddabdaaeebadcdbcbeadcdcbbcdbeadddceaeeccdbaaebdbdedbebcbcbacdbabbeeeccceadcbbcdbbdecacdadbbcadecddadbddadcacadcbcecbbedceeeacabbeababaebccdacbdcaeebccdebddcdaaccdeddeedecdcaebebbeadcddebcceaedcbccabaceccecabecbdbceadabdbaeddbacbbacaaaecabbeaedaabcacaecddddbceabaeecbbdbecaecaedeebadccbeeadaaabaadaedbbdeecbdacdabccabeecbcdcebbcbeecbeeeacecccedacddbeedababaadadbbacbaeaabeccbadeaecbcbcccbecacabebedcaaebeebacacadaabaeabaaacedcbdbbccadcdbdadacbbdbcccaaddceedccaaaedabaeceaccddddbdeeccdacddcedaaebdcbdadcddbacddbbddaeeeeacaddbbededeccdddaabaadbbbabceecabbbaddaceecaeebbedddabccededaeebcebcbbbabbbabbdebbbccaaaebccecccadbddeebeccacdaeaeccceeccddeabeaeacdadebacedbebaeccaebecddeacececdddadaceeccbcdeceddedeaceeebcbbcbcbdddcabbcbeebeaaadbcbdceaceabcabedcdbabeebaebbbbccaeecacdcbaddbadbccaeeddbaaedaddbeccabcebaeecabcddbddddedbcbbbacabdbdebcecbaccecedaececedbeccebddbaccdddbbabeeccaadbaadbabaebccaceaeedabddacbbbeabadaddcaecccadaedcdaccdebcacacaabddaebcbeddeabbbdcbbaceeeabdababacbbcaaeaccaabebdddbedeccceebbbdadaeeaeccbedcebcceacababbbbbdaaaacabdcdcbbccadbbebdbacccadaeeecebbbadbedaadcdabeccedaabbebadcedabcccdcdccadeeeaebccbacdccdcceabddeeebcceecbebddbdccbdaeaabbdadbdaceccdaecceebcaceeaebbceddabeeabadeedcdbbaaeccadecdbeceddcddbaebddaabccadbcbdcddcbbbdbbbdeadcdcbbcdaebdaeddadbdcbbcdbabacdeebedcebbebedebcdaccbbeabdadbdebabbcbcadcecaccdeaadaadebdbcbaaebabccdbbeadaabaebdaddcaabbaeccddddbdebedeccebbedbdcecebaacbbbbacdbceeecceaadddacecbebabccbdedbeeddbaadaeebacbacaeaabadbeeeeddebcdabadaaebbbbbeeababedbddececeeeeddbbbcdeaccbebacbeceebcaeccdaedacecedebbcbeadcebbacdadeaebcddebdcbbdabaaeebdadceedbbbdddbabeccbbcdceecebeaabdedeaedabadceebbbdedaabadcceeaededdbcbceecaeaacbecabedaadedbceabddccdecdedaabcbcbaeeceabedadaaecbacccdccabbccaccadaceabacddbbdcbebdebdeedeadaaedbddedbedbedbedeebbebaccdeeaddcccaceeeedbeccdddccbeddbccbdabdccbcdadebbadcebbbbddcccecdbaedddbccbcccecaecaacbadbacbdbbceceaaabeaecddeebadeaadcebdbadeedbceeecdbacbecaddeddcbdbaaddcbdbcdedacdcdbdabcccdcceeccababbebdadeecbeaecbeecceadcaceaadccdcdcecceceadddacddedcedbeebedbbccaddddeddabaaddbdcabddddeccedbbbbdacdddcbedbccbbbdacdbdcedbbeadcddbdbdaadaeebdcadbdeaeadbbeaeeadccaebcadecbcbeecccaecadbedddcdbbeecbcacacdcebadabedceedcddaabddbebbabaeadbbaabeeddbbbaeaaccdbabaebdcbcdbcbbddcecceccacbddcdbcdceecebeaeaebeacbdceabbbbbdeccbbbdcdeecdbabdbbcdebecedbdaddbbadecbbcaebddedcbbedbabeaadcdcdaadaabbceaddaddbddcebcbeacdededdcbccaeddcaebbedbeaebacdebadcaeacdbeeacadababcdaacbbcdcadcdbeeaabbebbdabddcddddbeacacbaebcccdbaeaedebdcaddeeaeececbbaaeaabcdacaadaedadcbecdecdaabaeceddaeebdcbbdaeacddcabbccdbebdeededaccedcaedeaaaccdaddabaaeccdcceddedeeabadeebdbcdeaaebcbadbcccadedeccdebcbbebcecdbedceeaaaceebaacbbdbeebcedeedecccdbecdadcaaacdbeadbdceeadedecdcabcbadbcacbcbddadbdccabbbbdadadebbadacbdeeadceaabbdbeedcbbdbbaaeecbbedbeeacaecebebecaedaacebeaddebbbbaeedbddbedbedabbdeebabdcbcdaabeedddddaacdbcbdadadeccebedaacbcbcbceebbdbeccdcabcabcbdccedccbeecaacbebadacedabccccbeedbdeaacdccdeedbcbacbdaacedddabaabbbcadbaaccaebeebddababdcdbebebdbbcadbdcdbdccbdeeabbcbcddcaebcdaabacbdcdbcddbeabbcbdadebbdaedaeccaadcbaddecabbaecaeaceaceecaeaeabdbddccbcacbdedcaadbddbacbcdadadcbeaceedebacecbbbbbbabdbdbddedeaaadecdcaedaecbeaebcedbbbcddceaccaacccccaacbbcabddddbccecdadebcbacdbeeedbdddadebbdacaedcebbbbbbdedadadbccbadddeeaddaaaaceddbccebecaeceebddaddeeccbdbaccabeabeccddadebddbbcdbcaceeeaabaebeeacebddacbddaecedbaeeeddbcddeadabdaeeabddcebdbdeacddacdceccbabaecebccbbbcaacbaebadeddbdceadddeeaeadcabebaeedcdacecccbabaedbbcbcaddeeccbecbebeaaaaccbbdeabecbeaddcdeeadddcebddbceeabaabcddbccbecbbedededeacabcedadaeaacceccbbbadddcebbaebceeedcdddbaedeabebddddaceddabceccdecdceacbcaebecdcaaaabdabccacdeedeaeeaebdaacddcaaeabcdebeddbcbbbcabdabeebaebeebebaaeedebeabceabaaabbdeeaaddbdaaccdacdebdeccadccdbbdbecabadcddbcbdeaccbdabceaccaeaeeeeceabcebceaadaaadceddcddebdaaaccbdeeceebeceabbeddccaeaebcbcbeaaebceeedcaababbeddbecabebaadebbbaaddccabdbbabbbabeaaedacdbbacddcbebebbaeecdedcbdebbbacdbabadebbbdeecbdaaedebabbcbbcedbdaeebaaaabeadceeabddabbaddeebaecdacbdddbeabeebeccaeabdabdceaceeddddcaedaeccdebdadaeebbaeadeadbcdeccbacdbdabdbdebcaaecbabecccbeecbbcaeabedbcdcebdbadecbebdaddbdbccadcacbbdeabdbcaddaedabcddddabeabdabceceeecdbbbcebacaccabdeacbeeeaeebbbaecadddabaebbadbacbeadbeedcdbbaaaaddbdceadccbabecbdaccaecabaadaacceecbbedebaabeeaabbeeeccededecbcbcaaabaedaebbadeabeedeabddacdcedaaceabecebeeadbcdeecbbeaacbdbbebbacceacacebbaaddebcbbcdccbbadbecdbbdcaccdeeaecbacadbdbdcaddbdbaaeaeadbcdbdacbeacddeccedcccbcebceadbbceeeaedbecacbcabdeccbdcbddabedeeeadeabceeadbddaecbdaacdbcebababecedbbcacdaaaaadcebdaaccbdeadaebcbbaaadbbecaedbabdadaedeabdabeddbbbadceeaedccbabceaaadadeeebaabcccbbcbbaaddcabadeacabaedbeebadddeecbcceebbbbaabddaeebcdcadbadadbeceeecdbacbcdaedacdaaebbedacabeacdddebbbdecbdaacadceabdbdcacebbecdadccbaabbceedceeaeeccbacdaadaadceccddaacbdaeceebecabcdcdcbcdcddcabceabacccdbaacbacaacbaddcbeeaabcebccbbbbbdeacddaeabaeacdbaabbbaddeccecdeeacbceaebcaeedaceaeeceaeccbdbeeeabccbdaddacbdedbcceddadacdadbdbebecddbaeccddedbebbabecbcbdcedcdcbbdbcebadacbcbeceeaedbceceaabdeebabaaebcdadedccebedcbdbbcebcecaeddecdedabcddaceabbacaabaeecedcebdebeecceedceacebdbdacacbdaecbaeacdeaddacbcbcabeaabcedebbbcaadbbacabbddbbecccbdecdaaaaacbdcadaacabdbcbcbcbacbcdecebbaacaeaabededdeaeacbccccdbddbaaacccbedaebedcedeedcccaddeeddcbcaacacdacedeccdabdbdcaaaaabceaeeceeeeebebcaaeedaedccaeeddbbaceadecddbccdbdadddabdbcddadbbcaadbbeddbcdabcdbeaecccdebddbcabebccdbcaabeaacbabbcabdecabcbecdbecdaceddaacabecbecdabbadbbcbeccaabcbdbececdbbdecddecdadeeddebdaaceabcccacceabbeddeebdeadcdcbcdbdcceebabbaeecddebcbdedadecbcebbdacceabebbcbdaababdecbaeadabbddbedbcbdbeaeecdeecebdaeecaeadaebeabacaadaadbeacdeebcaaedecacbaeccacedadeeddbddbcebdcaaeccaabeeeabaedcbcbcddccbbceaaabebbbebcdacbebdcababcdaabbddeadeecadebebbccacdcacdbabeeacccaebccbddeceeeaedcaeaabaebcedbeebaecaecebabeabdceabcabceadeabaccddebdabaacecedebcdceaaaddeaaecdebaecdadaedabdacacbacdbbcdedececaddedebddbdaecaaadedcebadeecbdddeeeaababbacdcccaebeeebedddeecdcdbcedbddceaecabeecbbdceebccebcebabcccbcdedeedceddecaccecccabacaeadeeebcbaeabdcccabbdedacceebebdededebacdaedeadceecacdcbcabededdedceccbebeaecdeccaeacaaacaacdaaeacacadbcabcabeedbeecabcebdabedcebccabecdeeecbcebebeddbcbaccbdcaceccbabddaaaeabeeaacaceaddddeececcbeeaecdddcedbabaeddbbceeeeaeabcaabcaaaecbeccbabbbebaaeebeadbeabeedadaabcadededeabaceebdcdedbaceeebebbebdbaddbedeebdedaacaedcbcacdbccedcdacdeeecbbecceeedaedceaccbcabecbdebbbcddddcadbaeccddeddaeeaedbbeddbcbcdedbaadecddabccbdcccddaaceceaeacceecdbabecedbdbaaccdcaeadbabbbeaacbeababcaeedecbccacbbcacacbaadebbedadebcdeaadbedbacdeeeaaebbadcaecaececeaacbbdababdaeecaedaeaceeecbdddadddeaadcedecadbdacecdabcadbeecdaeeccacdaedcbeddaebdeccbbeeecdbcdbeeddcdcecdcbbbaeebebeddcacdbbcddcccececcddecbcbcbcdbaeeeecaebcadaeaabeaedecbebdcecbcedaccaaeebceddbbdbddbdccccaeadecbbcdeaaedaebdeaabebbdeeddbceebdecdddcabbbcbaeedbacdedcbbcbbebbcdeaabceacaeecbbccabeacdedbcdbbdeaabeaecdaaddaeaedbdaaaacdaecdadcecacdadadaeaaadcbccbadeaabbbddbedecbeddbbaebebcdcecaccababbdeadeeacdcebdbbebebdbecbadccadadbadbddddbaeebcecedaececdebedcaeaeecdcebbeacabccdabdbbdebddaeabecbecbeecedceadcecdcabbcbddbdaeceadedcdcbcabceccceaebddbaedeadebebdddcbaccaecbdeecbbdcabbddbdcadbadbdbdaecedcbbadbdacddaaedeadcbededbdebccaacacadbeddaddeceadaadaabbcaabcadaaacdeaeccaabdaddaaceaadbcebcddcbeebbbdaaaaceaadcbcdeccedecacddbadacccbadccabbcebcbecbaadedebbdaeeebcaebceaabdcdcaebbcdabebdbdeeacedadacbedccbacbbeabecaeaeddbabaccbaebddabdbdeddccbccaeebbeeabeaabbdabcdcecdadcdbaaacabcaebdebadccadbeaabbeecebcbbdeaaaaaedceabacacbbaabeecadbabaeeaebcedecbaabececeacdebbbdbbcbcaacaabcbbbdceadcbacdddedcceccecdaaabeaedebbaacbccecbbcaabdcadccaddbeddccccaaccacbbdbbabdebbcbdddcdabababebcadebcecebedcbbddecacaabcdabaaaabddebecdabeccbbbbeedcdecaadeeceecceebdcabebedcbacaceadceecadcceccdaeddedeaedceeebeecbcaaeceaebaabccbaeebbdecdddcecabddabaebebaeacbeeaaabbabedbcdddbcadaccccacbbccebccdeaeabeeaebbabecbbddabdebccdecdcaeebbbdbcddabeceacdccaaaebacccaabaccaadbbcbdcabaabedeeadabddedbbdabdabbddbbabadcbabbdabcdddbbdeadcbeebceddedbbcdbdaecdddacaccbcbdcbabbdcaecdabdeecceadbcbadaeedbaccbeaaeddbbcdbadcbebcddcdeedeeccaeddeadededdbabaeeaaeabeeecdabedabdedadbbedccddcedcaebbdbbceaddcddeabbaaadbaeccdeddabbeeeebbddebacdcdbddabaeadcdcaceacbcceacdabaabcdedcccdcebabeeeecbbadeeadeabbbcedaddeadeabbddbbabbcdcdaebbacbcddbebdbeddcddbbdbeaaeeaebabdeecdabeecbdcbbeaddcebcbbebbccbdbeabbececedbdecdabacedacaaeebecaeaaabcbcbdcdaaaddabacbdabbbebbcdbbdbbedddeeabbddaabeaeceadacdccdddccaadeaedbeebceddadebecaaccaebdcabaacaddeaecedbddadbbadbacbecabbaaecbdeeadebdcbacbedcdeebaccebecbdbdaebcebadadecaedddaeabbbabcedbaaacaceeaaeedacabbddcbddaeecbdabdaeeedacdcdababeaedccaebddeaecadcbedcaabbcbbdcdcdeceeebeebdbebaaddbeaecbcdaeecacbbecbaceaceeedebdeaabbdcceecaecccbcecdcabbecebbeebeacaebbcacbcbbaeeebdedbcadbdeebedaceeddcaabeaeadabeaacabcedaeeaaedbeecabaeaacacdecaceaeaedaededbaecebacabeeeabacaadccbeedbeedadeaedecacbadbdeceeebaebcbcdcbbabbedadaeabeecebeacedacbbcabecedbacedecdadcdcdcbaceedbaeeecdcdebaddbeacbdbeedcbdadaeaaedaeccabbdadaccadccbbbdbadeadbdddceedaeecdabbcdbcacdcabbadbcaddebbdaaadcaebbceccbaecaeaecdcbceaddbbdebcccceacebdcdbacdecbbebbddceeeaaceaddcccceeeedbcecbccbdadeeebdbeceebeebbabacbdccebeccaacbecccecbbccdaaadbccedbacdbaadabcecadcaeadabcdbccabedcdccdecbaeaabddeecdceadeeccbacccddcbbbddeedaedacbbdaecdcadaeecadcbdccabdedbbadcabcbdebeeeeabbcadbeccdddbaacccbcdecacccedbcbabebcdeddabccaaeeaecdedccdbabeebebebeebbbdddcdcecdebbeeddadceeeaeaeeedabbadcaabbdcbaadececebecdcabbcceeebaabdaeecadbdbddedcdcedbaeecddebbcabbeeacedcadaadeecdebddecddccbbcaaabeeeadcbaeeebcdbddacebaeaadbeccbaddceaeedeeadeaaeabebdeabcbacebeadbaacbdcceccebdbeedceccebadbcabbcdeccdeecbdaeeedeeacbceaebccdcaeaabeeacdcaddbacdbddcceabbbabbadadbdaabdececcbdeaabaeedbdaabccaabdcedbccbbebecabaedceccededbdbddabbeecbdebedbebeececbddbbdaedacdedeadbebbabebbccdaaadcecbebeaaccbbcaeddabebbabbbbceedeceabaacdcbacadcebaeccabeaabedbeebbceddbceecdcddeabbaeaababedccaeddbcabeeccaecaceaaeebdbdbcbddcacdccdabcaaaecaedbbdbbaadeeeccbdaeecadbbaaecacccadeabdcdbadeccdebacbdbbdcdceedcdbcbeccdedcacebeaabdecabadbbacecdeedebeaaaccededeabdbdcebcebedaeccebadaabacbacbbdbcdcaadbbabbaaaebaaeacddedcecccdcceadacecdeedcceaceecccbbbdcbddceabedeaccecabaeacbddacaddbabedadcaccccaeaadaaacdddcbedeceaeecbbcddddbbccedddadecddcbdeeddacbdeaccbcbaebcccbbadddccaeceeaadeaecbdedacbbeadbeeababdabaddbbebdecaaedebcebcbbeceecaeebccdcbcbadcecaaabbdaebbcbdcedddbbcdabbcadcaebaddeadddecbacaecedcbcecceccadecaceaccecadceacadacdeadabbdbddbbadeedaedebbbbdbcaadaaccbdeeacaacbdaceaebeceabbaaecbedbbcccecbadadaeccbaaddddeddcacabbeabdaeeccdaedeeecdcbaccedbcacbdbdaccbcdbbeeabaacededabebeeaadbdddbbbaddcbdeddaceadaccbecadbbaeabebcccadbaeddbadacdbdddaaaebeccddbdcbdbedbaeaccdcdabbadeddcceacbddcbbbeeebeeecbeaeaacaaabccdabcbcdaccdbcdeebcdbabeabbbebdecbacaadaebbabddedbdcdccacdceaddddbebecbacbcabdcdcbbeaebcddeedcabccbbbcdcbedbbbdccdebacaaedbecaaaeebeabdaaddbbaebbaaeaaeddecbaaeedcacbbebcdcecbaceadedbbbedaeeaabacdadebeedabaabcbedacdceadedcbeaaddeaccdcbaeddbbeeccacddeedaeadbbdddeeacbeedaadaeeccaeceeddbceaaeadbabbdedecdebbacedcdeedeeeedbcbdcebeebcacbdcecdbdbcabcbbbedaaceadccacbdccbeaaedcaceeaeddebeadcdedbccaceebacdbababbabaebeaedcbbddaacdcadcacaaeeeccebdcaadcdadbdecadcbacdcdacdeacebaaaebcdeaaaaacecbacaabcdebcddcadaabeeadedebbabaacebbabbdaebaceaabacaddaaacdcbdcbbacdcbcccdaabacaddabbadbaccdabebabdccbdcdeaaeaeebdccbdceebddddedaedbeddcdebbcbcccbbbbcbbeaebeecddbabacbbecedaddeecbaaeddccaacccdedccdddeebccedaeddebeedaedaecdcebbabaeacdaabbedeaabbcacceceebacccceceadaeccdebcaacedbbaccbbcceeabaddebbdbcadaceceddcdcdddbdbdabbbeaecceddecedbcccdaaeaaceeececeaedaadcdebcccacacddeecbdceabaaccaacbcadbaccdbdebeaaceaccacedaabcbedadcacaddcccaaacaebadbadadcdbacbddacccacbdbdbddecdcaaccbeebeabedbdcbecaeeedaccdeedaccebccaeeaadabcbcddaeeeeacbadebbbccdcbdcaddcccddbdccddabddbadbdedcdadebbacccdabcabcdddacebebdcacbeeebadcbedcdadddedcaedcabdbabaabdccddbacbdebbdecbbdebaedadcebdeabbdecbbdcdddeeabbcbbdecadedebedaedcbbdebdebdbcbecbabeadbddcbecbbebbaecdeebdedbbdbbaabadddbacbaddeebaacbcbebcccbcceebbdecccdccbaedbcdadebbccddbdcaadbdceabdaaecbcaceeeccdcccabceebbbbdabdeecdadbacdcadeaabadddeabbdcddcebdaeabcaeebaeadccceadacacadaebcabcbdbcbabebeaaeebcecccaebbbecdbecdbaccbacbddadbccdcdbaadbceddabaebabbdbcbabcbdbcdecbbdccbbbbbeabbdcdabcdcbbdcbcceccdbedbaebadceedeedecedeacbaacbcabbcccdceabaaeddcdeccbbdebdeeedccbcbccecdcccddbcadeeadbcdbabaeaccaecebcbaebeeedcaacdccabdcbeaecedabdeecdedaebabedebdacebcccebcdcccceccddabddadcebabeddccdeadcedccaecdbeabbbeaedcdedbcbceaeddbdccdceddbeeccaebdcabecddaaccdceaabebcbecddaeddaabeacacdccdabaccbecdabddcedceaacaecaaccabacbedaacaadeacddeadedddeceeabdeabbcbbbbbdaabddaabdabbeaacdbbecceabadbebaecacaabbabaaeeaddebeeddcabbebdaaabbadedecbcaeccaccaabdebbdcedbabceddebcdeaaaddbeeaedbbbedecadaaaebdcabcceaceedadaeedebcdcbdabaeeadbebacddbacccdeeeabaabeddecabaebacabededcdcdaedcdcdcbabaaaadebcadebeaecbcbeaecdcacbabdbcdadabbedeededcdceaedeaabdeacddbadeccbeeadbeeacccaceccbceecdbdcdceabdcbacddaeaabaeacdbcddbdddeeadeeedeadeeeaeecccccbebdedcbdaeadacbbabbcdcbeebcabebdcdcbebcaddacaeddeadadedcceaddadcadccddcdbedecbbcddcdebcccbbbcddedabbecabeaecddeccadbbdbabaaaedccebbeeacebdabebeaaeeebcaeecddeedccbaceaebaeeeacecaedecabbccedcdacacbddddccbaabbcdedbccdcaacdbbaeeecdacceeabdedbaaceccbdcacbbcabccdcbdabadabbbacecdaccdacccbaccadabcccceadacbeceadaaeeaedacbbbcaecdcccbdaeadbcedbcbaeeabdceaaacaadbdaaccbebaebdadcaebeeebbdeeddabaccccdaacebdacdaceadacedbaaabecabcaebabbcccbadcadbeceeaadbebbeaebcbeebccebeeececddceadcccaeebcdadddcacbeaddddcadcbbcadbcaabebedddddcadcddcdadaabecabdcdaacacdcebddeebbbeabcbeeadcbbbaecadeaacbaddbedbeebbcdbebcabdebacbaaddedaacecbdcbaeecbebecadbdabdbeacdaaddcccdeaabbcccdbbcdecabaeabeaabbddcadbcbbbbcbcbdacdadcebcbdaeecccbebcdeeaecedbdbedceeaedadaaaadbcdbdbdccdabcdbabbdecadbbcebaececdaecdbeadceddaabeceddedaedcbbdeeaabbaeeccdbdadeaeeccabeaaeedcededcbecbbecdeeaccdadccdecedbdbccbabaadeceeaeeedbedebaebecbdddeaabadebdddabbeaddaebdaebddeaaecddebdcbbacdbceccbeabacbeeabcadccebdddbebcdaedddbdeaaccaaabdbbeaaaaaedadebabccddbbdaacecbcededdeaacabeddeacaabaccddcdbedacccaedaabecbdacdbaabadebceeedbbabecdbebbdbbeddcebaeabbdbcebbdaecaeceacdbedacdbcceaebdaadacbeeebabacbcdedeeedceeccccadeccbabdddeccdceeeecaabaebaebeaaadbbccaeccddadabdecbeecbecabdaabedbedecaedbaecdbabbcdeaaacedaccecdabbeadbbdcccdbdadceeeacbbbbebbeabbbddbabcddcbbbcacbabebcdbadedbbdbecdcbeaceddcbcabadceddceaaebededbeaebacdceebaabdbeabcdadadbbaedbaacdadebeceddbbcbeeadeedaaaaadedecaaadddebbebcdadbdceaeeecbcdedaababebbbeceddbcacbdbaddeceecbabcbbebbecdeaeabecaaeabbbcaaaaebbbdcbcdeddbeacbdbacbcceccadcbbcbcebacaeebaaeaaebddbdeccbccabdabbdeaaaaabdbebdaeacaeccbcacccadbaeebbcceddcacadbeaecaecdececdbedcbeacabadbdaaddcdeeecbcaddebeabaaaecacabcbcbabebadabcdaeccacdaabceaeabaeaceeacebdaeaadadbbeccebaabedeeebeeaddbeeececaaeeddacebcbadedbdbdebdeededeacaadebebbbecedcebaaeaeacbacbcdbcbcabcbcaadcdbeeabdabddeadebabebebdbcecedcaaccddbeddcbebaebbeadacdcaadcebeabeceadebeddbadecccacacbececaddccaadaeadadecdcaadccbdcbbceeeaaeaddcbbeeddabedbaedabbaacddedcccbedcdaecaadbeaacdadeddcddbbcadabbcdbedabaabdbcebdcbdeeddddcecddddbcccbacdacebbcbedeedbdcebbddbadacbcbacbdaebebccbdbebacecebaacedeabadeddabcaedbdaeacaeaaabdabaabbebdabcbebcacabddabadbacabeaadcbebdbdcacabedaaeecdeadccdeacabeaeeacdbcebdecddaadbadacbcacacdbdedcaaacbbdecdacebbebccabdacaeddcebeaeeaacdbcebdadbbbdebbbcbdddacdddbeeaeeebccbddbdeaaeeeabbdeddcabcdabbdbcbceabdcaeeababececbaedeecdaaebadaecabecadbecceebaebedddadcaaadabccdcabddebababaeaececeeddabcaabecedbdabddadaacbdebdcaedbbdacbeeeadebaeedebdedaebdcceadeacccdaecadcdebebbcbecaeddbcadbdaeadddebcaabadacbeccbedbbbddeddddddaadedcecedebdccaaaaeedcaabedcaaeaebabdeceadbacdcedbabbeeabdaadcbcdecaceeedcdcedcceaecceddddcbdbabacebdedcaddedddccbaeddbcaecacaabdeeedabbcadabbdaaaeacebaedcbbdacaeddcbeaedabaabbabacbaddabeadaacdbaabdbebcacbedabeaeebcdbecaddbccdabcbaeedbedbaaebbbdeaccdbdeddedbbaebcdddeebacaeaedbacdbdcdbcabbdbbdeecceabebdecccdacbcaebdececdcecdddcabbceeccbcaebeebabdceadcdacaedcbebebadbdddaaebcdcebdababcadeebcacddacbcecabdbecadadcbcadbcacdccbbeccdaccccbcebebecaabbeabbdacbedcbbaabcbedcbaacbbedcccabddaadcebbabcdcdeaabeebbdaaddddaeabdecdaebccdeabdcceaecbaeabaadeabebcbeadebcedabaccbdcceebbeaadaeadecdacccadabecbadbabeeaaebebcaeedeadbddabecacaddedaecabcbeceddedbebabaaedbabaadddadeccddcacccccbbdcbedcecbcdaadcdcbdeeaacddbdcdbeeebeebccddddbabcaedcddeeddcbccecaddadedcacacddcbdbedeabcdedbbeeebdedeedaaaacadbabaaeabbceccedddaabecaaabcaecbceccccaabaebcadcdaacdebcddbadbbbbebecacdeccdbedbaedadabbaabebeadbeeeaccacaabcecbceebddbeeabbbcbadbceddcbbabeabbcebaaddeaacccbcaeecdaebcadeaeaedcdaddeceddabceddbdbcedbbacdedbbebddadccdeeccbdaaccbeecabbabdecbabbcacedccceceaadececbbaadedaebeedcaccceebbbbabbabbcbaaaecdacbebcddedeabbacceeeabdeddedbaeecbdccbcbadaadbebbcbbdcbcbeeaaecbebabdbaaabeabbcdbacdebbacbbaccdcaeecdaddcdcccdaccaccaeddacddeeddecdadcceeecbebddadcccdceadacdacbedbedcdbebeebabcbdeecbccaabbbdbacddcdacaecadedadaebdddcdecbdaebadbbdbcaccbacebdbaccaacdcabdbedbabebbcacecdbededeaabbedcbeeadbebdadcaadaaccdcceccebaacdbbedebbdaddeaaeceabcbaddeeebcbaddaeabaaadeadbebedebbdbbbdccaaababaaeedddcebeadcaceaadabbedddaeecccadadbedcebcebbebdadacbddaccbedacebcaebcacbaddaebdbcaeaacdbbabbaecddbabcdbbbaacacabcabcbdbeebaceabacbdbeeeecbaedcaccabcbcacaaebcebdccaeaccbadaeaeccaddadddabadebaabebcbcdbebbbbeaaceaeadeddbcdabedbdbdbcebbcbdceeedbaedcacbdcdcbaadedbecbcddacbaedcdcecbeeceedecddbdeddcacedeabbcbdabcccccadcadbdaebebeddcaaebbaccacddbeeeaedacceaadbbbeabacabbaedbbadeceddbebcebbaaeedeceababaeceaaeeacedcbdedddcdaaabadeeecdbebdceeecabecadebebcecebeeccbceaaaceaadabacdeecaaecdaabddabcacbdbbababcaceabbdcaaabcbaeaebeccbbeacabcebeccceccdeeeedceedddcadcbbdedeceeaebbcecbcebaeebbebdecaebcaccdadbdaacaebbbcbedceabebacbeeebdaaccebbccacbdaccbbebcbbbecaaaedabdabdbccecebbabdccbdbadcedacbaaadbedcacaceacabbbbeebaaeeaeaacbbaaaceaccbecbaaacedaacbcbeecbbbaeddeadbcabcaebebcbdcdadbecaedadaabcbdceecdaecbdeacbceddeaeecaddccaacdbaeebccccebaedcedddaabdbdcbcacdbbdecbeabececccbedcaaceabbadabbacbccddecabbeeababecadbacdcabdadccdcdcceecbcbebcaadebccaccbbecdbdacdabbceddaaabdedcecadecabbdeaadeaebddededbbdadcbdbcbccaccedeaaaeeaecaeccabadecdeaebacbbcbdadcdecbebadddaaacbecbeedaadbeadacecabbabcdaeaacceeaaaabbadbabadebcabdbcdadbaababbccaaaebebcabbdecbdaddcbecbeadcabbdcedeebcaebdcecaeadbeedecbbcccbcacebbbbccabdbddaaabecbedcaccdebbeabeaaebbbbdadbaceaddadccadcbcdddbcaeacacdaaaaaeeabdaaacccbcbacdedddbdadcaecedbccaeabdcaaeabbdcecacddabbdbbcdababdebcbdaddcdcbcbeecbbbcedcaeaddcddbeacbddaaddcabeebbaddedadbdedcabddbaddbaedcddcadbadedddebbcbdeecdcaaeaebbdedaaadccbdacadbbadadbdeabdbdebbdecaabceadacadabbadaaddaebbbddbbbccbcbecbcadbcbeeabbbdbeceebcecccbbabebbacbeddbaaaeaacebcdeadaeaadececbddbcbddcbbeaaabcbacdabddccdebbeadbaebddbeebeebbcaaebbeecaebcdbbdceacbeeeaedeaabeccdbaeccebcababaaaddaebebbbbaeeabbadcceeaccdbabeaeaedcabaddcadbeeddbecdcadececcdeccaeeaabeedebceabaacbbadbdaeeddebdabdbeabebbeaacbdcbbbaebacacccaaadeeddbeebdbdddadcacedacaabbbccbeeadadeecaadbaacdaeccaabdceadccabadeadedcbaaadcbdeadddbebcabaebbebcaebbccddbebbecbebdcbaeabbabdedcacabcebaaccebbbccbcaeaecebadbbeaeabebdbadaedabadcddbcdaeeccbceebabeddeabdecdaabcbadbdbbccbdbababcdaceceeccabbbbeceacbcaaeabadbcecbdaadabaabddaaeddcceaccabcdcdcbeeaddebaededbabccebecbaaeabacacacbbebdbbeaeebeacedcbcaaaaddabeabcbcabbbbbaeaeacdbecbbedcaceedcceeabcceeeacdabebdeaadeececcdcdaacecaedcaeeecaeebebdceedaceacddcebbabdabaecbcdbcbdadabeeccacacabadadbddbbcadabedcbbdeacdedbbeebcbdedacabcebccdaeabdbceeeaaacdbbedceadaacacadeeccdcdcecedbbbaaebceaabadabbebdcdaedaacedaebbabceeaaecdabdacceaecbaceaecbaedcecbececaeeececeacabaacaebdddcabbdeaecbaddaadccceeaadacdddbdcbdeaaabdeeaceceeadbeeabacbccaddecacbbcdeacbdacebaecabcabdccdaedaabeecebdacdaecebbbbacbcbdccdbacaebaccbdcdcebdedecdbbceeabecacbabedcecebedebaaedcdaedbcbddcbaadebbadaadaadbbeddcadbdbededdaecdcaccddcadabccedeadbdedebdecdbeaaaaacaabdddaaedbbaedacaaeaecbceabdcceedeecceeadaaaeeacaebadaccddaaaaccabebdcdbccdbbaaaeccbcebabaeecdabaadabeebedceddbbacbabeaeaeacbcecbbebebccbddacedbcaacededbbdaabaddeeaebeccdcdecdadcbbdeecbecadccacbdeedddeceabddbebaddcbedeceedecdecbedddaabaeedaccedacaceeaaaaacaeecabdbedbdaabbaeacdcaabbaddbdcbacbcabbeedcabddebddabdbebadbeabbabccdedadcaddaeccdaddbbebacbdcdddeccdcbcedcecddcbacdbadbdeaddedceeeaecbaeeaaacddbdcbebbeeebbddddbbcbeabecddeecaabcbbdcceaaacbedcdaaddecdbabaeccaeabcaeabecdbaceeeecbcecaeddcabbeadcbaedeebaceecebebeadeeacccaabcadcceddcaeddadbecbaeabacceebbecaadbeccaededcabdececcadddaaeaeebabdedbecdcbbdcaeacdddbaaeebdaeccbbbeeedccdeccbeeebccbaddcbccdadeccdbdecdbcbbebaceccddedbaaedaabedbdaccbdabbdcaeadabbdecddeaeecacabdbbbbebddeeebdddeaebcbecbeadccbbeebaaacebbcddaadacadeeccdaaeacecddcadaceaadcabecbbdcaacdbbdebcedecdadceaeebeaabbaedbeacdbbdadbaebdccabeeaeacadcdbdaccdaabbaddeacabdbeccabbaccbabbbccadbcdacbcdaeeebbbbccebbcccbededbaabaaebdeaaeeadcddeadecbadbbbecceecbbdeaeaaaadaddbaccaeacaecdbdeeabdbebcbbadddbadbebdbdecdacbddacceacacbdcbdaaaccbececadbedbdaacbceceadbbdaeabbaeccdeebadacebaecebeaebaecdeecaeaaaaebceecdaecbdebcdeebdbdeacaedbcaceeebbadcaeadceceeacdcdedcbaedcbecdaaebcccbeecadacaecdaebebdcaaecacaedaccbdedcdeeebcbccdabbedeadeabacdbabcdaedeaaebaedadcbdbbbcaebecedaeedbcecbacaecacadadedbddcabdcbeaccdeececbcaaebcdbcebaabebadcebededbeaeeaeabbceebaaebcdbcabeacededcaaadbacdbcabddebeccaebeeaebcbcaeeabbaabeeabbdedcdcedeaabcbdddaccecaaeeeeedeabcdddcaeebeabaebadbecaaacedbdcbacedacecaadadaacddeeecbcadaabdedbbddeeaedeaceeeceddcaaccdcacadcdacbaecebceaddaaeddbbadbbbebdecdddadcdbeaebcaadeeeceeebaaeadeadccecdcbabdbcabdcdcddabdceeecebcadbebcdeadcbbebeaaecdbeeaabcabcccdcbabbbacabcbdacbbddedbeccdeacbececbabdcadeaceabddbdabcebdbbdeebabcedeacdcdeacbacbaaaecaececceedeccaaaaceebddaeddcacccccbeaaebaabebaededdecbabbabedbbbbeeceeddacceeaadcaedabacccacebedbbbbdecbaabaeebabcbacdeacaccabbcaccbbebaeaeebeeeebdcedcaccbccdaaeaaebacbaccbcccecaedddbdbaceaeceacddaabeecedcccbdacaecadcbdcaaabdeacbbabbceeaabedbbedadaddecdddeceaeeecabdbdbaccdbddeddedbacabdaacaaacbedabeceddaaacbecabaeabddacaebbaacccbcdedbacbadaaabeddeecedbadebcabcccebccbcbeabcacecabebdcbeccbdacbeddbccacbbeeeaecabbddebdececbdbbbadedacddabbdabeadcecacccaaeaaacdcddeaebeceebbaaabdadededbededcbcdadbcbdebaaeeeaeeaccdadbcdbdcbacbaabcbdcbdbbdeaedccadeddecadcaabaeadcdeaadacaadaccaeadebaeabceaedaedcaacabaaedaacbdcccbcddedbbdbcdccecadcbccaeebcdaecaeccaacdababaeadddebcecccdecdebccdedecedddbeeaebcbebdeaebbbebbbeedbeababbdbeeeeceebeabbcaddeabaccceeeebdacaadaeabceeaccbebeddeaccdcddacaedcedbcbdebbbebbbdbebcdccdaacbcececcbeabbcdeaddeebccaabbcbcdaddcdeccddaaaeeadeeddbedaaccaceeaceeacacbbcdbecaadedadadbadbdbdacebbbdcdddacedebddddcbbcadebadaacccddacddccacabcadccaebaedbdeecdeaacadddddbdcedbdcdedbbbacdddebeebcbedcedaebaaaecbebacadceabcaebaedcbcbaceeeddedbbbaacbadbeadaaebcdadeaaabdabeeddaabdccccbcdadebeeccbcadbbdceeaeeabcecbbaaaddaeacbeaeeacaaacdddcecbdbaaadcabebeddadbbeeacbdacadcbbcdaebaedbaaddedbceaeaaaabbebcebceacecabedacecbceacaddccbabbdeaeebbbcaeddadbcbbdeadbaeabcbbbbebcdadecceeeacaccddcdecbcbaaedcbdcabdbecddbabdbbebbeacdddaceaeeaeeabdebaadcdbbadcdadbceedbcbcbccdbdededcbccbbebbaccdddcacdabbbcdbeeedcedbaeddadadccccecdeeeecdcdabdcaaebaabeeaacdeeaabceebaebabeabaebeeededbedbdecaaddcceccdddcabaabeebdbecaebbcddcaeebaecdbdbdccededcdbeadebddcddcaeadaaeedddbbdeadbcdcdcaddcceddaebdecacabddcaacbbbdddbdecdadbbceddebcaebcaedacdcddcaededdededbdaceecbceeeeebeeaabcdcaddddaeeeabeddaadaccbaebcaaaddcdaacbacdbbecbbbcdacdbaecdeacaccaaadcceacbccadabeadacdbbcbbbdbaeeebcabdaedeecbdaabbbebeabcccaabaddeabdcbeabaecbacbeaeccababaaddceeccecbaddeceecbbaeeccbecdacbeadbbbdddeaaeddacaabeccdecaedaabdeadadcaadbecbebdebcbdedbdaebebcbedeebbababdedbcacdedeaecbbbccdcbdbccbebddaaceededaebecdebbdccacecdbbeddababecedeccccebbacececcaaecaddebdceedebaabbbcebedecebccbdbddcbecdceaecebaeddcbcbbeebccbdacdcdbddbdcbebdedbebcceebadeeaebbdaaabbdedddbbbacccccceaabdecacbdabadbbedcbeacdebdeabbccbbbeededccbacedcccbeeaacdcbbcacadedaecebebdadaececccbbabecaeeeeebedcaecdccaadcedeaecdeeddaceedaeccddcecbdacaebaddbcaaccbbddcddddcaaacaddebcdaddeabacdaceaeddadbdbcecbebcedebbcdecedecccdeecaecacabeeecdeceeebdbaadacbedadeabdbcbaccadabdcedaceecbdaadbcaddddccacdeacadedbbbdeaabcabbbabbecebabcdcabbadeaaeaadbeedbebcebacbabdeeccdedbdbaabcadadebbddbeecbaccdbbacbedaeeaecbbebeeebcddeabbddeddbdcbacbbdaaccecaadabaddceedcaeceeddecabeeadeddaaeabdcdbdeaabbbaddeecedebecaaebdbabaceabacecbdabbdedebbbbebeecebcbcccebebeeadbdacedecaaabbaaabecdceeaaaacdbaccedddedccbecceaacbedcabbeacbaceaeaedaedcebabceaeeebeedaaddecbedebaebccbbbbaeadecbebdacbadaeeeecccbdbbeddbababdaedbbddabdadbcaacbdbcdbadceadddebebdadcbedcabcdadedcbdbebaebbdcabcacedbddceeedcabbbaebeddcbcabbdcbbebaabdeceabbadbcdcdcbccbcaeaedecabcbdceebabcadbdaadbacedecadecbeddcdbdcebaacacdebdebdacdbaabbacbbaedaacbdaeeadaadbbbdddcbcddabeceaddebeeadceaedecedbbecaacbccaeadeddaccdabaabccdecccdedaaddbddddecbdcdcbcdeceaddbcebcabbaadabcbaedeeedebbdabceeadcdaebcbeadeeedcadcecdaaebeabeceecabcbdddcadeabcbedcdcbebccabaedececcbbacbddabdddbccacabbbcdabdbcbcbbedababccccedabeedeebdebaccabebdbdecacbcdeddadbcbbbcececeecacddccaedaabcbbdbeebeedddddcedecadcbbbcbadcababdbacecbcdeeeadecbcdeddeeaebdcdbacaaaeaeeeabeeecabdaceceeabededeedddaecaadcdcaddbabebccbdeceaceadcdaeeadabeabbadeedbbbeeabadcdeddaeacdbdbbacadbbdecadeeeeabaedcdebaeaabbcbccaedeecbedededededbbdebeacabdaeacccebaaeedecdcaceeabadcadebaddabeaeedaebecbbeecddcbcbeaaeadbaaaedecaaecedbecaceeabedebbdeeeccbaaaacbacebbbaabbdaedddebcdaabccbabecbeaeedaacbabbecadaaacaaceabdeacebacbbecaeddedebadabedabeeeadaaacadaecaabbcaeccabdacebeaccacebacaeadeabbcbdadddeccedcbcbaabdceebbdeeddadbbdbadaecababcaaeaadcdddbcabdcbbddcecadcdbdbeabdbeddcccdddadcbadeacecaacecbcededbbccaaccbaadbbdedcdcccbbecccbdbdeacdaaeaeebbbaaeebdaeebaeeadbbeaeaaabbebeadadcbdccbcecbdedccaedadebdcceabcccdaddaeebcabdbeceacdcbeaebaedccbabcebaccadadacebaceaecedbebdaecbbdedddddecbbdddaedceedebeecabaacbdcdeadabccdaaccababdbebededdcdcdebdcbdebcdacaeedddedeeacbeeaeceacaaaeecaaddbdeadcabbedcdecaadeecdadebeadebcabcdbdddadabccbbcdeedecedadbdedeaebbbdcbdbaccaeeddaedbbdcbaaecedbcddbccdcdbeebbabddcdeeacddedeeeeeaadbbeeacedeceeabaadbacbeaecbdebbbdbdbeddebccbdddcbdbabebaaaacdeaecdcdccbbdddaaaeeeacdbbbbddebdcbebdaddacedbeeddceaecdcbbaaedecabecdccdcbbaddededdabecbccdbcaadcaceacdedeadcdaebdedbaebdbcecabbcdbbeedeaaedccdadabdadebddbcadddcaebbaeeadcaecbdcbadbbbaeeabeabccccecddaddbeadaeccdbceedcedeecacadaaadababbdecebbaabbedeaecdaebdcbbebbbdcdbddeeccdaedcacbdbadcadccaedebebdcededcecbaeaeecbaabeaacacacedcebbbccdadcbbdbcbdbbeaedbcbbdcdceadecbcaedbdeacedbbcdeeaaececebaebeabbdcdacddebadaaaacaeabaceecaddaeebbeaedbbeaacabeaeeeebbeabbcdaeccaeeccbddcacbaadabdeddcabdcacebaaadedbbcaaeeaedabaaccbddddaaadddddcbeceddaccccabbbbbaebccabdbbadededaecaddbddecaceaeacdebddadbaaabcaccebddbcccaacddedccdabebbdecebabcbdaadeaddaddbdeceededebdbbeeceadacbabadcbaecdadabedbcebbbcedddebeedccacaddbadbbbaeadceececeaebaedecedccadccebeccaedadcddebaaeeaaccdbeeabaedaadbededdaeeeaabdceebcdcbebedebeedbeabacdaaeceeaeeaabdecadaadaceaddaabcbeaddddceebdebbebddbdcdbdeacbbdeeaabbedaadbdaaccdacbdeeeccdeccddcecaceadcabacbebadccaeedaaedaceccebbdebacbdbeaeeebcdbecadcdeaaedcacecdcecbcdadcbbdaaceecccaddbddeacdbbdbadceedadaaecccceaaecdacbcceeccbdbabcaeeccbecdddeeceaaacdaebdacdddaeeadbeaaeacabbaadcdcbcdddabdabecabcebcadaeebddeabbabceebbdecedeecedaeabadaeaadbaeecbcbbdbdedaeeddbbbaadaaddedbcbacddbcaedebdbcdadeeddcaaabbceecdcbbecebacbcbbdddeecdcbedbbeebedddeadcadddbbacdabecedebdcdeeeeabeddededbccceabecacdaddbeccdeddabeadaccaaeedcdddeeededccbbdcbcbcebebdcedecbddbbacedaddebabdbcdeeeddedaadbdcddbeddecdadaabdcceeebaabadcbdbabedddedccbaeecdbddccdeaabcdedcbaadbaeaedceccaadabdceeeccaacadaccbcecacbbeebbaceacdecdcdbeabcbdadbdabcceececaeabeddbaeccaeabebaecadbeabbcabbdaabadadbbaebdbeaadcedabcdeaddbbacbacaddcbbcdceccdbceaeedbbcebbbbeceebeaadbacbdceabdbadaadcabebcbccbaebbcbdacecdbdaecbbbedabbdaadaceadeaebcebdcbeabbaccaeeebbaccdaeaaeaecaaebecddbeeaeeddaacbbeeadabcdedbdeaceeebddcdcccdbbbebdadaabbeecccdcddcbacbaaedaeedeeeabeddaabbeeadbbbcedacacadbbdcecbeaaeedabceacdedcceebdaedecabaeebaeebceccaeccedcccbeaebedadcebbdaecdddbceddcbbebaabdeecccdabdeeebbddaabceeeaecacdbbcdedcdeacbbadbdaaecdadbabdedbceacdcdedaeccedcceababbaeaacaedccadeecdcdecaeaecbdccdbdcdcceabcbaccbceedcadbcdedbdbddaeaabcbdeebaaeddbeeeceaecbedebcbeaeddecdbaccacacdbdaecaabeeedbaebcaebddddbddbbdacdcdbaaadbcaebabcdbbedbdeaababbaeeeebcceadadeeebcadaedeeeaacebbecaeceadbdaebcebadcabdeadcebdbebedeedcedddbdccceebbdbcedaeeddbebabdaebceebaeaebcdacbaacbdeeddbaacceaceebeeabbcbabaceaedacedeaadbcdebeebadbeaabdbdbcaedbcacbccdbaecaccaeadacebbcadebdbbeadbbaeacacedeacbabcdbdabacacdecadaecddeaaadcbdedcbeceeaeabcbedbaebabacaeedbcdecccadecccabbbeedaaeaacbabdedabbedabacceeaeadeeabaacbddececbbeaeaadadacbbedcecbeacbbcacedbbecbccccecaeddeaebeeeaddacdadcbaacddebbbeceebbabeebcdaeccdabdcaeecabddacbcbcceccededbbcdaacbaecaebebacbdabbbcbdaedacdadaccbdeceecdebbddedaddacbdecdbabddeacbebedddbdaccbaecaecbbceddbdbecbedacaedbcdbddbdebaebadbeccddccdaaaccbeadaceebdbaaeddcbcacacaaabcdebaeadaeecdeccbacdeecbdedbadadabaeaadaebdbaebbabdcceedeebeaeeeecaaaabceeddddcbdaeedbadcbcdcbcabdedeaccbebbbedbaedaacdbadaccacecddaedbcdaaeddaaeeccdceebdedcdeddbadebaccaabacebccaedabbaecbaebcaaadaabebbbdaebeaeaacbceecebacabdbeededdaaccaedeeacbacecceccdadeacdbbdebadddaebbaeddcadcdeaaacdadbeaebddddedaadbeabaeccaaacacdeedadcdabccbdbbeebbdbddccecdacaecddbedbcebdbcdcdcbbcdddaebddbaaededaabaebbceecebaccadcdaecdbececedcabceabcaacbbceedaeccacbadeeaacbdebababbdecbceedcebabceeceebcbebbdddabbdcabbdeaccdedcbabdccdebbdcdbdedaccbedeeacdaaababecbbcceeabdbccaaaeacbcbdbabaabbcdcecbbddbcecdacdbaceacbeaebacdceebaadeeaaabddaabdceacddacadcdcdcbadcddaeddcbadbcddceecdaccbeebeadcccacdcbccadcdceebccddcddaeacabadadbdbabaaddcaddcdcdeccbebadebbeccdabbbeddddadadaaadccaaeceaadeeceaaeadeaecadacacbacddbccebebacceecdadcedacccbdccbbcddcdccbebdeececacbdedeaedbadbecaccddddcaddabddecadecdeeaadababcaabeddcbcededaaebcadabaaedeaadeaadecaaecabaadbcedbdabebcceadcdddededebecacbeedddbeaadbcbbccadebaddabbecbeeeadccbaabaeeecdbadeabdebacaebdbbdcdcbceabcdeddeabcdbdccdeccebbacabcbdccbcbdbdbaaeeeabedecbaabddeededbcbddaebacdadcbbbedcacabdbaadeddaadddebcddbcabbaceceedbceaddcdecbcebdedbbbcbdbcbccabbdebcadbcdbdcedbaeabbaabbaacecdbbaaacacacebcccbcaacbcaebcbceddaaacadaecbdeecddadecdbcbaaebaaedadbaadcdebadacccccadbeedbcbbaebcbdabcbdcbcbcecbbbcbdabebedbcebbecddbeadadacabbebabedbdaedcecbcceeddbbebbcdabeecabaceacddedbbebcdcabaaebbddaebbeaacbbccbbcceeaeddbdbacebbdecbadabaaeddeabccdbebcbaadacbaeeaaedddcaedacadaccadcacadacbeebebbbecbcedadddcbabecacbdbddcebebbcddbcdeceaccdcebdadaecedbebccdbbccedeeddeeaeabbbdecddebabcdcbbacdbdbedaadeebcccddecdcaadceacccedbddebaedbbeaabebdacdacbbbacdbcabddeaedebdcdcebbbededbbdeebddbdaaccebabbdaaddaccaebdcdebacbaadecdedcbdbaceabacdadebabcbebccaaaaaeeacccaadcddabaeeabcbbeedbcdccadebcaccbbdcdcedcaadbcdedccebbcdeeaeeeaeeaeebaadbeabddbaeacadeedcedbacdcdcddbedddedcebaecaaaeacadadecbabcbddaebccaeceebebdaaeeebddecaddbaadbdeaaabbdbdcceaddaebdacddaeeecceaccbcbbbebdadbadbcceddbadaecceaabaeacdabccadebedcbcadccaccddedaecadeddacbcabdbaabaedeeabcaacbbdbaeeebedeacacdddbabddaacebbedceeccbcbeddabcdeaecabcdeccebcaeeaebeebeeabaeddceedeabddbbbcbcbdeadebadcebcaeabbbbddddcaddadabaaadecabcdabaebebcbbdbcbdcbecbdcaedbdcdceaddbadadcdeebcbbeebebeeeeabcebdcdceadeecaedcdcbdeecdbdabcddeebcaaccdcbadebcbcdcdbcbaaaabdccbcdeacdddcbebcaddeeaddaebedcadbbdbddbdebecdceecbbedaeddcdaaddbacbdadaaeeccccabadecebecdeceacabeddbdaeedbeeadabcdbeaecdbbcdbcdedddaacaecbecebdbedbadcdaedccdbabdcbaecedcebaeacecaddddeedeacbabceeabeadedbdbbaaabbdbebbacacceaccbadcddadccdabeeebbdbcadbedeacddbecebdcaacdeeeccedadbaecdaaedcddddcddcecbbedcaaacbdbabaadbdddcbccacabcbdddddabebceacceabbcadbbedccbdddcbcccaaddebbeaaeccdbbbadabddbeeadbaabbaeabdecdccedeacbedeedceaaaaecccecdadbcaadbeecaebedebacbdeadabeceeacdcaacdeceaccaceecdeddabadacddbeebdeaebadcdcceeaeebbceaeaacacbaeebeebdaccceebbdccddabcbbcbcedabceaecaceebeacbacaeccbbeeaababcadcceeeddedabbbccaedcceedbecbebeaedabeecdcbdacacabeabaaecaacbbdebdaccbbdeaedacdecbaceceeeacbdeebbdedebaedaabbeeaaedbdedbdadadbdbcbdedeccdadddbaedaaebdbaaaeebecedbcdcaeacbccaceecbdedcabbcccaadacebedcdebadedeecbcebdbebcceaeacbcbacbaeeebbaecdaedadabedacaddabeeadedccabbbdccbeadeeececcecabaabbebccbbbdbdcdedbdabcdaabcbdccacceceaaabcaebbbaaeadeeaeceaecababdecaaeabdaeacccabdcabeacddbbdaeadedebabcdcdddbaacdbeddcceecadcccbeeaaaedabcbadabcdceaaeccabadedebacaebdabdbdacbabaacbedaaabcaaebcaacccdeacaeecacabbbaadeabadedeaeccccdbebabdcbedbabebdcacbbbbcccdbaadadddcabcaaacdbbaccecacbdedeecdebdbbbbcceadecabbbdececbddabbcedcdcbddcdccbdaeebabcadbecbeeaedddcedcbdaabcacbebeeeaeaeccadcdecdddecbbaaaadbbbebbadacdbeddabdcabadbdadacdaccabcbdaeeebbacddbcbbacbcbeadeadedbdaeddcaedebddcbddaedceaeecadaadbccdccdcddaacdbeeeadbcbcdabaccbcabcccdedabbdddddbeadcacddbbbdeabccadcaddaaebdccbccddebadbabccadbcbbbdaedcaaeeebdcaeccdbaabedecccaddcdabecdddeceddcabcebebbabcccebccaacbadcaaedabecaceeebacbeaeceedadeeabcebdcbdbaceabebcdcabeeaecceecdeaedcdddbceceadbaaabcbcececaeedecacddacdeeaaeadbdeedcceccbeaddcbcbcceabedbecbbcbebacbcdcbbdeabadeebaedcaedbeecdbdeccdadaccbcbedeccbabddbeceebdceecaeebdddccdceceedeeadabeebadcebddbbacdcdaedcabdbaeddcbeaacabaadaaecbeacbecbdaaebeeebdadcbbaaeaadbdadcdbacddbcbbbacdccdddbdaaebcdeccadccdeccccceaecbaabbbcabcdabadeadcdabdeeaaebaaeecdcbbabecbdbedadeadcccaeabecaaaacedcdcdaaebcbadababaabdcdedcecadbebdddeeaadaeeeaadabaadaeabdedddccceaaaeaeecbcdcbaeacebabaebbdeaabeededcbcecaedddedeaeedaebbaaabecdcbcdbdbbaabbaecbedbbcbdcbedcecbabebedeadeecbecbadecdbecbeecddeacbbedabbbbceeaeaedcecadaadbadacccdbeedaceaabeceadbededebbaceebebceeedcadebdcebccbccccbbaeccccbcaaeddbcdbdaacededbaaaccdabcceebcceebccaebcaeeaddceeadaddaeaabbddbbeabacadcbecacebbaedaecbcaedbabaaeedbebdddbabeadeacebcdeeabbbdecbeecccccdeebdbbbcdecdecaccddccaaaeaabbcdddacaacdadaddeaeaddcdcaeedbbbbbbeaacbecebadcabaedeacaceadabbccbcecdaabccdaaeceadabbcabedddcbecadddecdbeadcceebbeedaaddcbdaeaaaecdbbceaddecabbaecaadccadadccdbbebcaaecdeececabdceeebbcdcdaedceddadbccdbbdebecacbecdbdbeeeacedadceadcadbebadadeedbcabccacdbabbbcdccbacdcdeeababeeadbbecddeadecebbedbcebabadabbebacabcddaaebeedaddcdabccbbcddecbacaacbbccceecacaeedaccbebbcebbcebdebcaaaddeeacacabbbbbdaabdccaebccbceebaaeaaececdedaabdaaecccccddebacddeebedbbbddaccabebdbdcdccbbdddacccccdbcdaeebbaabbcbbbbdcbccbbeecbdabeaeadeaccdbbaacbbbadceabbebdaccbeeedcdcdebecbbeddababbbbadcbdceeaabaceddacaaaecdcebebbcdbdaadcaadddaddcbeccacacdcabdabeeacdcdcaedbcdaaedbbedacccdaacecbdbdcebdcbcdedcaaabdcbcceaadccbbeadbaddbeadcaeecbbcdacabaeceebddbbbdbcccbeaeabddecebddecaddedddbeadcdceaabaeaebbcbdbcedbcadebbdaececccedcceacacbadbdeccddbbddebcbbdeeecddbeebededccdaecddcabdbbbaebceeebadeacdebdaeaecaccebddcededcacaaccdcbbcbcecaebccdaeccbacaedbaaecebecdbbcddeddbeabeaacaacccabcebebeeceececcbadebedecdceeadceedbddedaaeadeeccbdbaacaebcdecdeabcabdbaaedcbaadecacbbaaeaebdddcbbdbbcaedacbceceabcdadedcedbdeebdbdcaacceccaebdabbcedaadddbdeadecbbcccaeebadaedcbeedaacabeeaeacadcbaadcccbcbabcebeacbdbcabbaaddadbdbbcdcdbccacbeadaccabebbbbbecdaabeacdbdebabecbdbeecaceeebcddcabbcddcccecadcceddacddcaeeebeeacabdbcacbddadaacbdaabdababdecacabebbcaaaecbcacecccabaeaedbebecadecbbacbeeaaeabebdeaecdaeceedebbdaedcbcecdaececccabccbdbbccabbbebeaebeababddcddbdaedaeeccaacaebccdbbcbecbeecdbceeaaeeddaedcdcddcddabaddcedbabadadacdacebbeacdbdadeabedbbcdbbebbecdabecedeebeedbbcecdbddabaacabdeeadcbdbeecebaddcbeaaabbdedcddebcddcdcdcceeadccbebdacbeadcdccbcdbbdebbddadeeaceacbceebebeccceebcdacbbeeeecadecdddeebcdbccaaccbbebeadcebcaccdedeccedabecdcbbcbbbcbdaceccbcedeceebaecdeaeebcbebaaeadbacceaeadbbaabbcbdabcaaaacebddbbcbccdacbaebedcaedadcdcbacdadbcbbdbbbdbddadcbceebeecebdcbbabcebcabbbeaadcddaebcbaacceecabeaaaadcebbeaadeaeebdedcbcdcaadeecdaacdcdeaaecbeddbedbbaccbeacdbdbceddbdcaebbdeeabdcdbddcaedadeddbdcdedcbcdbdeebbabaacbdaceeacdcbbeceeddccabbebaaceccbcceaaaabadabccabcceaddcbcacacdeadadbbcadbaddaeacbeeadcdabdcbcbcbbeadabbbdbdceddeeedabdddaaaedebbcdccbbaaedabecdeebaeebbbecdedaddbdaddadcdeeebacaeaebbcdbcebbcdddaaacabececeeeadabbdbbcdedaaadbbcdddaddaadeccccddbcbeeaeecdacbbcebdeccceaaddcbbdaeccebbdeadcdddccbddecbeeeeeaabeebaeebbddbbecbcedcaaeecbedededaebebebaddccaabcaebcadecaaceaabaedaeeacdaaeeaccebadceceadbcbabaeebbbbeaccedabccebecedddccaedadbaebdabdaedccecacedeeabcdcaeaaacbeddaadadbdbcbcbebbbcdbccabdbbeaadecbababbbdcbeceadedcbcaeecbcbddcbdcbeaeacbeeecbcadbedcbcceddceedeeebabcddbdbcbccbaaeedbebddcbcccabaddacbeedbbdaaeadbccdaabdebbdcbeaacbddeedaadddbbdcaecaebcecaddaadbdcdbcaaaccecaecaedabcadeeaecdadebabcbaaeccdccaeaeaebabadeccddeeaadcbcbcebddadcbbeecdccaacceebbccabaebeceadebddeeecbeccebccdecbddcddceeebedcabcaceaaeddaecaaaadceacbcaecbdcccadbaebaaedcebabaaaeedbaceaedecebbaedecbccabcbbbeabdccebddcabadacaceadbaaeadbebbdebbeeabccabbecadadeedcabceaecbaaaebcdbeebebecbcbbacaebcbcdcabaeedddeacdabadbcdebcacaaeedbbbaadabcbeddaebaeeeccececdceaaeeccdecdaddcbbdebebdabaedbacdaedcadccdbcdccceddebeedadeadaedbcdcccecebeeddbdcddccecabdebcddebadaaaedabdbedaaeaeaccdabdbabaeedabbbadcdededdbdadbceaedbcdeebaebabdbedbddebcdabeeeaeddadceeabaadcdcdddeaabdaececcedcadcdddeeddcaccaecebacdbbebbeecdeeabbecdbdeedaaededebaacadcabaaccccbbdedceeadecbcdececbdcddcaaadcdaebcabccaabacacdacbecbcccecebabdddcbedaadedcdbdbdedcdbcaccccebccdacaeaecccdabdadcccdcbdceccbccadcdeeccabbdabccadacdbabcedcccebbaaeecbcddaedeedddbcabaceeacccaecbbcabcbaeeeecddadeecbbeccbdbcaddddbdebaabacabbcdaeddbbdbeaacddddaccbabbccaddeabdcdeddabdddbedecccdaceecdbbcaadacaedeeecebdbeecdbeebcceecbecbbabdeaceeedbeabbeacaedbbececbcbeeebcbceeebdeccebdddeacdecdeebcdcaddaccebbdbabdadbaebaabbebdadbcbdebddeacbdacaccbdecdedaecccbdaebedeabceaebbcebceadeacaadcacddbbbedceeeaaeeebabbccdcbdcceeadbbabcbeccecaabddccabeeadaaaaddbaceabeecececbaaadacaadbebaaadcedecaededdcbaebacadbcbeaaceeebebcadaeeebcecdbebacedcbeddcbdcbadceeeddedbdaabeccaddeeaedecaccccbcbacaacbddcccddbaaeeeaccbeddcebdcdbeddbbabdaabacedbbeaebaaedeecbcdbabddacbbbeaddeaacaaacdaecaaecacacbbcadaaabdadccecdababeadadcaaccdcbdaacaaaecabdbbdbdcdacbacbceaeeabdbdadcebcceeccdbbaddaebcdadaacecacdcaabebedadbaceeebeedbbdccdacabceacbcbaaccbacbbddcaeebabeaadebcdaaeaeeeededcecdccdebeebaecccaedcdabcebbccdbbcaccbccdbbbadbcebbddeeaedecadeebdeecadeaeeeeebbeaeebddebbbacdcbecdcccbebaeabeddcaecabbedebdcdcbeacecdbeacdaecccbabebbcbcacceecbdddeaccedecaaececddcedebeedbdcebeccaddecabbbcddcabbcaceccecdeedacecbcbdbdddbbbaccaecdbceadbaeadcacaceadbadedddbdacadddebbacbcdceedaebeeeaecbedaeebbcaeeacbcbbeccbcadcbaebbcbdaacbcaeaceaaaedddebbacbcaccbeeebbbdbdacbaecccbcceeadabbeddcbbbdbdaecbdbeeaaeebdeebacddaaddcadebdededaeeebeadbceaeadaedebbaebcedddbdaebaabbaeacbeecedbdacddabecaceeaceebccecbcdceeeabdadecceacbcdbcdeadccaabbebcaaaabaccbbccbcdccdcddaabdcaccbecdeebedbdcbeacdedceebbbbcecedaacaecbadeeedccdebededebbddaedabddaeccabadebadeaceedddeebadcebabdbdcedabbdcbadbbddbdeacbabdeebbecebeecdeaadabceedcbaadabdaeadddaebbbeeaacbbeadabedaecbdacedacddecccecbdecedccbcadbeadebaeabcebbebbbddbcdcbbeadceeabddccbeeaccceecebaeaebdbdeabceacaacdddadcececbcbdbbbeacaaacccdedddcdabcbabdeebeebdbbbcbaabcebaeacadaededbebcaaedaadebcdebeccdbadedaadbbedcdcebcbedadccaebdbeaaecbaeeabbaebdadddaebdeeeaebecaecbcddaceaedadedaeddaeccdecdeeeaedccddcaaabcedbcdbeaeecbbeadcdacbaaebeeeecccedddcbbedddddaadeccebabcdeaccacabbadeeceeaeeaaabaeedabbdaacdaddbcadaebbeedbaaaaaedcbacdadbeebcccabbabaeecedcaccbbcbebadadabeaceeeadeabaaaddcdaebaedcecbccbadecbdacedaabbcacaebccecbcaebbbdcdedabeaeadaeccbcbddbbedebccdacdebbbbbcaeabbabaccabebedabcabdbceeeeeacaceaaaecaaecbbaeecbbcdbcaaddabccadeeeccdaaedcadebbcaaaeabbbdbdcadcbaebebcdaaeacbacdceccccaeacdabdaeadcababcaabcddecdeedddcddcadceccedbacceddbcdbcbddedcdcbdebedabeebcabdbcbcbcaacdbcebabccceadaeaabccaceadebeadbeeeecabdaabddabceedcdbebadbbeecaaeaeaceaeaeeeacbcbbeeddebcdeacaceeebecbcaabeccdecacaaadacdacbbeaccbeebbbecbaeadacbaccbcdeecdceaabdacacabebeccdcaaceadadaebeedcdceaeceaecbeacedccddacbdeabcdacddccddacaddeaabecdceedaeebbaaddedeaecdcedbdededbbbddeddbbdacbdcecdcebeadcebdeacbecdaabbaecebebcdbacbcebcecedbdedacaccacaebcbdaedcacecedecdaddbdeeeacbbbbdbbecbbbeccdaacadeaadbadcdacabbbbcadeaebdddeebeedeccecccbcedaecdedaddbaccedbdbcbbdbddeedeeebeaaaecceacbceadcaecdeaecbcabadceddbeaabbccdcabbcacdebdcacbebaccacbaedddcbbcbcdaadbbdebcabadaacedcacecdecbaebbbddbccaccadddeeaeadaacbdadbeadaccddeacdccabebbeeeeabbdbeebddaaddeaadebdcbbcedadbcbaadbdcebdccacedccabeddddbadebedbdeedeeeeeadebadcaeedadaecdbbbeebcdcbbebccbbadababbadcccabadcbaeeddcbccaceacdcceddcedabedbddddcdadaabdecebededededddcceeaaebcecebeecbcbecbcecbabdeecadaacdbcceddbaeeeccbcedbcbadcdbbcbbdbeeccadecabaceeeadcaaccebcbbcaebdedaeccdbbbeceedbadbcbddbdbacdceddddaebcbcbadcdcccaceadbebcaadedcbbbecceededdacccaabdadbdcebeacbbebaeebecddbbbdaceeeebabeddaaababedbebcbcadbaeecbeabcdddbceabacabdbacbcccaccdcecbccbaaeeedeecdaeacecabbaaccceacdacbeedacceeabedeeedeaecccebbeebcdceccdbebbadaebbcbeeeebbdcaccdcdeceeeeeaaabbaceadbdaddcbeddecdedaedddebedadacacecaaedacacbcbcdeaeadeedabcdacbcaeabbdabaacbdcdeeeebcceddbbbbadbcaeebeaeddadedecdaccbadcaeddabcadcbabcadccebddbcddcddacaceebabaedbeaccabdbbeedcabdddacaacaeaebebadbbcddebdecdcccddbcddddcbbcbdbbdbebdaabdeddcbddaaecbecbdcbedebbeaaebcedcaeedadbbaadecdacebcbddaacbacdaccaeebbceeedecbcbcbabbeddbbaeedabcccdbadaedbbbbcdaeacedededaeeddcebbceecedcdececbdccadbeaeaadddceccabadcdcebbedbbdcbecaaedacbebdcccabaeaaccbecccadbaeaadbadacdccdcaaaadbedbbbeecbeaadbedebbeaebdcbebebedeedbeddceddcadbcbbaeacdeeaacbaabdbaabbeacbdbbdcecaccdbdacbceededcbdacbdbcceaecaaebcddbeedaebddaddcadeeeceddeeaebadedededccdbbeedaeedccaacbbcbdbddcdcacaabacbbaaddebcbecebacccabeeaceeaaddcbddccadecaebdebcadcebdecdddbbdbaccaaeccacabeeeadeeabcdbaabdbababeacbdcdadecdbcededccdbdbdcbeddbbaddddbebaeddecbacabedbbcacdceccbecbaecebdaaeeaacabedeeabadebeadeeaecbbccdddeadabdeabbdaadaddadcabdadcabedddcadbcdbeedebceabaedecceeabaedbeceaadbabebecbaedbcdeaceeaabbeeabedbecabbcddaeaccbbcccceecaceabccceeadccaeaeecbcabeceeaddeaededbdbeeddaebeeadbbcadcbbbaecedebbdeceecacdeccbcbcdeeeedcabbcdcdeabcedccabeacecdcdddddbdbbaaacddedbbcbabaadddebadadaaadeeaeeedbdbeacbccaeabdebedcccccbdaeebabbececbbcbaabaaebbbeecdbdadadeecbbcbecebdebaaacaccebaaacccddaaaecccddcbcbbddeecddddbaddbaaeddacccedeabdeddbdabaabbaebedbceeabadacacebededdbacbdcccebabbaacecaeacaabbbcdbcdebacedbebeacaadbdabaececcddadbdcbddccccedabdbbdbaebbdcdcadbbedaaaeeeacbbccaeaccdeaccceacedbaeddedddceabbceedaebcbedbdbcbedbecaedebceaeceacdacbdcbdeebcacabdeacadabdabddcccbbeddcbadcbbabbadedddbdbececdaeedcacdaeadaceadeebddaaaeeeaebeadcbeaccddabdddecbeacaeeabececddcceccacdbbeccdddadbcbaddebecebbbdeacedcdaaedcecaceabbaadebcbaabdcbbdcccaedbadecebcedeacbeacddaeacbdccdeabbccbadacadebebbccecacceaecddadcabdbbddcccdaeeccecabccbadebacceceebbadccbabedadebabdbacddcdaabbeebaadebceaccaddaacdabcaadcdbbdecbdbcecceededcdcabbceabdbddacdeccecdcbdeeaddceeaadedcdedababbdbbdcccebaebbeecccdcbebdbecbdccebceaeedbbdcecebbdbcbccbdaccebebbaececcdcebdabbdccabccdbbeebeacebcbbcedcddbcceedccaaaccbdcbcebaabbbbddcebdcaceadbbbcdbadaecdcdcdedebedcedacbbdddcdcedecaaeaaedddcdddaebccdeadabdbdebaababcedbebaabeddccecedbeaaecadaadbebeeabebcbcaebacbdadbaaebbaadeaabdebbaabccceedbcdcddbcebaecbeadeddcbebceebcccebbeaeeaccecabdeaebebddaaabacedccbbaaaccbbbaecbbaeaeabebadbdcecddddbabbcbecbbbeccebeaacacecdcbcbacaaccabdcbadaaaeacdcacdcecdbbebecedabeaceacaaddbcdddcccdcccaaabbedeebebdbbddbaccbeacccacbcdbbdbaaeaceeecddabdbcadadccceeecbdcecebdddaaaebdaabbbcbbdbadeabeeccbebdacbecaaacdbbdbebbcadadbbbaadebacaeadcdecdcaaeccdbedacaebeaadceddddbdecbcdcadcaaeadceedaebdabcecaebdececccbacdcdebddeaabcaebbdcbbccbddbedbbdcaeebbebdbcdacacaddcbdcadaddaadcbeeaabcecccedbabcaeaeeabbccecededadceabdacededaebcecbcdeaadccdcbdcebaaecdecbedaeecddddeccddddeacaedceacbacebcdceadcceaceaeecaebbccbaeaacbcddebbacceebedaeabaedacceacdbebcaacdbbceebeacdebdeebbdabaeaebbdacdcbedbcbadbeebdbedbebdecbcbebdaeaedbcaeaaecdeebcaacaacaebaaeddeeedcbedaadeabbbdbbbbceceedebeeedbbbdcaebacddabebeddaabccccabecaaaecedbeadbcdbbdaeedbabcccebeeadeadcbbaeaabdddabebbdcccebcdbcecbabdeaccccaccedbbdcdbdbaadadccceceadbbceedbeceaaccadccbecbbadabecedadaaabcbeaadaabcdbdecbccacbdabecdcddbbeaebdeaecdeebadcdededdecdadceaebdebcbdabedcddceadaedcedcaddadddaeaadebaebcedacbbaebdaccceeddbaebeebdcddceaedadcbeadcabbaecdadeceddebcedbddbbbdbaadcdbabbacbadebcaddeeddcbcacacedcbaeeaaedbdcbcbbddceabcceeccedccaaecebdedcedadcdbddaacbadabcbbaadabdbbbbaaacebcadabbbdeaebbeaeabbadacbaabaceaccdbadcaddababececebdcabceababeadabbabeebebcbcecadaabdeedacddccebdaccdcccdecdddbdebebdaacedeceddebdaaeacedbeacdecceabcebabeadbebebacaaccedebbcccddcbbeabbdecbdecdebabaebccdddadddadeccacbbdbedbcdebbcdeaceecbcddedceccbcbbdbbccddcbbdeaadecbaeeecbbcadddddcedbbdebdcaaebcdedbcddcaceadcdedacabaccbccaaedcacaddedadaeeccdbebbcbddeceabbaeaddccedacecaebaeddacadcbedabbddeaeabdcaeceedcdcdcdebcaebdbebeaabcdddeccecddecabbdecebebcabdccdcbaeaeabedddbaacdcadebbeadaeaeabcdbbcceedbdddebbccecedcacddcccbbcedecbeedcdbdcbdebceebeadbbdeeacccaeebcebdcdaeacaadcbaddeabadabdeabcbbbdeeaeaacbdcbbadeedbacaecbbbbcaaddacaaaeabaadbbbebcdceeeeeeaceddebadabdabacdaecdbdaeeeebeccccaccbcbcbaebaeaaadadaddcaaddabedebbdccdcebbaceaeeacaaccaaedeaeddbbacabdbacabedabbaaebaeecbdddedaedcccdcdcbaccaeddadbdccdbbadedbbeebaecbeaabbcaceebccccabaaebaabcccddbccdcdedcdaedbdbcebacddbcdaebaedabbeddadcbbaaabecacbadaacadcddbeddeebbadbcbeadeecbcebcbcacacedcbcecdaacdcecbeececccbbebcccaabebbcbecdabdebdbaebcadbbcdaedcdbeeeccabccbdeaabbcaedcbbaaccacedbcedbbeeceeecdcccdebdbbbaceaadaaabcbecedbaebbcbcabccabecdedeccddebbdaeaebccbdeeeeeabaecddbaabcbacabccebddacbcaaeedabeeccacecbcddceeebaadbdeeadbbdeaebadbdaccbaecbdedbcedacdecabdebbcbacbcbbcaadccacdacaabcbcdcaaeccedbcbaebbacecbdeaaedadceacebbcceaababcbcdbcbbcedbdeaebbebabdadcecbbccbebaedecbbcbdcecdceabedaacbcaecaddbbcebeddbdabebcacbadebcdcbdbbdaedcaeeaccdeeabbcccebbcedcdceaeaadaaebecddbdbbbdcadcbadacaadbcaceddaacadbadeaedddbcdaadabecebaeacecbaeaddcccaeeededecadcabecadabecabebaeddbcdcbceaaaeebedadbcbcccbaeecaacdaeabcbcceadcaeabebdbcdcecabddaaacadbaadceadbddbebeaeeedbbceedaaeabcabccadebdcdcabeeaaadaaaadaebeeceabceeecaabdcdebeebdbdcddceccadbceddeccebcbcedcccdeadeacaddabdbeddddecceadbacdaacabbecdebeaaedbdcdcedcaeccecbeabccbbdcdadbeecdaeceacabcddceaeebdbbeabbeebaadbdbcadabbaebecaebbcbcebcacbdeccabcbcacaabdbccdbdaeabadcaeadaeadadbcddaecdbebdbadbeceaeccebecebeddaceeebceaabbaeddeeebaeebceacbcdaccbddedcccddebeeaeebdecebbeedacacdbeacaeededebdbaaeadcababccebbeaaaaaeaccedecdeeaaeaceedcebbedeaadabbbbbbcdeccbbdedeeeddedaaedcbdbcbabbaaceeabcacbacebcbbcecceebdabbcabbdaedecdcdccecbbdddcdeddaecbdebdcabadccddbcddceabceadcdadaecadcaaccccdabaedaacaecdbbcbbeadcccaebaacbeaaaabbbcaeacdadddcebdaccdbceabaedddecacdcdeaccbeccdeaecdbcdeeebceeaadbabeaebaababaeedcdcbcdcdbbeedeaacdceeeadcbaceeecebedacbeaeecadabddeabbcdedadbdbddaacbbdecebadeabaeeddecdeebaaaddbbddbdbdebbacdcbbdcaebebdabacabbddedddbdbddeabdddaaeeddadeaeadaeacbdcbaebebbcdcebbdabccdbcbcbcaccdccbbabbaccdcacdedbebdadedabcaeeceddddaedabdaabadeabbddceabbceebbcaecedebcbdbccaeeeaeecbaeaeaceebddedeeeaeddcdabaeebcdbdeddbacecacdaddcdacacecdbceeeaeeedbedcebdeacbadadddeeabcabeadcebcbdeadabcdbbeaeccbbddabccbcebcdabaeebddececaedcabeccdadcbbeccaaaddeacaccccbabeadeacddebecbcdedcddebabdccebcacbedbbaeedeebaccccaaddccdbeadebddcbccadabcdecaeccedeedecccacecbcbbbacedbeabcdeeabddbebdcbdedddbabbaccbdbbadaebabaeacdecabadeeeebdbaabdeabcdbbccdcabbdcabbdababedccbeeccdeceddecabbacddadeaddaaebdcdabccbbdcdebcddabeadddaabcdcbaabacddcaedeabbadbbccdbceccbbaedbcaeecaaadeeaeecdbacccadeeacecbabceccbddeabeddddaebccdcddcebcdedcbcbebccbcaeadcadebabedaadadddaaabeebecbbaadaeedceaadadbbbbdbbceaddcbceecdaaddbbdedecedacacbcbebacddececbbbdbaadbabcebdedceabcabbccbaccececdeabadeadedcbdbaeadedbabeddacaeeadebbbecacbdbcbceddbbddecebcbbbcaceadcdbeebddbccdcbcecacadaecdbcbcabacbacecadaecabeacbbaaeecceedbeecbbedccdbdeccbacbecdeededbcebcaedeceaaddacbcabbacdadccbaceabdcdcbaeeecbcdddbbeaaecddbecdbccdeeddbbdbbbedaacadeecacadaedbacbdcbdebcedcdabdbdcdcbdbdadecbbedcaecceecaceeebacaaceabcdeaddebcabaabbbebcababeddeccaaedbdcdbadcdcbcababbbaecbccdeebaaeeddbebebdbddcdebaaeebdccdcbbbaeaceeeabcccdabaacdcaaeaaeaabbaadbeccccacdbaeeddbcaecbbabbadddaaacbecceacbdcbacaeecaccccbebbaaebcbddadbdeccceeeaebeceedaaeabbcbaebeeebeacbaaeeeaeaedabdeddbbbdacaedccdccdbcbbacebdaccacceddecedddbccebbaadccebeacdcbdbcdaaeecccdaaabddbbbebcaaabcececcceedbbcddbbabddddbcbccaedbcbbcdaccbbbbcdbdeaabddccecdebbceddaabeaecbdaebeeaddaadbbbebdedeabccbbebadebacddeeddbeaaceecdccbceabddbdddeadadbbecdddbccceccedebaeadccabaabcbeabceebcceadbebcabdcdacedabeebcaeeaedbddbaacaddacecabcebeceedaaeecdcebaedbebbcebadddbaaaddcdebdccccbeebddaeccecdbdadeccbecdecdaeeceacddbdaabdddadbeccedcdadabbcdaacabaaaedcebaeceaecddeabdeccbdbbcbdbbdbdeacddeddcceedaadaceacadcbdeebbdbcdbcaacbaeecaaadbedbaceedaacebbaaedccadebcaaddaceacdeccddebbdecddbdabdcaaebdeceeaceebcbdbaeccacbdebecbdbeecbdedebbdabbaabbcecabdccdcbaaeabbdacacdddedddbadeecbacaacccdbbbdaedacebeccbcdeaeeecceebbbccbbbccbabdbcdbdcbeeabebdebebcdbaecbbdcbaaaeecbbbbadbaeedaaceecadacbcbeccdeedcbcadedeacbabbecbcdaabadbccbdabeeaeadedacabecaeadcaebacedeeebdbbeaeebbdadacbbdecedaddddbdcbbebbccebbceacdeadbbecedbbebdbbcbdecadeccecceabddeaeebccadadabaabaaaadbdadbadaeecbbabecaedebacbecbeccdbbeaabdbcccbbeeedececaddddeceecdcabdbceadbebabdddebaebeeedcbebccceadddcadceabbecadacbadbacbbdaadccaecbceabcdddcadbdceccaceddbcaecceabeecabcdaaecaccaeeaeccdeabdbbebcbcdecaabcbdeadebbebacccaaccbebbabdbbcaecaddeabcdaeeaaeabbbbcabddecbebdaecbeedadbcebdcbeebaeacecdaeebdedbaacbcebeddbadecaecedbadecbcbbaaadddacdaeabcaeedaabbbcabdeeadbabdbcbeddbdbeecbddacccdbcdbccecbabedaadddacbbebccaaedbececbedcaaadcadcebcabecbeceaecdeecabbeaceabbceccebebebbaeddbebdeebabaacdccddececadaebdccaceecaedddaebddebccebcdccdebddbecabbaecdcdcbcbddadbeaaecdeebdbcdcccdbbabbbcdeebcdacbeabdcebaadebddcbbecdebdbacdcebbbbecaedcceccccdacabbdcdecbdcaddabddacbbcdcdebebbebcccdbbdedbbcdbbcacbaadcbcebaeeaddeaccebdcdadbcddbcdeddcbbeaddadaeabcccaaddebddeaeabcaeadbeccebabbdbcccdcbdecdeeeddacdcadcdadcaebaecbbacbcbdadceedcaaaebddbcaebdebeabaddbecddcebaebebaaaecedbbedeacabedddbaaeabceacccaccacdeaccdcaeeccdacceabdeebbaacaeeaadbccddcabeccbccedebebcecebddebbcdaabcddebbcdddcaaedadcaedabbccdebbabaebdadecceeeeedbcabaabbdddaeededbaecdcecbbedccaceadcebbcdeebebceaadeeaeaaecdceebddebeeceadadbcccaedcbaacaedeebcebabbccabdccecebbcadbdbebbdaadccdceaeebacdceddedebccbadabddeaeebddeadcdedecbcedaccbdeeaedbbdcbacbaaebcecaaeadedceaeeddddeededaeaadaddcdbacbdceebddacadbbeadcedbcabcbdbaebbbbeabaaceeccedceddbddabbbacabcbdadbcbdabbcceeeaeeddeeceeabccaaddedacebdadaddbbebcbcdbcdccaebbbedeecadccdbabbaeccddbcebdbbbcbcabdaaceeaeceeeeeabceeeedececddebeadcebdbbbecebcacaeaaabecbcdaedccdbbdbbbdcddecdddbabebecdeebabbcccdecdbbdbadcbcaebeddeecdaccddadacebdcdedcebeddeeebadaeacadaccdeabcabadebcdcdbaeddaaaebceeddbdddabcaceacaaabddaeaeecdebdbeceeccbcbdbcaaddddadaabcadecaabdaebdeddbaadedabedbccbedcbcedcaecddccecabebeadbbdcebecedeeceaacccababbceceedcaccacddbcddeccdeeebcaceaddbecaecdeadbddeebbbdbdcdcaadadeaecacddabeabebedecbebcaadadaebdbcbbabdbcbaeeebbaecbbbeceacadddcaabeadeceabcbedadebbcedddbbabcdcaadedcecaccdcdcadabbceeaabecdebedddacbdcdecbadecdbdacbbaaeeaeaeaedeeddedbabdadbdbedcaceeceddeecbbdaddabcbedcaaaceabcabbbaeecddcabebdabbceaadeacacacabdecdbdaaadddcbdedecebedceddebedbcebabaaaddacaecbceadacebedbdaadacdbaecedbebaedcecdccaceaecacaeddabeaaaeeeeaebcbdceccaaccdddeabddedaebcdcebaedeedbacbeadbeddaaecbebdaadaabdaacccccbbaabaebcccacebbecdabaadcbbcebbcdebdedcdbaedbbcecacebceacbcddaeedeaabbeccdcbaaccdcbbedebcdabcbeaabccccedeaeceaeeabdebceacacaabedaeadecbccacdedaecccaeeaaacbdcaaccbcadeceabeeacabbadadbdccdbebcadedceaaaaccebccacdcabbcababadbbdebbcdaadedbaaaccdaadedbeaeabaaeaebcbdedccbeddcadcbedadbaedbaedcecaaedeaccbbbbebbdbdeddbedacabaddcbdccabebadeacbcaecccdbeceecdbcedcaebcadbbcddcbcbdeecaecedeeabbdbabdceccaaddebcdcdcbeeeebecaacbcaedebbdcbadebdedadaddddcabeacbdbecbcbdddbbccbbecaaacdeeaabaddaecedeedaeeeacaeeebabadbbeadebeddcebcbedbacedeaeeedadbeaebcdadcecbdadcdbbbbceddedcaacdbecdedecadbccbedaecacabaabdeeaacbaadcbaacbbacdabbcceacebcadabcabebceccadaecddedcaeeeeedaabbaaabddceeccaedbabebcdddacbabdceccccdbedbbdbdaccaacaabcebeaaadcbaebbdbccebdaaaabaadeeabedaedbdccdcdabceadaabbcbcecebaeabbecaeceaabeebcedebaddabeadbaadaaacdaeabacaedddebbdbbcdbecaeddccbabacddcdebebcbcaceeeacbeadbcdbebbdeddadaddbbebaccbccbaadcbacdebdebddeabccbbacbdedbedacecbedbdadaeacbcabdddacaccbabebaceccbddeeeedbecdacdceeaaacbbbababbabaadcbbddbeedbeeabcbddbcbacbbceeaadcdaedabeaaecdcdebacbbbcbcbadedabecdcdbceccadedddcbbdaaedeecdedacdceaadaecaeaccacebdaebdaaaaebcacaeababcbbdeaecadceeceabcecbabcedeccadaacdadcbadeedbaaddcedeabbbbccbaebdcbbdbdeebaaddaceaaacdadcddddbbaeaeedebcdaceaebdadcbbaadaccbbddaaeebeebdaccdbdebbedebcbeccdcacbacdcabecdebddeecdeeacddbadacbbadacbabbabbeadeebdbcaabaaceccaceebebbeebbbcdddaceddabceeaacaaceebddcbeeaadcbcecaadbaeceeadaeebbdbabddbddecdeababadcacdabeabbbeacbaccdcecdaddebcedcaddddeaaacebdccacacccaeeccbaeddeabedeaedadbbbcccabeabceedaabcccabdebdaabddcdaadeaceecaeeaebbeaeebbddbcbccecaebabbcbecbeabbceadcacebacbccbedeabdaaacecbddbcacaacdbadcabcbedddcceddbcbacebbdabdeddaaeceeabebbaebcbdaedcabdcabcabcceecbdabbcabdddbcdebedbbbadbbcdbdeaddbdeeebabebaddceebabbaceeaeecbabcbccdbebebccbcbbddbcedcaeeaccebedceceecadebadcdabcadabccbbccdadcccceddcdeddccaccdbbbadcdcdbbcdeceaecadbcbdcddbceabececcacceabcdabeaacabbbaaadaacccbdcebacdcecaceaeeecbcbddabaceabaedcbadbccaaebceacbcaaeebbddabbacdcccdcdcbacedeecaacceececcbadbcabcdabbaacdbccadeceadbbacecbbddbcbeddcacedcdcbcceacabdcaddedbaeeddeebebcecbcaeecedcdecbdcaadbdcabadebcecdbcdbcbaabebacccbcabcebcedbddccddddcceeadedbdeabaddcdbabddcdbebaaaacabdcedaedbdebbaebcddaaedbedaebbeddcacebaaeaecbbbeccccaebdadaaaebecdabaeceaedadcacaecedaedbaedcbbeceaebdcdcddcbecdeeceddeeebadbaacdbdbacebedcdebccddbdcceaacebdadedcabaeecdccbbaebbeeaeedadccdbeabbcaabdbadcabcdbcbebccaaccbaedadcdeacbbebaacccbedcaebeebebeaebcbcddebeaaccebeebdaccebdaeeddbcdeeebccdebbaabebeaebedcdaeececabadbddcecbcedcacbdaaaaddacbabaeaceacbdbebebceaacdbbcceeccacaddcdeebaaacbcecdbbadaadbaddbaeacdddbcaccabbacbbcbebcbbdcbaccdbaacbeadeadddadaecadaddabdadaaadbbcbbcbadaceeccbcaacceacdbdbebeebdcccebabacbeecdbebdedabaccedababccdebdcbcbbdedeaddebcbbddabbadbdaebcdbddcddbddbbbbdbaeaeccbadebeeabaecbdccaeabaceedbadaaaadcbbdaabacdeceddacdccaaddbdecbdebacbabedccbadbececbbdccdcaceacaeacabeecaddeacaeceadbebcbeedbcdeacacbcdacecdacedbdeceddcbebabdcecaaaaaddcceaaeecdbcecdaeacdbbecacaeaeceecdddeabacadbdecaebaeeeabeaceabbdeddeddbcaecbeeeabcbddaacdeecaeccaeadccadcdccbdebcaddeebcdaabbbedabbabaaeccdbeeccedbadcbbcaaeccebcaaccabcedebcdddbeceaccbaeecbaebebcddeeaecadadbdbbdaedeccadeedcbdeacdadedbaabccedddbccbdbebeccdbbabbedbeacebacbdecbebcdacaebcbddbecbeaeebddcbbacdcebedddcbaaadbbdcceeaeedcaccbbecddecbdeaadaacecbdbcacdebcaaccaebcbbcecaeaeacddacdbbdbbcebeceaceacacadbdedcdcecaadbbbedacaddcebdaebddcddbbdccbaecbacaacdccbaaaaaaeddeacccaeccdecbedcebebeeeadbcddeccdecbdacdbacecadaccedecececddabaeedbceabdeabeccecebddaecbacaaddaebeccbbbadbcbcdeccceccddaeddcaacbabdaedbdebedddddeaabddcadcacdaadecdbcedcdcdeccaaacceaebdbbdadddbbbcbecadaaddcdabdbcbdbeceabeadcacccedeabbedeeaabeccdaeaaaaaadbadaacdeaeeeabededadebbbbbcecdbbdbcbbddaadebaabaccbddaccdacbddbaebdadcdabcdedbaebacebaeabacdcddddbbbeccaabedcedaabebbebbaaccbdaedecdcbbdcaabddaeaabaabddcbccccdccdeabddedecddcaceceddecaaabdeaadeeadcaabdcdeebcdabcecaecbbdeebbdcddaadedaaaeceeaedcbbdccedccebbecbabcbbedaacadaeeabbacaeadaceebeeccababebdceccacdeddecbddbbedeccababdebbcaecadbbddacbbedcccbebdcdaddbdcccbbbbbeccbbecceaecadaeebbbddeaaabaeaecdacadbaadaceaeeebdabcaddabebddceddebeeeccaecbccbabdbacacdecaebcdbcdbccebaadbabcbeadabedaaaaacbdaadbaddcecceaeacbcbbbcecaebcedcedcccebecbaaebeccdbcbbbdddaceccdcabdacedeaaadcaeddddddeabedcdedbbdccecacddeebecebeeebceaadbdabceacdabadabdbaaececabababddadaabdedbdcbcdcdcabaecabdcdebcbeaebdcaeaaabdeaebeaabeccbdeddcdebbdcaddbadcaccabeaacadaddebdeaddcceedaedaadedacbcaeaeabeabdddddaaaeeaabbbddbcbadedcceeebbdcdbbbbecdbcbdddceeabbeacbccedcadbdedaebacacaaebbecaeeacbeccaeebbdcbacbcbeeccbbaaaaebeaebcbebddcbebdebccaaeabcddabaccdbaaaecbcaceeeadabedcbecdecdcaeaaaaedcacdecbbadedcbdaaccbeddbbcebbbdcaacdbeebadebdbecacdeacbedcbcadbebbdeeedaceadecacadebcbaeceddecbcbeabbebeacecdaccdbdbdbecbceeedcdcedcdedaeccadaeececaebdacaddbbaccbeaccbeacdcaaaadcacbdaabdcecccdbdbbcbaaddddbebacbbcbedcadadcdbaadccbacbdacddccedadaacedcccaeeadcabecdebedbbcceccaedbebacbeeaacebbcdbebacddaabbcadcabebcdbcddbdabaccdaeebbabddcbdcaabccbbaadeeaaaadaecbcbbccaeadcedceeacbbaeeacecbedecaabacebacbcbbaabdacedeeecdbcabbbbaabcaaedeaebcaaccaadececeedcecabaddbbbcadebdeadddabcceabedeceeeebaceccacbadaeacdeceddabedaaecddbbbdbcdeabcbceedccbceccecbecabedbcabbaedccabebecaeeceaabacbbbeedeebadaeebebacdcbbddddcddcadaeaedcdababdbcabaaabdaadabcecceaceaabcddbacadaadbbaacabebdcdddbeecedcbdddeaaebabeedaeacccebedebddecbbdddbcaebdacabedbaabbbcaccbaccacadebccabecbdbdecaaaacccddbdacddcadbcaccdceeabeeaaadacdbedecbeddebcbcaeeebbeedcdcecebabdceddebabccabbecaebdcaadcddcaedebaddacdabcddaeacebbacadeabccdedcbccaeacbaaaadeeedbcdcabdeadabadcceedaabecaabecbbdccbebbdbadcdaecaddcadacbdcdedbacaabecceeeeeccdaeedeeeaadabccbccaceddeeebceebbdcabaeadbdaeadeaccccedcbeecddcbdeaaeaedbacbdceebeecccdabeeadecaddcccacebdeedcedabbacadcacddbaddababaadabdaceeeadacbcbcadadbceaedadabccabcebdcbbccacacddebcdebabbddadddcccdedcdbcbcccbeeeebeeebdacdeceecaeaebecbdcedcceecbbaabccdebebeeeacddcbdabbedcaeebadadcbeaccdeacaecdeacececcaecbaebeeebccdceeabecdcadbceddacbccceaddaedeadeecacecaeccbdacbddeaaaadddedddcddddaeedcabadaebcebdecccddebabaeceebccbdaaceeccacbebcbbeaccadaedbdcbccccaedadabbdeabcbdecebcbbbbbeaeaaedecbbabaeedbbebbeadcaeedaebabebddeabdbeadaccdaededeecaedbbdacceceecddecbcbaaecaeaadeaccbedeadabdbdbbddaddecbcddeeccdebbcadcbbcdeeedadbeeebdddcbddcdccdbacdeeeacbceddbbbccacaceaddbaaddddcdcbbebcaabedcebbecdceabccaedbbeddcaaddeedabcbcaaaabdbedbaecdbebbceeaacebbccbbddcbbdcabbbbedbeccbdceadacabdcadddcadaedbaaadcdececabcdbaacedcbbdbecadcbebbbecddddedcddbadddbbaddeeaacdebebcecacdeceabeccceabeeddebdaeeedbcbceebeeddcbcccbbbcbaeebdcbcabdeeaaaaddececeaddbcaaeddbdeaebddceeedceddbbceccbeaeecaaeecdebddcabedeecbaeacbbbdadcaabcdeeccebabaeddcecabedadccceadeeaacabacaacaebdbcbaebeccedddabbdbdacddebbabecedacdaecdbbcdcecbedcdaebadeeaecdacaeeceddbbcbaceaecbebabecbeabaddeaedaecccecbbcbeedeabcececbedebbbbadeedbedebeadddbebddceabbbbcaabbacbbdbeddabdaaaecebbedcebaeabddcabaaeabadcaabbbeababebbaabbaabdcdacbeedaabbeedacecdedccbdaedbdedacbebebbabadceeaacdbeacedeaedbecdbdaaadebdcccccbeadcddeedddedababecdccdedbaebeeaaceabccebadbbdcdaabcbbdaaccbcbccddccdabaabddcdebeaaaeacadeedaddaabbdddcaeeacabebbaeaaddedbbdcdbeedceacebaddceccdaaceebdbacdecdebbbcaccadbacddebdecbddaadcbcbceabbcaacaaadbaccbacdbddbeededbebaabcacceeebbbbaaaeccbaabbcedbeaecabceddeecaecbebecdeecadcecceacdccbbbeccccedeedbadeddcedbaabcdedecaacedeabdacbebebcedcedacddcdbbedbaeaeacbebdedbdceeabecbbcdbeedadeaaebceaacedcddcdcadaeeddcdaceabaadcedbbdbbdebeaebabcdbaaaceaeecbeedaabbaeabcdcaaacdcecabedaaebddbdbadeeacdebcddaeedcddcdadebbcebcebdbcbceeacedcdebbaaeecabbeebdeebacbcbdbcceecedacaaaeeddbcabbeedacedccbbaeaeeedccedeeccdadacdbabdebbcecaaaeadddbdcdcceedbbceaabcabeadbddeadbcaedcabdbcecdbbeabdcbbaaeddddcebadaaebeabebdacaabadcaeddeabbeacaccaacddaebacbbeccadbdeaceeecbaceddebdaaaaddaaedbeabedbcbbedeeebbdacbbcedeecbeacdbbeedceabceeebaaaacccceedbaddabceeddebecadaaabdaecdacbecbcebbccaddcdcacedbbaccaabaeaadcdcceeebcdacccbbbeacdcbecaecebdbeeebedbbaaabdaacebaaacdebdececdedceacaedebccaeaebbddaeabceebbdaabeededcadbcbdcbdeacaededbbcdacaceceecadcbebbddaaadabceacdcbeaaadeddaebddcaaeeccabdcadbeaadeebbcaddcebecebeebbddcbceebdeaceeedcdddbbbbeabdedadcebdadceebecebdaaedccccadaeaadddcbdceadcacdbceceaebccaaabeecbaedeaacecdeeeecdebbcdacbeecddcdbecacdddaebeaeaaeeebdbbebdacbbbedbcdcaeabdcdeccadccbaaeaedbbbaebccdebdedcdbebdcbcbcdcabedecabaccbcceabacebdedcaedcabeecbccedadeacbddccdaedbdbcedcadcccaaebaeddeddaaecdaadcedcbedeedeaecacbcbdcbabdcdbdedeeeaaadaacdceeacebbabccdacdabaaaeebcedddbecceddabeddaaadebbeaacdadbcababccaeddccdbabbabcabcebbbaacedbcedddbdeeeabaccbcadbccaabbecbadcacabbaedbedebbebbebdbdcbddbadacdcedaabbeaecddadebbbbdbccabdccdadceaeeaaeaeadecbabbaadcceeceebbdcdbbbaaededbddeadbebeaccbddbabbcacebacceeacddcdeebeddaabcaedcadeacebcadabbacccedaedcaebbbaebecdcdadbedccbeadacacabdacaeeacaedcbbeebdadadbdeacecdabccabcccccdacddacceacbcbeaccdacddaadcbdccbdbbaddabccabdeadedeecdeebeaabedeeebeebecdaccbadbbdebbabacbbaacbacaeeadeecedcaedabdabbdaccdecebeddadeaadccbcdcaddddaedacdaaecaeabcaccabdddddcbcbcbabbdaadcedbedabeaddceaaceaaaeaedccadaaebdaaabdaadbeebbbdaddcdedcbddddcbecaddbdbeacdeaeaebbaacaadabdbcaecdbcbaabeeedecbcabcdcdededebcbdeeddddbeaaedadeebabbabaebeedeaacabbbceebbddaccecbdabbababcddabdabedaadcedbcdaeeeabaddebaeabddaacbeccdcbaedcbdcabcbbcbddcadebecaecdbbaaaecddbccadcdeadabbbddbddeccbdbeedacdbbebcdeddeddeaaededededaebcaabeaebaadccbdbcdeebddbddacaadeddecdccbdcccdecadcbaebedbbdccedaccbddeabaecbceaedabeccbadcccdcaddadbddbddbececddaccdddceeaceeebedcaddbdcedcedcedbbaeaccebaaddddaaadbccabdcdcbddeadcecaaedcbbbedbdbedbebeeddecceddbedbccceecacbbbddbcabcbebdcbbebebbcecbdebcbeddededbcbbccbaaecabaeeecdadeecacccccdacecbcadbaaccecddadaddccbdadceceaebeedacdacbaabeebbdaecaebacbdcdebaaabbdaededebaaeccbeceeceddaeedaaceddacceccbbabaabdcaecbacbbdcbacbbcebcbcaacebbadcebcddbeadededcdbacabbedbaaeabdabbdbbbbabbddecaeceaacdcdddabcceebeddcaddbadaceeddeecabeeadecaacabbcdbaabeaddecbcdcabbdcdaeeeaadbceabcbdeceddddbabbaeeaccdadeddaabcdaccdcbcecceabaeddebceabacbedabcacaecbcbddbceabeeabcdadaeeadcebdcaeacaaadaaecdaaddabecdbecceecdcebdbacaeeeccdcbbcaacebddeeabcaeaccbbdcaebcedaadeabecbacddbeddedebedeeecacabeacdbedbdbadeececbebbdcbbbcecdbcbcbedecaedbccaaddacddecdcceedaaadddddcdebeaecacedbdbcddbabceebceceeccdedaabbecabdbbeeabcaaaaddeccaebccbabcbdaeeceeacbaaddbebcbdaabcddedeabdcecbeebbadbacabdaaccdddaddabacceebcdaacecabdeaedbbebadacbcdebeceececeeeddacaadcedadbeddeaecaeeceabeebbdebdbacdadaddbcaeeddbdbbeeaaebaaedbbcddceaeaabadeedbcacccbbaeabbaaddddaedadaeeddaebbbadcacddcedacdcaecdddccedeededaeacbebecbaeccdddeaaebbadaeeceaaddbcecbbeddcddddbadddbebaaeecccdedcdcdbeabbebdbbeadbdaabdbddbcaacedcebbabcbdbbaaaecccbdecebdcdacbbaaaceedcecdbdcbcbbedeecedbaebdcadbaeabababccbbabbcdbcedcbdcdeadacebdeacddedddcecdedbcebceecaaeededdcbbcbdbceddcbddbbacccdccaeebdabeedabcaeabeabbeeaebebcbeaeaadcdbcdbeeaebbdbbcbcabdbaebebeeaedbccedbdeeddcecedaeadabdbbdebeecddbabedbadddeaccebddacbdcaeccdededdeddbcdbdecaaaeeadcccbedbcbcceacddeceadacbcbbecdeaddbbaddbaceadddbbaccebeecdbeaddbdccdeecbacbccbabbbcadedababecbcdebacbbdaabcaaabadeeddacdcaaeaaedbaecaeebecebbaeccbedeadceaabadbebaaebcbdbcdebdcdecabcebbccecedadccabcadedcaadbaeaaeeceabcbcddcacedbbcbaecebcdacdbcacbbeabaacabcbccccdceedacaebabcbccaecdbacdbeceeeacbceacaedbdadbbaebbacdbadaccaaeebbbceadabcddadacdcdeeebbbabeecbbbddcebdcbaaabccdbebacbbdeacadeadeeaeeebaeeeecbadaabcbbbcecabceaceccdedaabaddbbcbbbcbbaeebdeeeeebbceaddeddceadaaddaccadcebbcebccdebdadeceadabbdeadeedaaabedaabedaddedadaeeecdbbbbeccecbcaccebbabdacbbcbedbbeabacbcddbadabeaedbbacecbededbbadccbbcdcddbcbadeaacaccddcdceebbbadcdbbacdceecceacedcccbddddbacdeadcadcddecbbcdcccdcaceaaeabedbdecaeedbabaeeaeaeedeceadedeebacdaebeaababdcbbddacdbebbecceedbbbcabdbeadabbeedaccecdeecccacaeeeccbbcccdbcadeedceabaaccbccecadbbaebcddecbbdddeaceecbbddccbcaebbdabdbbaacdeccdceecdedddecbaadbebbdccbdcedccaabbbcebcbbdddaababbcacebbbbecadcbbbadcceecccbccbdcbcabeceaeacbecbdacaccccdddaaebddcbcdcdccdedbaaeaccaeacddceebecbcecebbcaaccdadeadebaadaccaeddeaacdaedbdabcbdcbeeacaedceecbdebddaabdadcceeeaeaacbcdbabeeecbeceebccaacbabdbcecaceabadbcaaabcacdbadceddabecececebeaddeddcceadceaabdaeedddcbbeccbdecaeacbebdccbdeaddcbebedeaabbcaabedecdeacaadbcaeaaebbcdcdadbbbeabbaebcbaeacddbeceeedebcedaaaccdbcdecaddbdbeabdccbeabadbecacaaebdbebacecdadcdaccdebecbdbbedabdcbaaecabeedcaedeeecbbdbbebcbcabcecadcbebceeecabeacabeceeaddbdadbeaacdabacdcbddceabdadacbbeeadadaccadbcbabcacaceedebddebeaecdeecedccaecdedebbaecacadbaeeaeaaaccaddacaedadaadcaceedbdeabbeaddddbcebbeabeecbdbaecaddebcaaaecebceccdcebebdaebbebbacadceeddccebeeeaeaecaadaadcdeaeebcdeaadebaaecadeceddeecbbcaacbcdbdddecdccbdeaecaeceaacecbdbbdbeacccabdbbeeacaadecdcdcbadcddbdeabdecbabedcdedaebeabebdddbbdacaeccdbeabccedceacbbbababdaddbceedebeaeeeccebceecbaaecbeddeaddaccedcbaccceaebdedcbcdecbbedaebeeeeabbaebdceceabaeedacbdabacceeeececcbdbadeccdabeaeeeadaeadeacccedeeccadcaecacbeddbbacecbecceccecacabaaedbaddbdcdaecbcddebabecabecdecdeaadccaababbbdecdbecccdeadaddecabdbaeabbaeaeebecedbbccaacbaaacdaadeccdedbecceacaebdbeeaaaaddcebdeedbbabebbbecbbcebbdadaecdedbbcddaccdecabeccbbbceadddcacaaedecacedeeeccecabdabebdceceaaecacbbcdbceddedeabccdeeabbbecbbdedcbdbbbbecdadddcdecbcaddababbdaadacddcccebcdecbbedbdbaabcddedeceacebbeacdcbadaccbaeeddddabbeccddecceecdbaacaedebbddcacdaebcbbdcbadbdecdedbabccbadcaacdbabdacebadabcbcbaacdbcbebeeeecaedccadeceeaeaaeebcbcbedadceacbdbbcdeedecdaadbaaecabcdaddcecedcbedbeaaceeecabdeecaceecebccebacdcbbaedaebaeccbdcdadbaaabddbedabeeabeabbbbbcedaaebdcddebadecbdcdebaebdecadeeeacedbcbdecccbeebadcbdceddecacdcbcecabbcbdedadbbbaabdeccadeddbeddbadccecedebdbbcdcdddecbbbebacdaeecddecebcbbbceaecbbcbdabdcebddeadbedbbbdcaddccbdcdcabdbdeeabdddbdbddcbcbaaaeebabddabeceadcbebadddcdeedacbaccdcbddaeeaeebbacadbdeaacecacbbcdeacbcdcbaeaabcaceddacecaabebadeaebdccdbbaedceebbddbacdddcddacaeebbbaccdddcecddacadebadccabcddbcdddddbeabbbbccaacdadaaaeadebeacdbedecbbcaaeeadcdaddeaccbdcdaeaaadaccbdabaabbbedaaedcbdaaadaacaabdaeaacceddeeeddcdadacdcaabedbadddaabeebcebddeaababdcebeabeecbdddaadadeedcbdeccdccabdeaaacbcabbcccbecceaeacaccabeaddcadcbccdeacccbeaabbadacaaacdbbcadacccadeaababaeebaeebccebebeeebacabacebcadbddccdbbceaacbebeaaabebbddeacceacdcacbddadbebaeadaaaabdaeeeedbbaacbdeaeacecdeabcccaddbbdaabbdeadbedceaebceeaecaccdacaadecbdcadddccbcacbabedcbeeacacaaceadcacdcbbcceddeedccecdbbcccddaaabdcdaebccaadddaadcabbeabecccacaeaaccaadbccedeaceeedcdbacaaabddbadbadbbebedaadcdeddecdbaebdabcbdbbbadebcabdaebeddbcabcdeddcedcbbadcebbebbdeabecbbecdbbbaabeeddeeacededbcbddebecbcaabbecaedbbeabcbcbddbdeaaaeebecbaadbdadcceececaddcbcbcacebdaacedeaedbcbaaaeadcdacecacbccbbcaedcedddecbbbceacabeacdddcdeadebadccdbdddbbbbdbbacbecaeadeadbbdeabddccedaacdeedeebbbabadcecbbdedeaadadbaacbcbccddbaababecadeccacdbbaebaaaeddeaccdccdadedceacadaeeeacbabebbdceabaebbcbceeedcbbbdceaceeadddeebcdbceebdecedebdcdebdaacdcecacceadadabdacbdcccbdaadbbebacdeeeedaacdebccaacddddccdaacbaeaadeceedbbaceecdeacddebbdadaabbcdeebcbcaceddbebbbaabaadbeeabaaabbcdbabdaaacdabbbdedececdbcaaabedaeeaddedbccbbbbdedeccdedcddaddcdddebbdabddccbccbabccabdadbbaabddaebeaeabdaebcbdcabcceaebdbbddbdeadabedcbbbbbbbdbcbabbebdedadeaaabdabbddbedabdeddcadbeacdbaeaeaadebabccaedacbacaddaebdbeccccbbcdbccbdeecdabbeacdddceedacdabdaddaebbcadadbedadcebeaadbcbcdecdaabaeaabeddbdeaeabacdabbdbdcbeabdecaeadeaebbddaeaecdcabdaadbebadadeccbcceaabdaebbbeaadcddbcddaedacccbbcbbeabacebedddcbddcabbecaeddbbbccdaebbedbcacdcddaecddeeccbaebecaaebdceacaabacbbababccbadbecbcbbcbeebbeebccaeebcdccaedadbeddaaceeacebbcaaeedcdceebdcdcabadcccbedabaeecddcaebcaddaadbaccbacaabadcbdcdcbecadebcdedeebebbcdacdcadaaaadddeeadeedbadcabdeadbdadcdbbaadceaaccbaecedabcddadaeeeceadbdcccebaaaaeeeededeaeddcdcdecacaeceeeccedcdcabdecdedccedbaabeadceebbeebbaccaaacaaaeeaeadeccbdcacdecdadbabcabebedacbadacecacaabecdeadecbddcccedbddbdcbececdcebbcdbbccbcacdbdbedcedbabbbbdababaeeebaedbdcbcdccbbbbbbacaeceacbcedcdaaecccddeccbbcbaaceedbaccccdbabcaccecabceeaabdcdaabedebedacaebbbdbecbbdbbddddcccaddcbedabeccbeecddacadaaacbedbddeacbecababaddaecacdabccbbabecedeaabdaacbdcdddaeabbeaadedaaabadbaebeeaadecdecdaaedbeddbacaeaddbbebccbeeabcedeaebcecbbabedcccbbbeebdceedbbbcbbadeeedcacabcbaeadebbcbdbbcaadbbcbadabebecacabeceeaaebdbadadcecdebadbcaaaabcaadaedcbeccbbacceceebeeadcceabddeedeeaeebccdcbcaadecaecbabcceeabaaeaeaecbcccdeebcadccbbaaebdabdaccbbeccbbddbdceddcdedbeabcceedaebacbedbcabcdadccaaadeeababdbeecbbdabbabbacbebaaeeeeddaacacbbbcecedbebecddbdecadecadabcbceeeedadeccdcbaedecbbaacdeebadebedbaeedeaccbeeeeceddacaeaacbcdcbebaddccaeeecbeceaabacbcaceaedcecdeecdabeaabeaaacaaddbcbbdedcbdeaebededabadaecbdaaaadebeaadccbbabcbbedacdccdbbcebeacaccbaddeeaddaddbcceedbbbedebdddcdcacdedcedcccccabccaaebacbcbdcedeaccbcbacedceebbbccabaadeddcecdbacdebbebddbeecaaaddeddbbcaaebaeaaaacdacaeeaeaaeacebcecccdadecabbcbbacacaccabcceedeeaadaaddeccbbbdcdacdcecacaebaacbaaebcacdeebdcadbeeaadecbcdabbcaeadeeccacdedbdbbaddceebdcabcdcbeadbaceacadeadddccbbacaacebbbeadeabaebcccdabbcecaadeeabbacddadeeacddbecbdcdccddbeeebaceeceaacccacececcaccddeebacbebeacbbceaceabcdeeaedbdbeebdabebaeebecdadccdddebaaaebacdecbabeedaadabbcbcaedaaeaddedbddaabdccecdaeeecacadcadcaddacebeaecaaacddaeecaeaebbdddbddeeebcbecbecbeeacabcaaabeaabbecbdbdacedaeeadaedddbaabaecbaadebdbedbbcebacebcbcaaaaceeabdbcceeebecbdbeaacdabeabebbecbbceeddbedceecbaddbeebcaabcbbadeecbeacadebdeedbadbecaadbddebeddbecadcdbcecedeeeaedcbeabccacceeddcecbecddecdedddcdaccaccaebccecabaeeeceeaecdabbcccaeadeaeccbddbcdebcbbbecbadaaceeceabebaedeaebeababeedbebcbdcaecdabcddbacecbdeeebaadddeacaecebabdadbbcdeadacedbabaaabccccddbbceeeeabdbdddcaecadabbadadcbdadbacdeabbeabaabaeecedccbedcdddcaccbdeeadebcecacaabbbdceebbdcdaeadaabadadeeedcbddcaaacbadecdcecdbacbececebdcbdebceeececabaddadeadceabbcabdbbdddddbabeabedbbbddccaaeadceeadaeddabeadceddebcdaddaeceaecebecedcaceeddadbcdececdcadddadcacdbdbcebddbccccacdacaeaebacabbabeccbbcdaaeebbccdcbcbdcacaecdabaedecedbeabecbcdbaacdececaeeaaaeddcebaddceedcbbedcdbaaaeeadecaacbcdeacddedddbaecaabedacdcebbaceedadaaadaaebbbbcceecdbcbabeaccedeedadebdacddbdbbdddebebccecdccddbbedacdcebbbedeecddacacabaacbeadbcebcacddddcdaccdcbcaeaeaeebdbcbeadabdabcabddcecdbbbdaecaecbdaeccbbcdecdebadaadbceecbceaececcaedbadacbbbdaeeebcaababcaebadedccadddcddeadeecddeaeddadbeeeaecabebcbddbaeebbaeedadcbedeedbeaabbbaaaeeeddcdededddaecbdccdabbabbbdebcdedddedaadadcdbeceadaceecdadaaddabeaccbbddaebadeaaeecaecebbbcebeaecbbddacddebecaecbaaeeccedddaeaabcdadccbbccdaaeebeeabcaceeabaaccbccaeedecbdedeacaceeecabccadcceccbcdddecdeeecaabbbaeeececadabddbdaededbeaedecdadebdbdbbaebaeacbeceabbdcbecedaddeabbabeebeddbaabacbcabadadbcdbbdecbdcbcbceaaebbebecddceadcadecbbedbcbdceceabbdaaaaccadbdcaeedecdceacbcdccdbccdceceeeabababcaebebdbdcabeadccadbaaebecdbbdaaacebdedcedbbebeeeecaeceddecccabccddccaebcdcabdeeeeaccddbedebbadbbdaacdbdceacdbabbaaebaedddceabbecbbaaeaabbaaaeeaebeedbddacacbecbbcabdcdaeeceebcbadabdebedeeabeebcaeeaacaaabcbadcdbdbaacbecbdcacbaabbdedadcbeabcabdaebeedebbdcbbbeaeabccbbcbdbedddecbebbaccddedcebedbbcdeedaeaeecaecbdcdabbadddadbccaccbababbeadbdcadbdabcabbdeeeaadcdaadbbdcdcbacbbcdbbeebddbeedbccebdadaaaddecbdedadbdabeaebeaecabddbcabaaddeedeebeecedcecebdebbbdaebbabdedececcaaeeddaddedaabbcebcbcdeebaccbdbbcdeddaacebbaecadbadcbabceececedecceddaceccdebdeabecceaebdccacadedecebdeabeadabaaacacddbdaebbbbbceabacbbabaaceddecebdadccbecedddaecaccaaaeaaacbbeaabdccceeabdebbddecababbaeceaabaeabcadceeaeeeddaebaedbcabebbeacceeeecdceadcdaddbadaecbacbaddbcecbdddcbeacbaddbcaeacbaabcbdabbbcbaaecebdeabcacdcdeadbdddcceebcbeebcddacecdbddcddadeaaceeceabaaecddcebcdcedadbcdcbeceaebccadebabecceadabcdaabbebddeabdcbddacdaeddceecababdedcbdecceacdedbecbddebaaabbacaacecdabbbeaaeddcaceadedadaebeaabeedbaeddbdeebaeadbecceaacddcdcbcdcdaecdbecbbdacbceadbbcdeebdcdaeeabdcbebceeeacabdadbaaaaaecbabadaedddcbcdceaccbdcdbbdcbeacbdcaececabeaadaeaaedbbabbabaaedaaecbcabccebedddedcebdbcddddcbaeaacbcdadbaeedbdeddbeecaeabcaeaadbaabbcbecaeaacdaacdacdabbebaddedadbbccecacebceeedaececbbdcaeddadacacbedcaeaccbeebaaacbbbebaccaacdcddcdecdcabcddadeaceddccecdadecbcccdaeacbdaaaaebabadbbcacbaccbeabecbaddbbeeaaedaeddbcbebccebceeebeedadcdbabacccdccccbbbcceaeacadcecadbbbdcacdabebcbcadcedbaadeceddcebcdeccabddaabeececebcdbbbcbacbcadccecabebebedcaddddcdacccceceddcbabacaaabccaecaaeabceacebbbadbccbdecdeeebcdecaeaaecebcbbabdedbbaeaaeaedcbaccaaaecdaebdcccdccbeacbbedbbeeaecbedacbaedbbcdccbdacbcccdddbaaedbdeeeddccaddedcdcdebdcabecabeddbedcdaeaeaeeeebcaeaabcdecbaedeadaebaedcbccecebccebbabcacbacbbaabeeecbcaecdadbacbcecabeccaaecabeceeacbdadaacebcdaadbebcbbecbaaeaadcddbbbcdbebddadbabedcaddedeecbcbdebbeddcccababdeaccbbbcccbeebceccceacadeccabcdaaeadceadccecdedbacbeacedcbdbdbdedbcacccedccbcbabccdeddaaceadeaddbedaaeebbadcacdbecdddacbadeacdddceeddabecadccdbbbdddcaabcacaccbabbaabdddbbdbdedadcbbeaebaecccbccbbdebcceceabcbccdcbcbeaaacebbbceadbbaebbaeeadcbdedbbecbbdadaaaabdccadcdadcedddddbaeedbbaededdccadeabddcccbbbbabcedacabdaebcedbdcacadceeaecdadbbadaabdbaabcbcbaccadbcddeedadacbccccabdcccbbaebcedcebebaacecdaebdcccecdedecddddceebdcdcebbcdbaaacbcaebabebbeeaeaecdccccbecedabeababececbadbeaaedaadbcbebabcdabddbecebdcacbadaaebddccaebcbcebedebbdaababadeeadcaeadbebddbbdcceecbedbacadcdbdbdbacdccaeaabaadecdcbbabeedcecdddeeadcdadaaedbaeccabaeecaebdbccdabeeaddedddeaccddabcececdeeaabedadecbbbcadbaddeedbaacedccccbeedecdecbaedbddbcbababccdeebdaeaccbedbaaeeaabceecaadcadeeacebcbeeadcaeaedeebabbbcdedeeadcdabacceecebacccbeadcdeededacaddaacbedbecdcdeebbceccacdecadbacbdbadabacbbaecabcaaedbbccddecedacdadececdacbedcdaeebbdecbecddbdeadbaabbdaeedaeccbecdcadbbeaacccabccdaeacaadceabdaeacbbbeacabbbedbdcbcdbdbedbbadbbbbebaddabbdcbacaeccacddcadacaebbbddbcacdeeebccddcbaedccadcbeecaeeaccaeeeeecdaeecccceabbdabdbbddbecbcceccbecabcdbbaeccdabcaadaccecedebbacabccceedcbbecbddadebbcadcededecdbcabbcddaacecbbeaceacbadbbdeecbaceedabbeeedcbdaddabcbceadcbddcecdbeaacbebaedddcdeeeaacdececedeccccaaeeacdedcddebdaaeccdcccdceaadeeeecbebedcedaabaaadcaedeabddbdbebcbeababaacbcdceabcdaeabcebabdeccaceededacacdaecaeedaddbdacbbbaabeccaecbdeecaeccddcdcdceacabbbdcbcdcaebadddacaaaedaaaddbdcadcdaaeedacaccaadccbaacbedaeacddcddbddeebbdccaddcdaedccaaaeccabebdbceccbdccdaeacccbeaabdceacacbdaadbdaccaebaebecdcabeabbbeaedaebbbcceecbdbecdedbeabadeebeeeaeaeebceabbeceeacdabeebbcabbcbccbbacdeebdacccebacdbccbdceccdbdbdbedaccaddcdeddeaecadacaccbbccbecaecbabbedabddabcbeececdeaeddccddcdbeecedbbabeabbaebdcbdddeebdacbddeeedebdebbddcaaededeabccacabcecbebccdccdecbccbbeddeecebaeabddcbdebcdebacaeebedeeddaeebaababaddbddcaedaabcaecacebececdddedddcacaccccebcaebbcdaaebceacadacdabdddbbcbabcddcebeaceeebebbabcacbbaaeddedcdeacbaddbaacacbdddeacdedbccebdebcddbbddbdaebebcadddaeaecedbabdebdcbdbcbeeaaaecedebaacaeecbaaacbdadbddcdabceabbbaacbeeceacedcddbdcdadaeabbaeaaeddeaadcebdbddbdbecbbaccdadacdacadbeecdcebedaacacbbaeddadabcabbedcdeaebaacdbaabbcebbecaddcdabbebdedeccbbcbbdcbbaceccaeeaaedeedacbbbabcecbeaedabbdaadebacbbeddcedcebeebceabaaeadbbeeecadbcaeadeeccaacbceebadacedeebaceecadebbadabaaadaadaacaebbbcabeaabbcbabcaccbacaeabaaddbaceebacedebcdbddedbbbcdcedbaecdcbeabdabeeceeacbbbcbacaccdeaeaabdceaccaccceeaeeeddbbbdbeddcebdebddcbeabdbadeecdebdabdbaddabccdbcbdacaeabedbcbbbddbacbdbddcdcadcdccecdcedaecbaadbbbdaabeeaeacadbcebacebcbcbccebbaaabccacebcbedaaccaceccabeecddeacbebdabecbeaddddcebccdaeaababeabbecbbccbeeeaeeaacbebcaaadddccaabbbbbbeaaadcbeaaddadadebdebdecbcaadedcebeeccdadeecacbaeabbdaabceadabaaeadcaccccadbbabecabcaeddebabbeaeeceedcaeccccdabddeceaccdedecceeaeeecceaaacabcdbcadecadaebadbdeeddbbdbecadeddeaedeccdccbbadcdedadddaacccbdabaaccedbebcaeceaaadbbaeccbaabcbbcbedcaddebdbccaeeebecbdcdebbccdbaebbdeabddaedcaabaccacdccedcabcabbeccebaecccbbcdbccbcaedaaceaeebdcbbcceabdcaecedadcdaeacdaaecaaaaceabbacdbcdabcccdccbeeececceaabaabaaddbdcbecacababadaedaabaaaddcccbbbbcddabecacececaddccccacceceebaebaebcacacabdabaaeababaddcabebebdcebebaaaababebcbcbccaeddbdabacdaaaceacacaecdecabeedebdeaedcbcaedcbeedcddcbebaaaaddbebdeacbbcdcbdceaedbeeeedcdaaaccebeebbdbcdbacceecebbeeebedbdacdebeeecdbcdbebddebedcdccabbaddbbceacbbaacaaaaddcadebcecccddadbbebbbdcccdeeecebcdcadcceddcaeacbbeeeccbabdeaadbcebdcdacacacbbbedbbebcdddeaebacdceacdeeeeccecaebceeceecbdbddbcaeaedbdbccabbacabebeeccbbdbeaceadacbeddcbacbbcbebebedaacbcaeadacdbeadeedeadbcdaaaebbecbeddebceeaacceadaaeeccabbecaadccdceedcbdbcdaccbddecdbaeaeecacbaabcbcecbabedeccabddabeadcccabdccdacadeeddbcedeeadccaccaacabecabccbadceadececaccccacccaccddaecacbedaeacbdaaecaedaccbeddbbcadbeacbebabaebbceaebbadeacaaddbceaebabbdbbebbacdeecaaceeccdcebcceebaaeceaecbcdbbbebdaecdbcbacecaecceeddceaddaacdbbecbcdddeeecbebdbbebaeeaeeeaaeeeebdbddbacbeebecbbcaadcdeabdbcbbccadbeedccedecdccbebcaaaccaeedadeebdaecddcbadebbcdddcbdedddeaaaeedabbaceabaecebedeaaacbdceabecebdcdbcddcbeaaaceaaecaedddadebcbcedbccaecaccbaaaeebecbaaeeddeeebabeadadebdcedcdbecdbbaececbbebddbadecaaebeecdedddeaccbcabebbdcbabdbbbecdbaacccdeaededbbddebaeddcabaaccaecdbcdecceeddddcdbaeabebaedcbcaaddbdecdeedceaaeabbcddbbbcabbcbeccbaaaeadedecedddaccaddbeebeeaabcdacddacedacddaddedbbbceedbeadbebeccaeabaddeebeabeeeaaaeddbebcdcbbdbaecdcdedbacbcaebebdabecbdbbccadbdaecdcdbabbcadaddcddbcbacaddaeaddbdebabcdbedeedddddcbbbeadaedcdabdceeecbbeacceedddaedbbdaeaddbbaedebbbddecacbbaadbecbcdabdcbabeeebeacdbbdaccabaacddabcebddcaeaeadbabdcebbaccaebcedcabaedddaebdbadeaadcaaeabbcdbeeceeeabcbddcedeaabdbbdddbdeaaadeddbedeccbdecaaaaadbbeaacdabccdcaccadacbaeadbbecbcbaeacaebbeeaddddcaeddecbebeaccacceabdeacebdaeacdaabeeedecdecbecebbecdecbdeecedecabeaacbbcaddddbabaaacdcbeddbbeccedabdcbaebebdcdbabcadebdbccbccaabcaebeaaaddbdaaacddcebecdcbddcbdeebeaeadaadcdbacaacddaebcdddeaeeeccebecdabdcbdecbcdacedecdbeaeeaacbabbbcdaaadbeecebceacbddacbadabdcddcabcddeaabebdecebcdbadeedbecacbceabbaeabdadbaecabaabeaebecadceedeaeebcccaecdcacbcedaddadcededcdbbbbbdeacdcacebccbdecdeeadcacdecbcadacceddeaecdccbbeacadeacaaadbadddcabeeddebaeadeceeabdbdbcaebdacaddeebccbddebbacdeedebcabcdbbeddabecaeabbbadcbcecaabbeddaabceaeecbdacaddcccbcacbccdcdaadaedeccecddacaabdddabebcbccbebedbacbbbabedbbbebeaceabbeeddeebbdaaacadcabeedebcddabdabdeeededebbbeacaaccebdccaabeacbeaacadceceeeddbdcebacccabbeebadeedadbddbdbabaddaceabddcdcbdcaedcbdbbaabeaaeaeeebeccaceeeebaceaacadccbabaccaedbdbbcddcdebaabaddcdcbebaadbdbacaecdeeaaeeddededaaebeebbbbdcbdadadcaccddbcaeeecdbaedaecaebddebbebeacbdeeabeecdddcccabcbeaecbbbebebdeedcaaabdabbdaaaeebaacececdbdbdbecdecabdceacdecbceeedbbdbbcccaacacdbaadbbaecaacbdcdbcbcceeebbcaedbceaacebbabcbeddacdcaeaeecacdeceecaadddeceabaceabeacedadceaabeecbccebaddcdedeeedbeccadbdbebcdebdbdaeeddaaeedceabacaddeebaebeaeaaabceddaeeedccaecaeddeccaddcbaadeaeebcedcabbaccbbadcdbacbadeedaececeaacbddaceecabbcdbcccaadddcdddecaecabbbeecdeaddedeecbcddcdbeaaeecedaabbdbbabcacbbbedadbbdcbacdbbbbcdccdbbbaebcbeedcebaeccccdebeabaebecaebaeabaeecebbecdedeeeedadccedcbaeeaacadaeaddbbecdaebbccceeedababcdebbbacdadbcbaacedbecdddcdcaccddbceaaedcaacaeeacaecbbccecacbbddbdbbcacccdccbdbcbebcccedcceeacacbddeddceabaeebeeebcbdcaabdddecaaccacbcdddcaeaeebedceadedaecaeeeaacccccddbbaebdaeddaceebddadcaeceabedcbeadceaaecbcebbaeacddcbdabddbabdddeeaccabdcadadbdaecceddedaeaacaeebabbceebebcadcbccedacbdbbbbebccecaaeeadadacbacedcdecdecceebeeaeadeaccbaeecaedcaecaacaebadbeaaebcaeaeeeabacdccdccdabecbdbdacbbdadbedbceebddeaeccecaedebeddacdcbccacccccdbacababededdbbabbcccebbeaabaabdabdddcaeceaecaabcaecaecadeacdbaacceabdbdcecabeedcadcacabeaaddaceabecaadbcadcddbecabaacecdcedbeaadbaeaacccdadcdbaaeeddcbecddecdbbeedcedcebcaaecacbbdbbdaceeaadababcbedddaeaeebcadedbeacacdcccbcacabbdacadeeaadbbcadbccdaddbcbcdaaeeecdcdbbcbbadeccbddecceeecacdadaaeabcbdddccdbaaeaabacedaeadcbeaebceaabbaccbbcdbbecdbabeecdeceedccbecaceecdaabeaeddabeddabaeebaeebdcaabebaebcbddbaededbccdccaebbccedecdeebbbeeaaacecddacebabbbdcbdededecacbbdabedabcaeeeabeacebeeeccababaeeabcccedadaccaceaebdbdeaddabdbbdbdbaaadecebbbecbabddabdddaeacbaacdbedbaebcecbcaabcdebcaabeddbbdbeecdcdbeeeaecbdaadaebbebadbaadeeeacdcbcedddcccacedaccbdbeecadcdabecaabbdaceddebddbebcdddaaabaddbaedabcadaedeabaccbceadbecacbccbdedabcdbbceededdaadadcdccddedecdcbecebedbcbdcacadececbedadebbddbececbdedccccdaabeadbbbdbcbebdbaddeebccddcddceabeedceceedabeaecbbcdcdedbbdccddeadcaabdbbbabdebbcdccdacbadcaabdddcbaeebabdaabebebcbdeeaeaabacacaabcbbceadbeeaddcacbebbeeadadbdaadabbdababeecedeaaccacccbccecccbdaccbebaaaaebeeeceddceddbdcaddebcdebbcedecaabbecacacaebedcedcdabadcedadebcecadbcdabeaddceecdaacdceaadeeaecccdcaabecccecadeecdecaceabddaccadabcaaaebddebdedaceecabeddcddbaadceddbebceddaccbdcdddcdcbdaceacceaedebeaeeebcbaceeabbbacddaebbebcedcabacdeeccddadedbaaaccdecbdcddbabbeadabcdedcbeeadeeebaedbadadddcddcaecebbdcaeaacaacdeebdedeaeabcabedeebeeaaabbdddcebedaaaeeeaeccdceadabcbdedccbbaeacbcbceecceabaadcbbbbbcedcecccddbecebbdbdcebcdddedadbcaeadabbcaebbceadaebabebeadeeebcddaceddbcbbcacdbcedcbbbddbcbbdebbdadeaeeadcecdbecbecbdaedbcdceecbadabdebdacccdcbdcadcbccebedbcceacbddbdacdceebbcddcddaaeddebbabdcbdabedcedacdaaeadbdceccbaaeeebeacecddecedebbbdaabedececdcddacedaabaabbacaeedddacaccadbcdbadadbbcadadedbbbbddedcccccbcdaaadaaeaedbecbadaeeceeecccdbbaedccdbcedaadbabdacdcceaebdeeddeaadeadbdeadecaebcbcdbaedcddbdbadccccacbabcabcdbaacdebdeccdbbcbedaadceeddcdeacdaecebebbabdebcddabbebddacdbdebcdacbccacebaebdcacbdedcaecaaedeebecdbabaecaedbdaeaedeaedadaedcebbdddbabbddcdcdcadaaededeeddcbdeadcdcbaaaeeddbcbadddcedbbabaeeaadedbedeeadbdbeaaeaddaaccaaebaaecdcecacbdcdbccebddbdcccbcacaecaccddceabeebbecebbeeabedaaeacadcdbceadcbcaacdaaddaccaabcaadabceadcaddbdccabeccdecbebbadcbbadacbbdcaeadaddbecdcbbcbadaabaadceebccaccccdedbbbbdaeaeecabaaacecbdbbdccdceebdeabebeeabaebbaacdceabcaaccbbcbcbeabddadcdedbdccdacbbecaabeedddbabdbcbaebdaeeadccccabcebbccbddbaacdeccebeccbcdaabeeebedddcabceeaedddbbcedbbbaaddaeeadbcaaabccebaceabaebbaebdddbecdacbbaedaadedbdbbdeeccaabdcbadcabbaadebaececcbaecacedecebeadcdacaedcddebbabeceadcdbcdcbecaacddddaebdabeceadddcdbcbbcaedddbadbbaebbaaeaaceecdbeacdaeaaeaabcadbbbcddcbaeaceecaeceeccabadeeacbbdabadeadcabbbbeeedcedcddeadeeaabcbaecacaecaeeaceadeadebedddcaecccaebaaaebbcbaecabbeaeaebdadadcbddbdceedcedcbaccbadcaadedaeaeeddaeacebdcdabcceccdeccccceeadaaebbabebaaeebaecdcaadacdcceebcddeecdaecbeabebecadbadadabdaceabeedeadaebddaaeabdebaeebdbbebdbcbbeddecdacaadccdaddccbaaddadcbcabeaddeabbbdcbeadbcbadebedabdcbeacddcabedecaacdbbeaeaecbbaaddcedbaedcaaecbabcbaabadcdbacaeeabbccaaaecedededcccbeabbaabebeebabdebcbcbcebaecdbbabbeaaacccaccdeecadbbdeebcaceeaeeecdeaeecdebcdeebbbacebbbcabaeecceacbebadddeabdbddaebadbbbaeebbdeceaaddddedabaccdecebbccbaaabceaaadbdacbeabceaedceaebcabbecdddecccdbcdbeadebdccadddaacbbeababaadabadcabdceacbbabddcdbcadcbbcccdcebbddcbbdbddbeebebacaaaaeeddebdcadcdaeceeabebceeaebbdbbbcaadedaccadabbcddaacdbbbdddeeacdaccedeadbaaceccdadecddaacbbdbcbbbeecadbeccbebdabaadceeabaabbeecacaebbdbecabacbbaabbbaddebbaaedabadbdbecbccbcdbcbabccdcacacedbaddbddedcbacdaabdcbededebebdcbdcacbdeaacdbecabacdbadebcdabeeebedcdaabccaeceaacbbadcabbaabbbcebbacaaaebdadbaeadabcabaecaabeabbebadacdcabbbeeceaaaabcddcaecdeaccdeebcbadecbbacaeecaadbedaabcccbaecaddabdcbaabbcdebebadaebeddbccaebcdbaedbeeceacbdbcdbdeedadeebddebebeabbbcacbabaeaccdaaadabdbabeeeaddcbeceebecabccdbeeaccedddedebdccedadccebdeeaaadabeebbeadaadbdadbbeeabdbbbaddcbdaebddabbeebeddccceeddadabecaddbddbaecdcceeddcbaddacddabbbaeccdcaadcaebeadbeebcdcdaaaddbbcbebdcedcdbaeaaaeaeddebdbbeecabebebddddccccdddebcbdbebdbedebadececcebdbcdcbcaebdddbcccdabeeddccacacedeaaedbabbdaaabdabceceacbbedacbecacacdbadccdadabdbedeecdebddbadeabbcaddaaceabcdaecedbddccaaecacdadbbbebbeccbaceebeedeebcaebdabaabedcedbbeedbaabeadacdddbeaabbcbdabdaccbebcbcbceeadeddebdbcaadcddbbbdecbddcdcaddccdbddbeacbacddbeddedaaeebbbeeceddbcdacbebdcacdacbdccdbdeddcacbeababcdecdeeabbaccceceabadbebdbbdccedabeebbdabbacacbeeedabbceecaccecddbdcccbdabadabedaadccbbbaaaccdeaacaceadbdcbadaeebdeebddebecdecddbdaaeeaeacbebaecaaeceebcbdedebaabbdacaaddedddcebecdcdaeeadeeebbbdabedbcabbbcebbaceacaddbecdbcaedcdcabbabeadaddbadaeadaaedcabdbcdadcaddcbcadeebbcdecaabecbcdcabdeaadbaecebcceadaaceacaebedcdcbbdddaccbbceebecdccdcdeaeebaacbcedeadcabbdbcddacdabbcecbddcbcbdedbddebeeeaecdddcacacaebccceddaaccceeaacabdbcaacaedcdddedcbddbdaedcdbacbbaeadebecbaebaceabcaaadbabcaeaedeeacbdecedacbbbacadcbabedbdccaacedebbebcecbbeeceeedbeebdccaedaeaddcbdbeedbbccdbadccbaceddcbabbeeaedcaddcaeeeeaacdaeeceaaddcccccaaceecccbbaaadbaaacaebaecbecbaddbcacbaadbbcadcdeabceadeecccdedcdbdeeadecdcedbcdeaabebeeedbeabcabdbeebdcbcabeebecaebcbebcccccbabbdcccaecbbdeaeddaccdedabeddedaccadabeaaebdabacabaddacadcebebdaaacabbbccbdbdcaacaabdcabddedbcbcaaaceddaeebcabacebeceacedccbbbbcbdbcdabeaeeccaaadbdedbcababadedeadcabadcabdcdabcdcbcdabeeedcdaaaecabaccdcdbcdebdbcacedaccbceeedeaaeeacdedcacceccdeeadaecdebdbbeebbeaaedecbaabbadccddccbedbcedbabbaaddecebceeddcbcdacbbbecacdccbaceeccaeccbddbbcdbeedbcbaebedadbabcdcedabcabeaadaecaeebbcabcecaeccbcdaaecedbdcacdecebddbadbcaabcbeaadeecaaaacbceaadabbdeeceaeddddceadbbebdadadaebddadaebdbcdededbcbcdbcaccaaebeabdedadabbddadcccbebabebdebaaceaeeaaeebceacbeaaaeeaabdccbcddedceacdedbabceedabacbeabbbcddaccacdcbcebbddcdeedaeabeddcceeadebacedebdeabcbcdbcccaeaeebadbcbecdeecdbcaeeeecadbaacddeccbceabdebecacacadaebdbacddaacadedaabbecbdcdaddadbdbcdeaaaeccbccbdcecebaabdbbaaababdccebebabdbaabdaedbcdedbcdbbbadbedacdcabecaeacecbdacceccbcaabcceaacddbebedbecddccecbbdbebeeddeabeeecadbeabedcddecbacecdddbbdbaeaaeddeebcdcbbddbeeeecabdccceebcbeedccdadecebecbedacdebeeddeccbeaeacbaaedabecdeebeacdeecbaeeacbdeecdbdaebcbccaedeaebbcaeaebbdddaebeabaacbcbededcaabddcedabebcdcaebadeedaecaebaeadcebeaeeacbadbeddbeceeccacdadeedbedebccbaacdcecdeeddeececdeadbcabbcbdaeedbadcadeabdbccdceaababedbeddceabaddebcabebcaaebbdacccccceabeaadaaeadbecaaebbdcbebbabceaddccdaabbdabddbaacccaceeaaadbcabbeabdbbbcbbcdabaaebeedabdacdedceeadeaecccccdabeecaeddbcebabbbabaabeabdaebaeebbdceecbddddccaddaacdabbbcbabacdcadcebeaaceaebeadccadbbcaaaabaccabcebbaacdcaeaeacdbdeabdaebebaacdabbaaabaecbeaddedaddacadeecebdccececbcbadddbabbcebbdedeaddbccecbbbbcaeeedbdbbcedebadcdccebcacacddadccacbacebcacbaacaaaaeeababdbccbeeeeaeaabaccdbdedecdbbcedcecdadbbbdebbbeacccecebcedacbeaebbbeedbdbadebbeaeaaabaeaebbcccdbeaadcbcbadeebcabdabcedaabbeaeabcdcadeacdbdaaebbaebeaacbadeeaccbaaedcdbabceaecbecebdccadbebbcccaceeaaabecdcceecbecacabdceeebbcecbaedeacbeacaabcbaabacdcdcadaddbbdedeacaeeacacbacccabcbceebedbcdcceadaeeadeecebdeedbddaaaccabdcedcddecceeadeaeeaeacebccbaeeeebeaeadebeacbaccbdacddadabbceadeebabeaeebbddddbdedabdeccebcdceeaddbcbddebadaecdedcbecbbdecaecacadbccbeedbcbccacccbabdcbadaaecabbccabedeaacdbccdadaebdaedcebabaaaddbbbdecddeaaaddbdbbacbbdebcddadabeeeedeabbabccbdbcbbacaddbccdbaadebbadbabdddcaaadcaadadabbebbacecdbddcaaedecbdadddeacdddeaccdabdaedbdbcaeedacbddadeaaeadaeaccdbdcbeacaedbedbcadbabcaabcadaadeddcbeaeedbaacdbbaedbdecaeacdcaaccdbecbdbaeeccadedcbabbbddcadcdbdecdbbebedddbcdcededecdaebeaadadcbddbeeaebedcddbcdeeedddaeacbcacbaababecebbebcedaabaacbcbcdbdbbdeeabbcccdacdcbcecbdabadbccddbeaebaebdabaabddddaeaacaabcbedebaccdbedeceeebebdbdccdecaacbcbaccebddaecacbcdbeedcbedbcabedbebcdeccaaeacaaaccbcabdecaecdbabaeeacaedeabaacdbebcaaeacabceaedeaccbcbcbcbbdddcdcebebccccdbabeebeaacdccbaddbaddbcbeabbeecaedeecebbeeadbbdbeadcadcbbdacaceceebbadbddbacadbaabadbeaaeacbaaeaaacceadeceeebebbeebecadceccbaeeebacdcdccdbccdaaabdeeabbcbccdcacbdacacccacdeaacbbdaebedccbdaadebaebcddabddaddcabaedddbdabbaeeceddbcacacbeecbdabcdcbceedcadeaedeabeccdecddaabdddbcbdaebbadeeabcbaaadbeabdcabdedbdaacabcccbcbecaeeaddcaebcacbabeecbeedbbbdeaaddacaadaadaaadbddceeecddbdbbcedddebacaeccdbdbdaedddebaedbddaebdcebbddacbdcadcabadabacbcaabebbcbddcccbeceeceadbbbddbebaaadcbaeacedbddcaddddecadacbdebacaeaeabdeadeceeebadeebeeaaeceedabcbebccaddbcbaecdeebcaccaabbadbedadadcaabdacabcbceaddacdebdbcaadebebcaaaabbcbbbbccecbabecdbdbdecedbbaadddabbedaacdbbabbecebcddacbedcbddedbeccbbbcccccccecaeeaaddbeeabdaeaacbaaaabbacceadcabedcaceccabebdeabdeacbbbedbdabdbbadaabbbaebaaedcddcababccbacccbcbddebeaaddeacaceebbeaedcbbabdccddccaabcbbbbcdcdceaceddeebbcadcadebdedcccdabcddacaeccbdeacdbdcbabaadccbaeebbcdccdeedcecbcecdbdbbbdbeaacacaacebeabbdcadbabbebecaeaabdaedbdacebbccaececaabbdbaaccbdeadedcdaadcdcdaaeeeeeddedbcbbeaeebdbadedaaacccaadccaaaddbcdcccbeccaeccaebebbaebcdcbcbbbedaaeeeeaadceaadcedbbacdeeeceaaaebecceabeedbeabcdaaedaebbbbaaebcbaacdddccacddacebddbbcddbaddbbdbeecabdaedeceeacacbebcbecebabeadbedcebacdadcedbebbbdbaaebeacdcaecdadededdcbaabecbaadbcdaacbeacccbdeaabbdabbcadcbcdcbcbcecdbccddbeaaebacabacacaeaeaddcceaddaccaedcabeccdeaccbedecbdeaceeedbbbecdecdaddadeaaacacdccacdbabadbcdeabadcccbbceaedcadbcaccaadbdbecdaecdcbdbaeadceeacbdbccebbcaceaabedaadeacdbbdabeaceccebdddcbcbceccdddbeaaacadaececeadcbcaddccbdbddcaaebabdcbbeedecceccdaedaedabeebedcabbcdcbcbdaacddccaebbcdadeacbcdadededbabcbbdedacbdbbaeabaedeaccaebbcbccabaecddebeeecdbdbeadcbddacbcedbbdbbbecdddddccaaddcdeeabbdbaacdbebcbcceaceeaaacdacaabdccdadcdacbcddebcbacaccaeeeddedbcbeeabdcebeadcabbdacceaaeccaebaedacbcbccabdcddceecbbdbbcbabbceeecbbbeebeeeeddbccacceceabbeebecbcebdeecdebdbeddeaddbbacdadcdedbcebdbbddacecdaeababbeaacbecdbcaaaceacacebaaaaabdacebbebcbbbbcaeebecbebbaccedddaaedadbbcedcbbdaeeebeaabcddbaabaceddcbecadaecebaabdaeddcdcebabbeebdbabbaeebebbedccdbcdbccabdadcedbbeccadeebcdbbeabbdcceeeaaadabbacdccabdbedccedbadcbabbacbadbbeadbaeddcacdbbbdacccaeeecaebdbccdbcaeeaebbbccacacccbcbccdaadcaeceddbceadaadcbacedddcbedbadccdbcbcdcabeacbbcdaeddcceddbbeadabcccbadebcbdcbcbeedabbbcacaaecaadebaacaaaecbeeaeeeebbddcdaebdeebecbabdebeddbcddddecbebcdaecaebdcbecbdcdeadbaaecaaedcddddeedbadbcddbaeeddaabadcdabaaebaddcedaadccbcabcadeaaecedadaeaebeecaabbbbedeebceeecaabdcdecadecbebcacdddeccddceaecdaabacbccbadddcdeeeccceaaddabcdeacaccbeeebdbeaddbceadceacabbbcebeeeeeebedadececbbadcebbbdbbcdacbaccbbebeeaddedebdbbedaeacceecbecccaaabebbcaaeecaabcbeaddbdbbbececbaacecaeaddcddbdbadaaaceeccacccadcdbecdccadeadbdaedcbebbdedeadaaeecbcdeadbdddaaceaeccdbaccbbaedbdebcdacbeddbabbaceddbbddeacabbdcaeedddaaeddeddedbeaedccecbeebeaaccdcaaeaeccdcaabedeadacedcecacbcbaeabadcdcaaccaddbcbcbadaadabdddcddbacedbeaeeebebdadbdeccadaedaabbeacbddaaeecaadddabcdbbadedbcdeedebbdebaeeaabdbbccdedeaceedacabacbdcccbadecacaaaddbadcbaeddabeacdeabccdbeebcbedcbddcaccbbdacceeeaeaedcaaaceaecacbaadeaaaabcaaecbedccdcbebdedbaabdddbebdaedceddbceedecceccbcbdbbdbedecbcdedbcbdacecddeadcbcbadcbbbdcdccaacacbcbebcaedebecccdbbcdabebdcabebaeacecabacbaddabbcdeabdadbbaebcabaeeceedbadeebdaacebbdbcacbbbcecaaddbaaaeecdadbeadbceeedacaeabeaaabcadcedecdbededbaddeabadedcdedcedccabacadcdabbddbdecedbcaaebcceadbecddedeedbacbbcebdeaababbbaaacebcbdccabbecdaababddbcdbaaceecadcaeaeedbcbaaabdabcdcaccdbcdcaebaeccdaecaaeaacbdcddcddabbaaeedeaaddbbacacababedacdecaabbbdbccdacbddeeabbedecbecbbbbddbbbbbbdeaaebeeddcdcdbbcccdcadeaaadaacbbbaaaaaecbdaecaeeaecdacaaddbbdeabaacddabaeabeeeaeeaadebcdebeddecdeeadbedaedbceacaccadcaadaeabddbdbddaaecdecabddaedacbebaceebbbbdeceddebcbcdcdadcdbadcbceeeabaeacaccbcbeadbbcaadbcdeacdcecdedcecdaaecbddeadadbadbdcbeeaebdeaebdadbdddcedaabccdeebbeadbaeadcdebceddbeddabacaaadbcbabeedcadabbbcebcdcacaaebdeababdcacacaecaaaeadbccaceabedccbebabaabcdedebbadbbdbbdbdaeebcdabddabbabccecdabaeedecaebbbedbacedddecaaaccdebccedcbadcbebcadbceabcececcedaacddbabbeeaeacdaedeaccddcdcedaddbecbddbdebbbbebbeeaaedeeebeeeaeecdeecadcbcabedbeebeebeababeceecbeacbcabaabaaeacbaedabebedcaabdcabeacacecaeeebededeacdbaaccbaaaeedebcdecbccbeecbebdacbeaaadcbcabbecddcbbcbdedaaacedcbebedceaeaabeedaeeeabdcccaaeededaedbcaaadbbbecbadccecdabacbacceeadbeaceacdebaeabacaddacaeceaeeceeaaccacbacccbadbcdaebedaeacedcbabdcdbdbadcdcbcbaabedccccbddcddeaceadebcdcbceabcdbabadeddedddeabcdacaabeaddaebcdddabadaeecbdeccaeccadceedebadebaeebaedccbbecbcceeaeaebeddbebcbebddaeceabddceebccacecbcccaccaeeddacbdeaacebacaddcecaceadcaaccecaacddcdebbecabdbacaeacbbcebbbecdcaccededcacebdbaeaeabdcbaccbeaabbebbbaeeeebceeedaeceabbbeabadbdcccbaebdcbacaaceebdeddeecddddcebdecbeeedecadaaaddadbbcdedbaaddbdddcdedddaeeeeeccbaacbdbbdcdecaeeedddbcadbbcedecbcceedceebabdbddeedbddbcaeaaabeeebbcedcbaabaacbaabdbdbeedaccaebedcebabbabbbaebadabccbeddcecccedeedcdebeccabdbceebcdcaabcdaaeeecdcbecddadcaaaacaeabbebaecbcbebeabeeaaeaedcccadddeebcaacedbcbdbaeedacbcbedcbbceabdaabcdddbdcbecbccdadedbbaddbebecacbadeaddaceeceedcddbeeeacabbcedebbcdbadbdaeadcdecbebbbbacceeeacbbaacaeceebeecadadbacdbacbadcebabdabdabcadddccabdddadbbaddbdbbcacedbebdcdaddeddceaaaacbecdcedbceeecaedebadaecceedceacdadaccacccccdddbdabbcceadedbaacdadceedabaebadcecaecdecbeebbcabeabaabdaccbecbbabddeaaecaadddccbbecdabdccaeadbbedcaddcbdebddbbcbaccecedadececcacbadbdacabecaabeacbcacbbebddebbccecddcdaebeaacebcbaededcddbabadaacbbeaeaadadbbcecebbbeabcccedaabeceadacdabadacddbdaeadcadbcceeaeabedaddceeaadbbceedaaabdebaacceacebdabcbabcbddacddecedbaaaccbdbecebddebcbeecebaccbdcaabdabbdecdeaaecaebecddacbbbdaedadddeeebccebabcdcadeebdcacdaaeeebdcceebcbdccebeadedcebbaacbbdceccabbabeadeccbedddcadecbcbbebdddbaabddaaabccbbcbecadddecddcbcaaeebdacccaacdeccdaecdadcadabccdadecdaccddaabcbcbbceeaeccccbcdaecbcedabdbcacdeadecdddabaddcaadbcebeddedbcacdcddcbacedbecaddbecceddddedaebcceeeaadebbccdcadeaaaeebcacbbbccbecceeedbcabddccbeabdedddcaecebadbccbabaadacaadcdbebddebbeaebcdcceaeaceeccacdedeaccebbdbebdcdaeabaceaedabeaebcdebabaedeeadadeaeaaeeceeceaacaeaeeeddddaecdcbbabddaeadcdbcdbdbcaadddedabcaedadbdbeedabcccbbcbaaabaeadacacdebaabbcaccebdadabebdbbbcabaceadaaccbeceabbccccbbcedaeeedabecbecacbbeabdabbdabdadedbaccaacbdbddbbbeacebebabedcbaeabbdcdecbceeeacebadadbdcddeababdbedaedaeabbdccecdabedcdaaecebcdbbbabdecaacdcbebaeeeedacdbeaabcbeebaddadbabdacbcdeeebbedeecbadeceeccebddeabddcacaacaeacdbbccccebdcdbcbaaeeaccdebacaacabcbdadccaebdbcbbacdbddaeebabaedacbaadbecacecbbeddbbccebdceeacccbabacbaeebbcedebccdbebeabbccdceaeddccecdeaedeeddcadbcbaebbcdaddedbbcaeecaeacbecadccdcebcedddedeccdecccbbdebcceabcbabededeccbbddabdcbccbccbbcebebdeedbeacebbedadbdeededddedcbcceddebbecdbdaebdacdccbecacbbaaacaeeaebcabeeabbdeaeecabddbadeededeeedaeebbbdcebeacbdcabbcddbcaabdbdddbddeedcecbedcebdbceecaabcaddddcacbeacbcabdbedcdbddcbabcedbccbaadccbecbaeebcacdebaaacbaacadedeaebbebcdaccbcabebccecdcbaaeaecaccacedacdecdaccabbacbdcceabdeabbcbecdeccececdcccabbdcaabbadebadadcaedcdcbccebceaadacccaaacaecaebadecaacdacdbdaadcaaaeaeaaddbeddbdebabeaeeeddacbdeddcdcaebddebbaebdebccdcaabaaceeacedbbeceabebdbbadceecaecbbdcccdcbbabdddaadbbaadbeccadebbadcbeccdaeccadeeaddbddeeacbcaceaaebdacbdeeddabbdccdbbacccdeebeabacddbddcabbbcdcbaabccdaeccaebaaebddaaacdacecebeddeccadbadacbccdedababecdccddeabecadcbccebabcbabbcaeddeecbaabbedcabdadbbeccdcaeecbbaddccabdcdbddcdeceaaaddcedbedabdabdecdbbecabdaacddaabdbcbdeedbbbdcadecceadabbccebacaeaaacdecceddbadddcdebbaeeccbbdaccccaeeaacdcccdceddbbebbdaaaecbaeeadeccccbcccdbcbdccabecdbabaacdcdcdecadabdcccebcebeeddaaccccaeccecabbebdaaaccebbaadadacedccecbabbeeccbadedaccaebebeacaacdeeecdeaadeadabddaddbeceabbdaebadbbccbbdcbbdceebbdebceaeebbdeacabaeeeacaebebebbedcbbebdceaaeeedcacccddbbcaccebcdbcdecdaeaadedccabedecbdcdcbdedcbcbbceeeecaeaacdccceaadedebcdeeedbabecceddcdabdacdacdcbeeedabdbbbabeebacebccecaaddadeecdaaebedadebacccbceccbadcdccdcdccdbcbededeebdebaeebcbcdadaeeaedbeecaccaccceceeaadabadaebcbdedcdcaaedecbadaaacadbbdcdccaaaaebeedbdedbbecbbcbccccbaabdcdccdebcbaeabaccecedbdbbcaceddeeabcddeaebdbdeabdcababcbebedadcbabdebecccecaaabbbeccaecabaddccabecbeddccaeabbabbabcaeaeacbabebcecbcebebbbbdbeedacabaaceaddcbeadeeabceaeabdccbacabaeeeaacdacdcbddedddbeacaadbddaebccbddbacedaedecabbbbdeeebaabdcaaeabddcddbeabebbbaaabacdbcacaebdcecacabdbcbdecbdecaaaabcecbadbbdebedaecebdbdbdeeebebadedbabcacbaebcbcbdceeaecbaadcacddeceaeaaabbccdbcddadaccacebdacdcbdddadcdabacaeecadabcbaaacdaceedecbddbeeedadccbbdcdebecdbeedadbbbdbdaaadbacbbaeeebeadccdecccbeceabddaabaedeadbecbcdddeebbceddcebbbdebeedddbabebbdbccdaabdebdeeededcabadeaabcdeecdeeaacacbdeebcabcbeabdbdcccbddceedbaedcbbaadaadedbdcacceadccaaaaacedaeedbdebcbdbcccecaeeecacddaadeeaadabeddcbabddbcdeadceeecbeecedccbcceeedcbabedecedbbbcbbeeddaadddacabbdeeddebeaaabddecddaeccdeacbccedaabdddcccecadcbadedccdaacacbecbdacdbbcaeadbecacbcddcdbecbbcacbcbeacabaaedbbbbbcaddcacceebeabbedeeaeeaedcedeccbbcaaeddaaacdeaeaedadbebcabbdaaebdbebeaddcbbedadbdbbbadaabcdaeecaeceddecdeedebeaacecdcbebedababddcdbcbabcaaabcabeeacbedadbaabbadeecedaeacbbeaccdbcdcbeacabdcbaeeabeaeaaabedcabcbeecdeccedeacdabbceeaeebdeddddcdaeacdabddeccbacacbeeceedccdcbeacabdbbdaececcacbbeabdbccdcdabdbbccdbaaeacaddaddcecadadedbedcebeedaeeabdebcdbaeeccdcbedbcbbabacdeeacaadacceeceabecaeaaceddccdbeeaedbcaaeebcebeeecddeeacbebdbaaeecbbbcddeeaceabcabaeddccadcbaccccaaaccbcacbeddecdddbceaddbabdebcbdcaeeadeabeedccdabbaabedecbceedcbbeacdabaaabbeddbecdcbbbeeadaddbeabcbccabeeadbabccccdbdeddbadebcabbcaccbbaabacbddbeeebeebbdceaaeccddebabeabbbabdbabcbdadbcbeaabececbbbeacccccdbcdbcbeaccaccdaaedddadeeedeccdeaeeebbaacddcdabadeadacadcccddbaacaaabedbabaeccdceeadebbdddadeebbcadebbbebaecaebdddebddebaaabdedeabababcebebdccbeeadbadcedbdbbaeaeebbcdceadddcbeacbccdaadbbecabdeeeabeccacceaacdcbcbbeaaadcecacebebccdeccaeccbdcdacbddcbaeacdbeecaacbceeceaabcbbdccdeabbeeacdcdbebdccaeccbbdaeedaccccdeccedaedcecebddcdeadccdbbdbddebbcbedecceaebacecaabedcbdbbebbaeaaecbbdeaadabebaeacedeceddcedebacebdccbabaeeedecaececccddbdcaaadaddebddcecdacededdaaaadebbadabdebebdbaacbcacebabebcaebbaeddaadabdcdccdddebcbddbdaccaabbcdcdabaeeaeeaacbdbdbaecdaaecbebddddbacaadaeedddccdeebdddebaaabbcabedaccbcabbcbcaaaedaccabcabceeceddbbaeebeeccecbdebbdbaacabcbbbdedbccaeddbeebccaebaabacabebcbecacddbaeaaebdebadeaaedcebeedccaaaeabeeeabadecdeddbccdebbdedddbecabbdababdababaebdedcddedadcdbcebdedaeddcadaeeadbabcadeecacbadeeddebdccccccaeedacdeeeecaccaebbcdcdadebadbcdbcddddedaedbbeebddeaabdbdeecccbbcbcacdcccadaedeeedecaceebdaacaebcbcbddbbebcadaebbeccaabaaddaabceadeeddaccceaecaadadadbadceacddebcbbbedcddeaebbedaededcebbdcacbbbcedbceceecbdbccbabcaaaeeeecdabaebaceebaabecbbaabeedcdeeeebaddbcbadbcdaabdbcdacebaeddeaebdcbbdbcddbbdadaeaaaceceabaedaadaebbbbcccdaeceaebcbdcebcebbdddcbbcbccedcadddbceccbdaedbdddaddbebedcebbaebdbeecacbedbbecbccddadecbbdabbedebdacdcdccacbbbbecaeccabeeabdbeedaecddadbabcceaeddadeeceaaaaabcdacedbbedebdadeeabdcdabadeabadceaddbbcedeccddcbbdceaddaebbccbccdeadbaadeccdedbecaceeeccebdbaedacebcaccccbdceacbaecdbccaccbcabbbbdcabdccebebccacbcbcccdbdbedbaebeebaebdbcdcecdcdbadddebbadaeaeddecabdaeccddbdaccadbdeedbdbccddccdbabbbadecbdeeeebcbbbdaabbceabaaeaacdacccbedbbaccaebbaebcbeedebddcccacecbedccecccdcdabadcedabbcdbaeecdcccebacbcdcabeebbdeaaacbcdddeceedddaedbdecadbceeeebeaecaeabeabeeececeddbcceacbeebeecdbcbaabeacecdacdabaeedcaaaedeecdebcebcaedbdeccecdccabdebdecccccbccceebacdceeaeeabdcdabdaeeeaebedeebddaaceaaecabeaeeeeacedbcaadadbeeadcbcedaeadbeeedeaacadbcdbaaadeaeceadddcaeccdbcececbaabccbcbebcbbdaecebcbdacadeacbededabdeccabaaeacbaecaceedaadbedecadbddaabedbceaeceecbcdcdcbbdaedbbedbbdaddbbcbabdaccaeccadbcedadbabcbaeacecbbecdaaceecdcbadabdbbaeddccedeedeebbdeadccbdeaccbcabccdbaeeaedbdecbbacaebceaecaaaedeacebcceebaaedcbeadabbbedaeddbbebacceeecebcedbacdcadcccbbdcdbdcaedcedaaceecbceeccbdecdeeeebbdbaeceaccabeaecdeaeababeccdedaaeeddcbebecddaeebbbeddeecdaadeabcebbcaaceeaaccceedcebddadcdcbdddebeeaccbcaccdebdbacecedadabdaebddbeeaaccbcabccbaabededceecdacadcaacdeeaeabadacacdcadcbbceeacecaeceeddaeedcbcdddbeaececdacdacddcdeabebbabbbadddaebadebdcdddabdbaceeecabadddbbeabdcbbdbcaaaeedacdbeaccddcaeaaccbecedacbededbebcdcedebecebeeeadeaedaceecdbeccabbdceecaedcbbeeaadbdacdeddbaacbbdccccdebaccbdbebddbdbbeeecacacabdadebdcdbaadbcaebbbceeaaeedbdbacbdeaaddbeddbaacdedabddbeceecadbdbcaaebcebbcecbabcbedbcedebaeeececadacbcbeeddaabaabacbcbeedcaabceacebdcbabbbecdbbeceebbebecabdaeccbadbadcadccbcebcbbcececddaddcdcccbdbdedbbbdcbdeaccedebdadaccbceadceabdacdcbbcdabbecacaeabddbedcabeecbdecedccdadeaacbaeacadcecdbccabcadacbcbeebecaabdebdadbdadecdcdbdaeeeaabadbcceadcbbdbdecedddccddbebdeabbceaecabdccceaabcaaebbeebdadcacccbbebcbbaddcbaececadacaeabbdcdeeacdbadabebbeeaadabbabdadadcabdedbcebbcccbceeaddedcdaacbbccdcacbccdbbceecdacbeecdadeabcbddbaaecebbceaeeacecbbcbeabcaeedbebeddbeabddaeedbaedddecacebdcceedbbaabdbacbdcccdccdadeacebddaabcccdacbcdacebcacbecceaabebcbcbdeeabeabddcbdeeebbcadedeceeeadcdecaedededcadbbaaecedaacecadcedceeedabbebbcbbcdbeccdbecdbbbcecbbdabcdecccecbcbbebcbcbdbbadaccbddecaddaedceabddaeaebcdcaedddadabbcdedadeeaebccabeabcbddcecdbaeacaedbccbbecccdeccbcebbdaaddcebdbabecebedbddadeeadadcbbaadbccbcbedecaadccdaacdccbeddebbdeadcccacbabdbceeaeebebaccabbdcccddbdaddaaacdaadaabcaabeeeacbdbbcdccaedaaeaaecbacabdaeecbbeccbaaeaedcbdcaccceaaaaedeaabcecadaabbaddcadebaaaaeadcdeccbecdbccedddceccebcacebbadddcbdcedecbcdecbdedbccdcbceccbddaecbebecbdccdcebacdecbaeebeaabbbaacdcebaeecedeebadacbadbaedbccebdeaddbcbecdeaacbabceceaaceccaddabeabbacdcbacdcdccbacdebabeceebbaadeedcecbedadcccdbeeddcbeceabbbbdcaedabbeccdceaebddadadbaceadaacdcaddcdecbacaceebeddbdbaadeaeceeaddecbbdceeaadaabeeabeedbbbbedceccccdaabeedbcabbebeddeebbbebceccebbbebbdbdcdbcbeddbcdbbabbbccbddebddaeadbdadbeabadcbeeccaacadaededbccbdbcdedaeadabedcaaecbabdaabdaeeedecbebdeddaebadceabdbbdcabeabeacaccaeebcabccdcabadadaecbeedcaeeecacddeddeebacdbbecadeebceabeeecedecdeabcbecacdbaadddbecaababbdcabbbcaddcccacddbeadaeddaebececeeeeadbdaacecdcecaeebaabaebcaadaebaaccdedcadcebdedcddcdabacbedadebadbbaaccededccdadcccbabadeeaddadbedbaaeaddeeedbbaccaaecdedbaebbaeebbccaceccbcecaddbbabedbbabeddbabababebbbbeecedbdbddaadddadbabaadacbcbbdbcdadeddaacccdbcddbecdadcabbdcabbadbcdacbcaceddbadedaeddecddaaabcbaeceedacaddbdceaeeacaceeaaccdaaddaaaedecdacddbbcddebadaacaeabbaebbdbacdccadbdacdbcdbadbccabcbadebddaadcadbcbaadceeecababdeebcedbaaaeaddeadcbdebbdcecaaeaedbadbecbcbbddcaddebbebedcdceacdccceaecccbceebeebeebbdedecdbcddbdabebbdaecbbaedebcaedebdcabcccacecdedbbcddbddceceeabeeadbcccadaeecaebaadbccabaaaacbccabbccdceeadaeeeaddeaadeaadddcbdebaabebbebabeeaeabdebcaecacdebbbbaceedabdcaceddecebabcbebeabbdaabaeabdcaabaadaddcaabbdaebaedbbaecaddbaeeaeeacadccbbbdccebdaaaccaaeeaabeacccceeeacdcaaccedacbedacdabacbecbdcccbcecbeabcaebacabceecaadcbbbcddaccababbddeaddaebeabcbddbbacdaeaedeabdaebbeeedddcacaadadbdbecdebebbbeedddbbebdcbcabdebbbbabcbececeeeaaccccecdeedcabbddcbabcbedadeaccbddabbccbaecddecdcdabcbcaccbbcdacdeeeadbbbaecbaeebccbcaccdaceedacbacecaabeeadcacdacbcbaaebdccdacdebcdecbcaaecaeeaadedcbbecbccbabaecceedcbceadbadadcbcaeedcdadedbdccdacebabeaadacadaabcabbabdeebadcabacaddadabcebbdaeebbecddacbbaebcdccabeeacadbaaeddedadadebcecaaebabcdabcdbeccecbdcacccdcdbaaabcdaedeabccacdccdbddcdbcadebcaecadcadbccacddbdbcbecbaeadebdbeddbaeeeddeebebabcaaebecdcebcccaaabeabecdedaeddbbaeeddcebaebaebebcebddabecabacdaadbedbabbbaacebbdcabadedaedadadeebeaededceaeebbecaeeedceaaaacccbbbdccdbaaceacecbeeababaacedbeceaaccabaccaaedcbaeedbdddabeaabdcecbeaabeebbdcbccccccbcaadeaeeaadbccceabbccaacadaabbacddebdeaacdcebbccbabcdbaaacccdbcddeebcbacddbdddbdbcbeecaacdccbabdcebedacbccbeadedaeeccdbeddecedbadddaecceeecbbddbddcbdddaeaceecceccbdebdddedadacdcabddddabadbccaabccbaebedbcdaddebbdcccdeabdcddaeacbeebdbeebcacaabdcaccaaddbbdeedbeadaaebcadcacbdaaecaeecdaebddddbacacadabaecadabdabbaceeabeeeeedcbcbbbadcabdbcadbecdbdbcbecdabeccedaedabbdbaebebdcaeedbdcdbdbeebadbcaaadeecbaabceeddebdbcddecdccdcebdeaaaddabdbecbedddabaadeeacdcbcaeaeabcbabdacabdaccaecccddcbddceaaaddddbabbaaedbbddbaebaccdbabedeeedcaecaaabbacaebacccddceaabaabdbbdedddcbebabedcbcaeaadabacbbcedaedbaacccacceecedecbbbddadadccedabcaabdeacedcbeccaeaecaaabeeccbbaecdecededbeeacedcbceaaedaaaababaaaeadecaccabaaeeaaabcbceebeeaaecbdacedaccbdddbccdbddbdeedabbaeeddaddadbcebebbeecaaecedceadcbcdbbbbcaccbbdabbecacdcbaebaedeceaccbbccadeebdbcceecbaaabcddcaaadccddbddcadeabbdbccebdaceecaeeeeadcbdadccacbedecdddccabeabcebcbcedacacabaaebbcbaccacadcadbdcbaadccecccbbadcbeecabccaebeedeeeddbacdebecabdaddeaadaddceaeaacccbadadceabbacddecbdbbbceedbdaccccaaeeedccbebcdebebcaabddedcbbccccacbadeeeabddcdeabbecbcbeabceaaaddbbbebabbadaeeadcdaacabaeaeaabeeedadeaebebabbcebcbdcdeecacebbbcddbedccddcecabaacebcecdccaedcebeaabbbacddcaddbdeadddcddbecdbbaadbbdcdbedcedcbcbbeaebebaedacceeeecbabbdcdcddbdbbebadccdbbbcadbbcacdcbbaebecbedccddddbdaeebecdbcecddcdbebeedadecaecdceaeddddeeddadcddcddeddccddceddedaadbaccddbbadcdaeddcabcacbeaeacdbaaddbcbcaebbddaceeaebdbebaedbbbaacebaaceeadbaaaaaebedaeedddeeddcecdadabedccbcabdbbcbadddddaadeccdaaacbabcbcceaaedddbacecacecceecaceddedbebcaadbebceadedcbeeeddacebbcaedacbebaeaddaeaededcadacbbddcacceeabccbcaaabacccdcbeaeadadcadaeddecbdcdeacebbcebedbaaeaceddddaeeabbadbacdbeedbeceabbbaabcaebbeeeadcdceaabdbdaedcdadddecddebcdcaacddbcbdbbaaeedbbdccdddadbbeeacbecbddeabbaababcabdbcaedeeccccaceecaeacdabdcabdbceeabadeedebcddcdacbcbeedcbdbacbdabbebbcdaacadaaeaaecbbdcceaedcebdaeecbacdecbcadedbdacdcaccaeaebccdbebaceccaacaedaceedeaeaecabdeeeebedaeaccdcdcdcedbcaedaeceebedbcadceeedecababacbcaabdebaceeecacbececdbedbacbccabeaccadbaaeabadbbdcaadcbbeebbcebdcbedbaaaddbeeecbbddaeeeeebeedaeaceeaccbdabdceeccacddddcbbcebdebdeccddccdddadedecedeaacbcedaeeccbbcedbbbeabeecbcdbedbcddbdcacbcebceedbdbceaacddebaeaaabdceccecddbbdaedcccaeddceddadddcddbebceccbbcdacbbcaabdbbedcebccdcdaddbcecdaedbceeababaecbdeaabbdaaaebccadacedbeccecbacacacaaeacdebbbcaceeeeeabaccdcccaddbeebcdddcdebbcbaebedaecebdcaceddaebdbbaaebbaeaecacdcadabbbecdaaacadeedeccbeababbbacaebbddedbaeeaceaebddecdddadaabccaacccccaccacccbedddadbadbbadbdebddaeceebbcedcabecdddeccccdcdeaedabeabbaedbbcdcabadbbcddbbeecdbaeeaedeacdaeeeecdadbdbecdccebdabeebcebadbbdbdbdadcbebbddbbebebabbebdeedebcdaaccbaddbabbdaeaaacaacdeabaeedeeaeabececdccdebeecdcceaaedbccabdabeabdcdacbbcebebeaaceeedcccddcbdbbbacdacccdcbcecebccaabacedcaeadecabdacdabaedcdbaedeeaddeddbcddbdeececaabeccaaadcdecaabcdcaeaebadaacdccdadcceaeedcabcaacbedcdedbaaecaceeadcbddeeededbdbbdbcacaabbdabadeccbcebedaadececdecccccecbabcdeaeaacdacecadacbaacebabbdddabbdddaabbabbeabaeebacdceecebdabbeddaacecadadeaaaaacbcccbbdeddaaeaddbaebeabeabddcccbaecaeccaecbdeacaccbbdeadcaaaebabccccebeddaebcbccdbaeeeededbccbcaecdebbcbbeeeeaadaabcddeeeabceeabcbddbcbdedaabccaaadcaeaccbbcabcdcebbebcdeaacbcaaedabcdbbecadbbeedbaedaedabcbeccebecbbcdaeabddcacabbaadcccadadaadaeedcdeecdceeadabceeddbdccaaccbcaeccbebbbdbdaaedcbcabeaebabeebcaedebbbaeaecbbdbacbdcbbdcabaddddedadcabedbaeeebacbddbaaddcddaccdbcadbdbeedbcaebbaaeccdeeedadeddbecdddcaeddacaceadceaddcdccceebbdccadaedadeacdedeebcedaddcabcdccdacaadeaebcdabeaccccaaddedcedeebcabceadbbaaaeaaaddbabacababaecddddbcbdeaddcbbaeaedbcceaeceeacedaddaebcbddedddaaedaccbbbdcbceeebadbdbebabaecaadedacdcbddddacadacecbcadebdbdccbbdabcedcaddecadecdddbccdcbeaeecdbaccebddbacaadaaebabdaebbecaccbdbeeaededbdbdabddceabecddeedaaaeaceababdadcaeabecbdcdecdeedcddcdadaaebdabeabecbadacaaaaddacddddbaaeaebbdbacacaaedadbdebcebacccaabcddbadabcabbcddedccdeabcebeacddbbdcaebbcacacceecebbbceecbbddcadbaedaabbbabcbdbeaddbabdbaababaeedecadecacebbccbeebadeddaccdeebbbbcaaaddeeecbacebaaceebbebeaceabbaebedcebdbbcedebecaedeccdacbbcabbebccabcbabcebbeaacdccdbddebedaedbabcddababceabbbaacbadccaadaeeaaabcbdcbaedabbcddaebcddeaccddcbcedccabbcddaebbbebcbcabceacaddbcaaeedeaeaeadbbdebadaaeebddaeecacecaedaabbddaadedbcaaabcebecedbabedadbaebbcdbbaeddcacadbccdbaadcdbdecddeebdedebaceebacebaeddeaebecddeebccacacdeeacebdadaeacdbbcecebebaeeccdbbbacadeaaacddaaeaecdeeaeedbcaabbadeedacccdaeadcceacdbbcedcbdbedbeeeaaacadeccadaeeeaacddbdaeebcbeabebddcabebdcccacabeddecbdaccaaedbdbbbceccaeccabaddcaaaabadbaaedaadaadcceccebecdedecbadbaebdebebdcdbc abcbcaedbdbbebbcabadaadbaecccbdbabbcabddbeaaeaeeabdbeecacbabbdabbbaaaaededeeadcdbdacdbdeabaeddcadabcbadbaaedededeeddceedebaaeeeedcccdaacbddbdaceadeeedaaaabddcabccabaaadbcabdeeaccceaaacdadcaabdcceccabbadedebaaaaacdabdccaddcacaedcddcdbabacacedddabedeaccaecedabcbdedaeeacdebbbbbcceedceadcdccecbaeabedbacabdbaddcecceacbaedaeeaddecdcecadddaacddeddcebddbbbdabbcacccdcccbacbcababaddbacbcbaedcbbdbaadcadbcadbbaedcdecabedbadebbadddcccbdddbcaddddbbcacdcacadbabbbaddcedaecbecbeadbccacaeddbecbbabcedebdbbcbcdcbecbbabadaccbdcbddacbcecaeabecbddaedacbcabdeeccadbccdabedaabaceededaabaabacaccabededcdeaaeeeedeccdeabbcddbddbccedcddcaddcadabeecdcdebcadcccaddacddabddedbededdcedeaaecececceddbbddeabbeecddbdcbcbebacbcbdddddccbceaedabcecdcbceeecaccdeccacecddedbebcacabddebbeaacdacdbcdadacebabcadccbdcdddbdcbbeaeeeeadeaccdbdcccdcbaacbacbcdedceccbddaaddcecbbaceecdcdedbbeecdbcdccbdbbebecbaaaaccdadbbabeaebedeaedddbbbdeddcecaedecbcdceddecebacadbddabbbaddbccdccadeeacccdacabbedeecdcededaebdedadebeddcddebdcdeddbbdaddebcaebaceccaabdacbbbeeeaebedeedcbddaaeebdbedacdeadaaaaddaccccabbaedbdbcdccacddeacccdbbaaebabdcebdececadcbaeccacaeaeacadcabaaadeeabcddaebbebeadeddbebabaadedecbacbedadbacabcbcccadbddabbcddcdeabcaeeecaabcccbdbddbcbaaceedaaeeecadacacaebecbcddbbbdeacbaaccbdaeedddaadcdbaddbecabedeacdebbbcdcddeedcaaeadcddbbbbdaececceaabceebdaedccecbbdebbecacbbbacbaecdcacaebaadbbaeeeeeedadbbeeebbeaedbadcecbcbcbbdacccebbbcbedeeeddbbcaaaeaacdddeedcaacbeceaccadcbdbceddebaeecaaeebdbcbcbeebaddbcadcdccbbeebebaedbbecaeeedbaddeadceceadbdadaebaabbcebacbacdcaeadcecbeceedbbaedbeceababbbbcbadbbbebcdbbaeddccdedacdebcecaddacdcbededaceaccbdceeebcecbaddcaacedeceddcabecabebececccdeadacedaeedcccbacddeddedbaebcadccdebcabeddacbccdadddacdacacabcdedeabacbdcdbaeeadedbeabaaeedcdbcbbaadcaedcbcaeadcceddabdebcadcdbbabeaeaccabccaacaecacdaccdbecbcdabecdadccddaabdadeecbbeebdcbdddadadbaaccdabbdbaeddcebeaeabdeddcacdaacadcaedebabebdccebabcacadbecabebdcceccebbcceecbadcccbbebecdbeaeaaadeceebceccecccdeaacacaccacaadebcdedaedbbdcecaabebdeaeabeacecbcdccbbbeabbbdbbebcaeebdaebcdeeeaebccbeedaabbedededadceebbaadbcecbeaebcacebbaeaeadbddcecdbaabcdeedadbcdebadcbdecaaccbeabeceeaaabaadbdaeacebcdbcccdeaceebeebbbdcbbdcbacbedcebdebdebcdcadedbadcbbaaaebabacbeabdbdeacaebaccbeeabaccabacdcdbbeabcbbadbbcebccbbccdadbdeedeecdacadecbccddbbcdeedeadaadddeceedbeeababbcbbdcccdeedaddeddecbeaeaedbeecccbbddcceeebdeedbabeddeeebadecebabbbacdedeebdbaeabacdccdbccccacbbbaabadcbbdcdeebdedddadbcbadcdbbeaacdbbcaabcaaedbbdddaacabbaeccddcbbdabccaaeedebcaeaadabeeebcaabbaacaebeddaedeeebcdeaacbedebdcbeacaeeadbadebbbbdceaaeadbeadeddccedbebcecaedceaaacebaabdbcadddecbacbcedcedcebeaeebeaabdcdcebeecadcdbceceebeeedbdcaaeecdcccddccaeececeddadeabeddeddcadeaccdaadcbdcccedcaebdbdedaecbabdcbeccdadddcddbaaccaddcbbebcedeabcadceaadbbddbbbaeaedaabbbbcdaaebaedecebacddecdecebadccddccccceceadadabdeceddbaebaebaeaceeabecbbebcecccbeaabdcabbcdaaacedeabbadbcccdaedebbbeabebceccbedcbeaedecabdbddbcbaeeeaaaeadbaadebebaecdaeebdacbbabccdddecddcacadaeeeddcddaaaeaddeacbbbecdacdbddbdbbaaeaacbacdabecaaaecedbbeacdaddecbcacaebebcbddddcbeadbbcedccaeceebabaaaacaddcebecadaecaadeaacbeeecbdedcabddabcddaadbadbcadcaaeedacabaadbcceeecbddceadeaabaaaddaaedadebcdeedbedcaccedabeacaedbcaddddacadbdcadaccabccebcdaccaeabccecbdeacccdcacacbbacccdcdcdaecddeedbacbeedadedcbdccddcebddddbaecabebddecaceddddbbacdcbddeeedebdaaeaeadeaabecdbebdddaaddddbbbcdaedcbddeaeaadddbebbbcebcdcecedbeabadddeaacbdaadceadaaeaececaccbaabbcbcabaacacdeaeeeaddeccdcbeaeedacbecadeeeaaeccdadcabbbabcbcddebbeaeeedebccedbbbdccccabeabbcdccacdddbebedcacaaceceddadbbabdadbcbbcbbcbdadaadddbccdacbecedacaedcaaaedbcedcbeaedbaddeeeadadcccdacaaacdcbaeaedaeedaadcaecbdcbeaabeadeabaaeabadaadebdaacccedeecdbaedcccbeeaeaebbebabcbdacebdcbdeebbbdeccdcbddbedbadbebaddbbcdabdbecaaacbbdedbaedccbcbbacbcccdbdcabebcabbbaeebbeacbbeebcbacceababddaccccaaddbedbeecaadbbadadbbedabdcbaecaceebebcecadeaeaeddbebedcceaaaeeeccecaaecbaecccaababecebcbccedbbceaaedbaebbbeeababcbeecddbddbccdaedccebdbbadddbbabccedbedbcbebbddbccdcdebaedbbcdeeaaadbdbdceaeeebecaaacddadecdcbcaeebbbeddbbddbdbedbbabaccceadcdcaaddddadabeadebaeeeedeadddedaeebebebedaaddbbbaddeeedabcddeaabcdbdbebebbeeaabacdcaddaecabcebaecaeebaeaeebdbaeaadbdeaedebbbacbaabacadeccecadcdcaaeaeaeabdbadceaeecaccccbacbddcccaccddbebcceeeddacddbbbecdceecddbecaeaedeadbbbddccdcabbeaedacdbcadbddecdbbdecabecbeeaadaeabcdccdeaeebbacaeeeebcdaeeaaccdcedbbccbadaddeccadcaedadbecaecdbebcacbebbccdcbaaabdbabaeabedccbaeaadacabdbceccbdecbcabbdaeaceaeeeeeeaeabbdaaaccddedcaabcabcaaacbabdbecedeadedaeabbeeabbdeabcedbdabcabeceebecadcbdebdebcbdadddedddecbceaebadedccddceabacedcdcabddbebadbbaabaadcbdbadeeecceaeebedbdebeeaeaadcdebeddeddbdabbeeceeaceaadbaedbabdecdbdbdddaeccaedbccccebabecadccbabbeccaaebcadcdddbcbaaadcecbbbbedbcbedbdceeabbeeebaccccaadaeecbadceddbdbededcbcdbecabaebdbacabeebaeedadedbbbabebdeccbcbcbecbbdddbdabdeabddbdebaacadebdddebecaebaadcbdcbebcdbeeebecbbbebcaabcdeeeaeccdecdeadaebbccbbddaebbcaccaedecbeeecebdcaaeceeedbddccdbabcaccebcdcddaedbeeadbacbccdadabaccbccbbcbdbadceeebcabdbeceaaedcdaddbdacadacdbdababaecaadadaaececdacdacedbcabedeeadebbbbddeaedccacadbeeaededbcacaccbeeadeacddaeaccacceaebcdddaababebbaddcbabcabcedcaedacbaebdcecedabaadabbacacaedcbabeecccdcceabdcacccadbabdeabaaebacecdeedeeacaacdaaebbecadebbeedcceaceecaacceeaceabebacecbebcbbeddbccabacbcabbcecbacbaedbaaebadaaeecacdbdcdddccebcbceadabdaccebacabcadbcdcabeddeabecdabedebabadbebaeeaecbaedcdedbccebebeedbbaacddaabbbdddeaaeebcedacbbebbdebabcbbddececdadeaaccdaabccacacbedebecbeeaaacaacbaeadbaebbbeccedabcdccadecbaaabcdcddebddaaaaaccdbcdbaebebdbaecdceaeeadbceacbabbbdcbceceeaacbaeeaeccacbedcdbaedcedddbedaedbddeceeebacaecaaaabdbbdbecadeeadaeecbddcbcbcabcebaeedbacaeaebcddebcbdbaeabdbaceeaeedacdcbeedabedddccbcebcdcbbaacdaaddeadebaaeabecceadbcdabaecbbbbcabbedadabcdadcbdcdcacadaecddeaceccceeedeceaadbabbaeebcbadbecacddacbcdecabaeeebeeaaaaaeebaaacdbececeecebedebeccadbedbbcedccdaabeaeeabdabeadecdcbcecdebdabdcacebcebbdaebeaeebdbabaabcdcdbecadacbddeeaeaaaabddaebebdebbbaabcaedebaaaeacbdbdcaecedbeccadeaacdacbbcacccebdadeaecacabbeaebaeaaacbedebaaccbcddcccdeddcddaceebcadbadaceeeccacbdcbddbecbbbeadddadddedbbeaabdaeecbaadbeabeaaeacbbaacacecadecbebdaeadeebdaaccecaaeaceedacacaebcacbedeeaedddeedcaacabaabdeacebbdadaadedbeddaedeeaeddedbddbaedebbdabcdaadaeeabbceabcdeabaeebbbdedebdebccabcdddeeccaddddbcdeccdedaeaadbddcebebbedcbecdbcdeadbdbddedddeeedebceddcdaaacbcccdaaaecebcaabeaeaedcbddcbbacbebbbeaedcbcbdbcceccadebcabbbaedebbcbcccacbdbbcdddeddabecebdaedeebabdcdeadadcddbbaabdcabeabecabedeedaccabbddecbcaddeaeaaddcbbdccdbbaddddadeedddaeeabaebdccaeaabdbceecbcbebdeadbbcedbcdcdcedceedaeddeabebdaaacdecddedeecedabacacadedcecccdbecdeeacdaeedbadcccebcdaaebaabcbbabcbbccebbadedecacecbaceadcedbeaeedbadbccbcaeaeaadeaabccdcddeccbdabbcdeceaeeedaabdeaabbdadcaeadedbaaacdbceebdbdeeaeabedbdecbbdeccedeacaacdcaadeacbdeacdedddceeacadababbdbabbcbcaceaeeaaeeadebeaedebedbbcbeabcdeadcbbebbdbdeabaccbcebdeeedbcaaabdabcbeddbabebcbacaecbeccdabceaaaecaeababaddcabcbaaacbecbaddecdbdddcababdeabccedbecaaccebaadbddabcbceabadddbceecaaaeeaaecccdbcccdeedaabbcebdeceabbaababbeaaabbbaabbcccebaecabbeeedbeaccdcdcddadaddebbddeeddbabacdeabcceecbbebebdebcceeccdbedbeddacdbaebecdacbaebeddbcddcdbeabbdecdeeabeaeddcccbadebdaecdeedbbaedcebaadbaeabbbebbeacbdccdeabdcddddecdeeeadbdbaddbcbcceededcdbddddecaebcacbcbdeccdcbeaaaecabdbedbecdccebbdcdebbaebeaccbdceceadceccacaddecaeacadcdeeaeacedadadaecbaabeaddccbbdbebbcabbbdedbecebaeceecbdebadcbbaaecedbcbeedabdbdbceaadbadbcaaaabccdedbabbdaebecacadecaecdcabebaaadacdccbcdbcebbddcbaceececeeedbdebbdbadbbeecbdaaddbecccdddaabaccedebaecdcbeeddcdeccdedbeadbaadceaadbdcbbcedbbbecbbecceeaabdbebedecbbcbbcabbbededbdaabeaecdacaeeddedbbcceecbdeaacddddaccacedbdabcacdddcaaebdaaceeacbcecdeddeabbeedbdecbddaadeebcbedebcedcdbeeaeaaaceaaabaebaadbbebdabccdbaccdecadbeddecedddaceebddcdabcdacceadbaeecacddddbdaadddcaeadddaedccecbeebceeeacbbabeadbdbdeecddbdbacbdaaaceddedbdbbacbbbcebdadddcbbcbebdcbeabebbadedaaeacbeccceeabeccadbadbeaeeadeebbaeaabbccbdbbcdccbdceaabdbbebcdaaadbbcbebdbcddacdcbaeccecbebdceebabbbecbbebccdbceaeaddaaccbcecdbcdbedecdcadbaaeeeddbedbabcbdcabecabdcbcadbaaaacdadbbeadbecabdaddabeaeeeeacddacbbebcbbbdaadbdeaddaaebbcbbbabbcdcbbaeebabcdbaaceedbbdacccaceebabcaeacabaecbccbedcacbedadabacabddcaabbaeadebedcaeaaebeabbdedacdcaababedebdddccbbaaccecbedeeecaadceaceaedeeccdbbaeeddcbdaaadcdceadbeecdeaeebdbbceadedececcdddbcedacbdcddaeeaaebcabaaeaeabeecbeddcceeabeacbbbdbdeebaebdcbdbbedabeeabacdedcbadddedacaeaebeebeadbdaeacebabbbdbaccbedebabaabdbdddabeeecaacbeaebdcecdaebadebbceedbcdcabaeedaedbaddcaebcbbeccbddaebdadeecadbcdedecabaaaeeabbdabdbbcaeacdedbeebeeceacdccadbedadbbaabbcdcbbcbcdeaedadaceeccdaaacbcaaacbdacdbdabaebecebebbdbedcaaddcabdabbaadeedcadcebdbbeadcbdebdeecabbcaeaaeeacacddaadcbeebbebcbacaeecabdadbdeebbddecabccacacabbacccbeccccebbaadbbcddbadbaabdabdcdaadeacdddaebdaaaeddebeeeeaaaecceecebdaeaebadabdbdacaabbccaacacceedebadaeadddedeeaacbeeecebccbcbecddeccbaacdbcebdccccebeeeecbbabeeeddcebddbecdccecbadcbbdeabccebcaedbabcbcedaceabdeaaccaeccdeaecbdcbaeacdebdacaecdbdadadaabcbedbbcbadecddeebcadbdeebaadecdbabbccbcbccbeceecbbaedbabbdeedebdddcabdaadddbacbbceecdcdcccdcbdbebadcbeddedaceaeaaeceddecddcbeaaedddcececeeabeadeccadcbbabecbcbdbcebecbcaabceeaccbdcaccdadecedbaadcddaccddadacbdbaccdebedeeeaaaceeceaadcbbdbaddadcdeaebbbdadcdecbcdcccbbdeaedaeabccdbaeccacdeaccdceddceecceeccecceddbadecbdbbaaaededdcdcdedaeadebbceeaeedbbaaadaaeabedddadeaacaceaaceedcddcddeaecedeaaadaacddebdabbbcabbadceadceabacdbbdadddcbceabbceaceebdcceadeaceaaedccebdcbabbbeabcbbdddaeebeebdedacbeadcddeecedbbbbeebdadebdcbdaadaabbccecbdabccacaedaaadcecaadeddaabdcbcddcbdaeaabaeaddeddaeedcbdbcbeededcdebbdabaeeeedddcbebebebecbbbadadcdcdddcdbcebdcceebdadacadcabedddddccbeeaacaaaebdccaeecadbedaadcacbbbbbdaeebeaaacbebaccaedcdcadbbabdadcaeccaaadabdcddcabccdbcbbaceceecaeedadbaeccecededaaabcdceacbcdbcdcdabaceaaeaadccdbacddaeadcbadccaaacaddeeaabcdddbddabbbadcecdaacbbecccabdacacedbcaabceedbeababedeccdcedabadddbccacacbcddceeebbbdeddcbedcacdbabceacecbacddccbcdcdbcebadebdbabeabbccaddecacaadcdaabecebdaaaddcebededbcdbacdcdbeaabdbedbcdaceeeadaeaabaebebbabeceeddcccbecdcdbbacdeacecacdadceeeceacbceeaacceaebbcbdcebbecebeccbbeaaecaeeccdedbedadcebacbdbdceedccecdccecacbddbdedaedededddcacbbaedeccccedebabcdcbcccaebedaebdaccbbecbbbcecbdeedaaeabcadbedcebbdbaebdedbcbdbcbbdbcebbdabbdaccdeeddddaaabdccbeaecbceedcbbadecbaddbdabbdeedcdabeeecaedcaedabcbebdebeeaebecbcaebdcbdbeaebedccccbaccdeecececcecccbddbecebcdabddaecabaeeecedbaaeaeadcaeccbaeedceabaeeadededbeadcceabdedbcedcaaebcccbcebddedceeadbbacbbebcdebebdddcadecceebeceeaccaebaecbcdcdadabbcdaccbaeabbecadbbcdadcbbeddceeebbaabbccaebccdeebdcdeebdaccdadbbebeaabcedaacaaebbaabdaadadbeaaaedededcdecbebaaeabcbdadbebdcebababdcdcecbacbaeacbbeacabccdadaaeebbccdadebecabadddeaacbedbbeedecbbdaecaaadeacbaaeccdaaeadcdbeabcdceabeebbacdebaccabecbbbcbcecebedeeedbdebccdadeaccadcedcbedecdbaecdcabdcdabaeeeedcebeecbcababaebeedcddecaceabcbbdaedadbcaccbcdcbcaeceaecdcbabdecaeccdedbeeabaecabaeaccdedaebdabcbdaaebbaedbaeadebbcaddeecddebeabcbbbbacdbcedeecdaaeceebdbcceedcccaabcdcdcdddebdbaaebbaeccacbedddcbeecbdaabbeaaddbbcaaaebaaeeecdaaceeacadbcebccdebebdaceabebcacdadadacdaabeabbaccdcbeddbddceadbccdacecacabadcdddceecbaaabedcabbeceedeecabeaabcdddedebedcdeedbeeddddcbbcbebebdacaeddcaccbebbebbbecadebdcdadaccabbdedadccedcbbcbaacbeddcbebaadcadaaeecbaceaacbaceebcbabdeebaadaebaaacdcdcbcdaebaccedebeeadabbacbdbabdbbdadacedcbceacabbcabaacdccdcbebaeddacbdcdcabdceddbbeeeadeadedbcbbccbcceecbbddaeaaccadacabddabeeabaabeaedcaccbcceeeeedcebbaeacdbdabbbcdceaacccbcccbceebacaadebceaabdbbaccedddabdcebceababcbcbbcdbeabeeecdabceacddcaecdccbadabaebaeceacaadcecbcbdccbaaaceeadabdaaccbedcdbacdedbecaabccacdabdaebaeacccdaaacbceabadaaedcbcebcdaeeedeceaadcccebbdcaacdcbddcdbdcacbaadeaaecdeebdccaabeadeaadceddcdaddcdbedcbabeebbdecedabaceedaecdcbdaeabddebbacebeecabecbabbcecaecbcbbbddcbdbdcaadeeccacceebcabcaaddbeecaaeedadebbcebcdcbbaedeabdbcebebcadccdedebabaeebdadddcacadddcddbaeabbeaddccdeeabedbdaaccbeddbaabebdabbcadcaeebcbccbbdaeaadbaccdbaceccbabbdbacbddcacbaeacaedabbaddbbbbccbbacaabcebebcaebeccbebeeadddadebdbdcdccddcbdbcdeabeedacacedaaebceacabbceabbabecadeacbeadcdaaacaacdeeddeabccdaacdadbbdcaeaebdbbedabeaecebaaddcceeecdebdccceecaaebcebeddddccbcdddcdccecebaecdddbcebadceaebdebdbeecedddecabbebbcecdcbbdacbacbeddbdcecbebedeedeceedbddadccadddbdbeabbadecdbbdcddeedbbcddbebacadacadbadaeabdebebabbceeadbcdccdccaeaeccbacecdbacebdcabaeabdbbbdbdbdcbbbedececdbbcbedddbdcececeebeaeecdaceabebaabadbaaaedaddcdbeccecbeaeeaceacaedcccaadceddbdeddbdbcdabadadcecebddbdebacedbcdeecbddecbbcdaeeddabdbbdcedcbbdeaecedbadcaadebaeecceddcadecbcdccdaeacdccccacaceebdebedaaaddabbbecdabbcabcddbbadaddadeeccedcdbbbbebcdcbeecdacabbcdadeeebaedcdeeececedecdabdcedecdcaadcbbddbbbbdcdaaaaecbaccbddcadeeecbbcdbcebbadbbaeeddeceebdadadbdcebdebbacdaceabcebedbbdcaecbbdcdeebcaeeabdaaeecdedeecbecbaceedaedddcaaabdceebcecacecaaaabccadccececaeedcbaeeaddcdededabaccacddcabaaaacdaaaceaadccaccceddbccbbdaceeccebdaededdcddcbbecedabdcccdabcabcaadbcbeeaaeaabeaabbebdeaabebbccebdbaabeedbdcaeaaeedecddadddaeeaddaedceabbeabcdcbbebadecddccedaadbddddbcbaeabebaeeaddbceadaececcccdbdbcceacbcacacdbcabbebbeadaccddccedebeeaebdaebdeccceabdedeeadbecddadbcaacadbddcdbddacaadbdcbcbaecadbceeacadaceedbdeaebaabcddcdbdbeabadbdddadadedbbceaddebeacbccbaecbabbcbebdbcbabcbbacdceeabbebebaccbcabdaadaecbcaadcacdadebeeccceaaaeceaacdbaabbbeedcaadbbbddcaddcdbddcedddcddeeeedabbdcabebaccaadeeadcaaeedeadbededebedcbaccaddbaaedcedaccabacaadeddabedcbcacaacedbaadadbdcebdebcbeaadcaacdeaacbdabbadeaddeadaeaceccadbebaddedacedaeeaeabdeaaedadbeeeebbecacebbeebaaaeaeedcbedbacaddeeeedcaccbaedebceaccbecaeccecbbbaccaccaeedbbcbdcdedddabdbeedebcbdaeaacebacdabcaaceacbedcbbcaaaecbeebbeeccadcdbeaaeaeadddbaeaddbbcabcaecdcbbcedccbdbcebeeaededeecbdbadbeeaacccbedecebdccddecceadaeacacaaccccbbaaebabaecebdddcacddadbbcdaaadddccdbaabeabbeaaceebedeabbcdbdebceebacdacebaacbeddebacdaeecbdcdbeddeecbcbbbeccaeedeecbbaabdceeabecbeceddedadcdbeaaabbdecdbacdabbecceccaeeeeabbeddbbceceaabdbabacebbabdddeceadddbaeaadbbecebbababcdebccabbdacbbaacaddcdccbeebbdbedbeaccdaeccdceeccaaabeaadabacdaccadabbebcdecbccedcbeaaebedcdebaecdaeceedacebebdeabccceeebaddeeaaddddbaeccaebebdbcadaedcddebabdabceebaedceeacabdaedabbdcbbebcabccccbdecbdddedabbabddacdccbcdddecebaddcebbbeccaaeecbeedbdcdceaeeebccadabdebabdbadbdeeababbdbbebadadeedeccbdbebeedbebcbaedabeceedadeeddebaeeddecaddceccbaedbeddcdaaaabebdbabeddadcecdeabacdebbadcecabcebaeedaabaadddecdbcbbbaabeecadebccdacdeedcebebaaaabbecddeccbebaccaddbaddaaebadbbaeeedcbbcdbaeccbbaadddabadddacccdedccaebaabacbdcdddceebecebbeeadceddbeadadbebbbedbbbedebdcecbbedabaaabbdaceaabdaeaacebcdebbdcdbedecdcabebecebadbecaaabaeadcddeeaddbacedebedbedddbcddaebebddeeceeaecddccdeebacdeceddbbedbbcbaaebedbbeeeeedddcdeeeecdbaeaebcdbbdccccededbcaedabaccbebbcbcecbdecbdbaaedeedbcaaadeccedaebabcbaadcadbcababbdceeeeddcdedaecabbceeacbcbdcbcaceccdceeddbbceadbbaeceddeddaabbdedcecabdceceaddebbddcdaeedbeebcaacbeaacdbbeabcebbcbdaccabcadebebbaccdaecbdcaebdebdecabcbaebcaeecdddbbdeacdaeadaebeccacdadcddcbccccadaaaebccacaeadbddbacaccdccceccdaeadcdacecbdadbcadabaeddbebbbdbddaddeaebdedcaebaeaaaaecbcbdcecbcabbbedbdceaadbdaaaabdcbcbdaccaebeabbddcdbadcdecdcdaaacbadaccedeaaccadaccadabbdaedabcacdcccabeaacabbaaeacdeacbceedbddbdeedcabbedaeaeebaeeaeaceededbeceeedddeeacdbeebcbaedbcdebaaadcecccabacededbdbccadcadabdaacceeebdbcbddbaccebbecbbbecddccdebaecdceeaabcadabccddecbddddbbabcbbbdcacbbdeaeaeabdbcaebdebbdbdbebdbeabcadeecabeccdcddbcbcadbccdcbbcecebdedacdadedaaeeeaecaaeeccebcedcddedeaaeaaaeebceabcedaccbaacbdbcbdacaccbedddeadebacccdbcbbbdbcdccdcdddbcadadadeaddbadadeccdbddecdeecadcbbeacacadedcacdcddbecbbceaccbaeacdcaeaeeebdbdbaadadddcacddbddabcaccebddbddedbbcaebaebdcacacbcdecbecedbbdadbbdeccaedadbdaceccedccedcdebbdacabcdecabbeabdbcbeadbccccbdbaedaebdddbcacecdecaebdcecbeebcebcbccdbbcdebbbabebcceebbaebdadebeaaabcacabbceeaeedbdbedccdbaddcdcdbbbebebbbadcdebcdbaacaaaeadbbbcbcabcbdcbbceeacbddddbbdacadacbebacbdddabadabcaeeaaaacedebbabbedabcaddeedceaadedbccecacbbacbbeabaddaaabebbaeecaeccbaebeaaaeabccebeaebaadabacecbcacdbdedaaaebecedceaaeedededdcecbaeeebdeeacbedbcdedadcebcdacccbbcabceadddbedddadcecebbedabdcdbdaceaebcbbeeeebbbacdedccdbcebebbdbadacdecdcedbacdbacaaacceebdadaeabdbebeddccaabacccddddadbbbaceeecababacaadaebdcbdbadbbedadeeeaabbaacddddcceadcbeceaddcdedbaaeccabebdcdaebdcdcddbbadabddeccadcbcaacdbbeeedcecaacdddbebdcbdccedcebbeccdaacaaabababcabbecbaccbcbbbddadececbeaadeebecedabdccbebcbeaaabdbbacccaaadacaacdededebbadbdaeaadddbaadeacddbeeadcbedebaacbdecceeacdddbbeacaeaaebbebabcbbbdbcadccaeaacaaddecdccceabecdbccbaabddadbecaabaabdcabdaacaaecbdbdadaabdbeebedeeaeabecbcbcdbecddeddcaaaddccadeddebcabaecaabaadabdeaacebdcacddabbdddcaecdcdeadaccdaaebcbebeeeebbbaeadecedbedbdadcdedebcdcdeaadadaaddabcdbdabccacaddecdbbeadaabbddcaaacdbecdedbaaccbdcebabcceebdcdacdebacdcecacbabdedadceddccdaeadcbdbccbcbbcaecacdcbdccdacdeddccbbbbdcbaaccbbddbcaabedebdcdbaccaeaababeaedecbddddeecacebccddcccceedceeeeedadcabdbcacebcaacaacaaedbdddbaccbacbbebdeceaadcabdcccddcabeacaebaaacdeaedcaabaeaeeaeaecdbbedabeacebecbecebedcddedbdeeceeecceabddcbabaaebeebadcabbcecaedbccbcaccaecbcdbedacbdbdbeedebababdadeeaccdcbabcdadecebdcebeeabcbadeacbeebedbaaedbdbebaababcdccbaedabceebaacebbcedacebdececeaedbcbbaaeacdccaddbdadacebbecdbecbaaccecddbedddddacbaadcdbbddbbecdcdddaabccbcbcbdccdcbaaaaadaaedddabccbeedcadaceddbeeadacdbceddcbceaeeebaaebbdabebeabdbbcdedabaddeccabcacdbcecdbebbcdaadcebeebbcbdeacbcebeaeebbbbaadacdeaadcaaeebcaacdcedaaaebdaaeeedcddbeddccddceeaecdadababdaadaceeceabcdcbedeacbedabcccdeabaedbcdcecaceaabaccdbccdaabddecbcbdecccccaeeceeedebedabaebcaeccadeeaeaccddddcebaabadbbdcddedadbdaeddcddbedaaebbeabdcaadeccaddababbdbcbbdddbeaabedcbebdaadbdadcbcdadacdcbededdaebbbeecbdbdabbbcabcadacbaaccbbaedbeaedbbacdbedeaaabaeccbaecdaeccebdbecacacbdccecbdeebaaaadaaeebaacedbbdedaceecdacccdbcdeedbedcecebedacbedceeaaeeecdbcedddcecbcaebdbdedeeddcaadbabebccbaadcbbbeaebbdeecedaedbcdeccdddeaceebacaaddcccdcabddaecebcddebaaddeeccbaabbabbdabcbaadedaecdaaedaaaeebbbbabbeabedabdcadbbeeebdbabbbaccedebdcaccdabbbdddcdcaaeaadacccebbdbeddbabadbeaeadddeaeaeeedcddcaaedbcbebaccdbecacbacdccceebedabbcbdeacecaedbbcebedaaeadcbccebabdacabdeccecdaadaceaecabcaadbdabeacebdbdacdbccccedcbbdebedabdedebeedeceabdaaaeceddecccdccdeacdbebddbbbecbcacbdbabacecbbeeaddaebcdcdccdbedaeacadaaaabaabebecbdecbeecbeceadbecdbeaeacdcdedbecdebdceacedebeadaaceceecbcdceaeabbeeabdabebeedaabacbdcaccdceecaaaabccacebdbdbeadceebacaeeddadcbaeddcdbeccacdddabcccecbededaaeaaccedeecebddabdddcecbccbbbcacebeeadbeaadbedbdcddbddcebedbcbdedecccebdeaaceadbabccaedbceeebdeacdcbabadcedbbcadabebabbbabdbaaedbaaeecddbdebbdaeabbadbeaedbdcaebdbeeaacdedcdcbabdbdeeddbbbedecdaaeadbadedadaebbabcddbadeeebedcdedcdaabdccdceedecdadbacdacebecbcbabdcdccbdadebbacbeacabdebeacacadcadbcaacaebdecccabdebbaeddaebbaedbdcaecceebbacabddcccadacadebccebeeeacaedecedeeeeaddccebdcebaccaceaaaacbccaedddedeadbcebacdacbcaaeddabaccedeccbeeedbeebbabcbacaeaaeddaaabbcbdbbcbabddabbbebedaceebbcbbceaaddeaebadeecceebbdbeeeddabdeebdbdacabaecdccedcbddbbaacdbbecbaaecebbbeccecdededcbeabdbdbaaebeeaeebbadbbcaebbadecdbedecceadbbddaeeacbaaddccaacdacaabeaeeebacdbdadadcaeddcacbbcddebdadaaebbaeceaecbedcacdeaddcabcecebddebbecebeadadaceeddaabbebdcccedbabebeebccccadeccbdbbccacadeeabdeadedcdadcbbbaeebedcdbcdbedaeaecececaddbcddcdbababbdaccbabcacbedebbeeacdbaeaeccecdcdccceceadadcbacabbeedeadebbedaebdbbbcedcdbdcadbeaccbcbcceadbbedcababcedeacaacebaeacdbbdaabaabadbeaddebeebabdecdccadaebedbedecbceabbbcbbbaaedadaadceabbcbbebbcbdcdddbdbbeaeabcbbadeabceeeaecadbecaeecedeeeedaecdedabcdbdbabddbabebbeaedeacabdabbccdecbbacebcecebbebacaeaccceedcbaecbedcdabddceeadaccbedaacbddecdadbbdabadddddedacddbcbcadbcbedeebaddbcbdaacacdeebdadbacedebdceaaaadaceabedeaabdaeeedaebcdbdebeabbcdcadababbbbdeeedcaadcccdaeadbccaccdbebaebbbbaceeeaacaacbedeaecaeadbeebaacebdaaeedbdebcdadccadaacdacdbabbbecceacbabddebbebebaddeeadeacdeadcdecbaddbeabbdbabbdbabebacdebcbdebadeacecadadbbaecabacddbabdadcdedbebacaddebcaadeecccdddacdbaeeeaccbbaacbcddddabbaeedcdabbdedcaaecdcdcaecadebbdbaecaaeebecbccbdbeecdecbeeebbbdcecadcbcbaddaaebcbbdceabebaeaacdcedecbbacaedccaecbccdceebecdceedebabcacccdcedccbeccdadbddbbbbbeeebdbbdcbeadeaebccbdddadcccbbccbcdeaabccccebbbbbbaaaeaceebbdaeaaccceeecabcbabeeebbdbbccbbaaaaccaadbcadebbeeaaddeeccebebdceabcdaabddeacdccaccbcdcbdadcccdaccddedbebeadababebadecedcbacaaaeadeeeebabaadeddddbddacbecddaeccbbeeaddcbabbaddcbeadaedddceeaaeacbecaaaecebdbdeadbcaabebadbccedeedceebacaabcbaaddaaaccadebcaaeacbaabdccbccabcccdeccaaceddcdbdeccdcdccabadbbacebddeaabeacdcceaeababbbbbcaaebacaababedbcddaebcedeaebaacbcdaecdbcddbcaeecdaacdacaeceaaaecdedabaabdbacedbaedbedaacaddddeecaadabddedbdeeabbdaeadaeecbcbbabaebdaeadebdadeeecbaddbecaedeccaeacbccedbeeddcaaecabdaddaadababcbcdbceadcabebeebbbdccacaabdebcaeddececaaeaacdceebadaaaedbdbcabebecededaadcccddbbbdacddaaeedbcceeaacdabaeadddeaecebdedbbebcdbdbecaddcbdcdcdebaeaebbcdebeccebadeebeaddebaeadeebdaecedbbedbbbcbebbebcaaecbdbddeedddcdedcedddcddcddeeedbaabbeaebcbbdacccedddeecbbdcdaedbedcddcebbaaaabeaccdaabdabceeccccecdaeeebacaccacecccbbbbbbbcdacddbcedbeecbecbbbbedeaaecadcbbebcaebeddadaddebcbaeaeacbdcacacbdacedebbdbacedcebdebdceeabcdadccadbaabbbedccababcaaaecccdeecbbdddaabebebceeadecdacbbbbabecaddaddbbeebeeddbbbbbaeaedcaaeddddbbecabbacabacbccdaebddecccacababbccedbebdbcabdcdbcecedeecccddadbccaedaabaaeaccedeadeacedccbdcceddaccddacaadaccbbaeecaadbdedaceaddebbddcdeadbbaabebcbecaeedbdcdbaddbeeeadeecbdcdeacbdedccdecadbacadcccaebbacbabedbdddbaeabdcddacbbebddcbdaeeedadbcdeeeaeabbdedbcadecdcecaebeeccdeccdccbaedeeeaaebccbacdaacebeccabbaebadbddeeaddcaccceacbeacddcdceecbabaaadababeaabbdbdccceaccaedeadecbbaacadcdccccaeacbbbdebdbddecdcdeccebdbdbdcadbcbabccebbddacecaaccedbdbbcbceecdceeccaeebebcdabeccaaeebaccbcdeeabcacdbdcdaeaacccecdcdeebdeabbaeaadcccbeabdbccceecededadcbababebedcaccdbabedadaaebbdbdaebbbedddccaacaedeabaeacddaaeeeddbbddcdbedbeaccdcbdeaeacbdabacaeabecbdceaabceccacaedaeccbddadbbdebbaeadcadeaeedbdabeddeceebbecdacacabccdacebdcdceaeeebecaccbabaabedcadbbecabdaeddcedcdaacbeeccddabdeeecacaddbaececedaaccecdabcbeccabebcababaaabacacdcdaeaedeaaacdebcbcdbaecacdecdabcabbdcbaeaecdeddcaccdaedeecbceccdedaeadaecebcddcadacbceadcdedaccdcdbecbbeadbddebbdaadededdbbcddaeeaeedceaaaeaedaeabecbcaacebdbaacebcadacaebbdecabcadaacdbaeebcdcaedbcadbeebbbeeeccedcbdceaccbecbdebbcdaabccbaddcbabddaebaacaeccedacdaeabcabedcdbbeceacebcbaddbdeebbbddeebdceeabebabbaadcabececbeaaaeeebddedbebcddddadcedceadeeedaeeaddeebddadbadbabdedcaabdeeaddceeabdabdcdbdbeebcccbabcdebddadcacdecdeeadbccceacecbbeeaedbebedcdbbcceaaabbeddbdbaddaecaeeacecedebbcbabcdcaaadbddaeeaedbcddeeeeaabaeaccaebedebebcadaabccdcecebdebcedcdbdceaeabeaeebaccedddbdabaccedbcdecbddddaeebccecdceeceeaabdbcbbacdabbdddcebeeeebaaeabbbdedaedcaaccedddedcdddeabcaecabeaaddcccaeddebbbbebcdabdacbbcecebccddaecebeebaebededdeaaabecabdeacedbbbcceaaebedacbcdceaedbebaccdccaeaddbdcacdbbecadbacaabecdadaddacaaacebaceabccddcadbcbedddadabaadeaecdebbeedaccaccceeeaaabbeaabcbecbeeaacbdcacbddedaecaccebabcbdcadbbdbeedabebadacddceeccbbebedeccbaeceaedbbecadbcaccdeedbdecddedbadcccecceddacbddebbeaeadddebbabbcaedcbeceaccdbdebdabaabbceeddeeddecbebaddbcddedceedcabdbbeaecbbdccbeaadadebcdedadcccdbcaaecbaeecdaccbaeddcabdbcaebeebaabaccbbdcceebeddcacbedcaeaddaedcabcdebbddeceddcccaeaeaadcaeecebcacbcebdeacaaaecceddaceecdbeceddeecccbdaadaebcdbbebcddeeadedabdbbbcaeeedbecacbdaeabbdbbebadadcbdcbebbceedadcacccabbcecadeeacdbbccaecedaedbdcccddcdaadbacabdcebdaceacebeeadcaeabbecbbcebeecadcebacdbecaaacebeceaecdcaeaedbabdbbaecccacebccabbabaceeadbdcaaadadbebabeccabbdaacddbecdedabedaceaccbebceeeeaaedcdabadeebaebbaaeadecbdbceecacbabcbbabcceebcaadceedeecaddeebaadcedddeddaebacaceebaebbaadaceaccdbaccdbbbacbabcedddaaddcddeccebbdcdccbebbbecadebbecbbccdbdbeaeeeebbeacedcaeeaaadccaedebdaaaaddeaeecddacddbbddcebbdbedadbddccdecdceeeddeebbbedceadcacbedacdcddadadedebabebcdceedbeaedabedeadeaccddeacaaceaecdceadccbedacceaebbddbacceaebdbebccbbacdccecaddbccccdecdaaaeaacbeacceaabdeaeadebcbbcadbedadacddaececdacaddebaaeebcdaaedeabeecadbdbbaacbadebaeeddceccbcebacbecbeadbdecadbebedacbbeecabceeccdaeddcaeddaacdddbaccbaddcdacebeeebacecdddbdeebecedbbedecdebeddcbccaaeeecbccdcccdbddbabaccddaeddeecabebbccebcdcdacebaccbedbbbccbaaddbedbdddbacabaeccbcbdcdaecbcdcdaebbcacecdccbbbaddadadcdeeceaacddddebbaacbacebdbbcadabcecedaddacedddcbdedeebecddbbdacadaedecebbcadbebbceacbcaeccadaccabeedbdcabaabcceecccecbdbdabbdaeadeabcbedeaabeaacdcadebeaaabadedebabdaeaedcdabbdddedcbebbdecacedcbcababdcccceaabddeebddedebcabbdeadcbbccabccbcecababdcebbedbaeceaaddcdcebbaeecbcaabbccdcebeeadbcaaddcacbeabbcebdaacdacaebdccbebeaeebcbdcdccecadbdaddcdeadebadabcdcdbdedebeddacdadeeabaeedabbcbeccaadebedabcdcddceecbbadccbebaaaeceaebcceeaeaaeeeeaaecacdddebeceddbedeebcdceabaddaecdabeceddccadebcdbcccdcdeccddcabaddbdeeeecbbbcecbbdaedaebaddedbdbebeccacdcccbccbdceeeacdeaaaeeebdedbddddcadbcbccdcdabbcebbbccbdaabbadddeaaebcbcebeebdceaeaebccbddabaceeeddedddddbaecdcdddcdccacadcdedacaddebaeecaadbaaaededdedebbeabeacdeebdbcbcccaacdeddaaeaaaaceaedccaedaeebcceadadccadbbaaddebaaedebecadacababacdbaaabeedaeedaddaeedcbccadacddbaacdaccccdaaecbecadbeaebbcebccaccdbcbebaadeeabaecacdbeacceddcaeabcdacbcbbecadeeabaaebdbeedaddcadcadddeabaaeeaecaecdcbdbddeaccdedaaeeaddcbeeedebaddbcebbcceadcedccdbedcdaadbaddbaecabecedaaccdbdbbbdcaaedbcbdecdaddbeeaddacaababbdbcdaeeeeeadaadbcadaedbcccabcdcabddabaaaeddbcebeeacddaeaeddceeebcbcbbdccbdcecbaeadeadbbcceeecbddeaebadebccbdeabcdaadabdbbccedeedeedeeeceabdcdabeadddadeadeddeceabbaebeaeabacccbceabdaccaccbdacdecacecabaebbabcdaecaaceaccdcdcbdcdbaceaceeebeaccbacccbbeaaccccdcacadebbbccacbbbbeaceededcaaddbaeebdbdeccaedacbdbccaaeacbabddcccebdbcecdedeedceaddcacadadacebdadadebedacdeeeeecdbcdbeadcceaedcacbdbbaeaeecbcbdbcdcecabeccedcedacabdaedbbcbbeaaecadbecdbacdedcdcaddbdeadcbcdcbededdbbeabeabebaebedadddddeecadecdddeccaeceeaebebadabeddacabdecbbddbcacbdbbbccaebbbdcacbecadaaaeeebdebebbaedddabedadabceebaeedebdbebdcdeedebeeccecbdbeaabaecbebcbacdccedabaeadcedbcbbbabdabcabacdaccdaecbddacccadcbbdcbbaababbaddbeddbadadabdbeacdededeccbceeeccbbcccbcacbdcbbdadeadedcacccbbebadbbdabaccecddbbdebbdbbeeeeabecbdecedbbcadedbaaedadcdcbdaedecddeaaacaecbddacbdaabbddeccacdcaeecbdccaeacaddcccadddeeaeceebeecccdcbdbeabdcddebdedcccecaddeeaaebedaccbcedcececeabadeaadbbaacccdbdbbbecaceeccadecbebecadaedebcacbeeebbdcdaadebddeecedcebbbbaadbdbbdddbbaeaedecebacdaebdabdccaaeeacbbccdecbeeacddbcdcdcddcdadddadcabbabebbaebaeeadbbedbbbdeccdbcaecacdcedeacaeadcaceeaddcdbdadadabdceaccaaceceeeeeebebcdabeecbccaacceeaddbbaeccbaaadddebdbcbaeaebcaaceebceebdaaeebdbcecdebdeaedadeababdcbbdcdddcadedeccbaddbbdbdbadbcbbbbedcbcaddeccbceadaaebdeececccebadebaeeecaccbacabccebbcaaceccabddcaadabbaecbdbcecdedbaddbadeaaddccdacbeabdabedbeecbbbdacaacecaeecabcdcadaacebebaeecbbbcaaaeadeadcdaaedacbadbcbcacddddcbebccdebdeaadeccdcbededeebedccddeaedcbadbbcceaacedbeaabdddcddceebdecbccdeceeecadebeedaacebcbcdabeaaebcdcbcabeecdddeacebbebcaeedbabaedcdcdaaabcbbaaeadcdecceecdcbabeebeceabcdadddbedbecedeceebacacaacddabbecebdddaebbadbaccedcdbcebcdaddebeeeddaaeccbeaaadcdeadcabdeccdadcaadededbaaecbdebbaaadebbdcecaecadddcbbdccaaacedacacbcaaeaceddcddcbadcecedbcbcbcaabdccabcbdabbdbdbddeabdadceadbdddaaddbbebaeceeddcabeddbccbedcabaaebbaaaacaaeaeebdcaaedacecddacbcaabbbdebcdeaceaebcabeddbecccacbacebedccacbeddaecacddebcdcdbecaddecbceaaddcaceabdbaedaacccdcecdbadbddbdbbaacbdcaaebecdabbaeebdcedbdcddeabacccaceeecabaabedaacbcececdcbddcbcdeebacabedeedcbabeecaccbaadacbcbcaabceeddaabaeaeebaaebedbebcecaaecdbccbccecdbcbcbccdcdcacacedcceedbbcbabddddacbdbdceabcacaedcbdcecceaceadecaeacdbaebdbbebddbcdecedccdcbbebcbdecdcccdeddebceaeccaccedbcabbaeccbccaadccacceaadccdeceadeacedcaccedcbdcbbddedddabdaeadcddcbddecebddbeaeeedbceebeaceccbbecaabebbdabbcecacbeebdcddebcccedbcacceadbadeedabacccdeddcddbcaaccdbbcbedccadeeedbbaabcbebedaaaabddacecedecdcedcdecadeabbecdeadcedacdadadaeecaaaeddecedcdebdcebcdeeeaeecbebdbbddebaaeeedbaebdbdcaebddabcaeddabcbedaacaecdacbdbaaccbedccadcecbedcecdcbcadeeeccbedbcbeeacadbdaebbdbbaedbdcebbbbaedddacdaeeabeaaceddccabebaeadcaaedbcdbacebdeeabddddeebacbedceeaeaaebdbbaaaceaecabcdadcecbaaaedaacbcebecdcddaeccaacaeadaccdcddcbceeabdeceeabdedeccacdacadeebbccaeeeccabdbabdbccaceacaeeabcadeddcdcbacdbeadaabbcbbcddbbdccebeaeeebacadccaccabcacceccedabceeeddaccdeaadeadbcacbcbccecceaeaddbcabdaecacbbecdbedeacaceccaabcdaeccedbacecdabedebcedcecdeeecdccccaeedeebaedbaaeedeedcaedeceeaeaaabeeabdaebecdcebaeaeeeeaacdceecaedbedeadabcecdeedcababcebbdcbbccaaaaeaaaaeeeacdeabcbbbddcebdcbcecbebdcdabbbcdbdbabedecbbeeaebecddddcbcbbdeaedacceacbbabbdbccdecadaaaddbecdeeacbcbeacebecadcceecdeceedadcdbedcddcaeeddacdbadcbabcbdbdaedddcccccecaacbadacdaabbbdcdbadccddaeecccdbaeadaeedebcbacccebdaceacbceaceaebdaeeecaecdebcbbaaebeeaeecbdedaeebcebbddecbbcdebebbceabbcededaadddeddeebebddebdacdeaddadeddcabaeabbdadaccbbbaebccbaabeccdeeaecedaabbabdbdaacaeedccbaebdddcaddcdeebdcbbcddeadabbecdaadbabdbadcaddedbbcbdeddebccbcbbcabeebaceedaeedabeacebcccaaeeeabdbaddbeadddaebcacecdceaacccadeebdaabbcbeededeacdaccacddebbbdbaadbdaedcbddcbbbcdedccbedcdbdccddabdaddecdcbadccdeaeaedccceceeaaebcacedeedcbadddeabcdcabdceeaadaddaecbddecdaacdbadbdedaacacadaaeddedbeecbdecabbcedcbeecaaeebabcedbdcdadcacdadebeaaadbeeeabacdbcabaadabbbbcbacebcbcddaaaddaebbbdebceebaaaeeeabbeacdbceecaebaadccecdcdbceaeeeeeecbcecbabbbdecabbcbbbbddabababadadcbddceadceddcdcdacedabebdeabeccbebbddddababdceecdbebdbabddbaaeadadbcbbcabaccbcbcdabcaadddabecaeeadbecccabedbdcdabadeccdcaabcbacdddcabeeeebedbabeeceeeceeaebabaedddaedaeacbceabdabbbceddbaceeadbacecbbeabadecddadaeececbceeddaacbacadcacdbcdbdaedcddcaecdcbddbbbcceabbdeacbaeeebceaccebcddeebadbeebbdadbedcbcbdcbeeeceabaadccbaabbaecaeacddecdeeebaabadabcaebdaeddaeaadacddcccdbcbcceceadcedcbadcabeaacdcbaabaadecddabadaaaaeeedbbddbdabaecdaeeadbabbeababcabdecaeebdcaecdadeedceeaabbbecdecacdbbaaeaaddecaeeaadecbdaceadedceabecadacaabcaccabcbbdbecbcccdccbbcdccdbebababcdaccbaadddbdabbaccceaccbaaeaebbcadcebaaaeddedcebaaaebbecddaeacbacadcbdcaedebdeeaadbecdaebbadeddaabbacbceaeaeddeedbbdabaaabcaceaedabbddecdbbcbccbebcddaaaecbeeddcceddcababacbcceaacadbadaeeebeceadeaabacedceabcabadbebcacbeadbabdacbaeeaaedccabbdbdbaaadbbebeedbcadacecceacdcedebbcdaadbeacabcebacdceeddaaaeabdabdacaaebccbdebabbeacdbbbbeecacaceaeebecabddbeadbdceedacccbcdeacedaeceaceecdadcedbeebeddcbedeacaecedcacbedccccbbeacbceaeeeadabddcdadedebecdccadbbbcebaabccceeddedddaadcbaecbdbacadeccbeaddaacadbdbabbadeddedbdecbddeedddabbbbbabeadebdacbdecabacadcbeddcbaecdcdbabcaedeeebcdcdaaeeecdcadeecadedbccbaadcbeaddecbaadebebeaaaddeaebcbbceeadbaeccaecbaaacbcdbcaeebdbdeaddeeaacbaeecbdbbdceabdadcddddbdddddbcdcdcdcbdedcbebbbbcaccccbcaedbbadeceadcebdbbacaeaebbbeacdcebeccdaeeedddecdbcabbbcdccdeebaedbddddaeaaeacececedaacdabaacaedebcdcaacecdaaedeedecbcccadcedeaaeaebdacebdcbcbacbbdecbabacbdccabccbebdebcaabedbcaeadbeacbebbdcbcbeeeaecbdacabcbdeeebebedebbddabdcccdbdadbceebdbeadaadceccaecaadecabddcbcdddeacbdeebeebeaebeaceacabddcdbeddcbdbdedaddaebbeddabceebddebceccddacdceecebadcbaceacaadecededdbbbddbdccdbbdbddeaebedcdcceedceeeeccedbaccdedbbedcabddeeaceaceecbaadbdbeeebeaecbaccaccdbeeeadbeacadbcacaddddeedbdaeaacbaebcdeccbeddbccaabedaeabbacabbbebbccccdaeaddcdcecbaaabdcbeaadddcaecececbabcadadbdacbdccadeecbceabbcddadccadcaeaccebaaeabcbeedaedeeaddeedcdecdcdadacdcbadbbadabeeaacaabacbccbcadcedbaabbcadbaecceadbbeeecbddbebdcddadecbcbddccedadbedbacaedbaacbeadddccadedbdddedddcdccabaceecdeeebdccbebbcdcdadcccabbabadabdedcebcddcabbbabbdcacedcdaeaacebbcadcaceabdebaaadbdbedcbaddbebbbdaaedbdbdbbacddbdbaeaaadeadaceabedccccccedccdbadbdacaddcdcbcaeabbdedebeaaaeaedbcabeeaaedbdedbadbecadaeebbeabebdebcadaadaabbdaddceacaacbbddabbccdbeebcadccceaceedaabcebaccdaedddecdeccbebbceacecacdedbdabbeccdbbbdebebceebdbbbaaeceeecdbddaececaacdcbeabbadedbbdcebdbedacddbbbedccadedacbacedecaaabcbabdbbbaadcbddeacbdccacdcdeedbcdbceeabddceaeaaeaebaecceaeeedcdcbebbacceeeeadecbbadbceaeaeedeedaedeaabaacbbdaaccebcbbbaddabecebdcccabbedbebdabcaabddeebbedbddeeaadcaacdedbeeaeeabecacaacceebbdadddbadbdaabbaabcbbbcdebebdaabeccbadbcdedddaccecbeacdccabadddacdadbdbadcaaeaacaaddadaeccadcbddeedcedacdeaadeaaecedddbeabacaeddaecbaeaeecbecdbaebbdadaeccecabbcbbedeeaabeebebecebadcacddbdadeaeeaccdeebdeaadbabedaaaaaaeadcceceddeeddcddeaecebbadcdbbeeedaeaeacaaddddbbcbddcececcbeceaeecdeebbacceeddaeacdcdedcdbddacbdcebbccbbcccccbecddebccbceebbbabcaeabbeedebabcaaebbddeccaaaeeaddebadcaaabadecaedcddcbeedacaeecedbdcccbccdbccdadecbdcbaeebaacddaeecbaeacbbecddeaecacbacbcebabaeeaeebadebedbbaabaecabcdabaccebaacbcbedbdccecdedcacbedaeeaceeaabdbbaaeedccccbddebbcabdcddaccccecacbaabdbbbeebeeadaaeaecdbdbcaebcdcccbbaaededbccadeacbbcdbbddaaeecdddbbbeacbaaabaebcabdacbbabcbbbacbdddacaddbabceeaaeaeacebbdadedacabbacddeeeacedeeebcbddbeadaeeeacabdebdaeaacdececebcdbcdbcebbbbdbbcabadcdadddddacbccaddedcaeccbeeabcdcbceacdeeeaaceeccdddbaebddacbaddcdbedacdecdbddebdcdacceaebdcbeabecaecebabbcaeececddbcaeedbeeabcccebcacaaaedccdbdcbcededceaeeebbdeecbadebebeccecacebeadddbaecceebddcbbbbdeddadacdddedaebdacaedcdaacdbbbecdcdacaceeaecbcceebadcbdaeeeeeaadbeeedceaacedbbaebabdeaeeddeccbdebaeddadceccbcdeacecdccecbebacdeacedbaceebdebadccddbabcabbaaadeeddeecbcbabdebcadbdcebabbbdaaabebddacbccbcccaebdceacabeaaeccdcaeeccaeccebccbebccbcabbdceecebeedbceeecbeecedbcedeeceeececebccdcacedaeeaecbacacdecaeedabddcaecddcbbcdeecddcebebddcdaccddadceabaabdbbaeddbaeeceedcdcddeccaadadbbdeaaeaacdaeededbbdbedeedbaadecacdbccceabaeabaadceaecbbedbdbcebaeecedbadedeeeeabbdbccaaccaabbddbdbedbebeaeabdeecabedcacbbdaeadbbddbdaeaabceababbebcaeddbcdecadddeabdceadcbceababbbacdaeedeaececcbbcbbdbebeeaceeeabacdbecaeaccacdacaaabdeecebdedaadaebadbacaaeeeceaceccbecbbcaddbbdddddedaeaceebddabdcaeeacccbeaedbedadcdaeeddeeeebeaccdebccbadcccbbedabdbaccaeedccbedaccdddbeedcbdbacadbceddebebeedcccddaaeccedebadddabebdeadcceedcaabaaacbceaaddccdedbdbebcadeaaebedabdaaeeaedeceaeaeacbadcadcaadbedddbcbdeccbdaeccbcdebedeacccecddebdbcbbbbddedaadebedebbacacecdcbaeceecabeedacabdccddeaedeceacbbcaaeddebdaaaaedbbedccedaddcaadbdeecedacbedaacdbeddbbebbdacdededdceaacbdcaadcbceddcdbcbeadbabcbccbbadebbbaceeecebeaadcadeedadabebcbeececedacabaaabceacaabbbddcbccacaacabacecbcebaeeddeeeeecbabbbdbbeaadbdeeeeceaeececddddebcabdeccabbbbddbdaabbcceabecaacbaaacbbadbacabdbdbebcdcdacdeaaeccedcbbcaceabaaccacccbbbaedacecaecdceeeabbdeecdbabdbdabecdcbbbdeaceeaddcecbcbccdbbdadebebbcdbaebeeddacdcddbdbdbadccbacabcaaebceacbcbeccbacebaacccbdceaaeecbcebcddaedeecbaddadaeeabedbdeecceabaaddbedcbcaaedbedcbebbccaddebecbbabedcdcaeaabedbdddedccbeacdceecaabccdeccdabdcabbaaacbaceaeeeccbabdabaabadebeebaabcccedebaabbdecdaebcceccaedeadeacbdecacdbcdcaccbdbbcceeecdbaaaeedcddeaeadbceaebeddbcaeaaacdbbebacadbdaececeaadeccdececdacaeebbbebceedacbbdadabaceabbcdaecacbeaddbccbbededebeebdadebddcedcbebbdedbdbebddbdddeaddccdbdebabecaadebecbabedcaadeddabbdeacceccbbdeeeebdabdbcaeadaebddbcdddddbcecddcbaedccaddbddbabaababcdcaaebeeceaabdcccbbceacdecdedcccbbdbdaceccbbbbeabaadbedaadedbacedebbbeadeeaededaabeceedaacbecbbcbacedbdceaaadbaecdeadebdebaedebabdedbaadcbaddccddaccebbeedeabdcbaeabbadcddadbebececebdcdadeabcabddeebbecdbeeddceceadaacceebdaddcecdbccdecaedbbabcbcdeacbcecebdccbedbcbbaabebdcabcebbbbddaccbacbdabcaacedcaedeeacecdddacadddacbbebbdabcdcdebaabcebadbbaecebcbbaaadccbcaacebcdcbbdaacccdabcbdaeccedecddceecdbdaaadddcdbdceeaebacbddbabbaacdecbcaaceaedeebbeaadededabdcacdcadeeeadceccbdbceaadeaeebbddbadadddabcdceebebbacbedadeceececeecaebeeadddccdedebdedbbbaedbeadebbecdbcccebbddebacaabaacbcbbcddadabdcecaadeaccdcdbddacccceaeedcccdbddddbcaacdeaeaacadddaccbbddcaebbdadadaaaacedcaeacaceddddacbbdaaaabdeaedaaaaaaeedadeddbbbcbabdecccdceddaaeaceeedbdbbadedceccdacbbedcedbadebdeaabdbcbbdaedabccbabeaabdadacbdeceeccecadadcebacbdadbabebcedccdaedcadededbeaaeedbeadebaddbeabdbcbbeaccebdaebcedcbdebaddacbddcdaacbaddabdddddbaaeebbdecbbdadcaebabaeddccbcdeaddeaacbdabdeddcdeecabddbbaadeeeeeddabcbbbdebbdeebbdaeaaacaedbdddadebddacbceacddaceeedeeeeecbeabcecddbbcedccbdddccdbadbbabdcdacaedceedabecdadedabcbbcbbceeccdeaddeebdeadeeaddacdbccbecacedddcaaeebcddbdaaeebdbbdacdbbaabbdeecabcecbdcdddeeaabeeaaabaddcdaedeeaedaaeebddedaddcbaaaedbebceebececacccbeadddedbcceeaddbdaedbababdaaeeccdbeeabccccdadbcddebbebbbdbabcecebbcbccebedbeaeaceedebbcacbeaabccbdbbdceedeeccdabdcdadbceecdedcaeccbaccbabeaaeaeedeeabaedbbeaacaaeaababbbbceeadcbeceddbcaaceeaaaadaaccdbccbcaacdbcadbdbbbdaaeacbdecdddcdaadeeeddcadeaeaaeaeabdbecadaceeebbaddcdceaeaaecdbddcbadedabacadddcbccabadbbbdedacbedacaabecdbdecdbbeeeadcabbcacaababbaccbcaccaebdbabbaedcabedcbccadababeedbeadedecdeeaacbdebbdbabbeeaccdcbdedcecbddcbcbcabbabcccdceabbedceebbadebacaeecccebedcacddddaabbedddaecddaadcaebbacdeebbdcdeaecedebbceaedcccddeebeadbcedcdbcdedcebcedbadebcbbeacaaddabaaabedcccedadeebdbcedcbcdbaccccbeeedccbebaedbbcbbacbcbbbdaccbebeecdebebeacabdbcdcbdabeaeebcebcdabcccddabddbaacbbdbacbebcbeddbcdeadccbecadecccddedeedbedbbedbdebbdbdbebccacbdaadecbceacdbaaccdcdbaebabaaccbddcdbddaeaadbbdaddeabddeeddeccbbcdbbbbdbdbbeceeddececdecbebbbebcbbacdadaacbbccbaacabdaaeddbcdbdaaebbaabacbabdbadbdabcaddabddceddeddcedcbeccaccabbddabeebcadeebdcacdeddbaecdbbaaeaaebdbcabedcbeaadebecbeeadbdcdebcbbdbbdabbdbbbbeddcdadbeebcedeedcabecaabdddcbedaccdceabeccacddceddcbbaaaabdbecdadbbbcdedbdabaaedcdcaeabebccabddbdadbcebbdceacadccdcdacbdcddebdaceeececebedbbcdddbcabaedeaababbccbacdebbdebbdbccbbeabbcdbccebdcdaddcbadaeacecbbcddccebdbebaceaacabebacababdeceebceebeedbaeceebccbbebaedeaecaddcacbabbeabcdecbebdaddaaccdaadcacddddebaebeecbeadbcedddcebeabdaabdaababcaaceedbbdaaaaeeeacdeedcaaaaaecdbdebecdaeacdbcabbcaaadabaebaadeeeedbdeaaaaabbcececedcbddbbbdececdbbccdceaabdcbcceacdddcbadccbadccbdacdceedcddccedbddadaaecbddccbaabdadbbeebcecceaedbebaccbdeddbcdccbaebcddcadddbbebddbaedbacebcaaecbdceddeaddeccdeaaacebcabcdbccaedcabaedddadcacbaabaabdaeaaabddbcbeccebebcaaabddabbcadaaaaceadbdddaaddebacadaccdddeccbbbdedadecadabaebaacdbeaeddedbadedbedebeaadceaaadbecabceaecaedbeedcbbaddbeeeaceccbdbccbbcdbcbdeaeedeabbebccbcbbaecaccbebaabcdecdbcadbbdeadcabdcdcdcbebbcadebcbaecccecccbbdaaeecceadabbcbaebbaabccbcbddeaecaedcabacdadcededebbadcacaebabeeebbcbdcadadeadedcbbeababccceeadbebabddaaccddcedbdcdbeacabeaeaadcdeedebbaceaceebadbacbcddaabdcaacebdbbcbebbebcadbbaeaecdeabcbbceadabbdabaedbabdcaabcececabacbcddccbdbddedccdeadeaabdddbbadceaaddebdcaebbdadaeccbbebddcaaedacdecedbeaaddaaecdadbdedaaddacabaccdaecbbedbcddcdadbbeecdbdecdedaeccebcdcbcbaabdcaabdccebcdceaeddaaeaeacaecdcbadbbdcddbbceaaaaadaededebcbebecbbedbcbabbcdbeabeabdceaabbccbdaadceeeceaecbcadedaddbcbdadbbebbdbdadeecaaeeadbbecdcdaebcabbabbdcdcadeddbeaebdbaacccecaaeecbdcccaeeedbdedaddacbdedcadebdabacdabebedbaecddbdbebbbeeabbdadccdcbcdebccbdeebeabeebabcadcdebdadaceddabdbddbbecabdaaeabcabdcdddbdccaabededebacdbcdaebabaabbdccaceeeeebaeebbbdccadddeacdceeaddbabababbaaddebeedebbeacdbabaacdbbbbbcbbbadbebbabbbdcdbabddbbddedebceadacaacdcdebbbdacaebceaeccddcadeaeebaadabccbdbeecbcbeeebabdacdabdaeaebdeebbbaeabbaeeddddccacacbceeeacbdecceccedcaecbabdeaeacaebaaecdeecaeedbbebdbedaddbdedbccddcecacbbedbecebbabeaeccdbacccebdebeeecccbcccacbeedbacadbbcdbbcbbdcceaceaccbcedacbedbccbacabedbeabcddabdcceabdbcadeabbebeecabbbcebbccbeebcaecbcbacdebdabebedbabaadadeeedeaaadeebdaeabeabcaaacddadcdebacbcebdcdaedceebaabcbccaeddbcdbaaabbaebcccbecbdadcabbaadaabecdedcccaadadaeadbedacdaabcdbadbbdbddddbdeedcebdacabaecbcaabcadacdecabdaeceddddbceccecaccddeaddaeaabbadceecbbaccddbbebcebacebbbabcaebbdadacadedbcebbddbcbaaebbadebbddacbdebdaddaeebbbcadbaaecababeceabbaabcadbacdecbbeecadeddddbdaabddeccbdedbaebbdeabeedeabaaabcddbecbddadecdebebadabdbacdeabbdbdadccbbeaecaecbaaddadeebbabaaaaaabaecdeadcdbcdbadedcbddcaebabeeacbdeccabadcaecaaabacaaccccaabcabaeecabecaccdceaebadbcbaeccdcbabaedeccedcabaeecbabcddacdbedacadaacceaabddabcecadbcdebddbeadeaeeddbdaaddebcdebacadedbdcadeadebaecdbcbdcaddeabadbbeabcebdccbbeadbbaecdecdecabcaeddeeedeadbdaedaddddedebcedcddeaaacbcabaabecaeacebcebdbbedbcdecdabacddbeacbcddbdaceeceaecbeebdcdadcebbecababebbccdadbdbbceddcacdadcdbaaacaeedadbccccbbbeabaecbbececbadceeeadecaacedaceacbcbeadccccadbadebedeebacbbaaadbabbdeaebdeeccdcdaceeddedbcbcaecaeeeceacaedbceacdcdcabceabdccdbcbbdcdeecccedabceebdcdcedadcceeededadceebdcececccedddccecadebcacaaaecbaccbeaddadaeadcddeaeedabeaaaadcbaadaababbddeacbeeadadbbebbbcceeadebdedcaeecdadcbdcdcececeeadebdccacbdcbeebbebacddddddcbdbddbabcacebaaabdcacdeabababbeaacdcdbdeacebdacbcbbaeddcedbeaabcebcbeeadbacbbeddddbaddaccccdaaebdcdaaeccbacbdebdcdbccdbbbaecadcebbbdbaccdcdcaeddbeedbbdccbacbeddceaaeadcecdddeccadccdaedcbceaaddaebbbcbddcccaaceedeacdbbdaaedebeabacbccbdcbaebadebdadedabbadbbbbcabedbeebdabbceaacaabeabaacadddbdbabceccedbaceaaeebacbbedebabecaaceadaadaccddeaeddbbbdddcdeeadaeeccdeedbbeecedcbeaacecbeabeddaaddadebacedbedabdaabeadeebeaadececccdcebbaddabaeebbdecacdeedabccbaaddbebcebbaaacbaeabdcdbbdadbbcdaedaccacbebbcabddbeeccaaaacedacbbbeedcacbbebedccabcbdccdedbcebddaacebeceaeedcbddbececbabdaacebcdacbdeaaedacacadcaccaeeaadacadbbeedbadbebdeeecdddadcbdebcaaabcdccbeeeaddcebacbadaceaeeddbdecbcbceedaccddacaccbdceaacabbaaebebebdcaddaabdedcdbeecbacbeeacabaccddcebebbddadacdccdeecdbedaccacadbadedcbabebcabdbdbccacecaaabccaaeacaebcceecceaadeabaebaadaeebeadddbdcbabedededaedeccdedeaebcedeebacdebeadcacabcddecbcabaabdacadaaaacbebbddbaecccbbddbdbcaecdabbebdeaecaccdcdbbcebdcaacbddbabdbeadededbabedbdbccdbccbdbceddececabcadcaacaeacbebdaabdaaecbeacaecbcacbabdbdaccbdbbdaceaeabbdebaeaecabbaacdacdbcecbceeacaedbccadcdcdcbbacdeeeaaacbcabeedebbaaaaacbeeceeceaededebccaabbdcedcaacdabbaaaeaeededbbcebdadbbadcbdcaebeeebebcbbeadaaadcdcebeeeaadebbcbcacccdbccbdecbbdbccceccdebdcbedaceceeecaccccdeaeaacaddedddecbaadedecceadacedeedbadbdcabdcaadaacedcddebbddacadaaadbdabdbdbadcacdbcccbdecbbdebedaadbdabccebdadbccdbadbaddacbeeaceaadcccedcdbeecbbbcacbbaeeaabdebababaadabaabedaccdcdceeeedacacabcdaeeaddbedbeebcbbdcaacccceeccadacbbdeebddaeacdcdcabcecbdeaeecbccaeaacaadcbcdeecaebcbccaaaddabaeebebcedcbebadcdceabaececddedcdbcebaadbcdddbbeaeedebdbdcdeaddcbcdabccbbedaceecbccadbaabbbacdaeddecddcccaadbeadbccbececebddeecbeedcabbdbbeacddacdcaacbcbdaeceecebeedacbdadecbceacbbadcdedacddccdedadbddbedbacacccddeaedeaeeaaacdeecbdeeedbcdaaeacddaaaaacdebaccabaccbdbcabdeccbdeccebdebadecebeabceeddcabbdaebcbeaceeaededacccaaaacdcebdadedcdeabaacebcaceeebcdbbceaccdaadaddebcecebdebeaabeaeaaaccbcecebbdeedededcdabebaebaadcbbdacdbebeeeaeeabedebbebaddaaeaaddcbcbccaacecdcbadbcbadaadccdaccbaebadbbcadcbddaceaccaeeddebeecaaedeabcbccdbacedebabdaabddaadeedbedbadaaaaddddadeebdabecbcccdcbabaceabceaebaaccccdebaeaacbeecaaceecabdbcbaeaabcebaebcdaddcdbddbcdbcdcceeadcedbebbceebdbebeccaebcdbaebbadbcdeacbcdbbdaedecddadbbebacdabbabbaeaccacbbaeeddbccbcdedccbdcadadeecdaadaeaacadeadebbbdebceceacbeebecbbcbabddadaabdadacccaadacbbabaddeaceeceebeeaacebdcbaceeaedddbbaddeaedbaddcaddcebeddbddbcbaaecddecacddadccceecebbdadaabdecdbabcedbcaacdbbedecaddbdacacbeebebbaabeabdcdabdddbcaaeaebadbbaaebacbaeaaadcddeebcdddabddacaddbadbdcaaabccddddeadddcedecedbbaadcaddebdcdebaeddcebeabbbeddcadedaddadceddededeabdadaedcbedacabddeadbbdbecabdcbaacbbabdddecacabcbadeaebbcebeebdaedcaeddbedadbaeecbaecbeaacadbdcaccbeaaadbcecdcceedadacbccbedeaeabdbdcedeabbbcdebadeaedecedbaebbaacebeccbbeeadbbcedbbccdbdaddbaacdedbeccabeaebeaeceebadcaaaedadaaceeeaabeeaeddcacacbcbdcabdccedccabecdbabdebedcbbdccdaedeaababbcaeaadbbcdbecdbeacdccdeeeccadccbccadbeeacdbdecdaedadedccecebcdceceeebcccbdaaabdbbedbebdaccbbeedceddaabcaeeedeeaaeeabcabcbdccabdecbdceacaddcdcedebecbbaecaabbcbceeaaccbadceecdcdcdaebacaeacaabacbdaaacccdeccabcbbdedadabcdeedacbdcaddbedeeadccaeaaaeaaedcddacecaeacadcaebddbaeddcceabeeccaecbbeaaeacabdcdeaacaacdedaabdaaccbbdaddaaeccdcbbedceadbebcdabadcadcbacdededdddddddbddddbbbddebbaedbecbaaeddeedeeebacbecccdbaeaebeadccadebbadceedabedecdebdcbdccdeedbaeaeccddcdbbdeadccdabcddcaaeedabcacccbceabdceebddacaebbdaadcbeabdeeeaaecccbacdbdaeecaabeacedcccbeaeaadbbcaeaadaecbedeadeabdebdbbceedbccdcadbaedccaaaccccabdeabcaedaddeecbbbcedabebcceacbedeacaabddceabdcdcceeeebedbdebbabdebcddbaabceadabccccaeaaecddbeebecbcbaacaeacbeaeaababcbdeaabeddaacdcabbdbedcacaeaaadccabeccddccccedeeecdabeecdcaacacecbbccbebdcdadcbecadcacebadbebeaeeddcadbaecccbdaaadabcbeadceaaabddcbebcaeadedcbcddddcedebaadcdabcbecaabbeabcbbbacdbcbbaeeaeddaaebbadcdadaebbbaebdaeeaccaaebadadacbbaedabdeeeccdbecedbaeecdeedddbbdaddcecdeeaaddabbcdbdbebcadedeadbdceaeccdcdbacedaababceceebcddcccaceeaccbedeebbbbeecabaddddbadaeddaaacbddaecceaadabecbceccababdeababedbbcedcdabeeabbecceacaccbbdbaeeeacedceaacadccecacedcddccecadbddedbbaeaeeaadabbebbaadbbcdbceceacaddacbacebbdbeeeaabaadbddadaacbadaedacabeecabaedcadcacccddcbcecebbedeeaeddbeabedccddacbabbadebccebbbebdddaedcbbabdbbdbddaddeebecacababbadbdabcabadaeeaaeecbbcbadaddbaaacaedbceededdcdbabebadaedbdacbeeadceddccbdbeecbddcdbeaaeeabbddccaadacaadbdccbabdaeaedbdbbcadbebecdcacdcaacbddeecdbddeaaecabcbbcbdaabceaabcbbbeaeacbecebaccdaaadcbdcadceaaddcbdcdbddcaeabbaddedacbeabaebbbbddddeaacacecbcdcacccdcccaeedbeacedaeeadebcabaadaacdabbdcdbbbbaaccdbbbeadabcdacedbdcbbcecacdeddecdeacddeceeebacedcbaabdccbbdbebacadabceeeddaabdcccbbaabeadcedcebbacdedccbdbecdcaddbcdceddebcdeebdececcacccdcdbeccbebbcbeccaaabaacabddbebceddebebcceceddaadeadbdddcceddacbabcbacdbddaaacbcbaaeecddeabacaaebcaabecbdbacaacbebddbccadbedaebbbbbdbbaccceebaeedcdeeaaaadceabacebaaebcceeabaaadcebcbcaebccaebdbccedeecaddacdaedddebbbadbcbcbeebaceaeadddeccadcacccdbeeacaeecbbbcebcdaecbbcaabadcdbabebeaecebbcdddbcedbceddbbcebcababdbecbbdebeaddcdacbdeebbaaeeccdcadacdcaecaccdcddaebecdaaaeecceedeebbdbcdedebeddcaeabbadbcecbdabdcaebebceecabeebdcabcdbcdecaebebdddeebeeacbdcbbdbcebcdedbaabcebadbbdddabeebcbdccbbbecbaedeaebbcbacebddeaaecaccccadeeedacaaeccbebbadcbdaeccdcbdaabdcacaadcadbbdaabaecdedbdbecdaaaaeacbaedbdececaeeaabbbbaddeeadeceddaccdeacddceacbdabdaabdedebaaaaabbbccbccebebdebedaaabaeecaaadeeeddeebaddacecebaddabbdcdaacbdbabcdacedbeceebceccdadddaeedcdbadeaeeacbbbdeacabdadbbaddabbadbadabcbcacbebdcccdaacadbeebceaccdbbddebceaedbeeebedbadddcbaadcaadcbcdacdbeebdacaaeeaecaeedccbdebbbbedcbbadedbedcdbcdccdcbbadbcbaddccacdbececbcacabaddcdcdbaebdbaadbeacdadbeeaeacadbbdabbbbabaabacebbbccdeceadedacdbbcedcaaacccccccbcabeeecdeeabcddaaaededccddaddacaecdcaccadeebcbeaceddcbecadcceedbbeaedebebeccbabeadadcabbcbbeeebbeaebdeddbacdaeceedecbabaecbbdcbccedbaabaeebdccbdaebcadababedcedaddbadedeeaaeedaceaaaabcdaadccbdececebccecacbaabdacaeddadadebbbcaeabeaadabdadddeaebceddaabedeecaaabbdaadccaacbdbcaecdbcadcdeabdccabaacacbebadbeadbbdddbcadaabceacdedcccebaaedebeebddabaddbeccdddbcaceaecbaebabaddcbdaaabdeeabccbdbbdcedadeadaebbecbddceaadbccbaecccdbddebebddaeaabeadcbecadaabbebcaeaeaceadbbbedececabaeedbabbedaccaaacacedbccaeccaaeedbcadaeceedcadeeebbccbedceacadadacbebbbdedadcadaaacdbdbcbeedabbacdacbaeebaaacadebeeeeddedaecebbbebacdcabcaceeecbedbeacdcbaededccbbeaceaddbdbcebabdaceadbdbdbbadadedcbaaaabacdcaadcbabcbacddcbaccabacbbcbccccbbcdcecaacaedbebecdcaaebbdeedbeaadcbdedadbdeecbdaccceccaaccbcdbaeaeaebaedbbbadcbaabdaeedcdcceaabbbebcdaebbeecbdccabdabbcedecbeddecbeecdadbbecbbbeebededcdbddacbeeceeecabacdbdeeeaddcdaaebaeadcbbeaceaacadccaeebaacdbebddcddcdeeedeaddbbaeecddceedbdeaeaedaceaeaeaadceaeedbcaebcebeecdcbaceddebbcedccdcbaaabbcccceaaacedabccddaeaeeeedecabaedbdacdeaeeedaacaeddcdbdeaaecbbdebaaecbecbebcebebcbccebebdecbeacebebedadcdaecbccdecdbebebedcecbcbdbcdcecdeccdaddadbbdaedaadbebeebbaccbcecaceaeadcbbcddbcedbdcdcaecaceaddbaddddaaacbedbcadbaaeabbccdccdeddebdaabccbaabaedddbbceaccbeeaedebabbeadaedddbebddacddcebedccababacbdcdbdebdbdecdaadedbdbcdceeaedaacdbbddbbbabedcedbdeebeedcbebeddecadceaeeabebeaddabbdedaeacbabcabaceeebebbbbcddbccedeeecbdaecaddbaecddbaeeacdeebaddacecdeecbbbdbddcbcdaacbadeddbadeeacdcbbecebbccccdaaebddacdddbbceaecedadedddbdeebcbccdceaeacdeaaaaeedabcaccbbbccccccbebecadcadabbccebdadadabcdedaedceaaedebdaeedaadbdabaeeadedbcccbebedeecbbebaedeaaaddcbaaedcdcabdeebbbbcdaccedbdbededdbaacecacecbedcbdaebaaaaeedacacdedaebedcabdabaeabceccbbaedaceccdeaadaadaaabeadcaeebaebbdaaccebbcdaaaaebaadadcbbdadaccdbbdedebaacecebdbdaabbcdcdaabdcedaccbcdeaacbbcdeacadaeabdedcbccdcbbbdcbaeedebeddeaaadabeedaaabaebaacebaaeacebaeadadcbabdddbddddbaacbabaacddceeaecddbcaadcdabcdaebedecaebedbccebeeedabdcbcbabcedcaeeaeabcdadadadbbecaaccedbdccaebddcccaacebdeaebbebddbdceccebedceabdeecbeadecadebcbeebbecbdbbaaeacbebabdeeecabbdebeccdaedebdbdcaedcdbcabdcbeebaecbeebeebdbccdacdbddbbbbbebeeecdcbcbcbbeececaabceadcbdeedabacecabbdbadccbacecdcdeacbcdccbebeadedebecedbdabddadedecacbcbdbbccbdcdbcccbddddcbacbabdcbbcbbdeaeeadbcaadcabbdabacdedcabcdededeadebbececebcaaacadcddbbecdbabdeedebbbbaaeaadededebeabebadaaaecbcccdacdeaddcdeeecdccceccdbcdebbadadeeeecdeaaadbcbaacccedcccdcbdddeccccccebcebaeadcbcdeacbaebbabbdcaccbaadabbabaababbcbaabeddebddcddbbbbecaaceeddcecebdcaecbcacaecdaecadcedaadbcedabcaeedbecceadbaeacaeaccdadeaabbebbacaabbecdcaeebbacabaedeceaebadededaaceabdaecbdebeeaeedcebccadcaddabcececbadeebaaccbbdeacdbebedacebacddeeebabadacabaeebbbbccaddadaecdaacebbaaadccedbcebbdcdeabcaddacabaabdbceeabacedbbdacbbbbeedddbaeaecbcebceeeccaccacecbedadacdeaceccbadeaaeecbdaaecbddacadbdbebbcacebceecaaaabeebadabdeaeacdacbecdebadddbcbacabdacebbdecebbabbdaeebddcceaaababeeaeebadacaedcddcebbeaecedceecdecccadbcdcaedcacbbdcbababbdcbdcadddeedeedaddbaabeaadabbedbbaccccebbadcaacbbcaceeecbaadcbabacbdaecbaabaadeedacbbeecddddedbdddbbacdaebcabcdbececdacecedcedeeceecaddeadacceebdccabddaccebeccbbbbbecaebcdcbbeedbebacbecacdcaebcbdbdcdbaacabbeaeedccadcceddbababcbbeabcbcebdbcdabebcbbbbbcedecbabdabdddcbecbadeadcacddbcbdbaaedcdeecbceebaebdebeabdbbeedaaeddcedddeeacbcabbddabaecdbcbaddbecbaebdcddddccacdddcadbbbbbeddaaaeccbcdaaaabddecaadacccdecedceebedeecceddbcecdeccecdabdbbcdecbecbaeebcbddccdbcbabcdeadbbeeadbbacbdceabbbacedbceeceecbdbbdddeabbbecacabdaaecbceccecceacadcabddcacabeeeeddaebbdabebbcdaabdaaeeebddebdbebdcdcaedaaedebeaaeecbddddadcbaecdeaaebcbcaddbbdaabeeeaeaccabadcbbabeacabbbaeacbcaddcebeaaceaeeeadaeabaaddbabbdddababeccadabdcccecbaadaebbccebdbcbdbdcddaebddbeababadccbbaaabcdebabddbaaabaacceeecaaceebccccacbcecbdeabeaeaaceedaecdaeadbcddcaacbcbbdabaeecdcbccebebdbaddbbabcdbbedbdcdbecbecadbeaecdabddeabaaebeeedbcabaedbbdadadedcbeebbacaaccbbadcdcdeacbcbdabcedcdaebbecbcecacdecbceeecabeedbbbdbdccddcbdbdcceadaeeabaddebacbcbcaddbdbaaddeddebedeaaecbabacbedbbedabcabadcbbbadabdbcdbeabbeaedededcdccceaaaceecbcbecbdceacdceceaecbcbdcdbbccbcdccdcbbbaedccdcaebdeccaccdbdaebebeaedbaabdcdbdbcabdeebdbcbaaecdeaedaeaceacbeaebebdbaaecdbcdbdabdbadbbaabedecedacdbccbdecacdaecedecdeaceccebcbcdecacddabdeaedccebeebcbcddccdecdabccbaaacbadcadadebbaedcebcccaaabbadbceaadceacbedeedbdbdbbeccccebdccbaeceaeacbaacdbcbabecaebdedeebeddcacbddecadeddbaeeacebcdaaccabddadcceebbecbccbbeecdecacacaadccbdcbdddadedecddbebccdecdbebeeecadbcaebdcdaadabeebbcdbbbdbacdddbeaadeaeaededccdbbcaddcdceadbcaaddeceeceaaaadebbdcbbecdddecbcacecebeceaeeeebbcdcccecbdcbceaaddddcecddddddadbabeeeddeddbaaaaabdbbadccdbcacdbdaeeebabeccedeceddcacdeeccbbbbcaaadcecdacdcdcaaddbadccbdacadddacceeeecccadcabbbecadcaabeaceeacbebdbaeaddeedacbbcabbbbdebdcdeedbbadccabcbabacdadbdccdaebdcabeebdcbaeecabcadcdaeeeeaddcbabedddbdacddeacaacdecbadeabcbdaeeebabeabeeeeceecdbbebeccedcdecedcacbaedabbdecedcecaebcdacaaaadabdbdceaebebdcbbbecbedbabbdeaddbccddcecadadecaaccaedbcedeaacddbeeaaeebadcbdcddcbaeeaddbbdceedcdacaaabddcaeaaacddcebdccaceeebaadceecebdcdcaceddaebdaadbbdcdaaeaccebddaaeadacabbcbbeabeebbeceddaecdadeeceeaececdadeabbcdeccbaebabcaeebedabeeadbaddecdacddddaacabeecdadbdcbdaacdeedeadadccececeddcabeedcababecaaaeeaaaabdacadcdbabddeacbbecbabedcbdebaeedeadceeebeaedeaebacccbdbadcdceaddaabeecceddaeededeedeaeaadebeeaedcdbebbbabdebdadbcadebbcbecebaddeebcbceabceceabaabeeedabdbddeeddcdcdebcdcbddbbdaabeedcbadcaddabbedcbabadccbcdddaecceecbeabdebdcbeeaddededcbbbdceaadbeddbeddbdebdebadeecedeededbdbadedceedaaeaadbeeaceddcdcdacededdcebbccbbabdabcccddbacbcebdabaddbeecabeceedcdedacdcbaabbaeddeddcddaedededebaeaabcdcdcccbddedeeaeeadbaacacccdcaccadaddbedccdabcaeaeabbdaaaecdaabcbadadeaededabdaaecacecdedaaadcadadebbeadecadadbcaaddcadaadbdcbceadaedeaeacabbbdeeedbeaabbaabdeeaacaadadbeedbbbbcebccceedacacbdaccaeebdebbaadaceeedcadbdbcbaeaacecaedaaadeabdbdaaaedddbcababaebdacbccccacddaadeeabcdbbaddabadbbabeddeabbeceeeabbcadceeadaabccccbdebcceebedbabcbcbdddadaddbcabddebdeedadcbbeacbbaaaadabbdddcaccaabccaeebabdedacdcebdccaccccaaddbdaebeeaadbbbddeadecdaebaeedbaaeacccdadcbbbbbdbeabebadcceccadcabaaaeecabdecddcccdaadeddcdaaabccecaccdabcadbaeedebbaadbbadaccdebbbeadcaabcaabcaeaccebcacedaadaebbabccbceaedbbcaddbdccdcbcbdaaeddbccbdabdbceeacddcedeeeacaddeeedbaaaebdbbbebadadaacbbeeecbcbcbdcdbeadbbbadbcabeaddaddbeabbbcebbbaebdeaaccebcbaeaacccccbdeebceedacbbdaebdedcbebaedcbedaaeedaaddcbbcbdbceeeaceedebcdbccecddcbcebbaaedebecceadeaccadedaaceeabdacbceeadacaacacbceaebcbedbabdabeaaabcbdaaaebceebdccbaedbecebbdabbbbabecbbedaebababaadccddbeabcbadacacabeedcbbaddaecdbeceabdbeadbbabededbdbecbcedcbccbeabdbcecaeebacbcbbdaeccbbddbabeeccddbdddaaecbceaaeedcddecbeaabceddbabebbaaecdccbbdceddaadacbdcbaacbabdcccdaddeebaddabaddccbbacbacdedabeeddeeedcddbaeaaaaaacdedaabeacecbcbcceecbcedbdcbcbdbdaedeeaeabcbeaaaedcdeeeddbcdededeaeabeccbaeeaedcedbaabcbbabdeddababbeadccbeedeacddedaeabbddbcaeedcbdbaebcccdedebacadbeacabeaaedbeaaecdceceebaabbabcbdedeebacbaeccaeaaeaccedaaeccedeabccdbedccabcdbdbbdebdebedeeadcbbacabccebbabcdcadbeaeecedbeadbadacecabedbeacbedcabcbeddbeaeabeaeebbeceadcadddaccaddcdbcaddbccccedcdebbcccdeebbeddaaaaceadecbabdeecbabbdbaeadcedbedecaeecedccaeadecddaebdddadabaedbacdbcddcedbdaaedacceddbaedbcaacbccbcabedcaebccebeabadbdaececbadbadcdccaaeedadadadebccabebcbdbacebaddbedebdeebdcbdeddeedbaedeeebbeaebcddbdbecbededebbabecaaeaaebaccecddeebccdadadbabeeaecabedebdbcedcacadbbbcecedaaaaeeddeedaedacceeaaceacbeabdeabececadcdbcabbaeeddaccddeadcbadeacdaeeddddbbaaddaedbdeabdbeecdbeedecdbeecebdbecdbdbccdcbaddeacbebbdacacdbdbadaebdaeedabdeaaeadabccdbaebceeddaaadaacbeccacabadcebceaedcacdaddbebedcbdacbcadecbcadaddceebeeccceadebcbaecbcbbeebeaaeaccabddeaaccddbeedddabbededbbdaecdcabaccbccbdacceabdbbbdbebbeeedbccaadebedcccdeadadcabaeecbaeecbbeebeddebccedccbadccebaacdabedaaedeeddadeeaeebdedbcbedbbeddbcaabacadacbeecacdedceccdcccecbedeaaaceeaeaaedeadaeabddeceddcdcebaddeabeaceaddbceddabdecaadebcadcacaddbaabdadbaaabadaeeeedcabeabcedeaeacccdabdaeabebabddaeeecbbedeebabeadacaadaedececbabdbaddccdcacbbdecbbcceacabdadcbedbbbddddbddebcaabbacebcbcacbacedacdaccbddbbddadcdedbbecdecccebaeaecbdeaddcdbadaccdddbbaeeaddccbbabbabdaedaaccbbabcebbddedceddaacbdbdbbeeceabbadeeebdcdcdacaaacdddeebeeecebacbcdeaeddecbacebcddedddceeceebbbbbeaabddecebccecdadabacaebddbeedbdeeebbacbeeadeebccedadbebbdbececccbdbbeaeaccddeaabbbdedadddbcdbbdcabdedddceaaeebdcdbcaeeddddbddadeaccebdcaaaebcccceaadebeadcadeeddbdcdaabdaebeddbddebcabcadbecdbbbabddebdbadaaeacbeeaadaeecdcaabeeedbadbadacacaeacaccddbdccbdcaddceeaaabeeacbddbebbadedcecccabdbbddaeaddcacacceccdaadbbaddccbccdceaacbccdacacdbbdccbcceeecdeebdbdbedbaeccedacdcbeaecbbedbabaacaedcabeeedbecadeccbeaeacddccdcadbaceddacbbeecebdcbcccdadcdadcecdacabaaecbeaeedceaedddaedddecedbbaeeaecbbebdcbbebebbedecbdceecdbbbecddcecaacacebbbeaacedebacccdceaaecedcbddaedddaaddddbebebaaebbdceeecceacebbcdbaeabeadaccebeebbccadcbebbbcdebdbaeccbcaddeececcdabcceacbbedcaecaacddeccbbcecaedecdcdaeceecddbedeeecdaaeddeadccccdbedddcabebbdaebbacdacaaeadececeabbedcebcdceecaddddccbbdeacbbceecddeabebaccdabbebcabdacaacdcddeaebccbcbceccdeddddeeceaedbbbaeedecdceeddccebdebdeaecbcbccdeeeaebaddeeccabdacbebaaabbbbbbadabedddbeaebadbbcaddebceaaedcbaebebecddbdaaeceddcceaeaccbbecbcdebeaaddbbdcebcbdeceecaadaaebcabedebccceeeedebabcdabeddacacbabdecaecbbbabeedaaadaaaceeaacbcbdcaeeddcabeccaebecaedbaabebbbdacadabddeeaeeaccdeebbaccdccaeceabeebbdacedcaacaceeecdabcbeebdaeabddacdceceebcadaaacedeacbebcedeebeebbbacbdabbbaeaedacdbeceedeaedbdbccbcbabcaabbcecebbecdecaceeeaeeddbedcbbbdbadcddccecceeaadaecabdeeacbbcbebdedeebceddeaabbecebabcaaececbdbaeeaccbadceeddaddbadaceabeacddadeedecbbabbaeccddbcccdbdecaaaabbeebbccaaeceadedebcbddcbcdedeacecbaaecdccdcdacbbceeeaacaddcebdddaaaaecbccecdddbedcaccddcebcdceaacdddadeadcbdeeadabeedcadbbaccadebddcbbbacdbabbacddcbcadaebbcdeaabcdceecebdeededabbcbdaeeeacabcececdbaacadaaddceabdecaaddcdaeaeabeddbdabaddeaccbceddcaebdecabcacdceadaedcbebeaeeaaacddcbccdcaedbdedadcaadaddddadadedbacaccbadbbeabbdbacbddcacaaacdbbcbcaecaadcecdcbbeeecbeadbcccdabaaecbaebcebceaceddbcbdcbcbaaadbaceeebbbccbbdceaedabebdaeaeaddaddcccacecbeecbbebedeecbdbeaeaeddadacdaccecaddbeaecaebccbdeeccbddabbaddadaabaeebddabacaacceaaccbddcaceeeececaddcadeabeceacdbaccbddcabbdbccbdadcaaddeacdebbbadddedccbaeccdccedaedcddecccdbbeeeeeeaceabebaedbacddcaadcabdbccaaeabccccdeddaabddcebbbcedbecaaccdccedddabdbbeebbbaeabbeecabeddeeaecbdbdbaebdbdcdbbabebeeceabcdeaabbceaccebddaaaabdeeaededceeabaabcccdedeecaccecbddbdeecdddbbdccacdebcdbcaadcdbecabcaeddaedecdedebcedaeacecebedbbcedacedbdcbacdcebecccdbdecccdcbeecdedccdedbacbdaeeebeaeccbaeeedcbeadebdccccbcadacbcacbdbedbaaeecbaacdcaceeaddebdabbeceecadacadaeaeabbdeccccecbbaabdbcddecdcddeebadacabeddaadaabaceccaedecaccecccaceabdacbeeaceabbbbdcbcdebabeccddcdbaecccdebcdccbacaddecbcbdebcadabcdaacbbdddbabecedcdedadcbdabaedcbdcdbceeccdcbbabddebdebaecbdccbedcbcadbccabdabedcccbddaecbdecaacdcedcacbdbadcabcceaccdecdecddbdcebeedbacabebcacdededacbeeeebccbdaadbdaceddbccacadeeabbdccaebeacaadaabbddeeacacdaaadcbbbbecebbcddebbddbbdddbaabbbddbbdccbbbacebbcbabdacadeaacabecbddeddbddaacebeebeeebcabcceeccbebedcedceccddcdcedebeacedecebbdedbbebdbcbdeceaddebebccedaabcbdecdcdbddcaabebebcdceebceccacdbbbaeedcdeebeeaaabcbbecabaaebcbcdcabdceddcedddaceadeeedadcbaaebdbdccdbacadaeeaceaaadaebebcbceeeecdcebdbaebbeeccbddbaabeaacdaaadcbabddeeaaccccbcebdecbbbaabeeadbbeecececabbdaacbcaabdeeddbabebbaadabeaacdccaaadbeaebdbdedcdccbcecbdbacbbebddcdebeebabadddccebabebddbcebccbceddacaeaeddbaccbecdbddaaeeddaabcdceebeceecedbcdbecdaecdcbaccdcacdbdcaceaccebabbedbcaebcabedbecaceacacebaadddbdeedacccaadcecacceaacdcaddadceadceedcdecdadacaeecdedebdcabaaddabbdaddeaedbdcdcbeabebcebbcadebeaeecdadddaaacddbadecdadddbdaecebcacaaedebecedaceaddddaeebcaecbebbacddebceabbbcbbddadddebcbbbbeeeeecccbaddbcbdcdaeacdbeddcccaabbcabdbbbaeecddecbdcebdcbeabdbbcadcdcbeddcdbedcddddedeeecbebbcdebabdcaccceaaadecbecaddcbdbecbececddbdacedcdadccedbabcdddeaeebbceebbeaadeeaababcaedceddaeddbddedbbecaaabaedebbcaeddeaeacddadcebedddcaeedaceaaecdeedededeaeacaabbdaeedbabdbebbcdbacbeecebecabcacacebecdcacebadbaedacdbeeabacbeeedbeedcdbecbddeaedebcdebcdecbcaedadaadcbdcbdbaecdacbdecabcdaabbdecbaeeeeeddbabceadebeaadaeabbdcbdcabbbcccacabaadabdcaedadedbcbabbdcecedcdabbbadecccadeacabececdbdabdceabcedccadedecabdbacabbeddeeabdacbcabbaacdbbbcadcdddebcbaddedeccedbabeaabaadebccdeeeddbeaabeabadbcaceeabdbbcaebdcabeeaeecebabedcacddddddbcbdbcbeaeaddeeccaaabccdbddcbacdbacdcceccbdbdcdbbbbdccccdebdbebcbbaeaceccebecacabcdcedabbdddcbbadaaccaebeaaecabbdebccebdaedbbeddebebeddabeceddccdebbddedcedebabbecbdcaaaebaeeecddaccbccceabeeecebbcdebbebbeaebdebccbebeeadacacdeebdbcbcdcbbaaccdedbbaadbeebedcdbebebbbeeeccbcdeecdedadedbddcaaebdcdadcecdcacbcdcedceeeadbabedebcbdaaeaebaebaeededadcccaedebeacbcdcabddcaebdddaeeaccccabbdbedeabdeeadaccddcbabbedcacebddaceebeddbbbabbbacdeacceaaddccbbedcbaaccdddcecdbdeeceaeaedddbeebcaebabdeecaeeacabdbcceebadbabebacecccbceeaabcbeedbdddeccacdaeeaeeeebebbadbeeaedeccecddcddedbdebabeeedccadaeebcababadabbeaebccccedaedeaedecbdbcdddeececeaeaeeaebdbebcabcaeaebddaeaaccdedbaebddbacdebbadecaaccceecbadcdeaeccbceedbaccacadeddceddeabaccdeebabbaaebaddcbdcaebcbbbcdbdabbabdeaaadececeeccecebebedeeaacaaaadebaeeaebadbececcadeebbccddcaeeedadaecebdcecaccbddaeecadbdbebdaebcbcabeccbebecceabddeeaaeedaaaeeacbdabedbdaebdddecbcdcdcbbbeadddcdecccaedbaadadcaddddabbedcedbedaaccedbdbaecbeeaedaabdacbececadadbecabcdcaeadecceddccccbbdaaabdaedeebeeaeedaeceaedebcdeccbebcabaecdcdaeeccddcaacbbabbacedcdccecebeadebeedccecdcbbdacebdeddcceaeaaadecaccddadcccdedaccabbcadbdcbdeeddddedccccaebaebbddcaacbaaedbdedbaabecdacaeeddbababadadcebbdcadccdcdecbdaccbbbdaaeeebcaacccccedbcdadddcaeccaceacbeadcbccbbadbebdbbcebaceedaeccbdddbbdbcddaabbcbccbdceceebdcddaeabdadadeabcceddadadeeacbccceaacedadebadbaddcaabdecaeadebcaacaaaabaeddbceaaabdcaeaabbadbbacabcaaccdbdaedacadcecacbdaadebcadeabdceeeccbdededebcdcdcababcbbedaecadcddebdadbceeddadadbcdeaeacaddbaeacacddcdabecdeaddbaeecadcbacdadaeacadedbaadaeeebbedebeccadcccbcaaaeeddbbcceaaeebaacdddcbdaaaebbbcbeaddcbbdeebeaeebdcddebbeaebccaaccbbdeaecbacdaabdbdacecceabdacedceccaedeabadaceeecaeacadadaebeecaeabdacabbccdadbbdbadaadcaecbceebaadccbdcedcbbeddbbbabceacabcbaebbcaadaeddceacbdbcbcdecdaaeecbcdcdddbbcbacaedbbccebbccddddcebddacdcebbaebaeacedcaadbeeecaceebcaadcbcbcaddeeccadaccdcdacaedbebebcbddbbaebecbbbdcbaeecddbeeddbebdedadcbeccabcadeabbdebeeddeabbaccecbbdddedceeedcaeabbbdceebbadebbbabbdcacebbeddecddceececebcddecabcbbdaadccbdecaeecdabacdbdbbbbabeedcaaeddacaedeedadbaebbecbdbdbbecacacacecddeeaddceaacaecdcbcebeaeebccbabbdeeacbcbacbcdeaeceebaeeecdaeaceabbdbeebebacdddbadebeebbdcedadbedbcdabcdddbcadaacecebcbeddeaaaaedeacbdeecdaecaeeadcbdeceadbcecaaadddadbedadcbeabeccaaacddccbdabeaebceeeaccdacbcebdbcdaacdddaedbcbeeeadbeeaccdaebaecdcddacbaacabbaccbaacdbbbddddabbaadecdeaceadbabcccbbcddaedbcdacbebdaacbddbadbcacabcceddebedaeededcacaccbbeebecccaaeeeaaabeaecdcabeecdbeedcbcbceabaedadebbbbcbcdacceaccababcbebabdbdcaceceaeeccbcebabccbbccccedeadaeddcbbdacbeedadadddbabacacbcadbbeeeddbaeeaeaddddabdaaeeebdcecbbccccaecdeeebcddbeeaebecdcbddededbeccccacbaabebabebdddaddcaddcbcaabeaadbdeeacdcaecdebaecacbcadedaddcbaaededdbcabddccadcbcecbecacadbcdcbdebdabeeeeddadabcdcbbadaadaaeecdbbcbccddaeacadbdcbdacaebcaaeaddeddccbaeacaeddbaddeedbdecebabdeecdababccddabcbbdedddebeabceccdbbbbbdedbdbecacdeabdaddeadbdeeacbaaceebcccdaecbaddccbeaecbcbbcbbacebbacbcdeddbacaaeecedaadddaabcedcddeccdbeeebdebbeeeedcbdaebcccbeebeddcabcacecdcebbebaeeeedbbccecebacecebbbadbccbccbcbebebacdbbacbabaeddacbadaeaeebbeaaedbbebdebeedebbdccbccecacccacebbddbbdedabcbecbbabdcdebdccabebbddbdeeeadbcaaabcdbcdaecbdbdbccbcedbdadeacbbedeccdcecacecbeddcabcbbabcabedeebeaadcceedacaaecbeeeaaabcaecddbaaaeadeabdbdbdcabaaecddbbeeecaabdeaecccedcbcdaccebadbdabaabccdbccdbcbccaadbaebedaebdebbdadcedbdccaebcccabaeedcdeabeeeabaddcbbaaecdbbcacbbcbcabbaedcbbcdddbcbddbdecddbababaebdadcbcbaccddcceccbadbdacdbedbeadbeebdbaeeebaddbdebebbcbbdaaccecadeeabaeccbcdaebacbedebbcdcbeebedacdbcbaebedddeacabecbdaadcdcacecedceabebbbccbadddcdeebddbacabdacacebcaaededceebabcbbeceeadaaeceecbeddaceaeaccbdccdbbddccdcedcdaacbaeeeededaeebdcacadcbdbebacdeedabcdeecdeadbcbeedabdcdeeeeccaecbdaedecbeacbdaaaadccdedeebeacbacdbbcdbcabeadbbaadccceedceebcecddbaedcadaeabbcecdaacadcbbbcdecbbbcadddcdaaadebdaaedbbdcdbedecaeddbbcaddbddbdebebbaaadebedcdbdcdcaabbdbabbabeaaaedccceebdbdddcbecabcdbabeecbbabbbbcaeddaaedcaedacabebdaadbbeabacddccebedbbbecbcbeecaaddeaabadabbecaceaabdabaaeaababebdacbacaaedacebbcebecacebeeeaaeaccbedccdabaabadcceededcbccacebdbbadaebaaceacababcecdcceebdbbdedebdacacbcadbbcbdcabdbedabeaddbaccacabadcdcdbadbbdcabebcbeacacaaacecdabcedebdeaadeacddcabbcbdcbaebcacbbeaddeebdcbaacedaeceeddcbbcecebacddababecbbabedcdbeebeccddbdeacdebbcebcdaebaabadaeeccadcbaaccbcadcaaedbcdabdacaeeeabcdbcadeeabdadcdedaadcaececcdebeaacdbddebabcbeedccdedeabeecdaabdbcccddbaddebbdecaacbcdddaebdebceebbecbecabcacbbaeabebddabddcededbabbcaecbbebcdcdeeeeabbcdeebcacdebadaadbdabcbbcaebeacdebddaecbdccbcbeedabddbacbecacddcccaadcedcacaaadcedcececddbbccaadccccdabcdaddcaabcadbdbeacdcceedbedabdddaebceebeeedabaaaedbadbeadeddebbeddddbacbcdaeeadcaecebaedcdabbabeeaeecceaaeeaacddecedbbebdeebdeaaeadebacadddbbbebbeeaeccbabababbbeaeedcbacbcdcadeaabbeecbcabaadceeeceaabeddddbedaadbadbdcadaedabecbdaabedbadeeeddedcaaabebadedbcacdecdebdabaeadadbcccccaaaaeedbbdacbcadcddddbcddbeceaeebcccbabedcbeabcebccaadbababbbacbbabcbcbacebcbdaddcadadaedabaccbbedacebbbeebabeddaaaaeedadcceeaddabcbbbeeecadaaacabadbeecadbeaabeeccedaebcdabbeacdcbddceebaadcceeabebcabbcebeebeacadbebeabbbcbaadbaacbaebdaaabecbbacddcccedabcecaeebcedbaccdcbddbadbcddcdbeadcecbbeecbeebdbabccceaabdcccdbdaeceddddbcdaeeaccaddacaaacdcebebbbcaacabccebcebeeadbaddeaceeebbdaddabceebccbadabbabebbdcabdccadbdecaeecdddeececbebedbccddabcedccbcdaeaabbedcaeeaebbcdadbddddbbcdaabccdaceebabdbceebabbbeccaadaeeebdaeddaddeccbcdabdbabeccedeeadadbbdcdecaeadebabdadeeaeedcddcaeccaaddadaeedeceecdceeedddcdbeebbabcbeeeebbedbcbaadadbbdaccdceaacedcbecaebdbabcbbeccaccabebbeaeeceaaaabacdbbcbabdbeebdaeceecadaaddcaebabebccbeeccecddecdcebcbdacadccadaaedbddbcdcacbeaebcbdeeceddcabdabadeaaaecaeddbdbadbbaaeebcbcbbbdeaadebaddccbeccaddaeadebaaacbddebbbabcdebcaeaedeaabacbcdaadbebabeadccabadaddeaeabcedaeeacbbecabbabbcbeacabcddadeebaabacbebaacbeaccaebcaabcbcebaeaeecddadebbceddbbcbabeaedabbdbcbaaabbbceacdacedcbcccdebaedbbeecdcacceabbcbaadcdadadabbcbaddeeeeadcebdaaaaadbdaececeecbdeecbbebdacbbbbeebacddbbbccdbdcdecdbcdceccaeacddeaccaaadeebeaedbedededbacdbdcdacabddadddaaacbbcabaaecdeeabccaeaaebcdecdaeecbeeaccebedeecadddcedbdeabaaacdedaabcdbcbdcbbbdeebaaabddcbcdcaaabacbedeaceddbbabecacebccdacaeabcdaeeaeaeebbdddbaaceadebcbdeacbacbadabbecbcedcccdedbadbaebaaddbccaddcaabaadeebcedeaeccbcdaaddceeeaaaddcebcababbddbeccaaebccaecaddbbaeceeaccdbaedebadacebecddcdddbcbeaadebeabeabbeddedaeaebbbbbbdaeceadbededcebcecabeeaccebaededdbcacbcdbadccddacabcbceeeaaebacaadeeaeceddddebeccabaedbcbeececaeeeedeecbcadabcadccecbdccbccbebaadebabebddddeecaccaedabdecbbbdaebeabeecdabeaeeeccdccdaabeaaebedacdaccdcdcacbdcebadecbeeeabeebbadceecaddcabeccdbdacbacbdbbaedabdeeabebebdceadedbdbdadbdccddebabcdaacdcaeadbcdbdecdbbddbeccadbbdbcaddddaacdbaeecdadabccddbbacadaaeaeecddeceaabdceaaddbabeccdbecaddcbdeeedbadedabcabdcddcdeccabccbeebeedbdbecdcadccdcdcebecadbdbcdedebbdbdeccaaeeeeadeeadedceccbdabadcceacacebbdbcecaacceadecbbaebdbdadabcccadabcabcbdcaaaeaabeacdceabbebedabcbbecdaaebddcececedbceabbcaaaaacdcdbaaacecacecdddaaceceeacdebaecddcdbedddecabbdaecbabebcbaaeacaadbabedeaecadadcbdcbadbbddeabecabedbccedbbdbbdadcbdddededabcebbaeacabdcdbaaebdaebabcedceebebedbcacbcaecadeebcdbabdeabeddbbceebcededebacebbaaeccadbecacebbedcbaaabcebacdbecdcdccbededaddacdeceacaeddcabebeabceacccecdaccbcccccaaebeaebedadbbdcacaeeacdacbebebdbeaeabbbbddcbceaaaabcabadebeabadcebcacccbcadccceedacbdbeedbdaaeaecbceaddbcccebcabcaacacccedeebdeacaaaadabcbccddaabdabcbddeddbceeabeeaadeedaeeddacddbacbdaebddcdbddeabaaaeaddadcaddaddcecdaaccceedcecdcaecbaceeedcbddecdacccdcddbedcaeacdcbebaaebcdbdaecbdadcdeedeadebbadccceacaacbaedbddcccbaddbebcecbabdaeecaedbaebcceeabdbebacbabdbaacedccadcccadbbdbcaddcadadedbeedcdeadcaaeadaeaabaeccaadcbbacecdbecdcccdcbbabcedacbecdeecdcddcbbeebbabeaadbaaaaedbbeebbbbbadcaecaeaaceacdabceaededabcceadeaeadbeaadceabcaaaeeddeecaddebbbeaacaedbddbccebacbcceeecaebcdbacbbccbebcbcbcddbdccaabbcaddcededaaeacbaadccabcaccbeedccadbecaeadcccabdebbedbccededbdeabaebcaecbececacedbedcaaecdcdcebbddeceabacaabddaebeabcbabaabcacbdeabddebbdcacbceecbbeeeccddcdcabbeaeadedcabcbdacebcadcbcbcbbdcecbbcdebdaacdddeaabeadddedcdddbbecaaedbddcddceddbdecbadaaaddceaccbcdbbbacbeadadbeeaceadebaeebadedaebeaabbbcabacaeadeccddcdaddaedcadacddcaabbeabeedbceaaeeeeddcecabaabccbeabcaeadebceabdecdabbcabdcceecebbdceeaeacabcadaceaedadbedaccceecceddeecdbeacdbcbecbcdabeebedecddccbbacdcdcedddaebdbcbadebebedaedcccdbedebacbbadebdbcaeaeadeeaaebabbdccaeecabcccaebbecddcaddecececbdcccbdccbceebadbededdbdcbcbbbaecaaedacbaccdadacbccaddadebcaebcebabcbdaacddbcdaceecddaabdccaceeecacdecbdacddcaaddcbcccdeddeebcbbbdeadceeaaedcbcebeddadbdccdacebccdccecbaacacebeabaaeaeeaabeecbeabcdcbcabcdbaaceeadcccbbaeeeebeeaedadacabacdbddedbceadabcccbaebcbddadbeabddddbccbeecdccbabbcedaccacbdacabbeadadeedddccebaacdccbeaacedcbeccecedbeebbedaaaaeaedcbbdcacaceacccebdbadcabbabecdddebccdddccacdcccbdabbccabbacbaaeeadbbadedaacdeccaeaaaecbabbdaadeeedadbaccaaadbababdbbdecaaebdeadbbacbdddcbedcacdbaebabaeebeedbbedbebaacedacebaabdcabcecabaedddeebabccdeddeecaaecbadaecbdbaebaccbebabceabdcdaeeeadaceeeebdcccadbdcedaaceedacbaececebddddeacbbcdabddaedcdaeaaaaeabddedebaacdeabbbadcdbaebcaabeebabcebebcdaededecbdbbadbccadaecaebbceeaaeebeeeddbcbecaeeaebbbcbaadeebadcddaabbaeaeebdaebcbcebbbabebcbddadbeaecabdbecbcbbbbbccdeabeedabbceebbaddddddbcdbebbdacbcbeccaebedeedaebceebadadcdcbcccacceddcaccabdbeebbdeecbcbbaabbabebccbbeaaaeeebddccadcededdcbdeadbbdeddaaecadacbebddcececdbceabdecccceebceabceeecddabdaeccabdcecebcbeccbdbccbecbaadbbabdebcecbbadebcbdecaaccbaebaaebacadbaaeacedbabddedadcbcbaebbbddecbadddcdeeedbecaacbeeedeaeceeeedbdcebddadaecdabcabeaedabdcbbbdedeaecadabeecbbccbacaabcddecbceacbdbbbedaadbeceacdabcccabeaeaddaeabaabbbbdedeebbebbbcccbabebaddeccdedbecddbdaaedddccddededceeeadaaeeddddaebceceaaecddeebcdedebeedbdedabadccaacceadcbddaaeaabdebbaeecaaecedaaccbdebadcddbebbdcbcedceacddeebbeacecaebbbbcbbccdbeabedcbbbbebebadbbeedcbaccbcdcddcdcdabbdeaebeedbdbeebeabcceabeedeeddcaeebbbdeaaabdbeadcbeeaceebcdaeaeedabccdedebeccaaebbcedcaddccbbabbbceacecdcaeccbbacbbdceceaccdebeaacdeecdbbedeaedbacaedcebaeebeebabcacbdacdabecbececcbbcaebaaaeaccabcddedcdbeacccbeaddddaeebbbbbdabaadedadddaaeaacdaeedbebaacdabbeacabdaadcdedecbeeeeacaaadaabbadbdacdeddeaeeebceedabdebeaeaacabebbdacbedbabdbcbadaeecaebeaabcbcbebbcbacbadadcdaeddccabbdebeededaeecbbadcabadeadbeaccdcdbcdcbdbbcddaedadcbabdcccbeeaebbcdecaadadaabcdcdaeecacdaabcddbbaabdbcdadaebdbaeeaaccadcdedeebcbcacaaeadebbbbbabceaeddcbbbacaabaccbdadaecccbcdaabadeceabbebdeebadadddbaedcbdecceebecabbcdcedcdcacedacbdebeccbaecbbadabcceeaacdbcebedadaeddcbcaaaccbcdecadddcecaaebbdeaedabceaeebabbbcaeebaeaeaaebadaecdebebdbcbbdaddebeaecaeeccccaebeccabceabbbaacbeeabaabadbbacdcaaabaeaadaeceaaccbbaddedbdddeebcbaeecacdbedcddabebeddcadadaacbaaceddcdeeedcedaedbccebddbcddbeebaccbabbecccacddeaaaaadebcacdaccabdaebbccaedebdbcbddcedbaacaadecebdaaceaebdebadbbddaedcdabaeeecadddbcbabecdcedadeadceaabaeeecdaaaddeddcabbeabddeaaeaeccecadedecdeeebdebeeaedecbaeaccbdebbcbeaccbebdcadabdecbcaadceecdbcbcaacebaceacceddcddbbddabbbecacedeeaaeddaeebeddcdcddcedadbeebeaebccddbaabdaaccbebbabaabeabcaebadccadaeebcdcdbdeabcddbaabedcebedbbaacdeabaaabedbbaaebbeebbdbcbeededeccaaedeeaedaecaceddcabcbbbaabaccebcbcebcecdbbabacecbeebbeaeccabdeaabceebbebbebaddaabedcddaecedbecdbeacbecdcebdbedbecbbbbaebaaadabdbcebbbcbadaaaadaaacddcceddbebbabeeeeeadcdbaaddadbacdeeabdcadbeddadabdbebdadabebadbaecebeaaabceebcbdcebbdeeddcbcbadabedccdeacdbaccaacaeddbecceebadabcaaacdccbaacecadedededaeeddacbdbdeadbddbadaecddabeaddeaadbabacdbcbaccaeceeddeccdbcaaebbcdaeedadbddbdbaaadceeccebdaeadecbceaecedcaedcbacdadcccdcaccbacaabeabedbebbaaeeeaacdbcdbeeadaaeabddcbeacbbeceabeebeeacdcabdaedaaddedeebeeedeebccedbcdbdcdbddbeaaddbededdbabbaaaebbbeabbbecbddebcdcecbbdbaabbbcacecddcebcbdcbcccdbebccccbddceeabccdccedbddeacdaeadceebbbabdeedcaecbadbbcaddeddbbccccedbcadebdccbeeabeebcdabebbbdcadaabcaedecbdceeeeadcbcaddbccccbedababeaaecbecbbcebcaacbdbceaeceacaceaabddbabaeddecdcbacaddbdecddceeedbacebeecebdcbbebcbaebeecbaabcaedeeeacdabcdbeccceccabdccdabedbbcccbcecbeaccdbbcbadcdbdccabdcecbebcaeccddabceacedeeaddbbbcebdeedbdacbcaadabedaddaecbcebcaabdeeaebcbeccceacbcaecaeebdadbecdceddbbbcccaacddedaebaaaaceaebaeceeaaecabddaebebbadeeddddcdcabbdcebdbebaeeacdccecbbbbaaacdbeabbadcadcaeedbddeaedcceeedeeabbaddaaadeebcbdeabceebdebaaceaddccaecbccceababbdbcbbaacabdabdcecacdcdaabadadccdceedaabacbeedbabbabcabbabcdccaecccdeddaaecdcaaaedcceabddbedcaeaaebecbeccaacdecadcdcbbadddeaaecdabbbbaadeeeebdededecceaedadcbeaadebccceedbcceddbddbdedeeecabaebbaddbccdcacccaeeccaaaacbbbbeadeddccccdeecbdaedcbaccebdacbcdacaaddddcbbabdabcadccaeeeaddededaadedcaaadbdbdebcbdadebcbccacbaaccdaddeebaaacdeddcaecdaacaccacabbaeedacbaddbbbbeedacceeceebaaabeadedbabeabcbbbecdcabbcceaedcdacadabaaeacbbeeeddabcbbccbeaaddcdcacdccbaedabbeecedbeabdcaaeebccbacceabdcbaccbdddeccedaebceededdeddbbabebbddeabacebdcbceadbdebdcdabaeeeaabaddbdcdecdcbeebddbbeaceaebdabbdbbaedbdcbacaaebcaaaacccaebecdccacedacdccddcbbedcadabbdccddacbaaaebbdabebdaaaddbdaebbddbeadbbabbdadebebacbadcbdabecccebdbaacceecbdaedbdbacddbeeabacbaaeccadbacebbcccdcccacbcaebdedbeeebbeabbceedcdabbdbeeaaecaacbddccaaaebeddceadcecccaadacdbecbbcdeacedecceccadbdbaabdbdbebaabbbddcacbaaebdccdccdcbddceebedaedddbbebbdbcdeadabccadadcdeaaabaaedbaacdbadecddddecabddcaceabdadbeeddaedecbdbabdedcbaadaaaedddeeccbcdbcccbecedacdcadceeaaaedcaebcadeadecdebbbdaacadeaddbeddaeacdbecedcddebeebebaeebcdecbaccdbccaeaaaecacbdbeaeadacecdbcdbeecbdccabdbbebecdcbaeaeabaaeaaecabcbeadccbdddacbbabbebbdebcbaeeadccbdabdcbedeccaecdbdebccaaaddedbeadecbebedebacabdceeedbecbdcbcdbbedabecabddddebeecdedbaeaaaadebdbdaaabbdceeabcaedeebbbaebdbebddadaaacaaeaaeecabeeaceccebdeccdeeaccdecbdeeebbbcbbcbeabecabbbdcdeacedbccedcebcbbbbdaaedbcdcebcecdbaaabdbbcddacbabecbadbedeacaddaacdacdaaaecbcdcbbaebdecadcaaeeaebcecabbaacacbdaadbbeeacaaebcbecdecaecebdabdedededabbbcaeaccbbbacddecbacaedbbbdacbccdeceedededbeaedbcabdededbabcccadcdabbddececbaadecbedaebebddebdaacedbdbeadbeedccaddcbdeeeededaedbaaaabdedbeedadceeedebdaadcdbcddccadcccaabecdaacdebcecbbeabdeeabeddabbaddbddccaecaeccaecbceabaaaceceebcdccabcdddbcbecbdbdbeabddcedecdcabcbbdcddeaacedadeeddcabaecbdcbeceabdbaeabcdacdbadbdceddaabaaeebacceedebddcacabdbabbdddcaeeebadaedabecaabacedecdceecdcedebdeaeddcdaeccedbcaeacdeeabcbcddaceddaebbedbeedbddbcaaddcbaecebcaabdbeedeaababbbbcebbdcacaabbcbccbceadaadeaddddeebdaddbacbdaaddcbeedbbbacdeddaaadabdebceebeaaacbdbbbcacbccddcbcaadbbecacbeececbddcadaebbdeabccdccadecabbcdbaebeccdaeedccebcbacaaebbebadbebdcacdbacbcbdbdceecaadcabbdcdabedadbcceedecebaabbcacdddadaabcbecdeabacaedecedaddbbeaddabccebbedcaaabebabdeaabcbeebbbedeadddbabcdceeaecbabdabbdbeadbdecaaebecbeedaebacaadabdbbabacbacbaccbecbbbcadadaddcbdaabdccdceadeacdcebdddaebaedcebbedcedacebddecddbbebbdcdeecabdcddbbedaaacabbeadccadcbeccdbdccdbacbbedeccaacacccadeabeccadceccebacceebcdabcedbcdbaceddbdaacdaaeecadcaecccbecabebcadacdbceedebcccedcdadcdaeaacacdcbabcebebdedecccdecaddcbdcdcceeeacecdbeaeaaacaeedcceeedcdbbeddddddcedceebaedaebbeadbabbecacacbddaabebededdaceebacdccceeaebaaaebdaebeaadbbddbabdccddccaeaeaeabdbedcedbeacbaeaccdbeeacdaeadbdbdbbecaaedccaadccdbccdaedaaecadabbebaecebddccdcdedaaecacbbdeeaeaccdaebdaaeaacacddaaaaaddadacaeeababccbeeacbabeeaacbbbcabeceacaadbcceabbdadacbccdccdeedeedbacaadaeedbebedacbaaecbedabdbcbecbbbedabcbdddecbbdcddaadedbccacdbadaecbaeebdbedcedadecdbadcdcdceebadedbaddcbbeebdabbccabccdacbdcaebdaaaebeaeeabdedcbaaabdaedbbdeeadeccaddcceaedbcbbabeedabbbaebcccaeeacbebeeaadbdcdeadbdeadcabcaecdcdeedbabdcbabceaebabbacdaccaceadedbeaaeecedadeabdedccebbdaacddabeccceacebdcebdcebcadaedcedccbabeabceecedcbecdbeabbebaacdebdeabeacbdbddcabcccaddabeebbedaadeaaecaeccdeededdeacadaaabbccbbbdddabdeedbbcdeeadaebcbadbeecaddeccabacacadbbbdbbcaeedccbaeddbedddeddeabdccdcababdcbbcabbcdceceabeadacbccdbaeecdabaeedbccedcecaeeeebddeebdcdaecbbaabadacaaceebbcebeeccdaeabbcedbebdadcdaedceaaedeccbbbacbeacbeadcdacaedcadeaeadbaaccaababedcaeaacbbdaceaacdbaddaadbccdabbceaeadccbacbabcbbbeabcbbdddabebebdbeadbcadeadeebbadeeacdebecadeebeccdccbaabdeaaedaebcaaddbcbdbcddddbdadcadadbeacbedbecbaeaacaecbbcdadbeeedeecdcedabababccaeecacbcacdbdddcdaccbeccadeeaaeacdbcbcaaecbecbedacceebdbebcdbdadcaecbcaeebcaaecccebbdecebbcccebedeccdcebecbcebbacdcddbcddeabdecdcdadebebcecabdaedecccdaaadaabbcdaecebaacadedabbceaadadccaadedbbaceebcbbbeeecbeadebddabebcecddbcbccaaacabcadcedacdabccdeabdadeeccbcbcdcdeceeadeeebeedceaabddebbecbbecacbcbdcddccebeabacedbcedbdabdedceaaccdabaadcaaccdaaceaeeebdcacdbcbbcccdaeccbbcdddecedccbdcbabcadecabddeeeacbbebaeaccacebeebdcadedbacdbdcbadaeeaebdbebeabbedbacebbddceebbacaadabeecdcdbacadaceaaccdbaceaadcedeccadcbddceacabedeabababcdcebdacdbddeeadcdcddaeccbcaeceeddeeaccaccbabdcacdbccbbababecedadbaeecdaeeceeecdddadcecacabcbcbececadeecdeedbebbdceddcaebbecedaceedaeededcabaaebdcacdcbaccceeececaaddabadaabaeadcdabbedccecbbaceceababecacdbbbecadedbcbddadaeadccbddbddabcacaaaebaeadabceaaeceaecdcccaaececbeabdccaaebaaeedbbcadeebbedacdddbeebdedacaabeddeabcbccaccacaeadaeabcddcdddcdacecbdbbbadceacaccacacbedddbeadedaadedbbdadbddeedddbeddedeebaebeabdabeaadcaeabdaaddbcdbdacdcaacadbedcecbeadbcceedbcddbcbddcbeaedcbcedcdccedbaeeabbdcacdbecbdecaaaaedbeccaddecbbceddbeeecbedabadadacedbdcbcababaaaaceeabbacdadecdbecbddaddedeeaaaeacaeabcdbbdbcedddabcebcdbeabeadadddceaedeabbbdbaaabbdaeebaabadddedceeccedeaeeeacdcdebaaeeccaeccddabbbdbceededcdebaabbdeaedabbbcdbebeeccaedcdaadbdbbddacabcddbdbbbddeccddaccedcedcdaadddbdbeadacdddebeadbeebebcebebbbbcecdbcecaadebdbaccebdebaacbababbbbccedbceebebbcddacdceaeebdadeaeaeaabdeedcdcbeaebacaacbddadbedacacbddabaedecbddbbeddccbadcceadacddedccbdbaabcababeeddbaededacebabdadaeaddddcedebbebebdadacbeebcedcdedbcdbbdbaebddadaadcdbdddebccadcbccbacaaeccddbaaabeddddedcbbdbebaaebbedebddcdeabcdeceeceeeadccceadbbecabdddcebebbbdeceadadccedcddebdaddbbeacebadaaedabeacebaaedbdddcddccbececdeeadbaabbdebdeeaeddccbadedbbeccceacaaebeeacabadaeabbbdcadadeabeacbdebadbdabdabdbabebcbecbccdaceeceadabeeadeabaddceadcbacccbecedbeaedbbbabbccddddddacdddecdececaacacecececaeccacbaabdbbcaaeecbeabeccaccacabbcacbdccddbdecedcbbdaaceabaaedbcbbcacadbacccebebeaebcaabebeadaddbdcebdedbacdbdbadaaeecaeabaedaaebcdbeebdebcdbaaedaacddaebbbbbaaedabdedaeeeebadcdbddbdbaaebacdacdbdeddccadedbddedabbcbdcdcededbbcbdeeeebeccaabeaceabedbaaacdecdbdeedbaacddceaadbeddedecaedbbdccbdeddddbcabceaabaccbccbaeaaabbdbebdccbceebaccccdddbbddadabbdcdcdadeddaabdabdbbcbdeadaccbddabaaedcebaceadadeceddaeaedbeabcccdedeedbcdbbdcecebddedcebddceaaedbdedaeaecceebeaaabcdaeacdcabebbabecebecceedbdbacdbcbddabeaabeebbabdaeadbdedaecbcecceaeadcadaadeaaccbbeeaddbbbbcabedadbeddabaaceeedbddbbeedadbabebdceeebeebcccbcdeacccacaceceeaaeacbccbeebaebabbdbdedbeebbbecadcacabdadbdcbbdcacbdceccabccacebcbadbbdbebeeabdccedebcaaebdabbaaedbdbedbdcdbecdaaebbdaccabbdddbbaadbaaacecaeabeadadadcbebbddecceebabceabaecebbaaaaaaebdaebabeedceeaadcbedcbabacecbcbdeaabbdeacddcadccdeecbdcddbedbbedbdebabeeedaccbdadddaaddaebabbdbacdcaeeaabdccebedbbccededbceeaaebebcdadcbddbadebddcdabdaccdddebaeccaeaedbbaddadaecdbadbbbeacecedbacecdbbbddddadeaaebdceeeaebeeedbeceabdbdcbecaadcdbeeadccbbdebbdccacceeebaabcdcbadddceaababcbbbcdadaaaadabbabaabbeebaedbbcaeadeeddbddcbdaadcbdcadbdaceeaaeccacdcbecaedccbcddcedccddcececdadeceeebcadceeddcaddbebacdddcabbbdadcabedbeceadebbaddedacbbebbedeaacedecdaedadcdacebbcaaaaceddbccbcecedabaeebacccbddbecdabceabadaeedbcbaccbbadabeeadbeebcbbcebbdebbbaeeeeacdbbacdebcaaeaadbbaaacaeaedecdbbedcbaddddcadbeeeeeeeddebedabccbbbaedbceeeaacdaeccccbceedebdceaceaeabbaaaebbaeaaeabaedbbacbabadebbabeacecbbcebcaeddeeaadbedcebabcbbbdbaabeabeacbbaedccdcedcdaeeccdcbaeeedbccabbdaeaababdacacaaadbeddaceceeeccbeedcbbaabdededbaddaaaebcedddecccbeabacaacceabbbaadcededadaadbbdbbaeeebeddcccdcbcbbecacabecedaeaacdecacbdbcadababeeceadecbaaeeabcbceddcadcdddaccbedacadedcedbcaeedebdeccabbcaabbbeebebbebddeebaddcbbbceccbbcceadedbeecaaddaddccddaaadabdabddbbaaadbebebdbeeedaddcccaabddcecedebdeceabcdbdaeaddedcaaadbeeaacdcadcdcbabaecbccdacadbbbcccbbaaaaabbeceeddadbcbbdddabbbcdebaeddccabdbddadbeaadbbebbcdacaeeccdcebadadebccddadbaeceaadcbabdaaddabebbcceaecbabccbaedbcecadbcbedcdbeadcbccdededabbeecddbdaaddbedaacecebabceaedeabecbccaceeaaacddcceeaceacdecdabeabaaacbdebadaabbcdacaebbcdbbcacdaecebdbbaeaeedacebaccaecaecdddeaabedcddeccdebdcdcddeedcdcbccadeddbdaeddabaddcccaadeeaacbbdbaebadcbbdedbbbaadecbedeeedadcbaaabddbecacbeeadbedeceeacadccbdbbabdeeecdcbeabdedcccedabeecccdbdbaeabddbebcebccaceeadeecebebdbeaabacaaeabcbbcebccdedbaecaadebdbdcecbdcbbdddbaadccbbeebadceeccbedacdddceeeaebbcddeabbcedbaebcaedeadcdeabaebeeceaadbbbadeadcaebedceccedbbdacedcaeadebaceedbceabcbacbedcadcbbecbcdbdcedaabddeecacbeaaaadeaebcccbbabebcbbcdbdeedbbdecdeedddeccbcccebebbededbbddaedecdbecdabacdeedaebcaecbedecdbebbbedcecdceccebdecbccbaeeeeabbeebcedcceeacbbeaebebdeaaadbcdbdabbecdbebcbadabbedcbebdeaebceddcbebcaceedacbceabcdcaedbceddabcecccebcdeebdabeeaccdeeebbddddbaabccadebccdaaacbacedeebbaeeaecdbbabdeccacbadddaebdcbdcdacdbedeacddbaecbbabbbcabeaedebeacdcabbbbbceddeaacecbbeadededaddbaadeaeaebeaedbeeeacadedebcdeacbaacebadbddcaabccbaadbdbabdddebaaadeaeaeeecaecddaacaaeeecaecaaabbeeabaeaecbdcadccdbabacaaeeccaeacdbebebecdcedbcbebdaadbbcddeadcecbdaaaaadbcbcbadbdbabbebaaeceaadabceceddbceaabedbebbcddaaacbddbdaeecedadabebbbbbdcbbcbaeedcdcadcaebdcbdbaecaabebbbcbcadbaacbeccedaebeeaecaecceebebaceaeabaeecabdaeddacaeacabccdecdcdaddeebbeddceedaeddbdbadadcaadedbcaacbeaddecceeaadcccabcddeeedcdacbededbacebacbadbaabdeccbcbbababdeaceaabedaabccbedeaaacddbdaadebcdcbddecdcbdcbccabccdcdecaccdabcbdabcabbceddcadbabedcccccaaaadeeadcbeaadcedaedeacdddbecbacecbaadcbceaceacebaacaaadccdaaaabdccdabecbabaddcbdaeeccebdadeccaecddbbebdaddbecebcedacacededdceeedbeedadcebdacacbabeedaaabcbddbaeebcceabcbabcbaebedaeadadbedcabbdebdbccdddcbcbadbededdbebebacbcdaceaeebabcddcdcbeedcabbacdaecdbbebdbadccbaccabdbeeddecbedaebeebaacbcabaebecbbebbdbcabdebcdaaeeaabeebcdcdecdedadddeeadadaedaabacdebccebaeeeeebcbbccbacbeadadcdbaedcbeeedaadbcbaeeccabceddabdbbbdebeaecaeedeaadabeebaebabcedcecdceabccceedeaacaccebcececbeabadadcbadeacabaacdeebbaeedbdbdeeaaccccecabeaedcdeacdaecbaadbacbdbebcdedaaeacaadcbcbacbeebebbcbcdeccdbadaaeacadcaebbcceeeecacacbadcdcabaeaacbacdacbdccdcebcaedddddabeaacbedeeebedbeedecaeddaccabaceeaedbdbdcbcceccdacaebcacbeecbabecbcdadbbedccdedbcebcbdecabdebaadeaedaeeecaeeadbdedeaaccccceaabeaeedbdadbeeacdecbceddccceeabecdbcbcbdcccebdaabacadecbadadebcccccdcebacbdddbebbaddaeeabaeececebaacacedededecabddbaecadcdcebdaeaabcacabaebaebdeccedbaceabebceceabbceacadabcebdbccdeedcebedaaebaddadedcdacbeaebbaabbbcbcedecabceedcadeaeccbaddedadbeeeebeddceabbcbebecbcacdeadcedbbaabbabcadcaeeadbecaabadcaaeaeadedcbddebbadcbceeeaccdedccceebbdddcddccecaacbdaadcedecdeeaadcebedddbdaceeacebabbceeaaebeabbbedaedcbbacebeecadbddbdccebadbdddaebcadadbebcacecebbcebbaadedcbdaecdeaeaeaccaeccebbeccebadddabadeaaeabeadddbccdddedeccbccbdbaeccdbebcaccaacbbededaaeaccbebbddadadccecddaceecababcdbbbadbaaaaabddeaabcecbdadacdebadabcbbeedececcecacbddaaebebdbaadaeaaabceceaaabcaccdadbaaccbdbcabbbbacbbcdcaabadedbbadaedcbdcdacabebcecdbbcecabcadabdbaedcdaadcebdbccaabaebbceebbcbbbacaedecdcddddccccbdadadcacdcaaebddcdbecbacbabeacbaadcaddaadbeedeebceabaacbdcaeceedbddedbbedabcababecbdbeacebcbdbdcaddbceeccedbacdadeaedebddacaabaeeddeeaccdecbbbbdbbeeacddacacbaeaeaedcbcababebabceaeceaebdcedbcbdacdbaebaecaeabcecccbacdccabaeaebbdbaecdaedecdcbdbdeadbdbaedadeaaaebbeeacccbabcacbaecdedddaebddbaeabaeaabdddbbecceeeaeaaebbdddeaedcacbddddabddadddeedcdadbbaacccbcacbcacbeedcbebceddacddcaabaebaeceecadcddaaecbdcbcbbddcacbadaedcaccddbdbaceecabbbaaaeaabbedceddcedadbaedeeeddbacaebcabbceccbaecaaecbdcdbedcbcaaecacccdaedadeceebdbddcabcacddeadbbbbedecdbaeecceeeadebcdebcacabdeabebedebadedaecdbebadaebbaedadebececabebeecaaadccaeebdadceceaeaccebdeaccdeeedadceecddddedeadababaeeccceccacececddebceadadabdeeacdcbecedbeeaabdbcdeddaedcbeecdbccacceabbbbdbadbeeabecdacbabbeadeeddbcbedcebebabcebddcadacecddccccaeddbbcddcdaaeddbabddacdaeebbadeadababaedbeadddeeaadceacecacbaababdeecdbaccebcedbdddbcbdbeaedbececeaddccedacabdeabbbacbbeddbcbccabcabebccadccdbebeebddcceccaaaccdabacbdbccaabeecdcadaccadbaebdcacdbdbeecbdecbaababbccaaaeeabbcacacedbacabbbedeaacbdebbdcbbabeaadacaadbaaeaacdeddbeecbdaacaebdaadbbcdabaaddcadaaccabdadceebcdceacdecaedcbedecdaabcbcaebdbdebecdcedaecedacbebbaceacbdcaacbdbdabcddbcdaecadcdbacadbbcddcbeabdabdaecebbeeacbcaadbabebccaacabcadacbaeebdabdaeaeddabacbeaababcebedbdccbdcebecbdceccbbbeacbbdeadcdacedbbabcbccbbdedbddadbebcbeccbcbadebebdcedbbdebbddcddcbeccadcacdccaeebebdbcceebdbeabbdebdbdadcebebdaaaebbcebaedceececdeedadaaddebbdeadebadddbabdccaccbbeabecbdaadedacdcdeabccbdbeedeacadcdedaeceeccbcccbbadddacdccddbdececbaeccebbcaddeceaecbdbeeeceebeddaabadbcdcaacdbbbeaccdbddcaedbacbdddbcdbddebcbbdbbaadecaabbeccdcbdceacccbeedecceebdcecabecedabacecabceacabcbbbacaebaabbdaeacaebbdacaccdbaacdabdedbcceecbddeddbbcaccbeacdaaddceedacaabcbcaddbeadddabbdcaeaedcaedbeaabeaaadeccdecedeccdcbdbbdcdadddeaadcaedeaedacbdeccdbabaabadccbebeaaccabedeccaadbcedbacacdbedacdabccacdcaeeaeceebcbededadbedeaddaebbbddadebdcbbbbaadccaacdbdaeabadadeadcdcaedeeeeadeaceeceeaaaaceceacaaeebcabdbedcdcccecdcbecbceebabbdabacacbcdacbcbeedbecbcceeaeececbeddebcbedddcbdadeccebbdbbcdacdbabeaaaaabeedbbadbcdbacdeccabbddacbdeecedeabdeaebbeddaabdccecebcdddbbebabbdbbababadbeacdaaecadeacdeeaebadcabcadeebddbbcbeeccbdacdcbdaeaaebbaedaebdeebcabaadbacececddecbccabbadcdeccddaebedeebceeccbbdabebcdeceeeedddadacddecacbceaeedbaaabbcedcdbcdabeecaaacedaacededbeacdadcebdbdbedcdabdebacdececececdcbebbdccceccadaabdacaecaddbcebebacdbcadabaabeadbaadcbdcbcedbdcaebbeddddbaacdbedecedaccdbcacddbbeeddaddeadeaceedbccbbbadabdaeebbaebaebcbcbabdbccbaedabcacdecbbbbeeebbbcebcbeabbedaccbddccbdcebccddaeeacacabdcbeddaccccceebcbdaebbbbbecbcecadeddbdaddbdabeabdeaaeaacecbcadbbedaabdeeedadecbdcaaaedbaaaeaadeebddeecadabedbcbcbcbedddccaaaecadedeabaeadeeadabceaccdddeecbaedbdcacbdceeceebacdcbeceebedeeddeaeadaebaedbcdeecdaebaabedabcaccdbaeebcecaedbabdbbbdeecccecdcceacdedabccaceabbbccecbbcdbaabdccdcdbddcceedcdbeecbcbeddedcabeecadacedebedebdccaccbecbeebeeebbdbccceabbbebadbcddaccbeeeaabacbbdedaebcaaddeeceabbbacccaabeaebebadaaaaaabbaedbdbaebebcaecbaeeeddbcdacecaaaeccecadbaedbdbbbbeadeccbaacaccaeaecebeaccdebbecceabcaaeecbbcacbbcecabeceeaaacdedceeccadcbdacaeccbcacaedcabdadeebdbdebcbebdcadedbcebdebbdddbdebdcaeccadbaacebedbbceacbedebeccdcbdaaabaedeecedabadbecabeabccacddebdedeadcbeebcebdabcdeecccbcdcdeababddcacdcedaeeacacadceaaedadcddccddbecbeadbbccadeeaccdebceacaabbadcaccaadbbeaabccacbbacbebdcedbdcdedeaddcdededdccbadceabaabbbaddedbddedaddaccececdedeacaccabbebeeedcedbdceecaaebbdadadececdcccddebabdcbaebbdbbdaebcddccdcbeeebedcbbddecdcbecaeabcbcddabdbacaaabaaaeadaeddacebeddbeaddeaabbcabeabccabbcbeaacbcaababebadaaaacbdcecbdddddbeaddeabbcdbcccadbecccdabdaeebabebabeaaeeaececdbaebbcbecbbcaecceacbbecebbdebceeeaddbbebebcebaaabacbbaeadabdadacbeeebaeabddecdaccababbdcbdacdaacbdcedbcbeebdaaadcbbcaabccbdceceddedcaadebecdddacbdcceebbbecadbcedccdbbceaababdeccdedadbcccaeaccbdbdadbcdceaaebadbeacbecacbcbbcbaceaeabadaeddeaceddbbccaaecbeeeeedbbbbdbbbaaccaeeeaedbbaabeacaaedbabecadaecceadeeeadccbdbaccdcaaebaaeebdbabcdbbabccaebbdeadcabacccabadaecdcbbbccadacaecaaacdbaaacedccdebedceaccecdadeedbbddbeddcedceeeaccbceaaacdaaeedbccaacaeddcaeecdccedbeebeacaacedcabcbdbdeebcaaccddbadeebcdaabeeabdadccbabeebdcbababaeeacdaedbbdaccaaadaeeacabcccaaeceecdcccbbdadecbbacecaaebeaceaabbaadbccdbcadbedaebadaddecdecccbdacbdbcaadbbdcadcacdadeacedcdbdccbbdaaababcceebbaeaccedebbccadaeaeaaaeeeadcccebccdbbecbedbccdcdbbcbbeaebcaeeabacddbeadbecdcdacbddddadbccaabacedcdaaeadececebedadeccdbeacbacbebebeedbeedcceeedacbeedecbdadeccdbdecbccdabbcadebaceacbabbaadeccaaeabaaaacdaddceedaaceabbeacbeceddddbabbaecbebabecbebecaeeaeaaeccbeddaebcadedaceaddbcbdadcbdabceebebccceccdaacddacccbecbbcbccecaabecacdcaabebcaadcbccabaeacdeebdabbdcebdacdaadaddbdbdcdcdebabddcdbbabdedeabbadaceacccaabdadbedaabcccbadbccdbabacedadbcddcdedeadaeebdedbbbcadddedbbbedaaabeebedbcaacbbbacdbcadebebdecbeeebacccebdcabeadaeaddbceccbdebacceadaeeeddaeeebddaceddbecdedcadecbedddeadaebebcdaacbdbdbdbecebcdbccdecaccbaccabddceebcbdbccdddabaeaeaecbdccaaeccdccaacbcddecebecbebdeaabbacdeeacacaaadedaedcaecbaabdcaedbbcabbeedcdadecbaaeccaacbebadebdcdeabeecddacaddddaabeeadbdedacbadecdbadbcacbedecbbabaaabdbeeeebcdedeadcbeceaecaebbcaecaaacdacdbcdccbedacdabedcaecaceaabaaceadcaaaaecadebeacbaddcbbadbdddbbdcdcbedcdbdcdcdebcabaebdebeadcbeebdcccaaeebedbbdeceaacaaaecaddbccaeceddebeacbdeceaeebebeccadaecaceddaecdaababacaedcbbecebbcecbcceddebceabeaccdecacbcdeaacdaeddeecebadebaebebddbabdecbdecbcadbdecbaadadcaabbaebacbeadccecbacaccaeedccaebdbbeeeaaecdcdbaebbeccaceacedbbbdaacabbcadbcedabedacccbdacabadcedacbbcababaaacbddaaddbdaebeaacbdcbbbcbddcaeeecccaadecbacbeceaddbcaedceeeddbaeceeecaeeebaacbaaeedecaceceeadbbcbbecbbbbebcccbebbbabbbccabaccdbceeaaabaeccadcbbaaedaeddddeeeccdeeeedcedcabddcdabeadadbccaeeedeabcacaeedbceddccecbcbebebabeddededcdcabaaaeedbddaaeeebeecacccadcbaedeaadbbecdadbbeebaaaeadeeeacdeeebedeeeeccaabaacbdadadbeaeacdabacaeaaadadbcbdeecddddeaedbdbccccebcbabcecbcaddbbedcdbcedcbaadbdececadcaeeeeeaedbdccaadebadddbbaaedeaaececbbbcdaeacbcccaabddacbccaeabecccedaeadbaccddcdeeccbdbdacdbedadbbabeabecbacdddaecaadbbdbccacadebbedcdaccecbcddccddcebedccbaeaaceabdbcceccdaaeadacabadaabbaedacddaeeedeebbaeeaeebdbaceecbcceedbebedbadccbbecccaadccaebeaaaaccbbededecbabbbedeaaedaadcddcdbaedabaedbacbaeabedccdddcbbcdddebcdddeaeadcecbbaeadcdbcadbacbccbcaeceeeacacbbbecdabbcdcbcecbcccdcabedeaeededaddbedbdaddbebededadddaacbaeeebbadecccdbdaabecbcddcccbdecddaaacedeccccceaeccebbbadcacaacbccceddddcbbbebbddbbabebddacbdeeacaacbabbaeeaddedaaedadecabdcecacebbdbbaeadbceadcbacccccaadddabadcdecbcddbcdbdcedcebbbecdcabbddbcadcddbcdaabeccddcbbaaccbeacaabcebddacadbedaeebccaaedcedddedcdccdbdedeccedacadeccabdbdeaeebdaadbccdcdcbeddceeabaceeaaabaaddeeddbbdcccedeccbcbcabaaaaeddbbdcaaadcdcacaeaadccecaccdcebdbaabdbaddaeabeeaddbeecebcabcadacdeadddaeadcadcdbaabadcaadeeceebbdeaaecdcaeacecdcadebdaabedaabdeecabeebabddbcabebecabacbebbbbcbdcabcecedceeaccdeebadbeabccbcaaedcecccbbcaccccccccecbacdddeceacddcaeaaaaaeedbdaedeeaccebbebaabbebdabdaebcbceccbeabaddbabbcbcdaabacebbaeacccbeadeabacbbbdcecdecabdcedccabebeebbcebedbaeaecacabdcaaddccaadeccabcadbebcccecbbcdccbaeedbcdabaeedcccececeebabaeeedccbdadbcbbbbabbaecccbedbadaadeaccbedecbaddaaaebaddeebbdbdadaaedabbdaccddcebecbddecabccdcbcdcbedebebbcaadcccbbccebbceecbabdedaaebceedebbdebdaadcbebeaddceeabeedcbedeadcbdeddecbecdbdbbadcaedbedabbdbebbdbacedeadcbddcadceedbebedadeaedbaecdcdeeeceeebeedeaecbcdeabdbdbdeeeeaabcaabdedbcabddcadadbbeddebdcdecdebaecbeeaebbeddbacdbabaacdcbaeecbdcababecdeebaacdceccbedcddacccebbebaceacbbaabaeceebebacbbcdbcaebeaaecaeacdcecaddcdcaeeaddecadbcaeebceeaeabddedaadcadddccdcdeaaadcdcaacedebcceccdababeceecdbadeddccbaeecdaacabbbaebbbeacaeeeaacdcaccddbaddbdbbdecaaaccaabedceaedecebedddddbaccaacbcbbaecededaebcddadcdedddbdcbbddbeaecebcccacdcaaecbccbcabddbaeeadddcceccbcbbcdecbeceadabceceeebecbeddbaedceaaeecbddeecbbccadbdcbadcdeaddeabeaaabeccbeeadeccdbabcbddaedbddaadabeabbcceabddccbdaaeeeebdceccdbaaeccceecbbcbaacaacacdbcadcbbaaaadeeaccaeedadddbaeceeacccaddcbeedddceddabaddccbcbbacbdbebdcbeeedceacecceeacaccddaabccceadacbacdbbbdaeadccbeadbdddcaeeacedadedbceccdedbececbbeadceebeccdeeeaebdbedddbcabdbdebcbadebeaedadaaacdbeacbcaebbccedecdcbaedcaedadeadbecabeeaeabbabacdaaabaeebacecbddedaaebcdecadcdccdacdcdcadbecbaceccbbeacebedeeacedeeacccebecbccaebebdedadcabeccbdeaebaeeeeaeadeccbeaeedcbcaebdeddbdbcadcaebaeecebaabebddbbacceeeaeaacccceaabccabeaedcbbacebaabcabcbbcecddeabcbdabcbdddcbbecdeddceebdbccdedbeeeabeebbddabcabecdebacbabebcadabbcceeadecbbecbeaabecabadbbcaecbabcdeaeabbbeeddbcdadacaabddacdccbddedaddcccbaeaeedaedccabaecdeaeaaedaedbcbdcdadedbbaaadedddbdedbcabbebbcbeebaebdabaabaacaeceacbeeeedeaedddcbbaeeadcebbaabbdbaaeccabaabbebadcbcaadacbdceaaceeaeeaabeaeddbbcbcccaacaeceddcdedbccaacedcbdcadabadecdcbccadbcbbabacbbcdcbeabbdbebcdeaceedcbdaeccbdedeebdabbaadeecdcadddbeeebddabdbaadaedbcbcecebbdbecdaaceeebbdebedccacdceddcbebceeaaceaaaccacbbaabadcbadebacbaceadedbdeacddbbdccccbdaaacdaddadabdcbadbcbeadaebebedbeeeecdeeeedbcceeabddbddcdddcbddacacacccaacebbeadcdabecbcbaecbcddcbccbdaadeaebdbeccacaeeeeddcbbbeedcdbccecacdeddaebcceeceadbbaacccddedaddcdabdaadbdadbdbcbedeebecaacdcadbbaadaaaecbbbbdacdadaaabaeaddecbdcebbdcbcaababdebeaeeddecbdcecdcbdbcbdcbccbdecaebdbecacbbacabeeadbecbacbbddbebeadabdcdadedddebeccececadeedaeaeaeaadbabbcabcdbadedbeadbcabaddceeeedbbeecddddcbadcabbadcbeeebacceadcdceaddbabcaaceddadaaaabddbdbaaddcbecdeccebabaceaddabdacecbaccaeccbbaddabebcabbeeeebeedcbcaedcadedacbbaedbbacdeeeebacdaddabeaaceedbbcedbeaaccddbaaeabdeebdddbabaccaeeecedceabbeaecacdeeddbacdcacaaaebdebdcedeceadbbcddbaaeedeaebdecaecbacecdbdacdadcaadbaacdecbbdbddacbebcabecaebbeecdacccecebdbabcdbbdaddeedaddcbcdeadebbdcdbbeccadabbaaeabedceadbdddceebbaaecdbccedcaedaaabebdeaddcabdbecbebcbbcbeecbaeaaaedddcbdbeccbaadaebbcbcabdbabeccbebcabdabcdbeaacddbabaddabdcbbddbaadadeaeaaeaebeacaccdacadeadbddacacbabdecddaddabcbaacaeecbdeaabeaacdabcdcbbbccccbaececcebbcdbaeedcabbdbeabaedeceacbabaeaceeeabebdcdedbceaabaedbeaebcccdcbededcceeebcdeacbdaeacacddcdccbbaacaccdbddeccdeeeadaccdddbeccdadaaeeedeaeddcbddbecbeebdddbabaeccedebaebaacdcdcadecdeadbaccccedcbacaeccbdbcdbeabecdadeccadccbdbbedcbadaccbaeebdacacebbdcdeebdeccdcbbabdeedadccaebeeeaddcdebbabbadaebebcbadbdedadbccaccedeebbdeadbbedaabbecbbaabbdbaabcdbeaebedaaaedbeaeadeeadbbeeaacaceddabaeeacdcecaddbcedebadceaccceacddacdddcabebededebebbcdbcccdabbbeebabeecdbeabdbedbedcbbbdbcdceedaaaabaaaeeabddaccebaabbebdadadebdaaabcccaaedcadeeabbdeaadaccbbccdebeadbaeaecdaddbeeacbbcadccecbccddceabaedbbabcaeadeedddbdecdbdacedbddbdaaadddedcaccdbdbbeabbdbcecaacdccbccaebeddcebaccecdbebbebacabeacaeccabbaadeeabecaaaecdebcebecebecadeddaacbbcedbbaaebaceabedabaccdeabadcbadcaeddeeeccabddeedebeedccdcedbeeddabaaaadabeccadeabddbbdaecaebaecedbeeddaaedcdaedbbabdddbbcbaceccaaedeabdbaabddcacdedeeadeacaabcddeceaddbaebcabbabdadbeacedaeccecacaaecaeccbbcdddeebbdacdcdbebdcbecbbedcbeabadecbdacccbbedaeedbdbdabcdbebdecbbdbdbbaccdcaaaadaabeaededdbabbeaaacebaaddeacbdcccebeacbedddeaeadaddebcadeaaebabbdaeaedeedcdcbbbddcdebbcdeabdedebaddcdbccbbdbcabbbcccdcabaeddcecaeebdddaabbcddecbbeedadceccdcbaddbddeeabdbbeeddacecbddcddcaceacebeabcaedbccddaebeeededaccddedebddbbbbdadeebcddccadddcaacaeccceeeecdbbdbcacddebadcbdeebebaaabcedcadbdbaeabddeebdabdaeddbabcacbdbbaddbddeedbbedcccaadccbccecbadaeecbacdedaebbbdcedbedaebcbcdcddbbbadecdedcddbaddeebadcaabdbdacdbeddcbcdddcdadcaebccdabdadbeeebbedbdcdaceaddeacacdbcddacbdbacdbbcebdbdbedecbeebcabecddbdbedcebdedacacedeaedbeadaebdcadbedeacdcceedeaeccddddaebabcdaacebabbbcabbbdcbadbdccddababdeccbeceeaaabebbbdaecacebeddbacbbaaeaabcececdedbaeeaedbbdcededcddeacccadadbbaadddebdcabdecdecbbadebddccdebabebebeaccecccbbdeaebaedeedeeeddaecceeaacedbcabaedbacdbbaaaadeadeaeebadccadecbcccbaaaebbebaecbcbbeecdababacceeabdadeedbbcceadccdcccbbcbabcebcbccbacaddeedcaeaaecbddeecadbddbcabcdbdcccadddbcebbaddbeabbbadccdeccebbdccbbdaceabeccdcdeaccbddeadecdceccadadbeeabdceadcaabadaaaadacedeadbcddaaeabaedcceddbacdaeeeeacbbceaaeecdcdbadeadebbcaabeadbcababdaabdebadbbadcccdcebdeacdedeedacecccbaecbbacbebddebbaeaddbcecbecddeababeaabbdaacbebbedbdebaecedebcacbeabbbddcdabeeabdebccacadbeabbddeaecbcbebbdaaceaacdbecacbbdccedacdebacaaaaecaacddbeacbdecbaaaacedcbbbbcdbcaebcbabbedceeaddeadbaecdcddaaeecdcedbbabacaaccdddcaedbbdcacccacccbebedbccebadcdbdaeadcddcebdbcebdaddddddbbcdbaaeeebbbcebdecceeecbdbedecdccabeecddbaaadcbdbccbecccbacddeabdbbbbdbbaeacabcdcdaecbcbaaecaeecabdcedeacadddabdaaebecbdbcdeabbeedcacbebdbbbdcbbeeeebbaaebdeeabeceebceaaaedcbdabddbeaddcebadcaecebabedbcecbebecbcbeabeebaceeacadeccbdbcdbeddbabcbdebeaedcbcbcedaebdedeabcadddcabbbaebdcebeaceaadcadeacbdbcdeaadeddbeebdacdbdecdcbecdaeeecebbbceedbdeeaedbaecdabcbeacbaebeddbccabeaecdecbbdccccadedbcdedebdaceddeeccdddbbacadabbeaaedaebcddbdbbdddcbceaaeabaceaceedbedbdeeccbeebebdcbdedbbbdeedcddeecdeaaaebadcecccdedacdabaeecbeacdaddeabadcdbeaebcbadcdddeaaeaaccacbebcaacdadcccdabddadccbdebadbbdaaecbcdecaddbeebdabcacccdbbccbaeeebbebdeadeaaecaddcdbacbcceebeeebdcdcdeaabacedcddeacbaeeaddbaacccaabceebbcbeeeadaedabaccdbccadeebdedbcbdeebadaeeeacaabecadaedbcbcbcebddcdbdaddecebeeaaacadbabdcadbaebbedbdccccddbcebecbeceaccedaaaecadaeebbcbdbceadebdebccdcddcabadbdadcbdddbeccededbccadeebdbbecdcacaadbdbbdeaaeddaceeceadacecddacadcaacaacebdeecdacaeebecbcdeebcccccdaacdacdbcddedcbdcbebaaeadeeddddeacbecceacedecbcdeaebbdaacbdacdecbdaeedaedeaebabcdacecdccbaabcbaabcbeddcaeedbaacebddcceebeabaabcedcbdebbbaddcbbcebdbecccaebdcbedcebaeeebeceedbeebacddabaeabdeadcbcbaaadcaacaebadaeebecdcaddaddebaadbbeaebbeceaeddbaeaaaabeaddababbbaedccbacdaebdcaaaddedebbbcaaaadeadbeedebaaccaadcbadebccedbbedbdebdeedeeddedccbecddadeccadbaeecdbcccbececdeddddbcbadacebdcdcbbcbebaedcabdcaccdbdedecbbeacadabdecddcebaeeecdbbbdeecbbaccbebebdcdcbddddeecbaadaacababdceececadbdddccecbcaaeadabeedecbdcaeaaadeddcaadeddecabaebcacdaaabededbdbcdeeedbbcbcedddaebadebccccedaddedbceeaaaedbddebeeeccabcacaddeecaaeddeeabdbdecbbddabdbacceecabccddedbdbcdaadceeacbbcaeaabdcbdebbcbecabbcbbcbacbbddddbdeabccbaabccacecadabcaeebdaadeecbeedbaeebeaddadbbccbabbeeeebedbaebacdebdeeccaabbebeecddeaebabeeacccaabbebcecdadccdebcadddbdeaeeabdbcaececdbddeccabedcdeccdddddbcdeccbccddbdaaadaacecedebcbabbdbdeedbadabaeaedaadbaeececabcccbebeabaeeaadebbabecaebbeaebbababdcdbbbbabdbedebaeeeaecadebcdddcebdabdaddaaebbadccdaecaddcdbbecddacdbbbabdecbbdadaabecbdacdaadbdebacbebeecbcbcaaaabeadaddecbcbdcdbeebbedaeeccbcbebecadacabeccecbdaccbabacdeaddedabbbaebbbbcecbeabdeeecedcdccdcdbcdbeaddbcebcdababeebbbdaceeedbeabecedeaebeabdbcbcecebcbbdcbbbaeecbeaedeeceaeccbbcebaaabedccadccacaacbdabbbeceedabcdccebddaecbebcecddececbcddccbbdecbcabecddebaaedaecabebcdebebceeaecbbcaecdcceccbcdbddbdaceedbebcedabdedacececaeebebebdbadaeeeebcbeadcacacabbddcaeeaededccdaddbeeeaadbbdbacbcceaaddaddebbebcbdaeeaedeadeeeeabeeebbddaeedcbbcdcababceebeadbeeaecceabeeadbcbeddeadbaedeeccbeddcbcdccecdbcdaaceccaeabcaaaceaddbedeedaabacdccecdddaddcbeaeadbdbbebececaadaeedbdbbceaedadbdcdaaeaeabdedcdbbbbdcdcdcccadecdaacaaadcccebacbdbaaaacbbabadeedcececadbccededcbeacbbdecbebdecaccacbaaadcdebbecebcdcdaccdeedacbcbecceccbddaadaeeaeedadbcbdabadddcbedbcabaccdabccdebaccaeedddcaacccddadecddadacabeeeccdacbdadddccebabebecbdeebdeabaecbdebaeadecbccaabeedbeceaccedcbbbaaecdbeddadcdaddbbcbeaaeaccddcecbcdaddcbbddcebcbaaadcecceaadccdaeaddbabcecdbdaacdeebaccdddceaccbeeebaabeeeddceeedbbbccbaddebdeeebcbedcbcedadbeabeecbccbebdccceeebacbdbbbdbceaddbadabcdecbeebaddbbbcdcdeeaebdbeaddaaecedcabbadedaeaedcbcdcdaacedbdacbadbddbccdaebbcbaebdeedaacedaeabbdeedcdbcbcaacdcaddabeccedcbcbdbaddaddedabbebddccebbaabcddacacccbeabeebdacaabaaebaceeccedaeaddeacedcddacabdccedbdbcebcbcadddbbedabacbaddcbcbeaedbcbaddcadcddcedabcecbdabbdceddcaccddbdcacbedaaccabcbbbedccecdbeabdcececddcaabacddbbdbdccbccadbdebbcbbbacebdcccbbdeacbabebcbdedabdbeeaacadeacbebededeebbaeabddeecbcbacabdecdaddbeaccaecdaaeebbdccdacbdcbcaaeaabcbebebcedccabceeadddcebebcecabbcaabceeeaeaeeececeedbaaaacdccebdebabcdeebcccbbcedadeeebabbedbedacabeadecaacebabccdecebdaeccecaecdacabcecadaabcceecbcdddbeecdadbaeecacbcceaeccacdabcbbecbcaeebdeeaddcceeedacaddabeceeeeeaeccdaeebcacedcbddcaacdbbceededabbbcdddcbbdedbaaadbaddbeaeccdbbddeedbbbbeddaeddeedecaaadaceacdaaccabdadbcecdcbaacaabcbeedaedeeebabeedeadaebaedcabdeecaabdbaecdcbaabddddccabebabecabdebeaecdcebaebdcdbabdbeaddaebcdeeddaaedcaeeaedaccdcdaedeacddaadeecbdbbedbeddbbcbcaceebdbdedebadabeadbdedacbdababddabadbadabeaedbcbcebbcdccbadcbbaebacdeaacabcaaaddcceadabcedebabadddccaebebbabeacabeecbceaecbccaddcbeedcdcdceceaeeeaaededcbbeecbdeccbaaaabdbccbdbddaececcddbcddeebaeeccadebaceebddabceddeecdccaacecaecccededebedadddbcedcabaadabeeaddedcccddcbdcacbcaeabccbdcbbeabedcbbdbccdacadbbdbcaaacccaeeeeacedcedbdeabcecaebbabccaeddaacbebbdabecdaabaecaadebcdecebcccddeacdabecdecabccadeeadeaaeccaaaaededcbebaebadeebaebeaeeaaeaacceaaeeebbdacecbeeeabadbaabdeaecdeaaebdbdeeabeccedbcaaaceecdbbbdcacdedeaeebbcbbeededcbebaaccdecacacdcbddbaeceddeaadceeecacdeccdcbcceaaaaeddbceebdcceecbbeaebdcaaeaadaadcecebdbdaebddebccadbeeabecacbcdaaadecebbdcbecbddbddcebbadcecccccbbbaaabccadbadbaeaecadccaeacdbadbbedecbcbbeebdebeddbbcbeabceabbdaabddbabadeebbadeedecdecaebeeccadbbaedacedcbabacbeddcaccacddeadecabcdcaaedaabaebabaadedaaeddadddadebbbbcaacdadaecdceeacabebbdaeceeebcdedcdceabebebcdccaaeedabdadaaacdbcdbcecbbdcbbebaaeacadceacdebaadcdbeeccccceadbeebacaecaedebeebeccddbcbacbbcbdbbaacccdaccaeedadebbddacebddddabacdcaecbccdcdabecccdabdaceaadbacecbdbdacaaebdaeaccbceadbcdedacedaedbbeeebcdcbccdaeadeabdcbcdddadccdbebbccdacccacbeabceebdbdeceeeacbcdcadbeeccdbbdcbcbeebcaaceedbebeecedadbccebebeacebbaceebeecedacaaaebaeaaabdeaceedebeeaededcdbdcdeaecbedceacdacbbcdeaddcbeddceeeaaabbadaaecbcacdecaceddcdcbcdbaecedbbeaabcecaecedeaddebcadacccdcccaebeebddecaecceabaecacbbbeaedcbedcccccddabbabceaaadbaeeaceecbbceabeaaabaeabbdcadbeabebaacdeeceddccdbabcabdebbeeeaebcbcbccecccbeceabddbccabccacdebdaedbedacdebccdeeeaaacbcdabaadaabeebddabdccabceaeecaebcdaaacbacdcadbecdaaadabbbcdacaaededeeedebeeeaebaedeaecccbceaaccececdbcbaebebaaaccbacdceadebdeaeabdeabeebaeecaadebdadeccebddbbadcabcaeebadddbedbecebaadadeaaaceadcccadbbcabddecdaabcdeacedcbbdaeaecdacedbcadedcadadbebbedebceadeadaececeabdeabeccacbeedbeadcbcdeaebbacdbbadebceececdacbbaaabbecbeabcecdddcbbeaabbdaeccaddcabcccddbdbdbabceeaadcacbdadceababaeeacccbcaeacdedbeeeaaceeededbceededeacbdaeddbabeeeabaaebdeeeaebedbaaadaebadcadbdcdebbddeceeebbbbedaecceeeecbdbeeaaddeeeeabaaaeaaecbecbcceccdbdadedbddaaedbeaadabbaaaecaeaabacaccaceccbeaeecdbedbacdeecebdbedcaabeeeeeacecceacbaceeeecbbebecccabbdbedeaedbdeacebadcbdeabcaceabbcacdbbabdacddbceacccdbbdbbbeddbcdbecdececdcdcbcbeabdaeaeaeecbdabeecaacbabdddbceeddebaccbdacaabaedaeaacebcbedccaadacdbeabddbbcacdaceaddeeabbdabdadbeebbbdbaeceaaceadacbbeecbeecbdbcdbdeebabaddedcddbbaaaacccddeaacabceddecdabbdeedbbdabbaabcdcccbadbbdedccaebdbddbaceababbdbbdbbeabbcdcecaadbcaeeeecaeaeccbdaececbdbadedcbdeedadcababcdcedacdceeaddbcaddebbeeceadeacbcdcdaaeedcacbeacddcacaedabdadebaceddebcceecddbdeebadbcedabebabdacecbeeccbdeaebccabccaeebbcecceccdddaaaaececdeabeedcaeadcabacbdaeaeadddaeacbedcededdcbeeecceeeaddcebbebadcabcaedbebceebeaabbdaaadbddbaabaceeeaecaeecdaccabbeeadcabcbcdbceaeaceeebccebcebcbcbcabbbdcaaedbbaaedacbebbbceaddadacedddbcadbabaadbeabaabeabeaccdbaadabdaeddeddbaeaaeaacddbddbecaebccdaedddddeedccbccbccbcdaeaebdadbecaccebaddeeeeeeacceeadbcbecaeaadcacbeaedbbacdbacbbbdbedeeebaccdecdebccdceabaacacbeeacbabdbacdbbaacdaaebcecadbeeceabdcaaaeedbdacbdccddacadaeaabaacdbaacabbdebbdbaddbbaebebdabbdaeaabaedbdebebeeecacbabacbcdacadedbadeadaeccecadcacdeeeaeecacddaccacddbbcbaaaaceaabeadcdbbdbaceccecbbeaecedebabbcedcedbecbaebedddeaabdababcccdcbaeaccdedadccedaddcaeaddbebdadbadacbaceacabcaddcbdddeaeeddcdddadadaaacbcedcecaeebcddecccbdbcbbaeaebdaebecaaacdacabbdaedcdcbebbdeaaadedeeeeadcabbbbdabbcacacaeabecbacbaedddadecdecacdcddcaaabdeebadccccbbedeaecbadcdbdabaaadbcaddddadbaddbedbcbbbeecabbdddeaaceadeadbdbdeebdbeddbddaeccbecacccbcecaaebbdabcbdcbeeebcbdedecebdcaebbebabcbdbabbddbcdaadaaaedecedeababeabdecbdacedcebcdceddababadbcbaaedaebeebbbcdebeeeeaddecdbaaeeddddbdabcbeebbdbebceaaeabaabbceaadbbaacaddebadcbcaadcacddbbbdacaabcbccecbcdcbbbeeaeedbcadeeeebdebdebedcaaeccdaaebddeddabcaacbdacccabcbabacabdcababadeccebebcbceaadaeaecdbbcbebbaababbebdbbcbccdbaedcbaaacaeebdbbbaaaadeaecaacedeaeecdaceebcbbccbbdbdcdddecadedbcaddbdecbceecedbabeaebeaaacbdcaeddddcbacbbecdaaaedbaeebdacbbcebdcbabacedebecaeebeabdaacbdbcbdedccdceedaabbddacbaeacadbbcbdbadebeaaaabcacbadddbebeecebedaaeeceaebcecbdedaaedacbccaeeeecccdecaecbceacbaebbcbeeebcbdddaadccbdecdaeccceedcdcacececebabdcbcaaabdbeacacdeaabacbadddaddecaaacaacebebabbdebdbadcbaeadaeeedaabcabeacbaeeaceecbcacdcabbdeaddcadcadeccaccaddecccdaddcbabcaedcddecaaaedecdabbaccacaccadbaddbacdddeacebbcdceadbbabdeaaaaeceaeeacaeceeebcabcceabdeadedabbecccabebdeddeaddadcbebbbdacdeadbeacbabbccbaccebcbccaabeccecaedbabaeddadeedcccbabdbecbcdabbebdecbecbdabeaaecbeaccaccbbeddcbaccadcabcccacbaebaebebeceebdadaddeceacbeacecbaaddddeecbaeeeccdaedecaadabcaedebaeecbebaebedbbaceacddbeedecdeabcccdaedeacdbaceecabcadbadcbbcbecaabebdcbadcddbddaebbdcdeecebdbedbbaeeacadebcacccdcdaddaedabccbeecaeccbddaeddccdeacdeacecccbbbddbbbdacbdceacdbbacccdddeeeaebdbecacaedccaadeacaeabbabcbeaeedbbcaddbdccbcdcbeaaebeaedcadeebcbacdcdceccbbeebdbddabcddbbcbddccdbcbdbceeecdccaeeddcaecdaebeecdabebcabebdccbebaadbacdaaadbedabcdebcdaadbacabccbddbcedebceceebdeeadbedaecbbaaaeadcceebdcaaeaeceabbecdbbccaebbcaeeaebacbededcadcdaedbeecebbaebcdcaebccacdeeebcceaabcaeddabbacecceaebcaabebdacdadeedececbcaadbbedcbbdbceeebebdecebcbcdeadbeceacabbaddbbeaabecdbeecebdccddedeacadebcbbcabacbaceeabbccabbaccdecccadcbecbddbdcdacddcdcecdeacebaedabeecdbdcbbdaeabbecaebedebedddddacdbeebdbeebbcadeceddcddbbcedccceddcdbcbdedeceabddabeccedabcaabdeebceecddeebbbaddaaaceeaeaabecedbbdacdabebcaabcacacccbeebadbebacaeedbadcbaacaccbdddaedebbeeaabbaacaebdeceabecdcbcacbdbecddcbecceccbbcbccaadacbdcdcbeeedacdedeeceaaaeaedbdbccabebcdcacacaedbdbccddcdcbeacdabcabddcdebaeabaccedabacaccabdbaccabbaeaaeddeabcbbabbdbdcabdadeebeecdcccaeaabecbebcdceeaaedaeecdbabbbebecbadcdcadeeeccebbdebcceaabcacccaeebcccbdccbddabdadcddececcdcaabdcccdbadbcbabecddcbcddcbacaeccdeeecdbebeddcbaaeecacabeaabebeeebecdcabdeeaceeeaecdebdeeebddbeeacadccdcaaccaeebaeddddcebceeedbdbcbddbdaaabaaacbbaedbdcbbdebcbecabeecdbccdaabbcaaaecdedbcaceaaebeeecdddcbdedcbbcaecacaaeaeabaeaaaaddaaaabeaaadaaddbaddadbbdebddbdeedbcdbacdccdeabbdaacaceebbdddbdceeccddbedbabddeaecbedcdbbacecbabadbbbecaaadaeadeccdecdddcacbbeeccdbcacccecbebbbaceccbeedabdbbcddadacceccdbaaccdcbcdddeececddbcadbbdaaeadcdacddcdababcddedbcbecaecaebbbddbeacaabcaaeacdbabbbadbaeeecdecdceeddaadbedbeadabbacaeaaebaabadeddcddcaccbcbebcbaeebbecceecdcbeadccebebecceeccaecbceaebbbcadadcacecdbebbdcadaebecceddceaaecddbcaeaeaccceceddaeccabaccccecbacbacbccdeceeeaedcadecaaceddaddbbecddeadddabbcbdbbbcebdbccbabcdaebdcebeedbbabddaedaaeeaceedeeeedeecdbaeadeedccccaadcaeadbaaebbacbddbeeecbbccdbdbcbeddeaccadbcbdabecabbddaeddedecdbcbcdcccbdcadcccadeddaadebdbccdedceecaecbcdbacebaeddcebcaeaadabeaebbadbeeadeabaadbaabcceeeebeacbcecadbdcbeeeabdabdebbbabbbbbcceabeaeaacdaaeabcbeeaaddeaadabdecadadbcccccaeabdeadbddabdcabebeddeeedecdedcbdccabadaaeeccbbcdedeaecaaaecbdeebaeeaeeeaabdbacbbbeaeadccaecedebddebdbbbbaddbbeccadbeccddabeccaccaccadaebbcdcaecebaeebeabadabcbdeeeaaebadadcdddccaeccedebaedacbaebedadaccbacdbadedadccccbeaeaeecccabcdddeceacabacecccadabdebeeaecceaddaececeeacabacdddccbbebbacbebbcdcdaaaaaaacebcdbacebebacbeccabebddacecdacbdbedbbbacbadbbbbcbdeebbebccbcecaebeeeeccbabebceeaabadaccdacddccbccebbbbcbaccdeddaaceecbbadbecaaecdcbdececdbbcbedbbeeeddcecadbaeabbcabccbeadebdccaaeebdbededbdbacaebbcdccababbbddcbbeeedbbbeeabaedaebaaeddebbeedbdedcbeedddcbebbaaaaccccacbebaceacecdedeeebecaedcbbcdceeecbaabdebeccdccdcbeaaadddbeeddddcedabdeeeaadcddaeecdbedebaeccbcebacecbdbedbbdebaececbeeaebedcccadcbbbbaadadacebdcbbbbbcebbcbbaccbcdaaeeeaabdbbccedddbcdddbacbeccbeaaceedebaebacaeabadcadebbcdbacbebeeabdbcdbdabcdadbadcabcdaccbdcecddedeeedcebcbeaccedbcadbbedeecdccddeecdbcddbedcebadadbddcdbccacbcdbaeadebbaeeceaeacebabecccaceddebcdbbeaeaacadacbacebedeeceabecaddedeecddbdacadbbecdecdaebcddcaadbeaaccdccbaaebdcbacddadecaebeeebeaaebccdeeacbccbecebeccaadbdcacbaacecbcccccedddbacbaedebccebadebdddadddccdbeccdbceeccbbcbdbcebeccdaaaacacbebacaaaccebebdededacaddecaabeccecadbdbddddeccbeddbaeedcababdbbdbbceeeedaaaeaebabdeccbabbdeaabdacdaadaddaecdcbcbdebabcdddadbaeabeecdeeaaddaaddcdecbcedacabddbedbecedeecacbcdebebecdcdceaeaedccbdaabbcabedacbdcaeddcbaadbbecdbccaececdeaeddceabecccdecdeeaebddebedccdbeaaeebbdddbeededbcccacedcaaeedecababaaccdbceabeedddadcadaabaedeadabcaaccbeebaecbdddcceddcecaebddadcddabbdbccccebaceacbabbedabaeaeaeacedcaccecbbadbeabdcbbbabeebbdecaabeeaabeddcccbbddccbcaeceaccebcdeeaeccbecacecbdbeacaddeacdddaacecedadcdbbbdddabbbcddbdbdedacdaddbeccbbeccadbaaebdceaabdebcebdabcbcbecbeecddaeceeaeeaaacecceaaaecbddbdbbbdcedacdacabeebacbcebcebbcbebbeadaaadeaabdcbcbcdcceebdbddadcbcdaceacebaeeebeaebddcbdbececbecdadeadaddeabbeeacadabeedcabcdeaacdcecbeaaacbdbdceadbdeedececaeacdbbaabeecbccbaebeebeeedccbbabcadabddbecbebacedadaaddddbcdaeacbbcedcecadaaeaaddcaeadbdeedbceaccbeebaaecdebebcebcadddcacecaaaedebecedbaeddaddabeabdeeddacbdbebbdbccacdbddeedcbececdbbaebaadadaeadcabccbddeecbabedecbccaedaaeaeeedcdbdceaececdcebacbacedcedabecdcbcadedaaacdadeadcadcbaebeaecbabdbeceedacedacebbeaedabdeadcddcabeaabecedeacdbdadeadeeabdacbdaadacbcbcacadaedbdebdddeeeccabbecedddabeaceebdaadaabcebbcadcccaaeeaaccdabbdcccdeedadacbdecdaeeedabaadcaceeadceadaabbcacccbcadaaaaedadccabaceecbeebcdccddebaedbbceadbabbebcddbdbbbccacaecbdaebeeebbabdcbecedacbcceaeaecaaadeabaecbcbcdecacbaeeecaeadabdbadaabdaddecaeddddbebdaabeecdaacbeedcacbbcaebabedbbedeeeadbdadbcbccbeabcbcececaeacabaeeecccddeccdaadccabaddacacdccebdedbbdceccdbbaaabadebadaccacdcccabbcdbeecaacbdceeacadebbeddcaabacedbaaeeaaabcebeaedebdbaecbcecedbbedaaebbdadbeaadbbaacbaebaaebbeacbbedeaddbdbdcbbddbedbccadbdaadaecadbcbbddeaeebbcadcaaecdadccededbcabedcabbdacbdaacebcabbcedccacdeabecbeedcdeeebdabbaedeadebedcdcbcbceceeaecdcbdccbbeebbcbdccabacdbeebeccdeddebdcedbebebbeaebccbbbddcbbcedaabaaddedeaecacdeceabadaaaadaacebddccdbabdbccaaebbadeaaeeeddbdbdcbedccdacccbeabebbdcaddaeabaccbacdbcecaabaeabcbdbeebdcadaaaabddaeadbdadaaeeccdbbbbceaccdebceedbbcddbedaabdebababdccaabcbadeddaabbeecdaaedeebaebaecdeecaddccbccadedeebdcbdeaecbbdcecdbceaacedcdbaabbeacbdeebcaeebbeccaddaeddbaccabacedbedaceddcaacaddbcdbbaacabdaabacdbecedaadceaadbaecceebaabeaeacaecbeadbeebdeaecaecaceaaeaadbcecaeaabeebbabddcaeadceaaebaceeddeabacaedebdabedddbaababdaecccdaeacaecbaeaabbadbceecdbdabedebabedcedabbbbabaaeadecddaabbabbabbbeecaeccaeccbeeceeecceabcccaaebdebadaebcdedabadabcacdcbdeaabcbbbcceeecaadacacebecdebbcdaeebbdbbcebccaaeceeebaddcccceacacbbacbaaaacedaccdcacadbbbacbbbaedacebaebcecdeaaeeeadeaaeebdbdbaacddeeaedccbaeaaaedbcddacecbdcbcebacddbbebcbdeccadecadebddbbecbbeeabbbabdbcdcaccddabcdebdebdcebcbdcadeadcbeedcecbaabcbdaaecedbeddacbdaecedbaabbedbabdaccccabeaaaccdedeedbbccabbeddbeabaedabaaeeecebdbcbabddbcaebdbacbadceacecbcaeacccdeeabecadacbcbedddbddaabdbabbaacdcbdaccaddaaaceaaeeababaadabbaddccadbecaadceddaccccbababbeecacabcacbaaadeaaededecaadcaacecbabebaebddcdedaeadcedbbdbcabddbbddeadaaeadeccddaaecaeaedbcddedeaceccdaaddbecadcdddcdeebeddbacceceddcbdbbeebcbbbccbedebcabdeedbdaebbeadabbcdbeeeeeccacbeddeadacceabbbbceaaccddbbbeeaddbbbdbdceceaacecbdcbabbaccdaccebadecaeecbbccecccdaddaaccbcbebaaddeeeaaeaedaadbdcbbbaebdcebcbdaaacbebedaabcbabdebdcebcecdedeaecbabaceacccccaebcebacbabebbeedeaeabdeccaacdbeabaaccaeccdeadcecbebacbbddbddcceedbddebdeecabeccddadbceadbabccedeeeeadbcbdbbccdecdaadaebbedabeeedaaecabcbcaedbacacbdcdeebeecadecdcabbcdecdabbaadabbccadeaaeaeaaaceacacdaaebdbbbbadaddececdeaecdbeebcaaccadebdadaaaebaeddadeeedccccdbecaeedddeaecadaeeddcacdabddabdddcbaecacbebeddaabbcddddeddbebbaecabddabdbaceeecdbdedadbbdbdbadceadecccdbaacdaaecceebbebcbaacedaeeccbbdbddaabadbeaadeccbbdeeccbdbbccbeeedbbacccecebedeedeeeeabbcdbbddcdaadaebabcbcccadbcbbacedcbbebbabeedcdbbdabedeccdbcedceeddeccbcebaeabaacccadbaccadadacecbcbbabddaecceaccecbddcddeaaceaeeceeeebcecceccacbeadaededbccaccaeabbbedeabbceebddeedccbecbbddedabbaaaebdadbedacacdbcdacceedeaecccadeedebccaecaedcaebbbeecbccdeabbbcbccbbedbeccbaeeccbceadadedeebdadbddbdccbdcedcccdaecaebcaedabddcedcddddbacebbcaeccbdaaadaccbbdcbedacdbbedddbabadedeaadbeaaebabbacaaebbaadcddcbdebeedbdeabcdbdcbcbecbaadcdcaedbbceddaacbdcbeeababbaaceebcdecedeaddbccdbbccaccecdddcdcddeeaabeaddbcecdcecccbcbbcacdcaddddeeadacbcdbacabbabdceeabbecdbddcbbdcecabedbbdbdcbdedaddabcccacacceacccbaacdceacabceeeeadadbbdeaacadceaebdebeddbeaeccdcadaebcdeaddccddadebdacddddebcaaebdecccedcbdaaeabbbcadcdaabcacdbcaacedaecbacbbcaacbbbadddccddebdedaccedadabcadecbedaedaeaebabaabecbdbbaaebcdebcccccebcaabbeeaabeeeecbbedccaedaabeaaebebbdedddadecbcadabcadcdcedddccdadeccdeaedecacdcacbdcdccedcddbbbbabcebaeaeabecedcaddadcdadadbcacacedceccadbeedadadbeaeacddbcbceacacbbcdadbeeaacabbecbcbdcebacbdaeedacedbabaaaaaddbedeccbbdcadddcddcbaeadaeeecbadcaddddbebeabbebacbebabedadeaabeceaecbcedcedbecdaaddcbaaaaaeddaaebcddebdeaeddcebbbccdcbdbacaaeeceacbddabecccdbbbeeecaeeaeaedaacaadcdabdbddadacadcbbeccaecdcbeeabdddebebbabaecdecedcaaedaebaccabeebccbeacbceeccbbbbcddeabbdabeccaeadcddcccabaceabdbdbecadadcbcadeaaebcdbabedbebbcceabcaccaccddaeccbdeecaacdaddadeecebdbbeadddecdacabbedabbeecdbacaaaeceecccdebbbbcbdbecabbeabaececebedeeaceebeccdedacebbbabdddeaddddccbcbecceaebeebceddeabcddaeaedcacdcdebaaacadabdbaacbaddddbcceededcbcdbabdaacebeddecaabbccdadcdeccaadecdeeecbbdacdabdeeeebdaededddedcaadcbbddcbbecacaddeeccbadeeaeeacebbaadbebbcdbedacceabccbecbedbeebebecaddececdeaedeabccdebbccccdeedebdacceccccdecadbadbeedbdbedcecaccdecabaabedddadbceecaaccbbdbdbceabbaedbcccadaacccccdaedebaabcdadccccabacedbdcdeeebcedbdacdccebaecbbcdbabbccbdadcbeaddbcacccecbaebbedbcaddaeeacdbaddadacddaabdddebbacadaaaacdeadceabbaaabacbebcbeddddacacbbcdedeccdedbededdecacebbaacbedcaadbdeacaccbabddcdcddedecceeadbcdbaecdeaaccbcadecddebeddadbeaaedaeaeceeecddaddddedacadeaddbedabdbddeaeeaeaebdacccdbdebdcdedcbcedbdabcaeeeecddceccabdabaccceaedcdceccbdeecababbadccbeadacddcedcebedebbedcaabdeaccecbaaccacdecbedbecbbbbcbebeacddccdbadbdcaeaeadeceebdcaeaedbeebbdebddeebdeceaeaaecdddbacdbcaadbdceecdbedacddcbbcdebdebebbcbbceaaaeeeccbabecbaaeeebbabaaadbadecacbddebcdcdeddecbaababacebacacbbeeeedaecbdcecddeebbbedabcaeaeeaeddbbeddcaceaedabaacadbbedcdbeabaacdbbccccccadadaeddedaabadbdaaceebdedeccdadcccededdeadadbaedeebabbaeaddcccdbabdecebddedecacecddeeebceaaabadcdadaeebebcccaaaceabbbcacccaddceabeddeeccbbddebbdadccbdddaaebedbeedbcdcbeeecbadaceecabbbddbdbaabcedebcbebeeaeadcbeedaedceadddcbaecdeeddadaaccdbeebabbcdddabdaccbcbbcbcddddaabbcdacbdadaebcedcdbeeddccebbbdbebcceadadbdbaabedddbcddacceadbaddbabbbdeaeaaeedabddbaaddbaedebcabdebbccebccedbceadbcdbacdcccddecacaebaeddcdecbbaacdcbcddaaecddadaddddebbaeaeeececebabadeddacaecccedabdeacedcabcdaabddecedcecbdaceaccdeaebbbbdeeecccdbcdbdebeadccbdcbeaeeaebedacacbabdacaddcabdaedbadbcabcccaddeabebceadbcddaadacabbeddecbadcdaeceddcabdacdedebbeedccbccadbddeadcddbdcccdacabbaebbccdddeaecacddacbecebcebdeebaceebddcedaebdccbddaeabbbaadbcdecebdadacbcceddbcecdadadbadeabbcccebedcdaaabcecaeaddccadcdbaaddbcacbdccdecaebeceeeceddaaabbcccacdaebddeeaadcecbbbaabaecccddcbaccbddcceddcbeedadaaccdecbbdabbbbdabececeeacadddbaeceeaedeacbdddbeabddaaaadbddadcaaebbdeaedeabbaedaaccccdceccbbaccaeecbbeecedbaedcdccbabdcdaeeaccbbbdabbabcceacbceddedbeccadeaccaeddcaeecebebdbeacacdaddecdbbecdeadebaaedcbddbcdecddcbbcadbebeaaaccaaabaeaacabcbeecedabaaddcdbeedecabeeeeaabddbbcebddeedcadaaddcdadcbcbacbccacdaabdbedbcdbebeccbceeeaacddbedeaaceaaebccabbaddccbbaeeabdadeceaedeceecaabecccdaddbcabbbbcdbeddaadbdabaacebdaacbbcceedabaaebddeceeceeacccdaeeeecedeaceabdeccaebbbcdececacaecabbdcbbbbebacedcbceacedbaedbadadaaaeedaeacdcdbecdbecceeaacacbdeeeabbdccebbbeeebcdbdbabacdccaeccabddddadeaabddbdebabebcbdcacaebadbadcadbbeaacbbddcdbacbcadcaebcbbddacccdedabdacbabdbcbeedaecbbadddadbaedcaabedbccaceddbadabbcceccbeccbabbeebcbeccdbdcaabbaeaededabcbeccedebbaacbdaeedacdcaedeaadacdebeadddceabecceadcceecbeecceebaaadbeccbdedbeebbcdcbdbbdaebbdaaeabceecacebdbaaeccabaaadcdecadaedeccbacbabadeaaabbbbeaabeeddbddbdeeecacaecbccdaeaacbaebbcddccacbdddecbedabecedcdbaeaeeabaecdcadbabeedcabadbcabcddceecccdedabaddddbdbaccaccdddcbaeacacbcdeaeebbceeabebeeaaadabdccadabcebccbababbceacbbbdeaddbbbecddbdaabbedebcdeacaaadabbbddecacadbecdcecdcaecbbadbeeeaabdbdacceceacabaecaebaeedbeaeddebcbeecececcacbbadaccdcedeebebddbcacdacdaeaaeeaedacddcbceebdedbdccacabddcaeedadabecebdbeebdbdecdadcacdecbecbcadaaabacbeaeddaccccebddcccbdecadebbcaaeeaacadbcebdddaaaddbbeedbbdbeacbbcecccedbbaabddebcebdaceebcbccdadacbebaccceabbbbeebaaeddaeebcccddbcddbaadcbbbecbedaabaabeebacacaabadaadeddcdaccaeadbebabadcecdccadeccbcdadebaebbbadadbccebeecbeaaadbbaaddbcddcbcbbdaeabaddecaddbdebbddeeababecbcdebcabaeecbedbbabeceeeedadbdcbecceaedacacdeeedbbeeaadbaeadaadecaceaeacceedebecabaeadccaccabacebdbdccbbecacdcbedddbebbadaedbdcbbeebeabecddccbcddcccaebcedbcddbcdaaedccaeebccdbdcaeccedeedadbbaeedccaddcaceeceedbcdbdcecbcbaabebdecdeccbbdcceaaeecebbecbeabbdccebedadddebbeedbddbecaebbadeecbecbbebdeedbdbeaadbedeeeadaeceabdedaabedddaebebdebbddbbbbecceeabebbedbdcebdabddaaadbdcbadcacaedeedddbdaabbbceeedddaddcabeadcecddacecabdddcdaeebddcdcbaedddaadecbdcdadcbbdebceddbceacbacbdcececdbcebbcdacaaccaecbdccbabdeecdbbacbeaccebcabaeeaaedaeeeebbaebdddecabbddebedabdacbcdaeddacacacbbbadaadacbeacaabaacddddaebcbcdceeaddedecceebebacabedaeadaacdcddecdbecbaaedeceadabaeebdaeaccdedcccbccbacacaaacdddbaddbcbabbeeedcacdcceebedeeabddebedccadeaeaabbecaaccbbdaddcdcecbbbbaeddaaebaaababeaecedcdabcbeecadccaaaaacacdabaddaeebbddedbceeccdececdbdaaceeadbbcebbbabcaeeeabaaddbbcecebabbdeabbacbadbadbbcaebbbdcaabbeedbcbcdbbcbbdacbdcbbebeeaccecedceccebeeedebceedddcaccabecacebddbaeecdebbdaacadddedecbdcdebdcbcdecbcddcabeedbbabbdccdbdbddddbdecbebaeddcedaeeebbbcacdabdcdebaadcbcadeddbdcdabddedccadaabcbacdbddbcabcdbdcdaedebedcecbacccbdceaeeecddccbadeddbbadacdbdaaeddecaeddecccceedddeedccadcdbdeeecabebcaceabdcccaddbaadbaaddcbaedeaddeadaecacaeebabddabbacaddbbddbcbdadeeebebdeadedcdceeebcbbbaedbacacadabdccebadccadebbdadadbaeddbabbeaeecacabcbcebbabdedcabebaaabebdcedddbecedddacebebdeabaadbededcbdaccaacdaecbceebbeacedbceccdaaabbacadeeedcaebeebdacdacbabeacbaacbbdedcbabcdcddaadeaaabeecceacaabcccaacacbdeaccdbbdadccbbcbdbeabeeaeebdbcdeebaabeddaadeddcacdecbbddbabcacedbeeaecdceebbceadeedcbeeaeaecadedddbaacbdbbaacdabbbcdcebcdeccdccaabcdbdcbbeeabadddcbceccadadeecececdddbebaadeedbbbabceddbadbdaedcddacccebeeacaadbbdbcbbaabbadcdbddcdbbdbbaccbabeeaceeaeddcedeaaccddedeedcacdacdebebeaeadcceddceaaebdcbabceeeebdcaadebbbcbeaaebeaedbdeedcaeacaeccbdbcbdeedcaacbeecdcdcdbdcdeebbdbaeedacecdceddebbecbdacaccbdbaadaaececebbbaebaadabdcedaaccdbbededecbecbcdcdecbadedcbcaadcdbdaddaecadcdcaeccaeddaebacbdeccabeebacbadaaecdaddeddacddddeceecdcdbbcdaabbcaeacbdeedebdebacddedcbbbdadabbdddeaabcbcedacbaaacddcceebbcabccecdaebdddbedbdbbcaabebaddabdabdbadedaebacabddddceaceaeaecdacadbccbbbaebadaddaedcdceaacdcacbaebdebdeeeacbdebabbebacadbcacbcdbdaeaaaccbbcbcadceacbacceaadbcbecaceadbdeeccbcccabadbccbcbccceeddacecbbedbddaedaebbbcbdadaedbebbbbdcbbaecdbebdddeacccdcabcaabccaaddcedcbdddaddaababdccececccdebcabbddaebabeaebdaeadadcaddcacceccacebcedaddddaeecbcebeaeeeaadeedceabacaddbabdcbccadaccbccdbcebaddddbebdbcdaeebeeacbaabebdacaddaadbadaacbdcadaaaebbededbdeaebaebdebebdcbabddbccbaaaabcbcbcdccaaebbeeadacecceaaebbcdcaeebcaceadbcebadbbaeaceedcbccbabbcedcabeceadabbcbaeabbcebdbaaadccaeabbdedccdebbabdbddeececeaeccbaedaeaeddcedaccabadcbaacaddcaecebedcbaebcddceaedbeeebdbcdbcaeaecbbcddcbbdaadaaaddbdcabebebbceebeaeaadaccabbdecdaacddbeaecdcbddbcccdedbcedacdbaaadecacbbddcdaddbcceebebccebccebaaecdbceeecccbeebcabcdcdaedcdbceabdadcdadebaeabcaedeeebdbbbbddeabbccdadcccaeaabacdbebdbcaadcbeabbccedaecddbbdcedbcabdcecaacbdddadbcacbadbecabbedecabbcecbbcdacecebbcacaceabcebbacddebbddaaadedabcadbccaaadcceabdccdaadeebdebddeaeedaccecccaeedccdbaccbebbbccdedbdebdcacdbcaceebaddbeedaeacadacbbcbabbbbdbcedecadeadeedbbedebbdcbcaeececcbeacdbeaaddbadeeaccdcebeabdbcddcbbbaabbcdcabbdbcbbdeebcccabeabcebdaeecbeecedaccecaceeeaeeccbcdaebedbdaedeaabbcaaaddcbbdeebaecbbdebbbeabbcedeedccebdbdbebddcdccbbbaedabeccdceedeacebcdaeebbbbceabeadeddaaadbddecbdbeeacedccccaddeceaaecdbbedaadbadcecceeedccaaeacdececaeeacecbacdebeeeeaabbcaaabadbaeacbdcdbabbbadcdbdecaabeecabdeeaeaadbcbebebeacaaaedceecbedaeabbccbbbdcbeeaccdaadcbbebcdceebeabccadaeebaeeebeacadcaddcdccdabeacecaaeaacecbacdceedacbecdcabbdaedbeeccceeccacbcaebbacabbcaeddcbaacddedccdeabeeecdcccedbeaddcddbdbcbeeadabdabcaddeaceceedaeddbbedcddbbdbdcbdacdecdeceaebdbbccdabcbabceacedbceebccccaccceaedcadcabababdacdecebbbaadeaaeebdeeceabecaaaebececbbaecbbbdaaadbadbceadddedbcbceddbeaebadddaebccaadcbbcececdcbbedadbdbeccddbabbcddbdededadbbedabbbabeabaddaccbecbdcddabcdccdeecbcdeececabdcadbbbebaedccabececaeadadbdbbcbadcbacbaebbadcbeeeaaebaecabdaacbaadcebeccadcebbeaceccbcbaabecccbaaedcecbcadccbeccaeebbeebccbaabdaccabeceecbabccbeaedbaeebbecacdccccdabbdbabdeaeccceadaececadadddaaeadaacccdaceacaebcebbbddbdacaceaddbabdeacabcddabbecbecbcdacecadeceedeadacaeebaadcbecddeabebcebabccbebcdedbaabdaecccccccddeebdbebeddaacbccdecbedbbedebdaedbeedcbaaacbcdeaaabccabdceecdaddebddabdedceebbabdcabeeaeecbeabdcacaddececebaacdaebecaabaaeaecdebbebacbaadeaeeaadeeeeadebedbbeebbccbceabbcabbacdeaacdddaaccebbbabecadddacdcacbeddbddaccdddcbddaebdbaedbbebdbcdadabaaebdaedbcedcdadcddabdbaaccdaabededcbcedebeddbecbbacedcaebbacabaedededbecbdabeceacecdadbaebbbabeecccbbeadeeedecbaacbbbcdceabbdcddeacaddcdbbeeeacbeaeddacbedbbcbbebcabedcbcdbceddbcebbabcdcbbcdaacbcceababdccddabdedbcdbaaeaddabbeabedbcaeceeaadcdeabbcbadecbdebeeacdbadbebbeecbbccebacebccbddcbadeadceaccdaddbdcaaccddcdcadabceeaaddddcddacccddeeccaadbdedbbabbdecdabcaaebcecbadacabedeccecabbedcebcaebecbbaedaebcdadbcaacaeeceecbdceecaadacbbbceceedeccbeeacdeecececdddadaaacadbdabdadcadadbcbbdabbecccbadeeaadaddcdeabddcebacecbcbbedcdeedbccaebbbbeaeaacbedbadaebaecabdcbecccdadacaedbadeaaeccbbabaceecdcdaeccbacbebbeddecbbceacabaecedcbabaebbdbaabaceecadacaeecbbbcedcccbeacdebdbddaeddcbcceecebedcbbdedccecdaabcaabcdcadccdaacbeecdecbcaaddcbcecdecdadddcccbeddaecbdeadaaeccebbeeceacbddbccbcbccdddaecadacaedeaadeebecbeeaeddacabbcecaaeacaeddbeeeccebebbbdaaceaadacceabdbbbedcdbeaeeceadccebbcbdcdcaadbeeaadcbcaecbdcccaaecddeabbccaedccedcdeededbceebbeaebeceedeeddccdabccadaacaedccedebdbabcdadbbdeaedcbceccaedeccebebdedcbaedaabcdecabbdcaeeecceaaacdedbdabebeeaeebabbacdaeaeebededcccabadbeeebcabdadeadeaecdceaaeebdccdabdbaeedecedaeabaacbdeeeeaedecccdaececcdedeecedddbaadbdecaaedbabcbbdbeccaaacbbdcbcbabaadacdbbcadccebbdcadadceebdabbebcabeedaeecaadddaaedddadeebedbbccbdbabebeeceaecaccabebaeaebbaecbdeeedaecddaaacbbddacebdaeddeeeebbeeecbdccceddcdbcaababcbadcccaedeacbdddceacabcebdceacbdaddbcaedbaeeedabedebbaacbcdbeddebbdbaabcaabbebbebcbecabeebcbbcdbbdadbcacbeeeebcedeebdcaebdedabceceeebeddcadadbdeacabebdcceaaaaececbebbeacbedcebceddebdecbeeacbcbcdecaaaeacecaeacdcaedcccbacdbbacaedacecebecebbadccbaceaaceaabeceaecebcabdadaacadbeebcbecdbbbbcadebedbcbeddbeccdbebdeedddbecaeeeacaacbccecedeccddbdbdeeaaceaaeedaebceeccabbcbdbdcbeaabcedaeccdeeebdadabccdbdbdaacddaeecbcdabebaaedeaccbbaaedbbbadddbecdebdaddecabebceabdcacadebebcecebabeabddcecdddcccacaabcebaacededdceeaceccbaecdebcdbebadbabddebbadabbcbbacedbcadabdceabeedcddaabecabaeddaeecddcbcddaaceccecbeabebbcbceadceeebbedbdbbcbdabddceebddeabbadcebbbbdbedbcaaecaeabadeaddcacbdcddebbadcbbdbcddbbcabeeeecdccbbbcdadcdadbdbebdceaeeddabeeaebadeddaddeecabbdbdebdbadebeadbcecabcddaaadbdcebbccebbeacdcccacadcebadabbcadabaaebadedeaacadcbcebcbeebcecebdedbdbebbeaaaeecedcacddeadcbadebdeabebeecabacaddccabbadbdbcbaaccbbabdacceeeabacaadadbdeeaeebbacbeeabaaaedbdddcdbebcbcdadceebadddbdcdbcccadbcadbbadabeecbdbccdaebceadbcbaeedddedebeccebbeeaecdaabeaabbaccdacaeceeeaabebadecedbeddceeedaedaceaacdcabeaebcadccbbadcadacbadecbdceedaebbbaacebceceeaccdccbebabcedcceecccdcebdbddbbeaaecebbbbeeaaddedeebcddadcadeeaebbacedeeaecddcebebbedbcdbedcbbdceeaadecbdbeeddacdccbecbaeeaebdbcbccddbbabcabccadabeaaaebbaedbcdeecdaeabeececdbebbadcdecddebebdaeebbdcbbbcccddeddccaccadedbabedadebdeaaedabeccdaaabdedddedcabbeabdcdeaaacbbddabcecabdbdcedaacbdccedaccacabcbccbdcceaaaeedbadccdddbdabbbeacdedccedcacbdbebbedababbeadbddbacdeaccaccedeccaeababcdbceeadededdbebeeeeeeeeddaadcabaeacbbccbdbcedadabdecadeeccdbadbbaaedcebabbaaebdeccdbdabaaaabeacaababbbecbdbcbbbbaceababaecdeabcdeccadecdaebacbcbdeccedabaaebddcdddadbbabccddebbecedcaedecadbbbaabbdeaadecedabbebdeabbcdbeedebbeddadcbbacbbddbbbabeacdbecabbedcedccdadadcbbccacebbdabebbcdcbddaacadedeeebedcadbacecdebdbcbccaadbbdddcbdbddadddccebbaaceacdadbddeeeabcbeedcccbacebececabdecccebcdbbceacabdeabdbedcbcccdccadacddbedcaaccaabedebdeaeebdeddccbabdedaaadbaaceaadcdbabaaedbbaadeaabbcbbdaceedaaebbdceccbdebeccbcabceccceecebcecdbbdeacbbbabbedaaacabeadcbececdbceeedbcbebdbbadaeddaceedcabceaddbbcceaddbdcaecaebceabdedbabeddadaeeebcabbbeeebdceabdbaccebaeecbecbbceabcaaaaadcaeadcbdbaedecbcaebedaccdbaaaebccdcccbdebeabbcabaacecabadbcedadcdceeebcbcdeceacecaadbebeceabaecbaddaaccacedcaaacadcdadddecdeecebcaceeedcdcadccadcbacecaedadabdeddacaebbbcaababadbcbdbbddcadddbeddaebddbcdddeaadcaeeceabadeedecddcdddeecebdabcecdabeedbddedbbacbcdeeaeebebcedeacbcabdcdbadabedcccaaabcbcaaabdecaeeceaccdbbeedeaacdbaddeadceebeabceeadeebbdceedaabedabbadcbecbadedeaaeacbcdececdadedeceaeeeccbbbcacbcadeeaebabddabedccaecceeeececabeabeadddcecdddcedadbacaaaedbeceedaabcbcbabdceeaacbdbacaedccadcedeacecbdcedddddaebaaaebcbdcceecbbccaaaeeeeabbdcdeaccddccbacdcbabaaacadebeebbdaedeeceddeebaeecddecccceadaaddcacdeeeeeaeebdacedaeedbbcadaebebebddecddcbeedeaebaddaecbecdbabdcbcbeacbcdeaebdbbabedcbddaabcaaabeccbacadebaddaeedadaadebbcedcdedadbedcbddcddedbaabedceebabbebebccbbcacbdedcecbbcbcdaeebecdddabcbeeaddbdbcbaebcedbadeeddbebadccadedcaeeeadaaaabdaccbbdcdcdaaeddadcbcbceeadbeaaddacaedecebbaccbceeaaaeadeeeabacebadcdaaeebcdaedebddddcdaacaedeecbdadccdcecaebcabaeadcccbabdedddcbdcadeeacaeeeadbaeaeeecacdddeaecedebbdbeeaededecdeecdaabbedeadabddecedacabacdcceecdceecdcedcbeccaecaeccedaddbebbecdbaeadccbeacbcddeeddedaeeabecbdbccccbabccddbbcbebebaccddbebcbccecddbcccdacaeecebedeecceedebeeaeceddcebabaebececaccabbbbcbdbaceebceaacdaccaaedadaeebcccabbadbbcbedbccaebbcebdaadeeadabaeecbddedecdbaddbccaacdeaebbdaceebaeeaacccecabbdececbcebcdeabdeebbcbabebcaacbddacdbcddebcedadaadeedbbbababbbdeaebeeaadaaaadaebeaddceecaecccebccbbcabeeabbaabebccbdecdaceddbcddceadabaabcaabccceaacbbbcbcdedddbcdeddaeaadedaaabbbbaccbdeaddabbbacdbecdbccdbcdddbccebcddabaddbeeabceeeedccaecdceccaedcaeababdbcaabddbecddbacdaabedcddeeadecbccdbcbdaaaaccaabacbcebbceddcaecebdadbadacbceddddabeaebbceeaddaedeecdedbcabdabdbadcbadaceeccaabebbddaaccbdeceeaedddaabcacdcdabecebdbbbeebbeeedaaabedebedaedacbedebbaaebeaedebeeacaccbbeedebecbeacbbaddaabcdbddadacabadedbbecabeababeadeabbdddadceacedacebbaaeabbcececbbdbcabaedbabdcadabbbdcbdebedbaebbcbaedebabaecdeabbdeaaaaedeabaddabebadacebaaaedacdabbbbbbebcceecbeabbdbecaeeabccbceeadedbaeddebeccbedabcbedaceaedceedbbcaabcaeaddbaaaadccedececdceaebceabbcdedccacbedcccdbeddbbbcbccdeaebeebdcaeccdcecddecccedbadbbadaddccccbecabaaaacecbeabdbadcbabeedecddcebbbddacaebadaeeebabeedbdeecebbccdaededbbbaabecaaeeeebcddcaedbdcbeceaabecabbbcdaaeecaacbcbecaecceaeadaeebadeceeddbdcaeaeebbebcceabbaddcbbebdeadaaeeadcdeeaaecebcbcbebaebcaaacdddabcbaaaecbbdaadadcbcaeebcbdacaceddbbeeddabddabeeddedddddcaadbeddbbabaacbacdaadcdccacdeeacbdecaaabecbbdabaadebcebcecdecdacebeeedceeaaecbaaccbaeceecdbbbbcbeabeeddcacbdaceacabccebdedcdcaeaabbecdedcaebacabecdcebccbdeadcdccbecedcdcccccdceaddaabdebbebedacaeabcccddccebeccdeeeacaaaabdcbbbedbacaabccbdbadaccccebcadaceaabdcbeeadeadddcbaeeaebebbebbaaadabaadebedebceaddaedebcbebabeecbeceaddacedaeaacbeabccaeedcbdcbacdcecedacabcceecbdbdeccddaabbbabccdacaedbdceaaabdbbeadadaccecddebbcbcdbdceaabceddadeceadbdadcaadedaedabadaecbeebbddbedadeebbaacceaacbacecdceecacbebdaedeaddeaabecabeeaaadcedaeaeddaecbbbdabeeeaabcabdcebddaeccdbbecdccbbecceccdcacbaeeaaeabbaacabdbbdabaccebbdebeaaccbaccceadaabccabedeaaedaabcaaaedbecddabacaadedeccadceeebecacddcdbccddbbebadcdaeaddcbbbbaaeaddaaccddeadccacbbdcedadeeeeacdbddebabcbcbbaeebdacbbebbbccdccacddaadcebdcedbbecccccdbcddaaecddedbebeecadcaaeecacaaceedbbaedbedeaaaaeeeddaeabdbdaaeaccedaaecbcceaededceedaddcaceeaddaacaaebebdecaeabeeccbbdccabcebddadbbebadadecccabaadecbdceaabebaeaabcaedcdbacaeabaaadaeaaacededbebcbaadbbbbdabeeacbeedadabdddbcbccedbbbaaeccbddadceaeaebddbbaecadbaeddcabdbabcbbbbadddbcaececacecadccedbedbdaebcdaaabebedcdaacaccddeadbbbaebdcaebcbcecceeeeacddddabcadbebdadebabaeaaebbeadddbdabcaabcdabbcdbcaedadcbedacbeabebbaadacbeebadaaaedaacdacddccaeacbbcdddabbedaaacaeeaeedbbcccccccbeabcaddcabdcedaaeaabcbbdbaecdabebcacabecbbebeddaabaaceacccceaaeacbecedcbacbccceddaddbbcdbebaadcbeedccbdaaacceeaabcbeaeccdcdbebceeeddaebeeaeabbaaaaaebeeccecababceebeddcaedbdaababecbebebbccaadeeaddbedebabedbcbbbdbcaaaccbbadbaedeecbecaedadbecbceebedbebedadeaeddeebebacdbeccaacedbdbdebcbbdadbbbcdbbaebabdcddedbabbdeaeeacbebacbbebedbdbbacccdddabedeeceabcebbebacdcbaabbcaceaeaacecebcecadeadaeddbcabdcecedceababeaceddabcccbcaebdedacecdbcadadbcbbbcadaeabebcadcbaaaddabeedcbddcbcbabadeecbabaeaddeabeeebdcbaeeedecabdcebbbcaeaaceabccabbdeadcaededaebbeaabddcebacddebbdcdadbddcaeeabecabdbbeadaddceeccecaeebebebbabeaadcddcbbdccdacedaaaedddacdaddcddcacedabbceedabbededeeaaaddadedaaedaaeeadbdbecceadadcbecbebccdcbdbbedcdbbdcdadccaeaddebbaceecbacdbcdededcaaacebdeeacaeececabcacebadccaabceeacdaddecccaeabaaaeadcccabdcededebadcdeecbacbacceacbccaaadceaebeaaabdecdebedebddbcacdaabbcaaeadbdcdeecdacbedbaadaabadaabcabedbebbacceabbecebddabdeebbadedeaecedcbbcddaccedeaecccebdcdedbecccbbbcddbccbecdacccbddabeabdceeeedddccadbacbedbcbbeeaceadcabbedebebbeabebdceacaabeaedebcdaeceadbeeabacbbacdbcaddbcaeeedcccddbddaaacddbbcaccbcbabdcedaedabeeddcaacabbdcdacceeaebbaabaccdadecacedabbbdebbaeeacbacecaeadcdeaebcdddabecceaccbcabcabbddebbeceeecdaebaeecdaadccaedbbadacaaceaedcebbcaadecceccacdddbccccaabdcbbddeeadecbaddaeddcdeeeeaaabaeebdadabaeecceaaceeececdababcaeadbbceeeedeeeaeaacdaaeaeacbebcebcedbedbaeddbeeacabcaccdecbceedcadbeddaddceeaabdaacbcaeeaaedaddccebbebabdbceaccbacabbaadeddcddaaceaeeabbddbaccacebdcbaceeaeebdbebdccbddeacebcaaeddecdccadbabbeadbceeedccaabbddcbedcacbbceeecabcbcaaecaaeababeebcaecceccdaaabebdbcaceddeaeceaaeeeccdebdebdcebceeabcaaaddeeddbdccdcbcbcacbdbcddbcdcedeaaddaecddabecdcacdabdcdaecaceadedcabeabdaaccdcbacccecabebaccaaaeaecbdedebcbbdeccbecaeeabdcdeacbdcaaaebeceadcdacbcbececbebccaccdededeaaedeebecdedecbaedebeaebedcbecdcaacbbdadeaceccdebebecedddeccbebcccbabddbbdeacadcbadaeecedccaaeabcbabbdcceaaddeeceadceeabcbbcccbbcbeaabcddeccaaacabcebeeddeedebecbacdaaadccadbaddadbcddbaadebdcecbccbadbbaabdcdcbcddadadeabddebbeeeadadaaddebdaebcaaaebcabaddccccaaedbbdccaeccacadcedbddcaebdaccaaadadebbdaaacaeaceadbbbddcccbdcddeecabdbedbebbdecdecbecdecbbbaaecccbaeaebcdeceadcccbcadbcbcebebedbecdcddeadbbcbeaeadbdaeaedcaddeeebbcaceaccdceeaaacebdcaebabaaaacaddeadcacdceacdaeccdaebedddbdbccbdacdbaadcaacadcadddcbdcebaddbddaededdbcebcdaedcedcddbdaaecaadedaaedecdabebbeeeabeeacabcbaecbdebdaaabddebddcaedbaeeeabeebbabddbbccceaeaecbbeaaebabbcddcaebedcdcdecbddecdcdaeaeedebabceeccdbcaddabdaaceecadbebcbdeedeebcddaabdbdebdeccbaaacecbddacdaacdacbeadadcdaaaedcddcdeedecccdddaeecccebaadcccebebcdbbbaadaabddeebadacdeaecdcacdeebadbcaaceccadcdbdcdeccbeedcebbccccbcbecbdaaabccbcaecdadccbadbeacddabcccebccabbdbdadccebadcecbdccaeacaaddcaadedaccadeecdedaeccdebeaaccbbbbeaadcdeebbbadbdaaeacadabdaaddcdadabbbbcbbbdceeadcdedadecbeeacabaabaabcaacabdbacbaacaccabebccbaaadeccccdbbcdabeebcccdabdbaeeebddabacbebaccccebeaaaeeabcbcdebdbbceeabebadbeedbabccbcdaccaeaabcadedcadccbeeebadbceadeeeebbeacdbabbbcdcedcebcbadcdcaaddcabaeceaaebabeecdbceeacaacdcbcceaaabadbaddcedaccdbcbbbacceabaaccadecacdbebabaabdcbbeabccceebcacabdbcdbdacbddbbdcdcbeedebcdcaeddccbccacaabcdbcddcecaebeabaceabaaeeebeecddbedbdaaedbbdaeaaaeccbbabdbdabcebccbadccdaeeabeebadcaebeabbacdbabdbbddbdcccdeabddbabddbbbdebabacacbebdcccebceecaabacebecadaddbeabbdddceadeabeaecbdaddcbebaebccedcdeedadbceccaecdbcdcaaeebcbdebbeebcecdaadbeddeeadabbecadeeeaaebdebcbeaebcbaacebeedaecbbdcabcaeccdcebbabebcacadeaedaaceceacecbecaaadcdadeaadceeaababdeedccaaaaadababccdaccdceddebadeadacabdbdbdbccabbbdcacacbcbdcdddbccbeaabaacbcdedddaeccaccecbbcbdddedecaadadabcadaeaacdbaabacbaabacadbabaaeaaaabaaaabcceeecbeacedbeaacadcbaaaedeaceedaebddabaedaeacbeadeababcedddceedbbaaccddbaebeabebbadbaabeaabeadbccccbdbceeeeabbdbedbccdaadeaaccecbbdabdebaacbbcdaeeadacdececcbcdaddadaabddabdcecbdadeeeacadebadbeaedcaceaeddbaddbeacacceeceaeeabaabbcecabaaaceacceeeeadbbcdcadbdeabdceebdadedbaaddcdbebdbbcadbbbcdbecdbddcaebcaccddddbaaadeaacbaebdcbcccdbdadaabeeeeeeeeedceacbcddcdceabcedbacaabbbbbccbbddbccdbccacbcadceedeaacdcbccbaaedebdbbdbcbeceaadaecacccbcdeccbccacaacdaeccdeaabebebacacdbebeccebaadadaeddbcbddbccdadebddaecbdedcbcadeeaebacebdacdcecdbdedbbdabcebbabcaeeeccaccaddcbcbadccdbbbacbdaacccbcaedbeaecddcdcceeebaabaadcccbcdaccbabcceceaeaebeacbccceadadbdecebbdcababcaedbdaeeeaadcedcdbedaabbcaaaeaeeadbdbabbeaeaceceddcedaadabedceebababaeacebbdeeddcbbbdabaebcbecdbbcabdebecebcaeeabcbbebbabadededbdccbadabceedebaddbaaeceeadacbceccbcdbedeeeceaacbdeadabadcbabceeacbdbbcbdbdccecadaddbdaadaebacbecbadecbbaccbebccbaabeaeaeebccbabebbbecdabccccaddddacacdbecdeccdbdbcdacbaddecdbbcccbcaadbbbcbcddeaaeecebacdebeebaeedcaecbcebcedceddeebdabddcbaccceccdacedbcdeccdecdcdeadbbdaaaecacedaceeedcacbeeddbdeeccaecbccecdcdbeddcdcddeecbabbbdaeeccbdeedbcceaabebcdbaaadeeacaedededdbdeeeccdcabbaacaceacccdeddbbbadbedbdcdeaaddaccccededccdccdcbedeabecdbbbedbceaccadadecadbcdbddeeececaeaddaebeecebdadcccdebeeaccedcaddcdedceeaadbdcbcabddebbcbcaeaddcedcadabcaebedcaaaeacbaabebeebcaaedeedbcceedebadaeedbdccccdceabcbecedaacdeaebdccdbdccdeaccdaadabeeeddecbdabebdadcbbadecabaebdabbaddaedcccdccecdeeaebbacecddeabbeedacdccbdbcbdbbeaebaaadabbdcbebeebadeeaababbcbeeedaecdeaeecbdbbcddedcddccccccacdecadbabcaabdeaaabdaccabdebbcbdabbebcacdbceadacdbeabaadebabaaeacecdbbadbbbdeebaadbacaccbedeaaacddebbbebebadaedaddbabdeedcadeebdededddcbeeeeddcdbaddddbcdcecacceabdbdbeebccadaddcaaacddcaeaabdbcbeebddbcacdaecbeaeceeebebccedbcbeddddbaaabeeedddacaeedabebbaabdbbdcccaedacacdcaebebdabeeecdaaddecebeaaaeabcaaddbceddaebaedeaebcaeedaeedbcbebdcedddcbeadedadcecdddbbeaadbdbccebdbbbdddbcacacdeaeccabaccbceadbbbcadddcdadceebcbcaabbadacebddbbccdceeecabdeccbdebbebbdedadecbbeebecacceeacbcdaeddacbeaebebbddccaecedcddddceadbcbcdebdcedccebccdceeeecdceeddbbcaadeacecaecbceecebbddecdeedebecaaaabacddcdeaccdcedcbcabdddaaebbadacabbceacaececebcabccecaddbbbdccdacdccacceacbacaeeebbabeadeaccbaceaaeedbaeedacbccedbbdebcaceeeeecceeebeaadadebdcbdabbccdeddceacabbddcabcbaddddaaccbbcacbcbecdebccabeeaaeccdabdaeebdeacaeddcdceceabeddcedbccceddeedcddadbccddadbaddcdcbbcecbbecbcadbabbdddbbecadedacdecaeeccdeaeccadcbedcebcbbecdabdbbcdddcbcadecbdcddaacbaebbbcceeeeadebdeeecccddbcdebcceaaceedcedaaccaebcbadcdceddabddbccbbcabcecceaccedbaaddebdcaeccadbeabdaebeeeaeeecccddcededcccbdceebbaccabadedeacaecaccbcdddcbcbcdeabbcdedbbbadaabaecacaebaebeaaedbdcbeabdbdcdadcbaddbdebcadbcdbecdbdeceeedbabbcbacbcbbbcccbbbdbbecceadecedeaedacdebdcccabaadeddbeccccccedadbdacbdaddebaaccbeecceaaecadcddbaaceddddbcbeeeabeabbcccadbdbadddeaeaddbebacdabadaabdaebecdbeacaeacecaedbdcaeabadabcaababcaacaceaaebebbdacaebcabcaebabcbdcbeabacdededeccdacdcecdbedbcebaacdcebccadbbbaccacaebabaebdceaadcdbcebccaaeeecddcadbdccbadaedcddbcaebadeacccbdcadeaeeedaccacaceccacdedaaededbeeaaaaacdbedaeabacdadbecdeedadeeedccaeabacabceaebcecbbddbabecdbeeaccddadedebdacdcaeacedbdccadbbaabaaaeeeeacabaaeadabbeacdeaedddbdbebaabdebaceaaaaeaacadbddebdceddceeedccbaadcebbbdceaceebceddcbdacbcddaaeedbeacbebedbcedbceedecabcecbecdeadacdcadbabcdadcabbeabcaddcaeacbccdcdcbcedbbceaaebaecceeeecacaaebbdeccaabdaddaacdbcbeedbdacdbbdebbbecccacadcbbadddacaceacbccdceddabacebbdbebebbdcecededeccbecdacbebedbededaaeecceeaadcaccedcabddaedcaacacabedbeaeecbadcdbbddbccbdecacacadcabddacacaecbdcdebaececadaecadebbeabecbebaedcdbbdaceebebeeceaabadadecdacccebbbbdcabbdecccbaebbecbcdbcbeaeabaebdcdbcccaeaecacddbacdbbddbbdbeceeeedebaececcddbcdcbdceddceeebbeddacacadccddbdcabbacecdcebcccbedeebcaeeccedacccdecdbabbcdedadbaecaceeebededdeacbcbbcbacebdaebcebcadabeabdbddebcdecaebaddabebeedacbeddccecccceebdcebecbbaaadeeaeddccabcabcbbdbadaabacdcedccdbbcebcbcecbedbdcaaadcecabbbecaebcddbcaaeedcaedcdaebabdcddacaadcecdbcedaebebbdbbadacdcdebbbbeeebacabaeddbeceeddabcdcddcedcebddcdbcecdedebbcddbcdbbedcacccaaabababaadecbbecabebbbecedebcbbcaedbaedcdcbcdcecaabcddcdabcbbbbceaeddbdbbdabadcddecedaacdbebddaebdabccebccceedaabaecdbcccbedaecbaddedcabecabeaabdeecddeeebbbbddcaccbcaeadadecdddecedbeeaccbddbcedaadbaaaceaddedbdcbbeaeabacdaaadabdbccdddcaebdcdbaeaacebbcbbeddcbebecdcacdbbaeaebbbadcbeccbbdabaaeebdbeddbbddbdddacdabebcbaaeedbbbbceedbcceebdebbaccadbeccdbddcbdceceeebdaeeabdecaaeeadacebbdeaeeebdabaceadaabcecdcdceecdeaedacabbcdcdccdaaeddaeabecccaeccdadedcedacaeeaccdeacbeacdbcdaabaadcdeacdcdcbaaacaaadebcdabeabbddbacaaedadaccccbecdeebedbcadccaabaedcbaedcceecadcbdadbbddedaddbabacacebaebdaceddcdbbeccebbeeacabeebbacddaaedcecadbedcdabecdbceaceaecdaaceddeabdacedcccabeededdaeedaccdcbddaedbaacabaecbacbdabbccbcbaccceaeabecdbeaedccbbceeaeeddeabcaedacacbccddaaabaebebabdccbdbbcbddbeababeeaaabbdcbebdbdbebdedbbaeabeeccdbaebcccaebcabacaabbbecacaabaecdacbbdabeeacacdbeddececcdbebecdcdbebbbcadedaaedadbeaaaadebdccedaecdeaadeddadcbdddcabdeabebedabdacaaeeccaabeecaeedcdbadaaebaebbdbdeedbdebabadecaaeddacbcaababaedaeeedaceeaceddaddccdcddbeeecabcaebdcedbbdbaadcdbdbeddcecaaeaeecdcadaebdbcacbeeeecebceeedbdddcacbedceacdcebbbbcbcbaeeadaccbdabacaaeecedcdacddeccbbbaaabaecdabdedeacebedbbacadbebccaeaddabdbabccbabebbcbdcceecedebdebceccbeabbccacaceacdabcddbaadbccbcdebacebbeadaabaaddddeecceaeacaabbcceaddbeaebdedebaccedacbeecaaebaddbaebabeadbccdddeaadbeeeddadddacaaaeaedeeddbcbebecabbbaeeacabbddbcabecbdedaaccabddaedbbececcecbecedddbacbaeaccdbecdadddedcccedbdaabcdcbdadeeecbcbedabdebeedcaeeeeccbeebcdecbeeeebeedddabcddaddadcacbbadbbebddcbcedbceabccccadaedcbbbecbbccbbdbcdebaabcaacaccedbbbddadbbabcabbcccbccbbdacdcbdedaabecbeaccedaedcabcdeeeeeecceecbbcddcbeacdeddbebbccbaebbbcacbabaeeaeaabbeaadebcebeaabadedddcdacaaaaacbcecadbeecbcebeadcebbbbabcabbedabbacbbecdbbacabdcdcdebaddbbedeebccadbbabcedabdcabdddcadcebccebeebcdbaadecdeeeaddcebbecdceaabdeeebbccecadabeedcdabadbebbcaddaadddaeebbacaebbeacdecdbcdaaedcecdddaddecebccbeadbeebbeabadddaaadbcedddaacbaaeeacdbabadbdacbcebeeaecbecdacacadbebddbeaabedadecddaebebbdcdadcccedccdecdbadebdaedbdcaaaeccbcdbddabdaccbecacceaddcedbbbacddbadacbeaacecacdaadbaededbdcdcbadddcbacdcbaddeaeeeeebbdbcdecceabedabacddebebeccebdaabadedaabccedcedccaebcdedcecdadadbbadacabcabbaacddadabdacecedabbeadbbbbdaadeadccbeaadaacbcbebddeeecceecaedcbabccecadcbdeaeddcbbbcccccdccacdedaebbcebabbacbcadbaadcdceebbabbccadaddeddaeaeecadbbcbdbbcdeedaeacbcdcdbdaaaadaebcaeadbecadacecaaadbbbaeddccdbeabaaaaceebeeaeacdecaccbebecbdbecdeaccedacbddbbeddceccacbddbedaeadaedbdbbdecaaabeddcbbabcbcbcadadddaddbadcbaeecbdcbebddceadaeccdacdbdaaeaaaaecdcebdcadddcecadcebbdcbdaadeeeeebdcbbeecdacbaacbcdebacadbceaddadbcbbbbebaadbbeebdbecbdabacbaacacacaecdcacbadceceedeeddacaaeecdaddcadaacebadadcddddebabaacbdbcbbdcdacacddcdeaeccedebaacbddbdbedbabecaecbcacbdcaecdcbedbabdbddeddcccbcecddeddddcdcdeaeacabcababeeeeddbcccbbacadbbbceaacbceabbdeeabaaddbbcdbbbadebcbcbccbcdaaeecbbddadcaecdbcccdebdaabadbeedebbcaeabebeceebeaacbacdeceadeaabbcedbbeaecedebabcdbadeceadaecbabcbdadccedacecdbededbacebaacedddedcebddbccdcacddbbedccccaaedeeeddededbeeaabdbcaaccedeeccacebaedceccbcbaaabdaceedccbeeabccdddaecbcadceeddccdecacacbddcbbedcedeabeaaadbdeccebbdeabcaaeededdddccdbcccccedbebebbabdcadebeaccabccdbaaabccddcbebbecacccdeebbaebcbbdcbaaddceaacdbaccebbbccdeddbeddcdeacbccbcadcaabcdabbcdaaacbeeadaeeecaaacaeaaeeeddcccbeceedebbebcdeaeecadbacedadbcddededeecaedaebbdedacdddacaaaccbcbebdcdccdddccebdddbbccabadccdccceaedbcdadedebeaccdbcdccbccecbaadbdcbcceadaeedeacccdeeeeabcbcdcedabcbadcddaccaeaaeaadbeabdecdcddaccbebceccdadaeabaebaecddabeddccdbceacdddeaccecdcebcceebabecddddbdbbabecbdcdaaeceaeaebbbebcabeecbbbaccdbdbcdebecbebaeadbeaeeabdacabecabbebacdebbceaeededaaddcebddedbdcbaceeccbcecedccbaebaedaecbecbbcaebadbadeababebaebdecdababdecdcbcdabaaabbebedabdccbbcbbebaceceaddaeedbdedebeaebdbdebcadeaedbdeabdcdeeeecacbacdabeeaebcbacddaaceeacdcbdddbcaadcccebccaaebaabedddbdbceeddccdbaadbaddaaaeabcbebabbebbabebbbeacabcdeabedbabbbdabcedaedcdbddaeceddecaabeceabedacaebddcbbbecbeabcbdecdcdbcbaabdabcaeabbcabbddaecdebaebcbeadbaeddddaebbbccacdceddedebbaebbdacabebceaaaeeccaeacdddcecdbcdcddabebeaacdadabbeaaccaaaacbceacbdeadeaeaadebeedaabecbaddedcedaaabaceaeeecbacecbcbeebbedecbbbabaeadaedabdeccaaeacedeceedbdebedadeebacecbaaaecddcedabceaabdbbddadedbdbaacedeaeeaaeaccacaabbabcaebeacedbbaedadbddcccddbebbbaeedeabcecebaabddaeedcbdbacedaaeedabddcacbbcdcabcaaebdecedabadeaadcbecbbacbdcccbcddecaddbaeebdcaedcddecbacddadcbdecabededaacdccecebabdeceddbeebdccabeccaccbcbbbacaccabacebabeebbeedeceadeaecbbeeabdcddcebbeeecdcedcbeacccbcccbaabdacbddeacbaeadbdecbaabbbcbcbcddcdddebbedbbdcaebebbdddebddcaedbccccdbcceeddaaebabcadeaecdacaadbbcedcadaeaddabbdabeccabccbddabdbeedbbdddbddeebaecdbcdbcbbacbdeaeeeaebdbbbddbaeedcecaddbcccceccbbabdbeebecbdbceccbaecccbabccdcbadceceabebeccebcededadabbdedeeeaeecdeedbbedceacacecdbddaebdcebdcebdeddcbecabcaaecdecbbceeceaebdabecebaaeaaaedadcddbdcdeedcbaeceeadbebaabceeaceeeccbdbedaadddbddadeedbdbacaecaecbacbcddceaceccaabcacddaeacbccbbcdeaabbddaabbaadcdacbacbbcdcebdadddddecaeacdeaaaaebccddbdadadedbdcecccdaddcdeccedcaecadeeebeeeeeddabbccabeadcaeebecececcbecacceaadbbedeecbaeeaebddcdcdcbdbccecdcdbbabedccdaaebaccbbbaebadedadedaabaaadecaabdcecceecaadccdeddbbabdaabbdabcedcedebcacaccabdcecbccbaeabadbacdeaadcdeaeeddaeacaccbdebcadaccbcccaeeaccadcbcbedccdcbdedabbaecbdbedecdbebecadaaeecedeaedbbddeaeadeccdababebebddaadcebbeeadbdabdbbcaedaeecaebeddedeedeeaecdababebdadbaaeceeaaeebbdaeccdadceebccceaeaeedcaadebdddbdcccccaeaabdbadccdcacaccabbbdaeacbaeadedddddcbbebbdbcdcebccddebdaddbacbdedbabbabebaedcaaddbaecedeededcbedbdadccddaebbbacbceacbecabbacdddbabeeabcdbacddeeaeeccbdbebaecdabbcbecaaddcebccecdcedceaededdedeecdaeedeabbddceaddbaccdccedddcebccddbcbceabddaeeeeadeabebceaeddedcdbdaaaacdeeadcbaaaeebdaecbebacedbbabaebdcabddeaddecaddeedddacadcceabadbcdedccedccabbeccbcbeeaddddbecdedccdaabebdcddbedebcbebecbaeaabccbadbececaaccdcecbbddbadabadaddebbedbcbeadbebebadccadabaaadcabeebddbecadbabdbadbbcdadecbacceebdcdaccebdbbedbdbbdcaedecbbdacabeadabddbedcacedddabcebacbdbabcccededddadaeedcaacdadeaebeecedcaeeebddbeccabaeeaeabdaeebeeabdbdddcedacabcedaceddeacaebdbbebbeacdecbdadcdbdaedaeeecebeedabdecdbaaebaebabdbcbbccddcdaebdceeaabebeddacbaadeddaaebbadebaadccebbcccabdaeebebdadddddeedacecdbaebaeaccbddecceacaaeacdaeebaccbbdcdadaaecdaaabaebeabcbecbeeceecdadebebcebeceabdcddccadacbeccbcaeecbaaddcbdebeaccaebcbcdeeeddedacedcceecdcbceccaebbeaeadcaaedacacabacbaeacedbebebdacaadabebaebdbcbadebbcdeacbddcccbbaaeaccdecbdaebcdadcbaaccedccdbaebdbbdcdadebdeebaaceaaaeacaaadcccabbaccbbbcbddeebbbaacdcabebddacedcbcbbbcbcdcdaeaaeedaaecdbddddcbdacdbebbddddecaededbacdccbbebbacacccdeecbbaedcbadebbcabaeaabdbdebeaceacceaaceebabebedecacebceccdadeaadceaceeeddabacabadcbbcacccabedbadccbadcacccdcdadeaadebdadbbccedceadadbbadbdccaeaaedbbebbadbbbebeadaddeebdadabdddbeebbbaaacddecdddddbccdbbabdcbadeaebaecdbabeeaadcddadddbdccbccdebcecebeceacdbdacaeeaecaacebabceeccadebcecdacdecdbaebedecdaeeebcecebceebbbbceaababdcbabcdbeeeeddbcbedbcadddeecbccedaedbbdccccaaaacdaecddaecaccaccbccccecdababedccdcdbaabbbcebbaeedceddcececedcdcaedeeedcadeeabdeaddceccaeadebbddcccdccceabeedaeeebabeadecbaabeecdaddeddabbccbcdeecabaaadabbccecbadacaabddeebebddcdebadacdeeeecedcddbbabddbeccaaadaecdacbadaeeaeacdeecdaadbcbeaaaaccbeacceecbeadbddedbaabaecdeaedbdecbebadbaaebadcacbdbddccbecebcecaebdbccdaaacdcecddbbcebedceccdebececaddaddcdacabdaeedcebdaddcecbbbdbbbbcecededbacaabdeddbdcdcdbedccaaacadbcbedebecaaabadbccabbbadcbeeddcbbbcaccedadacbdeacaeddbcbdcbadceaddcadedcabbbeaededbdbdaabeaaceabcaaacaacbdbadaccaaacdeeaaecccacdccaadbcdaeecdaaebecdbcadeecedbcbebddecacaebcaececdabedccbebbdcaabbaeecacdabdbbebdedddbcdcbdeebcbbddeebeabceeacddebcaadbccbbecbaaeaaecebabecbccadddacbececcdcbaddbcbccadbdcaabadeaeaeeddbdadbbebeaacbbcadbcaadacedebeacabbcdedaaabcacbcdcaecdddabacebabcabeceeaeaabacedecdbcdcbbdabecdcdeeceecdbedecedaadeacdddabedaecbbebcdddcaaaeccddaaedcddcbccaaedcadbbebdaaaaeeabdabbebadbbdacbdcdcedaecedcbabaebeedebccbabeaaaaedaeacdcbdbbbebbeceaebcccacacadabaeaeaaedcdabccbebabceabbaecdaeeadeeebbddeecebbeacceadcbbeeecceadacbcbaeaedeedbcedaecaadceddedbbeadabbbbcadbdcdbaaaadcaebcbebdceeecdebcddecbbdabedeacabaeecaaabddbbeccddaebadcaaaeeecaedbcadcdcdaaeceddbbadaedeaaeaededbdbaabcbceaadcbbdcccceeeedadbdaaeacaccbecedcacaeabbaedaeabdabbdabdeecebdcbbdcdbacddaceddaeacbceedcccecebbdbeeddbceadadbabdbabaaeddacabdcbdbabadaeededbeeeadabdececedccbaacecbcbdbbcbcdbebacecacaabcebaaaedbcacabcddcaedbbabbeadbadeaddaceaeccccdedbdccaebeacdceecaeebabebdbccbdbccdadacdbcdeaeacdccabedbcebeabbbddececdacedeebeeccededacaeaeaaabaaeebacabcdddaaacacddcbddecdcbddcdeccecbacbebacddcbeaacedabdeeabdccedcdacabdcdcbdeddeaadaabbadcdcebbeecabceeebdacbaaedabedcadbbacaceacdacbbedcdbdaacbeaabbdedddcbbcddbaebbcbaebaeceebdedbbacddedbcabbecbbbeeababeceeedabadadbdcececebecacbeabdacacecedebacbdeecceececcaeeadacbecaccccbeeecbaabedbcabececaecceaeeceaebbeabdceccdceaedadbeccaaacdaddbabdbabecdcbaadcabbedabdacbcccbbebedcdecadccbbdcdcbeaccadecbdaebabbcaecabaecebedbbedcbaddccceddcbdbdaadeebccaeeeaabebccbcdbbcbcdbebdccdcbeeebcaaaeaadaecbcdcecbceaccdcdaabbeaadaadbdbcceedaeaecaedbbdbadbeabbaacbbbbbceeddddbeebabbadcbaabcdeacdeacdeadbddeebcaccdddaaeaddbeccccdadcbbdcbcdcaebccdbeddbdaecacddceaacccdbaaeedccdbaacecbabadbcccdbbeeebcbbabdbdbcceebedddbadbaeaeaebacacdeceeeebaeadcddeeceadccbaaddcebeecdbddedbeeabaaaaddbaedbdebaadddecddeeeedbcdbadecadbbcccdabedabbedacbbdeeedddecddccdccbceadbbbcbdabbdeeeebcecbdeaaaeccdddeddabeeececcbcdcceededacebebbcbdabebdbbeeeaaacdccdbcdcacaadcdaaaeddceaebbedaebaecdbacdaaedaddacdeecccebcbacbcedbdadbdceccbbeebecddaceebaeadcbacbeebddebbcbebbdedbacaacbbbebdcbeddeeadbddceecebadedebabcbaacbbcaeacdbaabcaaabbaedcadeeabcaedcedceebddbcbabdcabcdbaadedecacdeacbdbaaaeadddecacbbaabbaaabaceeaedbaceabecbdeccdbaccbeaccbbceacceabcdedbbcaeccbbecdabecbceaabcdeaabbbabdecebedbbebdedadbdcaebacbbebcddecbddeebaeaeaeebcbadbbcddcdebcceedaaebecaddaccbadebbdaddacbedcddcbaeeceedceebdcbadccedcaadadcbbeaebeacdbbcdbddecadaaeecadadaeccbeaabaedbdbeacecdcaceaeadaaaccdadbabbedceabcecaabecadbacbadeaddddddbbcdebcacdeedeaeecedcadaaaceacbebbcaceddbabbeeeabaabdacedcaaaeeaeeccaabdcbdcbbecbeecadddabcbdcacdbeadbbecbabbcececcedbabdcbadcaecbecbabdadcaabedbeeeabeababccbcdbcaeabebdebeaddadeabdabbedbaceecbaceddbbeaceaabbcbbdccbaecccebceaebcdbaecccdabcbcceccedbeadeacbdeaedccbeceadeaaabaeebcaadcdccaaebddabdcaedeeabbbdabddebadbecaeedcabadeeeedbdbbbcaddecdaaebeecddacacaadadaebbebebbedcecedbacacbdddbadebadbaceebbeccabaaebdaabcdceddeeedaeedcbbebddedbdacbcaacbeabebacdbabbdddaeecbdedddbbdbabdbaebcaddbbeeecbecdccededadaaededeabceaccccaaacceaaacbbdadbebdcbdeeeedeceeaededbdadbecaedaccbcacaaedcdbbeedaacaedcecabaaacbcccddddbadbbdbecdecbeaeddaccadbcbbaabcccdabecdceadbabebddbdabeeabaaebeacbebdebecbebceaacecebbdaadecbbdbcaaebbdcbbdbeeccdedaedcddedeaddddcdcdabbaedaaabebadeeccbaadebccaceedaedecdccebeaabdcedaabbecaacbacaccbcecdccabbdadcebdbcdedceabaceacbcbbebbbcacdbddcdecdbdbbccdbabcdacaaaeadeaccdecdacecedddeaaaacddbdeecbdecdbebebdaddcdaaccaedecacadbbdaeeceedcdecaddacbedcededeaaabcbdadbbcbaadccecabaaeabaeadbcdedcaccbbcaaaedaadadadaccedaecbdcdbeacccdeebeeabeaebabdaabccccdebcebbabbdeeaccaddceacdaebbceccadddedebebbbaedccabacdaecccbceacdaceaeadbbadcbeeecebeeeecdaaabcabaaeaacdddaedbacaeedbdbabaabdaceeccaebddadcaddebaacedddbbaaabeaeedeacecadbbebecbbcdaeaaddbcebcadceddcbaebdeeecbabbdcbdabeeadadccbbbabbbdbdbcbdeaceaccebbbdcbdcddacbcdcaebbdcbcacadaeebcdbeaaaabdaedbaddbaeaebceedededcbcaebcacdebacbcdabeddcedbddddbdcbbeecebeabddcdeceacddadabcaaadedbcaeaadedceddddaceeedddaddcbabebdccbcbcdcaadecebddebdddabccccbbddadeddecceedccabcdcbdaeaabbdeedcabdddbadaecabcdddbebacedcddacdeebcaeebadaedeeddaecbaccacdacccadcdbaaacbabdaaabeeeeaebcbcdcbeaeaceeddbcecdeadcdcedabbbdbdeecbbdcccaeeaaeeacbecbaaecaeddaddbaccdceddcbcacdaedaabcdedcbaabeeccbeacbaadeceaacbaeddcccadecbeecaaecdbedcbbbbeaedadddbcaaceabcebaacbbeeccaaebadebccedadccbdbdbccacabaadbebebeabddeebcabeaacccbbceebeadbcabaadbcdbeeaaecbebdcdccdcbadaaabcdbaeecabeacabdbcdcdebebeeaeebdbcbbbcecdeaeadebdddddeadbecadbecaabececbbbdeddcbeebbcebecaadaacbbccbedcbccabebcaeacdeececcbbdcadbdbacdeedcbaebaebcebecebbeccbcdddcadebbdadbdeacbccabdcedccabaccbdcedacdbcebeddbaccdaeacceccabaeaccbbdcaaebdcdddceddbeeadbaddcdbddeaeceecbcdaeccaacccdacbaccecabaeabeccbeebabdccedbaaaacebaaccdccdecaebecbbccaaebbebceaddbcbeddedaeaaabeadccbedddeddaadaceddbebcecababddbadcbdedccbabaeedcbeedbaeddbbbceabdbeacabdbacdcdaedcebcedaccbeabdadceddcdedaccacbcddddabdbcdcbaccaedaebbbcdacedddceddebbbacadbeecdaddcbdeedbcbbcbbddeeabcbbccccbdecdebbbacdbecbdebdcdecbbcadaabedeadeebcacaadeacaccdacaadbadbcbaebaebebceeacbacbdbedceceeccddbaadaeaabcccbcdcdedcbccbcbadcddceedbceccdeabdddbeaebabecdaccbcecacacddabdbcbbdeedbdaaeaceddeaeadaccbcaedbbbcdbeedeadeeadeeeecdcbccddcccddcedbedeeeaddecbdbdcebebedaeeedeaabbcdebededaccdccaeacdababcbecbcdcaeadacaebbdeadccaeecbccebdcddbddbddadedeededceeddebdbbeadedddaededcbdbdbbeccadcaaedbeabdadbceadedbbabaeeaeabacaccbccedbabedcdddeeedebdceaaabcbdbdbeadbabebedeedddabebdbdecaebeaccbcacdbebcbebbccdbcaeeddebdddbaacdcdeebdbdccebbbdbdbdaabcdeaacecbbaddbbccdbeddcddecaceaaacbbdebebaedcbbeabbaaaebdedadccdaecceaeadbdaaaeaecbdaddeceabeebdcbacdedebabcbbdaaececcaddcabccacdabacbedbbaaabcbdabebaedaccaeabebccabecdbaeacbebeadbcaeaacccebcaebcebadadbabedadddedcebcbcbadeeaedaecbdbcbdddcdaaadeeecddbaacbdeebbcaebadcaabbdcdcbbddcabdecbeaaebbbdabdedbedadccbacedeaecabcaddeaccaebeadbbbededadebbacebadeaccacedcbabeacbecbedabbdbaeecacaeedeeceddeeacbbccbeebcbbbebeaaebaedeecccabdcacbdbebbcbbcaddccbbaddeddddecaededdcbdbeaeabbeecdbddcadbabccdbdddbaccedcbadcadbbcbeeceadccedaeebbdccceaeeeecbdebcaddddedecabdadeebaebadebcdabccdcadebabdaecbbdeccbaddbabbcadcebbcaacabaebeebedacebdaadccdbbacaabcccaedccabbbeaaeebdeaceccadacdbcbcecaeeaedbededcebaeaaddbddedbdbdcddcadaceacabdcaabbbdaddccdeecccacbaceceebedcbcbeabccaebeabecccaaadbeaecdbdeeeecbdbdacddabedaadeaabcaddecbcbbedaaddcabadaeaccdcabbcdbebdccaaeedbdcddeaeddabdaebaaccbbadcbaaceebeeadbcdbeccbbaebecbeeeadbdabbbebdbaccebdbeaaebcdaabacaddedadcebabcbbaccbaceaebbcbeeabaadbaddeeecaecddaaabcdaaeedcdadeaaeeebdcacccbdceccaababcaceacccacabdaaaeddedbeabbbecadabdaadbedcbdaedebdcabecbdadcdabddcacacbbaedecebdccaebdcbdaaebbdaacdeceddcdeddaedddebecdddbcbdecccbcdaacecdecceacbaaebeacdeedeebccdeedacbeaaebdecaddbccbbdebdeaaecacacaeeecdaedbedcdecaeebbacccbcdbaabeebbeaabacabbebdcebedceaebbbcabccaccbababdeacdacdbbbacbaddcbaacabdcabecdecbbceebebceebdcedcebbbbadcaeaeccbbdbceadbdeaedeeabdeecdbbbecabadcdddcadeadcdeaadbdaacadbceccccedadcbbbcbbecaecaaebbbddadccabacebdcdbdaaebceebaeaccdeaacbdccbbaaaceadbbdcaabcdabbacaecaadcdecdacbbcaebbadebbbbabdcecedddddaccddcecbecaabcebaeccbeabbcbdeabcbddebcdaabdcedbddbeaedcbccccdedabeaaabdebebccccebeebccddccecabecdebdbeeeccaaecbbcdcbbbeababbaacbbddabbdbdbbacedeeaeeabeaeceeacebbdedbcbdcebbbcbcaedadbaaabddecddcbbcdceabcccacaedeccdcbacdebcecceccbbeebbbbdebeccabcdcdbaeaadadadeceeaeedebdbabcdaeedbbacebbbbceaceeadabeecbeeacbdebccbdbdbacaeeaaaddeedbcaaedddceecababedcdadcacacedbebddddaeadacacccebdbbaebbbdebecdcdeebcecddcbeacccadbdaeebcbeddaacccdccddcdabdaacbabeedddbdaabeaddeabcabcddeeeedcebdadbadbddcedceadeeaeaddeeaedcaeebadddadbbdbdeacdadcebccaccaaedccbedcecdccdbadbeaadeaeccceebecbcbeaaeaecececcdadcdaabdeadeacebeeebaecbccaedecdbddeabdeacbdaebddbbeabaeeabbdedabeababcbcedbdbeccaceeecadbeeecdebabeaadebeebaaebebeebddecaaaaacdceecbbdbbebebabaacdccbabccadaaaebdbbdaeabcdbcdbaabedbdabbaeecadbdbdeecaceeeaaecacdeecdbeddceaeaeacdbedadcaadedeaebdebbbaeaddbdbdebcaaeeeaedcbdcaeddbcbbbeeecadbaeacddbdcabcaeaaeddbdccbdbaececccdebebebadcccdabcaadaccbddeadcdcdadadcbebccbaabbaecbcaaadccbdaadcadeeebbdeacdeddccccaeebdbcddcabccceeccdbececbeeabcaceaebaeaaecaccddbccbbbbdecaceeecdddbeedadaaaebcdaddbdbaaedcbccacddeaeeadcbbabddcecaaaccdacdedeeededbbbbadbaceccdceebcceddcebebcccdbbbadaccbaabeceaddbeeacaecdeccbbcebdbbddbedcdbcbacbdbaaebacaccedbceabedbcdbebeecbccdecceabdaaddebeaeaccaeaadcacbeeecdeccabbcdabecacdcddccacbeabeceaccceedbacdbcedaaadaccaeccecdeadecbeccbcbeceaabbbbecaabbeeeacecaedeaaebdcabdbdaaaeaabbdacadaeeaaadcdbcdebdbdbacabbbaedddcceeebaabaebcaaaecadbbedececdeeebebadcabcddecdddabcbaeaaeebbaebaccceaceececdcccedecdcacdeadbbeedecdabdcdaebbabbcadabdcacbbcdcccbbbccbcadbcbdbcbebdbadbbaacedbccdcdddcdebdcbaedcddbcdaeaaadcaeeabddadaacceaceedededeebbecceaaaebebceacdcdcaebeaedeacaeecbbdaacebacaecedcceedebbedabcbabeeaaecbacddaecddeadabaedcebecadbedbebbeeebccccabdbadabababbbebeadabdaebddedbeebbbdaadbdcbedcbcedcaedceabbbbaabdbeeabeddddebebbecbdcdcbecbacdeddbadacbdbaadbdabedeeebbacdeabeeeaeabbeadeaaddbddbceddedbccedbbbaaedddceadebabcddebaabbababccdbaedacebebeaeedebebbdccbdaaeeeeeececabeecddcecebdaabbaebacbdbddbeedddbacadeebadaaccdeaacedceeeaabacbddbaaaceebdebbecbecdeccdddbbebdbaeacaecdccedddaebdceeaaaccceddcedddcacaabdddaddbcbcdbdebcabbbebbbdbdbacadbbcbedbddcddadaabaaaecaecdaecabdccbbdbcbaedbdadecaeddeecbaeabedaadbaceeabebddabacdaecdccacaccdbacceebccadecdbebcebbccbadeddbbbeabeeacadaaccbbebebbcbaddcccdbadaebbabbeaadeedbdbbcabbdadacbdbeacdedabbcabdcabebbcaddbeceecddecbaeaeedcbbabdbcddcbccbcedaedeeedbdbdccdecaedcceaccbcbeeaeadeeceecccbdcaedeededcbbcceecadbbacdccebcebbeddebbabccecaacdbeeeaaabbbdccbcbaeaeadecedaacdabcaebbbaedbcbdddadebeeccbacbbadacedadecaecabdddadabcbedebbaceceabdddcadcaebbdebeeebababbcebedbbacaacacecdbbcdbcaaccecacedbedcdcebbeaeccedeabbcaeeccacaaaacedbcdaeeedbadcddeebdeddcedaabdeaeaabecbdeabdddbcaaabbacabbbabcaceeccbebbbecaedbaceabddabcadbcaccceacdbaacadaabddcaedabcbcbccdeeecabebacdaabccbedbcdadebbbbbcdadedcbcdbaeaeeeaaabdbecdedddabcdedcecadeabcbdadecbaaedcbcbebeabceabdcceccacaecdddaacddaaebbdceebdacdecdeaaebbccaedbbccedcdccabaeaaddbcaeabbaaaedbadddcbeaedaddeaeecbacecbaedccbcabdeccabadadccbdbdecccedcbbebeedcdcebecddcadcadabaedadddadbaaeadbdbdebcceaccbebeebaccdbbbacecaeadbdeeceeeecddadaebbcaadbcaedddceacdaaaeadeaedadaddbbebebecacdbbccaaecaaddaeaacbbbebdebedaadebaaeeeecaedccbdeecedebecadcedddccdeddaeeeeaaccdeadeaaadcbaebadeecdaeabeecaaacababbeceeddcbacbcbdabdcbdcdabdaaceaaeddcdabecddddedccecebeaaacedebadcbbbadbaeeedcadbaaadcedabcdecabeadcdaebeddccddbadabbdaccdaaeddbcbdbbabeeeaacdcdbeedebbddbdaadaadbbadbcedcaaeeddaaddeecbdbeaaebabacdbadedbacaabdaeceabadacbdbeaccdccabeaeacaedeeaaabbaabeaaeadecacbcccddaeacecbaeeaecedabeaeecadaddcbcccabbbbeeaaacedbdbbaeaababaacbdaeadbeeecbeeaacceadaccdcedcceabbcdcbcaaaedbbcebbddeeaacedbcabccdabbceeacdccdcbebabcddcdacdbddbcccceaeadbcbdebdebbcbbdabeaacabddbadaebbdbbaaaacddbabeecabedabceccbbdceeecedcababcccddedadeadaabcebaccaecaebedeeddcdeedbcbcbcaedcceecdadbabcaabaaeaceeedebdadeaeeebbeecdcaeddbaabeccbaedbacdeabbdbccdedcaebcabadacccdcbddaaecdbdcebdbbebaebdedecedecbddbccdabbdabdbecdeaabcbbaeccedacaddcbdaaeceeceeadaecdcecbdddbebebabdbabdbabccaedadbbdeadbdbcbdebdeaeccaddbaacccbddbacaeedceabcddedbbcdbecabaababecaeeeadeaaeeedeeedeeeebdadeadbeeaacebbecbccadbaddccabccaaaceacbdccaadaacebedcaccebccdbbaeddbcaecddadbecddcdbabccebbeecbbeaedbbeebedbebaeedddeacdabedeaaccddddebeccbaceecabcdccccbaeeaeddecdbccebdecdabbeaeacaeabbecbccaeaabcbadecabecbaebecedbcaaaabcdeeaadbdedaaaedccabcdbedacecebebdecacabacbabaecbcecdddebdcedaadabbbaeccdcdaeaccadbacdadedbeaadcbbdbdeeecabcdccabbcedebaeedcccaadedbeeaeeaeadcedcddaabaeadaeebabeccbeedbcaddcadacddbcbebaceacccdecccdccecedaceececbabcdcdaececdadccdccabdcbcdabaeadaeadeeaedceeeadbdaededbabbbbbbbaaeadbceadcdebcabbcddddaeddacadecebebedacdaddbbbceebbabbbbccadedacdadeeacebbcdbacceedbeeabbabcbaaeebcddbbeebcaebcccacebbdcedadaebedadaabdacddabdebedcacecaaadcbcdabcdecabebbcabcebbabeaaacaedbdabdddbdbacbaaabdabbabbadeabbcddaceabdaecbcedcdbedaecdbdbbbeaaddaddbadabaeacebcdbeaecaabdcbebdddddcbdedbaecedcbceebabacaaedaddbacaecdedbedabbdbdcccaaadbecddddccbbcbebbabbcaadaedabaeddbecbccebdcadabcedaaddabaaedabedeeacdbbcbdeadeeecaaadbbacccddbdddeedcbcceabebaaccddaddecccbdeaaadddbedbbdadcaabcddbbeadcababeedaddaeaadabeddcaedbcecbcacabcbaaaccdcacaacddeedaceddaeacdcecbceddebaceadceeddeabbdeecadaaaaadaabaaaabcaaceceeccbbdecdbccedadbbadaeaadacdebbeadeaebdcacdbcbcccbcbcaddaecdaacbbbedbddaebccdbaaeeaebdceadeaeceedceeaaebbdcabbbaadadddaaaabcecabadbabcacbbbaccdeaabcadddbecaecacbcadbeceebcadeaccbeabdcbdbaaeebaabcdacedaedaadaadaaeddaadbbccddecaaaabcbdeeddcaadeecdcbdaeaacdacbedbcbeecaadadecadeccbccecededcbbdbaccdcabdaecbbededdeacdceabedeacdeeadcdceaccaabcededbcbbbeaceebacaabacaceaedacecbebddadbecadabddcccebcdbaeccdecdccbacebdbaaebcabaaacccbbdbecbbbaaacdbeecddbdcbbdaabaaddababeeaaeaaeaabbebcbcacccedbcdaecbcbcdeadcdeceedbcdcedcedceaccaaaacebebbbbdedeadaecacceaeeddbaecceeedebeababcbabaeaedccbceaeccaaabbcbbdacdeadbedbbecacbbcaedacbcadeebaebacdbececddbebbbaaedbceadddaeddcbaababcebcbbbceecddeceaecdcaacebaaaccdddbddeaccedcedbbcccbbecdebbebbcaceabacdedbeeacecabdbcddcbdceceebadecbebeacdcebdebaddbaeeaacacbaeaacdbdeebcbdaccbadeabcbddabbeacedbcdbddcedbaaccabecececbdaccecccbacabeddeeadcbecbebaacbbbbdcdddbaceebabdbeabbecdcbcddceabeaaabacbaadaaeabdbdecdddcaaebcedecdeeeaeabaccbdeebddcbdeeacbaedeccdaaeaaeaeabaeabdedcedeebabbdcedabebdbbeebaaddaeaeaadbdaaaadcbeabeabdaeebbedbabbcbacceaaabecbeaacacddddceaedabdaebeabadcbdaebecebceacdcbededaeeeaeddeccaebceebccddeaedababbcacbaaceabddebcbceecdbdceeeadaaeeaeabdbbbdddaeaadbdebeaceaceebcaadbcdcabaeecbdcbeaaebdedebcebabeebdedbdadddedddeddbcccbccccbddebdebcdddecbcbadeeedbecacaedabdbaedacdcbacdbeebbaebdedcbcacdecaddadddaaeacedbbaddbdcbbceddeeecbcecdcecacabdeeaddedeeaccedcddeacbcdcbbeebdcabbbaeccdebaadbcbaaddeceaaabadcbddeccbebbdcedccaeedbdaecddbabbaaaaeeeaacdcbbcbabeadcedbdeebaabccddebbabccdcecbbeabeececdbaadccbaddbabdcdedabbdaeabbbbbbdbeeddadabcadbecebdedcaeaaaedaacbeedbcaabdcedbdeaecaabedeebecdebaaadaeccbabaecdccadbabccbebeaaaaaaeacadaaeddbbcceaebbabdcdcbeadbcedcdcaecbeaebacaedccdbdaaaacbbdaeabdddbecbebdebeccdadccdadeaebaecbdddddceaddededdcbaabaacdeaeeabcedbcaeededeabddbdbcbcedaaeaaabcaabbaadbdceabcebaaeeeaaacbbbadaebeebbdacdddecabbdcadeebddbabbebbbecdaebabcaeebcbacbecbcbacbeceebdbaeedcceabdeebcbedecbedabaabdabdecebbbcaacbdaaebadbcdbbdadbcbaedeeddcdbdeabdabbbcdcadcdaaddedebbcdbdcceaeabdeddbeeabdcbeddaddaeecbdccdadebecadedebeadddcdcceabbcbbcadbedaeececcbeedbcdcccaaaddcdccbeabaccbdddabdeadeeaedbaecabebdccaaddeaddbabeccaecacdebedebdeededeaccaccaabaaceeebeeeccdedbaabacabcebaeacabacdadebbadebeeaaaddecebdaeabcedaebebcbcceeebaabdbcdccadcbcddaecaebaacbccecdcdcbbcccebabeaedcdabeceeaabbcabebebdceaeecddecabbeeddedceeeacbbccbabeebebecdbcaebcbcdeceebbcbbdaacebbeaabaebecacccdaeeaaccedabdedbeedcdecbabaccebbeeedaaecdadeadecdcbadcaaecabcbeacdcdbadcabcacabbeebbbadddacbddeeebedcddeaadadebbdcadeaabeebccecccccdbccaddedabedeeceedecbabbdaececeaaacdbbdecbbeccbcccbbdbcebabcdbcaeacebbbacacbbcbdaeadebdedcdcbcccacaaccbcdceedcacceabdeedcbaadcdbbcceeabaddacceeaeeccaebadbeacbceccdebddaabddebebaeebdecabbcbbabdcaecaaadbadededaacccadddecacebdedabebbdcddedcccabaebaeeaaabaceccdbcecbeaadedaeccaeebdcdbdbdcaeecddbccadadbddeeaddbbaceadebacdbcebbadaaabebcccceaeeeaabbccbaebeaaeceaedcbcbebacdbebcecbaebeabeddbcadddbecdacbabebadecaeacdbbdcccdeebaccecceebbbaadbdcdadcaacdabebedcccbccecabadaaeebddadcdaebeddddaddccadeadedbcbccabbebecceecadcbdeecdbbdecbdcabeebaceeddebccdcccadbbdadccccdcbbcabbecdbecdddebebdccdedebddeadbdeccccddcebebbebadecbddcdacdaabaccdcccbeddaeadddbbcbbdaabbcbececeeccbaacdebddadeaccecdaaabcadaadabacbdcbceabbeeaaabaceebcebedacbcaedaedbcadeccedacdcbaceaaaeeebbeaabcabbcdadaadbbebecacccdddeccbcabaeceaacddcbbedaaaebadedcedadeeaedaeaaaaeaacdabeeaedabaaadedccaceccabdecbbbdbaebcacecedddabedcbbacceecadcdbdcacbbccccccacccbbaadaddbacccbdbdabbaaebedaaedecebdebccbbcebeeebbecaeddabdebdddeddacbdeadcdabcaaeadbeddcacdccaaeeaedaabbeacabcaadbedecababbadbabbeeaeecbbedeabdcababdcddcecbccabcccecdbaddebeadceecccaeaeaebcbaeedaddadcccbdecabdddcacbcecdbcbdbddacacababaeaecaeaaaceaebdbdaeecdcbccbdacbbaacbaebbcdbbcdcbceaebddaaeabccabaabaadcbadeeaaeabaacaeaecccedebaecadadeeccaaedccbbdabcdacdeceeeabbdaeccbdacaeabeddeedcbcedaebbccaecbddeaacdbbeceebdcccaadccabaadbdbadaccaabcceaccbdacdddbedbbbecacbeddccedbcdeddaddeaecbacdedcedadcdedbbdedaebccdaecaeccabdcbdebbdbacabcbacdabbbaaddaceddacbbebaabbeaebdabedbeccacbbcaebddbaacacdbabdaaccbeaededdebcdcedcaacddeeecbbdcdeddbdedceccdbbabbaecadbdbecbbbeccaecaedbeceeadccddeeabebbccecaedcaebdcbdabadedbccebbaabdccacadecebadeaccbbacbddbcbccabcdbdacdcaaeacdaeabcedbcbbdedbcededceeababccdbdbcbdecbbdccedeccbdacdcbcbaebbeaaabbdddeeadeebcdedecabeccbbdadbebedaadbadadeddcedecbcaeeeddbbbbbaecabbabbcdacbbcebbbeadbbeccabeebecacdedbbccbccbaedaaeebcebbbdaedeebcbbbcebcadabecedcaacbceaedebdbeccceaadaeddceacbceddbbcbbbadebddeabbdcccbcbaeaedaedbbebacebcdcceddadddadbeebaeaabaecbadbbdddacceccbdecdedeccbcddbcdacbbdeccbcddcbdacabbecbeeeadbbbbbcdabcbdacbbdcbaaabadbedcdedbdecaeaceadcabeeabbcdedcedebebadddebabedeaadeeabeeddbdcddcedcaadaeedaaaccbdddaaadaadbaebadabeecdcbebbdebeadaebaecacddbcbaddcabaabaeebabeaccaecaacdddcccbaddcebeddbbeabddeaeedbdbaadbdeedcdeabecdbdabdaceeaabdddbdabcddebcedccbbdceedeaadeadadababccbcbbdcbaccbbbaccbdccacdebeeceadabdccbadebdeaccadacdaedaeeaaaecbebddebeebdddabbebedcedebaeaedbcdecbecabbbcdccedbeceeddcbbebdcdadbdedbabcdcecbabddedbcbaeabbcdebdecedeaaecedbbbbebaaededbbadccdbdaeaaaabcdeacacdbaccddbcdaccacaeebcaeaaecccbcecccbedcaddcccceaebabaeadaedbbcacedaddbcdeccdbbadceaaebbcbebeaddaceeadcaddacdeaacaccdaebecadccadecbbaededaaaceecdccdaeaedebbccddcceecbeecadecbaaaaccddbebeddbabeddebbbbedccccceacecbebbaebadecedcdaedaceeceacedddccaececaddaaeeeadbdddcceccadecbdacaecacbcacebcaaebdacdceccddeddbddbcccacbcdacacadaecbeeedeeabcacbeccceadbcaacaeeddbcaabaaaddaaebaadbcabdcdadaeaccbacceebbcedacbbcacbeaedbdaaadaabcdccadcdbbbeaddddedadddcdbeeacccdeddbdddcdadebcdbbededbeaeeecebccebbeaeababbeeaeabeabcdcbdabcbabaeeebecaabacbdacccaececeeadddcecbebeaedebdbccccebbabeccaaacdaeabbacaeabebdbaacedeaedeacdbdeeccbaaddbacaaacedaebedaaecadcbbbbdadcecbadeaaaacebcadaebedaacdcdadaeabbcaaedceeaceeecececbcbebdedebbcbbbeceecadbbbecaadabeaeaeeeaaacaceeaabaadbdadbddcccddaadcabacbacdbbdddbacbaeaeebccbcdeddadeecaecdaccbaddbddbbebcaedeacabbeededabaddacccedacdbaebaebbeecbddaeeeeaabcabacbeeaccebceebebeadadbddaddaccccdeaabdabdecdbbeacbceabebedadcadbccdcedeaecacdccbcabbcbbabbcebcbbedaabdcabdacaddeaaacbcdbacbadccdcbcebcdcbbceceecbbeacbeadbacdcdccddcedaaeaccaecadcbbdcecdcccacebacbbbbcbbadbcbaeecdadaeeaeceeddcaabbabaadceaeedcaceebbeceebbbbdbaaacbaacbeeeccababbecccabcebcbbeebdbcdaddbcadecececeaecddcadbddbbdaebcdaebabaececadbeaaeacabecdcacbabddbaddcdeacbcabacedcbecaadcaccbadbeceeaeabbbcbadaaeacdecdcdabbebbbabcdeacaabcbadbebdbdceaaacacbaacaaaeeedbbabdccdacabaeaddceadeedacbdcaadbccaecedaacdeecbedcbacadccebccbbdbdabceabedaaedebcebeedcddcecaebbecdcdcbdbabaadddbbceabcaabdcccaeacdaedadcacabdceeccdddbcbcadceeeaddbcbbcababadddeaecccedeebbdbbabceededceeabecbeebeabeceebaeabcccecadacdbacdebaecbbcbebeabcedadbbadebddbcaadabacbeebadbaabddddeeceebecdaaabdcdceddacdbbcabbcdabccdedaabdaeedbecaebdceecbeddaddcacaedbbbbabbdcedbeeeceacadeddeabeabcacadbcebcecadbcbcdcbdebdbedbccceadabcceebacdbaeccbacbabaaabaeaeecdaddbbccacbeeeaeabaaddbeaaaecadcddddaaababedeaebcddecccbccebdabdddddbeadabdbbeaceceedbbabeebcbdadcabccaeeddbeadbcdabcadbbceacdddaedbbeebebabdacedeabeaeeeeeabdabcdddaddbccbeddebbeccabbdcebedbbbbbaebebaaeceabbedabeaacaedcacdcceeeedcddbedbbbdcccdbdebbeadbaccbdedceceabedeecbadaaaeccddccaabdbdeaeeedeacbaaadabddbeacccabbbacdccecdbaceaeabcaddccdbeeebecbacbaccccebcdddabcedeacdaaeeccbeadcbebbacabdecceeeabeeadaebaabecacdbceacbedecbddcdeadacdbbddcdccadaaaaddbdbbbbdccedebbebceeeaabbdccdbcddcaebaabbcaebacbcbacbecadaabbbddddabebdcbacabbeadbbceeedacacaaecdbbebccbeabdbadbbbabccdcdbcceecdaaaeaabbbdccbcebacabaceadacddadceeaaeaacebabecdabdecbccdceeeecccddbbbeebbddecadbeccdbbabdddedcbababdbbadeadabaeeebedcaedaeebdcdbabdebdbaddaeeaadcdededeeaecaddaaecdcdaccdeecadaaddcbeaccbeedccbeeecaaaeeacbdadcdcecbcdedeeedebcdaabcebababeaadcaaeadbbaaecdcdcaabaeebbcacaddeccabbbdaaecbbaadaeaddcdacbedbcddbcbeaeacedbcdaeacaebdbcdcaedacacadccabadaaebcbedbebacadccceadeebedcaebccbbbbaccbabeaceceeaaddadbbcedcacdbdabebbeeeaeeadebbbbccebcbccbadcedeeaecaaeaaeaeaeecaaaeccbbbecaacadabbecdabaacbcddddacdbbaaadbbedccddbdbebdbacacbbdbbceaeddbdceaccedbbdadcdccddeaeceecaaaaacdcddcabedeccbaeeccbaadceaaecebecddabcabdddacbcacaeebbeeeccecccbcccedeeeeabadcbcccaecadcccbbceaececaaaadeeabadcaedeebddbcdedbcadccebabdebdeacadeceabcbdecaecaddcecdabdaceadccdbcaeedecadaeecbdcadbccdadabcbcebadeebbbddccdbcadbddbdaecbcbedeedcaadbebecbcbedcdbdabceacacaaabbecacccbdeaeceededaadcaaceeceeabcdaaaabdbdbbebeedbdbbaaccbadbacedebcadbbceeeebcceaedbacbdeeeebcaacdccaddeceebceaddcaddbbacaeacbaaadbddbdacdedddeadbabdeaddecaabaecbaaacacbdeabbdadbbaddecbbdbddecbadddeeecdedddbbbbcabdadbbabcedeebeecdaacdcdaeeccccedecbdabcdadeebeeacaedeacbebcebaceaadcbaaabbbbbcaaabcbecabcbbceabdaeaaedaaecdecdcbecceebebabceedaaccacaeccbabcccacdcdadbedbdcdccbdeaadacddeadabecadabcacecbbbbebeaeeaddcbabcdedbcdbaacdcebabceacdcedbdececabeebbabbedabebcebceaeaededbdeadecdddbdeddeccbdcebabacdaeaaceeebcacbadbaaabbdeeebcadebadbadbebcbdbeaceccaadeccdaecbbadaeacaedddbdddeacbcbcdeebababbbedbbceabaeeaecceeeeadddbaacbcdacebeadbcadcccbccaeacbebceaaeeabaaabedbedccdeecadacbaaaeeddcdbcdaaceabbceeaaebeadcbcababdcaaeeadeebddaaaddedceaeebeedeabbedbcaebccddebecaccbeedeaecdbeacdbddbaebaeaecededdedddacbbeaaeecbeaaaadaaacdbcecaeaebdacbadbdabcaeacaebeecccacdeaccbbabedcdaacccabaacdaddaeeccabecebbcddbcdccdcadeaddbcbdcdabdacaaddaccddbebabbebeeddadebddaadedcbadaacdbabbdcdbbbeaeebbabdbddbbaccbdebdceeeeeebaedcaeeccaadccbadaccaedaaacadccdbcaeeeeebccedabcabecedebebebaeaaecccbdacbacdadeabbbaddbccaadbecbdceecbcacedadacbcabcbcddebabbecddbbccaabdcecceecbeadccdaaadddadaaeabdbadeabbdeaabeebdceaeeaacddccbccdcecdaeebeceecbbdbacaecbacccbebdadeddbebcecbeacbedbecbabcaebdebaabbccbdacbdceebcbabaaeaddcacaaaabbbdbbddebeabcaaaebcdaeeadedcbdacccceeedabcdceccbbbccbdaddeeeeaebaedddaddecaabcaeceacbadedcdceaceeaeccedebcadccebeaaedddbaaaaabedcdcaeeacceaacebbdcdedbcebcbaeabbcbdcaddececccbbcedddccedcbbdebceeadadaaabacbaadddedcecdbddaceaabcadadbcabdcccdaadaeddacabeebacdbabdbebcdccdbdccdadbbbcdeeabeccceecddcbbccddaecbaabdaadaadaedeababbacabdaddcdeeedcadaaeadaadbadadcadcceebbdebcaaddaecebdcecddaedcecbccaccebbbcbdedaaacbddaaadeebccdecdceaceaaeadcaddeedacbbdabcbbcbbaecdcacdbadecceebedebbaaaddacaaeeadbededbabdecdadebdcbeaeaaebadbecedcaacecdeacebcbceebddbadaeadacaceeddcadecbaaddccbebeeeeaadddedadcbacabcecaceecaebaebacadbdedaebeabebbcbedbcebecdeeacaceeebacdadaaabdcacaedddbbdeaccceacdbcccbaeccbdaedccecadbecaceaeecaccabaaebdddeccedeeabeedbcbadabccededdcaebbbeadbdaaaeddeeccebdbbcaaebdcadbbcddabaccadacbedcddbbdaaddacaeccebacbbcbaaebedebddabacdceddbcbeeadeaddcccbdeecddecedbabcddedadaaecdcbeabcdeeccbedaaaebeadcbbcdeecdbccaaecdaabdbadcbbecceccbbddabcbbdbbbdcaddedabadbdbbacceecdeeedeaaedeedbdececebebcbecbdcbecdeaddcddaadaeeccbecccdbaadbacdebdabaabecceceaeddadbadcbeeeddddaaededaaaccbdbaceceddbaecadceadbaccacbcaaedddebacaddbdccabdbaccaeacababbebcdddacbeceaaaabaedadebdadcbaeabbcddbcdacaededccbccedabcecacebacbacbbcaaeabeecdaadebabecebceecdcbbebebbebdedcceaddedbaeedddaabbddcdebbdedcbecbedcbbeddeddadcccbbaabebbdcdecabddadccdebdabcbbbdddaaeecbbbbbdddeadcceacebeccdcbbebaacbdadbedcbaadbdaceceeeaddcdbadcaccaacadeaaceeccbddebecdbaeceaedaeacabbbdcadbadadebbdaceeaeebeaaebacdacbedeceeadbabcdbcedebbccadbdcebcaabebeadecacaeeebbacdeaecdeabaebccccadecebecdbacaeebeeebdacebdcacebdbeabadcbbedcdecbdeebddeddeeadccedadaaccaaecbedcebccdbbbbdeddeaccbbdceebcebcddcdacddabcaaacceaedaeaadcbecdeeeaeddedcaaaccbccaebcbbaacdbbecdaceacdbaccebbadbacdcaccdadbacaeacedceeceadcbebecbedbebdbbccdeaddccceceeeccbacbbdaaacdcaddddcaeaeadaceecceecceeeaaadcdceacaeaabcdbcdeeccbbbaabddbaceacbcdeeaaeacbacdaabdedabdcbbcdbdabddddcaaeddecbaeadccbeaaeabdcddeecdcdcdcbecabadcdbaadeddbcbcacbbbdadeaeabdbbebabbdbebcddebbbcbceacbdabadacdedcdcbdaabeebdbbcddacdcaaecbbeaababebcacbcbbdacdcebababcadcdccdbedbdecbebcbdacecacdabdedadaceecacaecbcadaebceaaddcddcddcbbbbeedecacbacaecaaebebeccaaacadecababcbbccbeddedbcbadddcbbeadabedbeaeeccecaadcababedecbceaceaecacbbbbacadebdbbdadcecbdacbbaacbcbacddeeeccaaecbeccdbeaceaabeddbdacceaaaccaecaacecebcbdbedbbcddedbeaedddcccbeddcccebbedadbdeeabacecdabdbedcdbebdbabcaadccbeacdaaeaceecddbadbddcddecbebbaccdedaeeccdabbaedcecacccebdedaeaaecaacebbbdadbdeedebeacdaaaabdadaacadbacdceabaddcaebccaacaeadbcbbebeedaacbccccedebaebeeebccbadbbebdcebdbaeccdaccdacdeedcbcadddeadcdecbbcbcdbdcaeaabcaecbdededebceddadbaccbaacbececddddaadbadcbccebedecdbadabeabceacbeabdcbbcdaddeacaedeedccebbaedaddbbdeeeabaceecbaadbaecceeccdbaabbceeeccabdcaebaaeacecbcdaadbeebedadedddbdceaaeacbcdeebeaebedeaddeadaddddabbdedceadceddbcaadcdbacdccabbdbaaecdbebcedbbbdedddcdeadbaebccedcbbeeadbaaeeccbcebabaecdccddeedccaddeebabdacbdcbabeaacedaaecedbdadaebddcacdcbdeddbeedcdcbbbdcaaadaabebcbdabceebabaababbbebaedcbbdccebccdaadabeacadbbeebcbabadddddbdbcbbddbadcacbcdcabecbdceabddaceaeceecdeccdcdabbbdebabadeaecbdeacbdedbbbccdbddaacccdedbdddcabcadadacabeaaebdabceeadccedaddcbcccaabcedcdbbcceebbdabdbbcccdccadebadbddbeecabdcdbeabcdbaacaebbdedbddbbddebabcaaeedacbbeadcacbbcbddbcaadbdbbdbddbbbdcdceebdaaccaecbdaedaddbaeeebebbebacebcececebbcdaeaccbdbeeccdbacacaaabeeebcbcabebbcbededdebdaccdddbeedcaeecebcbcbebddcdaecedaebcdeddbaccddaeeecdbeeabadddcbdaedcbceecbbbaccaaccbdbdcdaacddbaacaecbbeaaabbdeecaaedabaacacdecbcededbcbaddcaedbcdccecaedadedbbbebcddcedaebcbdeddececedeabebeaccaaabcecbbcbeaceaeddaceadebbdbcedbecbcdecacdbeeabccbddeebecaddceedeaabbbdbcddbdbbdaacbcbaedaeccdbdbecdbeaecababdcebeebdecddbbdecedadabdbaecdadccbcacbdccdabeacecdbdaacaddeebdadeadebbdbccbdaedabbcbbdcabdadcaeacedcadbaaeddcceabcacdebbeeccccacdbaacddceebebdebacdeebdbdacecaedacacbdbbdecdcadcdeeaeecebeddeccbaeeeebdcdcabedeceebbdadecbabbbebdbbbabdcbecbbedeacdbeaaaeabbeaabedcacdebbecbcddedcaeedcbccdbcddccebedcebbbccbeacccbcbbdbecbbadabeaacdeadadcaeabbaebebcacdaececebcdaaeedaaeeebabaacbcdabebeaaebddeaabdedcdadeaaeacaabaaecdbaebaacdbeabbedaccbeebbcedaeaeacbceccaedcdcdaeddcaeabbdddbcaebbaaedcbbeecdcccbaaabebabcddaeeabebccdddcbcabedbbaabcaacccaaddaebbcdcbebadcebeaacdedabceebdbdcbaebdcdbaddbcaaaaacbaeaddddbdaeddecaadaaadecadccaebaeaaebaabccdedcbcbcbeaceeeabcbddcaeadadccdedbaeeedaeaadcadbadeabeeadeaecebcecabbcdbcdcabeacaccdcdbcdbbaeedcbbaebbaedaabcdcbcdbcdecbbbcadbacecccbabaacabeaaaeeedcedeebcbbabbcecaeacebbdddcacdcacebaabdccddaaebdbaeddbeebecdebeaebabebedadbbebacbbbeeacdceaadebcaedecbbdcbaddebddaeededeaceaaaedccbdcddccacdbdccdaddeedcebccacbeddeedebebacaeacddbcaeadcacacebaddbceceaededcdabecedbdedeceaecceadabeaaaddadaeabdcecdacdeadceabeddaeaecaabaccccdccdedaebecdddacecbbcabbeedadccdbedcadbcbbebbbbceadeecadadabdeadeceddbbacebcdecadadbcbedddabbebbddaabbaaccccaccdeedacbaccdaecbdaeeedabbcdbcedaceddbbabcccccabbaaabbbbaecacabebdddedeeadbebadcebedccbdbcdaeedbcebaeecabdecddbcdecbeaaedebcaaeebebacbbadacedaeaceabceceecebebcdadbeddcbcbbeeabbabcdeabbccbabdabbddababbeecaebdbceaaeeebacedecdaebceacdaebaccdbeddcabdceaebdbcadeabbdacdcadaaddcdcbbaaacebaaabacaccbabeeadaabdcccaacddabdcedeabbceccdabedadcceeecedebaeebcdcdeeebeccaabbeeeacbcedabdaeabcaaceddccecaedceceabbdaacccbbbeaadbbedbcaaccbbbeddbaebbacebcdcebdaaabcddccebebdbadcadbbbaadacdabaeaacdbdebbdcdadbcabdccecaaecbdaccdceeaccabbdbadabcbaebbceecceecacaddebeabaedccddcebbcbeedddcbebeedaddbeeccedaabbeadeecadeabdaabccdadeebedcbeadbebdeacbcaaebbcaeecaccddbbdbcccebbdedaaadbebcaecadadbecdbdebacccacbacdacabebdbdccccabdeedceddacbebaebcedbcbbebdcbbdaabcbecdeedbcbcebceacabcabadcaddebadaaeeebabcedbabecbeabedbdbbaecbbacbdcecdeeececdbececcbdbebdccdddcbbddadaebcededaedeaaeabebbacacaebdecbebaccecceccaeeddbadeaceaadddccaaccdaaacebaaedebedbacbcbcebeccadccadbdbbebcbadceacdceadabbbaabeeddadcbcbcaadcbaddbaaadcdaebecabbaaeeabbceeeedaeaaabeeadcdeadabacabaccacacbdedbbdadbbaaccaecaecccadbeaeccbcaedecbcbdddbabbaeccbbadcccdcbbddebdedddaccdbccdaaebcdcbacaddedcbedccbccaaadbdabdddcedaeebbcbacdeaeabdaaaaeacccaeaeccdccaeebbbbecdabbdbdbddddeebeecbdeeecaceacebbbcccbedaceedabbeedceaaacecbeececbbddadbebbeecdaebebedebebdcccdeacaaebdedbeadebbadccaaecddcedbcaaeaadcbccebbcdaebcedccaabdbbbcbbcbdaaabcdaecdbdecacbddccaeaaaeaeeecaaecaabccdabbcbdaeddaedbaaccddaadcaebbcdedbadeceabbecbaedcbccccaaaaeeaeaabdeadcabedacabdadbedacdaacacaeeabcecbecaacbcadecdccbbeaccadbeebaaabeccdbddabedbedaecceaeaeaccdacdecacaaeaeeebbdedbaacaeeeeccebbeedccdcceccbcccecebdeacbacbcebbeacdcccedbcdbccdcdcebacdbcaaedaceedbccbacdbbbdadaccbadaaaadebebdbcebbdcaecaccdcdbededaddaedcbbaedbabdeedaeacabaebeebcbbdcacdcbaddbdeedbcececbbbbedbdbecabdeaacdbdebaacabdadccbbdbabcdaaacbbaeecdecdeedadeacdebcdbebedaaedccedbccdeeaacadaedbdcdddbddedbabbcbecbdadddabbacceacbdbbbeececdeeadeaadecaebcddeedadbbdbdedeabcacabcbccddeaceedbcbaedeebdcacdabdbeecdcabaddcdbcaabcacdaddeeaacbabaecabceaccddbcbbbbddcbacaaebcebcabbcddbceaedddceabaaabdeedadaccbaccceaebaabadeacbdecaaddcdbbdcebbabeceaccddeacacbceddceabeeeedcbdeccaebbcaacdabcbbadeaacbabbcdbadaacdabdadabbcaadcebbddeccaabddbdceeaebadbbedaaceabdcdceeecedbbeedbbaddeceacecdbaacadbedeeaeaaebcabdccbdeabbcbadeedcbeedbddadaaeddebeecbabbdaaeeabacdeabaaecccbaebdcbeeaedeeabcabecdbdbbccaacbcaaeedaadbecbacedbcddaaceeadeacabdceaabccbceceeddedebecacddecdeccbdadcbbcaaababcebeeeaeebcaecdabdaeeaecbcebcbedaaececbcaceedebdcedebebedabccaceaaebcbbdccceccdacadbbaebdcaedabceeabebadddeccdddcdddcaeaacdbddccaebbdbedbbeccecbeaaaaebabbacbdbddcbabecebccdbeacbbebaabeeccbbdeeedebccccdcdcadbccacaedcccbccaaecacddceaccaeeccedeaeadbccbdbceaadbeabbecbcabababadaccbaececacedbbaccacdadceaedadaccbcaaedbdddcdbcebeabbedaeeebddcdcacaaaebebadaaecceabeccaebabcdaaecbcceacccebddbaceeeaaedccdcebecabaedacacdcbedceeccdbeeebbeddaececeeacaceaaaccaedbbbdacccaccebdacdabedaaabeabdcbadaecccabceacaebebadadbccdcbbdeaacdebcddcdebddebecdeacdcebecaeeddbbdddeeeeebedacbabcadddabdacadddcbcbaaaeededbebdebecdaaaacdbebddadbaadeedcdaeaaccbbedcccaadcaeecebdadbeddddddacccdcbadbabaaaddeedaacbbbaacbdaebeadbaecdbddceecaccabccaedbeabaaebedcaaeeebbddbbeedccdacbcececbdeaebdadbdcdaadaaebbeaeeccdbdedeedccbcdeaceceaaaeaecbcebcacdeeaaecbdbadbbeacdcecdceabdbddeccbaaeddddabadcbbaedecbeebaebeeaaaadbdcaceaedeeebdddbdabadaeeaaabbdebcdaeddabacdbacebebacbdebdaeaceeaedbbccadebeabeceeecbccadaadaeadeedaddbdaebddbcebbddadebbccabbaeadedbeaeeceebbbccaabbcdaadccdebaebddbdcebdbdebccecececabbedeeacabeecbabbaebeaecabcedcdababdbdeacdaadacabbadcbbeaeeecaddbdeeabcebccbcabdcdbebbbcebdaceedbbdbbcaccedadacbeebddebbdcbbbcdbddbbdbacdbbaadaacdeddbbadaddeeaabcaaeebcbbbcbecbeedbedbccbddbaccdbdbaeccdebbbecedacecdecbddaabeaabaabbdbcaadcbaacccedeabccdaecebdedcaeaadbbbcadabcadaecaaccdbaeaaacdeceddcbdcebbdbadedbdbbaccccaedabecddecbecdeadcaabdcdbeeeccebbaecdbabbbbbeccbbecddaaaeddbaceaececbdaedeabcaebedecceaabbceedaadccecbedcbadbeaddaceeaeeadabeccabbbebcadabbdbacabbaedddacccbaaedbdceedecbbbccceacaddaadaeaedbdcceadeeeadeeaddeeecbacabedecceedcdcadaeeecaaeddebcebebeebbdbdeddbcabedadcbeecccccbcccdaeeeddcaeddcacddadecbbaeddcbabaccabdeededeedbcbdbeddcbcbceacceecadcaaccbbaabadaedceddebcacebceeaaeeaceaebcaabbcabebdaecedcaccdceebcebcbbababdeccbcdaeaeccbeadebbaddbedccedbacdddceadbccedbdabcaeebbcaadbdacadaadabbaddddedecedbbcdcceacebeaebbaaecccbcdddcbececeddbeecacaeccaeaaaabecbbadebddaaedcabddcbaeabdbcaceecebdeecaaeccabdbebaeccebcccedccbbadbdebcabdbbbececeebbeadcbeddbdadcbcbdbabccdccaeaadaebabeddeabedeeeecaebeeeabceeedaeecabeedecadbebeecdcdceadaebccbcbcbccadeeebbaacedaebdecbbccdcebeececaddaeabadcadeaaebedabebceeccaacddecacaaeeadebaebcacabadbedaeccceecabaadeabeaadbcaddcaadaeaaeacaaceeacddbbaeababcaadadcecbaabadcbbbbcbbcbbaabaaeebbdcdcdabcbdeabedabdddedebdbebeaddaeacabddcdacebccaeeabecaebacaeaedbbdeecbdecdacceadedddcbdebcacbacaadbdceccedaaadddacaeceedcdbdcbdacacacaccecadbcacebbabbbaaabebbbaccbcbbbdacdaeadddbcbdeecbaccdebabdbbdedddbacdcadabeabbdeddbdcabeaeeaebcbadecaedadbdcebdeebcdbbecdaeabdddadeddbacbdceaeccebdaacdeedccacdbbbacacabeabceaabecedcebbaddbdceedccaabdaaaadeabbaceaeaacbbdcbabbeaeeadbaabcedddedededebdabceeeeedadbcceadcdeccdcdbaeccaddaaeaadebbedabedbdcccabdececaacdbbececcbbaeadbdbbecdbcbecdbcecbedacebdbbbbcdbccceadecdeaceccedeccdeeebecedccdbacbceaeeccdcbadadbebbabcdbcdbccdedeeabecbacaccdccdebdeebcaeacdaeaabddaabbdbebaccabbcddeccdceddcddcccdddabcabebaaacaeaceceeaabaeaacabbaaeaabbeadacbbcdebecedebecdcdddcacacaedadcabdbcccbabeddceaaccdaecdacdaaeabdcbcdcbbdaeeeadacaaaeeeaeecdcccaddccbbbaaeeccbdbdcaeebeeabebcadcdabdddecdebbeeaddcceabebbcaeeaacaebcdbebedcdbeddacbecdbeddacdacdebedcdbdeddcbddbebdabdbcbddabeccbcbeceabbeddbcebabbcedcaabbeeeebbcbedcdeeabdcccbbadeedcbdbabcecddeedcaedaedacdabdaaeeecaeddacdadbcaedeecbaacdcdbcecacacecacbaedcaaaaecdedabebceabcebdceabcabbdcbeaebecaeeaaccaedbadeddcbdeceaecebdcbbcbbccdaaabeebeaeaebcdcacadeecbcdadcddddaccdaedeeddeaecdebaaadaadaadceadbbbaeeededdeeacabdbababeacedbedaeddebeabecadddabbccedbbebdcdabacdacecdcdcbdaeadadceaabbbcbbbddcdedbbbeebedccaaacabccddedecbedebbbdebcedccacaddebaacbadbdbddaabebdaaededccedcabaeacdccccbedbdadbdbddbdbcdadedeccaeaedddbbdeccdebdbeccdeccdbebdecadbacebaebcbcebbeaceebebcceebbcbbcdcecaadbcecbeabaacebcbeeaceecbecbcddbbeeddeabebbeaabeaeedcbbaadbbbeeeeccbcadbcbaeceecbabaaddbcbeedcdebbeaebdcaaebcbeabbedecebebbdcbabadbeeecbabadeabbbbccadaccbcccadcbaeeadbbdaecbcbaceddaceeadbbadcdbabcbaebebaceadebcedcaabddceadaccbeaeaecdaaabdcaeedddceebdadceedeeaaaeaceabdbcdecadbabcbadadcdeccaeccbddadeddeebebdcaaaaadbabaaecaedcdbedbedeeeabbebaebdcabacabddbbdcdabbeecddcaedecebeacbbbeacbbdcacbdedadeabdccbbeeddaeacccacbbcaabdbcccadbcbdbdeeeacbcccddcaccbcaacceeadddabedcaaeadaecaebcbeacdbdbeeddaeadcbaeedeaadccadedbacebaddabbcbbaecaaaecabdcddcebcecccbdbcabaccabbbabddeabaaacaeeebadacecebceaecccdebabaaeacecdcacdabcdbeeabbbbbdaadeeebdbababedcabecbbbadbecbbecbacececaeaccbbcbadecaaecdecddccabecbabcbebebcbebeacbcaddadabaaedadedeaebdbaaeeaabdaeaebdaccbbbadababcecbaaaecdbccabebbeadcdabdcdaaddcadbcbdbebceddaaabbaceaeacaceadaaedbcdeddbdbdadceebececbaccadcccacbbacceabcbbbcdbbbbbdeebddbacdbdedeccdacadaebdcadeeaabbbbbbcccbbddaeeaadececbcedabacaabbaccceeadeedceaacdaebebaeaebbaabbcaaedcdeecebedadbaddedeedabceeadadebdcacabcdbeedeecdcebeedbdaabceedacbcbbcedbdabbcbacabaedeebabaecdebeedeeeeccacbabdbadcaeadcaecbeaccacbdedebabdcddbbcdaaacbbacabaaebeacaddaeeabbdaacdabebdcdaababaccbaccdabdbcccbcaebcdbedceaabbccdbecaddeeebeabbcabbecdbbcbcbbaabcadeecdcdddceaaaaceaaaddddebddbcdbcadeaadceedcabbeebeaebeaddcbdbcbbaaeecbcaaebadcccddbecdaeedadecccedcbaecbdcebaacbebaaeaadeacebeaedcecbeedabdbccddeacadbeeabbbecbedadbceedeaedccddecaecbebbbbdcebadbdecbaddcecddbccbbeacbcdeaedabccedbeddaabecbcaebeacedbabbbedbccecdbbbaeacdeabbdaadacaeebdaaecaeeedbbeeccdddbdbcaaadbdcedaaedadeddbaaeddabdbbbebddebbcddcdaedddebdcdabbdcbaaedaecdddddabbcdbacadadcbabcbbcecabeaccdceedcaebadeeccbbccbbcbaebcdebcadbeedcbbcdbadeceadbeccbbcadcbeaebdddeecaeeedcedcddbdcdeadcacdeaaeacacaeaccedacbeeebaddcaddbabcbeadeeeabdebcedccccdbedcabadcbcbeeeacebbdebddccdccecddeaadabcdbebebbeabedeabecadaaeaebcacadeecabdaadeccbabcecbdabeececebcaeedbabbbddcaaeaeddaeacebdcedeabaecedccbcacaebedeebbbdaaebbbbdeabaccaedadcbbcabdbabbeaacedaebcacdebbdeedcebbbdeeeccdadedaceddbdaecaceaaadcbabaaacdbaddcbbccaeaeddecdecdaeeadbdedabdeaddacebcdeacdaebecbbaaecabbcaabcccbabcabcacaecdbaeecddabeeedebabbdecdecddabbbcadeaacdccdedadeaebacedbabcadcdecdecacaaabdabdbdabdeeabbcdcdaaebacdcaadaccacaeabdecdcbcbbebdcbacbbacbeaebceeedcdacebbcadbdabecdadeaccaaecdbbcacdbcedbdaebbddcddddadabddddecedaeddecabcccedbbbabdcedbabedbdddaeaaeebdaeabddbcdbeacececeebacdbecbaacbeedabccacdbeabdecaeaaeeddaeaaedcdbbddedcdddaaebcebddacdbeeebaecebbcdeeecbeaacaabcddcacbabebbdcdbbbbaebbabebdbcbeaaeabecdccebbbbeeaddedecbbaeacabcadddabeaddacdaadedaeaeedeacbeaababaacdeaaaedbcdaebaadecdbdceadbadcdeecbdcebacebdbeedaeecdbecdebdbeaaeecbcebaacabebeebbcabeaadbbcecaddbbecaceddeaeeababaeadccececdcbaadabdebdccadbedceccbdddeaaceeddbecabedbddcccbccbeeebcdbdbaccacbeacbbcebcbcbcbeeacbabbcecaddceacacebdbcebcbbccbdaaecaedbadabdecedadebddedcdeddccbdbccdeaeeadccbbccdaecadabeecddceeeaaeadbbbdbcbdbaeebbeaeecebeadabbcccbaaeabeadeaeaeaebccbcdaecabadbdeabeddcbaaecdcbbeebdcceadecbcebeedebecaedaebecabdabbbabdeabbebcbebdeaaecdceacadcccdaeebbdcebeadcebdccccdeaeecbaccadccaebadaecdcabeaddaebadbecdbeaccbadecadadeebddbadbeabeeaaeeadbddbebddcdcdcedbdeddeccbadbbdeccedcabecacabdebdacbdbabdbdcabecdddeccdebccddccdeebeaebaadcebbecdebcaacabdeaaeddeedbdebdbbbeeccdebcbedbdccbdbbcbacdbeddcccdedbbbecabdddabdbeeacccbbdddeeeccebcdacdabadebbcaabeaedccdebacbecdedebeaaaecbcabdadddeecdebddaebcdbacbadcdcddcdedccbbaaccccebbbecbddadaaabaadcdeaaaebabebcabcceacbddacbbabbceeeebaecedbedcedeccbadbbeaaddbadbecdcabdaccbecbadeababccacdbbaaddaaadbeaabcdecbbebecbccdcedadbdaccbcceadacdceabccdcdeaebeadcbbeaaedcabedaabeadebabccebdaaedebacdbaecbdedadebcceeddebddddabacdbacbdabdcbabdeaebdeadcbeaebacbaddddcddeaccdaaabeabdababaaeeddbcbbeecdeaadcedadebbbcaaaeedaebcbaebaedcaccdbcbcacaceeacddddcebdbedaacbddceadedcebeadcbeeababaebebdddcbebdbdacbabaccaadebbbeccbdbccdceaeebccbeaaadbdbcadddabaeeceeeebedccaaceadabbbabadeecbceeaeaabadadeedceeecebecdabddbeeebcbbebedbdbcdaeccdcacabcdabecaaccbceebbdaddedeaaddacbcdeabddabaddadbcdbacdccccebbbbccbedbcddaaaeadacededaabdaadbddeeddeecaceecccbcecebebbdddddadeaceddbceaddcbeceedeadaccbdddbecdcaccaecbecbceddeabbceadedaabedaccbbbbbeaeaeddeaeceabeaecdeadacedceaeaedeaeccbdbcdeacacccdeccceccaaacadeadcaceaaacccbaedccccdacdccacabceddccbebabbbbeabbaadedacdbbdbeecccbdeddaedeacaabdcadbadabcbabacbbdbdbadeaddaebacccdcbbbedacabdedbcdebcaecabaadeecebcecdcbcdbcdaaaddbceaaecdecbbeceacbcebcdbbddeebdeeeabddecbcacececaaaeadcacebbbbdeaebdceddbdbaddbeadeaaecddcaabdcbeeccdddeebdbdcedcccbedaabbeceabccbdddbcbdaeebeacdccddcbcddaddcbbcedceddacdbceaadcccaceccebceccddbadacaaeaacccbabaccaeeeadeadecaebecbdbeddddcabbaeeecdbdeccdcebcbcecdcdbaeabcaceadecdacabebcbbebbbaaeeceeabbbabcdaebaeaecdcbdebaedbbadbdaddcdbadbebdbeabcdbadaeedceebbdadbacdadbebbaedbecdabbdceaeedcebedabdcaebcbbedeccdaaabaadcadcbddbbbbbdbcaddbebaeecbdadeccacbbaebddaedddaadbbdddbccccbaaedbdcadcdeeaeeeadcbdbdbcbacedaabacbcccdbeadecabeccdaacccbebaeabdabeeaccbbabcbdbedceceebaeeabdaedaacadcdabacebaecceecbbcbeeeccccaccdcbaceaccdecdcacdaeeccbdbcadbcbbdeccdeeedbceabddeebbddbbbdddadbeaabcabbdddebcdadcbeadedacecbeaabdabdbadadcddecedebbcaaedcbcbbabceaccaeacaccbcbebbecebaaeaabcaebabceadbbeaedabedcdeedebeacbbaaaecdadebecbedaecbeaeebeccbcebadbbbcdcebdccebccddacbeacdcdceaeadedbbdeddecabaddbbadbcddeecebcabddeaaecbbedcdaeaeeadaeedbbecdccdcabbddebcdcdcbcbbaceaaeeedddbcbdcecdbbabbabeedebaababbcbbbbdbdcebdbeccaaacbbbddddbbabaeeacacdaebbbbeeeaabcdeddcbcbccecbaddebcdceccedddddeaabceeeadddaabcacdebbaddcadebadaacbacadccacbeddabdadccbaaecdbadbaeeabebacdeacecbcccbcaaddedeeacedabbbddedaacecedaccdaebeddedcddbebaaaeccecbbccceceacdbaccecdadbbacccccaaccccdddccccecdadacdecceddcdeabcdebaaecdcdebedcdbcabdecdcccdebbccdaaeabedabeeaddcdcccbcebeeecdcbaaedccaaeaeceedbbcaebbdeaedceddeacabadeacabceeecacdbbdceabdecbbacbdecacceccaeccceecacddbabadddbadddacccebbeaecbadabdaaddedbedbadbececbdcadcdeeabeddbddebbedcbcbccdbecbeccccdbdaaccbdebdcbceebeccdebeeeedbdcaababcecaecbcabadaacbceccbabecadcbbbccecaadabedebcabbaccecaecaeadabdcecaaabeabdeadcedccecceabebaecbaccdddcdbceacaaaadeccabaaaebebebbaabcedcbabdedddcbcbddcdebbbbdebbbbceacbebddaecaddabbdceaadbecdadbabddeaaeaebbdccaddddcedcbdbdedccdaeaaebaeaeaccabedacdbabcbddecacdbdbeacbebcadabbabbeeebbdccdaddceedbdbddcbaeedbabdbeebdaadcedddbbddaebcebbabbceedacccedaeccaeabbceeaadcdebaeecbbccccaabccbabbeccaebececedaecdbdccdaabeaabecbabecceacdacdcbecbabcdcdcebdcedbaacaecaeaeecccecdccdbaacbebadcdccddcbbaedaddcddedbccacdaccccabdbbcbaadabeaaebcccbbacdcddcccdcceedaecbaaabdbcccdbbcbeeaabaceadbaecedcbdcebccaaadbbddbbabacedeaddbcadbcaadaadbebbbbbdaaaedbebecebeceaeecaedcacbbbdacdaebcbcdacadeaceccdecceabcbcdacceaacebacdbdeedadeaeabdededabdbbceaccabddcadebaaccedaeaeecdaacacddeababbdabbceaacbbeeeedebbdebceedcdddedbdeaaddbaadccdbcaebbacdadbcebbcebcdcacbedbdadabadeeeddbaaeabbcbbbabcadbcbebdeaeddaeeeadadbbcdeadaaebdbdbaabbceccdbedcebbedbecaccebabbdbddccdadcabceecddaceeebecbaebddeebbabbcababccdabadbaeabcccaaabbbbaebedcaeadbecccacdcececbcaeaadadaadbedcaabaceaeeccebadecebeebbaecddedcdbdebbecebddedabbedadceebbeeaedbdeeeacaeecbcddbddabddddbcddcddacedacccebedaacdbacbecaabcabeceeadaacdabbddbdbccebacbeabdaebbeaedeebaeddbbaaaccbcadadaddcbdabaeeedceebebdaaaecceacbbedeaeeadaaaadeeeaeaaaecbebdcbcbacaebbaebacccbcdeaabeaeaadaacecaddcbceaeadcdacccdacacddcbabbebabccacdbdcbaecdbbcddeedbaddadbdebcddbdddbbcdbcbdabaaabdcccccacebceaeebbbcdadeecbbebdceaabebdedbeecdbdecdcdabcabaddcedaadedabcaadaeeacedcdbecdebbedddbaeabbddeebbdbcbdebdcacbeebeedcbcbeaceceebbdccdcdeacbdebcceedeeddabadecadddcbbdbaedbadcdecdadadbcecdbdaadaccbeaeddaceebecbbcebbbbbecbcdbbddbcbbdceaadabeececdbcbababdaacabcacdbcaabaeaaabceedededaaebdacdadbaddedbdeddacbeeaedbeeeaeebddcdcabacebbcecebabaecdbbbcabaceebbeaedcdddaccdabdeaecbbacdcdbcbbdabaabbacbbebbdcddacbddebacbbbedcadbeebeedeaeeaddcaaccdbbccacadbbeebbacebadbbddedbdbdbdccbbbbabcdccbaabbbbcbcbceebadedbeceecaddaecbcddcbaedddbaeadedebaceecaedadcadbeddbaaedaabbdbeaeeaaadcacddadedbcdbddcaeebebbbbbbcdaccdccceccaceabdcedcdbacbbacbaaadbddcbbdcaaedecbeebbdceecbacbdbcbeacaeebcaecbaadbeabcedcabbaebdddaaedacebcedddedeaeddabcabcbddbebbeebbbeedaacdcacebdadbccaaecbcabebdabadabadebdeabaddaecacdbeebeabcbddcbcbaddaabddcbaccceceacdbaedadbcdbeedbbabbeacedecdbddbbadbadabdaadbbdebaebbdcddbadcebaecabbbaecadcccdcbdcbbacadacbacdaaeebdcddddddbbddbadcaebeaeaaadcbdbcdcbccbbcddcdbcadbbdaaeaeebeaeeadadcdaecceecbceaeebaedbbcccdbdbbdaacccabdcaacccbceaabaedeeeebcaeedcacbdaddbcedacaebabcecbabeaeaeebbccdbdaddccabbcaeeceaaebacceadbdcbbabaaadceaeccebdebbacedbdbdbaebdcdebcebcedaacadddccdeaccbdadbaedceeeaaebabdcdeeeccceabddedadddacbdedaebdadbcdbeaaddacadecbedeabaabbaceceabccdcbcadadaedbececbcbacbccedadeabdaabbeeeabccdeaaacbccdceeedbedbecdeeebeeaaabceeccaadddaeaebeadebdbbedebdbdbedcceeeaaabebbaccbadaabbbceeebeeaadadeaaedbcabecebdbcebebbaacaabdabdcacbecdbcdcbeeeacbbdeabeaccaedbcbceaadaceedcdeccbcebacdaaaabeeabdddcdeacaeedebbceabcabbbeeebedddebacdedbdcddbedebddadcbabcebdecbbacedacbeabaccceabbbeebaddcbcabdebeeecdeeeedaabebeeeecaabebcbdcabdcabcdcebacbbcbceedacbaacdbdaacebaaedeebaaeeaaaabeeddecadaabeabdeceddeeabbecbadeedcdaddcaeedaacdbdebccbaacceeaaddadbeedabcedcededdddcdccbcbbbdaddcbceadbdedbabedbdbaceeccacaadbaceaeaceccdeededbdbadcbccccbbcdcdccaaaeebaeecceaddcedecdaadbecdeeedadcebbcecabaabdaedbdbdbdeeddabceabbbdccbaecbbebdbbdcdcbbecebebabaeaecedabebecaebcbeaaaaeecedcebbadacaaabbbadddadccbebbccaaaebcadceceacdeeecdceeeaddaebcbdccaabdbecdbaeacbcebcadccecaebbbebaedceaebcbcbbaaaaaeacaeeaaadcbdaedcdcbbebacaccbebcbaaebbacceebacbbbcedbdecaecddcbecaaebbeabcecccedeebdbcdadbbedecebcddcdcdcacaddcbeaeecadeecdaccdcacaecbbabbbedccbdeeaaadbdeadedccaabceedcabadeccbdbdbcdaeaccbcceceadbeeadcdeaeeeebcdcbcabaeadeaecacbbdbedadbaaeaddaecccceeaaeeccadeadaccadbdbacaaacbddeccddeaeddbcbaeebadaeabccdbcedbabaaeabdbeeaebdaebaebcaedbbdeabdaabcedccddaeadbdaaccabebbedeceebaccadaadaababbcbbabdcebebbaecabeadcbacacddebcedcbcebcbbbdbbaeabbeecabeadceebbbeddbbdcccdabdbceeceadbcbdddccbceeeadbabcbecedbcddbaabdacecaebdccdcaaceedbabedeeebdddacecbbbdbaedbbcdaeccbbcdabdbecabdcadccacbbeaceadceabccbdaebbdecbddabdeaeaeaccacdedbeebcbedecdbcbbeddbaacaacdbbebaedbccdcaaeeececaaacebdaddeeebbddcebccebccecbdaeddddabaaadbedabebdaaebabbccbcdeedaebeedaaaeddabcacccdabeebacabbcccaebbbaebddebdadacebdcdeebdeddabbdeeceacbebbdebbebcaedcbdddecabcccbecddeaabeceaadbbdccedddbeeeceeceadaccddedecbbdacbcccbbcbaebbacbacabaaaaeeaccedaecddcaebdebacbbededaaebebbbacdaedeaadedccabdeacbdacacebbeacdcbaecabbddbebaaaeebaacdbadaaeccebbdeeecedbcddcdceebabbbeeeececbaaaaddceaeacbbdacdccbecbecdddacdbcaaebacbabccbdbcbcbaccecbaeccacbbceabddaadbaaecdccbdbbeeacabccecdeaaababcbbbbbcddddcccdacadabdbaeacaddebcdedacaceebaedddaedecbbbceaabdeecaacbaaecabcadaccedaabddecccbddccabeeeccbaceceeabbbbbeeceeebdabcecbbcbaaaeabcebaebcdabaabdcedaccdcbccbccbdadcdaeeaadddababdcdcecceecadaecabacbeaceddebacbdebeadadaccdddcadeccdcaedccaaedcabaebcbccaecdaaaceccedbddcabacedbbebdebeadebcbabebaebeeeeccaaecdccaaebbeeaabdbaaeececbcddeaccdccecaecbabdbdcacccbccdbeeabadbdbbdacdcbdcdbcccbaaecababbbaecddacbdcedeaddddbbcaedeeecedecdbecbaacddebbddbdebebadccdedcdcaceedbdadccbbebcccceeeecbeeaeeccbeccbdcecdcdcbeabbbeddedbadcabebbebdabdecebdeabaacadebedbeaacccbebbcdcccbedababaebaedebdaddcddbabebebccceeecdadaacaeceeaccbbcbddbddaeddadabacbdddbbdeeecccbacdcbadeadacaeccccbbeccdadeceeccccbadbaebbcaedaedcadaabbeacaaeebbcdabaabecbabdbaadaaeebeadbebbebacceedcadbedeaaacbdcebbdeddccbbdbabaeaebcedeedecbacacbbababeacdecbbcaacacabbbeeacddacebeddceddaaccddebeeedccaaecbcdaadddbebcbaabaebcdecdabcecbecedaacccbeabaebabdcccaaeaccaeddecedcebcdacabcedbbdaeadedcedbcbceebbabcbeddeedcadbeaecbbdcdbaaaacdeabeedbddebdecbecbbcdaaadbbaedbeaaedabcbaeabcecabacaebabedaecbcbebbadccdcaeaeebebcbdecddbceeaceddcecdacbdaceeddaacdebdbbddceabdcdeaacdabacadeacbaaeadccdecdbbcbdadaedbacebeaadbcbbcbadaeacebbcabeaecbdbdbdecaebcebebdcbcabebeedebddbcebdcbbbacddcbbccbdecedeeeacabeebcccbbaecedabcbaddbbcbcdcceeacdaecceecdbbbecdadabaaeecdbcbadbbcaadabccdbabeddccbaaddbedcebbcacabddacedddddeaaeedcdbaebeedbccedaaabeedccabcacabddeceaaedaebbcebeeaeedbdcebbadbdbaaebdedbcceedbbceaedebeeccedbbacbbdbbbeeabcdebdbdacbdedbababcbbccbdbceadedcacaadeeeaadeacbdaddeebdedbddcdecabbbdeedcabdcdcebecacacdaddaaededcecdacbedbeeaddceddcacdbcadeeeadeaadadebcadeabaebbaacdadaaeadbccedbaababcbdedbdcccbbacaeebeaacdadebdecbaadaaaebddbecddaabbcdcebabdeddbeadedcadbedaceeadbeabceeccccdabacaeeeaeaebbbbbbccecabeaddaccdcccbacbbbdcbdedbedecbbdaddbbaceebccceaceaecbddcedcedbacadbbbabdcdcadacecbcedcededbbcdbbdbbecddabcadecbaeddadbdeaadcbaacadbdbbbbeeaedbbcecbecaeebababeaabbebbccebaaacbbedabaaadddadccdbceecdabacccaabeebeddaddceecbcbaceaabdabeeebdebbcbcaaceccdecbeccbbebecaebbddbaeeaecbcebedadbedddeadbabecdbbbddaeeacdebbdbdceebdcbaddbdbcdebcaecbbdddecbcebcacbeaebcdbdbcadcbcccbedecabcbacccaddeeebbaabaccedbdbdcecbeacabcbbabcadbececbedadcdceccdbcabbddaecbeceacaaaeecebbccbcdeaadebcbaaaaeceeacaeacaceddbabeabcbababdaacedbbebbeecbdbccdabeadecaccdedccdcdaeabccaeedacaadbabcaceabcebebbbadddabbbeaedadebbddccaaedcdddbaaeebceadebdabdaacddaabbbdccddcadbdbdeedcbcbdbadaebdecebbdbbeddcdaedcbbcddbaacddccceecddcbdabcbaecbdeaecddaeeacbaadeeeabcadebabbdbaebabdecbeaceecdabcaebabdbdcaceaebdbaadeeccaecabccadcbbbbeaaeadacbeebbeeacdadbbdbaaaddbdaebcdbbcecaeadbeaeaaaedbdabbdcaddaddcbbbcadbdcacdbdedcadabacecaccadecbcceecaadbcbdcaedbaedededebdcbadcdbeabbceebabdcccadbbcecaebdeabbeaaccaddcccbceedecdceaabdedadaadaadaeadacbceedcdeaecceedcbaeeccbdedaeedeaecdbbaddacbeeadddebedabdadedaeedcbceececcecbcccdcbcdcecacbacccadeaedddedabcaedaccaabeedacbdabbbbbdbeeeaadecaebaacedeceaecadbdceecbedacbaadaebecacbceebddaaabeadeecbbdbdcceaabadcaceeabdceadbedebaaaaeebcaacadcdbcabbaabccceeebcdcaaeeeccdddaecceddecaabeaacdeebaeccaeabadbdecabeacacecbbdedbabeeaddbdddeddaaabbcccbacbeebbbbcbceeadbbeebbeeabbcacccdcdeadeacadbecabdeabeeddbaaeebcdbedeaebbdebddeddddbebaadeabbcbdcdcddecbbddddbaceadcdecbdcadcaecabeaaaaaeabbbaeabcbaddcaccdacebeeaccbbbedecdecbeccebcbbddacaedaebaeaccddaedeecacadcbbdbdaaaebabedccddbaaeaccdbccebaeedccabcbebcdccaecccabcccbeeeececbdeccaabdaacecacaccbeadccdaddcaaababbacbcdaaeadecbbabadadcddbececbebdedbeecddaebcbadebcbbdcdacadddaeeeadaeceaebabdbadaadbceaecedbbeaacbcbbdabedbdacaccadbdbdbbbdaeabbebdaeaccedaaecceccebdbabdaaaacdcdabebcabddcdeccbecdebceebcabbbeeddabdddeedcaeeadaabbccedbcddbeabbdbbbcbaccadeddceeeabebdaabddeeceecaccdcaebdbdaadeaceaedebebdacbdbdcecebddedaecbbbcadaabacecceebacaaaebcdbbbaaccdabadabbcecbbbecbaacedaacadeacebeedcdabdeccaeedcebbabaabedaaebdeebebbccdacaebadacecedabadbbbdeccebceececcdddadcbabaddeeccdaccdccabebbaccadadebcacadccbabdaddecddbcdbbaaeeedbaabacecbdaebeeaecabbebbedeaaaacbdccaaaaeeddeecabecbbbbcedcbbeeceaaeaacbeeccdabdacccceddbbbeccbcadeaccddeaaebcbebdbdcbeabbbabeadcdcabeabbdaaadacbacdcadedcceeabdedbcaeaedaaebedbccaeaaeccbbcdacdcaaadabcdcccbddcbeccdcacaccaacbdebaccaabeeedacedeceaaedeeeddceeeddddcaadcadaaedecbbaccdaedabdadeacbbbebcadbacbccdeaedbbcdceccbeebbdacebacdbcabaaaeebcdcecdebbecddcadebedccdcaeaebdcaaaabaaaeeaabaecabbbdceedacddcdaedabddbdbadbdcbebceabadbeaecbedebbedcceddaeeddacdadcbdeebedadaababebbabecdbedabbdaacdeeadacaaeeeadbedceeccdcabbeebdeeabaadbaeedebbcddddcadbbbaaeaebebeecebabbccaaddcbbdbddaeaadcaaeababaccbabccddcecbacdcedcadceecadcaccabbcabcacbdcaaddececdabdddaccdeceddcbecadecdeaaecaacbbcbaedececaabcbbabeddbeebadceccbceaaeaecddbccebdeaadbeaeeeeaacabdaebadbdabbbebdeaeaccbcdacaebdbcadcbeaadedebcebdbbbaadedebbabdbdbbdaebdeeeccdbcbdceeacceceececaadbebaabcaaedbecdaccddedbedaebbcddbeecaebcddaaceadabcebbccabcacebaecebabaaceeccebbcdbcdccacabcbbdaedbbbeeccdabdaacbbaaeeecacbbceceaceddcaacebbdbedeacaccbdeeeccbbceeeacdbbdedbbcbaecdecedbcceadebabdbaecdbaaaeaadeabebddcaaaadddbdcbacbbdcdaecbbeeddabddcceabdabcbaacbabeebcaacbebcaccbedeacbacacdbbadbaeadccddbccaeabbacaddabcbcceaddabcdddecedceecaabddaaccababbededcacadebacbddcebdbcbaeaeddcedacabebdcbbdeccecdbbaeaaaeecaedecdcedacbeaabeebebeeecaabbdcdddbecdedcacdbaebbebecddbdabcaebedaacbdcdeeacbebbcebddcadebdadccbceecbeddcdbaedaecdeebeaeeadbaceadabcbaeecddcedcaabddedddcaadbbbbeadbadcdceabceadacbecdeaeddbabadabadccbaebadbccabdbaebbbaecdeecbaeddeeadccdaedabbeccaedebbcbebbbbadaaedbdcdbcbbcaddaaeededabdbdceaceadbaaeaccccbbecbacedeecbecdbbceeceecdbbebbaddbbeacbbcceeedecbdcccbcdbdbaeacddbeddcbeaaecdcebbcabcabeccbacaeabecbeeeadcdcecadcacaadedebacebecaceaebcdbbebdbcbcdbcdaeeeadbcbecddceeacdbeebacbbbcbadbeacddbbccdaddbaabcddaeaaccaacbaaeddbacbccacadbeccddbecbaaeedadccbbacceebcbcebecdccddccccebcbdacbbdabdcbbcbdebdcdbbcaacebddcaddddbbcbdcbaaadeaedbcadacaedcbdbbacceabdadecbcbbebebadcedcaeeeadaeeecadbccabbabddeeaeabaebceadbdbccaaecdedaeaeceaeedbadddcdaadecbbcbabeddabadeabbacdbcdaecaaceabbdcacaeacabacdaeadbdccadbbabbcecacaeeaedadddecbebbededbeccdcbbaadadebceccaeaedbbdcabeeebaccaeabdaceadeedeedcedddbbaccccdcdcaadebdabcecabcacaeadbedacaddeebbebccabbcbddedecdaeedadbeeddebabcdacaaeabbdcbaceccbecbbdbdbaceaeacdbdcbacedddddbeccbdaebcdebadaabccbaaaaaadccdecbeccdcdadedccaddcdcdbaebecdeabaebedccedbadccbcebaaeacccaebebdaeaeeecbdbdcdcaaeddeededaccccbdcceeddabaeebdbddabbbbbadccceddeddddaceecaaeceaacddaaceebbebcbbcdececdaabbcedeeeddbdabbbccddedbaaadcdeccaabecaebbddebeddcbcacbccbbeadcbddebdcddeeabaeaccaaeedbbeaaaeabbccaccebbaebcbaeedeedaddeaeddbddccababbeacabeeaeebbdddbbaebecbdedbcabbcedcbbbedaaeddadddaeccacceeeededbaecbcdeecbdaeeddaddecddadcaabacedcdacbedabadddaebcdedeaecbeaaaeccebeeacdceabccbbeaaabaadcceabcaecdcabbecbbcbbeedbadcbdaaaadaaccaabacabbbbcedeeeeecbcaddbdcbbcebbcaadccecaceceaabdadaadcbacdbbdaadedacadcbacdbbadebddabdbaabbbaaacbdcadbcddabbebbbcbeadcaebaeeabddaecdceecededdacdebcbbabbdadadadbaeadacbcccdacbaccebadcecdedaeaeabdcaaedaaeecacacaceceeebbbbbdcdebdeaecabbceacecceaeaecacdcbcbbebedbeaeabdccbdceaabedbaeebdbeaadabadaeadcaddaeedaceccdcaadcbdacadbbbdbdaaadbedbeadaebeacacdbeabacacacdeaddeddaeecbcedebdcaebcdbcdeabdbceaebdedcaebacdbcdeddbbaddcbaeabaddeeababdeaacbdcbcbecbbaebadcaceaeeceabbbadabceacaabcbcabbcddeaadaadeedcbdbdccdddcdebbabeccdbddeeaadcacecdbcecbabbceaaceecdcebaccdaeeedacdaeddeeeaaaeebdcedacdebdeaccddececcccdecdccbbdbbdeebcedeebcdddceacabceedaaddbcdcdcbbcdbbcdcbbebdbacddaecbccdbbbabacdccdacebcdbdcabdeacdbdedeabcbdbebbadedcacceddccddbbbdabddebecabdbededaadedadcbebaeaeedcabbbaddbbebbedbeacaaeecdeeaaedeabecadbaaddebeeabdedbebeceeeaacbcebebbeaabdececaedaadacadaeaccceacedcdbcbcbaccbdcddcecadeceaecabbabbadadddabdaadacaacdaccaaaaebecddeabceeebeaabdabdeebdbabbcdeabadbacacacdadbdedaadbcdabecabdabdedebbbeceadcdebcedbddcebdaccbccebabdbdaeddeaeadaccabcdeccbedbeaeabaeddecaaeeacebbbacbadeeecebdbababcebeddbbccccebccabdedaccbcdccabbeeebecbbedecacadceacaeaeeaacedadadaadacbbaadcadabedebadacdeceebbdeddcaeeecdbbcddbbeacaabdaaababeaeebcabbebbaeccdadeccebdccabdebbadddbbbbbedaaabbcdcdcdabeecedcacdedaaacbeaebaececdedeceacaebdeadecccaccadecbdeabbebcdbcdacbcabbcadbdbdeeaacdddbccdddceddebaddacaddacaabaaadaeabdabcabcedbeddedbbeecaddacdeedeababadcbcacadebddeebbcbadbeeedecdababbcebdaeacbabeccbcbeebceeacccedacaaaeedbeedaaceeeacbdbeddbdabacddeaebceddaeccedebddbeaaadbeebacadcabdadaacbeecceccabeebecccaaaeadbcaebccbedbcbbeaccababaaeddcbaccddddcebaeedcecbacbdaeecdbdccbbcbeaaaecccbecaeedbbcdddcdaaddddedebadecedeacdbcacacacbeccdeecbbaaeeeaeccccdceeedcecbabcdadedcbdbbccbcabbcbaeaaedecbdabaedcbbadecaaeddcaacdbdacacbcdebcbdaaabecdeaeedbeedaadbccdaacadaacdeaeddbbadebaabbeadbcbbaacecbeabcebdcaaccbbaecadeabdaaececebdeaebadcdddeddeccbaaccddadddebeadeeeeacaddeabdccbbadbccecccededaeedaccebbbbedeadbdecbbaebbdbddebacaeacbdccebcbdaabdccacadaeeebdbeccadcebabcceaaeceacdbddbecaddcdaebdabedcaadeeebdbaeceaebaadccbbdadeccbddbeadecdacbbbedecdcedceadbdecdeccecdebcbcbaebbeddcaedadcaebdaabeedbcdaaecddcbbeccadbbacbdaccdadadddecdaaeacddcaaaecccdceecdaeedecbbcdbaabbcaebccdecddebedeecdabbcbebacadaccadcceddadcaddceedbebaaaaadebadeaadbcddebedbabcdebdceaaabbabddcaaacbddaecdadaaecbacbcbaebbadbeabbcaebeeddaadabecabdedaaddbdccebdacacdbdaadabebbabeabaabacdaeeeccaebcbaededbcabaaeabceaabecadaabbcabbbabeabaadeddecabcdbcbebbebcbcecbcdddebbedadebcdbcadccadebabcddaaabaaceedaedbbeaccaddaaccddeadbbbacaddbaebedccdbeededacaebadccbaadbeddcbacbacaeecaacaeaacdeeacdebbccddeeeebdabcdcebbaaadeddecbdabcccbcbeedcdcdbbeecdcdecabeaebdcdcedbabbeecacaebcabbcabcccbcecabbeecbdedbadaaeecacabaabbedacadaaaaaaccccaebcecbddaaaedbeeadeaaceceaabeabbcddddeadabbababcedcbcedcedceecddccddbaaebabbdadaddaecdabaeccabbbbadcedebddbdcaaebdebcceeabeadbcccbededeaaedddaeeeaebabddcaadebabcaeabedbbbeebbdebddaadbacacecebbececcdacbaeadecbadecdbdedabcaecbceeadeadbecdaebdedcebcabedadcdbcaacabcebebdacbbacccdbcdcecdedeecdacaccddadedebcdbaeebadebbcbabeaaebcdebaeaddeeadbdccbbbbcbccaeebbedceccbebcaacbeaebeaadeaeecccbabeedbebcecaeeedcebcccbdaaaadeceaabedbadbbbecdeaeeeedeeacabbcdcebebdbcdddacbddcacaddabcbbaccebadabebbacbedcdeabaddceaacccbcedcbbacdddbbecbbacdeceabbddcbdedacdabbdcdcbbcbacccdabcabdaddbcbbaddeebcdbbdcaddcbdaeaaebdcedaddaebdddbcebadccaacaaababbcaccecdeabccceaaecbdeaeaadbacecaacadbbddeadbcadacacdbdcedecbbeeaedbebacaadbceebceaaecceeceebcdacbccebaebcbbccbbcddaecabedcaeeadaddebdadebabaeadbabcdcdacbcbaadecccabbdeeadeacccacebdeadbbccbacbbaeeaaebeaeecbabcdceebbebadcebbbeeabcabaddaceeebcceeedaadbaaaaedaabaadcaaebbdcbccccadbdbaeebdbccabdcdaaccebdeebbeedaccbdcbccccaabbcaaecebdddaebbecaecddaeaeeacacaebbcaadeeadecccdcddecbebadecadbbedcbceebdbcbbceadcdcbdadcaecabbeeccededddebbbeebdcaadbcaaaaadacecaccbaddadedbdcadaebdbdacbcdcbcaeeabbeddedbeddeddadaccacdbacabbaeaebbeaceaeaedacaddbccaeeedeabaaecedadecebaddeedaeadabebdddbeacebdebdcdbaaebbdedaaaddeebbcbeaceeabbcaeeabacabadbeaadbabdccaebbccbcbdbcecebbbaacedbaaebeaccbdeebadbbddccbebceddbeedacdceeadceebaaadaaebddbdbbceebdbdcbcecedbbbcbeeddcbddddaecaaacceccccbcdadcdadceaeaedcceecacbdbdcdaceadecddabeccbcaddacacddbaaeedbdaccebaaacccabebccdedbdbcdebbecaacbcecccdcccdaabddeeadedbbdcaacbdbcaddabcedcbdcaabbccedcaecbdeabbbbeeeeaebcceacccdcddaedbdbcbdacecacecacccaccbbcedeaeaaaccedbeadbeeddddbcbbcabeebbedbebbdacdbebddecabaaddceaeaaabeaedcdbcaebcaedeadeacbededdecceccbbaaddddbebcbbcabebaccbdacbaaadecadaebabbdecaabecebbecaeabbadababdcadcbebbcabceadbdcbaddceaceeabcaaeaddbdacaebeabccbbebeeebababdaceeeadbeadeacaceedbaebedeaeceabededcbcddaccdadbbcabebdcddbecddaedeaacacecadedbbbbeacbbdaecadabdbcdaabccedceadedaaddbbdbdeaddaadeebcbbbcdecccdeeecaaeaabbaeabeaecaeeacbcaebcbdbcdbeadacaabdddeaeedecdeadecbaaeadceabebeeedeedbcedbbeecaededcccdedbabdaebecbbebcebdbdbcebacaecdecbeedbcdecedacbedbcdaceaabbdebbabbcdcbededcbccccdecbdaebdcddececadabdaeeadcedbccabceadeacbaadeecbadabaabbbbdbbccacccebbbccdddbcaeacbebaabbedbeebbbbceaceedabbacbdbddbcbbaabcaccceedaddebdbbedccaddadebecddeecbadaeeeaccbeabceeabacbbbdbabbceeeeacdecdccddebdbeaebccaaaebbbccbceddecdcbccabedaedebcabcabbaabcccdadceecbdcbcccbecdadccbbcccbedbaddecbaadbacebceaebcdaabbbdddaebbebdccdccbbddbcaebcebaecddeceeceadabbcaecedebdacbceaddecaeaccacadebabcaeebeeadacadcebdebaeeeddddceaecdbaebcbabbcbbcdcadddcbbbdedecccacacdacceaeaeccedccaedcaacdbdadcddeaabaececcbaeecdbeaaadcccdeadbbdceecebbceaadbcdcdedccdddddedbbbedaddbbbdebadedadbcddaebecdebecccadcdaeaccbaceadaabdeddadccbdaaeddeeabdbedbaebdbceacaebbdaadaccaeaeecededbdaeeaedbeeebddbddadccbccceddadaabbdadebceeeacebaabcacdcdeaaeaecceadaeddaccdcbecbbacbbacacabbcbeeeceaaecacecdbaabeddeeddeababededdeeaeeeaebedcaececaabbddbeccbecdeaccddcebaaacededdbceaaaeccbeacacaecbaababeabcbbaeaedbbaaaabcadbeccecdceeeacccedececdcbbeecedaaeabcceedcdbeddcebcedcceeddceeddaeebcecbabedabddbdbbbbcdedecbcdbcdecbcbbeabecccddadacabadbdbeaadaeaeebbaacadcaacacaacdeeabcabaaedcacceaebeedceaaeeeeeebdbbdcaebdebdebcabaeaeebecadeaaaecadcaccbbeeabbdcdadccbecddebeeedeeacaedbaccddeecbdecadbbacbecaaccabbdaaedabeccdcceeadccacdabdeadbcccbcabbcaedcedacecbcaeaedbebcaecdeaddebadebabcebabaaebdabbeecaadeeddabdbcbaeccedacbbdbbccadeaeabbdbeabdabbcacdbeebeceabddceddaacbcbbceaaedabbaacaebbcbceaaecbadabcbbcebeebeebbebadbbdcccbaeacddeebeaeaeaacaaddeaaaaecddaadabbdaebbcedbbccbddcedcdedabcacddcbeeadcbcdadeaeaacdcdaaabdcebeeeecdbcbaccddcabbcbebdedeceebdadcbbacecdcccaaedcacbcceaeabcddecbdeaccbdceadecbabbadaabeeebebadabdeaaccbeacbeaabebcbeaeccecadaedacdddcbdcccecebacccceecceadcbcabcaebddbedbaaeacdecdecceaeeadcbaabcaebababdadceeaacabadeeccaddbbdddeebdcbbaabbbeadbdeceaacecddcddccdcbebddaabbdbabbbdabeaecbdadbbeabcbeabcecdbecabdccddeedeeedacaeecedcdaeccddbacacedeccbdddddaacecbadaccbddbddbaeaeecbdcbedcbbebadbcebcbbeabbbcaccaedeadadbcadcaabcaaadcdbbbcbbbdebdadecdeacddebeccdbceeccebbeceeaadbdecbaaadcedebbcdcaeaabaecacdabbaabaebedaecdabdcabdaccbdcbbcdeceedeeacdeabaeaccecdeddcedbcadeaabacabedbdcacdedeaacecdcaabeadcabbdbdcdcadeabbadeccdbdcbaeaadedebeabadddcecdbebcaeeadeddbdeecaabbebecadedddadcaedbedccabdbaddddacadcbbcddaebabcceeaeedaecedcbccbeacbeddbdebcdceebebacabdacacaaacbdaadadbabececacaaeecadbdecdbdabbdacabbaceeebadadbccebadbeaadaeebaeedebeebaadcbdcacbacdabbcbaccdbadaababbcabbbcdcbcbdecdaaaeaeddbcaeaabbcaaacddaeadebbbdaecbeadcdcdbddaacabddbcdbbbeeccddabceddabbabbaeeeccaeecceebeaccdbaebbebdacdcecdbcbbdbdbbeaaeaceceebddeacceaddcedcdebbacbbbeedebaaabaebdacbcaddaebbdaddadbaecacdbdbcdbbdecedbabbebecacdddabadcbecaccbeeaaaecdadbddbbacbcdadabedaacacdddbecdebeabcedbceededdddaeebcbdccceaabaaabbcedeaeecebdedbdacdceccdeceddaebcaeecadcecbacbddcdcccdaceeeecaabeaceeccacdaaebedbdcceaddcadcaebaabeeaeeececbceebdebdbcbeccbedacddeacabeaecbdaebccebdebcaeccdbacaeeaedbaebbcaebadebbbbdebbedebeacabcbbaaebcceddabaeaddeebaeddedcebcbedbabdaadcdabdececddcddeccbccacebacdbbaeaedbdaebebbbcaeeebceebaaabbdeadbedcbabbdbdbceecacddedadcbdeeabeaaacaddcaaebcbeabacbdbeeacccbccadbecbadddebaeedeeabcdccdaaaecbdbeddbcbdcaaeccdedebccdababcbbeedabbdedebdeadcdbcbadbbaccdaccbaeecbeadadedeaacdceebbcdcbcbddedcecdeacdbedeceddccbeddaaeaaddbabaadecbabccbaaeadaadadeceecddeaedbdebadbebceaabaebeceddcaaecacdedcbabddcbebecdeaebdaecbedbeeecacbdbedcadeadebbcbadabadbdcdbacacceacbbadddbbcbaaeccceacdbadcdabdeecaabccadbaaebcebadecdebcecddaabdacdcaecabdabddeeddeeccdaaaeecceeddeababcddeeabaaaecdddaccdbdaeaddaddeecceebaccacbbbacdceebdbadaccadbecbadedaaaabeaecaeaaccabeabaadaecadebccccadaddcecbbeaaeacaaabceccabeeaecbacaededabbedcabcbcdaabbeaebacbbcdbadcecdaceebaaaacaeadcceedbacbadcaecbcaeeeebacdedcdccbcdadcdacecbdaecbcedadbebeaddccabdeddadcedcebdbcdeabdddcdaabdcbdbeddebdceebeebaedbabbdbdeebddbedbcacccadeabeddcbbcbbabccaaddeeeebadacbeedaaabadcceabdadabdceabcbacdbedeaddcbcacebebedceeeadbdcacbacabbbabceceaebbeeceedeecaadedbdecddeadbeedceadecdeabadcbcbcbeddbdedaeebaeabdecbedaebebbebabadccceadbdcabcbbeccecbbaaecceeaceaadbcedbebaaedcbbeddacddcbbdeabdbdabbcdcebdccbcabadcddaeadeddbedbedadcdaecedecaebbaddecdbeaecbcdbcdeacbadbecacccebecbbcebacdeacccdcaccdeceecddcaaadabbebdbdbbecbaedabaabdbaadbdeadcacdebbaeccbcbeeccdcbddcebaeebedbbaadcadecadeccebabdbebbeeaacaddaeadcdeaddbaceedbccbaaddeeacabeeeddbdcdeaacdcbceddeacabaccceaaddaeacabcdaaaebcaeddeddbbbaacaeaddadcceabeaddbddbadeaeaaadcbebecdebbaecdbdebcdeecbcbbdeebbbdddaceeebcebacaacaadcbddebebbbebebcbbdaeeeeeeccdaddacebbcbdceacebddbbaeebabaebcbbebcacbccecaacaccecdeebaabebababbbceccacaedbaeeaecbebcccaeaeeabdebdcddcaedeabaddceeddbacbabdaddcbcbaebdadccaddadcbdbabdcbbbdcbccdacdbbcabedabcdebdddcbebdabbeddebcaaabeadcbbaecaadebcacedddeccbeacaebabceaddbaeaacbddedadeeaabddcebcbedcdacdabcbedeadaddeebbcccaabcadbdedcbbcdcbaeabeaadaacdaaeadbaabcacdbcabccaaeedaddcddcdbeeddebcbcbdbecebddaaadcecdcbbceadadcbeabcdecebdbedcacbaebdeddacaeeebbeeebbaabccaeedacbdadaddaeebbadeaceecedeacdddeaeddbcbdcabbadeacabdbebdebcbeccacbbbdabbbbbcdaacebbaecbbdaccaddeaebbddbbdebbdecdcadcccbacdbaebbdbeeededdbabaebeacbbabcdbacdaeedbebdceaeccdcdeecaedbcbaedbcacaceddbabdababacabdbaebadaccabedcdeacecedcecbbbedbbaacbecdbbabccdeaadedaddedbdbdcbecadebadeecdeacdebbaeccecbbceaababbdeaaebbccceeacbcaabdadeaaeecbcccaaaedeaedeedbeadceaeeacadcdebebdeaabedcaeecadadccaeabeebadaaccedcebdacadbccadeedcbecddecccdcdaabbcbcbaadcacdddccbddadcabcdbeaaccedbccadbbabeeabaeccbeddabaeceebabdcaacaceaeeedcdaedbeadebbbcacacedbbadbeaaeebcacecaedadabeabacdeadddaddeeadbcbaceeaebabcdeddbcdbdbcebddaaabbccdbdadcceddebdebaabcacaedbaeaeccbeaceecdbbbebadccdaabbcaabceecdeadcecacaeecdadacaaeaedcddbceebdcaabeeeaaeecbbadabdeaccdecdeeedaeedccecddbdcdddbedccebaeaadddceceeaaedeeceaaeacaaedbcccbbcdaceaeecbcabddbcceacaccbecabadabeeccaddbdababeeddddeaebbdacaeacabaabbeceeebaaacccbcbdddaeccbdbbaedacdcaebabebdcadaecdeeebeabeccceccabcbbbeebccbabbdccbbaabcadbbdeceddabebedaecebdcbbaebacedeebeaceaaaaecaddebbcbdccdadabbddeaabbbceacdeceaecbacbcbabcbabbeeaebacedaadcedddcabcbcaaeabadcaadaadbbeeacbdcdbcbcdedcdcaabaceaeeeecacaeaeedeedbcaddaecdbecacebdcbabaeecaacadbacecbbcbeaecdbaeeadcadbbcedbedcdcbebecedccbceeadadaaeaececddbceecdebcacbddecebdcceabaabbecdedbbdbbdbbacabaebcaeecbbbddedccdcccbbcaeebabaaaccbadeabeaebecceaaaedecaaeeccdebcaebcdccedadecaaabdebadddddabcaacecdaaebdceeaccadbabadecedbceabaaaeeabcdcebabdbcbeeaddbbdbcbcaccbeaabdcdedbacdccedacddacbdeeeaaacababdadacdcacbceabbeddbecadebdebbdcdedbddecabbcebcbedceceedbacddaebecdaacaaaabccabbcdaadeccadbedbddaeaeecbcbaedbdabdecbdcbedbbbeabcddecadecabbacebeeaabbbccdbdadeabcdaecdedccbbbebbdddaecebbdedbbcccbbdeaeaaecbddcbbabeaebebcbeeaeddacebcbbdbacdbeabdebdecbdadccabcecbcdbdbaeebdebbdceebbebddbaaddccaeeeacceaebdccdbddddbaaeaceecedbbcbbbaedbebdeadcbbeeeccbeeacceeeeeccecacdebdeabeedabaddadeeedbebabcb