bbdebcbbdcaeacbaceaecdccdcdbdeacbcbbeeeccaecbedecbaeccbcecaccebacbabccadbcbcbeacdedcadabedeabbeadbcaabedbaadebccbcdbebddceaabecadcddbebbcbaedbdcccacecddcbeabbcbcabbbdbdcdcdcdeadbceccaaeeebadaeedbeeebadcedbbaeabcacbabedbdcbcabeebebbeadaebebbcddaacbccdbaceabecaeabcdaaecdeaaeccdaecabbceadecbcdadecacaddebabcadbbcaeecbdedbaeddcadbedbcddacaeeeaabdaeeeabdbecbaddceaadcecbbbabecbacdbceddeaaedbbbeedcdbcabaeaddaeaedeedcaadabaadccebaeeacedddbbcbdeedebcccecccecceacdbeaaadbaebaecceddeacdbacbbbbcdbedcbcebdacecdccebebedaddceeacacdacecaeeaddcbcebcddebbedbadaaaecbdcebddaddeeeddcaecebeecbbeeccbedaadddaddaeedcebabceaccdbacacadeadddaeddcedeabadadadeeaeaeeebddceaadbededeaceeeccbaacddecdeeeebbeebeeadebcaddccadcccabcccdadddaedeccbecddaabaacdebaeddbcedeeaebebadbdbaebcabbbadcccbdceddccbaebbdcdacdeeecebdcdbdecaececaeeabcabecabbcecaebceeabdcdeabcccaadedbeadddcacadceeacbdceecdbcbcbeabdcdedcecbcceaedbcbcbeaedbecaabdcdaddebaaedebecbadaaaaedacabadbdcaabddacbbdaaeededeccdcceeadcacddbeaaecccbacebdebcabdeebddbecedaeebdbdbbbbedadcaabebaaebcddbecbdececaebadccedeaaebadeceeacaebbadccbdcdcdbdedebdaccadeebdcebbdebdaeacadacbcaeeaecddabbbbbaeaedabbdaceaaeeebdabcdcbaecbabcddceebabccbaaacadcaaaadbaccccdeccaeadaeeccceaaabedccacbecdddccecdcaadaddacdcccaaebdbbcddedbededaabcebaabcdcbaeecbcacdaedeebceadaeebbdabcabdaecddebebbbaaecbecbdaebeeaebbdcbadeaeabdeeddbdacacdaedbadcaadebcbbbdddbeadbeabccdcaaedeeabecdaaadaedaeebdbabccbbbeeebaaebeaccebcebeebcabcdeddbabebdbacebabebaeceeadabbcbeddeaaaecaecdacdcadceeaccdbaaeabdcbbdbebacbbddacddedddddbeddcdcabdecdcacdbbeababeebcbaaeaccaecbaacbecedebadbdcbedbedadddbabcbebbadaaaaaddebbecbacccabebeadbebdbabbadcdbadbcebcabcbdeacbecbcbcaaeceecbaadcaacaadcdbbadcaccbebdebbdebdaedddbaabbbbebccededcdbbceebedcecaabadadebbedbcaadeddaecbeeaceededdacdeecbdeceeadaecbabbbdbeabdecebaececbdaaeceedebddecabedbbccbcdacccbdadecaddaecbcbbecaaebacdecdebeceaabebeebecbadcbdcacdecdddacdebaadadacdadbcbcbbcdabeeeeddbddbcddeebcaebdcebcaddbcebaccbcadaabbcaddebdedcadacbcdcccecceebbdecaaebcddcdecadacaeaddabadebcdddcacbbbecaaaeabdbecaaedbaadbdacdcbbcdaceeadeeaeedbcecdccabbcdbcdadcabbcceeadcedaaaceabbddbeaecddccaacacddcacbbbcabacdedaabaeeaececcabeddcbadbecdeabcbdcddacddebeeeebbdbadbaddbcccdbecababcccbaecadcabbbeddcabeeabcccaddbcecddbdaeecebcdeabddbebabeeadebccbbcccccdcbaecaceceabcbaabbdabbbceadbecbaaeeababaaedaeeaebcdbeddcdeddaeeaadaaeaecdecdacbaceaaedbbeadbaedcbdbdddceaceedceceacbdcecdadeedcabbcbdeddeedbdeccdddaccaedcbccadcdccdadbcebcabcbaeaaeeaceacacbacacecccaaaaccbcaadaceeecacdcadabdbbdacebaedcadecaaedebdebbbddaedebeadacbcedcbdbbebdaecbaacbabecdbebdecabdbcbaccbceabbeebacddabaccccbcabbceabdbbeccaadbdecbcbbbebcedacdddbcbceacebadbaabbebbccaaadedcbdabaccbbbacdcbdeddaeddacabeabccddbdecdabeaacedbaacaedcbcecccbbbacabcecbcabcaccdcaceccbeeedaeceecddcacdecabdcdbeacabeabcbbebcdbbbdbaeecacdabdbcaedbedaeceabbeaacecdccdbcbadcaaabeeedabaaccaebeaeddcacdcdabbcdcccdeaeaedbdabbcddcadaabaeadbbaaaeacedecdacbedadeaddaececeeeedecbacabcdcebdbbaeaacaddccceadabbaecedabbcecbecaedbdaddbcbbbaebabbaaaeaacddadbcceadbdbbdbecdeacaecaacbbeabeacebddbedbcdbcbdbdbcbdacbddbccacddbaddebcdaaacdeddbaccceaabbbeeaecabbdcccbaadaadadbadebeaecdcbcdeeaababccabeeadddceeaeecbdbecdcdcbecdcacbdedbeccbbbaacecbbbecedcceaebbaaecbacabababadadedadbdccbbcdedbbbaacbaabecbdcbdcdcdcebebacceeabbbaebeeccbcebbbaaccdcaaaeaecccbcaeabcadeceebbbcaaddddbaabebeeccddeedcdccdddadcbdbeaedbaeddaedbddedbebcadedaedbadadbceccaeccdcaaaeddceddaceebcedcaccbceeebbecadecdacdbcaedbddddacbdaadddacabaadedbcadcaaeaeeaaacceacbddccaadbeebaddceddadebbcbddecbeceeedadcacaaddaeedabacecbaaebebdaebccddecbeddaeeceedbbaeacaeaecbeddbdcadcbaaeeaebadaebccbaeaecebbcaeecdabbdbcdcaededdcedebbcbadbceedbacdcecaaeaccddaddbccbebbaaeedbaccadcbabcadaeaebacbaeebdcbbbbccddbcaacdcdebedbecedbcbdbbabcdcabdebdeeaeeeaedeeddadaeeaaaaabdeedecddadeadacbacbbcbddcddbcecdcddccbcdbcecbacbebbddabdebdaeacaaaabddebebcdeacdbddecedaaeebddbbcbcbcebdbeeccccaeceebdadcabaeedddbebdadbaeadeebddcecadcdbbbddadaeceaeeaedecbdeeabcedbcbaccedeeccbeadadcebcdbdddcbabbabbaabdaadbadbababdbdadcdccbcecabbcaadeccbcbccedbebeacaededaadcacebcbddabbceedededdecdcdcabccbdeadbcdbbcdecdbadbebeacdeaaeeeeaceddabdcccaedebaacddcddeeeebaaadacdecabcbcdeedeabaddbebccbabecdbaaadccdaaadcdeabbbedbcedebdaccecebbcdeecadaeccbdbadbceccbddecdadbdbbebcbbdddddeaeebdbcadbeaabecbcabeeecbabcadbcacebdacebdbaccaddeecabdddbdddbbedeaeababeacecaaaeecdcacdaabdacebebeabedeeacbbdccebcebcbdaacadacbedabcaddeddcadeedeedecacebcababecaddbdbbbddabbbebcdabcbcdeacccecdcdcceabdcedabbaecbedbedaaccccedcadcadddabcedeabeeeecaecdedbdeabbabbeebabedbcdbecedcbebecbddedddbeaaeaaaaadaeabdabbdbedbbdadecdaeebccbeaebbaedacecdeedcbbcdaaadbaaeebabdcacbebbadeecbbdecdeadccbabdcbeeddcacebdbeeacbebdaaceccadebcedeabbaebeabaddbabbddcedddbdeddecbebeeacbcbecbabeadbaddeaebdedebaaabeccbabebbdedeadeaeeedccbcebedcbbccbddcdaaaebaacadbebdaacaaadcbeddaebccabbbacceaeaccbbceecacdbbaedeccdcccecddcbebeadcabcdcecbdccdeeabadeacedbcbebedccdabacdebacedabbababacaaeeeddaeedeccaceadcbcdbdebeecbabcceadadadadbadcdaccbdaedbbaadaebdadbbbcecbbcddecdcbbdeaceeaecddcbbbedcaecadebbedbbbacbcddbebcbceeceaadaaabdedaebeadaedabecdebdebccecaddbcdeacedcacdcabdcdadaccaabeddaccececdecdbabbacacedccaaccbbebbabbbedabddbccabedadcaceabcdedcdecbdecbccbbabbbcaeeabadeceedeabbcaeadeebddbcaecedabdedcaeeeadbbdaddedeebdccbddeddbdbcaccdbbcdebaadedeaccccdeeebeeebcdcadebcbbcabccbedababbdebdbedbbceaedadecaadecbeabecaeecebaaedacddadaebdcecaceecbaaebceedcdcaeabeaedbdeebddbbcbaeedbcdeeabdedccdbeccbdecdceedaebeaadeeededadbdcbdcebcbbcdedbabbacdbacabbbaebbeedadebacedcccdcccdaaaeacdaaedbbcbdebeeddedecbedeeebddbaaaaaacebeccdccdbdebbcbbeebdbaabbdedcdcdebadaddcddcddacbbacdbaaeebccebbebbddeaebaeaeeebeacddeeedecedbbdaaabeedbadbaadeebcabeaadcdcedcbbbbcaecdabdbdeaadbdccaedbccebebbacdbdddacbaecdbacbacebabddaedaababacddaeaddcabecdacbccecdeaabbdeabecbdeadadddbcbedcbccaaaddacdaebcbdaabddbbdceddabeabdceddebaeabddbbccdabbecdeecedddeaedaadebdddcbddbccadbacbebabdacdaaabddccedecebdeaeeaedabaeaebcbedddbeecbbcebacbbeaeeeabacacbbcaacadecbbcbceacdcdbccdbcecacadcbdccaabbacbbcbbcaccbbebabbdedaeabebccbadebecebcabcbecebaddedabdeddceccabababccdaabdcbcbcbbceabebbadadebcdedcbbdeaaaddcecaedbaddebaecabdceaaccccedeeabebadbacdceeebccedbbaecebaedbbccdacdddeddbdaacccbdeedaeeeccdbdbccaabaebdeecbebabbdeabcbcabbcbccdeaecebcebeaccabaebdacedcbbddbcdaccdedaecaadcacaceaaebbcddadcebcccadabcbaeaeabdcccebceabbebcdddcbeedaeccdedcbcbabbaebddbbeccaceeecdeeebebcdcacddeabcaeedcdebcadeeaccedeeddacadcddbdbbabdeaeeeddecbdecddccdcebdddcceeebdadaccbbdbadeeedbcbcdaeabcbecbaaadacecedeeccddcabdadacdebcaaabacecaaececcacaedebdccdddcbeacddbcbecebcaeacdadecebbbeccaddcddeceebaacabcadbbacaaddbddbbeeeccaceacbaadccdecbebedcaeedcecadcbddbcbddebbcbebcbbacaddbeabdeceedceecabbabbbabaecddabbbacadcaeacadacccebdbdaeabdeccdcdccddcbdadbdcbccbcccabceeddadccdeaadcecdaadadcdcdbceeccaadaebcccdccbdcbeebabbcecdeaabaaeaeaebeccdaccadbebcaecaddadabdacebacaeccdabeeadcabbccebedbcddcdccdacbccaebabebbdcdbbbbceaecaccadadcedaadbcbeddaeceddbbddeebaccacdbdeebedacaeebeeaeacecaaeaaaeccbeecaebddadcbdebacaedacceddadebbabaaaeadadadaecadaedbaecdddddeababcdbecbadedbdceaecbcacbdcbdceaaabaacaddbaadebcccbaacdcbeaeaeceeddbcaeadebebdcaeadcbbeceeeaaccbdadaabbdaecbaeebbcbbebbedaadaebebeaabbcaccabdcecdbdbdbdaaadeaecdddaaeceeaebebeccdbcceadeeaeaecdcebedcadeeeaabbaeebacddbbedcdcbddaadbbbebbaebdddbdeceddccecaecbdbbcbbdeaebcbaecceeeddedaeedecadbaeaededadcbeedbaeedaccbbaedaeccbbeacbeabbaabacabebeecdbeebdccaacecbcedbbcddbeacebddaaceaadedecacceadcddddceacbbdacccbecdaadecdaaeaceaaccbccbeacceadbedacedccadbdaecdebbebbedacdbeabadcdeabaeccaaaaaecedaaadcebcbcbeebeebedeccbcbadadabbcbebebbbeacbdededcaeeccacccaaebabcabaebdcdeebedddaddbbaedecccdcbacbaebaceebcccccebabceedcbeecaaaeccddcbeabededcbcddabcacdbabccdbddcebdbbdbdaadcbaeecbacbebddadceeabecadcccdeebecbaabbbdbbabacbbebeecacaeaeabaedadbdbabddeabbacabdddcbccccebabbebadbbeddbdecabaabaaaeaaabadbbdddabadbeecbebcbbbedbecdabbdccecbcaedbaccabbaeaeadecdcdddcccddbbadeccdcaedeedeaccdceaaeceeeeaaedcdabebacdcbdbdadbadababbeaccaceaebcaeecdbbbacabdbddabedabdcddcbeeabeaddccbbedbdeeaaacaaadcbbdedeadccaeacbcebebbebcbebddcacaaecdbbedbdbabccbaddebbedacaccddcbcacedebcebccdaadcebaceabbeddcdceeaaecadacecaaebeddeaeadbdbabcddabbeacdedecbaedddeaeaaeaaabadaaaaecbadbdbaeaeadedacdeedcbdccdebebdddacbbdabacacaccedbbbbebaecebacadedccaedceeebdbcecddbbcabcacdddddaaebacecdaeaaceabcbcbdebbcedcceaebcebddabecceebddcabaabaabaabebebcccceeaacdeacbdceecdabcebeeecdbcedeaabedebbdebeababecbebdbecebdebaadadbeccdbbaaeaebdaabbccbdbaacdeadbdbedabecabeabaadbaadeabedeadabbdcbabdaebcdddcebbcdbebcbddabcceeadaaeadbaadadbcaacbebdeaedebbeedbbcaeabbbdabedceabcdbdddddccbbabcabaedbdbdeedacadcdddccaecbedebacbaeeecdceeedeedccaaedaaaacbbeeccdaebdedabddbdedbebebabbdbddbdabdaeecdbbcebcaacaeccbcdaeaebaacebadbcceabdcdcbcbacdddeaedececbdddaccebdedaeacbcedbaabecbcdcdadeaaeeccddcadccceaeeeeeedbcaecedaeeabcabaeeeddacaacdccdeedaccbbdaeabbabebedcbdaedabcebcadaedebacdbbdeaaaddecbbdcccaaadebbdcdaeeddbcccedbcddbcdaeddeaeabccdbcbeaaadbdeeddcbbabacdcbedcbbbbeadbddebaadebacecbcadceaeeebdcddeaebceeddaececaedabccbedcbebecadeeaeacebcaedcddedecbcdbbeabbcebcabbaaeadbebaaededbbeaaccacebebbddadeecdcebbbebbeabedeaecdabbeabecdbeadedebaddaccaedcedbeacabccebdabededebddaeebbcebadaddeacaabdacbdbabbcedaabeccaeaaaabceddeeeadbbcdebcedcedcbbbdbcdadabccbdaaecaacccbbdbcddcbacceceeebecaedbcdeddbdbabecadeedecbacecdaeaeeeebacbecaecdcdddebdeebaadeadbaaaeabadecdaebadaeaaceecbbbdbadeedecadcbbdedeccabaeedcbececdacadaabdacecdaaecbdbcddcaabacbecbbbaacabaaadbcbbbeacbadddecdaaededebaebcbcccbaeceadabdbceaaebedbbaccbbadedccddccebcaeadaedaccddbceacdecdeabbacdddbccabaeeebcaadacdceecdbcdbddccbededaadddabcbbdcdeaacacbeeaedebaaabdcdcdacabcdbbababdcadceadecebeabbddeaabaebebaeebababbccdbcabaebbbebaabeeebdabcadeacaaabacdebabdaeccbdabdbeabcedeadaeecdcadaccadabacabdedbecdadccaacacbbaaabbceedacbdccbbbaebeeaeabcbdcdbecddbbeadaeedbbdbdaecccadaabeeebbcddadbbabcacaddeaabdbdaaecdedaccdddecaedbdcaaccecbcabaacbbbeacbddbcedaaadecbadaacaedbadebcbbeedddcbeebcbdadeadbebdbbbbbcebeeacdecbdadddebbbaaeeceeebabadabeedcbbbbeeacccaceebcceabaceeabedecacddbabcccdacaacdeedaebeeaeaddbcddbedebeebdeddadceeeeeceabcdaeecaecabdcbdbbdbeacbeedcdcddebccadbddbabbcaaaedcceaabcbaeccadbddecabadbbdaeaccccacedbabbcdbbbcbccabeaccecdbaceddeddaabeeeedaabbabdddebecdebcabedbcbecdaeabeedacaaeebaeeadedbaaabbdbebcceacccddeeedcedbcedcabbadeacadbbddadbbcbeadabdbadccddaaceecbcbdaabdedeaceacecbdbaacebcabdebaedbedecbcececbcadeeadbeabecbecdedcaeaccdebcbebcceebbdadecdceaaebbaceadedbdccdeebaccdabdbbabebbdecdbcbabbcadbacbcecbebdeddbaebceeccebeacddeeedacccdabeadbcccdbeacaaacdbcdddeedcdadaacdecacdbdebbbeecacaaaaacbaeaadeacbdcdcbaedabdcebdaeeeeeceeebeceaacecbebaadceeabbdbababdbccaedeccbeeacadcccadbcbcedcebeedbdbccaabaabdeceebabdedcbbebadcadcebbdebebaecebcadebbedceabdaaacbeababdacaeeccdacaaebcabdeabbaacccbcdaceebcbdbededdcadabadbdaadaddaebededbdbeebebdcabccdabbebcaaeaddddbddbebaceebebccbbbbdeecedbcaaedbaccabeacbbaaeecadbdbdabcabdbaaddaabeaabbbbadcacabecdeebcbcbcbeaebbebecebdacdcdebeacabaadcacbaadbbcedeabeddbbbeedcddbcdacbccbdeaaeabcccdeeacaeadcddaceeabedaddbdbccaeeaabddeecccddacbabcdaaaacdbeccecbbbdddacdccdecaabbbbaaaaaecbecedadcebbdcdcaabbcadabadecddaaceeeeddacacdccadcbbceeadcbbeedaccceddddadeaebddaabebdaaeaccdedebcacccdaadcdedccbbdcaeddeebadcaeadbedcdcbcdbeabceacbeedbbdbccedbbecbaaabcbcaddddcaecdcdbaaeecababddedadabaeedabdecabeeeacdddcdaedcdacdaaeeecceeeabacecaddbeedceddaaccddbeaedeeceabeebbbcadeebaeeaaaaddebaabdadedccdbcaceaedcaaebedcedadaeaebbababbdccebcaedaaaeceeceaeddbebbebcbcaadbaedddabddaababbaaeddcbebdbbaecaadbdacbabcaebbabebdaaeeabcbbadcbcdbaedaebeaeeddcebbbabaaaedeacecbadbcbaeacdcadebbaeacacabebcdaeeadbedaaddbcbebbabebccbcdbceccaedbbcabadbbbdaecebebcdbaabdbeaaddbbeecabaaccdbaedbdbcbbcecdbaddbedaccaccdadeeaaacdbdecedddccdeaeacaabbbebdbdcdaccbeabeeeedebcacabaedaaccdeabceddebbcddbbaebecacabbecdcbbdebcdabdcbabbebcabbbdeaabceaccadaedeebbbeaeeaabeebddbdebeaddeddacaccdbadcbebacdebaaadeacdecceeadadedecaabbbeacbcbbeedddeaedebdbacceadaecdcbbcbabcbcedbceacbcebcdcbbeccdddcbdccabaabadbccebddbdbdbdaeaaedddedbaaaecaaacbcdbdbedcceccbaeaebcdccbeecacceeebcbebbbadcadadacddedbdcbdaacdeeadccedddabcccbccbadbebdbeaeadbbbcadcbccedeaeabbedcddabcabccdbacbcecbbbeeddbeeaaaacaebecaeacdbbdbcbbbbebdedeceebeabbcacdcebacbdbbbceaedaddecbbceaedddbdacdecabbabcdbabddeadbecabcccabebcbceceababeaaaadedcdeacbcdcccdeadebbeeacdbaaedbccdcbadceeccaebabecbeeeadddddbbeaaeadbbececacedebedeecaebbbeaddbecadecabbeeacdbcdbaddacabbaedddcedcbbeddcaabcaaaaccbbcebecbdddecacdeeacadebbdebebbadceacedbbdaebabccdbcccabeaedceccdadbcdeeecebdcaedcebaaebdeddabcdbacdacbbedbbccbcbeeeecaecceeddbdceeaeebbbbccacbdbdebcadddcbbeaacaccdaeccadebdbbeaddeedcbbbcccabccecbbbbebccadadaaecbcbcedebbcabaddbcbbcceccdbcbdeadebaedbebaceecebdbbbacaaebdbbbcaededabebdaacacaadedcbbebbeeeabaeabeccbcbbdceabddabcdbdcbceecddeebbcedbcedaecdcadeadbecdaaceabbbdcedbbaccaaeeeecbecaeaeadededcabedbdbcccddbeeeebdaebeebaeeaaccebeccdcadbcaeedcbcaeedbebbeadaadcccabbedbeeddedccaeacaecccbdcccdcaceedddedbbdabddbebeaabeacceeacaaeacbecadecceaacddecdadbabededbacbcdbccdbaaebdcbcaceebacbbecbacdddcbbceabacbbedaeacaacceeabbcdeaabbebdddabececeaebeadbcebcbebbdaeddcdddbdcaddbecdecaccebbededbbcbdbedeabaabaccebadecccbcaccabbcabdcbeabcaaccccdebeeadcdbbceedaadecabebebadbbcdcbddbcdbabbaacadedbbddedddcbdaebcdaccebddbaedbeeadeaaaceeeacceccbdbaccaecbdbedbeaaaccddacaaeeaabeebbbabaaddadabddeaceabadedadaeeeddcdaecbbacddeececeddbddaccadaaddcbbccccbedcabeaedaacabceaeeaceaccacabdddebeedaacbaedcbacabcebbdddabccecacdecceaadacdddbabeecacdbddadbcecabeadeedabebadebdabeacdbdaabeebcadbeaccbcaedadaadddbacebbacceaeebaeeabeeeeddcbdddddceabbecababaeabababbadedbcbeedccadeccdabaadcbedeaecdaaebccbddeabaeecbbceabdbbdbaabddbaabaadbccedeadaeccdaceedebcbdabcdccccbeeecbeceabbabbedadedacbaaabdbccaacebebbcabebbcaecdbbabdedbdaaaedadbbeadabdeababdbdacaaccddecadaddbdebaabdaebaeedbdaccddedcbeeeebbebebddbaadceedaaeddcdaecaeeeebedbaaacbadedcecacdcbeaeaedbdaeadeacebaeadaecdceabaebedcaeebddaadbabbbcebebecabaecbebdecebadcebaccdceccdbaebbbccaaacbddaacbeeeaaeaebaddeebaeddaaeecbbcdddcdbaeaebaaddbcdddddebcbcccaaebddabdeccebdcabdcceaaaaeecbeeadaddceadedeabecaedcbdbeceadbedcdeddadacaaddadaeeacdebebeddadddbecdebbedadaecacbecbddedadeadedbeddcadbeddbabdbccedbabecbbacbededdddddddccddcddeeacaccbcdecebeeeacebeccabbcbabdaedebebcdbeddcaaaeacedeedbdedadecbbacbcbdddbbbaaeedcbddcaebbbbeaaedccbbaecbdbccaaddaadebbedddbbbabbaeecaecaeadabacbddbadecabecececabdeaeedececdbccdcddcdcebcabbeebaeedddddebaccdbdbadabcbbdbacddccabccddeebadbdaebbcaceadececcdabbcabeaeaddaddeeedbadecbcaaedebdabcbebcbceaebdbbabebbbdaddbbaedcdbabadbebbdbebaaacbeccaecdedabbeeebbccdceeaadaaacdbedceececdeedadaceeadbeedededdabdbbadeeceaaebebebddabdcdebdebcadccbbbccadcebebeecdabbddaaaaaccdcdedacdacdebedbeebbcadbdaacbaaebebdabbcdedcbdcceedededddeeeececcacdbaedacedccaaaaedeeededbeebbedcddddbbabdedceeebceeecbaaeabecddacddcdeedeceebdcabdbaacaddbbbbbaeddcdaecdedacbbdccbbaeceeccbbbdebbddadceeceeaddeadceaebaeecbbdabcaccabcadedbecceedabedcdddcdbdeddbbeecaebddbbeedcedecaadebeabcdcdaebadcedecbcadaaeacebbcadbbdbeddceecbddcdcbebaabbcabedbdacddeccadabaeeddebcddcecbadcabddcecbcadaadbbeabcdeeebdacdabbacbcddddaceddcbedacadeedbaaecabbcbeabbcdbabdeaaaaebeedeaddbeaecdaaeecbdbabeddeaabaaaadaebdcddbdbcaddddeecaeeacdccbebbbeccacacabeedaeecbebadeccadebcebbbcdaccbbbdeadbeecaaceacdddecaeadcecadbdcbaaccdcdabdcbaddaecadebbdeaaeabdcadacdaedadacbbbedbcbeabcdeecabadbdaddbccaeeddeabbaeeedceebaacaeecbbbedbbebacaaeeeedcddebadddacaeeedddadaccbeaaccbcdadbacabedabaebededdcdbcacdebbbebececeacbddcbeedcccccedaddaaacebcbcbaabccedceaaeadccbecccdcdeaadaeedbeababbedeaabeddcdbcdeeecaaebbccabdaeebcddaeacaddadbbbceeacbaacbabebadcebbeeebbecdbdadcecbbcdbcdecaabebadecedeaeeebcadadbccebdaecbaaeeebddaccbdceebededddcccbbebbbceaedebdaacaadeadbeeeddaadaedbadecddcacbabdebecaeebbacabdccaaddbcdbaeeccccbceecebabeeabcbdecccbadabcedeaadeaddcaacacedbcddedaaccbececbdeebceaeacedccbbadabebcaaedbddeaaaeedbacbecddddccdddceccacdeccdbcebbcdcdccacabecdaaaadddacdcbedaeaadbdddaeeadacabbcdcdadccadebeadbcbbedeaddccebbacdeecaeccddeccdedbedceaaeababbaaceaeaaccedaaaaebebbabbbcccadcbdbddeaeccdbccbcbcdeeddecedcebeaaeaabddedbeacdbadddacbebccebdadbdeeebcccaeeeaadbbbeccabdaecadadcecbeceacdcaebbbeccdcabdeacccbdcacbbdecaedeaeaaabdcccaededabadebcbadddceccacddddcdbbbcedbbabbbdeadddbbaddbcbcccdbedbebdaaecbacdddabbddebbadddddbaddcbccccdedaaadcdbcddaecddaebeebeddeeaebbcbdbdbaaebbbadeaaddebebcebedbdaecceabeebceaacceacaaedaedcccdbddeebbbecebdcbecbeddbaeddeddeccaeccedadbeeebedebddcbdbdbebcccecdcbcaaebeedecbbdbedeeceaedddecebdbabdabeadccdedcecdedabddbeeebeddbdbbcbbecdccdaeccedadebbeebdebaadcdcaeaadcdbeecbeabbedecaedeabdabbcddbbbaababdaecdceeadeddecdbecaecadcdecdddbbaaabcabdbcedcdabdeacbddeedcaeeddbaaaebcaecdbeddbdbdcbabbbcbacccddeccdecdaaccccbbbdcabaceddaeacbaebcdebbbaaaebedabbbdcbdcbbcbbbcacccdacaadacdaeddeeaabebaeeeeabeaadccecceadccbabecdededabdcddbeadcecedaaecdcbcbaeeabbbebcdccabecbeadaaaedeadebbbeaebccaeeddeaddeaeabdbdabcabcdddeeebcdbeeeadcbbeebbcdabdcacebeccaacbadeebbacedddbdcdccbbcecceeacbbdecdeebcbecaaaebaacbdbebeedabaddecacbbeaceaebcaaedbaaddcedabddedecebebdebaaeeeddbdcdaeeaeacedeadbbedcedbccaacdedebddecacdbdeedeecebbdeddeadccbdaaadcadbbcbdeadddebadaedbbeacbacbeedbeedcecdaceeacdabebeaeeedccbbacadcadbabdcdcacadcbacceceacaedbabbdeeccdacbdedbdedcebaecbcebbadadbcdbabddedbbedecbebcecabdeceacecccecdaabaccabbcbdcbbbedaabccaadeddecbecaeabbabbdabcadbecdacbebedaaabbddaacdeadbdecbadaecceceeceabddcbdceeeeabbccbecaecccbbedebdabedbabdccddadddadcaecbeeeabddeeebddedabaccabdaecaccaeebeaedeabbcaaedccedaadebddbbdeecedbadedeccddeedcedeaadcebdddbbccbceeaaedbebecebddeebebdcedbbebaeabbadeeedbddedbbbceabcabdcaddddaacccadeaebdcaadbbadddcedbdccacddaadbecdbcddacaacaceddeabbccaeaccaeccecabebacbdbabeeabebdcdceabdeaebdccbacdecbbcabdceebeeedcaadeedaeddedaecbaeaeabcdbeedbcbdcadbbeaadecdeababbeededadbbaeececacbcacbacececcacbaabcdbeeaceadeadbebadeceebcebddaaadadbddbabaeabdbddeecacddbbccebdbacbddeaceebbecacbececeabaabcaaeccedcddacbeeadbcaddadebebbdaeaabdcdacacaeebbdebecdccdbcedecccdbedadbeaacacdbecbebdeecedabceeacbdcabaacbceedecadbaeacaceecbecaabbdcbbdeadbeaaacbbecaccaebedbcbabaecdbbdcbccbdeeaccbcbedebdaaabadeedabeacabeeeaddecababacedecaedaadcdcecddbbeebdadcaccaabbeeddeddeeadebceacbacaacabdacecbebcdcacbdaddedcdbdbebcccabcbadbddacecebabcadccbcaabecebebbaaaabeedececaabbdedbabcbacdbedbddecdcbadcddaceedaedbeacbaceebeccceebcccebcecbadccedbececeacbdaadecdeddcddcbcaecdccebbbaabcbaacdaaadbbbabdeaceeaddddebbbaadabdecbebebebeeecaadcedbcbdabbcbddcdbdaaeeeeeeedceeeeabacebebddddaeacbbdbebdaabeebdddebedbaebbcaccaaeadacabbbebabddbcbccbadbaebcdddcbcddbbdabcabebebadddacdcbecdbcbaebaaadbeeeaeaabcdbcaabbdceebdadecdbedebcceaacadbbbebabeacddcdddbdbdaddbabaeacadbbbebceecbecdddbeeaececbeddbccdbddcdcdaaeeddadbabdabbddeecaecbeccbcdbdbbcaecaaeaebaebcccaaabdadcaecdbdabaceeeabacdeccbaacabaccacaacdedacabdacecaabbbbdaeceaacbbaddacebdccbdedbcbeadccaeccebecdbeebdbadcadccccceeaececbcacaecbbaabdcdccbcadecdbaabbaeaddaedbbcddcedaceccabbbcebbdbaeabbdbcebaeeadbccedccecececcaadbadaaddecaadedbddcbeebcdccdabdbbddadeeccadeccbbadadaacabeeaeddbadddbacbdbebebbcbcecadabcdacdcccadbeedabeeaecacbaddcdeeacbdcdeadaaaddbbceedcbccebedcbeacabadaacccdaaddcececbcdaddbaabeeabccacdebebabbbcbdbddadeadaddaeccaceeceeccccaceebccdbcdececdacdccaedadabbecdcddaeceeccaeeeeddeccaababcabeedcbcecebbadacbabecadededcabcbebeecadadebcbebceaecceaadcacbcbcdabceddeeeceeabdebeeabaccddecdaeaabacdacdceeeeeecacacbebcabbdbdbdcddcadbeccecdcadacaebeabebcedecaddaeeecbeadadcbacdeddaeccdbbacaaadaadcbbdeceaaacadcdaedcbeedecdbdcaecddcabcdacebdabdaadcacdadbedebaddaaeedbddbccbadabdcbcbaecedceaeadbeacecabdedededceddacedcbbdbbcbaaacbebedaebdcdeceabbbddebacabbcaedbaecedaedabceeaadccbaabadcbdcddbadddabcdcedebdbbdbecaeaccccbbeabeddbabaacbbdeeeeacadbdabebecdbabdeaebcbbdcbeaadcdbeedecaecededaceceaebeeacdcadbbadbbcabcaaecebbeebbccecceceaebaccddddeceacbaaadedbeababdabcadadbbaecacdcbaaabadcedacadbaeacaaeadeaeabdeaeacbccabaaeadeebaebcddbabccebecaabdacacdddbcdcbaaedaedacedeaaabaadccbdbeabdeeedaeaededaecdabebcdccccbdacbdcbeacabcdccecdceaeddabdedeaaddcaeedabdaaebbebddbaecbbdbaebdeaaebcacbacceaaaeddedabadaadeeecbadadabcabcbdddadacdeacaceeadbdabbcedebaabdcecbccdadbddcddcbdddedabdbadacaaabeadedcaccebacecdcdeaeaaccbbeccbbacebbdabcadccaacdabdceebeaeeceaeedbcdcdbecbbdedaacbabbbedecaedcdedbdccdbeaddcbbabacbabcdbbdeaacdbceddedababcbbecbcabeacccaaebaaedbcbeeeedeccddddbecbbacdbcddbddcebbddaccadcbadeadecedcbacccaaeacbecbddadeecaedeaebcaaeaebbabccbcdbabaadddabdaadbceeacecccccaaebbcdbbccdccdaebcdbabaddabeeaebdbbaadcccebbbdeeedbbecbccdebaececcbadaaeebabceebadaeecbebddaabbaeaaeddddacbccbbeeeebdbaaabecccbdeacddadaacacbcacbaeeaeeaedcceeddaebdebbbddabdbbcbebdebecaebcdddedbcdacaabcdcebadeedaacacecdadaabeeccbbcbccbdabbbdacaeedabecdcbecdedccabdcdedbeeacadaebacbdccbdedadadbeaaceadcbbcbdabebecaacbcadbeaacbebaaeadbdcdaddeccdeedecbcbdcebaacedadccbedbbbeccaaaebeeeecaadcaabaebcadaecbedeeaedcddddceaccbbdadcacdcecdcbecbcdabdeddbddbbeeebbbdcdcdabbacdecdbccedcdbaecbadecaeeeedbaaabcebbdcadaedbaabaecaadcadeacaaacdcaeceddacaeaacdaedcceacaceeebddbaebbabdbadddcdbaadebeccbcedaacbdcdcdcdadceceadccbbbbbddccababbebabbdbceaeedbeceeeccddccadbdadebdccccacdcacddceccdaacddecccbaaeccbeaceeecddcabbdeccebdbcdecebbdceadbcdcdcbbbaebbaadcbaabdcadaadbbadddadaabeeeeccdccdcaedcacbecdadeeadeaeebacbedcaedaeceddabbbcaaeddbcccbedcdaacabaadeaebedcebdeedabaecdecaeaebaedbdedcaabcdbbdcaaeebccedcbdacdabddcdbecaebdbedebebbdaacdeaacaabbaebadaebeaeaddeabbdecdedceeabaebaccedecbcdeedbecedbbcdedcdbbabbedcddebeecacbbdcddccbaeccdcbedcddcdddabeaedeebddaecaacbeeacbdceeddcaeeebbbcbabeeceeceabdbaecaaaeababedcaadcacedccaaaececedcecaddaedbadbcaeaecdedbeadcddabdcdeedcccecabaccaeabebcaedeebabbeaeacdcacbacababaeedbcedaeaceaecaeaaccbbabbbbccacadadcceacddcacaacceeecabeceadddbecbbccecdcceaceeecbcdabdeecabcbbbdbbbddbacdccaaedeacdbecdaaedebebdcdaaaeebbeaadeadebbbbcaaeecacbbcebabbeceebdabbaacbedbceddcceecbeabacbaeebaebabcacbbccbebcbdadaedbbebcacdaaeedbaeeaddebdddbadcabedcaabadeadedcaccdadadeedacdedaddcecdeacdbebcdecacbdeebdbeaecaaeeacaaeabdddbcdccbcdbdedabceaedadadcbcbaeeebcadddbdebccecbacceddddeddbbbbceecdcdacedebeadecccbcecebdcdcaddebcbebbadcbabdacccbcdeddcdbbdbabebabaddbeabbaacecdbdecbeabbdcabdecaaadedabbabdbdacdcadccdabcecebededddcbbbdcbdaddaaedeacecbabcbcdaadcdebbbeeeedddadabbcdebbaadddcedcdebddccbbacabcdadaceeeeaeceeebbdacececedbaecdedeccedceddcdebdebcccddceedebcbaaaadbeeaeabebbeedaebbebaabddddcbbbbacabebdaebcabedcaceecaacdeeedeedeaeabadadebbbcdacbdbedbaebceaaedbcaeeceaeacdbdddddeadbacaeddaebadbeabbbbbbdcebbdddcddaabedebbeebbdbcedaeddbccbaadaeedaaccecbcbaabaadbdaccebccbacbadaeecbbcbbcbdccbaaebabbbebedebeeeedacbdaeabebacdbaeecacebeeeeaeabedadcdaedaeecabeeeaecbcbeeeabdbaedeabeebdcaaebbbaddbdecabaaeecdbbcddacaecbaacbdeadaaaebdedeeacddbdcaecbbcdeaaaedbcdcaaebcbacdabbaedabecacecabbacdeddcaabceadccaecadbedabecdeecebbeddbcecddbaaeddceecdadbbdeeabededdbbaaaaddcacccdcebceedaeadcebbcdedabeadabcecdbcedeabcadcbdeddcaadeaacaebbaadbdbddcbaeddaaadecbacdddbeebbccadddeabccbdbbdcddceadecacaacadcaacbceadcaeddeeccecabeeacecdbeeaeadcbaacbcbdaeeeceabddedaddccbdcedacdeeeebaeaebcceacdbdbdabcaacadcedadebccdecacccddceebeabbdeddbaccddeeaeabecadebdecbdccbddcddeeebeeececcedeaacecddbdeeebeacbeacadacebbdebbbbadddadbaddeadbcbbbacebdeddccbadbddbededbbacccedcbedceaccdbceddadaeedbbecbeabeeaccebdabaeebccdaceaaebeaecacbbbdcdeaabbbabdbabdecdaceddcebcedcddecebdaacebeeaaaecebaddadbbcecececcbcacadaddeabeadcdabbecbbdaecbbcebecddadedeeedbecbcaedabacbeaaaedeabbccdeeaadceceeebeeacbaabcabebbaadddadabaceedbaabdedbebaedebdccedcbbacadbdeadeabadcedceeeaaaeccedeecbaeaddeacdabbeecaabcbaeeccabeedadeaaacceebbdbdbceaeddddeaeecaaadabdeadbbbadaeeebcbdbccacebbebeaeebccabbaaadeadcbebcabbcacacedbecbbbdcbaedbbeaabaaedcdcbdbdaceebdbdadbaaebcccbeccbeeddceaeeabdacabeeedaedcdbbebadaabddbebaeebddeaedaedeebdeccccbdadcdbdababcbabbedbabcbedbabcdedcbbbbddbaeaedbbecccbabedebdcaedeeedaaeeeaacbddeaeabddebcbceaccabaabebddcbadedbccdbbbaddbdedabceaedcbbbbbecbcdddddeacaabbecadbdabcdcdebbecccbccccdedbccbabcdecabcbcaeccbcbaedebbadacaecddcddcdbbadabacdbdddacedabbcddbccbbdbbaebdbcbcdaaedacabccbacaacddbbdeaabeededbecbadeccdeaecdaecddceddcbddddbaceeacacecaedaabbaaeccbbddeeedaedddaeadaceaceaddbabceeeddecbdcbbcecbaaaaeeabbdbbdeaeddecbdcdccadbadadaebccebeebdccceabcaddadcaebcbacdcadebabcecbaddebcabecdddedeaedeeaecacbaecbaedcaeabaeaaacacdcdbaebcbdacdbacadacebdbceaddaccebddcebdcdeaecaabcddcbdbcbadadeadccdaabdebacdcebeeacbebabbdecabeddbeeceadeaaacdcbadaabadcbbaceaabbccdcaaacdeabbcdcedbecdbdaebedceeebbbdacacdbbddceeecdbbedabeedcdadecaeddbabcedccedcbbdbadcdceadadaeeacecbecbaaaaeebdcecbbbbbdeeaaeeebcacbadabedbeeacecacaeeddaecddbebabacaeddaeeabaaabeaaebcbdddaeceaeeaddbabcdbdbccbadecbababdadbbccabeceddebcbcdcebbdedceaaabbbcecebaeaedcbdabdaaeadaeaceadabedcceeddacccbedceddccddbcdbcdbcdbbdddccceabceddccdbbbadaaccabeaddbababaebdebcdabdceccbadababbbeebdcbbbebbccdaaabebecbeedeccddcddddeccedccebbbebbeedacdceedacdaabaeabbaeabceabbacdadcebeaddedcaaecdcabbcebcbaecaecddbcceeeeabbddbedbdecdaecbabdadebeacaaaaaaeccbcacbbdacbbedebacabddeccaaaecbebabaedadacaaaeabadcedbcbbccacadaadcadecbdceecacbaeaeedddeccaccdaceedddbeddbdcaaeabcdeedbbbdcabeccecdbceddabeedbadecabbcdbeacaeebdccedcacbbecadeecbaebadecdaeaecabebecdeacbdeabcaddbadbeccadcbadadbadbeaaaadeeaebddbedcecadcccaabbbcbaedaedceeeaddddceccbccadebaeddccebbbaaaeddbabeebabdabccbdadcdeeabeeeebeabebeabedccbebccbcbedcddeaadaaaeccbcbabbdcedccbebcebecbdaaedaecaddaaccbceadeedcccdbcceaeaabeeddddcebaccadbcaabeabadeebaabebebdaecedcaacccaecdadbecabaeceedbeeecaaeaacbdcbcaaacabaacdedbcbdabaeddcedccadcaababcebcceaeaaebeeedbcdaeabbbedcebaadeddbaddbebbbddbdcedbeadeeeedbbdeeddcdeedaeaddaadedecadeaccabeaacbababdceabbdaebeceddbeebecbaebaaecacceccdddabbeadddcecabecdacbcdcacaaaeeedabeedcdecdeceddedaebceceeeaeecbcbbcdceeeaaacecaddddbcbaabecdcbdbbcddebaeddeceabeaedbbdcdadebdddaabaedabadbbebecdccebadedbbabdeddbaaedadcdbbbbdcbddecbbcbaebdcbbcaddbbdcdeeebceaeddcedcccdadccceabddbaceabeeaebbbaeaaedbdbeddaccbcbbdcddbdedbddeeaabeccbdcaedbebdaadcbdbaddcbbdeeddccbcbadeeeddcbbbbedbcbeeabcaaebdddebaaeadcbcbecdcecacacbbbcacacdbdbbbadecbaaeadbdbdcedcabdbaebcacbdeecdcddcceeecbabaabecaddddcadebeacedacacadcbdddadbcedccdbaccecbadaeeedabdebcdecedebaaabaeadecaccacdbdbcbcbebbccdebedbcdebebbadedaacddbdccdbddebbcbbbbbbeeeeaadcbecabbeadadebccbacceaebdbeecdaacdadacaadaaeecedaebeaedabebaaeacadebedcaeacdcbbadeabdcbccbdabeecdedacbaadbccdddbadcccaabbebdbbabbecbdebaccbabdadbbeaaceabdadadbdbbeedcdcdbcddbbededededaeeccecddbbaabeeaeeaebadcedcbcebdcececcacceaaccaccaeaaecccaabaccbbbeacaddbdedcacddcddbadbcbdbddedddecddcaebdbedeedadaadbaaacdcababeaaabcdbdbdedddbabbdaccebaebbcbbdbbecccacbdbcaabccbceedcdabdebbaeccbccdebabedcdcacdcaeaadbccdcbbcebecdbeddaececeedadabcbcedbcaabdaeaacaeebaacbdebaaddcbcacebecbbdbbdadccbecbedbeecceedcaaceedbccbaebddbdadbbadcbdcedceeeeceadecbbaaebaeabadaeccdbcbcabeacbebdecabbecacbacebaeeaebaaacacdcbecbdcaebdeabdbcabdcecdbdcdeccacbacbabdaabccddeeaabbaadbcaebddbabacdbbbcdbeadadeddbaceeaeeaaeddbbebabaabccacabbabcccaebecbaedddedeabdcdaabcecdcdbbbddbeeeaeecbbceaccdbcacadeabeadcacacaedaababbedcbeaabeaedaecddddcdbcebecdcaadcdcdadcdecbcaabceecbaddebcdabdabaeedcaaabcdbdbbeddcddddbedcaecabdceeccbcaaeceddbbcadebcebdbbbabddbececcddbcdaadacbeaedebbdadccdbbbeeacbebcccdddebcabbbdcdbdecbeeeddbacbedadcbeaedbaabaceabceecebebdddaecabacdeaeebcbebbcbaacaaaceedddcbaaebeccaeeeddaaadccdbbeecaedceabaeccabdcdeaaebabebacbebdacadbbccbddadcacaceeacbaebbcebcdbcbaceedbdeccbbedebcdbbcebcecacddbedaedcdacddeccebbcdbcabeacbddcbdebbddbcdbdedecdaebdcccbdebcbcbdebeaedaabdeedccabccabaaadddaddccbaaaebccccaacdeaeebdabaebdaebedcceeaaddbddbcdadccdedabdcbbdbbadacbacebdaedccddaadbaebedeadbdedebeecbabeecbdebbadabbadaddcccdbabbdbcdbbccecaedeaebcbebaabedcdbebcaceaeadeacbbedabedacaecaaaedcedecdcbbbbbadcbabeccadeaaccddebbccdedebadeadeeaedcbdbeddbebcaebbbdeaccedaeeadcaacbdebdedcdeeccdaaeddbcebeabdcaeeceeacbceaebdbaedeaccaacdbcddcdeaceccbbcadaeadbedcbbeebedaaacabecabadbacccbacaebecadeeeebebdbdedccbbcbaadabeeccccaccdacbaddebbdbaeccabbbbcdbebcddcabdeacceceaabcebabbdaacacbdcabbceacacadcdeacecceceeaabbcccdbebaedbceabcaebbcdeacdeddebebdcddaddaeeecedabebaddaaebdcedcebedbdbecbeadedeeaaebddacecdabdccbbaceebeacdcaadbbbebaeeabeeacccbddbbcecebaebabadbaddbceeecaabbbdacbbbeceacdccabedeeadcbaeadcaedbbddbdeabcdeadadbaacdcbedadcaecbceccccdcebbbbbadbaaaaedddddbcccdcadbebceaebccdddddbceaeadbdaacbcbacaabdeacdbdcacacdbdcebebebddaecbbecceddaedbabccabedeabccdbddcbbdebabdbabacbadcccdccbccedeabacacdbabddbccddbddacaecbeecbabcdbddebcdecedccbddbcceabedcabcbeaabcdcebbaedcecdcbececeeeabbcaccceecaccccbbeeedecbdecccadddccacabeeaccdcaecbdecdaddacabbdcbaedcadcbbbcddbbddedcacbcaabdcceecdaaaebdcebaebbcedbdeadbeeebacaeedaceeccddcccbeddcdadeddeeddcdedbcbeacbeceebdeacdbbbeadcdcddeedbdccbabacadecbbdeabcddbaedbdbaeeabebbceacddedbdaceebdbcdeeedcddabbeaccedbbcdadcccdeeebddacaebddddecdbcdbeaaacdbcbeebbdadaeddcacbccbcbbacbdddcdbebecababecdeebedcedccabcdaaebcbccbcbbaecdbacbdaaeceeeeddeccbbbdacdebcadaeeebbacbdedcdadeadecbbcedabcebbbedabbcedabbebaaaedabbecddcdbcdbdabbabdecbabdbddbeceacbeccbbdcedcebecdbdbccadacdaadedddecdbadbddcdababaecdebbcbdbeccccbadcbaccedbddbebeeacecabdcaacebdadbaeacdcbadcbbebbcceddbabcddeadbecaccdbddecdddeebdcdebcadacadbddcbbedadbddbdbeccedebecdcaddbcbeccaecaecbbbedbedbbdddbcaaccadcdecdeacccdacddddbeebbdaadacddbdccceedbecccaadcbedbdebecbbbdedcebdcdeaabacbeadcabbdbcbbedaeccbeaccdcaeaacaacaabeaadeddbdcbbbbebacaacbabadcdccbbbbadaadaddecaebecccdddbdceebeaecbcdedeeebbeabcbaedbcaddcecedacbdbcebceccdcdcdeddcbbbbecbdbcdebadacddeaebbbabddacacaeecbebabecccdedadadbbcccecbdededcebdbbbabdceedbabaccdababedacbeacabadbcdccddbeddddcacedccddaaeccaeebbddcacbaceaaedcabadbcacadeecaaeccabecedcabbcecaabeadadeeaaaaedbbcaaaabedbaccbbbbddceaabbceaacddcbbecbdcaaacdacddaaecdaaeaaaadbcadadabbabebaeabbcdcacddcccbebabbcdadceedeecbeadbbaccadaddcdadbaaeebecbdcbbddbeeebecaeaddebdbcbbcbbaecbcbdcadadbecbeecceaeabecadaacbdebcacdcacaecdebacdeaacaaebdceeccdeaaacdbadcebccadbaebecdddacabadcddccededbeeebdbebedbbaacabbcccaacdeacbedcddbbbaddadecbecbdbdaddbaacaaaadeaabadbcdbbaecaadccbdaccaedadbdcdcbdbadcacdbaadeebecbababaeccadaebcbcebcdadacedbeadbabadcdccbebbeaadeeacceddbdcabdeacabdaddaecaaeedddbabbcecdaabdedcdcbccbbdadaceaaeacaceecaddaccdeedaaddebeceacdbbabecdbcebdabecaeccebbeaaaaeecbbadedebbbcddaadedebcbddaaddbdebecabbcbebcaaacebbdeabcceccaccceccbbbeabdeedbdadeebbddebbabeebaeeabccdaaacaccbeeaeaecacceacaeaaebdabbebcedccdbdadcebdcdbecadeddadcccccccaeabebdabeaaddbdcbaedbcaceecadbaedbeccaacdbbdeeebeedcccddeccbaeabddabbbbccaeadebddbbcbeebeeabaecbceeaebddaaaebebaaedeaaeceeeacddacbaaececbdeeeddeadceaedcacaaedbbeecedddbebccaedbcaadecdebaadbbccdccadedaedbdadbacaebcebccbaabbabdecbebcbadcccaacaccbaecdecababceeccaeddebadcddbbcdadcdabeecabbbaddceeeeadaccaecbaecdbcbcecbaabceeaebccebaecbebcbeaadbdcbacdacbdbeeaecddebecdbacacbdeaadbaebaacdcbeeebdacecbdddcdbcacedbededeaadacaccccdbcaeddcaaceaeedccceacaedcbcabdcecbbeaacecacbabdeabebeadcdbadbaeabdeaaacaebecbbecacdaeedeeebaeaaaeebaebbdeacdabeebdbdbdeeadebeeedeaebecabddeecddecdbcdcbcaeacccaaabcccabecbdabccaabdcbbdddeacdcceccccabeecccabbcadbecabcaabedeeddcccbbbbdecedaadbdabbddbbbacbbacceeaecdbbbddabeddeccaabbbcdacdedbbccdbdcaaabbbaabebeebadabadcadaecaebedebcecceeaaebabeebccdadedbcaedaeddadcedecedbebbaccdbbbeddeebaacbbbbcddcababdddddabbddaebacccbecddbdeadcababdbbbcddcdbacdaeddaccedaeecdddabdbcecceecdbcabbabebbabdbbecdacacaabbecdcedeaaddaebdaccacacceaeaceadcebdbccabcddcababaabbaaddbacadcbdbcbacdbeaaadbcedeeacddeacdbcdeebbeedadccbdddcdcdacaeaabbaabbdcacacbbcbdcdeabccbacdbbbecbebaccaebedbceccbbeacdaeddedcdabcedacadbeeadceedecdddcabdaceacbbdccdaacadaebeaadcdeacddcecebcdebaacbeabbcedaeecaeccbbbbedecacadbaceddbeddcdadcbbaebdeeebbcdadaccdcedadbcdacabebdebeacebaedeaeaacabcdeddbdbedcbcaaaebbacacacacdbecdccadabcddadcdecbaacabcdbebeeaaaddbaedadbdeabddbecdcedaabebdbedbdcccaddddbedddabcdddebbeccdbcdebcecadebacbacaedebeeadecdcbdbddeaaeeebdcabbdeebcbecbbddedcaccdbecbbdedaebecedeebbdbebdedadbaacecbedbdaaeecaccbdabcbabbdabbbbaaabedeadeaababbdeccceeadcccddddeeadaaacadcaecdbbdcaaeebeecbceadeadadccebadeebddaadeedbddacbbeeddbebacdddacebcdebbecaaadecbccdcdebdeaccbbabdacbddeaecdcdbbcabddadadbdadcbcaadbccaaddacdbcdaacaeddeaadbecbddbbadbabbcddcbeacaaaacbccaacdaceaacaaaabccadadabadddbecaeebceddcabbebcccbecddeabeadacceadcbecacaaccccdbcbdecdbdaddedbeeacccebedbbebcacdaeacaababecabeeaeacebcbecdeceadcdabdbdabdbacaaaabcbebebbaaddaddbaeccabecccdaabcddedaebeedcccdadedaebecbcbddedbdeeaadadbacdcaddcacbbbddacbaccbacceadadcbcbbbaededcacbdaadeddcedebdceecadedcdccbccecbaaadadbbeadbcbbdaebddcdaabcdcaabadcbacbdedbdeeeabddddeeabdaebeaadccdeabaddcaaaddeedabbdaebabcbcdcecbcecbeabceaebbddeddccdadcccedaadcabaeebccceecbbdbacddbdacebebdcceacebccedebdeebecbbcdebcadcdbbdaaabddcdbeaaabaedeeeabadbaddedebeabdceaebddecbdccbecddababcaaddcedcbebbddacdaabdbaabcebcdbbadcebeecaddbdcddbbcadceadaeebeeabecccdeacbcedadaadeacdadabeadddedddcaebdebcdabdacaadbbaacbcbdabdbdbaeaaeebadeacbdcdaeceebedcecaeaddaddecdecbabcdcbddbbaececdcebabacccaceeebcaccaadcadeaccedbacccceddcbcdbadcdadbbbcebdaeaebbbbcedcedaaddecdebcbbcaecabeaeedbcbbaedaecdbbebaebbedcaeaedaeecaebacabbcadacbcaebbcdaacacbeaaaedbbbaebcabeeccdcbabcedccabcdcbcecaedcdcbbaddbeacdcabeacddcbccaebbbbcabaeeaceaabceeedddbbacebabccabeeaaaaddcadacebebaabacabbdedeacdedbbedbebecdcaceadabdcdaacdadbacaaaabdababaddceacbacbeceecddecdceeaeceadbacdebcdabbdabadbebbcbdcadaaadbdabbdecebeebdeecabccdaacabddbbadbcbcedaddcacbaddbeaccebbdbaadaaecbdcbeaccdebbcdbcacedebbeecdceaededcadddecabcadeaceccebabeaeeceebecaeedceedaaaeeeeeceeaeeecbaebcbaebecdaacacaccaddcaddbeeaeecbdbbccabebbdecceadcecabdedebdeaacaebeddaaddaeaaeecdeaacdeccccabbdccdbeceabbbedabaeabeadeceebceceddbbcbaeabbbdaccadecddeeaceeeddddebaeccbbccacecebaeaeaaeeaaeebabaabadaeeaedeaecbedccecdaeaceeadecceaacbabbaecdaecbacbeaeebcdaeeedebccbbdcadeabaaaeecadacddceeeedcaebdbbecebadacdabbedcdeacbdeeebecddccacabaccaadcccaeeebaeabecdcbdbdbbeceeeccaaabadaebcaabcddeaaebdaccccedeeccdbeadeeddcdceacbaeaeeabbbaedcdaebcaaacbacccdbdbcdccaaadadbdbbcedaebecedaecddabbeeaacaedeecebccebdabddbbececbebaeebbcbceecdddaeebbcaedcbbcccccebedadccbddaceeadbcecdceeddcdbebabcdaabbbcbebadcdedebddaedcadcbccbdcdeadbeecabddaaaadbecbccaeaceccadcdbeccabcebaddadecbbcaadebdbbacdedcebcecebedbaacdbcceecadadbcccabddcdbbeacdadbbdcbcddbceaeaeacbbececbbeaaaeaddbdedaaeaddbacaeceddebeecedeaaaccbebeaebcaaecebdccdbadaadbaecedcebecdddcadaeabcbdbbcacdeeeacdbcceeeabaeadbaadaeebeebbcabcecaaaddbedbedcecbccbebdbadeccecadeaabbcccabebecbcddbbaceaddcaedbabacbdebbecebeaadaadedbbecacdaeddedccaacedebbdbcabbbbbdbbabbacacdeacbdbccbdaadcddbbcbceeadbeaaeeeaaccdddeaeeeebbacdeeacdbeebedbecdbdbaebebacedcdbdbdbceebeeebccaeeebacabecdbaecedecebedaaabadcceeedeccbacaeedbbcceabbcbbceeacebcccbdcdddabaeddcddaddeaeecdaaeeacdcdeadcaaceabcaebeccabbbaddbedabaeacaebbdcbcbdadedeeddadbabbaddddacecdddcceeaccbbeaaececcdebeedbaadbaadbadaaeecbebeaabceaedddadbbddacacbdaaabdadebbeeeadbbeaceaebdeeaaceeeccedeaaedaeeabdaeddbebaceeacdbecededadbbbbadeeeecabaebacadeeebaacebdcadebbdbabbecbdebbacebbbacbcdabcbdbeaccbaaaeedbbeeeedcdeacdadcbdecddcbdcacecbeeedeedbbbbcedcbbecbcabecdcdecdccaacdedccdcbdbabaaebcdcbaaecaddddbcbedbbedbcccbacaebeadbbecdbbceeadbcbcceeaeadabcdaeeeeabdacedacdeebeaeacdbcbedbadaaeaabbedeaadbdceddecdeccbacaadebbebedbaccbbdaeaebeacdaceabebdaebdacdbbceacabdcebaebdddbacccddedbabebecceeecdbdbbccecbeddcbedebdbeadcecebceacaadedebaeeddaeacacddecddbabddaecdaacbbebeeaeeeebecbceacbeaacedabccacbdeabdbaaccbdaccdbaecaedbabeddebbabadaadeccdedbeadcdabbbcebedbcbecbeeececadecabcaddcaaeaacdbbdeebaddacaeeadabacebabdbdacbceaceedecebaeaaacadebeaaddeadedadedacaacececcabdedebeabddbaebcdbbbedecaebbcbcbbadaceeacdccadcdbdbaceecaeebeebcabdecbbbdaccacaccdbcdeeeceddbceddbdbdeeeddbecaaaeeeccaccbbbccecbeabaccbbcbaebebadaebcacbabcbdaddabdeedcaeeadaabddaaccebddcdacebedcebdbdedebccdeceeeeabaabbebbeaeddacacbceeeeaeedcbedaebdbccdddcabdcadeadeccbeeebdaabcaeebaedcabbebacaddcccbebaacedecebaebecaacbeeedcebdecaebeedeaeaacddcccecbdbcbbeadbbeadcaacdddaeeacabccddcabaccbecdbeeebbcaecebceaccccdebaaccceccbbacacdebebaccaecccdadebebcbaddadeebdbbaeddbebaebdbddadedcacdccedbddcccccecdaddbaaebedacaaeebbbaacdceccdbaecbaaecdeaecbcbaaccdbddaaadbececbdcceaaeecdddeedcabdbebdceccbaaccbabdcedbebccaabaaeecadbddbabecedbdcbbbacacddeddebbbbadeddbebabdbecbceddcceabdcabdebbecbadcaedceaacddcebadcbacceacbbaeabecaecdddcececaecdeeaebaaeedbacadbdaaabcccbaabdbebebbcccdccebbcddeaebdcbcaaabeaceaedbbbacabadccbdddacdbddbaaceaeaeddbcbeabdbbaaebdacbeaabcdbedeacdcadbebaacaebbadeadcacdddecbbbcaaaeababdabebdbcdecbeeabccadecbaeddeadecbddaccbadbacbadadbecdbdadcddbbeeabbddacdeebbdddecdaeaeaedceebdacdbadcacadddebbbaaadebdcabddbeebecbeccbadbebeeebacdaecaecbbceedcbdedacdcdabdceaabdebdacadaecaaebbbadcacabecdcedaaebecdbcdcdcccbccbbcbbdebbeccbbaddaedbaecdabeaaceccababaddcdddacbbddabdebcbedabdddbeeacbadcaedeaebdbceadbbddabccaadbcbaccbeaeeeddcdeccceeedadebcacecbbcdaadeccbbecbbdcbeddcdbcedcaeecdcecbaeabbaacdbaedeaadcbbcedaedcbacdcecdcadcaeadbdeaabbaeecddcdaacdceacecedbceeeeeaeedcbcdadbbacbdbcecdccabceadcaeabbdbbedaeabdaeaaeaeaddaecdaebcdeaaddbcceacdcecaccecddbbaecebdbdecdecddebbababeccadabbccecebaaebeabbdeacaddadbcbaedecdccdcbcecdabaaedadbbbeacaacecedbdcbcbdbcbabaccdcacdeebedaeecdcbaacccbeccaedcaadbeeabdadccaedbbcbbecdebdabcbccdeeaaeecbadbbdadbeabaaadedcdeabbbadbcecbeedcadcddbbebcededaeecabdeaabababeacbeeabdbbabcdcbdeadaedecdccaeddddbadcdceeccbddecbedadaaedbddbbacccebdcacabcbbeaebabbeecacedccdbedbdabcadaceaacceabcdadbbdbebbbbcebadbbdebdebebdacddadbbdbdbdecacdbdbbaebdbebadedcccaaeebbbccecdbadadccebcddcdeabdebdebeaeaabeadebeadecdacccaceedeccccbdabeaddaadeadbadedeabbbbadabbaadeddddebcdeccceaedaeaabdbbabdaddacecbcbabbcadaddecbbcaeebdeadbebadbababdceddbbadcddebacdaddaabdcbaeecebcebaaebeebdcaeeebacaccbeddceecbdbdbdbbaebcddeeebdcdbbeacedbbdceeebccbbdeccbbdbccadceabedceeeececbcededdeeebbeebadcbbcccdbdebebdcbddabadabcedbacadedddeadeabaeddecaaddaceacacebbdabbbabceabbedacdabeadaeebeaedbcdadebcbbbdaceceaabcaabaaeedabceaaacbdcaededeccedcbceeeebaddaaeebdcdbeabdcbeddaadebccbdabedadccccdbeebeedbcaaadbbdceeacaadbdecbeaccacddcadbbdcdedbadaaaaaaecbbbcbcaeedbdcedbddecbebdcecbbaeceadaedcbadeddaadedbeabcebeebdebebabedabaddcdcdecdbdbeaadebcbeecacceeedeaaaeccedebebbdabbedabebedccedccdbdddcccdabceeeabebecbeacdbaeaeadadeccecddecadcdbdbbedbbcaacbdeabbedadadaccaabcdcdbdeadaecbaadbbecdcededdccddbbabdaabebecebcdcaebbbedcbeeecdaceebaebedaeabcdecbbcbbcbdadcbbdeedbcbbeeddcbedbcbaecdbccaddddbccdbcebdecdedbdbccbcbdbccbddddeeccbdeaecdceebcaeaccedacccaadcbbecebbaaedeecdbbcbaacbacebaadcbdddeaadceddebdcdccccabbaaedbbdbaeedebdabdacccccaaeeecddcaddaadbcdedadbbceacdbecdbdbedcaccecddbbddeeadeaddeeebcdedeecadeaebbbacabddbdbaabecbcadedcbccbebaababdedbbdaacadaebaecaeedbcddbcabadeeadbeaaadebebdebabedcccecdeadbcddeeabbeeebaacbadacbadcabeadaececcbdebeaecadcbebeeaddaeaeaacaebdabbdaaeeaeaacbbdbeaaddabdabadeeeecacbddaecddbddccbdceabdddbdccebecbbcddeaedbceccddaecaabeddbadacdcacecbbcaaccddacdbeeabdbeabcaecbebdacdecbdcabbaccadbabeeededcabaabcdcabdabdbabdcabeaaccbbbdddbadcabdbeabeeecbdedaeabdbbbcadbcaaccabbaabedddbbaedcbdcedadccaeacddabedceaabcbaebaedbdaaaaaebcbabeecaebeedbbedcccccbbadabebdaababedbcdddacccaeaecaeeaecddcdaecedcabeddcdabecddddddaaaedbbcdddaebbeeacaaeaecacacbedeacdedcccadadeecadcbebddbeeeaaddcdedcdcededceaabbececeebadbbabccabebccecacbbcdcaccaeddedeacbccdabebaaedabebdcbbcccbaeadeaaacdbcddeccdaedcebbbbecddeddcdaddbdabdcdcbcccbcdaadedddbacecaedaebeedeebecbaecddcaebdbabcbbaedcbececaadaabbceecebcbbecdaabbeaaedbdaeabacceceeadeebbdaadddabcdcacddbcaabbebdbddcdaaaacbadebdcbccadbbebacceeabceceeabbedcaadedeacabcceabbecaceebdaceccbdaebadecddcdadcdbabaebecdaccdcbbedddeecbcbeeeccedbedeebdabeddaebebcdccaddacdcaededeeddbdccdceacabbeeebdebabcccebaeadedcdcbdcbdddabababaecadaccaddeeacdbddecedbdadacbbdeaeeeaeecddcddeecbeececbaaebacbdbdaceadbcdbcddaccdeacecdddebbbeabcbacbaddbeadbcedaadbecbddcdaabcddabaaeddbecacccedeecbebdddecbcabcddebcaddcacbcdcbebaedccbceccbcdcbbdeaadecabccdcdabebcecbadbbbabaeeedaeecbcdbaebcaccbabcbaccdcacadedddabbbaddebdddcdcceeeabedededbacecebabaaddbbeaaceaadcdecabbceadadcdcabdeabecdaedcbeabccdeacccbdddddbdedebcdbcaeaceecacbcdbdcbdeeedceedbedbceadbbadbeeecabadadddeaeaeebbedaaabbcddabcabecddcdebadaedeabedcaccedbcdbcbeebcdbbeadaccacbbeddebecabceddbdeabbebaaabdcaaddceccacbaadbdcbddacdddcbbabcceaaadbadeddedcddecaeecbdadebabccceaeeecbcecdbcacebeecbeabbdcebdbcdcbabaebeebdbdabddcaedeaedbdcbaaddcedededabbbcddbaacdacaecdeabeedebbccbaeaaadbecbdcacdabacdeacecbaeebbbbbcdeaaddbdacbcbadccdebbebdecdaecebcdbaccdbedaedeeddcbaaadebbcbcecbbbdbabbdcdbdcbdbabeeacabbdeecddeccedaebcddcbedacebbbbbbccdecabbecbacbbdbdbbbbdbbaaadbabbdccbddcaadbbeeebebadeddcccceadcdbddbcdadededbcbdbeccdcdedcddaeeacacebbdeedeacdbddeedbeedcddaecccebbabcbacdbbdeeddcbeccdeaeaaeddcaddababacdbdadccbdaaedcddadceeeaaacecebdbbdeebedcacbabddbedeeeaacebedcbbddeaadadcccbbdbeedbebebebedcaecdeeabedeeccccbaaecdcdaadccaccdeeaecdceadbedbabdcbaabbaeeddcceebccaabcecebdeacadabaeebaddcccbaabdcecacaadadcbbeaccbddebcdceadbdcdaceacdbcdddbabdbcccaeebccbbcbbecaaebaabebceeadbcedcebbacebcbdbaecaeecdeaecedbeddbecbcecdaaacacdcebebbecbacabebdcbdebcdeedadeadcbeadcabdaecbeeceeddddadaeeaeeabeeebeedcaeeabacbcccebbbcebdcaaaadccbbecceeebddcbecdecdcccbacaacdeedabceedbbaabedbdcbeecaaaabebbcddaadedaebabedebbeaceceebcebddbdcbaebcddadedebdbacbbcdccbccdcededcebcedbccdddaebacbcaabaeaaccdabccccaeccebdaddaabdecbaadcccddbcebcdddbdcccddbedcdacadcbcdccabbcebacbacbacecebdaedbcbcdccedadceeecaedbdaabaebadbaceecdcabeeeecdccedcebeabbdababcacaceddbcbdaceaacedaadbdabeaedccedbacaaadbeebaeebabeacabbaddebacdccceddeacdccdceedeeecbbeababeebcbabbddbccacdccdcbddecaadbbebabaaededabdeaaddaeddeebcbdabeedecbbeeddddcceedaabebaedebedabbeeaceebadbccbdeccebebcbaddcadecacaabbacdaddacadeaddcaabcecaebbdeeedadaceceedaaacebbbbbcdedcacdcbccbdbbbacabcaaebbbadeeccddcbaaaccedcbdacddaeabbbcdbccabeeeddbedececdccabbcbeedbbacdabedbaeacccdbbbeebeeedbecbaebedbbdcbaaacdcddbececeddcaaceccabeeececbcaebdeeebbcaddadbdaebceecacededddbebdabeddaeececadcacaeebedccebbcacbcbcedbcebeddabdeccaadadcacbeeccadedaeadecacddeaacdacceeabaebbdabcdcecaaeababedbcbceaababbcaccbaacaabdadceabbeecbeacabceaedcaadeacedddececabaeeddcbbabebceebdebddedbdbacdddeccdcabbeebbbeadcebcacecadbddcaeabdbdbbaadceaecdcaeddceddcecbddaccbdcbadcdceeebbdaabbebbbdedcddcdaecbabdaaddaecacaebcbbeabdbbddcbceccdaaaaeddcdabacdcabddeccbdccadebdcbedeacacaeaaebcecebccbdccedcbddbcceaadbdedeeccedbebbcaedbeecdacecceededdaabcddebdbddbbbbeacebbddabcccaddebddaecdcdeceeeeaacdaaaaeccadbaebcdbcddbadaeebeacadeaeceebddbbeaadacedbebaecbbeabcebcccccbcccccbdbedbdcaadbcbddbcbaceabeaaacdabebbddaebacbbdaeebacbdedccaacbdecdcddcddcbbeaecdabaaecddecadedadaadbeedebacacecadedddbcbddcbceaadeccedaeebddcaebdaebecacdddbbccbddbcceedbeeecedaceedbdcabcadccedebededacdccabbebaeddbcabedcdeebbcbdbcbbaaeedbacacaddceabcecbeabdcebbcaaadcaddddeeeccebeeecceacbadcaeccddacdbabbecacdabccaabecedaecaecececbebcedeeecbabcdddcbddeabddaeeeeabbeaedabcabbeeceebbadbeeecbccdbcbabdecacdeecbdecebaecdcbeaccdddbddbbebbabaacbbadaebdaedecdeeecabaaadabddbdcbbdbcceecddcdaaeabbebddebedaebbbebbbbddbebdaaccddceacdccedcdbceeaedbdeeecbeedbaacaadcdecaceaeecdedadeebdebcacaddbbccceedacebacecebcddeaeeadacddadbdacadbcddbeeaaaeaceaeaeadecedcadaecddddaedcdaebbcaaabcaedbbeadebcddecbebbddcabdbadeeceaceccdbccabdecadaacdbcaeedcaebedcbcbebedeacaebdedeccaeddebebeaaedaddababadbeaccceeacedebdcddcaddbacbeceedbabbacaecabdbdeacaddddbaaeaaaaeacaddcaebdcebcdcbeedbbddcbcdabcadbeceabbaecedbcbacdebcdcaebdecbdcdedddcbbbcdceeadaadbbbceababcceacbbccaecbeacadcecbddbbcacbdddbbedaedbcbaacdeecabdcaabbcccbeeebcadeaacccebeaadcbbbababadadbddebdddbbcebdaeddadabdeacbbcacceeaeacdebabaebdadbcecdededbcdddaaadcaecacbeaaacddedceddaedadeaeddbabacbabccbedbdbedbbccaecbcbbaedabcbeaebbaaebedcdaeeeeabdeeaeedececddecabccdcecdabcbdbddcaeeadecaaaedbdcdaecceeaedbebddbddcebbeedaccaecdaadcdcaddaccdadeecbaeaedcaaecaaadbcebdaeeeadcddeececbdcbcacadaaebcccadddccdaaeeccbddabdeeeeedbaadeebecdbadedddecbccabcaddacaccceaaabcdbbecaddaeececdcbacbbceaeadeddececadeccdeacabeaeddddddadbdcbcbaeccebcdcbdebeedaadeaeddbeccbaccecdedebdeeacdaedbdabceaedeaaadbacebeecadddbedbddcbdacabdacdcbedabcbddceadeeeddaedcacadeeeadbcccecbadbacbacdbaaaadbcabcececdacabbdcccacbdbececeedbebacedeeadbcddbabccadbeccbbeaccdeddeeedcedebeeccceeeddaecedebcdbbccabdbcccabcdeadaaeddbcebcadddcaadbdcdeaddbccbaabbdcebdbabeeebccdbddcaebbacceaebbabecedbaacadaaceeadbcebdbaecaaeceededbccacbddbceadcdcbacdebbaaacdbccdeebecebccbdaaacaccecadebcebabccaeddedddbbdaedadeecabcbaaedabaedbcaceadaedaedbebadcdebbadceaaacbcdeceaddceaaedaaecdcdbbbbdaacdcbaaedeededabaaedcccedebaabaeddbbaceebcadaadadbeacedbdcacaddcecaeaaddebdcecbbcbcedcedbeaecaaedcebaedaccabaddbbedcdcebcacddaeccababcaecadbcdcdabdcdcbdccbbaacdabcbeedebeccccebdeaaaeddbcaecbecbeebcedaadbdaebaadbadceeecaacdaacbacbcbcddbeeaecdceddaeaacdcebbbeadacdbeadebddddccddbdddaeaebdcadaaabbeccececbadccacaeacecbaccbedecacacccccaddabeeeadceccabbdacbdaaecbbdddbabcacebbbaeeeceaeeaacaaaebadcabdaeddddeeebacbcedbbcabeccebddbddadddabbcacdbbdabcddeccedbaabbbebebbeddbeeeeabaebbacbaaecaabddbbbeecebbbddcdbcdeecabcbadcdcccaedaaecaecabadcaaabdccbcebbabdcdebdbbeabbcbeaaacaaaeacbccecebbedaadbdbbccecdabcaddcdbdebcaaedcdbdbdbcbecebdcbabbabbaedbbbaaaebeabbbbeddccbedaaaeeabdccabccbaadbddddcadcededaecedddaebccbcbacaabcabaceabbcbddcccacdedaecdadcdedebbabadaccaaccadbdeddcceecceadeededcaeaacaabbadbcccaabbcdedbebdadacdcbcaadeebeedabebaaaaeaeaaeacedcceaadbbadcbcedcabaeccaaebeeaebdebeecabbabdaaecbedaecadbceeeedcededadbbebddeeeddabaecaaacdeadebaccebcabbdbdaaeceeedcbaababebaaaadceeedbbddcaeedeaaabbcecccdeeebaaaddbacccdcacdbbeecdebcaabddbeecdbaabaaaddcbceaaaaccbdbcdcbaebceeddeedbdcbabbbaadecceececabedadeadcdcacadacccbcedbeeeddcceeabbdcebbcacbedbddbbcabdebeadbbbbecdbacacdbaeaccaecbccaebcbabbcacbdddbabcabddcebbcecccabebacebecbdadbdcdeabebaaaadcddaecedbccbdeeabcbacccccdecaabacbeaccaabbdaddbdbdacebbdedcddbebbcdcbbecacdbdebaadaaecbccbbabbaeabeccbeeeedbbabbecddadcdceedcaedeccdccadaaddbbedcbbdeeaebaaebeceacaebebddbcecbccedccddbdbadcaadabbcdcaacbbdcadaebabcebbebcbdcbcbecbadabbadeacaceceaeeebbdaaaabdbdaddbddaeceaecbedeaeeaaebeebbecdecdedeaabbcabcceadedaacabccdacdaabdebbcbbabeadcaedbddbabbebccabddbcbbacaeaeddaabaeabcbdccaeccbbabcbadeeaeeaebecbaacededeaaebaadaaebdddabdaababbcbdeeadabcaceedaeababbeeaeecbedbbcbaeaeaccbeedbaeadeaddacbdeecaeaebcebbeaececbcbccaeebbaebbeaaededddecbbaeabcedccaeedebaabdcddccceccbaaebeecddacbbdbbaeacdaaacbdeecaeeddbeadaeeabbdadcaaaebeabecaeddaceacccccecbcebedccddeeaacdaaeedcececedddcaadeebaacaaabdeccdaebecbbeeebaaccbcaebcaadddbaaceebdcebdebaeabcabaaabeebdebdbebeececeabeddceeeebaaaeebecadddabaadecebbeadcebdbcaeaeaaaccbdbbddcabeaabceedadcddeddaacbdceebeeadaaadceddebadbbeaeaeacaeaebebcdbcaeedabebedbaacabeccacdcedbbbaeeaabedcacaaebdddbaecbeebcbbdaceabbbceeabededbbbdadccaabebeaccbbaadaebdadbcdcdaccdcebdbececcecbbacecedecbdccbbeacebdceedbeaecebaddcabdedbdbcceadeeabbdacabaeddeadccdbdcdaabcbdaacadcecbabbacaacbdecbbdabdbbadaedaebcaceaaedddbcababbccddedadbebdacbeadedeaccbcbcaeeecededbedebcadbcebecdacecebbcbdbcaccddbaacaadadcccdeabdaacdbbeccabeddbaecdcbadceaadaecbebbbeabdacbdddaecdeaaaaddeddbbbdeadbecceebddadbebeccccadeacaeeddaddbeeaeaaebedbbcbaabbbeedebdbcbebdcbcbdccddebbadcbbbdbbdeacaccbaeeeabeccaeebaeeddabacdbaeaecddbaadcdaaaaecadedaabbcacdaedaebaabbacbdeabeccedcbeabbaedbaccabcddabdcdaeadaddcddedceeabcdcabbebddcacadbbcceeccddaeebcaeeeedbacaadecdadcbbbeeacebbbecedacececdbddbedaaebeceddddaddecedcaceebcaeddddaeebeccdacaccbdeedbaaaeacdbbbbdbcdaabcaebdcbecdadaebddcecbdcbadcbcbedcdceeeecdaadbebadcbaceaddeaaebdcddbecaeebebcebeccecebbbadacbebacbaccbdaabdbdcaecbbbecdecbbdaacdccbdecaeabdebbaebebcecdddaeecaeeabceacbbedcaccbcaedadcedcaaaeddbacdebbbeaebaadbcecededbeaaaceeaadeedcadacadccdaedecbdccebedcccbecabababbecebddbdccddccaccaddeebccaededbabecaeabbceeddaceabceebbcbedaeedddbeaddbbbebddedebaeebcaadcdcddbeadceadccecebaceedaedeadecabceedebbdaaabacbbedbdbdcaddddadbdaebdbecbeedaabdddcabbbddcdcaaaccbadccaccadaacbcebeabaceebebccebadcebbaabeedaadbbcadcbeaaacdbbbccacbedadbbbbbdaeeedbabaabbddeadbcabeceacebaacabaabaadbadeeaeacebddcdbabadabcbeaddceedebbbdcacbbcaebcdadbeaadaacddcadaebbdcaeadebeacbdceedaeabeadebaccdaecaabddbeacabaecccaedabaddeeecaebcdaaaadaebacdadbebaaaaaaedbedeaeccbeddbbbeeadddcbdccbbadacdaaeaebbbdeadeadecacaeeaaddebcebddbecadeeaeceadcbdeceeabcbbaecdcceebbdcedcbbbacaeccbbaadacddaddbcecceabcaedeaedddadcedadebbebecdedebcbeaabecaddcccacdbcbcadecbaddabaddeadacccbbdcadbdbeeeeabcbeebcadbdddccdbbabeecbcceecdbdbcdaebcaedcdceaeceedaecbcbbccbaaabbedaedeedeeabaeecacacbaddeceadbadcadeebeaecccbaedccdecdaceacddbaeccbeadcebaabbbedbeaabdcaeadeecebeaccebaadabacbbebeaaddbbebecccaaecdbecbcdebdcccdabbdeedadaaadaadbbcebedacddbbcdbdeaebdebdaadecddeddadcebcbccdeeeebdeeeaabccdaebcaacdabaceddccdbbeabdcecbcdcaedecbdbcaddaaeedbdddadeddbdbeaedcededdddacacbbeaddaebadddaeaabdbeacbcadabbdccabdeaecaeebecdaaccabbadeeabeaccdcacddcacbebeddcecaaddebbddcaaacddbbbbbccddbcacaaacbebedbaadeeedecaacedadeadaaeedbbdeacddaccbadbbbbcadaaddeaadbcdadcbdaadccebaaedbcecaeecbccbcccbdddccabbdaeccacdaeedcabedcccbbeccbdbabebcbcbcbaecbcdcdbddecbecddcbaceeaaabcbeedcdaeeabcbddaeedceccbcdbbcabceeaceabadaecbcededccacaabbbebacbeccbeebcadbbedbbbcaeceeddbeccebdbbadececbcabecbdddceadebcdbbcdaddcdccbecbddecddccdeaddacbbbbdaebaecccdeaaebdbacbaeaebdbdedcbcaadcddbbeabdacbccaadbcadbcacbcabdaacbddcabeeeccdbdaabedabcbcccebeedadddeadbbddcbdcbbdecceeaddeeaadcacbcbdaaaccbaaadeacecbcbecabbebabdcedadbccbcccdbaccabeacaedacceeccccaeaddeebbebdbddadcbbedcebccabcadccbedbcadcddbcbbadeddaeaaaabdbeeedbecbddaeddeaecedecadacaaccdbbdebceababbcceecedeecbdeeecaeabaeeabdeebcbcbcebcebcccadcbcaaddeeaddcdeeabceeeabcdaeabadeedcccabbdbabdeccaecbaccaeacaaabebadaccbbcadceacdebcaadaabebbcbecebbebcbedadbdeeadbebceeedbcbadbaecbdcbadccdecbddbabccaededccdabbdadbadbcddabeaadbcccdcbeaecebcdedaddcbcadeededbbcddabbadaecbabbdddebcdacdcdbbbedcbecdaedaadceacacbaacdbaddceedddeaabeccdcbdeccacbdacaaaceaebaeddebbcaaccaaedddbeedebebcaabadececbdbaabebaecbedbabbddadcadadbdcabbabdeaeeaebccebdceceacabecceceebbdddacdaeadcddbebbaedcdbadabcbacccddcaacbdeebbcadcbccdcdbdadabbadebcecedbaedebeebeabdecbbabcbbeceeddaecaccbdbbadbdddeeeebcdabcdeeebceddccddacaabbaaebecbededabdacbaddcaccdeecabcbdcdbedbaaedddbeddcdeddcebccdeedbbbdaebbababaaccbddcecbddbbddbaacdecaebbdacadadcbadbacedddddeccaeedbdedbabcccccbdbaaedbbccdbcbccbadcddcbacbbdedaeacdaeebbdccbcdbbadcdadcbeaaaecaabdbcdeabaebccccbeeddeeccaaebaceebaeedbdbdabaaeccddcdaceeededeccccbcaaedebeedcdbadeeaebededeacddbccaceaeebcaabbebadecbdcdaeacddabaddeaabbacbceeaecdbbeaceedcceabeddbcdebeaabdccccdbcddcbdaaeeaebccdcbccabceddeaceebabdccbcedabaddeccdaeceeadbaeadcaccecdabbaecabeddabdecaebbdceebcaceebbcaddbeddeedaaddadaeddbeedebbeddeadadceebebbbddeaaacabbbccabecccacbbddaebccccacabbbbebabdccdbdcddcbadcedabaebddaaeabccddcdeddacedbdeaaaebebebaaecabdcdccdcaeacdadaddcaecadedabebaebbaaeaedaebedaacdbaaaccdddccacbcccaeddebbeccdbadbbdebbedbedbbbcdaeecacadabedeeedebebddacbeebdedaedbbccaaccbaeeccdeeeecceccdabddcababeaceeeeedbbeaadacdcbdaecdadbacabdceaeebdcbaaedcbbeaabdebbbacdccebbcbcececabbbbbdebbcdebbaabaceadeadddcdedcdbedccebbeaeccececcdcdbabbbbbccbbbcdbdbedbcabeaaebbcdcaabbdeaacaddbabeccccabaebddcdbdcebaaeeaabaebbabacdacbbcececeaaabdbdbeeaeecaeaadebaecbcccbbeeeaecdadcecacbedaecbedeaacdcbcbcadddcdbeebbbddcabdbceccbaecccbcdaaeedaeddbbcaebcdeabbdeabddeebbabdabdebaddeecbcdcdcbaedbabcdbabaacbccaacebbebeaddacbeaadceaecaadcdeabedecdcacaaaababcbeeeaebbeaecaecdccecbaaeccbedadabcedddbaedbcbbabbcdabeedcbebcaecabccebbbdabdacdeacacbcaecdecabeeaeeacbbddeacaaacaaebacdddaaebadcadbbbeaacbdcbebccabbedcceaccadadeaeadbacccdbbbabbabcecbecbaebeeeaeeedabeecabdebccabdadebecdadbadbadbdaaecaceacdccabcbadbcbccecaabdddbcdecccdadacddaddabcebcdbedaaeaacdeacacaccdbdceaadddbacbbabebcadddadedeadabcbceeceacebdabcbcbcabaaaccbedbbdcbcbdbbeeabdaeccadbbeebbeacaaadcadbcccbadceecaebababcbdcdcecccdeaececaaddaecddacacaebdaddbadcabadcebecdaeccbdccdecbadabdbddbcbcdaaedcccedddbdcdcadcdebdcbeadaedccecceddccebbcdbcbcbdbbaceaedebdcaecadabedbadddbdaabdecaadeeeccebdcebecdadddbadceceeeaeeaeceabeceedcacaeebccbecadceeddbedbddedcbdebdaeabccbeeacaedeaabbceeaceeababbacacdabadcedaeadaccdaababbcddbdceeadabececacebacadabccbaaeebbdbcdddbbdbcbdcceceedacecdcdaeedbdccdebdadecadbebdbcddcbaabaedaaaacaddbeaeaadbbecdddbcedeccaeacccbdcbdeedadbabacaebdadaddabdccdbbacecccacaabaaddcaaceabbedeedeaeeddacdeeddebddbdaacecddeeaccdadeeabebdccabcdcdbdddebcabcdccabbcebdbdaceedbadeabbbbebbbebbacdadbdcbccaadceccaaedcbecdbaecdbeceeedbbceabbeadaceabcbabeeeccdcbebebecdaccbbbebdbeccaacdeadcaebdcbdbaaacdbedbeddddcacaebeeddedabaacaceccbeabbcceebadbeeedbceaabedbbcaeababedeaebacaddcceabdbceeaaebcdadaecbccddeabeeecbebbbcebbecebaadedacededbcebaeebdbccdbeceeadbdeeacdaaacaadeabaaddeeecbdacdcbbbeabecbeecdeddceeccacadaccbedccebcacaddecbcbdabecaabadddccbadbeadcbdadbbddeddabbaeeececcdccadaccdccdeebdaaeddacdbbeabeaceaeabddbdaaaaccbceeaeccbeaedebedbcbebddcaeecbeabcabecdddaebdbaaaccbedeaaddadcaacccaeeddbadbbaeedebdcbdceedceadecdcecdbdaddadcbadecadbacbaeabacaebcccecadbcbcbdeabbacebbeecaaaddeacaaebddccbedbbebeeabeceedaacecdacaaeaadecbbcaecaaaecdaeecccebdeeacbedecbebceebeeddcabaacbedcecbdadabbcaeabbedddbeeceeeadeacadbacaeecedbaddbdcbcdaabbcccddabebecccaedeabbebdccebddddecccdaabdcedccaaddeaeaceacadbcedaadcaecccecbceaddadabbacaccbecccdacbabaaaccbcddabeecdbcedebabccbbaedcadcacbeecebbcedadedccaaceccdacacbeaacbeeedeaecdecbebaeecddccbdaadddddeabddeebddbeceededcbeaceccabbdddcaaaacadddadebdcbdbdaceedcbcedcdbbbdbdbccbeededcbebedcabdeadbabeecdebdeebadacdaadedbeaeaabecccbdbbcddaebaedaaeededeeeabadadbccccbdecebcbadeaabeebddabacebaeecedbaebaadabaccdcdebedcceabbbdbcddbdecbecbacdacebbababbeddeabcbeaabdebdbbbbadecabddbebeaeedabbaadeeebccdccbbebaabdddaadabcceaadcdadcdeddeadeedbecadebabcddeecbbddecbddaebeccecdbbaacadeaeedbedbdcbceadaadacedcebdebcdadeadbbebdcdcceabdccabedddacdddebdaadcaaccdbaecacabeacdbdaaeccacbdcacdccbecabdaecaadadadbeaebcdddbabdeebbebaabcacbccdbcebadbedebbbbbbeebddaaecabbcaecabbcdbbadcabebeeabeedbbcbceaeeeeaadaabeddcedacaaabbeecbadaeeeddccccedccbbceedeeacebebadabaebddeeccdabaaadbbaebbaddbcccdbabdebadddebbaebdeddccadbcabaeabcababdeaedbdacedcebdceeccdddecabbeeadadcaccdbbdabbceedcdccabbaadbeeddabbddbddbaacdedeedbbcdbbebdbddddeebddebdceeebbdcccbaddcecbabbcbabedbaabcbdadaaedbadbcebbbdeebeabcbeeddceaabaebdaecbcdcbedbcbaceabbbdddaccecbdcaaaaceacabbacaaadbcebeadadbdaccbeecbacabeebeeabcaebedbabbdcaccbbbecaddccaadecdbacadadbbaceebcbdeeddbadedbccbbeaaabbaabadbdddabdededcadcebcededbbaabdeedceedeaccaabcbebbcbedebdebabdcbacdddebabaababaeecbabbdabaaabcbaaabebbebceeaeddabbebbcaddecbadeeabcdcbeebaaaacaedcacbdadcbddbcdbadcacbceebccdbcbeaeeebaddcbdecdeeeebedccccecaacaaebcacaaaceacecadbbddccaaeddcaadbabcedecadedccbadeedcdcccbcaadbddeaecbeeaceecacdccdeeabbdeacccceecacdcedcaddbceacabcbbdacaeaadcdacaccedacecaadbeecbbccebcccecdeeddadcadedabceaadbaebeebbadbbabddeebaabedeaabbbdbdeadbaabdacbdeacccaaecdecedbbbbceebeabbaebccbedeedeccbeecdcacddaeacacddbbcddebbaeaaecebdacbcdcdddababbbaeecbbcaaacaaebcdccbaecaccbbdddeeaceedcebeeabebbdbbceeecbeceedaedabeebbaedbcadbbeeadadaeaeaaedebecadbbcdccaacdbadbcbddcebddbcabcdbeeeaceeecccdabbadcdaaeaceeccccebdebddcddbaaeaaaddbdedecaaeaaccbccacdbdeabaadcdccaaeaeabacdcbeaeeeaaeeeeccaebeebbbaeecbceeededbbdbdbeaaadaaebcaaecacaddeedaceaeedccecdddaebaeacbaadcdddbcacadaedeedebcbabdceebcededecddccedcbecbbaebbebccaecedcbccadddbbbaebbebddabbdaebbbbecabadcdbedcadeedbdaecbddcaddeebbbeeaeabdaaedabbbedabbddeeccccdbeabeebdaebeacbbacbbddeaabcacdaccddbdbeacbbadaeaebdceccdaadedddeebabeccdbcdadcdaeecddeabbbcadceabbeeeaeeebcbdbdacddceabbcdeebbabbeaccccbcaadeababccbbdebbdaabeaddabddcabccadbcbbacadacdaccdebeecacebcbedeaecccbbcabedbbbaddceecbdcbcddacaedaaccabbaedbceeadcaaccecadcbacddeaabdbbabeebeeacccadeeeabeccbdeebbaccebeebcebdceaddabaabdeddeedbbbaadcbbbebccedaddbdcaeeccbeaccaacaddecbbbbcadedaecacabbaeedbeabbdbaadcabceaeebdaabdecdedbadcebcddcceeadedaeabbaaeecbcaeaaaccaddbccabedbbebccbddbaeaddaaccbebcbaddeaeccedbbaadeeeeabbcededcbaadbcceacaceedeacdbbaeebbadecbccabcbbeaaebbccaaeedcdcbbcabcaceeabdabeaaaeeeabadbbacdecebccdddcecceabeedbbdcabeaacbcdcbbdeeceeebdcdcaaddcebbeedbaeebaebdbbdaeedecceeaecddaabaebeddacdeaebdddedbaaaadcaeaaabaaecacdadceadccebdebbcadcabecdccbcabbaebecdbbcdaeaebabccaeadbcaaaaeccbeeeacaaaadabebbeabdaeedaddccdbcadceadcdebddbeebddaadecadaacaccbecdbddebddaadbcedbcaebdccaebbbdadaadabaaabbbcdbbaddeddbedcecaadbadbcbadaacbadcbbeddbadaeccdcadbddbcaabdbcbceebbcadeaddaebbeccccedbedaecdacbabadacbdddacaeadacddbecdcedcdbeccdebdcccaeadceebacccbbbeeccceccdbbbbdeddcccdcacdeaacccbeeacadadadecddbedbabbccdccbbacdaedadcabecaebcedacdeeabbadddcdbaecdbbcbebbeaebdabbbbbceeccaadcedaaacaecaceeccabacccaadabdddabdaaeaacededebaedbaabdbecebaeccbcabaeabecaabdcaebddbcdccbeadcdacdecabdccccecababceeaedddceeabdbdbaacbceaeddeabadeacedaaebcdabeebeabdadaabaeaebbbcceacacbedadecbbacdeaaabcacdaacbaedcdddabbebdcbccdccecdebaeecaeecbacebdaecaecacdadbcbbbbaacdbbecdcaadbeabbddaadbebcaecdaaadebbeeadecbeacdedbeabedbddddeeebbbcebeebdebbadccdbbcabaeebebbcbcbaebbcccadeedaabdeeacbeddbeedbbbbddcbbdceeeebabcabdeabdbcadacedaccbdcbdddbacadbcabbdcccdedbbbbadadeaddcdbbebdbebcbeacbbceddddcddeacdecabdbbeaebdbbcbddaeacbeddbbdcaaccdedcbebadebdeabcbaaadbaeddbcaaceeadabaacdcaceedbaaacecacbdeadadcdadecbbedaeccbebacbaddabdcbccaacdbcbcbaececeddaddabcbebbdecbaedaaaaadcecaaccdcbedeedbcaeecbadecdaebaeabbcedbdbbbebebaedccdbbccbebbaebeeaccaaebeeebbbbcbadbaaebbcabebacdaceaebeccdacceadbaeeabcdebcaabdacaeabbacbdbacdddbaabadeaccdeedeebadbededbdbbbcebddbeeaedbeeaeabdceedcddccdaaaaedeeacedbbbbeeabbaceeeadcebaacebdcbbddabdcdececaabccaaccbbbddbdcdecebacaaeedcecdeecbdacadeebeddbcbaedeacbadbdaedacecbedbbcbcaccedaebbeccdcaddcdcebabdaacdbbcebaabbbeaadddcbcebcccdaceccbbabadccbdebdcedaceeaeaaaabdedcdaddaabbaeabcbdcdeadcdeceeaadcbaccebcbecbabddcdbebaebabbcbbabbeddbacaceeedddaedecdcecdeaaeaebbbcaddebdbdbaabccbdcccbecabedeeecbccdbdbbbadabacadcacedddcbaeddbacecdbeadbdebeaedcbeebedebdaecbedabecaecdaaaaceadeceddbdcaeaabaddbbdeaddebbbbbcdaddabdecddbeabceceabcacbaedaacdebeacddeebbeeeedbcccadceebbebdadcadecaeabbaeddadbaaeabacbdebdbecebeecccbabdbdeadadbbaabbbacbabbecdadbeecbdbebdbaccbecbccebcdeebdaaccadbabcebcdddbeeceedbebdcbacedadcaeedaecbadbdabdbdcdbddcecdcaacdedbcdaabaadabdbaeececbcbbddaeeaceadbdeabcaceacceecdaeeaaececbecddbeeedaeddbddbceedaaedbcedecadbdeddddabcebedaeeeacbeecbaaabaaeaabedbaecadadebeeabcaebabdceebbeccaceddaeedecccccecebcebceaeeaabaaaeddcccddbcdbcaeadabcbbcdebdcdcbbeabeaedbbbdcbccdccbecaeabaadbeceaadbcdbebaaddbbbaaaabebabecbdcebaacecbdacbbbbdaeacacebdabdeadeccbebcddcbeccaeddbdbebccbedbbcbeaeabcbebdeaeecddcbcbcdddcdcccbdaadacadacdbabaeedadbebbaeceababccdccccebbcaadabcecbddacedebdbebcdddacadeadccbdcdebbbcdabecdeacabededdcdceaedcbadebedacdbbdacadedecddddcbdeabbcbbacdadeedacacccdbaccdbdbbdceadcacccdacdedceccdcecdaccacebebddccecacaabacaeadcacddccebaceebdcbeccdbaacaebeaaecbdbccdbeebaebdaacaababcaceaeeaaaccccccecdbedbcdddeeedccccceaccbbbdeceeedeacbbbecdeedebcabcceeaaebaabdbbdbccaedbadadbdbbdeedeecebcebdcabaaedcccebadcaaaabebcacebbccecacebbcaddccecccaaaecadcbcddceedbeacbaadcdbeaecaedecedadcebacdcaebaeeeadeccebcaabbdeedaebbeceaabebcaddcdedcbcdedbddeccdadbadceaacacbceabbbaeeebeaebecbccdbbeaecbbeeccdaccaeaabbebaceebceeadaeaaedaaaaebcababcdeeeababdddaeddecbbceebadbdcbedebdabccacabbcaadaccedbaccdcbcecbdbcdedbbebbdccaccdbaccabaeeeabcbaddbbbcccadacbadadacdaeecacabceadaaabdedceddaabaaccbcbccbeaeddacaddacbebabcdddddddcbbbdccddcaecbbcdceecbeaaebcaeaadcbcbceadbceddaaabdeecabcdadcdebaaaccddeddbeadddebaecccaceebdabcabbebdbeaedbdbdaaebaedcceacaddbbcdedbeebbabdeebcddeeabbedcbdaeaceecdecdbbbdebecbbcaedddecadbdcdcbeebadbdbeadbaedaaabacdacaebaabecceababcdecbaacbdcbcaddaaecebbebdceabdbdcdcabcceeaabcabeaaeccaadcbdddeaeaecaeabbccbececbbbdbdeebddcacacbbadeedcbccdaccadbebddabebccdaaadaaabebdebaaacceccccaacccbbbdccbbcbceedcbacbcdabcddaceebdacaeecccbcbacadeeaceacdbcbdebdbcacadcddaaeebdaddebbbecccdbbadbbbbdeedbeeaaedceeebeceeaabacaaeaddebdcedceebeabcccbaadbdeaccdeeaaeacbbeceaccecdcdbeeeaebedacbedacbdceeaaadddabeddbebbddccbcddebdecbaaacbcdecccbcbdceeecedabbdbaadaedadcbbccebdaaabecdebebedecdbbbebeceabecbebaeaecccbaaadacaeaadcbacbdeeccaaddcbcedbbbdcddabdbeaadeebebdedcdbabebceceaaecdaaeeeacbaceceddcbbbbcbccaaaededabbbeabdddbcbbcbcbbeabaecdcebedeacdeaadeadaaeecebeccbbcebaebdedadbdaecbdcbecaaaedadbeedbddeecdbbbcaaacabbbcdeebacbecaccabcaeeeeececbbcdccbadeabecddcadbeccbbccbebedbabeabecbeecdaaceebdaddddadcbbaaabbaddedecbbaececceedbcadeabcbcdcebeecbbddeceebedcddcdccecdabdcbabbdebbcadbbceabdccebdeedcbcbadbbdbacbbbbadcaeedeceaedeaecaaabcbbcacddeadcabacecadccaddeadbddeeaddbbbeecdcddadaaaccdcbbdeabadbaedbaecbbbedcebdadaebbccccdddeacacaddcbbbeabebbcabaeadebcdebbedadbdecdccaebbbabceeeadbbadeedabcebdcadccaccaeeecbebeedbbbecaacadedecaeadcadacbdaeedbbdbdeaaedabdcadebabbecdbadbbececcbecddcdebbeeadbcdcabbbbdedbcdcaebecebcbacdcccdddcddaeccbaebccabccdadbbdaeecdeacebbdeaabbbcebaecabaebeabecdedaebbadaeddbccdbbacceaddacecddebededbbcccccadcacdcbdceeabcdbedcddeedceeaeebbcdcaaceecaabddbdebbccdedaebaaccacdebedadcadbbddebeaaccadaccbbebceacbcecdeadabdaeaddcbdbadecedadbeeebebbcbccebaabbcdbdddadaacedaabdbbeccecbbdcabdccccdebaedbccecebeddacecacbdddebbdddeddbdeaadebbdaaeddebbcbccbacaeccdeedaadaecccdbabdedabbeadaeeccadaceeaddcbdbbddebcdabedbebdddcccceabbddaeadedaebdababcaaadbbbaababdbeacedabbbabbebbdedeeaddabecadbbceddbcbaadeddbebdddceedcbecdedccbdcebacbdbddadaaeceaabaeaebcdbccdbdeeeddedbdddeabdcaaadcbdeceddaabdbcbeddcbbebdcaddacabccbaeaabdbecdaaadaddcadeaceadaedabcedcdecddcbccdeacedeaedacdedddbbbccdbddabeaabcbeededaccbacbeebbbeeebabedbcbdbdbcabacbeeedddddaabbbbbaeeaaccebbdcdaeadcbacdeeddbbbaabebdebcdaeecdccccdccaaacceccbcbdddeeeaeecaddcdcbadaedeeaeaabbacbadcedadcaccbeccecceeecbcccccbcdcbecceebbbbbbcbbdbbddeaedcbaaebdaecdaccadeaabacdabadaaaabaaaddedabbceabdbecbaeacdebaecbbbbebceccbcbeabebeedecbcaaeebbccbdbbbaeebedcadadbeaeaebacdebbedceddeacdbdccaabbaacbebddbadbceaecddcecabbacabcaabdcbdbaeabdcaebbeddacbbabbbacbeedbbdacaadaaeadabdbabecbeebbcdecbabcdcbddebbcbabbcebaecdadeeeaacecaeddddbdbebdbdaebccddbddadcecaebbbcbaecbaeeabbbedbdeebccceadedacebadcbdedaacbdadecbcecddedbbaeecdededadaeaedabdcbeaadaaebbaaccdbabeccbebeaebbbcacdaeaceabdaebbcaddcecaadcabedbedbdebebddccbeaecaecbaedcdaaabbbccedabeedeecdaeeccdddecaddacdeedaeaaeddbedbadaeeccbddcacddcbbbaaaeadcbaedacadcddaeadeecdeaedeaaabaccbeaabdbdedbcecbeabbdccbcdadbeaaecaabdeaaacabedbdeebdcaddcdddeeccbabaadeeaeaaabeecccebaccccaecddcbacaaceeecadadbaeeceaabebaabdeacbedacdaebbaecaeacbcdcaecececdccbaebbedceddcbddaebcceeaaceccabeebbdacdaddabedabddeeecccbdcbdbadeececdaaacacebeeedaaeecabaecabbaeddaaceccdbceccbdeceeabbbebcdbeadeacdeeaaeaadddaeeaeedbdbcdebcadcaadccbcbeeedaeacbaddeaaaabbbdbcdaadcddcaebdceccddebcadedbccaabbbcccaeececebadbaeeabeebbaabbaabbebdbdbeebcbbdeeaeaceebaceeecdeeadccbdebddcdbbbedaceadecebceddedbbbacebbbacceadcbddbbecebdabcededbebeaebaeedbdbbaceebdbcaddbbcdcbbddcbbdedaadcaccadeacbbecacaecdadadbedbceaeddacdabdbedecdabebdaadbccaedcdeedeedacdabbedbbcbdeaebbebdbaaebebabaedbacedacbebddadeaceebceacaecadcbeeabebcddbcbcaaecbddeabddddecbeeddebeadbceaaceedeecacababbedcdeaaeedabedaaedaaccacbeaacddadecdaebeadaaabecdeeedcceceacbcecadeebaeccebeebbcececbbdabdebebeeaadcaabbdeebebbaceeeeabceaaecedcdeebdaeccebbaacbccbaabbdbddaacbdceebcaeeecccbcdccdbabacdcddbdebabcbeceeeeadbeadddbbeadaaebcddadcebacdbdddeaccaedededdeaabdabbeedaebbaebaeddaeaebabeeaddeeeaccaebebebccdabecacabeeacabcebaaacbacaacecdbdedceddecaeadadcdaebedccecdeebecdebbaaccaaaeadbeebdbeedbceccdbadbdcecbdeabcbdeebecdaedeabceadebecdbaaccecdedbabbaebbbaccaddbbdecbaaedbceacaaaeebeceaccddadcdebcbacebddeaceedaeeadbdaaececbecedbeadbbbcbdaaebcdccccaeeebdaccbebbdeabdcabeeebaebbaceedebcebeadccbdbccbedaedddcbcbaddaebcbdbacbaccbabaebecdaaebacbdaecddadeeccbededacebaceeebdbeedabaaebdbabeabebdabababbcbaceeeeaeddbdbbedeacbdaededbaeeccccdccaccebbcbbebeaaeabbcebabceaeadaeccddebcedaedaeadabbebdeeecbecadeebbdaccaacdbbacbaeeabcbcbcbaddbebcbabccaaccadaeabadaeadbeebadccecabcadaceeccadeecbecaebcebbdceaaabcceaccbaaeedddbceedbdcbcddeddbdbbadbeecbcadcccdddbbceeaedcccaacaaccdcddbbcbbbeeacbbebbddccccbdbacdedcecbdcdbecebacddbecabccbbededabecaceeecaecabebadaaaedeadbccbaddbbabceeeebbebeeaedcdcaceadbbadebdbbedcdaddbcdccdabbadeeabadaaedecbdecebeabbeaeeeddabbbdaebaacdadddaaebecdedcbeacdbaccbbcceaaeecaebdbdecbeecccdbddbbbedeaeeaceceeddcbbddbecbedabadeecdbcecdbbbadaaabbcbeabbabeabceceecacebebedccaceccebeccceebcaecbaedbcbdeedebbbdebbcdabaeadaccaeabdebbbdbbcabecdebaedadbdddbceadcaadcaebbcdecbedbaebebcbeadccaeaddddcaecaeacdaceaaeaecdcdabcebccedddbebaecdccebbbdadecebcccbeabdaddaaeadebaedbdcdaceedaebddbbcadeabebddbdeeaecdabbbeecdcccbebdebbdceebcabbecebddbdeaccaaaaddaeceecdcebcbacdeaabdaaadaedbcbeeacebacacbccaeeeadadecbdddddeabdadceaedccdacddaaadceacccaadedcaadbdbceeddcaaeccadaeaaccaaececbcbaaaccaddababdeaedcdddedcbabcbebcbbceceeacebeaaeecbecacdecdebcdaebcddacebcdeaaaaeababaaaabbaaedebbecebaccddebeabdaccebbaeecadacceaebaeebeecbaecabdadbebebbbedadccddbdbaebeeacbdabdbccecbcecdcdebbbaaeddaedaeeabbabcecebcdbebcbecdcabdbbcbbcdacbddbaaabeeecddcbadcdbcddeaeeeaaadccaaabdaeaadcaeeacdbabaebacaeddccdeabaabdcccbdcaebccdebdcabccdeeeadebcdedbcdbcaeacddececcbccedcaaebebaabcceaadabdebaedbddbddadababaaccbeeebbabbbeabddbadbaeeabccbdacdaeabedceaddebcebebeceeeddccbacaebcaadeebbabbcecdcacddabdbcbeccaeeadadbeeecdcebbbcedeeeedeedaecacceacedcecbddbbbcedadbbdcccadcabadedbecccbaeecacbcccbcaadaabacededabbdabcebeacacaaabddecddacaeacebdaeeaccccdedbdadbdadaddcebbbcbbdddebbceebaaeeeddabebeccdceedceaaacbcaebebaacdacecaeaeeeeabaedaeecbbdccddadaceceeeeedbbceddaaaddcdadbbadbceccdeececdaacedecdabeccdeeceaccedeacbcbeaedbccbabcdcacbaecaadbdedaedabdebcaacadccbecbaaedbdcdceeeeaddeccaddcedacdeccdbbabbbcbacbaaaaaddaeadcbdcebaaacdcdeaecbdadbcddbeaebaabedeccbdaebcdcdbebebbeddcaeacebbdececdedabbeaceaebaebddbbdcbcacceacadbecabbddaadbaedbebeadeaeedbdbddcdaaeeacbdddaecdcabdddcacbeecccebaaebeaadaddecbcabbddbdeddbcbddceeddbceebdabeebdbaabedddccecaceccaeccdedabaeebadedadbbceddbdaeacacabbdceeebaddbeaeeaababaeeedcaeacddbeddcbeaadbccadbbcaeaeacbccdadbbcdaabbedcaedbbdceabddcccbdbeeadbbeabcddedbdeabdcadeaebedecdaaeeaddbabcbebeeaddcdbbccaaededaddabacecdcdeadddcdbecbcbadddbabaaabddcdaddaadadebeccdeaebbadaeeceebedcbaadcadaedbebccdedbbbedbdedccadacdecbaebeadcdeebadcecabbececeaaabcadddbdcdedbcaceabedcaceeadcaecaedacbaabcdbdaeedadadbabbcebdddeddbccbdabeedccdaadecdeeabaebdeabddecdbbdabebeaacdebbecceccedcdbaecaeecdeeeadaedeaadebabceabddbccdedccbdacaebaceaeccdedcebdbcdebdcdbacdeaacceaadddeacddcaaebbaacbdacabcebbddeebbabdaabaeedbacabbacaccdacbcddbcddebadebcdbebebaeedeaeaaaedebecaccddacbbccedcbccaacabdbebecebeaaaebbdcbdddededdebeeceebeabccbbbcebbaddbcabedabacbcdddbcecacecbcbaecccddcbacdaaebcececdeeeacbecbdbecebadadecdcebdaecbbdcdddaeaeebdacaeabbebaadceccbedecdbcedcaacaeecbbdeaccebcdaacddaeebdcdbdeaecbeeecdbcacecaebbacddbebaeecdbedddeddeeabdeccdccbeadeeecededdceeeddedaecabcbebdccdcebdedbeebcccaeabeccdbaeaaccccdabbeabcebcdcabbbcdeebedceaadacaaabbaecebadbecdbbcdedebbdbdbaadcdabaebbbdcddcabdebeabccbdceeabdecdaeaddbbdaccddaabcdbeeedcddcabdacaadbabddcddecaebabecdceedadedaedacedcbccbeeabaeecabdedaeeedecebeaccddeccdadbacbebebeaddedcceebeceedcdddaaaadcddbcabdebadedccccccdbdbbacbdbedbaedbbedbeccbdbeecbdabdcedeccdaedeaedaebbabaeeacaaebbeebbeeacdaeebcababdbdaaacebabdaacbbbddcaacbdcceceaaaeebbddbadeaecdaecabadceaeeaadddccdbbedcaaabacdaaddbaeeddaaaadeaddedeecedabcdbeddeaebbbccadeaceeeecabeaaddbaddaeeeebbaedccbeaebbabdbedeecbcebabdaedeeadaeeebcabcebcacccacbaebebebacdddabebdeecccbaaeedbeaddcbadecaabbdcabebdebbdddeedcadcadeaaddaecabdbedbbddcedacbdbdabeeabbceeeeeddaacbdadecbbeaaaaedadbaacedcbbcaeaecdecadeccdebacbeedeeaebadbcbdecddacdcaeadeeaabbbadadcecbcdeaeeeceeaccbbcacbbecdddbbeadbbdaadbecdddccdccaeebecdacacbddabdbbaabaadcedacddbaceedacdadeddbadeceaaedececbdebdddbdabedeacccecedceaaeeceddcbdecaadaaabdeaeecdeacbedccacccbceccdebaaadeadddcededddbbbeeaceecdacdbddedeedaddbbabaebaeeedbeabacebbbaaccbbccbceaecddbbbbaaabcceceeedacbdcbeccbebbbcbebcccbaebadbedbbbbabdabcbbbaccebeebabaebcbdccbebcdddcbebcbaeceabeaabaeeacaccadceaecddcccacddbdaecedddbaaeabaebaaaeabadebcceadeeabbcbceeeceeededbeabdbececbebbcceddcdacecacebeaecaaeececebceebbebebdaeaaabdecbcebabadedeaeeaebeccadedacebddaceedaaddbdedbeadbaeeabedadaedcceacddacdeaaddcccbbdbeadebddecaadeeedbccadbdcdcedcecbdbebdedbaeeaaadedacccacaacaadabaedaeddccdbbaadbdbdccababbdcaacadedcecaddbbebddbeeabeebccabcbdeaadecccaddbaebbdccbbbaeacbbeccebccbbaeabaaededeeeaacddaecdacddadcbaecaeadadeaaceecbcacacceaadcebcebdbbcceeabbaedddadcbeaaebcdcadceeecbdacaccdcbccecdcbdeaddcbacbaaabeeebddeedbabebacccddbeaaddbaeadabccbaaddaecebbdabbbbaaadbaaddeebcbedeaabcbacdaeebdecedababcdbdecebaaacddcceccecedcdaebaabadedcadcceddebedabaeddeecededddccbbbbcacdbbaeaaadebbaabaaacbcbbaacabaeeabbbacaddcadcccdbccbcaecdedecccceaeacbedbaacebbbdeacbeccdeababacadceebabecbbdedacdedcadecabacecabcaeeaaacbeaaeadbdaeedbadcaceddaebebeaedabdbeeedeeaddcccecabedeeabeceadbdadcbcaebdadaecaccabaeeebebacdcebbaddecdddccaaeaadddccbdcaaceddbcddcadbddcedbaccebbccceababcbcccddacdabceeeacabcceebdccebebebbbaedecebddceecaeadcccaabadeaeaecbdbcbdccecdbaabcbdaceeeeecdaaadeddbcabbdacebbabbcebecaacbdaacdbaeecbbecdaccbdcceceddaebdcdccdbaaeebdbadccbeadeadbcccbdadecdadeebdabadaebaccebadebdedededdcbbecdcacaaebeaccdedabcbdcedebeeccacadcddbdacdaabddeaebcccaddbcbcdbdedcebbbedcabbaabcdaaecaeeebeceecbedacabcbcceddbcdaaecdbeedbcadaceeabbcddbbdbacaeecdeebbdeceeebecaeaededceccbcccbbeeabaacedaadbedcdbadaaabedccecbeadabaeccddbdcbcacbeddeeabcbddbedecaebececaeaadbecbeedcdeddcabaaccdadddccedeeddceadaaaecddebcadacacebdbcdaddddadbeeaaaceaccdcddeddedaaccabeebeabdaabbbcbcabbabbabddadcbdcbceddbabbbabddacbacaabceeebcbaeaeedcaedabeaaeceeceacaabadcacdaeddcccebedbcaccbccbcadaacdddeeaabdaaaebbceccabdccdebcdadceccdedbacbaddeeedaceadabdbecebcaacaacbcbdceaedcbbbcabecdcbbdcdcaeeacbdccdcabcebdabbbebdcddbeedbaccaabbbbdecabbaabbcdbbdcbcbaadbbeadadeddacdbeddcaacddcaeecedcacbdcbebebddeabcadbdcaaebbaddebceecaeebdceeeeabcdbedbdbedacadeedeebababbceddcacedbcacadcbaceaebcacaecaceaaabddaaeaaeecedbcececadcaececceaaaccaebbdbcdeeaeeeababceddccacdceacedaaaabbbbcacbcdebdacadaaaedabeccaaccbccaceebddddacabaebbbcdabadddbbceddeacbabceacaaaadacadcedabebbecdcaceaaddaebdcecdbeecceaadcebbcdeeebacdaeccedbbbdbedbccbaeeaebebbdacbaacccbbbacccebceecabacbedeecacdbecbaebaddcbcaedabbaadaaebabebdeebeabcbccbbeceabbbbcabcbabaabeaabdcacddeeebeadcbebbbeacddbdabaabbcbacbedcbcdecdcdeccaaabdceccaebacaddcbadeabcadbecabdcbbdeaecabbcbedeeccaedebadbbadbdbecdbdbcaedadeaeabddeadaddacccacedcabdabbaddbaacbdbaecdeeccbdaeaeedceeaeaabbaddaeacdbbadcdeeadbdcecbcadadebcedcabdaceceadbdeaeecaccaaacddcbebcccbcadcedbdbcbecdaebeccdddecbaeeecbdcbccbecacbbaaebcbabbebaecdebeeaecdcccabbcdbeeededeecaaeebaaadedddacbaeacebeaebbdddebbacbaadababdeabcddececadceadedbbacabbbeebbacaeaedebebdbebddddbcdbdeecccabbbadccbceceeebecdbeccbcbceddcdbeeddebedecbacadcabbebaccbddbeceeacaedaecdbdbdabdccdcedaaabeddbedecaccdabdcbecaebbececcecbedddaaabdbdeacaadeddcaaaecdbecdeddcdbdaedbdeaedacecbacdebaaabcdaaebccdacacbbbacbbbdccaebeecddbcceeebbaaaeacbecdbeddecdbaecaacdaedddcddaceccebddabebeacababadadbbdabccbbcabcdebddeebdabecdcdbdeeceaaabddaabbdceeedeeeebadbaeeebbddabcaddecddcceceacceaaedaacaeddddeccaebdadceceeeeadcaabbadcdbaccdddccedeacebeaeeaebbeecccddcecbcccbecebeebadbeadbbccbaadcabaadebaebdaedcebbecbbeadcbdeeaabaebddacecdcabeabacadbcabbdabdbadcaaceeacdaebcdecdddddcabdbccdecdaedeeadeadaebeadcbdebddadccebceacccdcccdebcbbebbddccdbaebbcedaababadbbdcbeeccdbcbdebddbcaaebcbcaeabecbecdbdeebaddeadabbabddebaebadaadcccdedecbbeeddcdaaddcebcaeaedadcacecdcadcbdeacbccceebecbcdabcbccdaaadacdecdebeddbdecaacbbedbcabceedeababcacadcdcdadcdadadccbcccbceeebbddedbcabadbeeeacdacebadebdedabacaebcaeedeedbbdbaccbdbeaccbadccdeecdccabcbbaeebecdbaacceccabddbcebbccdaccabcdcddcbebabadbaeaadccdbaadebaeacbddbccdcbcbdcbecbcbbbadeaebbabacaaaecedeecdbaccdbecadbcdacbcaabdbbaecccedbcbaddcecbddeabdbedebcddbeececacaeebadecceebbcdbeecaeccbacdcabcaddbedbbcdebebbbcadbbbaedddbcaccebcadcccaaacbbbbcecbecabdeadebbbecaddeabdacbbbecbecadabcadaccaeddceadaeeceedbeaedabdbcdcbaedabebddcaacdebaccdcedeededcddbcccbbaacbdeacaabadaeaaacacdcbaaceadcececeadcebecddedcbdcdbeaadcceeeedadecbadbabacbbbaabbdccadbdecaebdcaecdaddcdbaeceeaaeedcabacecaaecadddaebebdeebdabeaaabccbedbbdacebaccecdebeeadebebbdedeeedceaabbdacceceebebdadcbacbddaeaedcecccdceadedaebabbcbadbcadbeebcaaaeeecaadadeedaadeacbbbcdaadbedcadcaaccddcbbbceaebccbbdbbeaebbadaaaceccbebabaaddbdcaeadcdeabddddbacdaeddbccdbcacddacecacddbedeacedcddeebeaaaeaadeeabdbcedadddadddabeceeaecbdebccabbdccbedbbedcdbaddcebcdccacbbbaaceaaeabcebbeecebcedadcdecbcedbbddddcbdadaceaeaadaaadbeddcbbcbdbbcaadbeeeeaabbbdeaacadadeaebcedcbcbaeebbadccbdacebbcdbbecaacddccbdaaddebcbeaebbecbbecaeadbbbeddbcacdaabeaaaeaaecedccadcbcbcddbdceeeadbddeeccdbaabcccedeecaceccedccceadacbceceddedddedaedadeeebaccdcebcadbcceaadceeccddeceacebabbaddaeaeeddedebaeaeddbddcccaabddeadcaebbcbdadeeeebabdaccebdcccbceacceaececdcbeddcbbccdedeaaacaacddaceddabdeedebceddcdddedeecabedaeeacebddbbbeaedcbedbacbdcbebccbdbbaccadabaabceeacadcdaccdcaaeacecceecbbbbbeeeaedbcccbaddccccedcecbaedabdedcadccacdecbaaccdeadccddbaaeaecebdadabacbdaacacdeedebcdcaacbeabccbcdeeebbbbabcaeddcebeeccaceadcbacaebeaeadbacdebdcadeaedbaaeacacbdebcacadacabbddcceaebbbcbedeceedddcaeebcbeddebecdeaccdeeabecebaededdedaedbadcecccdbaebbddabbdccadbecddcbeabbdcaaccabaddedcecdeabeaccdeddaabadeccaadadbaaaeccacbcbaeedcadbdaacceddebceebdbbebaaecaacbacacaadbbaedeecadaadccecddccbeedcacbeeaddeabcddbdcebddcaddcdbbbeadacadeacecbceadeedbbeedaddccaedbabbecadedeeaebaddeecacbdddeacaceedeaaaeeecedbebadbbbccebceeeaccecaecedccedcececdadadeecdeeeeacaebbaaabdeeeeeadbbecbddebedcbbabddaaedadbedcbbedbbbacaaebcddededccbcadceccaebceecdceecccceddaeddedeebdeaedbabacbeccbabcebeacacbbdcaaaacebaabedbebcbbadbcaeaceeeacedbbdbdceecebddaaceddacbecedaccdcdecbaaecaaebbabeabbbcdabbbaccaacdeddebddbadcdcadbcdaaebaaedbebeecadaddedadbababedbabbabcebebecbeadabdaebabddacaedeaabcaeebcedbeeededabcebbaacddbdabbdcddcbeaeadaecaeaaadebcdbdabedbedcecaabbddbbdbbccbcbbddeeedcdaabddcedddadecbbedcebedbbaaeeabdceaaabdebdbdcdbbecdacddeceabddbcbdeadbebabecebeeddbcbabccccadccedbcbddadbaebccbedaeddcabdbeacaabcbcdceabbcedaeadaaaeacdaaeeaabbdabbddcdbedaedbcbedadcebaedbbdedcecddeabcedcbedabcbbeddeaaecbddebcadecbabccadeeebbbddbdbbbcebabbdbcedcadbeacbbdaacedacedebbeacdbadaabcaababbeccaeebabeaeadcacadddcbeaccbaacbdebcadecdbdeaebbabcbbadeeebddaebbeacabccbcdbabbbdbabceabedeeedacedaaaacaeecccebbcbdbaadcaaadacdacaccbebebddeeddbddecceadbaebabbcdcaccbeececdbebebabeebddedccceacbaeaccaebedaadecacaeaecdcacaccbdebaacedecbaabbddeabecbceaceccdeebebcedebbbbdbecebacbaacacdcebcddaebcdacacbcddddacdaeeccebcbeacaeebedacbbaaeabbedcacecdbcbbcaeeddaadcddaededbdacbabcedbeeceddbcdebececaeacbabadabacdababdeccdcaceeecbecaaddabbcecedbecdddedcbdcaddbbdbcecccabbebdabaadabcbdcaeebadccaeedbcbecbccbbcbdbadecebaceaeaccbeceedaaccdcadeeaabacceddbbdcceeadecacedbccdebcbceedecbedabaaebdbabccedbbdccedccccceddcdccebedbedbeeeaccedaaccbebddcceeebeaaeecbdeddeacbddeedbdbadacaaebecdeaeccbdccceadbedabdbbeadedbebbadcdbeedcedecbbababcdeabcebccbadebbeeedbbcaccacdabaaaecdeaaacaeeadedaedaaccdcebcecbbebaacbeabddeddaeeeeebbdbdcdedaadeededaaabccddbcacccaddcbeddaaeaedddeceabbbacdeeecedeeceebcbbbcdacccadebdbaebddadbdddeadcbaacaaadaebccccebeebacdbeadeaceeddadcaecedbcbeaaeeddbbebeeaaabebcedbcdaedaeacaccdbbbceaeabaacbeeabccccebaceeeddadcecbebacabddcebdbcbdeeeddbbdaebaceeacabbdadcdeabadbcabcbdedcdeabadedcdeadcabcbbeccdeacabcabcdceccaccaabebcabdeaaaeedabbccbadaaceecadcbdaaebadceecddcacdaaddeedeeacdceabeedcebebaabbaeacdeaceecaeabddaeceebdddededbecacabedbaebeecdadcaaaadbdeddceadbcdebdaadeececbeecabdccaddebbbceccaeaaeaecabedbaceddcdbcdbaabdbacabbcdcccdcebdcaecabedeeeebddbbbcbbdbbadedeebcecacedbdbbcdbedaedcbbcdabbdeeadecdcbdaaceeceabdaddebbbaaaaeeaedaaecddceebeaebbecedabceebeacddeeaeddabadddedeebeeaddbcbbddabadeaeaeddedaaedacbdceccabdccacdedccdbbbbdabadbdeebbbcedaabaecddaaecddcadededddeddddbdedaabdabecddabcdaaeceddcddcaedbeeedbbacbdabbdddeadeabcebadcdbcbacdeebcaddaecbceacdcecccdcbacdbadcddccdeebdccedcacdabadbbbbacccccedbccccbcaccadeebacaaeaeedbaaadcbdeaacabdaeddcdcccdeeeaaaabacedbeaebacdcddcedbbdadccdbecdcbceedbddcbddecaadbadeedddadbdddebdcdbbabceebdecbccddaecaeeebebcbbeabbdceabcabdbbcaaaeeeeedeccabceeadaaddbbbabedaebebccacdbeebecddeaabedaaaacecaddbaaabaeaddbcacaecdebaabeccaeadecccdbbcccecdeddddeceebacaadedcacacbebacdddaeaedceabbccebddaadddeadeebeabacaebeedbbecdceccdccbedaaadebbdacceddcbeadcecedbbeddbdabccaeebbebbbbddbdeebbdedeeebeaaaadbadadcebcdaeeadbaaedaedbebabdbdebdecbcaddbbbbcaeedcaaaecdecbabdceabadabdaaceecdceebbbeacadcdbcbbdddbdacebdedbabcdaaeebbabedddbcababbccdeabdccacddbcbaaadadebacdaedbbcbbdcdcbbeebdaccbabdeabebeddbabeaeeaceacadacdceaebcdceebabaaccdcecdbecbedabbcabdcecbbaaedcededbbcabebdbdccbddadcdcdedadccbebbbccbdaecabeccebeecaeedaecadcaaedddbdbaadecdcbdaabadddbedcaeeccdceabbceecacabccbcdedaacccdbacacdaeddbeecdeacbacbcabceacdbeabababcccecbcbdddeceaaedecbeabacddcbbedbccdcbcdcaadbcbdaebdadedcdcbdececcaaccdabddedeeaedbdcabccaeaadcbccdbddbdbebccecebdbecaaaeeecaabaaabceabebddeaeaecacbeaebabcdabccadbaabedecaeeceaeecaedbcbacbaeaabcaedacadcdcbeadeddecacecdadecceebeaacbcedaeaeabdcbbbcaeacccaeddbadebabccdadaceddbcacdbebcabacadeddcdceaebcccdecddcaccaeccbedcbcbbbbbbbebabcaebacebdeeeeebbdaaecddddbcaaedcdeedacddcebeeddecadccbbcccacdcedbdcdabeddcdabeaeaaecaeebdcbbdbddceeaeeebabcebeadcbcdabcbdbaecebedbbdcbdcbbedbbebeeccbeabbccebdbcedcabacdeaddadbabddcbbbbbdcacebbeeaeccbddcedaebadcaececddecebccdebdaeaaadbdccdbbaeadccbdddbcddcaacdeddcaabeebeecadaeecccaadcdacbdacbaedaabcedecbeadacccbcbaedbceebbeceaadcbdbacabecdedacbccbabecceacecddeababbeeaddabebdbdabebebdaabaadbdcacecddacabbabcbabbebbedcdbddedcaabeeabdedeaddeedcadbacbddbceaeddbbedbeddcacaccbeeaebdadebbddcddcdbeceeeccddcadddcceeecbdecdebdcacaecaaccbddabaccedbceacbcbeedbeadaaadaecaaecebdbecaddbbdbceaaedbeedaaedecbebccaebebadadecdacaaacdccdcbaddeddcaeadecdacaaddbaeacadabeaceccdcccbdecbbabcbdabcbbbdeadbcebeebdddacbcddedcbeaaeadabeaacddeaecdccddaeebbedbeabcaddddeaeedeadccacccddbcabdcdedbbdecbbacacdacbaadaacededdeeeacedbcdebbdbdabbdbbeecddcbccbeadcebcabebbcecdeadbeccadcbcbacaabaeccbbeccaabcbdaaabebabeeebcbcacdccceabedadcdcbbecebacbbccdceedbdabbbeecbcabcdaabeabedbaaeacabcbdeeddcbcbeecbedcecdbebbbacdceaabdeddddbdecacadbcccaadcdbcdaededbaaedccceadccedaeecbedcdeceacdcbbcbbbcaabdbcbcdcdaaadcdaaaeabcebabbeccdcbdcedbcdbeacaceddeceaeceeabdbceebeacbcdddcdecedabcdaeabbadaabdaaecaaaebdbdbeabbdebeceecebeaeebcaaacadbcebdceabbacdceeabeccbaaccdadeaacededaecbcecdacbaceecdddcccbbacabebbcabeecbbccadaacbcedecddadbcbcaeadaaecbdbcadecabadcdebbcadadbdddacddebbbbabedbecdbdbabeeeadceedaaaaadadbdbbdeccbdbdccabebbdabdadbdaddedadbadcccceaacaeeaaccdabdebcccadceadbdedbcabbebcaeeddbeabbdbdcebddeeacdceaccaeebccddacabbccaeedaaceeddcaaccaadcccbbcbdecdceddcadbbcddbdaabcbbebccdeacaebbabebbbeebeedecbbcdbeadaeedabdebbcdbbbecbdcbdbccdeececeedcdbbebeeaeaccbbacababeacdaccdedeabbdcdcbcecadaaeaabacceddcdbbbdeedadecbedeadbaabbcdbccccacddbaabeebdeaebcaaaabadacdbcaabdbedaaacedabdadbaaececeeeaaddbddeadccabaddcabcebacbddbaeccddeaabccbddbdaaaeacacbbcecabeebecbbbedadbdbcccddeaacacdabceebbcaacaecebacbeaebaeabdbccedadabeebacabdeebebadcadcdebbeeaaedaedceebdaeabcddbbcaeccebbaedbbbdbeddddeddebedbccbbbcdbaadaacaedeeddbadaedccedbbcbaaedbdbbbdacbebeddcbcbcdcebccbccabcdabdaaabbbbcacbeaeadadbceaeeaeabcdcdbddcacdaeeadbadccbdcbeeaceabbecacacaaeddeadcdeecabbcebcededeccbbbcebddcdecacabeddbcebcccecdecaaaaacaaecacecdbebedaabcddbeabbbcbaebabaeedaaceceacbecaeabaeddadeddcbbbacaaddaadcdbcedcbcceecdccbaadaaccaacdbeadaddccceececdcadbeacaabebecccdbbebbceadabebceaaccbaeadaececcadcdcccddcaeacaaeacccddbdaacdceacabaccaeaebceaaaedcdccabbabddedecceceaebcccdccddcadbadeddaaeccacaeecbcbdcbdbaedcbaeeccaddcbcaeecabeaedeececeedaaeceecaeebdebdbddcacecebcdbaecbebcaedbdccdbeedbbdcbccedadcbcbdddeaacbbeedaeaaaecdedddadbbeccdbecebccbedbbacceaceeeabacbdacaebadddceadcbdecbbababcdaceaaabadbbbbebbacddabaedcdccaaccdaececbeceeaadbebcaeaaeebcdacaeeaacbebbaeadeddebeeeedecaadadcabdbebedbddbbeeedecdceacbbdcbbaecbbacecebabbcddaddcaeabeddbebdbebeaedaecbbaacbacaddbcedbdccdedeeaeceadeacecdcdbbddddccdaedbccaaecdbbeaabecdaababbededbaaebaadbeabedcbacccdbbeaedcbbadbebeedaaeadcecbbdddbcdadbcdaabbabebadbeceeeaccdabbbadceadbcbadeccccebcbabdeadcbecebdcaddaecbcabeddacecbeaceceaeecbdedaabdeeeeeaaabcbaeceacaedabdbbaebeccbebebdbcdeeddaaeedddccabeacaecbcaeaabbaecdcaabcedadedbbadcccacbaeddabdeaeceabeeedabacbdcaadacbaaabbebcdbdbdacbebdbabcdacecacccdecbcaaccbecedabbeceeadeedadcbdcadcccbabaceaaddcbddbabaddcadedceaebebdbccebcbcabdcbaddbcddcabaedecaccdababbbccdedaaaabddcedcbbaacaebdbdadbdbaacbbcbdcbacaecebaabdbaacacccedddddbeceeccbeceaceadaebabcabebdbbdabaeaebedebedcacadbbbcbebbedbeecdbeabeaeabdecbacdcaadebabcebbdecedaeaeddbaecbdceaeecddeabecbeccdebdebaeecbedeadccbadabdbddebeceecdaacbcdecbabdeebbbdaabdeaccbabcabaadadcdddddcebaeaddccbcdecdcaebdbaeeddbaabbedcbcbaedbedbeeceabddceddbacacbddccacddbacecabeecaaaaabeeccadcacadedceebbedbbdcadacaeadbdcdbaebeacdcbaeaaedabcbeabdcaaaebeaedbecdbadeacdaeecacbcabecceabeaceaededcdaeedcedcababebbbaaadbbbbddadbebdccccacacddbddcedeeaaddbdbedaaadabcbaadaaeebcbbeeabeeeeedccbcbadcedbddcbccebbbaddbecabcccebecdacadddeedbcceadddacedceaaedbbdeeacecadecdadbccadbeecdbdabedebbbdabeebaaddddeadedbebbceadddbdeccbdddebeaddcdbaaaadadaebaabcbbebabceabeedadbbddcdcbadceeacedabaeedbaeabaadbebcdcaceeadedddccebdaacccdeebdeecebcecacbbdedacebdacbabccddeeebaeabaeabbceebdabcbceaabbbcbbbedaacbbdaccbbddaeadececcebacebccbecbbbdbbaecceabcadeeeadadedebadcbadebbdceccadabbdbadaedcdecddcdedbbcaceecececebdcebdeaeaabbbcdeecbeebebcdaebdaddbcecebeeebdcacddddbbedcddedccbacbcbdbaddebbecebdcccbdacecdddcecedcbebedabcbcceeaedecdbebcbadaddbbeadedaeddabadddacadbddacdaaccdbaaebdcbcaeabbbbdeecdadbebdcbcbacddbcaddadeaddeddddeaaaceeecbbdaddedeecdceeeaabacedceacbcdeebbabbdcaccdeadadcedeeedcadbccebdecadeacbddabbadeaeeedcabaeeebeddccccedbadeabeeacccaacdcbbdececdadbabbecbeacccaedacdcadccebddaacdcdecbdcadccabecaabccbdceedeacbbbeeddedceceacdbccbcaaecaeebccdbeeabacaeeeacddecceadacbdcccadbbdacdcdcbdbedbdeceacbcdccbcbeeaebabddabecaedeebaeacecaccebadbdddcabeddadadaedaaeddcbeedaccdaddabbcdeccadddecdaedcdeeeacabdadbeeaecceaabceaeddebeedcddedacbedeedadcccbcdedccdcbebdeedeacdeaeebcdcecddcdeccbeaaaedabbacbceaadadeeebbecaadccdcdddccaceebbbcaabbecadacadddbacbcbceabaccbbbdcdbadedcbbacdecdadeedcbcbaadbedacbaebcabbdebabebacdccdcaadbbcbacacedbbebaeaecdbaaedebcbecaaabdbeeacbccdceacdecdaedcbbaaeedbcbaebbceabeeeadbbacebbbdddeabedbbcacdccddaaacadbaccacacaaaecdedaaecccadbedabaeedebbbacadcbddceebdbccaaeaecbbbbaddbdccdcbebddaabcbbedbdbcbcebbccdaaeacbadcbdcecbecedbdbdbaedbeedccabedaaedbeacebebdcadeceaceabbbedeeeaecbbcbbccbaaeebbbbcdcbbcdaaaadedabbdbaabdebaaedacbbebdcbcdcbaacdcbbdeddbabcaecabbeebdacbedbeeaeddebcaaaabcdebecdddaacabeaecdcaeddeebceadbaecbbdaddcccbeebeceebbcbaeadececeaaebdaeeeddbdabbddceadebbccacdcaeabacebedcdbeeadaebeaccdadadabbbbdacceaacaccbdecaeecadbccdabecbaaeacaeddbcddadeddeeabbbebabeccecdbaadcdedbbbcaaddcadedbadceccbeebbebcccccceabcaeacebcddaaddebeccabcadcbdcdddadbdaeeaceeaaeebbebbacabcbdbaceeddeaadbbbbdaacaebccecaaabbdbacbdcbdeceedcccbaadeedbbdceeaccbecbcdabdaeceddaaedbbabbecbeaabcdbcdbdeecbbdcdcdebacbdbbbbddacbdaadbeedeeaceedbdaaddcacdecabecadbecedeeaeedbacbababdeacdbddbcaceaedeecdecabddeecedecabaceabddaccabcbeebcccbdcdadeeaddaddbddddebcadcdaeebcebbebdabcccebbcbcbdbbdacdbedacecdbbdacbaacebaddecdeeaeaacccbdccbaabcbdccdcaceceedbbdedebaacaaeadcaaaceacbabaddbbcbdcdeeabadeceebcdeebbbcbcabacdeededbabddadadaabbadebdddaddcebdbdcaadbdbcccababecbddadddaccdceacccbcadabbcecbeecddeaaeccdcbebacadccedbeabbedeeaabedcebbaacecbcebecaecadebbeaabbacbddeddcdedebdbeeaadeeabdabdacbaadedbaadeeddddaabbecdcbcecaebcbcaaddadacbaedecadeaeeeedbebabadaaebbcbebbdaeddaadddcdedeaebddbaecadcedaadecbcdeddebbdccebdcdbbbbeeedeeadaacddeabaaecedeacbbecebecacaadddadeeddeaceabcdaaddeeaeabcdcabbbcccdeebeddaacedcaddbecaaddbddedadadbdbcccedbdcdedbecbebbbbcbaebbeccbabdcdcdceabcdbbeebacecccdbbeccabbccbbdcabcbcdbcdbdbdecabecaadacccdccdbdcedbbaebadbcbebdaeaeadccbebcacbccdddbdeaeeeccecabababedaaaecbedebbcedbbbeabbdedcceddeaedbbbebdeebeaebaccabcbbddaeacdabbeabbccaaadbacdaccdeddceeeeccdecbaacaedcdbcbdcbbbecccbcccdccbebcbcddbaceebceccaaabeccccecbbcbabeadcbdaadccabeebbaebdbaececdaeedbedbeddceabceebdecadcbbccccedaeeacacebdaeacbdcbebacebbdbadedeeacacaceeaabacacdacecccdcaeccacedabdeacedcdddabaadbbdaeadccaeacdcecbcebceeaabcbeebdedbebdddadbcdaeadaabbedeccdbedddddddedbebdaaeddcbaccabcdccbbeededbbbededaabddccbacceadaeadcedbeacbbedabeadbdaeaeadcccabdccabeacabedadeebbacbeddcbaddbccbdaedcbeccaccbccbbeeeddaacabedbdcecccadcdbaadcacdaceddabbbebacadcadeebddacedaeaddcddbbdebaadcbeebedeeeeecbdeccbbdadeaadacdceaacbedbaeeaccbbccbcbebcabeadddcabbaddecccabebdaaeecccaecdaeeaacddcacacaaaebbbedacabcaabdccbadeaedceeecaeabaecabadaadddeaaeecababeadcdccddabbdccedaccbaecaceebdbaddaecdcedbeecdccbaabdeeaaacbbabaddeacacddaabdaecbdddccadaddbdacccdbbbabaadbedcacdbcadabbeebcedebdceeceabaaabaddbbccdaecaaebacddadeeddbdeeadebcceadabdabacabebeacabaeaccaeeebdebbccaabbddaedabacbbbaeaeaaedcebdbedbedeabcddaaebacdccecbdaceddbdececacaacbdaaabdddaaaabcdbbeabbaadbecdbdeacbebbeddddbdcdacdbaabebebacbabdaaeacddccababcdacaecaccbeaccedcebacecdaaaadcbaaaaedccbdbcaaabbbdbccddccbdbdabbbddeedecbcebaedcadcabeaabadbedadaeaebabcdccdbeddedeaacecdbbdbccaecbeadecaabecdedadbdeebdaedbedcbcbbddbaebaecddddacadeabbddabdacbcbdebcbccdcaddbcdaeaccbeccaabdccbadeeedcadabceeecceccaadebdaccbccabbdeaaaaaeccddacdebaacaceaccacbecedaadbcccdebecbdeadccbdbdaadddebccdcdcbdbccccddbbdaeceacaaccadecaedeeadabdaaeeaeecedaedbbdcaabcebeccdcdebacbdacbeebcbdecdceacaebbadbbadcaaadbeadbdeaeadcabcedbeedabbadbdedceacbbddcaadbeebeeeaebbccccabdececcaecceecaebbaccebeebeeeddaedcbcedcedeaceecdebebedbbabaeaadcdadaaeacbaeabcdbcdbaebaccebecdcececedcedaaabbbadbdaeaeabacbbbdaecebdbbdecaabadbdeacaddeadbedeeaebcacabeeabeecaeabaaabadeebdccedcadadadbcebdceadbddaecdbdbaaecaddbcabddcbcdebbcbeaccdaadeaeddeebdbdbabdedccceabeaabbdbbcbaaacceaaacaedcbccacbdabbaaeebedcaaabaeadcedddbcdeeedbcaacaacdbcdddcdeaccbaabcdddeaaedadccbbbebddcbdbbaacebdddacaadebcdedcbeaacdecabaecccbedbdcbeecaeabccddaeadaddaedaaccddeabdadadebdaeaeedbddeeeeadabcabbaeebbaaddcdeadbeabeabaebcaadeabcaebddccecaceeeaaeebdadaecabcacaadccbabdccaeecbcedbeccccdeeceadbcdeadddcaacabbaeebcaccabebdbdeeccdaaccddeadbdebdabcccdcadcdcebdccbbbdbdadbaddbeeddbaddebaaedadaccdbaecbbbcbcabcaebabeabdccdeabcaeacececaaebbedacdceabccbbccbcbbcabcbedcacbdacacecdbdaedeccbdcedbadcdaecdbdebebbcecddedaaddbabdcccedabbcbaaadccccbddcbebdddabbbdeadabdcdebeceabbaaeabaecdbdbecaccdedaaabeabadbcccadecabbcdbcabdcbbdcadddbbbeaeadeeedadcbaddcbcabcdbdceebcdddadadeaaebeabdeadccdcceebdecacedcaaacdbbadcdbbbbcedddeceaabdcebaaebbcdbacccecbddddcacaaddebcccadaaeedeeeeaeebabaadbdbbebedebaebbaeacddbddeddaddadaadeaaccdddddbebadaceadaedbecccedceaccaebbdecdceedabedbcdcbecdacdcdddabdadcdecebabdabcebaebabdbbaadbabaccbeeacbeddedbebabeaccaddcdaabcbecbaecbcddaaabbdcbcbedcbcceaaeceebceedadddecceacbecebccbceaddcedaddeadaedbbababccaaacbcbdeeaaebbaebabbbebcddbdbbdbaacaeaebbcbacbacacebabcddbaceedaaddaedecaacaaedddecaadedcaccbedeccbbedeeaeccadecdcdcbaecdebeebdcdbbeedbeeaeabaddcceeacebdceecdcdccdceacabaecadeadedaadaaababdecabdbbcdbceaddaddbccacadbaecabeceddaedbcbbbcdecaddddaacccecebbbbedceacecedaaaaedabadcdeddbadceedadebebadcbeacaddeccebbbaabbacebccbddbeaedaccbddaacecbaabcbaaaeeabadceccaceaedeeedcbabaadbcaebeadebdddeedbecbdebababceaaaebcddddeaddabcedccdbbaccbcabcabbcbddabcbaeabaeeacedaedaecabaeceaccddebeeaaadbecceedbabaebdbbbabcbaadbbcbdbacdaacbaaabaabaabdebdaeebedeaceadcdecacdaeddbaecbacdbcdbadbadbcbbcabceeabbbccacaddecceedeecbacbeedcdabddaeabebabceacbacebeedcbecdeeacdcbeacddccccbccdeadbacdcdabcecdbecebaccbccebdcaeadebcceabccdbaddeaedeaccebceecaaabeaedaeebcaedbdadbddcbaedbdbeaeadebeccaedecbeeaebdbccbdddabbbcebeddcbcabcabedaacadaadebacbeaaaeecdabeebddccdadcbcacccbcbdaecadaacccddecebcabbcbcdbbaadcbbddddadabbcdcdeecaedeadbdddeaabccccaebcbaaecdcabeeaccadabaadcbadaaabdbdecdeaedebdceceabeebbaebbaacbceebbdadedeeccbadeaaaddaebdbabcaddeebdbaabcbbeabeedeaecdaccdcabbccaecebbebeedbabedbdadbdcdecceabbabeaacbbaabdecebacedeeeeebacdccbbbaebbccdededcdaabebbeebebcbdcbaddccdecedbebbeaeeaecbcdcdccdaabedabdeaeacbbbbbaaeacbecbdabdbdcdaeaceeababddcadcbcbddebbaadeacbaedcbcbbcdddceebbdbccccacaccdeebacedabccbdbcdeaeedcdebdbbbeeedbdebdbdeadaaaadaebbbdaddcecebccaeeeebcdcaccbcbddeceddedbcddcaedbbcdecedeedadcaedbceaadbdcbbbcdcbcccddcceeebeaeeecadeabccdbabaccaeeaccbbbeebdddbbdbbcebbcdbadaabccdbccbcdbaccdeadbbbabeeddbabacdecbeeecebdedecbadcbdaacebeeeeeecaebebecedcebacdddbbbedeebddaddeebbbbdddecbccebceeceecebccbeeacecedebaddecedadbdddcaebaeeadcdccddbcabbdebeedbcbcdccebaedbaaabeedecacdcadacdddcebddccaeaedebabdebebabddacedaaadabbbbcbacdeaddaeadecccbadbbeebccedbcddcacbbcebaeeecdbeeaeeebadedbdaaedeeebcbddbbaeadaedaeadcaedddcadeeebbdaccbddcacddabcdabbcabdbebdabdcddddceaaedcbaddbdebcbbdadccdbaaeadccbeaeebbdcabeebbdceedcbccdedacedcdacccddbdaedcaacecbbddddeaccaecbdcabbbdbebbeeeeeedaaececacbabeeaaebbecbaecdadaebdcaddcddeeeecdbeecbeacbdcaaecbcaaaddaddcbbbadbcebeabadaebcdcdbeddadcabbeeedcceadeebaeeceabedcbeeeeaaeabdadaddbaccadddbcaccdecebeeaddbdbeecdabaabacecceedccdededddcabbdbebceccacedaaacaceaaaabedddcddcecdadaeadaaceabbaebdeaadcebdddeddeecddccbaeddcebaebdcddeedccaeedadcdabacdeeedbcdcacacdccbcebcacdeeeddabdeacedcadacabebaeeadcbabdbcadeedacdabeccecdcbabacbaadbcddbdeeabaecaddadbebadbceaddceaacecccdcdbdddcdaedbdbacebeaaebadcaacdaccbbcdbddceeaecdeacddaeeecdbbaeeaccecaeddeaaeebaedbceabbbeeedadddeadedaedabddddadcedebbacaeaecdeadaceeabcebddeacaddabecdcbceceecdcaecddebedcddacbcdbdbbeaceadbcdbcadddcaeaaedeecedacbbecedbdbbbceedacbecacabedaceacecbeddcccaaaedbabcbbabcbedcacdcbeebdbacbcccdeabdeadcabadcadabedaaaccbeecaecebbacbdebeeeeccdcbccddacbdedcadcecababdceadbdbebbcebbebdccecebaecadecebabdcedeeacdbdebcbcbeeeeeeccbeddecbebaeeebadbadcecdbdbaabbedaeaeddbeebacaaedecdcecedbccbdccbdeceddccbbbadbeaeaabdbdeabaccdedeebeaeadbeeabaebecbadddcdeecbadcbaadebbebaeecabddbdacacdecdeaababbcbcadbddadceeeecdbdcbdebabebdaabcaaabcedadddaadeabbbeeaeceacabbcccabbdbebbaabaabedecdddecdcbbececdaabbbebcebeacceeddbaabcbedaeddceccaddbdadcebccbddcaacedecabcaeeebeedeedecaeadebaaaeeedeadecabebbeeaaaaebadabadaadebaeddaaecbebcbaccdcdbebbabbbadebeddbaaadaeedeccadbbacdcaedbdcecbaedeccecaeeaddabcacadabbadaceccbeebdaacacadaecdeaeccacebcaecacacadaacaaeeccdcaecbabdcdbcdcebccacaeeeedbbebaaebabdbbeaeaaacddbcdbccabaedbcabaeccebdabacceddbaaedbbbbebaaaeecddaceceecceeeebbbaeabcdbeedacbcbccaeaeebccaabdeaaeddcbccacbdacadccaeaadbdeaeaeaaaedaceeceeeaaecebcabadeebbcbbdacbabdcdaacbcdcedcbbeadbbeedbccedecaaacbcdbabacebdcedbeccddbaebcadcdcdeabadadcaeedaceaeabccabbaaccabaccdecdaebaceacdeeadcadccadbbcbaadecbdbdbeebbacccdabedcbeacaadabadbeedcceebbbadbdbaebcaacadaaceddaeaebababcabeadaeedababacedeacadaeebbceeabeaeeaacaddcbbeacbddeeaeddccaadadeeacbeeaecbedbbeaebdeddaaaacaeddccaecadaaecacabcbadeeddbceaabbddbeecdeceeaeeaaacdbacaccdbdbaeadeaecebbbaddcceaaaebeadbaaaaeabdbbedbddbdeabbdcbecbcdabecbbeceeeeecbcbbedecdbdedddaaeeceddceebeaccebcadcaecceeebbeaacdacddbacababacdabecaacdbbbcdcdcebcdddadcbeccddcebeeeaeddbcceecbdbcceaeabccaecbccccacaeaebadbababaacdecbdbcacaacdbbccdabaaedcbcaecadadebcebbeeeecaecccccbbedeecebddbbeaacdcdbcceadcabcbeedddcecdedccbaceecbeeacabbbbbcaecbbedbdeebcccceedcdebedaadaedacbdbcbceaeaabdabbeedaecddabbdacdaeadbbebcaaddbaaddccbeaadeaeabdacbcaeedabcabcbbcaadccdacadbabadbbcecbdbdceaadbedbdcbeeeeeebeeccacadccedbeececcddebdaabadacebcdaeaccadbadbcbebabeaeedddbcdeebdbeebccebdbabadccdeaebadeeaddcabaeccbadaeebeeecbdbaecababbdcddeeccceebcdaaaddbdecebebbbabdeccadabdadbbdabddeedbbaddeebdddeaadabbecbbedaaedecdceaadabeaceebeaaccbebcadeaadeecdddaddeedbabbaedcacabacdbcbeabecadceeaaccadeedccddbadadcacaeaacecdaebbccedbdcaacddbdccbecaedcacabdebbcbaeddbdbebdcbdcaeabadcdeecddbcacabccdbcbaecdbccedccdccdcdccdcbbbabbdccabedceedddedcedaecdeecbdeedcbdeacebeacedecacaacadeeabaebdddeddccccbbdecadbceeadccebeecccaebcaecabdaebaaeeceebaccbcbbacddaacebaaeebcdcbcdcccdbeadcadeeaaeedcaacabdcbeddebaebedebbbcaaceaadcaaeccdeaaddabbcabcdaebabadececeadcccabbbbdcecbcbbdccdccbaaeacbadcacbdedebbdaeceabceabbaeadbbbddabdbbacaaddcabcbeacdadcdeadeadadedeecebedecbbdcacaadecdccbdaacceaddcabaeabedddbbaedebcbdadcabaeeccdaeebdedcdebdcabccaeaacbaabdbbbdacbbabcacdabcbcbadabaeeeecbdecbcaabecccbdccbeeaaedcdebccebcdabacccabeaaceeccccdebbddedbbdacbddeadaeaceeceadcdbbcaeddbbeadeaebdcaaeabebebccdadbedbdeacbdeeebdbeaadccbdecdadebddecdbdcbccdecacecadeccdddcaadcadedcebdccebbdadaeccacecadabbddbbdcbcdbaacdbeacaebcceacbebaebcbbbcbecdeeaebbbcccbecbadbceececadeccbeeddbaacbbcdababbebcaacacbeebbebbaaeaedaaceccbdbdebcbcbacedbbeccacecebddaecaaddbebdbaebecbcdabadcbdaebcaaebedeaecadbecebeaedeaaeccacaddddcebbebcababbbdbedddbccadceacebcacaecbdcbceddadceaccdecbeacddeaedadddedbddbcaacdbdcaecececdeecaabbcbeeababebaabcbbccdbaaedadcdbaeaecbcaaeecebbbadaeacdceabcbecedabccaaaaaeacecadeebbeedeaacdeaddeabbccebacaedeacdebeeccbcbaaedcecccddbecdbeadadeabbcabaeaccabccbcbaaedeaacdbacecaccecaaaedebedebdddbecbecbceabdaaaeaececcddeeceddaccaaaabeedbaeadcabbecbdecdbeaeeaaedbaececabbdbcaebbabccbaabcddaadbbaeaddaaedadbabdcbbabbbccaedcebacacbeeacaaeadcceccabeccbdcacbedcaaeeeaaceaccbeadbbdaeabcddcebcdaebdeacbdcedeeeccbbcabebacdecbeddcedeeacbbbeabeecedaabacbbadabbdeebcbbeaaadababbadedbbccecdebbdecaacdebbedcbacaaabedbeeaecacebadbceeedcdecdbcdaadaabacdbeeeebadcdbeeeaaedaadbdddbbdaebdccdeccebebdcebeadccbeecadebedcacaaaabcacceaadcdbdaaaedeeecdddccddeebabdccbbeddaedeabadcbaeaccaeabccbeadbbacdeddcdcdcedabbcdbecaeeeeccaeeebaaeaabbbcddeaeeaaeabbbebbacdbabaeccecedeadcebcdadaedaebdbcadeccedabdaeaccdddbaadbdbdacadcbaaaeebabbdcaedebbdebbaacccbedcaedabadededdbabacecceaceaddebedaeccdacdcaeaeccdebdaaccedeacdddcadaceeaadbdaabaaacacdebdcdbcdacaaadeccedbdbcdadebededabbabcacbcaccbbaccddcdaddbacabbcaeeaeeeadbbaacebbebbbadeddbdcaeabacddaebbdddecdeccdbbdabcadcdeeaeecaabdebeecdebceccabaababbcdddeedceeecceacaadbdaeecbcedbbcabecaecccaebbabddeceeeaaaebdbbecebccdbdcbdabaaadedeabdceaaaebdbebeadadaabbbbbaeecaeaceccadaabecbbaacedecaeaaadcababbcadedebcdcccaecaccedeeceabbedeecdedccdbbacadaddbbbababecbbeabceddbccdbabcbadaacaceeeececaabbbccaddcdcebebecacdedcbdbaabaeeeadbeadecbaaacabeacdccbabcbdddeeaadacaeabcccaacccddceccbcaecdbbcecebaadcabeedeadabcbbbbbbecedadcccbdadebdcdaeededbddebdbbebaeccebcecebcdbdedcdcecbcddcbabbaedcdcbcbdedddacebadeebdaaecbaecdddadaedccaacdcedecbdcabedeababdbabcbecaceceeadecbbedebbccacccedebbaacbbebcababeeeedbedccaceaedbdceeddecaabceeaddecabaedcedadecabcdbdcbbecbeddeaccbaecebddcbdeabddbecabcecaaddeedbbbbdaebaabaaccdacaedbeacddacbedccbccabdeaedecdddddaddcdddebabbaccbeaabacedcdedeedeccceacbaadcbbcbeebaecaeaacedecaebbacddedbeecbaaddacdebabedaceeadbdceceeabbbcdabbeeaacbceeedccdaacabdbedcbcbaebbacbabdeebddaeedeaeababdadacbbcbcdeadacddbeadbbbdecdcaaadbbacceddeaecbdaabbcdcdbaacbdacbeedddddabaecdcaaeebeadccaddabdeaeccecaedbdcbbbbceecbeeebdceedacadeebbbbebcdcacedebeaddcbeaaeebaeeeabadedbeeadcbdbeebaddcabccdeedeabeeceddbebdeabcecccbdabaadbeaaaddcbadeaaccebaaaaccbddaaabbddcabeabdddadccbcaedeaccbcddeababaebceaddcdeeacdddcdbddbddbbeadececbeceecdeabbbdbdadeedddbcecbbbeccedabbcdbdecedbebeddbddbdebdbebceebaccbaecacabbbeaabbbedaeeedbdeecbdcbbeebedeadecdebebbdddbdbeecbcdeaabcecbcdaaedbdadaccedccbadcdaacedcdebbabeedeabddcececddeaebbebbccbecaddbcbaeadabaceebbccabecbcdeeeeabaeedadcbeeddbbaceedbedaaaccddadbcdebdaacaeaacdbacddeebcecaaeacdbcedceabcaaaddacccedceaadeaabaddebecacdabaceddaabddaecdbebedaecdabdabdaabdcbdddcebdeeccaacdadcecaaebbdebdecbceceeedabaddaeccababacdeecebeaabbeddddacbaceeacbdecacebdcddbcebbeaddcaaaeceaeecdbeaedcbccbedaebdedcdeaddcbdcbddaeadecdbbabdeaebceacccddcbacceddbbcaccebdbcedbdabeeecdddbcddccddacaeaaedabaeeceddcadebbacdceacaababeadcaebbbcecdedcaeabadcbbaabbddecaacbeeacdecacbccdbecaebddcbceaeddccdbcbdaaddbebaeceeaecabaaebcbbedcacdababecbddcdcddbdeccadadbadaadbabeadddebeeacdddbeddcbddbdaaaadbaeaadebadededccbeabbaabcdbcabacbdcbcbeeddbdbdddcaedceeadaeebbcacabaeeeaddcdeadccbecddaeeddabcbeddaaeeacabccbabedbbbabebaccdcbcabecdeebceeadbeeedcbeceacdceedcabacedeacdbeeeaaecebdacbcdcbcbcdcdecddaddbeccbccceeedbddcabcdbdcadedaabeaeaceceecbcdebbedbbdddeddeebdacaecabadbdddbdceeeacbcbeaabeabbcbbdbaabceacddcdedcdbcdcaccecedbacdccbbcbcecdeeccaebdbbecebccdabedacddbbacaebacdeedcbeddddcadbdaaaaedaaecdeedbebedbcdaedaacdbdccbeacdaddccdbddcbbdaeebcbbacdecceeebdcdcccdededdebcbbebdaeebacdadedaaedbbddecccdeadccddbdcddcdcbadbeabeaaecbeccacbbdeaccadccabcdbeeabbedacddaedecaaaacaacaeddcaaaceeeddabddabbebeddbccbbaceeabbaceaebbeccddecadcbcebddaccecccdacbabcdabeaadddedebecdabcddbedcdbadeaeceeceedcddddbebbddccadeecaeacbabebdecbcedebaabdacccddadcbaddcdcdedeecaacdeedbeddddbbcccedbddadbaabdacebcadaccabaeedededcccbacdebeccaaeacaecacabacdbabaecbdbebdeedecbdabbccdaaccedcbaaccaeeddddacbbaadbacbbacdbcecdbabbbdaeecdcccbdccdcbdebdeaecbabaddeecdbecaaddcdbacaadedcbdddceedeeccdcccdbaadcddcbedbacaaecbecebabaecddcdcaadbbdbcceaadbecbcaecdeebdacdcedcbbdcdceadcddeecdabcbbddbeebaadecdaeacbbeceedbbcbbcccadbbecadbcccabdcbaaacbaeeaeacaaabcedcbcaadcdadcdcbbbdbdddbaaccdbbdbabbbbdaaadddacbabccbbccbdbebbebbaeacccabeaedeeceebddeedbdedebbbedeaabdbedcabdbbcabccdeadbdecacacbaabbacaaaadeedeaeecdabeeddcdeeabaaddaacadbbebbbcceeedaebcddacebebbaeecddecbcdddaabacccccdceadedadddabbebacccaabdbecdbdeeaceaccacbdbbdbbabdaedcdaaebcdaecadabdaabeeeeeebbeebadbeaadaacddabdcdeeebbeedecebeebabecabcaccacddabcecdcadcaedacbebeedbccdcceabcedbcbbebcbcadbdbabdddbbecdabaedadbeedaaabbacbeecebabccbececabbcebedaaeebacaaebaceaedbcddbcbbceaabeadedbbeceabbdabcddccedeeedebcbedbadcdcadbecddbccdccbeeabeedeebaabbcdcadbddbedbeabbaebdddaaabbecccaecbbeebadacacaccbabedaadeadbbeabcadceaeaddbccaadaabbbbcbbaadaddddeecaabbeceeedeccadebebccbaaecbccccdbddeebbdebddcadedadcacacaeaaeebadbbbaceadecbaabdeadddebbdcbbcddcaeaaaaecadcabeebbadacccbbbdcdcaebcddcabbbdcbbdecedbcebddadcddceeaabadedcacadebbbecbecabdecddbdaaeaeceadadcbcecddceabcdddaaecdccddddeedecdbebccacdcbeebaeaeddcdbedbbcacbcabbdcbcbaacaabdcdebbaaebbbccbabbbcebcabbbbacadedacccdcacebcceaaeadaacadaccaabdaabeceababcdeeccecedabcebebaeabdbddeadbadbeeeadecaceeaacdbdeccdebdcccbcddbaceaadceadcbceaddebeabbcaaeeeaaaceebceedcaeecdbabcaadacceccccabdbadaddbdcbdeaeaadeeebbaaebaddaecebdbdacacddbdbdeaeeadeccaababbdccbeebceecebadaceeaacaabeeacebebddabcedecbaadbeeebebdbbedaeebebcabdcdcdccccaceccecdeedaabddadecaeaebccdbddbcbcacedcadeeccacbcbdbabdccaeedaceedebbbdedcbabbcdabdbabcacaebecebadaeabeedcddaaadcabaecbecebeddcedbdeacccdeacccbdababadbaaebceccbcadaaccabdabdcdbaeccaaecacdadcabaceebbedcceccecccbddbbbeaebcbddeecdaecedbabeeecdadeebabdcbcbbdaceddacecbbdcebeceabaacbcccdaeeeaddddcaaacebcaccdeebaceacaaecebeddbaceebdacaceadedbbceeadcabdeadebebbccaadcaebdbdbeebebceecebedaddecdabaaaeeeebedceeaadcdadaeccbacaaaabcbeeedbceedeaaecebeeabeeeeccbadcabbedcdabebeccebaadccdeaadbcaddeddcdadeaaadeeebeeccbdaacaaececcdecedcacabdeacdaaeaaecedbbeebeeacaebaddebbcacaadaeedecceaeccccabbbcecaeccdacebbdccacbedeacaabdccebdcddeabbaeaebbdbbcbdceedcadccabdeaccbccdcbdaaeddaebcdeebeebcdaaeaebabadebdedbbeebebbbbccbbebceeaaedadedeccdacbbeccbeaabeeeccbabbcbdcbdbeddcadaaaeaaaabdcabecbcaaebcccdcbedaceeedcdbcebbdeacbdecebadaddadabcbbebadaedddddaadbaccbddbaccacdaecacddecedabcabbdbaadabcecdadbdabccccbaddcadaacbcebeaceedeeabeaacecaeeeeabacecabcadacdadceabcacbaedcbeebdccccddccdbaaeeceacadbabbdccbbdbbdedeabedadeccecedcbbeedbdbaaddeebdcbcbddccbedededbbedebeaddabbdebcdbadecebcbccaabaecdbadbccbdcebbcabcaeaceebeebdecaeeddcadeebcccedebdebebdebcadbebcacceeaebdeadcbdcbeecacaeaccccababdddbabbeecbbaaaedeeaeabbaddcceeadddbeccaeeadbecdbeabeeadebbabbdaabbdabdbbcaaacdaceebcbacdebbcbaabeedebabecdabaebaacabdecebdeddbbbebbeccdeaacccbbaaedbceedccdedbbecaacbabdbaeeabcdacddaaecaeabcceabbdbededabeabbccababccdddaaabddcedeecbadbbbdcceadcddeaaeaeacbcbbdecbddacccaabaaadbccccecbccebccbcceacbeddbaadcacaabaeabddcedbaddccbdcaebaeceeeabedddbdeaedadaedbaabddcdbebaaaaecacddeabcadeaebcdbdebacabcdcdeccdaaceeeadbedbbddbbcedceacdbeadeadcdedeecaeeeeddbaaabbebbcbdeaadccbbaebbbcceeadecaecbeaabcedcabbeaedddddbacbeeeebebcdabaeeddadcbaeacddecdbcdedcbecedbcdeaeebcaabbbdbbecabcaedbcaebaadacbdbebcbadcebacedcedaedbeeaddabdcdceadddaacccaaeedcbcdcbdaecdceebedbcbbddcdaedebbaabcdeabcededacddcedaeeabeadabdcbacceadcddcecdecccaebdddadcbabdccdcddaecaadadcbecdeedebddcedacecceedddcceeecbaaabeeeaccedbedcbadaabdbeadeacddcdaaceceeadeedcdadcaccbcebccacececbabaeacaeddeeadebbbedeabdeecedaccdcedbecdbcbadeecbcbeeaaeecddeebdeeddcbdbaedbddeecbecbabdaeedbbaebabeedecbbcaddcdaddaeecacaebdcbcaedaaaaadcccecabaddcaeadbdadadbcabcddebcabbccceacebbeddcecbacdaecbaecedbbabacaedadeddcbcdecabcdeabbeaccbbcbeeedadbedebbcadaaddaacdaeabcdeaaeecbccaebcbabaaedbcbdeaaddcbeabbecbdeccbbbdedbddeaabaeeaecccbcadedbdabdccbccebccbbebdbdaddceddadbeadeacabeaceedababeecbedacabeccdebcdbaaebbbbdcdaacaeceacdebedccbdbecdcddeeccecdecadbaaebccedcdebaeeccbaabdbdaeedcacdadddddbbbbeaaabcbeacbbdacecaebdcebdbdbbedbadeeceacadabbddeecaccbacdbbababecbdbcbadbdbbcedccaaeaaebaedddcdeaacccbbeaeadeacecadcdcddcdbabcdcacbbeebcaabbecbecebecbceacecaceedabcdeeaeacaaceedcaeaedeeecccedddbbdbebeededabbaacddbacbcbceedbeeebeacbdedcaecebcacccceeaceabbedbbcdebdccceeaccaeabdccecbeecbdcacbedbdecaeacaaedacbabcaeaddbebdcccadeedabeaeceecacbdcceadeddcecaccedecaaadeebaebbabdcadedededbbaaddaadbebaeaaacccdbcccdbbdaceaaebdeacecbbccccbcdeddedbebcdcedaeeceecdeebebecdaedeeeadeddadaabcdebdddcdcdeecceddbeddeacaeddbaccaacddaaddbcbcaaacddaccaedcbadcdeaaecadebbcaaebeeabbecbedeaebadecddcdbcbcadcebaabbeadaaaaccdbdcaccbdcdacbbacecdaabacddcbdebebabaeccabaceadcaeeadceadcabbbccacdaedabeadbeacbbccabccabdbaddeadcdcdcbebedaaaeadadbcccdbeebdadddedcdecacceeaeaaeaacedabbdceabbbacdbeadacaaddbcedbbcdbabcabbaacddccdaeccadbbaccadbbcedbdddeaeedbabcacabbaaadbcacacbbdbaeecccaadaececeedebdaaeaeeeeebadbdedcbbcdcdaececccaeeaddeacdeacbecbdedaaaadbadbbcbaceacdecbaaadabacdbbbededcbdbaabccbedecccbbabacebaeceddbbbbbdedcedbddeeccdeecedeecdedceabbcacaceadaebaeebedecaaedebddccbeaeebabecddbecadedbacdccdccdacbcbcebeacdeabeedccbedcbbbabdbcdcbeeebdedcbdacbccadddbebcabdbbaeceecababaacaaeedeedccebeebcddccabcacbeccaaeadeeccecbdeacacacdbcbcaecdbdaebbdeacedcaebbdaacdddcecceadccdaadbddabeaabebecdadddbbabdadbcddcbdedccdadbbebdacecdbddedccbcbaaeccbedcadbdeabecbbecbdeadaadadececbddebdcbbddebabbeaaeececbabadccaedeedecbaddadbabbdacbbbdaccbeaeeebccdeebdbdaabdcabadcadadabacbaeacdebcdbbcaaddaaceebabaeeedeccdadaebceebabbeaaaadbadbceddbedabedaebbeccaabedbbcbccdbbaaabeacaedecbeeaabeeaccaeadbcdadaeeadbddccbcddecaeddbdbceadeaeddecabdceaccbeaecbcbdcbdadbcacaeabceaedaeecaeadceaddeeaccceaabcbbcdbacbabcdeacddcbbcbbcbbacccdaaecebaeceebdedddcbdeecbdcecabaabbecacbdcadbbdaddebddbeebcdbeddcabbaacedbacaebadbdebecadebeeecadcaccbcdcaaccddcedbbbdeccbbbeaeaececacbdbdcdeedeebeadbbdeeadcbcbddcabdbccedebcddbbbcadcdaebdbbeaddaddedbdeadabbcdddaccdbbceebbdbaebdebbdaeeecbdebdcbedacdeeecceedddabbadbdaeceabcbcbcbeadeaaaebbbbcbbbaaceceabcddbbdacbdaaaedeaabbadebedbbdaedcebbacaddecddaabeedccabbedebdaabbaccbaccdaecdadaddceeceebdbbeccedddcebdbadebddaecbbbaaceabaeebecaddbabddedaebcedbadaaaaaaaccbaecdbbaaabaebbbbabeaaecdcaabbdecbecdedebbacceeddceacdadeabdceecbbbecebabddbadecddbbabceeccdaebaecbdcaabbaacedaaeddccbaeeddeebeadbaaedaaacebcbadcbdaddcedababbabcbacedabbebbbaaaadcbecadebbbbeebcdcbcacccbedceaaceeddecadbaacdebbcacdeaacebaddeedabbbddaebcbaccedabbabaaabdaacdecdabdcbcdaadddacabbacebecbccedcedacacbecedaeaecdcdaccdeaabdddcaeacceddeaedacbcdccdeccddaacbeecaaaaeebcbdbcdcdebeeababccdeacaeddddebbdebeeabddeabcbadbccceedeeeecabeebeccbddeccedcbdeaaacadbdcaccaecccbeacdcbadebcbbdaeeeccadacbbdebdccdeeaebdedddeadaaebabdeecacebbaabdceaaeebddeeaabbcccabebdbdadeedadedcaabdccedaaeaddedaebceaceaaaeeeaadddaecaedcaaaadecaaaeccdddaaccabeeedecbdcedbaaecceddddbdbeabdcacdeebaccecedaebdaeaabeadbedacccdbcacbbdbdbbeebaeebaeaddaacbcdadacccaaaecceabdbdccdaaadeaecbeeeeebdeccdccdaabcaceabeadaeccadebbadecbddacdbdccebddddccbbccabddaeabdccaaeeabccecaaedebabcecdcdbbcdddaebcedcbcdcbcbcccaeabadebcaddadceaeecdddebabdadcaaadaadeecdccdbdadcbdccdadaabaceebeaddaeabdddaadcdddbcabedbbeacdeeccdaecddccedcbbceadeeebcaedbdbeadbdcdeecacaedccbacccccbbcdbecadeebececacecbebbabeebcbcddeeebeaceabbaccbbddadeedbeebabbadaecbcedecebccbcadedaeeacbbacceedcdbaabcbbdabccddbdeeebcbcdbecabceadcacceeabbeccaedcbdcbceebbbbbcdcdcdabadddcedccdebadaaedbbacaeceacbddddedbabebbcebdeecddaebcccdbecabccbdcccccbdeaaaaeeeeccdcbbbacedecdabebcaacedacdecbbddbeedbbacccaccceccbcceaacddabbabeaecaaebcaeaabdbdedecaccceaebbcbdccccbaeaadddbcedcdabddbaecacbbeeecebcbeaedbcbbddbbebaccadcbdcdcdccedbbcadedcaecadcbddbbdedeaeaadcaddcdbccdcacdeeacdebebbbdbaebbcaaadbabddacababddbeadabcacecaddeeccadbbbeeedababccbcdbbcbcacdaddeddeeadddbbbdaebaaaabaddacababdaeececbabaabaacdcdbcecbceccbbbdaabbcdaebdcaccdbeaeaabbecbdeabcaacacdaddddbceaeaacdebeadbbdccebdaaddaaccecbaebeaebdbaccddbeebcddeeaddaeaeedbbdedddccecbadeabdbaebabaabebdeeececedddaaaeabcecebaddebaedcdceacacacacbaeebdcdedaeacddbcddedccececdaebebcedbcaaebecbabdeacdaccaaddaaeabcdcbadddcddcbdaeeeeaeaeabebccccdecaeaabdcbdecbeddacceeeccdeddccedceeccdccdeadbcdecaabcbedbcbeddcacccdbadcbbbeaeabeacbceddcbbabeddeaeedabeeeaecbeabdcdcdaaeedcbdbebccacccacaadbaccdbdcaadbdeacdbcabeebbebeeebbcaaabecdcdadcabcabadbeeeeeaddeadabaabcddcbbecdaaedcbdbacaceddebcccdcbeaaeabebeaacccebebebacecababbceedabcccaeeaccbeeddaecaabcbccdabeceabddcdbdcacdaaddccaeecdebebcadbceacbbddecbacbdcbbecacbaceddabadacabcbaecdcbcaaaacaaacecdbaebbbabdbdbcbbadadcbacdaaabdccbaabcecabeadadbcbeebcbccbabebceaceaabeaebccacbacaedeeacebddeaddbcdcebbecebadbbbeecdbcceaaeeecaecebcabddcaeedbeaedcdeecddcbadceaaeabbcdecebcedeeabecbeadebcbcedbddcdbcabedcdceaacdacddaaedabbdecdabbbcdacdbdecabaccbacebebdabdebcbbbdabddcedbbbacdbdaaacbbceebdbdcbadebbcaccbbdaeecdcebdbbcdabbbdbeaccacabddbcbceeadddadacceceeeeceeaecebedcedcdbdecebbbaaaacbcabcaddaccadcdaeaaeaedecdccaeeabebdbcceeadbcacaedaeadbbdeacabbadaedaabebbabecccebecbaeaeadcdbebbbdbadbdbadddaccdbcbcccebceebdedddbbdaebdedadbeeacbbcceccbbbedbddeabebeaebcccedceeacdaddacaadbbcceeaacbccececaabaebdeacdbacabcaeeeebeedbeedbdeedacebbabbdcccebdebeebcaeddcedddbecbbccadacaeccacacadbbcbcdcededcaedbbcbcdacacbdbabbcecebdaacecdbadedcabddcddcbeabccbeeddeeceadaadbbecdcdeeadcababaedaacacaccbbddcdeebaeedebcaedaaadaeeaacceacdcccabbcbaeeacbecacabeedbcbdcaebeabdcceadbbcbdbdcbbebdeeceeaaacaeaeebcceeecdbeeaabdbdcedacabbbedeabaaaceedcbccbbbaebcbecabedddeaabaadeddaedddddcdbaeeeceeceddabdbdaebadabbeecccbbbddcbacbebdeddaabbcebabcddeadbaaacbccdaaceaabbaebdaaedbdbdecaddddaadbbdcceecdbccbebbcdcbbbcccedacccccbbdadcaceeaebcaacdcdebcbbacbbdaddddbacaddeeebcbdbeabcadadadbeedeceacabeebebabaacdaddebaccddeaccabcdbcaceecccbddbaecedebdadbecaccaabbeedacbadbdcdaeebecbbabcbeeeacbeaedeabbdbcbabbddddaddbcedbcedcedceecdecbcadbdaacbeddeddadabdbdeadaaddbbebbcbededbadaaaacecedccdadcebedaabcdabcdebcbaaddedddaeccadedadeeeadabdbbebccbcddeeabdbeccbadaacabaababddbeecadececddbaecebeeeadedeadeeedabbedcedaebeecbceaaededbeecadabeddbdecddebdaacdccccdddaaddeacacabbbeabdcadcacbbaeeaeeebbbcccbcdcaaaababeecbabdddeccdcadaaddbadeeaabebeebdaaacaeaedaacedaecbabbbcdcddbadbdeccaeeebbacebbbacbeecaeddbdaebcbabeacecbccdbaeabeaeccedcaacddcccddababbedbdecaceaabbeaaedebaacecbdaacccdcbcbeaeddbbacacdecaabbcbcbbcceebdcedbcbacdcdbdcdabcabdeccbebaeadcbdbeaeeaeebeedddabacbbddaecbbbcebedcdbececcdecdacdadeaacdbbbeaceeacadccabdcbbdebacaddebdbcabaeeeecbeecddaccadcbcbaebbbabadcaebcbbcabbacbbbdceaebcabbadddcdaadeaeaacaccecaddecccebbcbaececaacacbcbabedbbcaaddaeebcddcdcbeeebadcbecaecbecbabccdbbbaebaadabbaaccddedededaebcbaababddbedcedebdbeebededeacdcbdbccceadddbbacdaddccbcbcbbbdbaabbebaabcbaebacdacecdcccbacbebadbdbcbcdeebbddcaaadaeaaceadaededcaabceaaedbbacececcbbbedaeddabcbcddbdbcbdcccccdcaaadeacdcabcbeaeecaeaccbceedeaeccadbdabeecbadcccbadbceedaaaceaabbdbbabededecaaeeecaacaedbdaadeddcaacdecceecbbeeeedbdcebbebcdbcdabadaaabdacebacdeacdecceaedabdbecbcaccdeddddbbcebbdbecbedeccebaaadeeebbccccadececabeddcecbcbaaecaddeddeeecebecaedebeeeacbcabeaeedeecbdabbcaceadceacbdaeaeaddddbecbdbdbbaabdcacdeebabcadcbeecabecbeceadaecadecaaaceebdcdcdabdededbeddaebdceeaebdeabaccabcdebadabeeecebeeebeecabdccaaaedbbcddacbaaaadadcadcdccebabeedaacadadbabdccacdaabccbcaadaabeccbdadeecaacdcddedacbbbbbaabdcdcebecdebebddedeceebbeaeaaaccebedebecdaedebdbecdeedcaebeeebbecadbaecebcdcceebaccbecdeabbaceccdaaadbcdeceacbcddeeabebdabaecedcbabdeebbeccdecbdcaeaddcebbdbdbcdabebdcbeaddaeabaceebaaadeaebabccecdcedcacbaabdcccdbdccbbbadbbecabbcbeababeaebbacbebccbaababaaecbaecbebcdbadceecddaebdcbecceaeddbedbebebebbebecadddbaeedecbeceebeecbedeebcbdecebcbdcbbdcccadaaeecddbdaddceaeacbaeeeaedceaceaeebedbaeebdbabadbeabcacacbabbebecbdadeabdcabdcebcdcceddacdedcbdecaedadcbaaedaeebaeecedeebdcbbeedaddcaaadbcbaccabecabcbccbbacedccbcbecebcaadebecccabcdcbeebebccedbcbbbeabaaecdbdedaccbaeaadcbaccdbeedeccdbdcebbbbecbaebbbcdccbbadbdabbbdebcdcadcacaceadaaccebedadebdedcccaeeaedaacbdceecacabcccbbbedacdbdbcecebdbaeeaedceaeeedecedadbabebccdddbdeeddaaddaddbdedbedbccbdddcaaacbeaeeceacaddcceaeebbdbaeebadacadddbdaabaeebadcaedecbbcdbacdbccdccacedacaababaacacacdaacdbaabcabeecacdecdbbddececaeabbeabeeebccbabcbbbdcdcadedcaaabbcbcdadecedecdcbedbbeaaeeedadadecdbcceeddceedebbcbbdedacbebbcedbdeaedeabbeddddedcdccaaaedbaecbcdbceabeededaebdabbadcdaacabdbbbdeadadaeebdebacbeeebddbedebdaacbacabbeadeeabaedaddaddaaeadbdbcbeecbcebcebacbabbecccbedcbcbedeadbbbdbdccddbbeceecacdccedbebcbbebbbeadbcccbaabbddbdebeaaebcdcaacabdcbcabdccadbddaedacbcdadcddbddebeaeedeabcdeaecdcbadaacbaaaaebbdbabbeaaccdcacaadbcaaddcbcabedaadddbbbaeeeabaaebeaccacbcdaadebabceabaedcbbcdedeeaaacbddddcbbdbdaaaedbabcadadbdaebdbebbdbecceacadbdcaaeccdcdbbabbcabeddcccdaccaabccdbdaebceeaccebacdbbcdcacabbbeecebadceaccddcaddeabdebbccbbdebcededabadbdcaeebeedbddccbaccbadeeeeacbdaeacddbbcbbeaabbcddeececdecbdbdecebebeedeebbbcbbaeaaddcbdceeddaabaceecebcdcdcabeabdadacceeabccbbcbbebdeabdbebaaebcbeccaeeebabdcaaeaeadedddeadebaedcebadcabeaddedddedaebbbbbdceccbaacacadceebbcaaebeaaaaccddebedaaaaacebaeccedecbdebbdcabdbbaddbabcdbaecabeddaeabcbbbdbdcdabbdabeeeaddcbdbecedbcabebaaccabbaccbbeaacccbaaddcccbbdbacaccdcedbacbedbdbcbbeccdccdecdbadbdbdebbddabacebebaeabeeddddadbdbeaadacddaeeadbebaeebcddacebccbebbedbedbacbedbceeaaecbdaacecbcdcabbebbcedcdccabbdcdabbcaeddbbabbadadcccccdcdeebaacbcbbdbcedcaeeaebcecedbcabecedabebebadeeedcebccbdbacedbddaddbeeeeaadcadcecbcabdabcbadddedceeacebeeedeeceacbbcaeeacceadbccbaebdcddbbbbcbecdcccecebbdabaaabbbdeebcbceceaecccccdaadaaeaaacceccdaeedebbadecedcaccedecadaabdecbdcbadabdbcabdcaebeecccadadacccbebdbaeccaacbcaaadddeececabbabdbaaaceadcaececbdcbbecadbabcecabecacedeaeeaaeadaebdbbebadecdedeaccceacbdaaddaeaadbbdbbcaddedececeedbcedbcaddabdebaadbbdaaeabaedabedbbebeccdcdddbdbcabadbcaedceaccadcceaabdadbbeabdcaaeceacabaaabdcdadccdaaccabaceedaacbebecadbdbbdaedbbecebdeedbedddccdbaaedbcaeeeaeebdceeddeeeeceedadcccdddbddccdbabdaaacdadcaaceaaecededccabdbadbbcbabbececaecbebbebacdaabbaddbeaaccebdbcadaecaacddeeeaaaddbccecbdeebdaaadaceeacbddacbacdacbedacdeaceebdceadcdbbaacbebbbdbceceeedcecbabcdaeeabbcaedeeabbceebcbcceedcbcbddceadbbeadbbbbdaedbdcaeccecbcbabbacacacedbdabaacdcacbcbacddedccceceeebbdadbaeebbadbebaccadabeccedaadbcddcdacddeabdacddeecbaaddccaddbbbcddaacbadacaadbbeeebedaacadacbebcbeccaeebdabcabdccbecddbeedccbbbcaccbbdddceeacbaccedbcbaeabecababbcdaceeddcbdadcccecddbadcebccaccabbcdaabedeeacacedbbaeedbdeeaabadcaddadedeadcddaaccbdddddedeaddcdaacddcacceeaeaaebadebceeaabbeaeaebadcbcbedaabedccbcdecadbdecebbbadcaacebdddcebeacabaebdbcbbebccacedaacccecbecadabdbedbebaeedadabaeeeeaadbdabcabbbbbaaabcbeccecacbeddeacbcceecaededadceeedaecabddeebbbbcdaddaeeddaeedbadceeeecdedaabddbdebdbaacccaaeebeeccaaacbbbcbceacbecddceabaabbcbdadbbdedbdecbdeacabdbcccddadaccbdbeaaadbcdaaaceeaebbbbecbcaaedbabdecdbcebcebcddbdaacedabaeeccacceeadcbcbdececcbaaebbbadddbcdacebbdacaeacadacedaaaecebcebbaaceeebeedddaaebcbdeeaaaabdaadaedbbdaaceeecedbeedcbecbbebaadddaceeccddbbadcbdaaadadaabcadaebabddcaebcbcdacdeeedcbeeebcdabbacbaebaeeabdeadcaaeaaeabcedaeecddcaebbbdacacaabcdbbdedcebbbebeeadcdccdcddbbaeddadebaeccbbabecbdcddcabbbbadecbbeecbcececbaaceeaaebbcbbdbdbdceaaeacbdcedbabcdcebdecdaaebedeacaeebebeabaaeceacaeecddaaccdeeebcddedbdcccdcbdcecbecebebcabbbeeabbcecebbdcedcceccdcebeacaacaeddbaaacebaccbaabcaedbcaeeedaeeceeedeeccecdcbeecaaabdedeeabbddebdadebbccebbacacdabbcecdbdadbaddcaaeaebcedcbaccdbeadcbcebedebededdbbababeeacecabbdbadaeccdeddabaeeeecabcbcddaaebdbbdbcabecacbbaaadcdebaceaebaaeccaaecbbcbadbbdcbdebeaaccbecaddbdacbbbeaaddbcaeecaacbdeedbbdacaecaeeabeabdeedaedcccedabcdadcebdcbbabbeabadcacaebcecbecdeeaaedeeecadaabcedddcbcbeddecbbddbeadcebdddbbcccaededbbdeabbdcbcdaedeeddecbbebdccccccacaeddebcdbbdbbbebcaeeaadeebaeadcdebaecddaaebceeceaeadebaadbeeabebccaccdedaedcccaecbbabbbcbdbcbcbbdaebdeeeedebaebddcebeaecdecbdaceccadbabddaeccdbeaaadeeacceecbdaadcecbbcccdcebeadbdaadeecbdcbedbabcbccbbdbdddcebcacacccdcddaabebcbebadabbcdcbdadaeebcbbeacacaacaedddadebadbbbeedddbbbbaccacbbcaedcdedbdeddeeaacabbeaceebabbcedbcebbebedaddadbacecccbebbedebedcecbcaebecaacababecababacaccecdccdebabaadcceeabbacccdacedecdaeabdddceadbeabcadbbcdecdbcdddcdeeddceeeebcbbcdababbceaddecccacdebbbabccaddedebacecddaccdbdccecdaadbcaeceedbbabcebdbbadbdeeabbbdacadbdbeeccdeddaecdbaeedbaccaaecbaaeecdbcbceadebdccbeecbdbbbbedaecbcebbcbbddebbdbabedcedaaeedcbcbeaadcdceaabeaedbdedbaadaaebcdabdccdcbdabbeccabcccbccbabbbebdecebcbdaaeddedebcbcecddeacbccabcbdceeebdaadacbbbedbaddddaadaceacacacccedbeeecacbacdebdccaedccacaedccabcbbbebeebcdbbdddecdbcebeabcebcabccdcedebadcbcbcbedecebaebacadcacadddedbecdeebaebdcbbddddaeedeeedeeaddbbdedbcccaabedbbdecbcaccacaebdcddaecbcbdcdacacedbbdcabdbcbedbdadbbcbaeccabbabdabdeebdeccadebeadbdadadbbdeadecaabceecdbdcebcaeccbadbaeadbbcdcbcbcbeadaecbaabbdceceaebaaecbdabadebaeccaddceabcbdebacaacebadcebddaaebeddaddbadeadeedbededaaebadaebbdabdabecccadcbccceeddccacbbabeadcabdadceccaeddbaeeadeaedaedccccaeeebebdeaabdbbbcedbbedcdaeecebcbcceeabbbeabeaaabeeaacbadeccbbdaeebdaaeaedbadeabaaadedaeaaebcdbacccdcdeececeeaebccaaabcadceaaeacbddbdcbddbebdacbeabcabccaedcbdcbccaceeeabdbcaebbdbcccabdaabeddbeaaaaacbaccdcaeaedadccdcebbbccdadaeaeabceccdbadbdaacbdadbcdeebceeacbacdbacbacecebbacdadadeacedbbaebdbbebaedbdacbebcebcadaeeadadedcebaacbbdeaaaecbaeaabdcdeeebbaaaabaeebcbcadcdaaedeaecdcbddaeeadeedaaabdcebaababcbedddbaacdecdbaededcacabedaaedcdddccbaabebacccaeadeecdddcacabbdeadaacabeccbdcbbeacaedecbedbcebbdccebaccacbbbecadeedeeebdeddbeedcabcbcabbcaccbcebeaccbcacbceeeadaeaebdcbceeacacedacabaaadbbedaadbeedacaddeecddeacebcebbcdcdddbddaeaaebaeecdcaeaaeabbbeceabecbccacdbcbdaacaeacdbbceccdbdbceecdadebebedeebdaddabcbecdddbdeecadcbdebdbdeaaceecebeebeececeddbadebacbacacbdcedebecdddceeecacdbdeeadbdadcbebeccdeaccbbbccdaebbdbbadaadacbaaadcdecbdceaeabeeabdaceadecdedaaaeabedbbdbbaedabeceadcbceddbaeecabeddbdddcbbcacdccdecedeebbeedbdcdbdeedbacdddaaededbaadadcbbbbedddadaebcdacbddcbecdbbbdebbdebcddcbccadcaeaaaaccacdebbcbcbcaebccbbdaabaccdddacbecacabbeeeaddeecbbdaddcaebebdeaabbedbcabbeaeeaacdddbedccdecaeacbabedaebaecadabeedbdeeaddbcbcdadcccceebaebbddabbcabacaeebecbbebdcdadcaeaaddeadadacaaaadababcabbabcaeddbddcdaaeecdcdaebbaceeeabebaccbecaebddaccadadbcaacececbdacebcabccbdddbabcdeececcecddcdedbabdbcbbcdcdeccadbeeaadcaebeaeacacacbabaddcdcbcebabacaebaabecccbacedaeacddbccaddbabcdecdaabaedbdcedcdbbbdcbbceedaaabaeebabadececcccebaccbbdcadbdddbedebeebaceaaacdccdceacaeabcebbebdebbdaabeaaedbdcdcbbbbbacbdbabebdbaababcdcadadeaaaacbbaaccaddcecacbcddaceaedbccebaaaeaadeaadcbedcdcadccdbdadedebdbebcaabdecddecbcdddebbceeeecbcaebaeaadccbcbbcbdcedacbccebbbdcaaacecbddccdaeddedccddedecadadababdccdecababbadcbaeadceadbbdbddbaeddceeabedceaaadeeeeedeeceaebbbbdedecaadcbcabcbbecaceeadeadabacccbddaeadadecabadecbeaebcccbcadceeaccbbebaceacbcdbcdadbabaadddabddcdeabaaacceabcbbdcbbbbaabebdbbeacadcebbeaaddceaebacacdedebcbacadaacdaeeeddbdbebcbdabaccbcadbcebacbaceecbadebccbbecebdcedbdedddaabdaccceaedcdaaeddacccbcdeeacdbedaedccdddebdeecdcadabcbebebcdececeadeceebbdbddedddaddcaeadccdacbbabbdaacbbcdadceabceaebeabcdaddccdebbbebbecceeaabccceaaebeabceddcbecbaeecadacdcebbeedeeeabcdcbaaddedeceedeeeeddadebcdabbbaeedbddeaacabddcebaedadbeecbcaccaaaddeccadaacabcdaecdbcadbecaededeecbcebebadcbadaebcbbebedcdceaaecacedaccccaacceabadaeaaaabccadedeceddbcababacdedbeacdecbbbacedcadbcabebddbdbecddaeadcaecbdcccbadbacacdddceaddccddeeabbcdcedeadbcebceeeccbdbadebcebcecdedbebecceaebabdcbeebaccdbdbdadcadedabeadbddcbbcaadeaddeebdaaddcebdbdaccebbbaeeeecaaeabbaaacbbbaacecbccbcbddaddbeaaccdbecadeabbbbbaeccabbecbbbaaabbbdbbaabeaaabbbcedecdbbabbaaecbbebbabeabbacbcebbcebaecebceadabdeeeecccdbacdbbcdbcedcccdaeccacceebccabadcacebdaaceabedbcacceecabeeadeacbaeabebdbcaadbebdabaadbcbbddcebdceeeddcbbceaccabbdaeeebdeedddbbcceeaecdaccdbbdbdbaedecaacbbbaceeebaaeceeccecdccbadccdbdceaaaabbdaaedccecadbacbdaaadbcceeeedddadcbcbdebbadeecbceddaedbbcbaddbcdbcaebdbacebddceeacdababacedbbbdeadebcddbcedcdcedebdaaeeaebcbebcdbdceaeabacdedeedaaeceebedcbaecbecdbebddeaedeadabbbcdebcbdcdcdbccbcdbbeeebebcedcdcbebdaedbeedbbdabcaceacbdeeaadeebdbeabaaaabceccddadebadabedaddeadcdabeaecacdddcdedbdeabaadedccdaceeacaebcbaaeeeccaeacedcaaacdcedceebbeabedacadeaeddcbcacacbadabcbbbabeaeaaceabedbbeaededccbcdcceebddaaacdcedabcbaedddbadcccbeceabadbccbacaeeececbbdbddbaebdeddcadcebaaacddaccecbeeecaaaeccacaaceccaacabcbcdedcccaeddacbdbdeacbceacbcdadbedecabdedbabbadbceedcaabdaeeedccdababcecbcebdebdabbeaecccebbdeaddacbeccdacbaebbabbcebbdecaaaadeedbeecdcbbeeaaadccebabedbcabcdadcdbaabbdacecbddbeeacadddbdbaebeebecccbedbdcaaaedbebbbeadbdbddbddbdaabbeadacaedcacbcdeaeacbddecccbdebcecaeacbdedcdbbaedeaabbbcbbcbcbebecbdbdeacebcaddddedcbadbbdbcbbdbadadddeacdeceabcbbceacbbbddebadcaaaceadbebcbbecdbccecdbddbeecbcbabcedbcadaeceeadcbcceddcbaceeceaedaadbdcbbccadeeddebeccebdeddcedeedeaacabdbccaecccbacecbedccadbaeaadadbabcceadabecdabbeccbdbacbeadcdacdbbdbceabaeaeedabceabebeedaceabbbeedbebeccabecdedbddbbdecaebbbbebbcabecdedcaeabebedaaaabecbeddbebbacadeddbcddcacbedeaddcbbbdbaaaeaecbddabbaeebebbbcecaebbcebbeacdbbbcdedcbdaeaeebeccbccabedabbdeecdbdeeabdbabdeadddeabbcaacecbebedbdeaebcdaadebbecebdababbaadbeaacddcbeabcbbacdbecedaebaedacbddbccdeeadcbaabdbdeabdbdceeababecbadaacbdcdebacddcdceedbdcddadadcdeebbcaceadedbccceadcaadaecbeaacdaccebbadacdbccddbbcecddeeeccabeebecadddcabdcbeaaebaaccccdacadacdbaadaddeeaeabebedbeddbadaebaeacbeadeaaaccbedbeeebddaceababdebcacacddabcbbbdbdebeedaebcdecdebaccceddebdabceeadbacccbcedccdeedbbccbbeaeacabdddedcdeeccbabdbcaacedcceeceebabadadaeabccecbdbedcebaccbebdaebacdbbdcadabbbaddcebccbabbbbeaedacdceedabcedaaaeddbeaceaddccaecdaedeecdbcdebbceaabcceeaddccadcebcccdbdedcbacaedcbbcacebabcabadecbccbbdcaccaacddebccacbcdecddcebcaceccdecceeaacecebcaddbbbeeaddaeaebabdddeecdeaceccaccddeccbdedcbeabceacacdeaeabddaaadebcccaeeeebdcbdccbcbacadcabdcaecebeadddebcabbbddccbcabeeeacbdebadadddeedbbbbacdcddddabeaeacdaaccbeaabebbaadeaeeeebccddecadccebddacaaecddcaccbdccebeabbceecdebdaaceeadbebbcebdcaabacccdbcbaacbdbcdcacabdccdacceeeabbebbbecdccaeedbbdedecbcebbbecdeeedaecaeaecaacaecccabebaaabdceeaccababecdaccadcbcabdaeaebeedbdeadcddeabdadcedaaaeebdcbddbaaabebdbdaabcbbbbdbdedeeadbcedacbcbdbddebcdbceccbebcbabdbcdbaacbbbcadecddcddcaebcdadbadeacccddbbebcaeabeebedeeecdceacbabaeaabdddededadbcaeeaaeebcaeaaceebdaeacbebeebaedeaecbececbbbccbddadebbebacbaacbaddaadbdabacdebcbebececbbdaceaeddcddadaeccacaeecbaccadcaccbddbeccdccacebdcabdceacbeeddcebdbadeacedccabeeadcbaacaeacaebdbdccaabbedcabdceeebbadeaaaeaceadbdceeeabdebbbadceeeacdcddbabdbdaaacebcdabbbdbcacaccdbabdbebaeceeebacbeadbeecaccccebdaecdbdddebdddecdbbabecdedcdabdecccecdbaabbdeecccbabcbbeaaabcbdbececeedadbceacaeabcccbddedaacddbaaadeaabcdbccbeeabaedbeecaebdcbaddaecdecbdbbaeaceddcebbdadbbdebdaedddeecaccacaadcbcecbcbbdeebcaaeedeebeabdabcecbdebcccadebaccddcddeddcebabbdddaceddddaacbecebbdeeccddddbbbcebbedabcbedbbcaeecbaadbacdabbaeeaccbabcbececaddbdaaaabdbddaecbaebcaadaeacdcdeacebcdecbeecdabbceecaeebcaabbcaccbdebcddddeeaedeeabbbddabddbbdeaebcbbebaedbdcbaccdecedeaadacecdbbbbeaccaaadedcbaeeddcaacccacacabdbcebdadedbbdbdaaebaeceddebdbabdccedadcbaeeeeeabaacccddedeedddaeeaddbeddaeebadebcebdcaabcdecaedeaeaabecacaadedaadcabedcebddadbccbecedaadcbeaacaccdbcebbdbbccdbdcbdaaeeedccbbaecedaebcedcadebcbdebbeaebbeddebcadcbabeeddbbcdacadecacabdaedbaebdddcedddeabdbbdebaeeeeeeccecaacaecbebcbcbacababdcdcdbeeccdbddebcecedbcceadebdcceacebcbdacecccddbaecaeaccdeacadeabadbaeceacedcbcbdbdcbbaabceeacdbadeedaceddbbdbdccbdcbaedebcdbaeaecdcbbcdeabebaabcdeeebbdbebbabdebebcdabebccadcdedceaaaebccebacbacbdcededcbcdaaccaeaaddaeaddebeebcceaeedeecccbbdaebcdbeeabccddeabcadaaebdaecdbcedcbaaeabeeadeeaabbcccdbbceecaabebdcbeecedcdaaadceabbbadbeaaaabedaabeebebbecdacdeaddaeaececbceeeccddbbccddbaecabaaccecabbcbabacaedcbddacddddedccccaeebeacadcaacabbcedcaaeeceedeedaeddbbaeceaebabbdeccdddebacacaeddedcdaeabbdeadaeabbeaacceaeedbdbabbebddedeeeadbcecadcbcaaedcbdaeecdecdedeccececaaedaeceaabcecccaebdebeaacdcddddadcbecaeddccebeaabeadeccabebaedebccabdbeacdeaccddedebdcebeeeaeecbceeedeaceccaeadaccbdbdbcdacdecedccbacceaeeebabdabecbbdacaedaddbacaaaadceecbebceadcbddcbaddbdccbebbeaeedebbbaebeacdcabecbacdddabacbeacccddadcbdcbcceabbecbabaedaebabcbeeedbbdbaadebedadeebcbccedaaadcebebadeaedcaecdeaebdbcacadbddbabcccbabcecdeedbaebcaabdbedaedaceeacbebddbcecdcedcecdcceeabadedaebcaaecbdbecdecdbedeaedecdcaebadabadaeaadcaddebdbbbdccbeecabedeeaabbbebaedaeeeaaeebcceabcaeedbaeabcdbcbcdcabcddeaaeceedaebcdebdaececacdacbbecdebcdcdcbbebaaddecbddbbbbedacceedbbceeacaeaaaebabeeebadcdaeeadabceeebadbdeaceecceddecdaabebbbadbebdacadccbdccdaecabaaadebaaaaaedbadceabdbbaddddabbbddcccdccecebaccaeeeadebdccacdaadacaedbcaeccbbacbeabededaacbdcdecdccaabcdbedcabbdacecabaddbddbbbacedabedbebdbcebcdeeebacbdbcdbabbbacaabcbaebddcabddecaeaabcddbccdadeadceedabbceedbaeaaaeedeeebabbaebadccdeadccdcebcaeccaebbceeababbbecbebabbaeabacbaadbccbcdbdbdaabaaeeacaaabbcddeeabecabedcdcdeaeadededbeecdaacdadbaccdedaaecedcdeabbacbdabeddecdbdeaabebeabcddaeaceccdcaabacaecacdbbecceabddacabddcbaecabcdaaabecbddbcddaaedcbdeadeadcaebaacaedccabcbbcdabdceceecdaaebbbdcedcdaedcadebbcaeecebdcebeeeebeaeaaeadeedbdaadbcedbabeabbccdbdabaeacbabeabbdaaccbbdbdceaadedbaedadaccdebbcadeadeddebcdcbadaadeaecbaedddbbbcddbcdeaceadbbbbedcabeaeceadeceaaebeceaeaecaccbcbcedbddebcedcadcabddeaceeadbaaadaceebecabeaaaddceacacaecdbdecabbaedcabcecbebaeceeabdebaecedabbcdaeaacabcaecaeebddcdcbcbbddeebadbebbbeabaaccdaadcbcacceeeccedcccdcadcbbddbbbabddecdeceddaeecebcbbcbaadaeaebcacadaaddadaebbdbecdddcdbdcdcdadcecadeedeceadeaadddeedecbceeadaaadabcecedbaddaedddabaabcceeeccbeaabcbedacacdabadeaaadecedbdadbcaedebbbccdbcebdbdedbdededbcabcdeacebdeccbacaeabbddbeedbaadbeaddaddceaacbccccdbeeccbcccbceaceaeeeaabbdaabaeabdeceaaabdbdcaaacdacebddbbcdababaacebbecaebaeeadeaddcdeaeaabdaecdecceeeaedeaccdcabdaebaeecedaacdbaedaeedccedbdbabeceebbaccbebdecccacaeccccbccbadcdbbcdcaadeebacbbedebccbdedbbedddecddcdccdeaedebedaabbdeebeceeaedbcaaddaaceedebeddabdedcdcadeddecbebceebedcabacaccdaaabbbdcaaabebddddaeaeedbbbbdeaaebbeecedeebdacceeccbcbebaadabebaabddbaaeceebddceaaaaddbceedbecabbdeeebdcdceacaedeacebedebcddecdcdaadcedbadedeceabecdaeadbeababdbdcaabdecccceceaddaeebebeeeeecaeeadcbcddccbebbaacbecadcecbdbedddebacadaadaadaeebdbebabedcecbdbeccbabacedaacaebbeebbdbbacebeacbebbbdedacebdcdaeddadecdcabbcccbabedbeecccecabddaaeeaecebcaebedcddaecbdcaddbcddbbeecdbcededeceadecbebabeaddbdddaeceadecaecadceceaacdceccbccbcdebacadbaecccabaedbdacadbaebbaabddbaeceeecbaaebeceabdeaeddabcbddbebddedcdeaeeaaacddbcecdbdcceebeceadbbdeeebbccedcacaabedacdbeebcbabecbdbbbdedcdcacddcedcabbdbbecacceaecdeccebebbcbdeadebeadbeaebdcdddacdeaeeeeddcabbddcbcceabeacbecbdcacccbdaacacadabdebdebcedddaedaacdedebabeaaacdaacaeecdbeeabebbcabdecceceabcaadadedeaacaccedbbbdaeacecdedcabcbacacedbcadeacdbcbadeecabecaeaaaacdaaedcbadacaebdbeaecbeeeebdccaeaaaadcccdccbeabbceaebbadcaacebeddacdeecdbebeaebcaadcbbdaadbabddbcbdbeeadaccbbabbbececcebcdcbdddebdaaaeaadcbbcbabdceadeeddebcdccacdddeababcdcbdcaebabbebcedeaddddbdbebabecbaadabaebbccbbbdaccdbdaaaecbbbbcccedeaccaeedcacddcdbdadcceccbeabaeaeccedcbaaedaccabacecbcccdddaddbabaeeebaebcebcebcccadbabeacbbaeabcebceebdbabeeadbeaadcbbbdedbdecbccaadbdcacddbdbabdcbcdbccdaebaccaabecabbadbbcabecbedaeeeadddbaacdedbebcccdbbbecbdcecedadccbcedcebcddecadaacabebaaaeaecdbbaceccceebbdcaacdbdddbbbddcdcaaecceaceacdccbdaedaeddcacebddebadbbddcccacdcbdceabeabbcaaabacbaacdaacbaaabdaaeebeedadaeccbbbccacababdbadbaabbebbebedeaadacaeeacceddaabdcdbadddaeabcbabccaeccbbbabcdbedbcecaaaeddabbeebabaeedcadebcebdabcebdbcebcccdbedeadbbdbdbdbebadcceacbbcdadcbcbbcedecdbaccddaddebadabcbbdeceededdeddddedaacaaddadcaebadcdcdbcedecdbdebeddaaedebeaebcccabbebaeadebcabebbadbcebaddbddeeeaccbcedeabdedaeeaaeebbddcbdacbeeabbbdeabcbdbdddaddeaccdbebddbcadabacdebabeeccabceeebbdecddcbeaadcebeaceeabcbebdbedacdcdebedceabadceadededbeceecbdbdeabbcdebbdacdbbadbcacaaacecebbbebdbceaedbbabdceeacdedceaeaeedaadeecceddaebbdecdbbbeebdaeeacaecbdeadeabaeadaeacccbcededbdbdddcdeebddbeebccbbccebeaaeebcacddadecbeeaccddeaaeebbaaccebcdaddccdbdbceaeeabaddaacdbaedbaaddbabcadbaabebccdeadceeceadadbcadcababbaaabaabacabeddedbcbabddcbcaccabeacddadeaaaaeaabeadecbbdcbebdebeaadbcddcbeeaebabebeaebdebdaaaabcddecedbeaacbbdbebedccebeccebdeeccebcbedcdcbacdadaccbdcdabcdedaaeaeabcddbacaedeaeacbcdbeeabddabeebdabedbbbcaedbdebecedabbabbdeeacbacdaceaadeaabdeabbbeabbacaeadadcebaeadddacdeebbddbdedbddedceeccbadabedabbbdabacdbaeececdeaeccebeccedecccccbdbcbdecbeeaededacecdeaecbcebaadddccbdcceeddcaeebddbbbadbdecdccaabbabeaaaceedeaacebadbddeadaeedebbdbedededbadebadbaeaaabebcedcaadecdbecabccedddbcebccbbdcceddbacebcbacecdaccedccaebdbdeababcbaaaaddacaeaabdcaadbeedabedbbcacbeecaddecaceaabcdeabeeebbebabedaccecdabebadbdbceceaecebdabcbbdababbdadeedeaebbcedceaaddeaedcaadebdbaaeacbbeebeeaeedaebbeaddbbedecdcdbbdddedaccaebbebdaddcdabbabcdebcadbecceddcdcadeacbbcdacaabaabccdeecaddbbacdbddcacdabcceddddbeeaaeccbcceecdcbcedcaaddbaaeecbbbceaabcadbaaabedcdebddaabaceaeddcbdcabbedebbbcbcbabddcaddeccaabcbadecabccebdaeeaaecdadeccdbdabacbddbceadadbaadcbdddcbaaebdeaddabdeedbbebbbacecbeaceedacebccbbbcdedbceedbedeacedcbedbedebcadadbbbbbeeabdcdaecbbeebadeeccdcedcaaaeeeadbcaccbbdecbdabbecaeccabcccbcacedccbdcdaccedbaedacadbcabcaeaeacacdebbbedbcdabedbaadeebeaddbdcceeeadcbeaeccddbdcedeadbcdeeedadebccecaccccdacdeccbbeaccdbbacceaadddbceacdcbceecadbedcedbdaaaccecacdcdccedccbeebbadaddeccabecbaeaedccadaedabdaecaaeadebeabaeeeaddabbcdacdeacdbeabdbebccaecebeddbadcaaeaecdacedacdabaabdceeeaaaccedccedcceebacecabcebccacdaeebbdbbeeacdbbbbebebdeceaeeccdeeaaaddbdecdaddaacccedbeaeebabddacceededdbecbbbcebdeabdeddbceeadccaeabaeceebaaaebbebdbbdcdbcedadcecccdebacaeeadaaceaacaccedbeddccbaeedeeceedbaaacdaadbeedacdeacedbcccbdadeabeccdcbccdebdaddcadabbeacaeadadbecdaeaacecdebbaebebaecbdcabdbbacdbeebceeeebddbacbbbeacdabcdacebbbadaccdcaddecaeadbbcebcdccaadddaddcddcddeeebdcbcbddadabacebdeddbbbceccdeabadbededddcccbdeebdcacbadeaaaebaaebaeeadceebdabccbccacacdbcdbbceeadeadcbbaebcaaddacbeeacadaacbadcceeeebebbcbbceedeeaceabdeceddbddeceebceaedbeceeeebbcdeadedabcaabcedaddabbacacaecdcdcdebacccebbbccacdadccabacbbcbeaaaadacabbdadacccdabcebeaebbcbcccecdcbedaacabccabeaeddcdcececeaabeeabdceddaadcaadeadabedeaedcaabbdabccedecaeedaedadcdddcaabddbccceddadcaeeadbeaecdccaddebcecceedcbaaeccededadbddaebdcccbbdbbbcbcbddbdbbdaeebebebedbdeaaedacadbabaacabadbbcaacedaebbcaacbabbeeaacdccdaacabaccedcbbadbdebcdecbebabdccabcebeeedebeedceeeeabebdddddeedbacedeeccceeacdbaddabecdbdedddbbedbbbeadedeebdecddceadbaeacbccaccdbcdcbbddadbedaccadddddbebbeeabbacbecbcabceeceedeaacdabeceeebaabbeceebeeeeaeeebbeaeadceedecccdaececbbaccbdcecebcdbbdbddaaabdacabccaaaaeedbaaadbadbddbaaacebbbbdeeaaeaadcebcdeacdbadbceeddecbbaacedadebdcdbdadceebdaadccdaacedecbcbaecbecdececbdedcaebbcbdbdbeecccdaebbceabccaaecddebcaedaabbcdebeccecebbeebddbbbdabbebcaaecbbccdcbcbbcaebbeacaaabbaadbdcecaadeaeecaaeeaecabaacbbbccebaadbbcabedaccaaccebdebadeacacdbabaeceeadddaeeccebcebdeabdeadeaeaacbebdaacdedacaccabeadcaecedcdbdaadbaedddaccaebadacdbebdbccdeddebeaabdccdcbcababdeccdebecaaadddceaabcebcbadaececbbdbaebcddaabdceadaabaaeecbdecdedaecbcbcbcbdebadeaacbaccebdcbccecabbebdbaecbedcbcbeacbeadeabddabeccabcbdecacadcecddabcebbcaceedbedddddecedcbecdadcabebccbbbbdaacdeedcabecbddeeedbcbaaedbaddcabbccbeecedadeaebabaeadaebaabbecbcabadbabcecdccdddadeedececbaeaddbbadaeacdccebcdcbacdddecedeaeecedcadabbcaabbcaacbabbbbadebcadbbcbaaebaacabccbaedbcccdeccbeecbadeecdadceeecaddcecbbbbbeaddbabebdebbeeaabdbdcbbdecbcbeddddceebaaacceecaaecabbcaadececbdbaedcbacdeabbbaeadabacbdbccacedaeaeaacbdaaedbddecabcbcaabcabbceedbaaecbcbbccbbecddecabbeccbecbcabcbdccdeebbeacaeaeaddaddebdccceedddcacbbebeedeaedcbabeaabdebeeacdecaccdbaedaebacaeccdedbdbdeccdbabbcbebdecbbaebbedaccccdceeecbaeededdccccbdeeaababcabeecedeadddbbddcdcbabddcbaeebdaeceabcdacebbdaabedebbeababcbeabcdedabbeebebabaeddcaeabebaabeaabbddddbdbaeeadeddbeddaaadbdaacaedbbdeceebaecceacecaaceaccaadcdadedecaeabdbbdbbdccbacddcaddcadddbcaeeeeabdeaccebdbbeebadbacecddeaedacadbcbabcedbdebdacdcbcbdaeabcbbcbbccddbbbbecceeebddabdaddabbdeabdedacbacbecbdbbcdbeedccbdabeaaaacbdeeedacaeabeeaedcadeedebeabdccecbaaaadacaddaddaceebdaaaaaacedbcedcbbabbedbaceadbeaaaeaababceeebceccddbebddebcdcedbaeadceecbecbececbdebbdcabbbececedaeeacdbdbceddabaeddacdadeeccdeededdeccebaabbcdaebcecbbceaceaecacbcacaaacbedbbcabdeceaccdddbeecdbabbeaccbecdbedabdcdedbeeddcdceabaceacbadcbbbccdbaccaccaeaddbdabeadcdedaaccececbcbdacabebeabbdbaeacbcbbbadbbcdbaddebdcceebcddbbbebddedabcbbdbbeabeedbbbbbaabcbaeebdadeaccbeceebeacbcacbabcdedeeedcbbceeceeccddecdabbbadabedeccdaeaeeadbcceceeeeebdcabacbcabccdceeecbeebdcdadbedccacbcbdceacbdbcecdaeecbcccdaddeebaaacdcddeeaeabacaeebbdcdcadbcababadcdbedacebaaccedbebeadabbcebdaaeeacdcedbdbacacaacdacbeaeadcbdaceebeabbecbddebecaebdedadbdbbbbcdaddccbaaabdcdcbaacbcbbbbedecabebdebbedaeeccadcbeaaaaadbbbabadecaceeaaebcbbeabecebcbaeeedbcadeedddbaedeabbcaacdaedbbbdebcbeecedbbdadebaeddceeeaceeeecabeccbaeedeabcbcaeeeaadadcabeceeeebabddaaabbebbdabbbbcabdaeedaddeeedcaadbbdbaeddbcadadbceecdddbccecadaeacddeacceebdbaacebadadacdceedbabebabdceddaacccbdcceaceedbdbddeebaacddddedbaaaddbbbcebdceaebdbbeaddadcdeaaaccebcaeeecaccabbebadaaaccabccabceebeeabbeccbbccabbdcdcbccdacdbdaaaabbbabcabadeacddcabadbbcbedeebeeaeebeeddeccdeaadbecdbecdbdcbccbcaeecdbeceedddeebaceadaedcbecccbccbbaeadbaeaccbedebdebcacbedcedacdecbbbdcaaaaeeeabdcaaadeddcaebbdebbaebdecbdabbaadacacaecbaecadedaacbbacdcddbeebbceeacbdaeacededaaecedaadbabbaebcceeedcddbdcaabbaabdbecdaacabeaabbccadcdcdcacedcedadbdaebbccadbacddbaeebdcddebccdbaaeecebebdebadaaebadddebabdcdcbcbceecceaadebbcdbbeaacdcdccdbcbaabbeeeebecbaeccdeddcdacbcecabdbbdcdaceacbbbcabbaeabdedbacaccbcdcbebecddbdbbceeebbeecdedbdcebbdcaabdbcccdaecbdddaadedadbebdbbddecbbeaceccbcdceabcbdbdaccaebececeeacbccbeaecdbdacbabedccacedceaddaadaabdbdebeeabddbcadddbabcdbbdddebecbcedcccbdbcdcccebedaeddaceaaceacddbddcedaaceadbccaceedcabbceaedaacaebdcdbeabcbeacaaddaaceabeabeadeacaaacebcaadaddabcebcbecbebadcaacdbbdebcadbbdbdabacedacdcbbdeddecdddcdcdcbbceeacebdcdcbaabeedabeaeecdeeddebdcecbdbbbaddadaeebeebabbbaeeebeaeedaaedbbcbcbcaadddebbbcaabdbebaaaebbedbcdedcaaceeadaebcbadbbaadebcdbeaabaabdbddcababbbbbdcbdddeccdaecebbaaecdcbbcdababbdccebabdaeabaebbcbbeaddabdaddddddddabbbcdccabedecabdcdccbabeadcdeaedbeaebedbcabdcccdbdcdadaddeccbdeecdcdbbccbdddbdeaebbaddbbdccbaaadccebaabceedccdececeeeebdddecdebecbdbddaeddbdeebecbeadadadcdbcdceddabccdabcabdacecbbabcbceabaadededdaecdbcaaceddeacabbabdcddeebdaaadddbceaecdbbebdaaaecedcbecacecabbccaebdebabbeceedaecedeaabdbdceecaeaddebeaccdbbeaaaabcadcdeeabdbdcccdebbacaabedbaacedecceedeebcbcccddaccdbadbddbdbacbdccbbaddcbcecabacadceedddbbedacaedeadabcedaabcaeadedeacadaaaebceedaedbbdaaceededacecaaeacabdceeaeedadcaecdbaeebbaaaebdbbdcbbcdcccdbbbbdeecccdeebbdebaddcdbeeecbabaddeeeeeddeebebeeabaebecdccbeccbcbacbcaeeeaadddededdebaaaddddabeeccbadbdedecdabceeeedecedceeecbbdbddebcdbccabeadecbdecbdccacdadbadddeaaddedecaeeacadcbbdbedbebecbbabdcbaabacabddaaabedbcdadbeeabcaadceedaeebddecbeebdcdeadcddbabdebbeceebdceeaaedaabcdeedeceedaaaadbebcdeddbdbbddeeaadeddcecaecdddbccdeeaddcdacdadeebcdeacceddceaebcaacbacbcdcaccbbecdcbecababcceeaedcbddbacaccbaaeaccecaaeacccdcecceecacdcdaeebeacbebebebbcbceecaacacbdaadbbacbeeacedaadcdebccbdceebeaccdbeaebbacbcbedddbccacaadeacbeccdaccaabaedeceaecbbdbbdabdabcbcaddcabcbadcedbccdadcababbeddaaeebecdbbcddacecbbccbbabeebacccabdbecadddcddebddabcaceaccebdeecedbebcaaeaabdabcceedcedaedcdacbadcacacbedcbcdcbcecbebadcababbbbacdcebabcbebaaccaaeeceebbacaebbabedaddbaabddbcbcaadcedcbcbecbeaebaeedcdcbbbdbeabeebabacbacccbacbbccdacabedecdeacbdccbaecccebcaeeeecdcecedbbcdeeacbddcaaedeeeaabcacbeecdecebcbdbeebdeecddddeccabebdbcebdeedeaeecacedecceecabbedaeceedbdabeaaedbadebadbeaebedacdbbbbacbbbcbbbdeaadebbaabbddaabcacaeddbdbcccaaddcabaddcebeeedacadadcbaacdbadbacbaadbbbceddcdcabeaceadedbcebaeadddbabdacadbadaaaeadadccdddbdcbedaeedbbaddbdbbcbaecbccccdbeedcedadccbbcaabaaeedebdadaaddcaeaddbbdebcbbadaddddecdbaebddecabdddddedacaaaedaadcccbbdbcdeedecaebcadbdcccbedbcdbeacdabdcccadbddbcadaaabbcedadabeeabddceebabeceabccebdccdcbebccdbcaabeedbeeaceacaabdaadbaccebeaacebeeadbcbcddeddddecaabcdbecbdebaedaedbcdeaaecaadbecbbdbddceacadccabcadbeceddebdccedbbbcabdadbeecdbcdbbadbacdecbbdedbedbceaaacadaddbabeeddeaceebcdcdabeaeaebeececddecbeeaebdcacccdcbedbedeacbbaecdecacaaaddbdbcdeedecacbecdbebecabdcccbadcbeeebcedcbdcaddaabccbaadbeaeeabeeacbaebadbdbebbeababeddabadacecaeeaeeebeeebaadcaadabcedbaacdcddaeceeddcbdccddeeadbcccacacaabbcceddaddeeedaaacecdaeaeeaaebbcabdbdeaeadeeeacceeddabbdeeadacbebbeeaccecddcbcadbdeecaccdabaaadaaabaaebecacadaabebacebddedadeeeadadddaadddacebacdcdedededbbbedbccceaaeebccdcacdedcbeaadddbcdbdeabdebddeababbbdccacedaaedadcabbabccbaebcddddedeaeacdbdebaebdedaabddbdaadcedeabbecbbdcbcddbadcaeaeacddecabedaceabcbecdbeecbbeddeebecbdcdccbacacaddaabaaecdcdbcabeeadabedbebcadacccbcdcadbaedcbcbaeeebbbeaadccedaceadecebedaecdebabadbadcecbbddbcebbcdbedebddbebcbcaddddeeaadedaeeabaeebababcbcdccdadacbcccbebddaeadccbaadbdaceedbbdacaaccebbbbaaeeeccbdbacdccbbcdbbdcdcdecbabcedebcaeddeebeaabeecaabcadeccecccdceecedbcbdbeaadebcdecadebdacaacdaabeeaceadebcdebeaacbeaaaedabdaedaebacdeadebabdcebaddaecaabebdceceeaccbdccdbcbcdddabcbddaacbccdebdbeaaebaceaabbedebcbaadecdbcccceaecbbaabcbbdeccbebbdabedcbabcdaeeaeabddeeabbaceceebcdbeedeccbeddbaaadcbdacdebaccaeedbabddcebeeeeecaacdebebceecceaccdaaeebdebdecbdbdaddcdbcbdecebdeddbdbdddaeddeebaaeeeaaccceeebeeeaeaeeeddbabcdecadbaaadebcaaabcbddbdaedacccddaeadebeedbdcbdabeceadbceccddddedeebbadaeccdccbbeadbddeadbebddbdacbdecbbcacebcacbedaeabbcaeabbbdceddadcaecaedceebccddaaedaedbebeebdadadeabbeaeadbccaeadcdabeabebebbdbebdcbddbddbccacbcbcacecbeacdbdbbdbebddcebecbedabcceddcaedbdcaceeddaeddbdabbebecdddeeeabaaaddddaeaebaaeeebadabbbcabddeaedabbcdacbcdbbdeaccdcaddcccadedeabedaecceadaaeabacaabdaecbbcabbbeabcebdcddbdeabeddceeaebaebbedcacadbaddabeaeabdceebcdabacbbcecddbcecdbabccabacddceaedaebdceebcbeaedeedbecacccabbdcbeecedbebceedebedacdddbbabadbdbdbbeecaddbbcacbacddbbaedeebadcccdbdededabdcdeeebdcbbcbdabbdddeaaeebcbeacecbaeccdceddceeaabdabeabbcaaabeccdcecbbadddbaecacbcbadbdcadabaecdcadeeeaaddacaadcebccababaedcacacabbbeadbbcacacacdebbceccceccdedcbbcabaabdbaebeccbbdcddaebeadbaacacadcdaabdbdaebdacdecadccaebddababdeaeadabbadcddcbceaddbccdaaaccecccebdeacccacaebbdaccaeaedceccbcaaaddbecbcbcedbcebaacaaccedcbebabbbbbaebccdebcdadaeeacbebceedebbccdcbddbeacccebcaedbedcadecddbcaaaceeceacdaccdcaeeaebaaceedaaeccceecececabdeedbdeacacddceacbbdcebbbdcacaedceacbceadddacbdbbecccebdeebaceecbdeaaebcdbdcdbcbbaabbadabeabddcbabbcacebabcdcccebcdbbcaebcddbacbacdcecedabbcaadedbbcaccacbbeabbeabcedbceabadddcbeebbebadcaaddbcbdaabadbbceccbdcbcecccaebeecdddbaabecbdeedadababbdcdebebcdebdadcdadaedceabeebeaabcddabeebeebbeadecebaabebabbceddbaeadaeccbbdcbeecbcaadadcebaecceabbbbbeeaadecdbaaecacbadaeadcbbebaebebeaedbdeeaeeecdcacdadadaebaeacccdccbcaacceeeadeddeaedeacddebebecbabbccccdbbcadcdaccbaacebecabbbeebbeebadbcceadacbbcbbdeddbccaaaddbabbdccdbddceaecbcbebcecbdcdcbbabcdeabacececdcaeceebccbbabbadbcbaaebbaeebaceaaddbcaaddceccdbeacecaeabcdeddecaddbbaacbccebaecbdcbceacabdabecddaacbaaaecddddadacbccadeeadcbbbbdabcbdedacbebaaebdbccbccccaecacadedaabacebaddbeeedeeadcbddebbabacdacddaeecaccbbebbbccabdebccccadaaceadeeecbcdbebabaabdacbaeedcdddabbbdcbebcccddccedcebcdaeadebcabeebaeacbbedacdccacdaaaaaceeebadbecacacbcaebdcbccaebbeedbbddeebdbecadabadcedeccacbbbbdddcbadcaaacccccbeabddaaddeaacaddeedabbbbebcddedeaabaacaabaaeedcebabebecacdbcdaaabcbeceebebceadebcdbacebdcaaabcbcaeeececeeadbabababdaabeddbedabeaeeacdebecedeacebacdbdaaadadeccceeacbdbdbdbddbcbacdbeedcbbeeccadaebbdccacaebbdbceaecbecedacaacbbbdecddedaeaadeececbacebacbbbacddacbbeecdcddadabebeadecebdaeecddeedddbbdebbdccdddaaacddbdcbeadbeaeceeebddccaaebdbcaaeddaecebacadadeedececdbdbaebdbbaaedcaeddbedacbdaaacbedaaebbeadbeacdabbcedecbacaeeedcebadccbaaedadeaaaeedaeebbdebcceaadccecacbceddcccbbdbedabcddbcabeccdceadcebdceeacccaeaeaaedbaceddeddceedccbdbdeadaadacdbaddbccecaeccebdaecbacceeaceebacdbecedacebbddacebcdbbdacaebacdddabddbbcabcccbdccbdccececdaccebebeebcbcbbbdabcdebbaebddacecebdcdcacecbbeedcecccaeeeadddbcaecbbcbacbbaeeeacbaedebdbbabdbadebedecacdccaabaacabdbadaccaedcecddbadceeaaddabbceecdabecceabdeadcbdaaadebdeecbaabdabcebebaecebeedadbcdcecaadeecdbaeacadabebadddecbcacbbceabcbbeeaecdecbcdddccabcacdeabdbeaaeeedebbecabecdecececbadcbddaaadabebaadacddabedcdacbaeeccacdadecbebcadccedceebbdddccaedaeecebcbcdcdabdebcaedadbdddacbaccbaaecaddacadbaadeabadebdceacdcaeccabeacbbbbddbdaecaddeccdaaeacaeaaeacdecbcbdccbeccdacabaeabbbaeabebeebddebabebbdbdeddadcdbbaaaddcedeabcbccbdedbeeaecdcbdbaedaacecbcbbebbccaeeeeceabeabccdcdeabbeeeabdcbcdbdabeeabbcbdcdaecbcabecadbbcedaddcabccaeddacecdcbceeeddaecceeabcbddcaddbaebadbcccbeebeebbbbbcbccbddadedaceaebbaeeacabdaabbcadbabaccdcdacacceaaabeccabbcccbceacaddebdeecdccddbccdaebccabaceaababbcdbbdeccabecdbdaeadcaabbebaececdcacaaaecbabbacbbddaeadcaccdbbecdcbaacbaceedcdedbddbaaeeadcdadeadcdddcaaeaecadddbebdadacbcecbcbcceebcabcaebebcabddeeabacdecdeabcdebdddacddabacaeaebaaabbbdedadeecccbabcedaaaebbeacaecadcdecedbeebeededcabaeeebbdaceebeacdcdccdbcedadededebadadceadabbbebbeaeeacddabcaaebecccecbadaaacdbdedeaabbdccddbcdddbdbccabecbdadbebcdbdcbddebabedeeeabbddcbcaacadebcbddcdaddcdbadaeeaeaddebddcebdecdadebaecececbdcccbecdbadaabdeedcebaebbbebceababadcbaadaddabccbabdbdacadacccaabbddbcceecbaeecccaabbdcedaeaeeeddebbaededdbcbabebecaeceaaddcacdadceabacbddbbabebebbcddeabddbebbbdadcdbdaedcaaccececdbeabeadceaaaadcebbeaaeedadcbaeacbbeecebcdcbacabcdcbceebccbbdacbbdcdaddeedabdcdcddaedbabbceeedbabceaabccecadecbebecbdcccadcacbcbecbeddbbbabcbddbcbcaccacdcdbdcbbcbecccddacaddedccdeebdedcdccbeccdacbdebeaccbbaadbababbceccdabdddaabcbeaaeeddacdcdbddccdebeaceacebcdedacebebeeabcadbbeebebaeceabbeedebebaeceabbeeedbacdbeaecdddbdaddeeaeadcbabaadddeeceeadddaaccbbeecebaeebddecaeabbcdaeccaacaccadbedcbecebbcdaedacccaeaecabccdaceaecccecaacaebeaddcaccbcdecdddcbbaceaeaecbacdbcdbdcbbabadcaecceebeaeedebcaeeeeeedebedccccbebcaabebecebabeaecccbcadbdeccbbccbbaabeeaecddcbdbedeeaaeeedaedacacabdebcccabcdbcbeabdcceacaabbaadcdbebadbcbdacbcbbececeabacedcebeddbdabdadddcebbaebbdeccdcdbdbdbbbdcbaaccdaedebaaceabadcceadbdaadaabeabddbcacacbdbdaebbadbbaacaccccebeeaccedcadabaaeaeaedcbecdcdabcaacedacbccddeacbabedababadddbadcabbeaceaeacaedcdbdcdeedcdaeeecdbbdecbcebaceebaebcebbeedbddadbcbcdbecebacaccebbabcdedceacdeedbccdaacedeedbcecbabbdacdbbbdadbedceeecdcddadccabeecdddaddadadabbaeaaeddbebdcdbdedbbcbeebdbdbaceedcaeecdbaaddcbdebcceecdddbabcbabebbdaddbbdaabedbdaddbaddbddcceadbebeecadbdcbbeebdbeabdecceeecbceaacbeababdbccbecacdbcaedccbdadaceddcecdcacddbbcbdaeedbaacbadbabdeccaccdebaebeebccdaeedbaaaaeddecceaabdbbcdcecbeadabdeadcbaacbbbcbeaaacdeacabbccacdbbadddacbedbaebccecbebbdbbbdebaccaddeededbaaabacbbedededdcadbdebebbeaeaaaabaedececabababcdadcdadaeedcdeacdecadaadcbaacdcbecacaaeddcabcedabddbcbeebdaabeddecbbeeacdaadddbddbcacbcadbdeeadedabcbbdbdbacaecbcedbabbceddcbadbaeecdacbdbbdedddbaeabcdedbbaebcecaedbdcacebcbbeedcdccccbbeccbedddbadeedcecaadbaccbddaccdbaaadebdeabbacadeddcdbeadedeedcadaeeddcaccbcedacabeabedaadccedaebdbcedcdacedbeeebcaacbebcaeacdbabbacddbdedaeebaddcccbecdbbecbdaeabeaabbbdabecacadbcebacaccbedbbadabacddbedbaebdceaeeedcacedeeabbebdebdcbccdddcdbdddcdcdaddaaadaaeacbdcdeeeadbbdbbeccbdabdaeeccabceacaddeaacbdbdcacabadeababdabdabbdbedeceecacbcedbbaedaccaedddbbdebecbeadbeecdaabadddedbbdeabbeaeaebabecdbdddaddcdddbbeddbdbbbcaccbacabcaeaedadadcaacdacedddadbbdeacbbdaeaceeecaedbadbcdbbacdaceebacabddccebbaacddbdaeaeebcdecadbdedbdceaecdcecdcecedabbbddbabbaaebbdaedeacbadcececbebacaceabeaddecdedbceccedadbbaeeaedcdbeebdbacaeddabbabbcdddabaaeeaeddeeeebaedcbdedbddeaceabbddeaedeabacaabccbcacaccbadaecdabddbcceadebddedabdcebebadbcdbbebebadcabacdbbeebabcaabadeacbadadbcbebddeceacbaaeedddcababaebcddeeccabbcddeccbbbddccebecdcbdaecedaddebdcbbccbbceebaaceecddeeabacebddebababeaeaeddbcdeddbbbeacedbdebccebcddebdabeddbcdbabbdcadecceaeaeabcdaebececebcbacacbebaddbaebcacbaeecddaeacecaadeccbbdacebdaeabcbcdddcbccebceaecadbcbcabdbecaaebdddaebcacbbdbdadbcecaacaeedbecdccbbadaadbbbaddccbbeddaadaaeeeddebababbeebaebdcbeeabcbaeccbcabaeaecaebebddecbabadddbcbbadbeceaebaadcbcbbbecacacceecdccbececaebaebdccceecedaebbcbdebbcacbacabeaeedcdabaacbeddbedeebbedadbccadddcbdebbdbcdabbabacbdccbadbdccebdaabeaccdeabceacaeaacdbabdeaadacbccebeebadddbdaaccecccaabadcbdededdeeeccbdbaaacbcecbbdeaaeebccbeaaaaddadbbaaecdabbdcdeeabdddabeccddeddcceeeabebecabbbabbccacdedbcecebedaceacbeceeeacaeecdacdaaeaeaaccdabcaebaeacdddaeccdbddeddabedeebcdacccababdcbbedbeeccdeaabaaedbcbacbbebacbccacadabccdaecdeaebabebeecbcceceddceddedcbbddcaeddceccaedeebccddedebceaebabdeeeedcadcabbbebabaebbddecdaaabccddaeeedaccdcceedbededbecdcddedaaedbcbaceaabbdbcdcedaabbbecaaaccdaeadeaecbacdbcccbdeeaaeeeeeeabbcadacdeaddadbadeaabaaeecceedbdbadcbcedeaaeaececeacbeababceabbaaddadbdccabebceacebeddbbbdebcebbaceecbbeeccddadbdcebbbbabbabaaddaaadccadeeceaeabdddbacbadabbddadecaceacaaaaeaacacddbbeadedeebcbebdcbcebbecaadccacdedaabaecacbdbdebceccacaaeeaecebecbaacdebccdebeddedbeabaaedecedbcdababeaccbdcabdeccbeaebddeaedbbeddaaedabcdebcbbbaebcedddcceeccbbdebeabdeabaebaacaeacddacddbbddbdedbaeadbbeebccaeddddbcdebdcebcaaccbaceceeecdcdedebaebceaeaeadabdedbcbedcbccdccdcbeaabdaecededecaccecdababecaeceecdedecbbaecbddeebccadaecedcbbabceecddcccdbbbdcacddccaecddaceebcacdaeedeebdadeddeeddedcddaeeecababceaebcacaeaecebededdbadedaeaaeaedabdecbacdbbdbcdbbdacbbdbcaabbacedcbacecadcaabecacacebacbcdbdbbbbacebaebdcdeaccdccedbbebddbccdeddbedaecdbadbebccedceaadeabadedbbdbdebcedbcbeeaabedcbbccabbaecadbbaacbadcebaeebebacdbbaecbaeabeaacbaaeecaedaeacbcbbcccbebabddbedecbdcbeebbbeabeceaaaecdeeeedbceedeccbbbbceeaeaccccabcedaadbedcdadaedadbacbeebadbabcdacdebeabbacbadacacbdeebebcdeedecadaabebbdadceeaaeecebcdbabdbdceebaaeabadbabdeaaaebcbeaeacabaedcbaeccdbdcadddeabeabeebebdceeacdeccaedecbbdcaabaedebceeebdecbaaebaeaddecadccbdaaeeecdceeadeebabceeaaaebcbcbbccdbeadeabdeedbcedcbeabbebddbedbeacedceacecebdbdddbddcebbeeaebeaeceedbacdaaebaebbabeeeeeddacbdaedacbaaadcbddaecaacdbacdeedbdadbbceadacabaeacaabdedbaabdcacccaadadeaabdcadbdeaadbdaaadbcadbacceceeaccceabadccaaccaaedacdcadeaeddcecdecbceddeeddcdabaadcceaeecbdaaebaecdabeceaddbbcedacadebdcabccbedbccdcdbdeeeacceabbdcddeabbdebdcaaccbddbbaccebcabbbaaabbcadecdeeceacedbeadcbacebccdccebcaacaadddeecbbccbbdaadabdeaaacbbccddbeddeeebacbbebdbedbbceddcdddadcaceebcaeeceabdbcdcdcbcdaeebcebcdccbeececeeaaeaabdadddacacbecdccdbebaadaceedeaecaceecedbcdcbdeeedecbbbeaceccbaacabdacccbaddacdedcabaceaedabdbbacebabddedaedacadedeaeddcaedccdaceccacdbaadcccdceeccbeebcbbaacadbdbaccbbbbbeaeadecaabecebecbbddbeaceebabebeccecabceddecdddbeccdcbeaabcbbeeeddeacecacbcabcbdeecbebbacaacbbaeeeeeaddbeddaeccdcbcedacaebcabdeaaadeccbecacddcbdadedbddcccdbecddebabbdbeecebabdebacbedebbdebadebacdbbaebcbbdcbabcccaedbbdaaecadbaecddbccaadeacdaededdabcbdebbaedaddcecabeddbcbeadaebadceaeeadabdbadbdeebdebddcddcabeebcbccaacbbeddaabeceaebcecadcbadbaaebaabddacedeeeeabeeaccececdddbadeaadeabcedacaeccaadbbeddddadecbdaaacbedaebbdceedebcbbdacbeaabcaddbabacbadccdeeeddeabecdbaeccaadeceacceddbecbececcbecccdecdcdeccbeeabbaacbbecebcebeabbaedaacadaedaaeebdeacbababdddcceebabebdbcbacdeeeaaeeadcdcecddbbaacedcaeddbdbedbbcdceaedecebdedccdeedbacbdcaeebbeabbebdbcbbeddebeaeadecedccdbacdaedcbedeaeedcddbcaccdedadcbeeccbbbababbbaccdaeeeadbdbcdaedabaaacacbccebaebcdcabcedeabaaaabbaaabaadedaadadaeeecbbaedcaaaceebeaeadadaecaddaccdebcdcbdbaeaddddaeeaaeedcadbcdbbdaeaccedbacdbbdbeecdabcabdddebcebdcdeebeeccdbebabbbcbeaaaacccebeccbeebcdcebebdaceccbabcbbdddbaceadcadecaaeebaebacaeaaaacaddbacbacbaadedcebeeaddadbecebebdcadcbaececdeaddeaaecabcadbeeeecbbdbadccedddadbbbddaebeabbaeeacbebdbadcbdaadabeebcdccddaccdbecbcbcaadebaebddcccaabaeadccbbddeddbbbadcbaeedcadeadaeacacccebbacdaedadeeabbbaaaaddcbeebdaabdebbbedceabadcaccadabeacabbccbdcacbaadaeacbbeacbdbbdabeabdcdeeebddbdaaadbdddacedbbacaaceaabddbdbcdacaeddadacbaacdaecaadbdabdcccaccdcdaadcaeeecbabeaebcaacdccdbacbbdeaaeaecebaecaceedeeaadbcbcdcdcabacbabdbeddbacdcecdecbeebbdeadbcbbbcdcaebacbabaeccceeecebaddcaccebceaddbeabcbaedeeabaaebdbeedaeeaecaebedcabbecbecdccbcaebcabddbaacdadbcacddbdebadeadacbdaedeaaebcbdacbbcbcaedbdacbcbeeaacadbeeebebcdbadecaabadadbebaaadeccdaabbcebcdacdbbacdaaeaccbbdbecaebdaccbbeadceddeabcbcbebdcdaeccecbeeccaaddedcadcbcdbaabdeeadebbdeedcdbcdcaabacaddcacecdecabbbaebeebdebbabeddbceebeadccdcbdaeedbdcadbaedcbeccdeecccebbedbcdbedececcecdbdbcdcbdbdecabacecbdbeacbeecebcbecbedceaacaecbcdbccedaddebdcaccbcceddedcabeedbbddbbcabcedcccaacaaaeaeeccabbbdaabedbdebcebbebceccaeccddaeeebabbacaedbedeccecebbbeeddeabdeacaaeebcceaceaeacededecccaedeecdcaabeebcdcebaadccdedeaededacaeaaaeeaaacacbeeedadbeecdbedcdebbccedceacbceddccdcdbaebbddbabaadbccaeadbdedebeadeacacecbcbeebcaebbcadeabbbaaedbaaeeecbdabdbededdcdeecedaecdababdcedadbaceabcbddbadcceeaddbdccbccdedbbbbbabdabbecddbcbdadeddceecddebaaaeabeedeeabbdbececdddbabecdcabaadaabccaedbbabadddcdabbdedadacaeceacdbcabaceebcbedceeabaebadcbebeeeedaedcccdabdaedecebdaeccdcaddedbdaceeacabdbeaccadccccbddebecbcbbbaabaaeddacaaadaaeacbbcabedcbcaaecaaebeebbcaceacaacbcbacddedeeddeaabdbdcbcbabbbbdcdaeddbaacaacabbeebbaadcaeebccdbbacdeceecbcbcacbeaeceabbddbeceaebacdacbdedcebedeabaadaebbbbdbaccbdbabadabdccaeadbecaeeedbedeebebbaebdcededeeebdceebebcbceeadeacbaadcabbeecdceedaaaacaddddaddccbaceabdeaeecaaacbebaaadddcceceabacdcdaacedbebdcbacdcbaeeedcbccbebacbebdbedcabddcaedecadbbbacaebadbedeaccaecdbedbbbddddecdcaabeaababcbbddccadeaadbeabaebdceedeeeeddaadbeedcacdadcbebedabebaeaaaddcaddddeebccbbdbeaacbeedabddcedcabaedbeebcdcabccccececabbdcbbcddcaabdbbdbcbabbcdbbeccabeeabadabbbddbccdcbdcaedceeeedceadeaceeebbedebebdebabcbecbaabdbcaeedbdabceddcdbcbaceeedbcdceeadcdcebecbadeaecbdcacbaacddecaabeabeccddadaacbaddbbddedceaccdccebacccbbdbbeecbeacecebbcdedaedbbbddaeadcaceeacdaccbecbcdecdbccdccddbdbadbbcecbadebdccdcabbdcdcaabdebddebbbeacbdeddccddbcdbcdbdeceddececcebcdadbcdeccbbcbedcdddedbbededaabbdcbebadeadceebadaaeecbabdbaeceadcbeaedeaeaadcbcadaebdbbbcebbdbccdccdaacdceecbebbbacabbcddcbcddbaceabdedacaaadacabdbabacbebadeaedccabbcaaedcbbbdbeadbeddedcdbbabbeaabdccadccadcbdccdebabbdddedbcaebbdeadabedececcbabcbaccbbedcbbecdebcbccabaaddaeaaecbaacdaaddedababdacdbcedebbcdeedaebdddacdbdacedbabccaedadaadeaaabbcdabcabddaabcdddbaecbaacabbebacadaeaaeabeaaeabecbeedbddcbedcbaaebabaeeebceeeaedddadcedcdcccccabebdeccdbdabababaeeaedeeadacaeddadeaabeeaddbdaddcdcceedcbbacbaeaaaecdccbeceecaaaedbddacdcbdacdacadcdbababbcaebacbeaeaeddaacbbaeecaadedacbdeeeadadbceddbbebacccadacceebacebaecbcdcbdadacbcadcdadecdedcecbcceabbeebbeedbeaeecbdacdaebddaaecdecbccdabcebdcbaddceccdddddeabbbdbbbbcbdacbaeddcedacebdabdeccadebaecbcbeaabbbeaccbceeeeaaeddecdabdaccdeaabcacdcbaaadeddeabdcaeceabeacacacedbedabbadadcbddedddeadaaeaadbeceeecebdeacbdebeaaabaeccabbaadadbaeddbbcedbbeeccaccddbbaeecebbcceddeddbdbebbbbbbdcaccdadddaecdaecbedcadecbbcdbedaadaabdbebdebbdcddccdaaaedbccaddccdbebeccccbdddbdadecbbcdddedcebedebacdcdbbcbdaecaeabdadabbbaeaabbadccddedabdbabbeedaeeacbeaeebeaecabbbddbbedebcabbeababecebadcaeddbbebabaecceeaebccebddbadebddcecdabecbddbebeadbddddddcbaeabcaeddcecbceceacbcddabccabaebdedeedbedccadebeeaeabdaadabcaadddbeebbacdaaddabcdbcadbacebeabdcddbeddeecbcbebacdaccedadbbaccaaeacccbcebbddeaaaabbbcbcaeebdacddddecdcabecababcbcbecacddcdcadbdcdcdbbeebacadecbdeddbcebcbabeaccedaaebbddcebdbaccdadbceaeadedeacbdeeabbdeeddeaaeadbaaecddaeedddedecbdeadcacaeeeaccabacdbdacccbceabebdbbbeebdccccddcaebdcdabaebdcacebbcbabedabaeeecbceacaeadbabdacbeaababaebaeaccccccdecabebedbacdcbdedcaadabedcbbdebeceeeeecccbeacadcebacaaaeaabadceeacdeaabeebedadbcecbdccdadecacaddbabbeddecababeaddcdadecbdcaebdddcebbccdbbebcbdbadeadecebdbaeadadeeeceedbededdddeccecddadebbbcabeeababecdacbbdbeeebdeacbbeecaeaddebeccbbceceadcceddcbdbeedaaacdcadebcbbdcaadcabdabbeaebdadbcbbdabbaaadadbbcdeedbedbacdcadcdabaaacddacdacaaddeeeaaaaaeadaebecebbcebeedaceceadddaeeaaddedeeedbbabeddeccdceeecebacbbbeddaeabcabbdbdcadcdebdeeeccaeaedcdbcabbdeacccbccaccbabcadbdedeabceabcdbbacdccdbebeccaaebecaccdccaccadadecadccdbdaadbddaedcdaddaabcdbeeeeddeedaddcebedbecbbbbcadeebebcccceedbaeccedeaaeeccdaeeeebdebedbdbeeaeddcdcaaeeeadeebcdddaabdbcebdecbeeeeabaeabccdacdcaecbedadeceddbcbacebadeeccacbbedbcbbdeececbaabcbccedaacdbebdbacebddecdeeaaedabeaaddbabccbcadcbeaabcdecddcdcdecdbbadaddacdbbbebadcaddecaadacaebabaadcbeadebacbdebdaddadcdadabdceaeccacdeecbabbccbaeeaeacecabaccdeeddcebbdeaedbabaadaceaddebdcbbbcececadeccacaaeeabebceebcecddeadbbcdebdbcaadaacbbebbbdecdcedeaaacadaebeadccbaebaedaaadaccbdadabceccbeddcbaeecbecebeccaaabbdadeeeeabbdbcaaedcdddacbceccdbbccdbbedaebcbcdbdccaeebdcabdcccceadeaceaecdbccceaeabbcdcbdedcdadaaeeeaaeecbcdccdbcdddeadaacbcdeeacedecdeecabcbeabdeeabaacedaadaeddcacbeebbedccecaabcdeabdebcaaabbacabecabaeddbdbacddeccbaaaebeacaeaeddbbebccacbeddccecedadecdadbaacadeaddacaaddabaccbbbedeadbeeccacccddeeeacbbabcddbadbdcdbcbcbacdcaacbddecbdaacbdaadbdadeeaddacdadebcdbccbcbbbaddcdbcdbaddacddaaebebbdaeddecdebcddeccbccaaedddaeacbebebcbcddcaaecaadabeeccbacdedbcebaecccabaebaccccccbcbbaecaeebeadabceecbcbbaaacbadddeceabecadaccbccedcdacecceabacdcddbdadbaabaeedabccaddcbdedacdcddecadbacbeebbeebceccaeebecadceebeedeebaebaabbaacbbacabbeeccadcbaedaacadcccbbabbeadccbbdeeddeedaacbecdcceeeedaccdbaeabbaabeddceeadddaceadeabddeebcdcbeebdcbdbbcdedbebebcaeaabedcabedaaadedaceebbcbdccddaedebedccabbcdcccebbacbcebbeaaeebbcddcedcbceaeaedbeedcbabedcdadcaebacdeeadeabdaacceabdcdeeeccbcedacdaebabedbbeebaabbaedccdaeecbaabdcdeddedcbadcdadbccbedcdcdcaaaedbbcbadeccadcbdbcaccedecbeeaccbddeaadbdbbcbacacbbeddbcbdbcdeddaadcdaebadcbcbaacaadabaeddbbedcabadbaebdaaccebcebcdaadcebbababeeacdaccbaeeadcbdbbaaacecccdbedddbbdcebaccdbdcbdddeecbcaddabccedceddcdddedbaadbebdedaeedbbaacccecbdabbebdbbbbbebaccaabddeaceabbdacdaeaacbeedbeccecbcecbdadcbbdcbbbcaeaabdbaeeabbacddddecdacbbacdeddaaceddedabedacbacedeacaadaabeaaabeadaeecbaebaeabaaaecdeecdcdbdbcdedecbbedecdeddedbdceddaaeaaecdbcddcdbcaebbabcebcbbacdcdaaeacbaeeaeddaabdebbbdccbbeddaeaedddeadeaaecdcebedbbddecedaedeccdceaadcbdceddceaaedcddbaeddedeacbddedeeadaacaecbdecdcbbccccbcbdbdaeacbdbcbbceadecaddbcbeeebbaececcadcbabccaadebbccaeaaacdeccacaecadeacedeccacdebdddaaeecebeacbeceeebdddbcaaabcbddeeaceaadbeccdaaceeecbeebebeaddbdaebbbeedbeebbeeceeabebcbaccecbbbcecddedcabddbababbebbacccbdbebcecdeeedacbaeeaedeccdedcedebdecbdacaedeedbeebdabdecebababbaabbccabacecadccbbacddeedcabcaacedbdeceeaeadbcedddaddaddaebbccbccdaeaaecddbdcbdadcbdbbdababbabcbaaacaaceabcddaaadbbddaddbedebdbbbaeddecabcecebcaccbbdeeeabaaacaaddabebabcbecdaccdbbabeccebaeceacbabbebeddceeedcabecbeacadacdaebdbcaadcbbbddbcdaaccedadadbcdbeebecaaadecbabbdbadcabcaccaabeabdcaeaebcdcccbddcadacacdaabeadaacbcaadcdcacccbadebacaabdbdeeadedcebcadbcbeebdcbaeccabceeeaedcdacceddadecbdcaacbbbbcbeaaeaabbcecbedebdaccaebdbbaebedadedbaddaacbdabcdaeccaeadaccbcdeebdaaddddaccacaadcccdcbcedaaeddddcdedabbbddbbaedacbeddcadecaadeacdaedccdebccedadaabedbcadeeaceecacdaaadcbeddacdbdcddacceccecaddecacccecdedbddaeccbabcdeaebacacceeedcceaebcacdcbbdedcaeaeedadceeddeadceccdddcccacebccdddbabecddeebbedecceaacaddddaccbcdadeeebddcebcceacbdeedaddbaebecacbbadeebbdeeeeecbceabdbbececbbbddadebeedccacbecceadcaecdeaeaaaeeaeedcceccedeebedaacbbbeeacebaeaddacdcdaccbdaababdeaddababdbcbbbceeadbbabbdbaddaaacccebdbdebdccbcbdeebddbbceccdebebabdccecbdcbbacbaedbdbeaeabbcddbceebaeacaeaedadbddccbebaaebedcaddcacaeedbadeaabdaaacaebaaabccdedaabeaaacbcdddccdedebdcddabacbeceeebeebebdacdcceebebcebbccbebaddaceedcdbcdbdaeeadbcdccbbcdeeddbaceebcbbecbbadecceaaddcdbddbcdeeeeddecabaeacddaaaeeebacebeadeceeacddedadeaeebeaaebaecebebeabeacbdbaaecceccbebecdabdcaceeebbcabbcdbbdbaeeabbacddacccccbbdcbadecdccdecbbdecdecdeacdcdbabacbcedcbbbbdbabceaceaeeacaabbdbbaddccebcebcbebdddaaaecaeddaecbdadbcadbbedbcbdaedccaacaecbabbcbedccbbaaaeebededeeaeadcdacdedddebececbbddcacddcdeacdcaabaeabbaebdeedcdbbabeaececabeccbeadcebecdeecbcbeadeeaebbbaacaccdedacbaacdecaceceacdeeabddcecbedbbdaeeeeaabcedccadbaeaecbebdbbabacaddeabdbbaccbbcaadbcdcddebcecbdaebbddbbedadacadabbeeccabbaeabbbdebeadeaccbedbedceabedabbaceebdbaaddecaeddbaceccbbdabaeeccecbbdeadbdaabeedbbbddbbdddbcacaddbbbddaacdbddceabedbbbbdcdabaeecacbedbbeeabdebbecccbdbcceccdaaeedaedaadcbdcbbedeaddceaedceaddddccacbedcbcddabceaceacccbbcbcaedebcdebaeebeecdeebdcdccbecbeaccbdedcebccccadbdecdeceaeaabdddebcabdeeecceeaeacaabbabdaeedadbaabecaeceeeedededdcdddccccadebccacdccbdbeeeeeedbabddeedbeeabadeadaccceaacddabdaabbbbeedcececedddbecdcaadceaeecbccebecbdeeeaeebaadcebabddddecedabdeebadcaceebbaacaacbdcebdcaeccbaecbebdddccabdebabdcaedcbdddbadcccbccbcadaaaeaceadbdbdaaabceebabbcbadeadbbddbdabaeaecadbdbdcbbcbddbecdedbbabbdaadaaadeadaeebecabbedbaeccecaadbbcaaaadbeddcaabbcadddddabdcdadbcadbccbadeeeacdabcaadddadedebdeceaaebeabcedbbabbeccdcecaabbbcbeabedacbcdabeebcccedcabecdbbaebaeeaddabbaccbaaebebbdcdabeaeedaaebbbcceebbbdbbacbaabdecddbeacdbabcecebdbdbbacceaacaedcbdacbabbebcabcaceccbebababadcbeebeeeaeadbeceadbacaeddcdecacadceacdedbbbedbeddaeaaedeabbaeadcbbcbcaaeeddcdecdcdbddeedbbecabeccadebabdabdecdcecbedcacbdcdbdbeebcaecdcccbdaeedcacbeeeacccbecabaadbadecaedbcbcdbecddccadbcbdeabacececccbabebecdaddedccedaabcabecceaeedecebbeccaaebcddbcdbeceeddcdaabbbeadadbcebbcccaaebaabcbbecaddedbdcdbbcdeababbdaaaddacddcdcecaaacdcabcbaebbbdddadcbeeeeacadbbddcdeaaeaabebbaadcecbacadbaadbbebcdeaebeddabeecacdddaeacaebcddeacecacecaaddecbeedddbbbbdeebbbbcbbcdcbaeaceabbcbaacdeccaedeeabcaeedaadaaeedeeacacaeedbbacadabededddbbeceebaeeabbebdaadddeddbbbcdbcaeaddeacaeabeddbeebeacaaedcabddaccabaacbddebcaaabdbeccabcadacebeececddbaacaadadeddcbdeeacaabcedecdccddbebbdadccdabdceabdcedaeabcdcbaddcedcaeeddabcedcdeadebcaadeeddbeadbadecdacaebdbdeeddbeabddeadbebcabaeaacabeeaabeecddbbcbecbebceddaecdaebdbcbbcdebbedaeadeeccdbbecabdddadedebcecbedaadeaecdcbcdcebbceeddaeadcaaedebbaacaaedccddcabacdebeecddbeacabbccbbeebbaecaecedecbadebdcabedcdedecaabeaeaabacbaeeebbeeaeaacbdcdaedddeccabbcecdbbecbaddddcaaaecddaadcebeaecacbddebbbcceeeeadbcbabddecdbdeadcebbcacdedcebccadbecbbaedadddcebabccbbcbabcecababecaacaceccebbbeccaddeebaeeddbadbeeacdeeebbeeeeaebebdbeacdeaeedecaceabaecaabeddcccbadbdccadadcbdabdebceceebaebdeccbbdbdcddbeebeccebdbecbbeecebaddabaeacdaeadabdaeaceccdedbbdaecbcaaeebebcedacceeadeaeeaccabcceecedacadbdebaecdecdbabbeaabbdbdadecbdcaedaabdeddcaedcaebaecdebeeeaaeaabdabdbbdddecaaaaebaebdacacdbecaddecabebccaddaeacaabacbdedbdcebccabdbceadeacbebebeedcaeddeeacbceecdebebdedcbaebebadcbeedcaccdbbccedaabcbececcebeacbcdbddbdbaddddacdddebbbccaceecbcdcaebadbeaaaaebdaddabdbcbabeaeecdeeedeaddacaddbbadecacdddbecbeebbabeccebecbeccbdacaadcceddaadebdecceaebaacdddcbeaaaeecdaeebcdbededdeaecbcbbedccccadedeceecddeddddabacebbbeebaeeaaeeeadeebbaaecbbaacdbccbbabdbacceedbadddcceedbeeccedeacdecdccbadaebdeddadacbdddbbbeeecdbdbeadbaeceebceadeaceecddbebacdaacebceabbdceceecbbabebcbbadbecccdedbbebaaebaccccdceddeaacaebbbbbecabceeaecdbbcdbcdeeecebebcbbacddedadeeecbdeccddacbcdaeabdedaeeaceecacdadcacedcebabdeaceeaaecbdbcadddeeeaedcdacaeadecedcbcddbdcadbdbdeacbcceadeecbbadaabaddbcbdbcbbaadaacbeaabaccebbddaeadecdcbcaeeaebcbbbaaedceeaddaeaeececacbadcadacdbbdbaabaeeeeceddaeddbdeaddcdabcbebbcadecdbacdaecebbabbcdadabccdbaacbbbbbaadbdcaaeaccbcacebddccbccbdbbdbeedadbeceebbecbaedaeddecabcdecabcbcedcadebbcdaceccadcababcdddcdcdeadccbdeccbecbbdeabcbcabbbbeddeaaeceaaeeeeaedbeecddababbaeeeeabcabcbadcebdaecceadaaabcbaeaeaeadaeddccddcacadadadedbcabececdbaedbceedddabbeaddcbeeddaccbbebdbeeeebadbbdebeabeecdebedacbacedeaadecdacebadbdbbadbebebcbeacbdebdaaaeddbddeeeccbcdbeddadcdcbdbbaeddcbebcacebbcdcbbaabcedabcdaebdddbeacebbdcadbcadeccdecdabcbadeeeecaadaceedcdbdbebeedcbdbcebbeedbdedbeeaebcbaecbbcaeebcebacdcbabcebeaaaeeebcacebcebccceaedcebecccccacebbeeadeecebdcaaebbecabbabdcbccccebbacedebdcdbadbbeedaeadadeeecedbdaecbddbdaedaaddbbdcddcbedbacabdcacddebadbbabdccccabbdcdcadeecedcbbceecacddcbcdbdaceaebaeabbeaaaecbcacadeeadccbaaeebeedbcbacabcbdaacbeaadecdbbbaacaedaabbdbeddcaaddbbbeecaabaceecdaaaedcdeddceaadebbebeebceabbeacaacbaeeeeccebcbbeabaaddacebbeddabeccaaedbdabebddabcdabaddbabdccaeacbadccebcbdaecddcceeececacecebcbaecaaeddbebcaaeabbdebabacbddddcaedddbaeaaedaeeacddbdbadcedccabcdddcbeddaecdcbcbceeecaebadeaddbabcceeacbabeaabccdbeeddcaebdcbeadbbaebddabecaddeecccaddeceddeadaebdbeadcdaedeeebaaadeedaecdceecadadcabaeebcddbdeaacadceeceddabacececdbdaddbaacececeeabdacaecbadcaccdedebabcdccdaaaadecaadceabddbcedebcadadacddadcbeeddedaccabbcebcedecdebcbdcecbaaadeebbebdbacbbaebbbaacaceecdadcaebaeaeceacadecdbecdeddcceabedbccccbeadbbcbdbbccdaccdecdacedbbccbebaaccedebcccedadaccadeddadcddadcdeeebabbccaccccbcbceadacbdeeddcddcdeeeacccebdddeeebbacdeabaacbacbbedeadcbeaedabecdadcdbddabcaaddadabbbdebdadedcbaaadcecddccacadaacbabeccaeaaeddeedbaaeebdebbabdcbdbdbaadddaaceeeebeacbaddbcacbeeabeaaddbbaedaaacbdabdcacabddcbdeebabaddeeddeedabdcdaceecdeaccebaeeceedabdadaaabacbacdaecbbcbccadadccadcdecdeaacbadcdbcdeddedaccecabcacaecacaacbeabcdcdadeaacacdcacdbdedcaeddadbcecbadedacdcaddaedeaeaacdceaccaccaecbbcddacaaacbbddcbaddcccdbccbbcccccdadeabdbddecdbcbbdcbdabebaeceabcdaadaacbdddccdadbebdceccdaeabbbbaeebeceaaecebbdccbcaacacbdedadbbdbbcabcddaebddcacebaedcdbdcbaaceceeacadcaabaabaaeeebddedcbacbbdacbbdcebbdceebabaedcebaeacacabbceababcdbdaedbeeacbcbcceeaeadbdeaaabcccccdaaaaeddbeaeececbdecececbeacdeedbbedebceebaccdcbaddcedeabbcddbcaadddeecabcccabbbedbaceeedbdbcacdeedbaaeeceddecebbdbcdddecaebedbdcdadbccdbdcebcdebaecbdccadbebacbdabadadabceccdcaeabdaddcbadeedaadcbcadbecadcaaeebdeaadbcbeaacdcaddeaeddcaecaececcbabceedadeebadbacadccedecacaceedccbbdedbaecbdecbacbacbcadbccdcdcbeaaabbecbdacdadeacaaaadbeaacdacdbccdedecebddbebbeaedeaeebdacdbbbdedebaabaaeaabbbabbedddaacdadebcdeacebbdaadcccebdbabecdadbadecededecadceceadaedbebccabadcccdddeddecaecbedbceaacbaadececacedecdcaabebabdcdbbddbebacdaedcdcaedcedbecadeeeebeeadacddccaeecdbaaddabaaaceeebcbacaceccaacaadedeecccebbdebbbbedcaededebeeaebcebdcbacedccbddddddcbbbcbdcdadeaebceccdbeeedaaaeebacacabddbccebdadecacecaceaaacadadbceecdbbebcadeedebbdeeceeebcabeecbdaaeccecbbbccedbbceeabdbddcdeedddbccadddbbabbeeadcedadaeebaeddcecbebbcadadcecabdeaeeebdebcbceabcadcddbcabddaeabeadaeabaccbaedbdceebbecbadcbeaedbaaadaccacecaabbdaceaeebcacddddeeadaabcbddbadeaacdbddcacdcebecdbeddbacedcdedadbdeadebeaacecccdaecabdceccbeedacbedbcdaeeddeebdcbabacaadbabdebccbcccbbdcdedcdbbbedeceeaacddbbccceccbcbdceacaadccdeedbbcdedabacdedadcbecbdbcebcdbceecabaccbdabcaaebdeadeaceebbeeeadbeecabeadabcebeaaeccceddaebdeeaadcdedbeaebeeceecdbdbbdecedddbbabedbacdecbeaeccaaaabcacaacbabcdcdbdcaabdaebcedaeaeeaaabecccededdcbbeaabeabaecceadcacdceedbcebbbbaeeeccddddedeaecedddcaaeeddaabbecaacebeadecbbeeddadaaeaedeeeeedeecedcacaeaadcadbdbceebecebeebdbcdbbccbabdaadcddcbaebebcdebbbeeaabcacedccecabdcaddcbdabdebcccaeedaceebdaecaecddeeecebdaeeeabcbeebceaeeadbeaddbedbeccadbeeaededdbacdbaabadbedcdaabebdcbccabcacabebbdbbedeabaeeaacaadbbacdbecbcbbbdcdccacbbdbbccccbeededbadaedccdddaceabcbdaebcabceaaecbbddaeeccaabeecdebcbccacebdcaacddbabbebadddcbcdeadddbadeaacbaceecdcbacacdcbbbbacdeaabbbbdcbdbabebbbeccabbcdebcadacbbbdceaecbddaecddddcbbdabaacabdcdbdbccecaededbacbbddaceaaceecaedbdeabaeadcbdcbaadaedbbdaddbadaaceecabeaecceedcadaaadbbacbabadadbaaccbdcddbcaaedcdcbadeadbdeebbdcdbdbdeaecaeadaecdecedaacadebcadbcbcababddaeaaacedeaebcccbbbdbdedeaadaaaabacddeecdbbcbcdebccbdecddddeeecdadacbcedcddedcdcaccdeccdadbbbadeceeaeddeabdbeceaacbdcbeedebedeeabcaecadbbbedacacbdbacdbabccacbdaddcedabcebecaebbeddcbdcbdacadebaaaaddcdaacacadaebdbbccbaeccaceacbaeaedacecbaaceaacabacbbbaaaeceeddedbbceadaabecebcbceabdeddeeebbdbaadedbbbeecacddedadcbaaadaaacecabdcecaeeeedbecdaabcededbbdeebddbeeccdacecaeeeccdecaaaddebdeaddebaaebdaeccddbbbbcedbddcceabbbaddeeabaededdecbeedadeabebddaedcaeeaddaacbdaaaeaddccabccadaaeedaddabebaedacaaccdbbecceadcddacbcdcddbbacbeacbceaeeeaacbdebbaaaabecedaeecbebcbabedccbacaeeeceaceabdcaceeaeddeadabceacceacccebddebcdbadcdaeaddbcdcdcccdceecaaeddecbbeadbbcbdadbdbcebbbdbbabdeebadbcecccbdadccbcadddcaaabdcceebcdbceeccacacecdccbbdcebbedaabddabaeeecabbbcbbedebccecbdecbdeccabedadbddeeeaddbabeeedabdcebbbadaecbbaebeedaecbcabecccaebddbceebabcbcacbacccbbccdcacecaceecadeedabaddebcabedaabbeddeaddebeaeecdaabcaacccbcbbdeacedeeccadccbabeebdddbabcebedbbbdddeaaacebbacbabcdbdecddaeeaaadbbbdcddcedadebabbecabcbbbcadacbdecbbadabbebcacceddbdecbdbbdbdeccdaaabedddbaadaacecabeabccbeaabccbaebdcdaadabebbaddcbadeabccabbaebbebddacecacbebdebcceccdccccedddaeebcddebbecdaacdabdadadbdeeedeaedbbebedbcabdedacabbbedcdebbbbddaebcdccadeaabdcbdbbaabdaabdcaddabececeddeedcbdbbeecaeaddbaabeeecdecaedeaddccccdddbddbbdeeaceaacaabdbebbddbecddaebbebccecaceababadaeeaceabbbaedcaaacedaddbbbdebccedbbadebdebdddbdcdbedacadadeebaeadebccbbcbbdecdceabeceeebbdecacedebdbdcacdccadcbbcaccadaeecaacaedbadbdcedbebdeabbeabbdccacceecaacecdcddeaaddccbdaecceaacdddcdcacdcecaabccdaeeacaeabbecddbebbbcecccbdbcadaceabdccbbdacbdedaeabeaacacedeabcbddbbadbddebeedebaabebbddbcdccdedddecdeddcddcdcbbacdccbccebcdbdcaabdcbadacedbebcecdebcabbcbacbaecdaaebeaabdcecdbdbacbcabbeaaaeaeaccdebeadadcbecaebccaaaaddeaedbaababcadadaeeaeecedcdbbebcabcebeaadaaaccbccdbcaaadeabcdceeddddbbeecbbbdeaddeebccbbabcdecabacbedecadbaceaddeeeeedebceaeacbababcceaeaaeeaabaeacdeeccdaecdeeeadccaecccdddaabedccacebbbbbeecacdaaddbeeebbceeeebaeddaeebcedaeecbcbcedbcebeebaabcdacbaebbaddeaaececcccacdaaaedbeabdeccbdeecddbdabbddabceacdabaaeddabaeedcdddcaacadbceadbdaecbbceedcaabebdceeeecacaadbcebebbbdcddbdabaaabcbacedbaabaabcebcccddacabddebacddcbeeebaebbcacacbeddeaeaaaeccbbabaadcaeadcbcbadceccbcdbdacedaeccddaeedaccacbedebbbbecacbcdbbcddcbadceebbaeecbecaddcddebcbbdecdcccbdcaaecbbccddaadadeededbacdedcdcecddcabbbbcdaedceaadaaccebeeaaebcdccbbdadcacaadbaabdddebdccbadbbdaeababaeacdeceacaadceeeadbacaadbcbdeeddabdcaebaabdaeddebdecdecacbcccebbacbdbababebbebecacccaeebbbeeaeddbebdadcbebaabccdaaebebeeeacbcbdecccedcdcaaecaeeeeaacaaccbaccabddcedecedceedcabeaabbbcbcecedbcdedbedbebbacaebcbceaceedecaaaadedaeaabceeeacedbbccabbadbebcbccacdbbbcbdbebcaebcddebaceaeeccadeadacccbdbdccabbcadcbeababcdeeacaaeaeaeebeaadcbdbbceedabeabdbcdeddacdbecaaccceacedcbaacaddeaddaabeaceabadaceaeccaaeccbedbbebaebbddbaaebcdcbcbeeaadaeecacaceddbabeebbbbccbaebceecbedbaaccadaccddddeddcaceebeecdebdbeabddebcdaaacdaedcabddbebcbaebabbbacbecdecdbdacdedacbbddbaebedeebadcdbcceaadbbeaaaedeacccaecddebebccdbabbccdeebabdaabbdeedaacabebddbdcaedecccdbebecbbecaacdecbbcdeecbbbdeddbdabcbaedcbdaeadececdebebcbaccaccdbaabdccccbeceedbabbedaaaecaacedbcdebdddbaaccbdeddecebcbbbedeeadbdacaaadbadecadeaecabbbabecacdeecedbcbdebaaccabbadbbadedbecbbdeddaeebaeeaedcaccbecebdaeeeeebbeabacdaebabcddbbbabbbcadebabeecdceccccaddadcbdbebeeabaedbceeeddbcdcabdcdeadddebbcdcdbccdcbbddcdedcddbddaddcdbccedaeaedceccdaeecbcbbececeebedcabebdbaaceeabeaadcedbebbbbecaccdbeeaaaeebdbbdcaadccebcaceeecbeaaccacdeccdbdbebebdceecaadaeeeddedbdecebbbdebeaadbbddbbcebcacaecccdbedeaaabaeaadadaebcadadecceadacedccaeccadebbcdbdbcebccecabbbacbbbddcdcedbcabaacdbbaaadbdeeddbdebdcbacbcbbdacbadaaeaebebdcebbdcceaeccbbadbbabbbddbdccebdccecbaaaacaaaebdbcbacebbcceeaaeabaadceaeeecaddacdedbadaaabbedbbdeccaabaaedbbcdbbceccecdbccbecabdcccddebabbcddcccdccabeacdcaaaecedbbaddeabbdbdccacebdcaccdbaedabdbbcceeabcbbccbeedecbedccbcaaaebabeedcbadabcbacaaddcbcbdbebbebabebacdaeeabddebcbdcdbdaeaececdbcdabeadcacbcecceaeecbaaebbcccbacbeeababeedcdeecaeacdacdcedacbbcacededacdcdcddcebbedccaeecceaaebebacacdecadaeacedddbeabbccbdeeadedbdababbcbebeddecebbbbdbceabcccecdbaadedabdcceaeaeeeccdccecaddeeedbdcccabdeebdabccbebadddabdaccaebcaeecebadbeadbabbdbaeceacdadcaedcbddeecaadaebcdadcadcbeacbbbdeabcbacbadcdaccdeddebaabebeaeceaddcabecbcedccdebcdeedbdedcbdcbbbbebaccbccddcaaccbebaecccaeecaacaebdeecacccbdaacbabbbecaadcdbedaeeaebcbbeaaeaebcebdebdbcadaaeecdadceeaaeebbddaecdbdaaeeaecbeddddcadacbecbdddaaededbabdbbdbdeedacbdbdbadebadbaebdedbeacccdcbbceebacadbdeaccabeaaeeeedbbdaecdadbbdbebceaadcccbdacddbdaadcdbcdbeeecbaccabaceebdacdbdddeabbeeebecbbccdbdabbcbbbcdebddbdcdecbdacbbaaabcceebaabcbebbbaaaedebeeebaeebdbaaadecabdbdecccdedaebdbaccdebadabdcdecabcdbbcaecbdddbbbbdeebaedadceeaadbddceabaedadcaecdacedddbeddebcaacbadbbbccaddcbebdaececeaecdcdeebbdbcdacbddecebaddccbdcdbaadcdabedbddedebbccbedeeabaddeeeecabbebcdeabbecddcccacaaedabebabdccdccacdbbbcbabdeedadcbdddddddeebdcbbbdacadbdebededabbeeeaaaabcdddbebbeccddeedaaaeeacbbebabcbceababbbbbdadeeabcbadabaeaabebeecebacbecadaeebbdeebadeadceadaccabaaacdabccdbacbaaccdebccdedaaedaceaeaeeecebdbbadcdebbcddadedabccdbdaacbdcaedeccdcabcadbbbacedbadccdacbbbcbbedaeaaadeddbeadaceeeeceacbddcebdecdeaedcedadbdceeecaabeabcbcbbbbcebbccadbcaaeccddcaedebbeccddebdabbaebcebccdaaddedecbeecabbeecbdebceabedaddedcbecbdddbedbaddabebdccadcecdcacaaeecbbcebbcbdabbbbbcddcdadbcbabcbaedabeaccdaeceecdeeedbadcaedbeaaabddbcdaecccdceacdaadadadadcddcaabeeccebedaaebedcceabddaeaaccbcaebddbddcdddbacededabdeebcadeaaeceaceebcddeabcabbdddedebbccbdeaeddaadcdcbbdbcadeecdeaebccbdebbddbbdabdaaddbebeeeddddedeacbbdaeabbdbcabdbeaebdaeaaecbdeaaedacdeecdcccccaceeebcccdcabceddbcaaddcddbdbbbaebcbaccdacbbcedacedcdadbadabcdecaeeadbaabdccecabebeccccaadabcaeaabadbeaeabacaeabccccdcaeabddcbaabaddddcddacdebedcedaaddeacdeaeeadcdecabcadadbbdadacbcaaaeadbeeaebedacddcecdbbadcaebacceeaedbadbccedbdbecddbaadbaedddeadcbbaceabddbbededcdccadeaeacceaaeeeebceeaedeaeaebeadabbbeabeeedebbaeeaacaaeddcaaaeaeacacedbceaaabadaecccccbeeaaaedbaaddaeeedceaaddccdcbeedcdbecceadecbaabacedbdadadeccdabceacabbcceaebebbbcecbbeaabdcadaedeecacbdeebeeebadecbbeabedceccddaedcbaecdeadcdbdaadbeeaaabbeeababdcdaabbbdebbbecbbecdddccabaabeecddebdabddbdeeddcddaecadbcbdeeeceeecebdbebedcceddaadcabbaacebdadeadbbaddddbadeecadccabababceceebbaaacdecbdecaabbcdeadeaaadddcbaabcdaeccbbceacabeabdaeecccbaadcebdbdebaaddcabedcdadcdaeacddaeddcbceadcabecebcdcecccaecbaaeeacdcbbcbebacdbdebaddaebdbeccbbbcbcdeeedddbedcaacdadddeeaaebbabdeeeccdbccbadaaebedcceacacdbcbaabcaeceebedbcbacceadddcdbecadaeaeecdabededbecbedcddacabaccbdcaaececcbbdbaeacbadcdbeedcdbdccccceadbdaccddacadaeddadbeeeaceeaaceeadadaedebbdcabcdceacbabdddbbdddabbcaeeddeeadacbbbdeeddddaddedcbccbaaacbadbaeccbeedcceaabbccadbeaedaacabadcbeceaadddaddddbedbacbdddbebacbaecccbdddeacacdbeedebdbdebadbebadacacedaaaacacaaceccdedadeeaddecbbabccadacabdbcbeadabadadeddeadbcdeddaeabcecbbeddbedcaddccbbbddddcaacedddddceabdeaababeeaeeeccbceaabeabdaccabaadaedbecdebccddaaaccddddaedddbeebbbceacbbceccbdaccdbaebecacadcceacbcacacccbadbddbcdceabdabddcebdcdbbdabeadbacbbeabdcecdedcebcdcbebdebbcabcaedcdbcababddebaedecadddaeeaebcdcadcbdbbecadbcbdaeababbbcdadacdedecbcdbecedbadabbdeadcaeaacbadebcbbadbbaedeeecdebbceedcdcdcbbacdbecedcccadbcebadedcdcddbaabcaeabccceebbebbacaeaccebbabdaddcadcbbdedbbcdecbdeacabbdcbeaeceacabdeedccbdccbbdebbbeadddeaaaaeebaecbedddabebcdcbdccbeeaecaeadcbdcbdaeeaabbeeececddeeaecaabaceecedddbecaaadeeadadeecadacdbdaaadaaebcbedceceabcbddacbadbdbadebacabcbdcacbcbeaabebbaacdebbadaacabcbdbcbbabacdadceaabbccccddecaeaadecbdadaeccabcedcbeadcdedabbdabccdaccecbddcdebabbaabebbddbdebeabeaadccebcedcccbedbddaaddeccceebccadebbdacdbbaeaeddbbddecabcbddaadcbcbdbcdcbcedbaacbaeeacabccbaebaabecceebddebcdceabdcbaebebdbedbdddbbccdbdceccdccbddedaecabedeebdedbabadeeeacccaadaacbcdacbdccabbbeaecdeedaebdaeccabccbbbcdeedcaedcadabcbbaabcbdbeaaccecadcaeadbbbccaadbbbadbbcadeabbbbaeabbeecdcaabdcdacddcceadaedebbcccdabdcdabcabaeedbcceadbabcedacbacdbcccadbbbabacbeeecedeabbaabcadcebeecadebeccbdaccddcbcdebaeabedddaddcdbbbddddceadeeecadececdaccddeeedaebcbdbbadadddaeeaeebeaabdccecaebaeaadcdcdbaeddbddbccaebaabdaadbeceeaaddaedccbababecbaaddadbdabbacdcedadadecabaeddcaeeecaebbaeddaaddadcbadacaeacacbcbbcdbdcaebbdcbbceeacddbdabcabcdeeeaedbddbdedcdebcbdbadecedabedbdbebcaeecccccceeebaeecceecaeeddcccaaddaabaebeccdceaaeedaaacadabcdbbccabdacbcbcdabccecbbdeeaecbbcabecceddeccbcabadceccbaeebabdebcdebaacdedbdceccdeceecdaccbceebdbeaccddcacedcddbbaebecdeecbbaddbeeacdebedbaebbcaceaeadcaccaebcbdedbbededcccdbdcdcbacadaaacacecacebbcbedaaaedaadbdecaeeecccaabedecbbaeebebdaeeddadceaceeddedaebcdbceebdbcdeddebaaddaceebddcdaaeaeeecddcbcbacbeecbcdebbeabcddebbadbcacedcedaacaceddbdaadcdacaeddecbdcacbbeeddbaaeadeeadcbebceebadaeccebeccdaeedcdababdadcebeebbeccbddceaddebaedbabadaaaaaeeabdcceccdddddabccabedddebbcdbccdccdeaccaaedeebbbaedeeeaddecdaddbbacdaececdabccbeacceeedbdaeecbbbbddeadbbbeeceeacecbcedbabecdbaecdecdbdccdecabdbdbceecedbbabeeddadecbadeaadedecbddcbbaebcadadbdcaaadeadeebaaddbcbaaaddebbaeaceaecbbacecbedaddcddbacaecbdcdbeeceabcdbabeeeaaedaacdadacdbedccedadccceedaaebcecaacbdbadbaeedcceceeaccaadedbacdeabdceceadbecdbbaeadedacbeeaaeebebebdcbdebeeaacceedeccdaaeabdbebedadcdbadbdabbbbdeddcabddceebdeecadbdbccecdcadabcbdadcddbabcacaaceeadeeadcbbbcabdacddacbecbdeeedebabbaceaaacbcebdcaedecaccaabeaedcddcbdaaaaabdbcecaeeeedcdaecceaecebdaebddcdeebacaeadbedbebdabaceadcdbebebdebbcdeeacebedbbccbcdbbccaebbadaaabbabcacbaeababecceeadccdaebbddebacdcaddabebbbdbdeeeedaccaddeeeebcdaaceeebdbaacbaccaecddcbdbdbdcbcacdbadbcacbacbcabdbdbeacbabdeaeabbacdcedabedabcddddadeddbdaecbbabdeaadcdaeedcacaddbabababdbbbaddabbbaadedeebaedaccacdbebebeedeadedccaedbadadabecbedadeecccaeeebebbedccedceebebccbcdcbccdedcbaacbbecadddecbebdecbacacacaebadeeaabcdcbbabbebbcbdbbcabadccadbaeaeaddebeaaccbeeccadddedbcadddcacbeeadddebbbbceeaedddcecbaaedaacabdebadaaedddcadacbbebbbbaececedaaaadecdbcaaabbabeeceaebbbbdecdcbcbdbdcadccddedabcebebdeeaeddcadbaaabaaadeccdddccdaccaaddaaccaaabdcbbdbdadeacebaaecddbbbbadedccccabcaaadeaabdcaebecedbdcdcaceeebdaaeaaeccdcbacbaacacbcebbcacaddcebdbecccaecaacbcdaccedaacaaeceebdadcbcbdcdeecbaaaabdeabcacecebdbdedebebbdbadebbbbeaadeceacdbbbabbddeedeeadbdceeddabecabeccbaaaeadcdcdeaaeecbdecaacddcdaedbadecbecabadcebcdedcbbdbbaecabcabdadcbbaddcdcecedeceebacbebcabdacecdeeeaceacabdabdcadddbbdccdcadbacaadcbddeddadccbcecccaeedaecdccddeaeececcbecceedbaecdbadeecaadbeabdabcbceeccacababbeccbdcbdbcabdedecbebdbeeeccacaebccaaaddebdccaddaecdbaccebbcdcecebedeadeceabdabcaeaeeedabdadcbaeeabbccbebeacdedaeeddcaeeecdceeabaedabceedeeadbaddeeedbbadacceaceaedccceaccddccaddebbbeaceadedededebcbcaddbbebedaaeaeebbdcaeaedebbedebdacedceabdeabbebdbebebcebdecdebbcaaaddedcdeaedbceedacddbbddcedbabbbddaadbeadceddaeecadacceeccadbbeeeccecbcaacbccbcabbabaabeaedeededecdabeeddcedaddbceecaadeabbabdeaecdebaabecdedebdecceeeacbaaddebcaedcaadabeeaacbeadddeececacbacbbbaedceecebedaabcdbececeaabeaaaaddecaabbcaddcdaadaebceeeedadebccbdeacdcdecdaacabaaeaecbabbeedeeccecdcdbdcdbebdbbeceaaecebbceabacaacebcabbcddddeeacdaedadcbabaebdbecaaaabddcaadcdaeaeecdebbbadccbeaeeedeaabdbaeaecddaeedaacbaededbabcceddcecaaeeeaeaadeebcbaebcadebbaaeeeadeeebddbcbccebedecbdecaaaeaecddbabaabdecaaebaecdaaaabeeaaadeebbaedadbeaadbbdceeeacaacdbdebbaabbedeabddedcdcebaddaeeedccabedcdedbcbbadbbaabbcaaaccabdbceeaadadceddaebeccdadebddebaedbeeadbeaaedacaaaaacadaceeadbeaacddddebbaebaddbbbebccacaadeaedcaccddcbccabbeabaeadadeecedecbccbaaaaabddcbbdbbdadeebbdbeaacdabdaccaddccbebbecedaddbeacdbdcacdabedbdcacceeabccbdcaceadeeeeceeeebddedaabccdedbabadccbdacdacabeedceebccbabeeaeeaaabeacbacceceacbcabacceecceecdcabbbddbecbbdcdbbcabaeeccedaebdaaebbdecdeacbebacadecebbbceceacbbcdccbbbabdecbeabacaddcaabedaeeaeebbddebebcbcdaabbeddcaaecddbecdcdadaaeadbabcaccceadebdcbddaeabbeabbabeddceddddcebebedbacaceabbaababdbbbbabebdebbbbecaccbaacbaaddaaebbedbdcddeebeadebeeeebbabacbbeaaaaccdcecbcccccbbdbbbaacaeebeaedbecbccebcabbebeabddaabdedcccacceceadbbeabedcbdccbabbbaaacbcdbcecdadebaeaaacaeaedbaecbaceceecdaabadaacdecbabeebaeddbbbeaadcacceccaaadcdebdbadcbcdedcdaaabceeabaccabeebbbdcadcbbebeccbdbedacceabaaccdbdacaaebeccccbacdccddcaadbbbdebecccdeacddeededeabdeedcdabdabbbedaaeeacdabccdbacbeeeeecacaddbeacdadddbcedacdcadcdbedbbaeaabecedcaccdebdcecbdadaadbdddcabccdaabdddebdeaddbcbabdccdacddecaedacbaddaaaaabdeabeaedccbeabcdbbebdabcbccbddeecbeedbabbeaaceddbeeeccecdbaadcdedeaadcaeebcaaaccdacdcdbbaaeedbbeaaaeecbaebedecbcdcaabcedebeacbeccacadaadabceaabcdcbeaadddbacdaecbcbcadaaebdcbadeaadaecabaebbebbbaaaadebdcaccddbbcacadedcadcdbacecdadcdecacbceaabddeeabccaddbdacdadeabdecadbecbdabccaeebbbaeebdabcecbeeebecdacdabbeaaaceaacabebbdeebececcdcebbbdebeadbadbbbdcccaabeaabcbeaaeceddaecedceacaedcaabbeaeeaaacdaaecadeecabdbccbcdddcbceaaeccdbedeedccaacdddaadbccccacaecadcedacbecbddedddadabbacbaebabcbabcccbabccdedebcbdacebedabacbdacabbddbbaabddcabbaadcbabcdbeeabbebbeaabacbbcaccbeedcddcebedeadbdadadcedeabeccecccdbbcdbdaebdcecbbeacaaababddaaadaaecbddcebddabbaabcbbcccbeedddabadbdbcedecaaabcedcbbbdbdaddaecaebdaccbdbbceaaeabacacbcabaeacdbddccacabcaaadcbdcbbeebaaadbbbcbbeccedbeeecdbeaddeeabeededbeeacebacdeaeddbdaadbebdddcdddcecbabdbeeaedcddbbceeccbbaabbaacdcceecdaacceeaadadababcdcebbcaadccabacecedccbddcdbbdabcebcecbacececbeacaacedddacbccdbeacebacbeecbaebeeebccebacbceceabdcdbcaacedaedbaabedbbbaacaeaacaeebbbacbedebdeabdeccebcedbbeacedabeaedebbdbcababaacbebeaecaaeaddeecdbdacdabbacbcdcadcabbbcaeaadceaebcaadbddeeedbacdcaddadbecebdeddbdedcbedbdebeadeccccdddcbddadbbddcbdeebaeddeaaadedbcbbcbdeaaceabcaaedeedeacaeddacbbaeacabdceddeaeacaadaccededdcadbbbdddccdcbeadacedebebddbcebebcbdaecdacadadaaacedaabedeaaccecadaebacabbccaccacdeeaccaceebdcddbedebeccdababdbbbaaebdaaeeadedacebdbbaeaaeccbbcebdabbdaedecadcadcebbbadbecbbaabbccabebbdabaaaeedcebcddbabeadcebeeccdbeedaebccbecdeeeaeeccdbbaacdbdebddebccabdedbcdcbacedabdceabbebdbbbccceebecdeacdacbcbbcbcebbacabcbcaaddcacddededdadbcbccceacbeddbadaabcdaacccbbddabcdbbbecdabbeeccdddaeeabdecaaededdabdcdddcdcaddadbedddeeaadcebcbadaebdddbebabdbcbeadbcdbececadaaddcaeccebbdcccbccacbdbacacdcebbdeadaedaededdcdaadecceaeeebaccaeaadabecaddddadcadebdccbbeebdccccbccbbddaaaaadbeedbadcdeedcecddeeeeebebeddcabcdacbeacbcaceebaadcddedeeebaeabdcdcbebddebedaeebbdccbabcceaeadecdabbeabcbaaeaadedbdaeecacbcdbeaeedaabddacddbbcadcdcdeeadbbcbbdaeacbdbeaabdcbbcceeadabeecadecaeebadbcbbadedebebccadebceddaedbdedbbbeebccbcacdcddaddcccadcaabdbaebeecbcdedeadbecacdccacddadeadabcbbbebebbeacbdddbaecdddbdedbccdaccecebceedabeadceaabcbdabbcccdacccdebadedbedbcebcacacebecbaaccdbeeceabbbdcdbdbdaddaebccdaaabaedbcdbadcadaeabaedaaccbedeccaeeecdeacdaedacadaeceaddaedcadcaceecbbcedcacdcadedbdbeedebecbadddaeeeeccaacccdbaaacbebbdcabecdbabbebaddecdccdbabdebcdecdcbabedbdaceadabdbececebbdacebcdebabeddacaeedacdccebebabdbcaddcadaaeeaaccabbeacaddedbbeedbeadbacbdbaddbadcbabbbbeacbdcebabbaeaeabedcaeaadcbccebcdbdbcdccbadcaedbababeaaeecedabdddaadddadddcdbebbeacaaeceaccacddddeadaddeebdcdccadaaeeaedcdadbbcbdaeeeecabeaecbbbdaaecacecdedacaaaebebeebdbdcbaaeeaabaabedabadbceebbcddebbdccbcaeeeddeadedbddbbbcbbaeaceacacbebedaddaddcbadaeaebbdacebcecbcacbbddddeeeabeacdbdeedeaddadedaaedbcccdcebdcaaadbccdcacedecbebdecbeacccaaeebdeedaecdbbbdbabacbadadecdcbcbedeecbaaadccbebccceeeadcbbbacdccddceadebecaeeeacadbcccdbbcbcddbacabcbaeddadeabaccbdcddcedcbeadaddcacdeabeaaccbeaeebadcbbbceacecceaccceaacdadaeddedadcdacaaebcddbacaccaebebdcbcbdedccbecadebbeaeddadebccdbcdbeaabbdceddcbacbaaebbadeedcacadcdcbbcadddebaddbecebccbacacbdebdedebcaedaedcaaaeecdbadabaceaaaedeccedbadceaaaabbbbedeeeeeaabebdbedbbeddaedcbcbbebeadbdeecacccabcebeaedcaeaedcabaedeedaabdbbaadedbaadcaadecaaeddcadedaaececbdaecacabbbbbeecccbbcbeceacdbebddcceadaacdacdbaabaddeeccbabdddadebccacbcebecccecedebabbceddbacddecaecdbbedcaaddbebdadaaebbebaacecedbbdbbdbacdecbdedceceadbbacbdecdcbabccadecddbccacdddcdedbdcbbeaccdcedbbcacbbbabddebedeebabecbbbcbcacabdcaedbceeecebedabcaecbdcadcdeccddbaaacecdcbdceaabaacdeedcccaeaedabbebbbcdebbbcdcabbbbcaeaccadbccabcddccdeededbcedabcacaeadbecaaebdeaddaecacbadbccadedeaaeabababaebcabdbddbdbacebabbcdebbdadabecaeebaadeeaabeebbcadcaedbdbcbcebcbbbcddebcaacbddadbdaeeaadcecadccedcddcddcbceebaeaeeecbebdebbcacacadebdaaeeedbdccedceaebddcdebbacbccecdbaccdddbcdcdebaadaecbbcdbbbbdcbdacdaaddaeaacddcabaaaddaeaaabadaeddddcaebbebdcaeabaedaaebdbbdccccdbdecaaabdbbcdeeddcabeebdbadaabceeaadcbebccbabdddccebbadeaaeddebaaaebcdcdacdadabaedbbacabeedaadeaaadbbbcaacdececaabbddbcbaabcaaabcdcbccaabcddabbebeeeedceccbbeecebccebcbcbabeecddcebceedcdccaadedccdbbcecbedeabccdaeebdccddcabaeaaaaaeecebbbdbaeaadccbcabdcdccadecabeebcabdcaddbdabeadecaedabeabcdccbccbdaccbaadeaeccaeadbdbbdeecccaadbebedeebecbdadecbdcedadbadddeedbddcedbbdadcdeccbdbebeeeacebbdbdcedbcceeaddcbcbeaadbdaedabceacebccbeabaccecbebebedebeabcbcabacecddeddedcacdbadccbdeaebdcbbeaebddeabcbeaaeebcdeeaaadeddabbaaeaadedecacbbdbddcaecbadcedbaddccacecedeaeabbcdcdddcbdcadeeecdeaddcbebdaaecbdaadbebdeddddbceaccdcebdcaebebbeeabcbebebddedaeabbcaecacedcceccbdadeeaaecbccddaecaecbabdceebdcecdaaecacdbddbebceabbbeacbbcdcdbcedacadcbcabddbaaebabdcabdacbabbebacdabaeecbbabaecdbaeebeeabbbeaebcdabaceaadcaaceccbddcdaddebcedceccedbeeddaddbddbadaacdcbaaeebadaebdddbdebdccacbdcacaceaeaaaeabbdcadabcedbebccdacceaeddaaadccadabbdaaeabeebcceaedcbdebebaabeaaeccdbcdcaabbbbeeaaccaceebdbaaacbbacdecccbdbdbecabbdbdaeaecbeccdccccacabbbaceccbcdbdedeabadcbecdaddeddbdbeccacbdedceedabceddadceaaedeacaedaabccdddacebbbaeacedecdccdeadbdccadbdcccdccacaaaedabdcddbabceadbdcbccaebedaadaabcdbbebccdbeebcadccbbcbbeeabdaaacaedddbaebabbcbdcbadbdcbdaeccadbaccedbcccddcaecadbeadacdaaebeababcddedebddcbedaeebbaacedbbbdedbebeacceacaadbedaddbaeaeccabeebeccabdeeaedabdceaeaaedbbaadedccebeedcdaecddbccbedeebadaddbcddadeacedaddcecebaaeedecaaaaceabcdcbeddadbedcdbbdbccdeadecacabbaedecccdcceebcaabdbbdcbdcadaccaceccdbdcbeabdeedabbbccccacbcddcbbcadbacdbcacbbcdebddabbacdadaeaddbcaeaebbaedadeebadcddbaabeecbbbadbabedddbaeeddbdbedbaeebabccceacebeacccdccabaeedcaaccbdcaacadbbebccaeaceeacbaeabdabdaeeadbdcddaeaeecbececdbebbcbbdcdacddbaebcbcddcaebedaacdbdaedaabbadcbcadddccccaaeeceaeecccbbbeecadbbecadeaadcbbbbebccddbecddcebaaabbcebdbcbdbebebdacdeadebddedaebeeccccbdeaebeaacccdbecbeaebddcecddbaecccebbbdeecbbabdedccaeecaabccbedaeddbaeedadbeeebbcedbbbbcaeacddcbeceededcdaeecccebcbaedadeebbeebdcbacabbaaeadaccdeaaaaddbdeaacdabbbdaaedcabccbadcedaeadadbcccdeaddbabcadadbcadecaebaabdcdbcceeddeceeddddaeccecbcaeeddeeabddcbecabbbdbddcdecddbcdcdbdcdddcdaababcebbeddddcdebedabbdcaeeeebddbdceeadbbcaddbbebadbaeaeeeabadecbcecdaddbabedeeacbdccbdaaedbebecbbabccbadeabbceaeebacecdcabcddddebddbbaaadbccbcbcbeabddbdacccccbbeecbdebdeaeecbcddacaaaeeaddabdebeeddeacedcabdaaedbedebbebbdddedbaccbcccbdbbeddebecdebbbcbbbceceedbbaceecdbdeaccecebcabcebeedebdadcedaeacbaecdbddededcaaeacabdcdabedcacbcaddbbdbbaeeadaedbceeebaeceadbbdaeebcddbdcbaaaaaeaeebabdbaacbabecaaedacebaddecacabeaccdecaebcdcaaddddaeaeabeaacdedcedecaecebaeddacaebbddadcaceebcececbbabdededecadebbadbebcbdcceebaadeecbaaccccbedebbccedacdccbbcdbcbcdaccebbecbcbadecbdeeebdeadeeddaecbedddccbbaadbbabbabcccbaadcadaaabdaedcdacbaebdecebedceacecbbeaebbacceccdaecbaacdecbedeccaddcdeaeeeeadaeeadebbeceddbaedbddcdcaacbbbdedacbddecbacdedacecaddeedbbdccdcedacddadcbecabacabceaccdacdbddabbbbbddacccdbdacceeabaaacdbabcbceaacebbcdbdcdeebeccdbdebdceaceedabddbbeecbadccddabadceaccabdabbcbdcddaddacebbcdcceaccccadcecccccacdbcdbdddbccaaeeceabbadeecaedaaacbeebbaeebedbdebacedcabecacebabccaccbebbaecdebeddeedaaabdeeadbebaacbedabbdebdbddbdbcbaebbcadedbebcdddeeecbcaccdddcbaabbcacdeeecaedcebeaecdcbdacdbdbdbecadbbbacdabadaaeaaaeaedaadcadceaceabaedaaebccedeecaeebcacaddcbbbceebedbaddaedddceccdceacaddddcdccaabddccadcbbcecacabacecbbbbdcdbeeddbdbbcdebcaadcabeacabdacddbbddccdbdaceeccbceeeeeeeebeeaeceebccdaddacecacabaadacecedbbbdeccbbaaaebadedececdacebadcddbccdbcbeddecbeeadceeddcbdcaacddccbcbcabcaddadcababdbcdabaeadbaeeddddbbbedeadddacddacbbaebedcccaccbaccadeacceddedcdcbacbddcedceedaceacceaceedcbbbdeddebddcabaeabababddbedcdcccebcdbdcdcdabebdccbdeaacddddeccbcbcccccbbabbcebbdcbecbedaeeedbeebeadeabbeebccbadbaaadbecabcedcbceeeeeabdabcacbebceccbdbdcabccbbcabbabeacaadadbbaacadbaeabceecddcadeebecbaaebdcebdadaccbabbadbebeeabdccaadcbabedbcecaacaceeabacccedeebaabeeececaaeacbcdaaeabddacccaddcbbddbacaadadbdaeaddaadccadabcaacaebaedbcbbcaabaeeaebbbeedbbbadebacdebacaeceeaacbacccbabaabeeadabacadbeeacaebebabedbbceabaebeeccbcacedccabaedcdeebecbbadcacadccbddeeeadbccbcebaebaeecdbecadcdccaeceaedeabddddeadbbbceaacdcbcdcaaabdadacabcebcbdbbbabdcdddaedbadebdccdaabbedabeecacedebccecedbaebadbeedbbddbbdaddedadcadabecbeadbecaaccecdcabdcdccecddbdbddcddeabccbbccbdbcdadaacebccddbadedcdbacddacbaaddadbedcbadeaaeccccaacabecdccacdebebdebbcddaababcebceabeccdcceaeeecbcededaeeccceabcdebddaaceebeeeaadebddbbebdbadddaedadedccdcaeccccddaebbeadadddddbbbcacabdaddaecceeccdcbbcccaebbcbeeadbdccacbeeeedeccbeabacacbeaaeddeadaaeebacbdcbadcadcaadcbdbaecdbbebaadaaaebbcdcdebcdbdcddceebedbcacdecaaabaadeeeababcacbdbeaecedeabcdcaaedeededbcacdddeadaceabccaeedbcbeaddeadccdadddbceccbbecdececdbddcddddabdcadcdeeebdccddecbbeacbaccecaacaddeadccdbdcaebbccabedbacecbbdabedcceaebaecbbeccddcacecdacaddaebbccbbdedaaacecddedebbbedacbccebaccbacbdbccabccbaeaeadcadabeaaddaaceabeedecbeadacebdeebedecaedcddcadedadbdacccdbcbebbcceccbcebdadbdaeedaeaebdcdbceedddcadacbbcaaaaacecddbbacacedbaeababbacbcbbcdaaeedcadbbacdbbbacbbdbbcbcaacccdbadeaaebbaeedcedbcaadcdabbccdadcebcbaddcbaedadedaecabbbbadedabbcceabeabbdbededcebbbcdbaebabaedecaadedbdbaaacbeeeecedbadaaaabcbccebcacdbaaebceddcdcedcabbcdabebcebebedeecbdbcacddadccebdcceadcaceaeeadbaddacaedbaeceecaaccedebcbbdeaeaeecbadaabdaeabaeabdddebdccaeadacaacccbdeeacabbeebdbecbaeaddeeeddbccdbbebdddadddaeabcccaababdabbbbdeeccadeacbcccbdebccacaaceabbecaceaedcbaceadeadcbeeceeacadbecaeeadbbbacbcdaeeaabadebbdcddbaecccccaaecddacedeabaadabebcdebadaacaeeceaddeebdedcdbeecceaaaabecdadbecacccdecdebeabecaeeeeaeaadcdaaaabacccbcdbadeedaaabdbbdcceeaceeeaabeeebcbebbddccdcbbdbecdbbdaaacaccdababdcecbacdcdaccabdebdabcdaecceecceaeaddaaabcaadddeeadeabdcbdeceaacdcadadbcadccacecbcbddcedbadbebeadaadaddbcdbeabdbbcebcebdedceaccabbaaeeceedbecbbdecbaedededccaeedbbcecebdadadcbceadcebccbedcdbaebbcdcdbdbdddaeaceeeccaabbbeddadceeeceddaadbebaeecbbaeedcacddedadacabadebaebacbbaecaaeecabbbaedadebdabcaebccaecededbeecbdbccacbaadeaeebadebccdeaaeddbebdacdebcdcaeeedebadcceadaaeccddcedadaeebecaddbbbddeacebcabdaeeeeceedbeddceddbeacaadedaecdceadecedbaccdcedebecdceaebdebabcebedbeecbaebdcadbdbddacbbceedcbaedcdbaeeedabdaccacacedbaecddcdbcabceececaaceeadbbeddaacccebbaacebabcaccedbbabbbbccceaaadacdacdadbceceacebeccacdcccddaedcbaecadccceecacdcbbebaedcabaecaaaeaabacecacaeccaeedcbedadccdcbebbeacbbabbcebcaebddaadebdccecdbeaedabbeaccaedecececbbbeeeececaadbebbededcccdecddbaacacccdccacdeddbbbdaaadacbebeceeecccebdcaeeaaabaabeddddbbeedadcaecccddadadaabcdccebaabdcdaacaccddacadadbaaecadddcabeaadddedaacdbaccdaaeeebdcddaccaebdbbdeabcadcebadbbedbddbdaceebdecacabbebdccbbeadaabbdebadeabbabaceeddbdeecbecdcccccadcaeaeacecdaddaeeaaeecbbecdebaabaeebaeacbeedaecaceccbdbcdbbdeeebadbcdeacabeadedeebdabacbaadbbceaaddeccaddceaaebeeedbadddbbdecaceaaeaaabeaecaaabaabeaacbeccddcdcaebdbbcaeebebdbcdbeccabebbdccbbcbbadecacdeccdcedaeedaeacbeddaaecabbbeebbabcabbcbbbdcebecacddaadcdedadcbccbcadddccbbdaebcbcecaecebbceccadadddedeceecedcaccecacdbbbbebccedacdbadeabcaacabbaadcbaaaddabcabbdceeadbacbabbaceacaceebccdbabedcabcdcaadbaddceeadaccabcebdeddbbdeaaedacbbdabbadeeeaaebdcaeaebaaeeecccccedcdeaeeaeebbbaabbeadebccedcbeddccecadaebebeedaacdbbcacccaacdcabeaeaeaabeabcccaeddcadbeecddcbabaaebcceaacdaeecccaceebddbdcccddcedaacebceedeaccbaeccacbbcddbddcdccdbdadeeebbabbddbddededebddbdacceeedaddadccaeabadbdcccbbcddcaedecdcbeebdbbcbbdacdcaceeddaecadebeddbedacbcddbdebbceaaccbddeacaddcecaaceaddbbceeaabebcdddebabacbaddecdcebedbbadbcbebbeeaeadcbabeeaaaeeabbbddeadeaceceeeddebdaaeaceedbddaeddeeccdcedbcdbcebdaebbdadbcbdaedbcdccaddddcbbeeeabccbeedeabcaccebceecbcabaaedaeaaeceaabebcbbedbbdabaeeeaebbccbedaaaccaadddbdddecdabdcedadcbededcbecbdacceedebeecdcceaabddeccdaeaeedbdacdebbeeaecbacbcabceeedbbcaadecdbceaddddedeecadebcabcdaebdcbececaaedaeadecabaaccceeceeecebdcbebecadcadbbaacbbcbcbbaacdddecaceeddbbdbddbaeeeeccadeceaedabbaaecdbbeddbcbcbcabacdaaaeeacbbcaacaaabedbeaaececadeadabbecebdeeacdbbeeeeecbadcebbdaeeededdeaccdaececddbabedabdedbcddcbcbdcebacabcebecebacaceacbbbaaeceedacebeedbecdcededaacedaaaceeaabbeccebcdaebcdeadcaadaddbebabeaaccdebbcedecbaccbdbbeabdebbbaddbdacdabacabcebcbdcbbbcdacdddcadcccbcddbccecbeaaebaceedaeeddeeeeaeabcaabbaecabdadebcdeebacdaabbeeabdcacaaecabcbeadabcaabcacecdebbbeedbbbbcebbceceadbaebcdcbbeeedeccbabdeecbdbaeccceacbabadcdbddaeacdabeaecadcedcaadebcebdaeceaddbcbaacdcbbecdbbecbdacceaaabadcdcbcacecbacbadeeebbdecccabbbadcedebcaedccbceedddbdcbcacbddacaeabcbeadabbbccecdbddbaeaeecabdebceceebeabdccaebdedcecaabddcbeaceaabceebaacaadbbbacacbcddbaabcdebeadabcedebdbadbeebbcbdaedbbeaddbcceedeadcdccedeabdccebaccaacbccbadeacbaadddecaebebccbebdcadebcabcbabaaadaceecbecadeceacadeecebebcbbbecbdeacbbcebbcbdecddecbcdadaedbbdeddebedebbbbcebbdcccadaeeddeaeedceacedcbbacbcacbbeaadbeacaebaadaeabbeeccdcdbcbcadbdcabeeaebbddaebedadeceeccceaceceaeaaaacbbcabdeececbebccacdbcceeadedcebcaedbeebbeeabddacecbaabbcbdcccabbdbcccbdcadaadddceccaaacecbddadabcaeecbbdebddbaedbecdceccdcbaccacacdaeeeebbabcddecbabaeeaadbaedbacdbeabeecebbaeaeceebbcbebceaeeebbbdabddbedcdedcacbaaebbdaeccbcbdbbaaadbcaaeeddeebedbabbecaceaddbcbacacbdacdbbaacdbaaeaaaaceadcacdbdcedbabaaecdeccbbcbbddbebabbaeabcaebbedebcdadadeaaeebabedadeadbadbcabaededaccddcdcebaeaceacbaceecaadadaddaebddcdbdcbbedaecdbcddaadcbebecaabcbbadbabebbcebcdaaaceaaeabadbededaacbcecbbeecebdcdddcddeddbbeacdddaaacbeacdeaabddeacbebbaaaeeebcdaddccbaddcdcbdcbceccaaeabceadadddceeaaabbcbcdddebacaeeebbeecdeaebdeedaadbecccbeecabcdcbebcebecececccbcccdddcebccabcecbdababeeadeeebeccdebbdbcddadadbebdedcaeadaacccdedadabdbceabccbdabbabeaedbaaedccdbdbbdcbaebeeeadddceeaeacdbeacdcbdbeceabcbeaabbbdecceacceddadcdedeedcbccbedbaedaabebedeeabecccddabcaedcbcdbeeddaceecbbdcbaabeeadababcdbcebcecdcaaaceebaceedacaadbdbcaddecccdbddcacbacdabbaaedaacdbccbabeebdabbdeaaedaadceadadddbddadecaebdedcddddccbdcedaacbccacacdccceeadbdecdccdcddaaacabbebbedddbbabbccdabeedccdeddccbbcccbcaccbecadaadbabbcaecdbadbcadecbbbbddcdccbdeaedbccdbbedcaacdecacceaecabccadeccdbdaaecebbdccacabccbacaaebdbaceaaddbcecbccacbabaecacbaaebeeccceaceacdaedabeeaebddbbaacadbaeedaadaaacebbdedbeaaabbbdadbddeccedbeadaebbccdcbabdcdaaaccacedaedcddceddeedadcccebebcbbaaacaabbdccababadbabedbcaccddcceddebdeeaecdcacdaccebeabceacdddccaaaadcedaecacaddbeaecaebbddbbbdbccbdbccecceddbdebaeceebedcbdedaccecaeabbdddddbbacadaecceeadbedeecbddcdbebeebbcdbecebcdbeebbecdbacbdddccbcebeeadbbbaceddcaeaecbedabdcbbeabbdececeedadeccbbcadcbeeedcbecabdaacdddadbeebdcaddcdbdcaebaebeaddceeaabbacdebcddcebbeeabecdeebdccadaceaabdadbbaeebeeabdcdaacdecbdadcaaecadeddaddcaddcdbeddabdbcacbcceecaeaedcbdbabdeaeeebedddcacdcdebeedabebbdebdadcdbadcceadeaacedcdebdbebdcdecccaedbbbedccccbddeaebabcbbadbeaadeaceabddcbdebbaabeecdbadccddaeabdccacdeeacaedcbdebcdbeacdeedcedcccedbcdcceddeacdabddaaebadbaabeddaebdebcbbbdbcaedddcaddcebdeadcecdebbeabceacebcbaddedbebbecceacddcbeaadeecebbcdeddbccadacbaeedcedbdccecaeaabdbadaabddcdaaccbeaeeaccbcaeaecdecbadabaacedbbebcacccbbbbccbeceaaebeabbeebdeccadcaadededdcdbcedaedeacddbcbbdaddebcbbbcbeaddeebeddcdcdcedccbccabebbdececabdbdcacddbeecacbdbbcbddddcedbedcbceedadadebeaaadbdcbebdcdbedaceceecddbeadbcbaaecdaddaeeaacbacdeaeeddabdbcbbdadedccbcecbcddeabdeeaeadbbcccabebbbbdbbbcbcbbcacaaeceddcdeeaeabbcbbaabebcbdbbacaccaccdccbcabcacbecdcbdeeaeaceddbdccebdeebdcdadbdaadcbadedeeeedecdabacabceaadeaaaeadecdbeedabddbabbcbbebbceabbcddcdebcebbacdebaeabdbbdeadcaabccaebeaeeceaecabcbdaedbaaabacaceeaaaaabcdeaaecdccdbbeeaeaedabbaabbdddcbaecedddabcacdbbebaeadadcecadccccdbadedcbecceacabebaeedeecaaddaedabacbbababbadbbcdbcaeaacccecdceecbadcaabdedbbaeaccbdedacaebccacaeedcddedadacedebebbeebcaeabadcacaedbdcbbaabacebacadcbedcaeaadeaddeeedadbebcbadceccceedbbdcdaecdaeeaaaeababdcaadbcadecdceccdaeedebeaeddcbbdadeeecbedbeccadcbcbbeeaadabbbeadbcaccbebbbedebdcdddbaebddaaadccaaeebdadbbeaddeebcaecbcadccdededdcceccdccddbdeeecdcaecccceacacbaddcdaeecdbbacccdeddbabbeadeccbbadbbddaecbdeecdaceeadedbdbdedebbcacddeccebdbacdcabbbcecdabbdededceaeadaadeebdbbdacdaddbeacdccdacabccbdeeaaecabcaaeacdacacbdbbcdbeacdbdeabeecaceccebaaaaeeccdeeccebeeeaccedcedecaadddaebaededdbbeedbdcadeceeedcbacdcabbbdbcbcceecaabbddaababbcccebadaeecebcdcbaebcbeaedbadecceeaadedccbbeacecadbbbaedcbbcdbbedccbbdcedbcbceeecedeeaadbabbeedbadabbbdbdbbdaabadcaceadaacbcccceeeebbecdaddddaebacdeaebeeeaacacddaacccaccacddacccebbbaadeeabddadbebeaddeedaadddeedacdaeaeeceabcadbddbcedbdbacccddcdecaeadecacebedbbbdbdeadaaaccdedaacbadeaaebbcbcdacdabaebabadbebdeaebacbdccbeebccbeaccbcccaaddeddcebbbbacadecdaaceaecbedbedcceabaabacbcabeaaccbedaecdeabcdbabaadbddebcadacebcaabebeccbdbedbcacbeececbadedeececccdeccddcdbcbdebbddbaecbaaccdeaaccdaaddbedcdbbddbaedbddbdacebaaebcabcdacbbeebadbcdbaedeeaadacecbceedaaceddeddcaeeadaaaaccbeaaceeadbceccddebdbcaacdecbbababbabaaeceeddacceecdbabcebeebddbdecebadbeededaebedeeecdcbdbdcaeccdaaeaccecaccbaebdeaeceabbededeaeaccdabcececeadddbeeeacbccceacccaeceeaddbdcacaeabcedeeadeadbcacdeeadaeceedccccaccadaddceaeceaecdadaacadebeaaebddaddeccabbaacbacbcedcbceaecdccddecbacedbededbbeecbaacaebadcaeacdecbebacbecdeedecdbcedbecacdcbabdaebebadeeacecbaddacbcbaddcedaeedacccdcaededcaeeebbedbedaabcedeceededbccbccebbedccddeabaebcbcdebbbbcedaeeadbeebacbccdaccecccdbddbbebecaebcacdceecaebcbdedebdeddebadeddebeedecacdbccbccedeaedadececbadbcdabccdaadecaaddeeabdaaceadeabbcbecdcbddaddadeebcbadeebeacbedecaabcabdcaceeccebbcdbebdceeecdcdbcbcbddeabaabbceeccbcdecbadabccbaceddbdccbaddeeceeecddccddccbaeaadcaabebcacecbcedcbdeceadceeeebbdaccdcedabcebceabdcbddcbeaabcceeddcdabbcacadecddbdcbdccaedbdabacacbacbedadcbaaebadbceedcdeeecdbcedeebdadeaaadcaceddedddddeedadedbcaedbaedddebdcaeaceccadebecaacbcdbdabcbbadcaccabaecddddaacdacabbcaaadcebddbcabdbedaeeceebbdccbdbcbebeacddcceebcddddebbaaaaaabbceeedceecaddaaaacecceaedabacddaedaaceccbcaaeeedbcabebccadcbaceabcdbbececdeacaededeeabebbbedcdbccaaeacbaaedceeeedcebdaeaaebaedeecebeeedbecbeeceacccbbdaeaeddddbecdcaccddacaecdabbeaabaeeedcacabdacbecaddbceeedbaaeacaacacdeebcbceccddedaeededddbbbbbdebbeecbeaaecebabcddcbcdddeeaaabbcebabecaaaadeebedccbbedceadbbecbedecdcbdedddeaacddeeaddbdeeaeceddebaabaacccbcedacecdcaaebdabeaaaeececbdcbceaebbabacaaaadcecdeacaabbdbcbebeececeeebcdcacbcaddcaaedccdcdcaaecaccdcdccabaddedbddeacadeccebecabeeeebcebeadcbcaaeddaaccbeebdabbecbdaddbcbbabedecaadabadaececaebbecdedbccdcaeceadebecddaabbcedbaacbdeceddaaeecdaeaddbcedceddaaccbbbdebaaccaecadebabaaecddbbcacaccebabebdbcbeccdbdbaeabcbacaaeabcbedcadcdbecbcadbeaddbddeecedeaddcaeaceeedeebdbccaaedddccdeaadebdedccdaacbdbbaebaeabcceecddbeadcdabceebdbaaabadccbbddbccbceededccedbdcadadcdaeaddeaeadeebeaeaacacacccdcaabaabddebadeacaedccddadcdaebbceacedaebbacabaadbccabdaceeeeddbadeabaaddcebcddadcedaaceebaedeceddaeacddbbedbbdeabdaccaaaeaaaadecccebeaeddaadbcbedbaababbdbbcadedaddecaeadbccbbadadeccedbbdaccbadedacbdcceabceececaeaddbabcadebedeaddabdaedaecdbeecbbbadbdadeddbebecdadecbcdcacbdbcdecebbaeadacbdaaddcdcadeaadceaebccaacbaedbdbedbacdeaadaceaddaeaabbddbcdedbdebbbeccccaeabdbabadceeacbbbadeabedbaecbadbaaeaaeebbbbaebeaacadbddabecbaeadbbdabebeacbbdecddacbeeebadecadebedeeedaeecededdebaeebdaabccebcedccedcedceaddcedbaeeeedddbdecabcbeaedcdeeadebacddbdccbcececdbaabedcabbadebcacaadaeadaaddcdbeddbceddbcdbbaddebcdeebbdeeacdeaeaeeacdcecbcaaabebbeaacbbcbcdcbaacbacedceabddbddebdceacebccdeaeebeeceaaccedbacaacededcceabbbbaddbaaebbbddcaacadaaddccdecaccbcebdceeeeaedaceccdddedccaacddcceccdaeaecdaaacedabbeebeeaeeceecbadeabdeeecbdddedbcedccbaeaadaaadaedbccecadbdedbccadeaedeacdbbddbbeacbeadabbdcdaecbcaaaeeebdcebaabcecaddedaadabccdeabbadeabbdedacebbbabbbccaeddddccaceddadbeeacbcecacddaaeedcacdbcedeeeeddbcdcdcdddbabdbaacaacbdcebecddeeaadebcdacecdebbaabbeabddebbdcbedeaabbebadddbecadabbddbadbdeeebedbdcdbeaabbeaceddcaccbebdbddbedcbbcebdcdebeceaceaaaabeaaebeccbabbdeeceaaeeddadcbacadaeceaabcacacddbeaababdbeeedccdaacbacdcdcdccbeeaaceadadedeebaecebaaaeecababadebaeeedddadaacbaddbecdbdbaccdabebaedcbdbbbbecbeaecacaaddaeebeadaddedcadabddacdeccbacabdcbeeecabeebbaebdbcadaeadcbdebdbeabadbbcadaebdcceeceaebbcebabadeebcbcdeedaeccebadddeebbaceccaeeaddaeecdbddadeadbbdaddacbaacdccdcdddabcbbabaabedacabedddbbbebacabcaaebbdabeecaecdaabbdccceecebeaaeeecbeadadcbceecccaceedbbdbbeccdcedecebbaabbbadccbcaebdebaaabbccbddcbbccceadabbeddabdbceeccceecededbcbbdbeadeaeaabedaeceebcdabcbbcacaedcadcdeadbbedbbdaeccbcacdcdbeddebccbaeeccddcbedccbbeecaabcccadecedeedeccccbcaceddaccabcebddcbcbeeeadadccebcdadeceeedaeabcaeaaabdcababadcabccddbddceabdcbcebbdbbcdbcecaeeecdcdcadcaeedcaebaecdeadebdadadbccaaccadcedccaebebedeeabedeeeadedabdceebbbebdbebbcebdbddaddacebbbdadbdeacbcaddccbceaadeddcccbccedbeececcaadeeabaacabeeedacdebbeededcabaceebdcaacdacdedcbcbeabcddcddaeaddccaeeadbdbaaccdadecdbcbeeaeadbabbcdaeebeaccedbbbdbacedabbeeedccadcacaacadabacceaddcccccdadeeccbccebcaccbcadadbdbdccbcbcbadacaccddcddbccacbbeeeddbbeaacdecacbdebcdecabddadeedaaaddcbcdbbdadcbacbedbcdbeedecadbeabedeedaedadbdaeddecacabeebedecaabeecacebbadbaccddabcaccdecaeecbbdbbdbadebddcbeacecdadcaebacdddabcbabbebbbedbaaaeeaccdcbabdeedadabdaebbcabacadecadcccbbecdaebacbbaabbeacbacedcaeccbecaebdeddeaeceacdeedaceaedddebbaebbeebbceeaabccadbacceaebcdeecdeedabebeddebebadeecaeaaccdaaeaaebdabcbaeeccdeecadaaaadeebedcdcdaceaeaeeeaeeeaeedbccaabcaaddabdbedeaccebcbadbcecaebacdcadaaeadebcbbbbcdadedbcbcecdcceebeebccbebaeeccebbdcaeaebaebdeeaeebecdbbceadbbdeadbdcbbddbddededdddbbbaeabbbccdaedeccbacccdeabcedbdddbaaaddbedecceaedcddecbededdcdebcdbabdcbccecaacaccbeccebcdbcbeddaccbeaceabecbbdbbbabaceabdbaeaedccdcbbbabddbccaebbbbededadbeedadeccccaeabeeeaababbdbbecaddbbdcbbddeaaadeabecbeddbebbaccdbbbecdecbbceedeeebadabecdadcecedabaaacecdaaaaecadecaadaaceadeedacdabbbaedabaecabdbdbbdbcaacddcbdddecdcbeaedcedbdedaaebcabedceebdceaecceccdbcaceababcbbabadcdabeddedaaedbdccbdabacdcddededcbcebaaddbdceabdbaaeaaeedecbadacccbebccdcecccdacadbbbeebdbdccdddaabbadccadecccdaadcbaaadedadbdcdedaecddeaaadbbaecbebbdccbaccebddecbbabdebbcdbcecbbebeeedaccbecdeeddcecdbaacabcdbcacddcabbcabbdbddeedaeaeedbdedcccbaaaebdababeeacccbebadbcaaaeddbbbdbababdcedccaeaddaaddbcecbbeabcabdbedcaadebebaacbddadbcaccdbdbbdadaccecbbbdcebedccdbebbedaaebdeabcaabeebdabeaddaeaebeebdcacbbeabbbedcebaeacaabddbceeadecdcaedabaacbadcdabdecabcaecdacddddbcbbebcebebbcddebcaddcddccaabdebdaaadebddeeaeacdeaaebadeddacaeacaecbeaeccbabcddccbbccabdbbeeccbecbdbcdeebaedcececaededceeebbbaaecbbcadcdebebbcdcdadcdbbdcdbeeecebecdaaeeceaebebdececedbbebcecbbcdbdadbcddddbcaaeabcdebacdaceeecdcadbcbaecddbbaadabeeeadbcdbbecebbdcadcbbdadddeaaaedbcaecbeecaededdbedeadbacabcbbededeecbdebadadcdadbdbaeeecdeaeccdbcebeddecdebbaaeeadbdeddcbacbceabcbccbacbebaeecaeaceaebccdbabaedcadbedbcabbdbdacceaeabaedbccabeaeadadbacbdbbdabecbbabccebbcbeacebdaacbcdcdaceaadeaeccdcdcceeddedddbcacbcaccedcaeddaaaeaadcabbeacccedeecddbecccbcbcecadedaebbcebcbdadabcedbeebebacbdcddaacdeccccebdcdbddbcdabbcdedeebebbbbbebbbbaebdcdececcbcccaacbcbcbcadbbdcdaaadddcbececedabaeddadddbdcdeeacdcecbedacadccbcadaceaacdacdadabeacdedacdbcaedecbbbdebdebcdddecccaaeeaddedceeebacdaaeaaacacebbdcdaddaeaabaedbccccbecddebedbebbbeeebaadcadacdadeaddccacedbdaeddbcebaecedceccbecbdcceadcbebaddadbeeaacadbebbeeeccabdcbcccdcaaebccedecacbddabbcedceaabbbadeddeaeeecabaaeebeacecebdccaaeaccdabbdddcbeaeeccebeebeadbaccdbdddbbadaaebbcaeebcdecbcdbbcaccdcddeeccadecbdbaedcbecabaadbaabacdaedecdddbdcdbcbcbbbcecdbaeddaeceebaddbcdcbbcbdeedcddcceedeaaaacbceaceaebbbbeaebeddeaadcbecdeaddcebceaedcaddcecbeabdccdeebeddcabcbebbeddedbaadecdacaeabecadadebabbebbeaeeededbdbbededebedbedcdceadeabbbeaebebcbebbdacdbcbbcaeceecedbaecbebeeddcdabcbdbdabcaeaadebcaaaeebbaabeeebacaceeaeeecbeedebacebbdeaeedcbddcbedaadbccdeaeaecaabeaeeeddecdbbecccbedbcbdbbccaaeeddbddecaddeabdabdcdaadeeaccdbebdcaabceeadabddebcdbebddceadbaeadbbbbdceaaecaddeacaaccbbcccddebabeaebabedceaadbbdbeeaedabaabbbcceeebceebdbebbdccedaeeececadbedccaebceaaeeaeccedcaebbcccadaabecaebeabeaeeccededbbeddaceecbbccdbecdaeaceeaadddbdcdceeaccebedaededceaabeaddcddbbbdceedeeedbeecebbdeacdedadaccccabbdacceeedeeddedaeebaadddccebbaceaaebbaedaedbceadecadeabaeeacebebbaddddcbccedccaddededecdbaaabbbbabcdedbcbbbbadbabeaaacbebdcacddaaedacacabcceaaddbebaeecaabeddbdeeeaecbeddcecebeceacbcabbebccabeeccddadbaadcceccbecbdaededcbdaedecbbdaeccbbcaacdacebeeceabcabdacebabeeddebcedebcbaaaaddeabdbcadebceaaeebcbeaadcccacccebdeaedaaaceaebdebdeebcddbcbdadddaddbbdcdbecbcbdccdccbaaacacddeedeaaaaceabaadcdedcddccdcccdeeeeebbceedcdcabaedbaabadccbeabbdcbcdbcdbcabbccddbddbccbbbcedddebaceebecaaacbeceeedaceeccaabccedebbeddebeaeceaeedcbbbaceceaaebbbcebbebdbbccbecddaeccadecbdabcabdccedaaddddbabaacaccdcccebccaabdbcbadbebdcbebbaadcbcbcdcacbceebadacecaddeeebabaedcacdbdaddbcbdbbcacceeecbaacadcedbdbccddcedbcebddceabddbcccaeadbdbdeecaccaebabebdbbccdaebcbcddbebbccbbaddeabaedeeeddadeeeecadeececbaedbeacbdcdcdeaededbceeaaaebedcaebeaaeebecbacebbdedddeaecabbbacdbcdaeecaaaeedeabccebbdddcceedcdeedcdbcbbbdedbeebeebecdbeabadaadaaaccebddcabdcccaaebeeeaabbabcdabadeeabebadeeaaebeddaaacadcacccddaabbbbaebbbdeacedddeecdddcaaeceadaabeabdeeeaccaabaecaccabdeaebddbeedbaaeadeebeddabecdcbeacebadecababecacedcadbdbdbbeacacdcaeeeaebaeaeaeebebaebaceedcbebbabcacbdeeecebbccdeadeabeeaacebedbabcaedbecdecddbaaadeebcabcaddedccbebcdcbdddddeaeaacebabdcceaeeabcbbabdebaddecbdebddaaecddcbcbceadbebbdcadcbbaccaedbeeceaaceaceadaccedcdabbeaaabccbebeadbaeddbbaccaaecddaeedaebeedcdccdbcbaaedbecdbbacbabbebeaccebeecdceabecaeadcbdedecbbecaeeedbcdbebcbdccbadedacdcaabeccbbdddbdacbebeddebcdecebacdabbecdecdbcbbeeadebeeeeeecacabdbdabceebecabcbbccdaccaecdacedcdaaecabcaaddccddeeedbaceddbeeccdecdbbdadaebeddadedbddeeacbaaeadececcaccabeeedbaeddddeddeabdedccbdacbceaddebcbceaabddeacacbdcabbdaaaddbcddeabbcacaeccdeebaecaeccaaedadcdbedbadcceeceecaedbbedabaccdbaaaedbebcabbcedcdbebdbacebacbbccadbddaedcaadbabaccbcdeabebebcdcedeaaadddbaedeedcaabeabedcdabededbeeeecddedbabebabdababecdddcbdeeaecceeebecedaebcddbddedcaabdeeeddeaebebdacbccaadbbbebcbdcbeadeecaaeaeadaaadaebaebccabdecebdddbeedbbababedcdbcbceeedbbebebcddbedbaebbecbbeadccccdacceacdbcabceedebeedbceecbbeacdebedacebcddedbacdaeeeabeaeddaaebdccacbabecbacdedbddccddebdeaadeabdecbbedeceaaddeeacdddcabaadceeedbdceaecbebcdadcccedcbddceececeebacacaddbdaedbdbeaedbdceadbcaedcacaebddaddcdaaddcecceaeeddbebadbdbcedadbbcabcebedccaaebcaabaadcbaacdddbaacdbdecdedbcbcbcadbeeddccaaecbedbddaadceacccabbeeadabdcdaeecbecdadbebbeebaebcedaebdaebbaaacdbbbaddeedecdccdddccddedebcdddceeeddeabeeabdddcbbaadbcbddaedaaaddeeacbeddbacaceceaabadbbdacaecbdbeeddceeaeddeadbeccbbbeacaccecebebdccdddbbeceaccebedababeebdeadbacbedabbdecbcecbebabadcdebddedadbbaaedbebebaebbbceabccacbcabdaebacdcdaaebadbdaddbbbeacdaabaaaebcddbcaabaeccecdaadbaebdecdccdabcdcbcbebaceaadcaeebbceceababccccbcccaeaaadeeddeecdeababbbebbaacbaebcadbceddbdaacbbbaabecccaacebabbcadaddcacbdacceedacecdbbeedbeadeaaccbcdaceececdaebabbecaaaaaacbdbeabeecabceeabdecceceabcabddeccbcaecbdeaeabbdbbebdbaacabeeaeeeceecceacbbedebeebdbecacbecbdcdcedbaddbaecbedcadabdcbcdeddededeceeaeaeeaeacbbdceecdabedbccdcceacdeaadadadcedaeddccddcaacbcbaacacccebecceaeccceceebbeacecbcdedeccdadcebaaebadbcedccdddaaebeccadccbebdeacbbeadadebbaccebacacdddcebbeaceabaddebececdbbccdecceacbcaddebaccaecddbbbbeadecbcaaaedadcebdabdeccaaceadeeaebadaabccbaeeceebecdcbaddaaabdaeccbaaeccbcecebadcbdceededeededabebcaeeddbcaacecbedabcaeedbcabdacaecaeeddbdcbaaaadcdadaebccdeaaddacecdeccceccabbdceadddbebdadbacceceeaddbbdcacdcbcedaeabcaecacbccdeecbecbeeebeeaaaadccceacdecacecbecdedecadedadeaeedecaebccbcbbdbeddcadbacadddaaddbdedeadbeccaacebbbbcaaecbbbbdcadacdcccdaacaeabdccbdacdbecbdbabebcaebaecabecbbdcbdeebdbcabcbacadebcdeaaacdabaabdbedbbdceaaecccdcecdadaaedbdeebdbcbceabbdddaadeeaecaaadadabebbbaecceddddeabcaeaddaabccbeaddacebeeddebccebbbecddbacabacecccccededadaedddabdaebccbedbaccdcaaeedcadbedaedecbbdaecbeeaadadccdccacaaaabbdbabcacdcaedaacdbcdeabadbadadacddbaeebccacecbcbabdbeacbadbadcdbedcebadbcbaeeeadcaeaeddcaadedceacaadcacabbacaecdcbcbbbadbdecadceaadccbecdbddcccceaacaacabcbabcbabebddceebacbebecaaccaeedbeeadcbaedddbcbdcebdcedebbeddeecabaaaebdedebcddaceacabbebbdedeedcebbdbcecdaaceeceaaabdcecddceacbecdccadbbabcbcdceebdceababaeddeeddeadaeabcceedebcdcbabecdbbdabceaededbaabcaecbdeccbdebbbcbcbcebedcbbababaecaeeebceadeacdacdcbdddabeeebedbacabddebaaaceaedbbcdbbecedbdceaeeccdebcdcddabeecbdeccaaedaceebdcceeedcebacdbaeaaedccdaeaecdcddcabdddaedaaccaddbaaaeaecccbdcccdcbbeaebacdebdadcaebdaeaedcdaeaaaabcebdacebabdecbeecaeebacecbdceecabcbeebbaddbeaceddccbeabccbaadcbebaaddaadabcacdbcbedadbabcaaddaecbccaccecbdeeaeecabebeabbcbdeeaabcccddcbdcdcbadaacaacadeeebaeacadeaacccacabebcbdeeadeadaedebcbcccdebbedcbccbcdeccecdddaadceaddebddabadddcddedeeeeecabcdbeeeacaeabdebdacbaaedcecddeeccaceadacecabeaaeebcebbcdaebbcdbbaddeadeedaddedbbdedeebcbcccbdadedebddeceddcebbacebdaadebadcaeeedceedecabecddaabcedbbbaedeaedccabbbabcdaceeadecdcbdbbbcecacddaedbccecbeabdceabadbbecbbabbdaebeeadacaedebbedaceadbdcccdcaaabdbaadceebbcddcedeceedcccdaadebcacccaaaacebcacdbbbabdbaceeedbeccaabbcadddddecaccccebbdcddadebadbcadceabbcbbedccbdbdabddbebadbbddcecdcbecaeeabbdcabbbdbadccbdcdebaaedacaeebcbbacbeecccbacbaabbeedeceaeedcdceaaeaacaaadcabbacecadbebbbbbecaeecaacebedadaaebbadacadbbcadcdbdedcdbaddbddddaacacdaeabeadabeedbeedbbcabdcbedadcaaeeedabddbcadccaacddcdddcbaaeadeaedabddeeeeabcdebddbececaaebadebcacebaddaadcddecddbaeabceeecaacebaceddaeaedcbadadbadeadbaaddbaacbaeceaeceacdeabaabeeaabbdaeecacbbcbbcdecdbaebedbddbececaabadeaddaadcbacadcbaccdedcbacbbcbdeaccabdbabdcceabcdacdcccadbdcbcadaadaccabebbcddccabbeecdeeabddcaeeeaeaecdbbeadcdeeeccaeedcdbbbdcdaebcceaaacbeebbacacddeccbcdcaabaacdccbadeadacdccbecabdddceecddbdecccaaedaddbabbbcdaecaccedbabecdeebcaeaaeeccaaacadedcddaeaaadddeeaedcedcdbaebabbaabbcdecbbabdaecdaabdbaaaaabcbbcacdadcbbedebaedadadbbcbecabcecebeebbbbadddaceeedccdbdcecbdbcccdebeebbbccaeccccdbeedbecacdaeaadabeeaceddabdbadeeceaebbceecacabcbbeabadaeecebeceaaeeeebaadaacdaadbadcaadeaddceceeeddceacdabdeedecaadcbabdadebccbebdebbcaaaecadaedbadcbeecdeaaaadcdcecedbbdddcdabacbeeaaadacbddbdddcbcccacbaddeddbcaceecaaddaceadaacaebaedbbcaebaddeeedcdabaabcbdbddacadeecdcbdccbeebedcbcecdaaccebaddcbaaacdbbdeaadbadbeabdedabcccededcdcedaddddeabbacdecacbbcccbbaccdacaabaddedceeaeeebcdcedaebadababccdcadcadedbbcbdbedaeeabdabaaadabaceccdeabacacdaceadebbbabbabebeddcbaacbdbccdaaabacaacebaeacabcedcdceddeecedbdcdbadedcbceecbaeabddebcdcbebbbbdccbadbbdcdbecbbcadadebbdceabeabcdbaeababeacbdaecaddddbbcabadaeeebdbdbedbcedbecdecabdcadcbbabaaecdcdabacadcaddedabbebddcacbabcaeaaedbabbdbcbeeebdcabcdbaaccedaeebdceaabdceecdaeacdeaebcabeeeecebbedbedbaaeeadbecaccdeeabbccbceadacaadebababbbedebbeecacacaebbcacecbbaddbbcabdbdbeaeadccbaccacaedcbddddbbecacceceaeeccbabcdbcacaadcdcddbcbebcbeccceaabcadededdcbddadcdeaaabaaabcadeddbebaeccbcebcbdbdabddadabcddaadceacddaabaaeeaebbcadbdaaccdeabccdcedcabacdeeeebdadaeacdedccebdcdaebedbcbcacbcbbadbcbadecedddceacbdbdcaccaebceebadeaaabaeaabaacaeedcbddcabbabcebbdcebcbbeecbccedaddebbaaeeaeceaadbdaaadedbebbbdcebaacbbceddbebcddcaecaddedcbdaddbedcdccebcdaeaedbbaccbadddedcddaecdbdebbedcedceacebcdbcbddddaeabbadabacbacaabaebadcabeaccaadcaceebaceebabcbabedcdacddcabcdccbebbadeadbbcdddecdcdadddccbededcacdaccdecbddbaccacdacccdeabdceeedeebeaaedbaabebdeacdabececaecccebcbbbbebcddcadccddaaeceabaabeaaabaaedcedcdbdbdcdadaadbaaeedcaabedadbdcedebeceecdcaaeabbeebabcacdadcdabccdaacceaabaacacbbbbeecbaeebccbbccbadeebbccdcaecedbddceedaeeaeaedccdbedaeeddecaecaebeebdedccdaabdaceecbeadbeecedacdeccdcddadcaadcaaecbdeddbbddeeedcccbabeeeccdbcaaaeeacdeecddeaeacccbeecdcbbcddeeeceabdeadccccedcebbaceedccdcadceccaeabeacbaceacecadbcbddadedacebbdbaacaaccbadebbdbbbdbddecdeedcacceceaeaeeddcaeeecacabacdbdbdaeebdadcbbacbbeadcbebabdeaeaeeddcedbadaeeaecbabdabeacbbecadcbbedbaaadcaebbecbacceeaddccbababbdebbbbecdbbecedbbcecadcbcaebedcdbacadbbadcbdbedbbdcbdcbeaadbadacdeddeb eaaadbabbcadabcbedebacaecebaacbedcadbddceacecddaaedbacbccbbdddedababadeeadcacccdcdcbeaebbeaecbbacebecceeaacdceddedabadcdcbdcbaaacedebbaeabeadeccbadcceeeeacdcdeeedacdcdbbedadccaebaddbbebcdbabdcdcdcaebccdaaccabbaaecccdecbeeadcabbedbdcbdecdedebbdcbbabdcccbeccaaedaacaeccdbabcedaddbbccbaedcacdbddbaebabdabcaeedabbbaaddaeceecbdbcdcbeaeccbbebcbeeacaedccabecbdbcadbabdbebedbcdbedcdccbabdddedceedcbbdeaedebbecaacbeeaeadcbcaeeadacdecbdcbdeeadaaeaeaadeadccceecceaecedcaaddbecabececcbeacaadeecedacecbcecdadbacbdcaedbbccbbbbccabdededcebaccdebbaaccdeaabbeebacadecbcededebcdcdacbbccdcbebbdaccbbccadbebaeaaeebccabbbabaacddecbcddcbacadcebeebcbaaecbebcbeececbedeabbdbecbabcdccacaabcdcadadbedcccbacecdcbabdaeeaacccdcececbdbdbcdbaeebebeaeedbadddabeecaecbdbebedbccbedcdedebecebbeecbddaceceaeccccbaedaddaadbbeabdadccbddbcbbbddabccdecedabdaceeebcebbdbabedcabcaddcacaabbbdaeceeedaeacaebbcbbecabeccbedbbbbcabaaeabaccbcccbabbaddacccbbcaeaaeacbadaedececcbdddebdbbbaddddddbcdebccdeaadaccdbeaaceeebdaacaceedcaeeccbdadaeeecdabeacdceeddbaacabbedddcccdbceddbbecbdababbdcdaaccabcdbecdeeadbaecaeddbeaeecddacaabcbadbadebbddbdabceaeeaacbedeadccaccbbddddcaedddecdbdeeececdeacdeacdceeacadacebdaabaabaecdedbaaeeaccaceaaebcbccecebadebbdcbbeadbbdcacadeceedecddcbcdddecbecdcaaebadddacedabdecdebaeeaaacdbbeebbdeabdeeabdbeaaeceecbbcdadabcdbdddccddccedcebeaaaeedaeabcaddeacbdbdcaecdeaeebaccdaaeabadcaeaabdbaadcdbeecbdbaadcddebbebdadebeaeeebbecaacbacebebbabdddaebdcbabeaaddadadaabbeedaacceaaadacebaaacedaccbbbbaaebedbcdcaaebaceaaacbbaadaacaacaaeaaceeedbdeabbaceadceeeaaeebdedadcbccadbddeaeccebaedadebceebdeceeccdedebacaaddbbbbacbabebadecbcdaaadedbaacaaacaccdaabcdebaeeacccbddddcbeeceeeeeadddaaecababeacdaeeabdcbebbeeeceeaecaaaeaeceaeabbbecbebadbdbccbacddeaabbaddcecccdbebdcccddcdbbeabbbaeecbebabbdcceabeaacaedbabadeeddcdeaedaaaccdeeecabebdccecbeebebdeaededbeabaedeadeaeaabeabeccbbdecdaaccebaaadbbaaaeedecbeaeebbbecbdeabaececdeebddacaeececedcacccdbcddbcccbbdaabcbaaecabdadddedaecddcebbcabaacdacaccaaceecaceaeddecbdcadecedebccaabbddccbaebababeeddaedddbcabdaedaadceadeeadddcdeebcceeacecdbceccdaeaeebaabbeceabddabbeeceadeaedecbdeadebbcecdeabbcadbdcebacaaabeebbebbbbbaaeaacdcecdeacdbacabeacdcbccacabebabedaaaeabdbebeaceecaccecdcacdcddeecdbdbdeacdceddcececddeabdebbbdaebbbeabcdabcdadbabeddeaacdccbcaebbabebaedaeacdaecbbcdcadccbababccbdebadedbacacdcdbeaaaadadbddddcedbaacceeabeacaaadecddaadeebaaaccdceaedceecdcaaeeddaaceecbdbccbdccaacdbeadacbcbccdbbddcccecabcbeedebcbcdddeecaabcaeebdaddacedecdbbcbbcacaababadcceeaeeaedaeaaeaeeddacccbaeeadedbeeacddcdcdbebdacdababddaaeebebdbcdeedccaaacccdaddcdecbdcececaaddabccccceebeadacbececbcbdddbcbdcaadbbdbbeceadbcddbaceabbedbbedbdaeeaaceadbbbdaabaaaabbdbcdbcadeabbecbdbecbbbadeebebbbacdcbcbddbeabdeecaaecadcdcbdbeedbaecbadbcebaaadbcacceadcaeacecbcddeaeacebedbcadcbbdecdadedaddaedbaecadbbbaadaeebdaacbbbebdbaceedbcdbabcdcadbdcbaabcecdddadebeadbbeaccccabeeeabbdbbabcacccdbbdebabedbbedabccdaaeaaaddddeecbeccddaaaadeeecdadccdebbbabbdddbcbebcabcddddbdbabdbbbaceedeccdbedceaadceaaabeaebabcccccbeedadcbdedcacabddbdeaaadcbeeadeddeeccdeedcabdacdcbaaecedbcbcccaccbebdccdccdddbcdeedaeedcabeadebcdaebbdabeadccdcceebaaddabbccbbdddbbdccddbbbddadeeccabbecaaaadcecbdccdeddaeaebdedebbadacacbacbcdecbcbebbeeddaceeabbcaeecababaeeedcdedcebcaaacdaedbbdecedceaeacdcacaaeacdabcddeebeedbbcabdaebebaccceaacadabeaccdcbabdbeeeaccbbdccdacebabbcbbabdbadccbdccebdccaebaeebbacaecdecbbaeadadbbdaaebbaaaadeeeeeebcdadabebacbabeebedbeeabecdbeecddbaedadcebdecbceceaccacccbcbecbedddaeaadbeeedcacdcebdaabdcceacbecdebebadceaedddcaeaccdeededccdecdaedeedbdadeacdeabbabaeadcecedeebeecbdcdbbbeabcacbbccddedabedaecccdddbaccdbbbadbcbecabbdabbecadaedbcdcacacbedecbbddbebdcebbdccddcaabdcebeebedccaacaeaeecdcadcccacaaebeaccaadbdccdeddaaeacaaddadaebcdbadaeaedeaeaedcccaadecaabcaccebaecaeecbbeecbcebbdacddcaecbdcbdbaedeedaecdccabdedcdbdebbbdbcbddaaaeaddadebaedacabbecbebabceadcdbadcdbebdccaeedbeccebaedeaeeacabbcaeaacadeeacdddecbecddcedcecccaaeebbdbaadcbadbbddaaeeeecabcaadcebecdabecedcecbaeacdbadecbdbcecbcaaceedcbbdbbdebbbaedadcddacdbcbccbecbbebbbeebeccacdeabbcbdccdbcaaadbdbebaeceaccdbdddceebabbbabdcadbedbddbebebbbaeaeccedeadaeaebebdeeebbacaddacdceaaadedeebebcdcbcaeeddedbeddabcdcdadadbbcbacccebdadbbbabbbeeddbeeecbbabbecaecddaceacedbbbcbadecccacdbcbdccabaedbacedcbdeceeadededbbbaaaaddceacdacdbabbecdbadeeaaceccaebebdcbebdbcbddbcddbedbebddbbbcecdcdabaebeabbaadebccbaabdbeaacbccbbacdbdbbeaaddbdabcacbedaeadabadcbdacddcbdcacbaebdbcbedbdcacbbccaacdabaebeeebaabccadcecbcaabebbebdeedaccecddacbdaceddbdebeeaeaccbcccdcdddcbbadbecbbcaaddaacbddbecdcdabdbbcacabddecdabbaedaaeaecdacebaddadbebedeecdecbddabdebdbdcedeccdebacdbaddeddbcdedebbdacdeddcbdccdebcdbdbdaaacdacbdddbdeeabcddcbabededecbbdeccaeaccecacacadadcbccbdbcaeaeeccddaeeacbbbcbccebceacbcabbdddcaadcbbcedcadebbbbceebdbcadceabdbeedbbababaebceedaccdeaaedcdadbcddeddeeacddccdbedeeabdcceeeecdcbbddcaccbdaeebdecdbcbbadbacaebadecaeeeadbaeabccbacdbbeabeccebbbaeabddadbdeaecedbedaacdacebaddddeddabeebdacdedadaaeacaecaabaecadceaacccadddcdceaededaaaeddbdadabedadbcbccabdacaaeeadcdbbddbceecabaededdccaacabcbedddaaedcaebdeabcdcedcdbecbeeccbabdaecdbcceaabddadbababaeecbcbcacbaebeddbeeedebcadadaeeebcdaaceeeaaabaadceaebdacbedddbcbdeabdebecbadeecbaccacadddcaceabcccbcdccbacbeecddddbcdebbdccbeadcdccadaabeccccbdcecceddddceaadeecbbbeecbdbedcedcacbdabacccddcecdceeadcdabedbabaddddcbbebebdcacdcccedaaaeecdcebececabcbacecbabdddaedbebaebeeabdaebdbbdacbedcddadbeacdbecdaacdecacccbebbbaabcbaadbeedcabaababcddebeabdbcdaecaebdeccccadbcdabbbacbdcabcbeacdabcbccecbdbabceadcecbdbaeeddbebaadbbadaceabdacacbeaaccceebcdedbbaededaadeebababddbbbbaadccbaacaedededdecdebdbbdeaaadebdbccdcecacdabeaddabadbcdeaddeaaeddcdcdaadacedadeabbaeccbdedbdaeaedaadaabacbdbbedbbcababcdbdaaaaacdbaabdeabaeaaccecaceabebeedaedecdbecadcaaddaccbcacecebcddccecabeaeaddadbabdaaabbbddcbeededacbdaadedccaacbdbdaadedcabaddadaccbcedddeccccacdecaddbedacdbccdeabcdaebbaeccedccbddaeeacaedddbdeacceccbbebcbddcdadbceedabbddbadddccdebaccbcdbdbedababeddbedeebccdbadbcccacebcaeddddceeebbadaecbdeaeaeebedabebbaddcdeedbbcddcdbbecbccebbccbdceeeadeedceacadacceceeaacdbeaadbbaeeadddcdeecbdeccccbddecdedcbeadebebaacbdadceeccbedcaababcabcebeacaceeddbaedcdddaedbbbbadeeaceadcbeacecacdbacaddcbdbbaababbceaebbbcebacceaeddbabdddddbeadaedabdcbcddcbdaecbebdcbaccbecebdccbecedbcaceeccaebdcbdbcbecbabddddeedbbecceccdeddbcabcecbeedebbedddedbadbdddabebcaabdedadebbbbacdaddbbbdeadbddeebaadbdccecaceebaedccabbeeadddbdadaaeaccceaeedcbeabdccebcadaeececcebaebeecbdeecdededaadcabdaeddbeabcbcbbbddcabddaacadceecbaeceddeecebaeebaedeabcadeebadbbcdeabbcdcdeaedbedcbbbaaeadecbbaaaebcedaaedecdeaedeabaedaebcdbbddcddeacdaaedecddcbdaeeacbbabaacdcaecaeeebbbeaedcddcbcdbceeacdebecdbaabeccbccdbbbebadeeedcbcabcdaadbbadccaddadabbdeddbadcadddbcbbeaeaebcaacbeadedebbadabacbbdeaededbabaaacaeceebcdaebbdedbddebcecddcbeddbaeaeaccdaddbadecbcaeebddbdacdccbbddedacadacdcadddbaebcbcdbabdcdccadeebcaecabcddbaeccbeebddccceabcecccedaedabadbeaebbcadbdcaeccbbaedbdccbababdebadbddcadbccdacceebdeecccbdbdeeeecdebacdddcbcbdeabdccbecaacdbdeccddbceeaddbdaabeebccaecaebeabbbacbbededbeaedddddcecbdbebbabbdbbcceccabdcabcddeacadbcbcaeecaaaadaecccebdeabcbacebbceddbdcdccbddaebbebdceddceaabeebbacedebcbebaccaedeedbbdbdcbabeedcdbeddbebdccaedebabeeddbebeedbedeaddbedeebddaaaaebeadddbcbbedbdbbebcebdceddeeebcadeddecdbeccdeaebddabdeebaccddababbbcdbdecdcabacadcbbcedeecacabaeeadaeaceecacacadeeedbccadecaacecbbecaabdbeadaeadaddbcabeeccbacbcddccadbdedadebbbaecacddbdbbdaaecaaebacccceccdadbcbdeddecbbabbcadcadccedccdadbcbadedeaadcdbdcdbcaabbcacedaeeebeaaddaabababaeacadcdcacdebabeaadaaaeebbbacbbceceebcbeadbcedceebcdeaeeababbdddbcbcbbaceedccccdeeddcabbaeeecaebbeacecaaacbcdcddadeaaabebbcaccbeddbbabcbcbbdbaececdcdddddbcdcdccebcebdeadbbecabdbbacbebbebbbcbcbbeecbabecdacabbaadeeccaccdbddbedeeeadbaeeecdbabbbdeabeaeedadccacecaeedcdcabdaddcaebbaaaeddcaeeedbeacbccbaadaccddeabadaedcabeeeeebabeaeaabcaedbcabbacecaeedbebcdccbcdbdbbabecdaeaadcdecdbcedcacccccbaaeeaadaeeabacccaaeaaabdbaeeedabdbaeebecbaadcebceeadeaddbaecedbddcaabebcecbeeedceaeeecbaceeaacdccbeecdabeccaeeecddacecccbdbccedcaddaacaececcdaedaaeeadaeaceadbdcbcaaccedbaaabddcbdbbecdeebdcdaeddccddaedbbedcdabadeebeeeadcabeedbabcadbedcbaaddbbeacdccdbdcbbdbabceedacbdccbbcedebdebeadbdaaacedecbdcdacaceaacddbdbbecddebbaecaadaebdebbabdedabbedebdcaaaebdceebcabceaedbcbebbcbcecdacddabadcadababaddcedbabeebddacabccbbeeabbbbcedcaadadedacdacaeddbaaadcdabedccbdabcbddedebcabbabdebdecbcbecebeeededbaaeceebbeebeecdaedebacbecdaecebaadaebacdecebdaecaeadaabaccdabdecbaccaebeabcbbededdecbcbeaeceabbebacddddccaeceddcccbdeccedeaecdaadecbddaeabeaedcbaeceaabdeddaecdaeccbbecedaabecadeccdbeacbcbcbaacecdcdddacddeabeaddecdadebeeecbbcbcdbeecaabdadecccdbdbedcbebbcedadebdeaddecdeeaecccdedccccacbceddabbdeceacbecdcdccadebcedbdeacebddedecdbcdebcabddaaaeaadeaceeaeedecaeabbcdacedabcaededbadacdbcbbbdbaceabeaeeaedaceeebdbcccaababbdcbdbbbabaebebdcebdedceecbedabacaacececdcdcddcdbdddccaabaedbadeabccadcdadcbbeebacbaeacbeadddaaadcddceebebaeceecaebcdccaddbcbcabdbeedebedbcbbaabaaeedadccabbeeebbeedebaeaadcaceabccacbddeacbabbdcdbacdeadbbcadebcdbcbdceaebbdaaabebabeeecededdeaaaccebdbddcdbbcccceeceaebeedabeaccbcbacdacddaedddbabbedcaecdaabdcadbeccbdaddddbcdcdbdaceecccaccbeadecabeecadabbbebcaeeeaaecccdeeeaadbddeebdededbeeacbaceacdabddaeecceebcddbaaabcccebeaaeddcadecebecddaeaeadcbcdecacceadcddedcabeeeaebcbeadeacdeecbeadaedaaedbebdbbcadceeadababedebbcddddacdbceedccbacaddbeadaaeeaacddeddeddcbaabdeccacbbebcbddbceccbcceeaacdaaacaebbccabeebaadacaadeaeaaaecabbdabcbdcaabbbeddecabcdaedbbdbdcaccbddeecaeaeccdddeacdbcdedcceecaedcdaccbacdaccdcbcbddbeebedadbbecebacbaadebdcebcbbabeccdcacacccddcecbeccbbacbbbadcddcccabdbccdceebdecdecaebccaabdacbcdedaebadedaecceaddeabdeaccacebcbdbdaecccaebbdcbbbcdaddbeeadecbdbdcabcdebbbebbabeaeddbacaceebcbdebceebddcbbbcdeebbacabcdbeebdabcdbbaeecebcecbaeabbaaccaacdecbaaabbdbeeceecdbcccbcdddbcadddeaabbeabdacadddbddccdbbcbcbbbacdbcedabdddcbebbaebddbbebedbeeebeebaedbccaacdadbcbcededeeeeaeccecbedeebcdcbbeedebccbaeebbaadcccbebeadcadaaaeccababcecdbadcdbebbceeaceedbccbeedbcdbaabecccecebbebaacbcbeddcbbdaedddebbdccceedccecaaeecadcabeecccbeccbbbdaeedeccaecbecabceabcbacedadeaedcadbbdaddcedabaaeadcaeabbaabbbaababdeeeadeddbceccbdceabdacccbccaeabbdcdcccbcdeeecbedeaaaeeeebeaccccdcadeebaaaaecceeadeeeddecacddecceeaebaaeaeceebeaadecacdcacaadbeabadbaeaabaebeacdaceddbbdccbdeeeebcddcaecbdbacbeeabededddbeeedaacedbdddeaadbecaaaabbabeaaeccbeeaaacababeebaacbabedadcbccbbccebccddacdebbcceeacadbabbacaddbdbeecdededebcdcaeedcbaeaadbaecabccecccecbdcbbdaeccddeebbbcddedadaeecabacdaeeadccdaeeadddcdabaceacbddddeaceeeeeebadbaeeeebbcacacabdbbdaceadebaccabaabecedacbaeedbeddcecabcbbbaecdeacdedecbbebbdeacebbcbdaedeaeeddbdbaecccabdcdceebddeebecbaacebbbaecaaabdabbddabbbadaebecbabecbeeebebceddcbbadabbcebaacadcddadcccbdacaaddcdeabeeceabdbecedddbdacddecdbdabdbeceaaaaeebdabbdceeeebbbecbdabecdbcdcebbcbbbaccdeaeaaedecbdebebeeebcaabdadcdbecbddbcabdcacebcedbbadbebeaabdaebeebdeccdeeeaddacdbddcdbdcbeaceedddccbbbddcbbcaabeedcabbeebeceecabbbdbaacaaacbbcbedbaeeaeacdeeadddcadbabccdacbdcedceeccdaccaebddedbaaeeeaccdceccaeadeaccedacedeaadcdcdaecccccaedbaebcbbcddbaecacccedecbcaeadaccaadacbbdadcdcecdacceadaabadccbcbeebaddaaaebbabeabeadaaedddbaceedbeededaddebddcecabbedddcecdedeedebcecaaeabdbcedbceebeecbbcabbddbdececabbedcbdabdddbccbbcccadcdaadcaaaebceacceebdeceeeaddebacbdedadceaebeaacbeedacdecbcbdaeeccadbcdbeddbbbbbacdeecdddababccddaadbdcabeeaecdddeddeacdeddbeadbbadccbbdeaddecdaadedcdaecdbaacecbbdaedeecbdbadbaddbcceddcceebebaadeedaceecbddabdccaeaedebeddccdebbadcbaeecaedeecaebebbcadccdbccbeeabdeedcdeacceddbaacebbcdabdbbdbedecdabebacaacaabadaacbabceecbdececbedeadcbbdcccebedbddceccbecaadccdaadeaeaedecbbcadddbdeddceaaacaecbcdcdbeccdbecdcdeabcddcaabadbcedbbeeaebbabdbacdbbbbacddabdcdaabbcbdcbbdaeeaadebaebcaaeddaabcabcebeceeaddddcdcdaaaaedebdacbbcbcbecebbddbccbccbaeaabbbdbdabdbdcbcbedaccbcdaadbdcaeadebeebdbdbcacdaeeebdacdbacedecbababacbbeaccabebedbcacacdedbccdceebcdbbdccdeeeceedcbaedbcbbcbcddadaaeeeeaaaedbdddecadcccbccaaeacaacdbbeecaccaedcebcadedddeeebaedbcbbedcbbeadbbebbdbcadaccceaecbcaabdcccddbbcdedbdcbedccdcdcbbdaadebbddeccadaeeddbbceebaaadcbbeabaabbcbaeadeaeccbddeedecaabddcdcadaedccdcdbdabbaabbdebbabbcdddcbcababaeaebdceecedbbdeaaacaabaabaeccdedddaebcedcdcbcddecabbddeeaccbeaecaeeeadccecbddebeabcaaceccdbedacebebdebcbbbaeddeabbaecdaabebdbacbadacaeaceabbbccaadbceebebddbdcdadccabdbccbadbdaeaaccbbecaaaceaeebaeeeecdebaceeaeebaaaaaeeaaaccbacdaeaedeedbecedaddbdaddbcdbaabacbedaaadccbdcbbaecebdadbeaeaadcedeedbdcdaacccabbdacacadabecabdaeacddadbebacbbdbeccaaaeebedaccbcebacdebccabeacbdbacdcbabcaeeeacedbcacbecbbcaeaedaccdcabaeeaeaadacdceabcdecadcbbccaaabdadebdcaeddcabbeddcbdccecccacbdcbcaeeeceaceeecadbadccddcbaeecdbacabdceeccacbcdcbddbeeadaccbececeebdaabbadecbaebcebcaeababebebbdcadaccacceaeceecebeeddebbabcadedbebbdbcaacbaeaaeaadcbdcdbadaebbebcadebaddedeabacbadccbebaebacedadadcbdaecedbcbdcbeeeebeebebdcebcccdcbbcaabecdeebbaedccaeebbddeaadcbebaeeabdbddeaaeebdbcddeababcddbadeeeaeedadaceebbebabacbcebdbbeaecbdbbbeebdeddaaccddccacdbceaebeebbcaaedbaeeabdcddcaceadbbaeeaaebbbbdacadccdbcbeaadbaceecedceebacdbdecbbbadadebcbccdeeaeceeeabeeecbaaedcdccdcadbcbccdcbbbcddedbdedaedccdebeebeebccdabcbddadabbcadebeeabaaebcbaabccebebbeecceacbbaedcbdaecaacabecccbdbacebcdaabcebccbcbacaabaaabaeeedddececcaaaddccabecccaddcdccddccbecdbddaddeedabebdbccceadcaeabcbddebededcbbbdedeecbeeecadbbbdecbedcdacbbadcdaeeeeabecaabcdebdebdebcaedbdecdbbdcaeadebcaedaaceceeaeaaeaaaedaaabdedccabbdaeecdcbedbbabbaaacdcceaddeebaddaabbdcbaacabaedcbdaaceaacdaaebaeebacdeccbcdcddacccadbeedcbbcccbceabcdbaabdadaeabecdcdabddebccbeaaecabeadaadccbceaceceedbcbbbdedbcbaeaddbabadbaaaacdabbbccababcabacddcbbbcbcbeececaccacbaadeaaaddebceeaaeacbacacdbdaaddcbbeecccecbdebbddceddbcedbcebeeeaecbcdecebddadadbadbaecddbeebbdbaecdbbaaddaceeedbbdaacecddbbbecbddccebcddabbeadaeedbeacadceadaadeaeedacaecdaeaedceddccbaedebebcbbbdeabdbebeeecdcdbacdedcbeccddccecbdeebebbddcbecbaddbcbeeeebeeaaeabdaeabddeaacecababbbaebcecbbdbedaedcceeacaeacbaeeccbbcbdbdcbdcaaaabbacbeedbcbcdedeeacadbadedcbcaccebbaadebdceaacbdeeabbbeeeeabeecadbadcddabaaabccaeeabdaeabcadaadeebaeadddcaecbeccaaeeccbaecacaddbbbbdeabcdeccbdbbbdebabcdcdaadeccddaedcaabacddbcdbecdbdadccbcbbcdadccaccbeadecaaecacdbeccecdceeccbebebabbedaddccaaeedddeeabcabeaebaebbdedacaecadcdcebecedbabddeccbbabbbabbbdbdacccbcdcccbaeaeaeeddceabeabdabdcdcbcabcaebdeeeaacbcdeddedddcbaebdaacbeedceeaadaabccbcdaaaecedbbdbadaccbbcbabbcbdbeeeeaecabccbdcebbcddeabeaeeaebaabddaddeadeaebcaedaaabadbbcabedddedebebaaeaecdbbddceabeacddbeaddbebddadcacacbcecccbabcececaadeeabebecadcddaebcacebabdacabebabcbddecaeeededcecccccecdeeacceacbecacedeccaebaaebcaecbededdecbbacbbeebcdbeceedceadcbdacbdbedeeccbdedebccaadbaebecccbbdbedbeaabbcbadcaaccadbebccaacbaddeabbbcedaacdaecbdaedcebeabcdbeeebcdedcaeecedacbbbebacedeeadcccdacbacdddaabcccddeedcbcadbdeeacadbddcdaceeebcaabeaaeaeccdadbabaceaaebcacbbbaeabcbddecaccadedebedeacccaedbecaccdabcccdacadabcccdaddcbecedcdeedccdeddccceedbceebdbcadccedbeeccdecaaeabbddbabbcacdcedddebdccdccbeeecedccadedbaaabeddcacacbaccadcebcadeabaecaacddebecaccceecdabbeceddcaeeaedbcdcaecbaeddecbebddacddabbcbbadececdedbbbcadacacbcbcdebeaccdccccbdeebbbdcabecbcedebcbedcebdeebdecacedacbadddbaaceebebaaaabeededcebcdebdcacccbdaebbaebeccbedcdeacebbeabdcceebcddceacaabaaceadeddaadeedcaddebbdccbabaddebcdceedacccbcededcaddcbaeaecddbaccabadeeadccacbcddadccacedcacabccabbaddcbccddeddabbaeecddabcbacbdcdbbdcadecdedbcaacccdccdbadedbeadbcbdadcdadbdcededdddbeaadaadeececbcccbbddebeeacdceebecdcaebcdaaecaecddacecbdebbbbabdedcccaaadadccbacbdbdacbbcdaedaacececdaecbeccddddbccbaaaaecddacdaceecaeedebebcabacdbdcecccbdbdcbcdceabdcbbecdceadebaacdcacbbdbbaebcbcbdeceaddcedebdbdcaeaabeeddeeaebbaddcbdaddbbbddabcbebbddccaaaaddaeddcedbbedcdcbdbcdacccbcaedabdbaaadbdcbdbeedbeedaabbacceebaacdecdebceaeceeadccddbcbdcebeadaddabdbcaacdaadbaccaecbeddccacebceeaaabaebeabdeebeaccdbdcadedebbebbebacbabdbdbccadbeadabacebaadaacbcecedaeedbcdbbadeebbdcecaebdcededbdbbdbbeacdcbaabadaeccddcbdabebcadeebbcccbbdacabccecbcecdacbdaaddadaceeeeaddeddedbaedeedebaaaeecaaaadaeceaceededddcdeecedaacedaceaccdaaaaacaedbdcecabaeaddaeaadcdcebbbdbcaccecaadeabaaaabdadcbaeadecaaedeaceccecaaecbceacaebeaeeaedaedcdbceeebabcbcebaebaacdbeacabeacdbdbbecddaacbecebaebdecababdcbadaaeabcabdecdeddceddabbebaadebcccedaccbdedbcebecbbdededdceeaebbebeaadccccaceeecaecbdebbcdadaceadacbccccdebdcacaacedcbbbaccadedcbaadcbbbabbedeeebcbbbdbbdcdadaacdaababcdaaebadeeceaeabbbeaccdeadadabeccadebeeabcbeaacabcecdaaaaebccdbdeceaddbedceccebccbdebedacebcdddeaaadaddcdebcadbeabaaddebabaccdebadeaeabdbcabcaecdedbbbebbdbadaebddbcadccdabecdaededbcabedcaaacedabcdcbadaabeeeadadbadcdddeaeccaeecdceeadcbbcaebebbcececbddbadeabaeaebbbddbecbdabcdddaeabddebeaeddacadbdeadebacabdeddbcedeeacdecebbdcdcedbecabcbbddabddcabdecbeeebaabcabdeecdedeccebadcbddaacbadcadbaccebbacbdedbaaacdceacddcbddccbcccadadcedcbdcbbcdacbdbdccaedadbedaabcabaccadadaddbbacabcdcdceebaebdacedceadbaabbcdcedccebcaceebdcbabcbcbbdbbdebedabebecaadedacdbebbbbbcecbebeabccdbaddbdbebcceabebbcabacbcaedeaacbdedecaebdabadbdbccaccbabeedaaeeddcbdaecaecacdbebcbcccdbadbbbdacabbccdcebcdbbadadbeaabaabcccdeebdcaccaeacabcaceecadedebdedabcbcdbbdadcaabbabbaeabcbeabeceabecacdbcccbbaacacebdbcdaacedcbdeeeebcaadadadecedaaeccaadcabcbbcdcdecedabddacecaedacbcacaaaceddeebecabceabbccacdedebdbcedbeadaabcadacaaddbacadbabdcedceaacdaebaaaccbbcedababceecacbedbaaeddaabcacddaeeddcacedaaaeecedcebdadcadbaceacbbecbaaadbbaaebddcaeecadbcaedbceaceaabadeeeabedcbbbeebeadacdcaddcecdcaadcbbcbccdabecdeddbdbabadaaeecdeadaddddaccccbedaeeaacdeecdbebaadccabbcccbcdaeacccdbcabadcabaddeddcdedbaebceccdebcaabadcaaeddeebcbeccdcabeeddabbdeecbeccadcececdacdbaacedadbbcacddceeacabeeacaaeacaaaebaddeebdaebbebeaadaebadededccaebbaecbcdacedbcdcdcdeccbbaabedbabbecdebcdbdadbddaabcaaadeaacccceadccbcccbedbaeccdcecaaaaaacaedcecceeeaeebcebcdacdbcebedababaabdabeceddcbeaeeedaadaddcccadceaabaaaadbdeabbbbbdcebebdeacecbcecbdeeeedbcbdabacceecdbcdaeacecdecbbceeededeaaacaaecaeadbbabccbeaecdeacddbaaeeddbaadbebccddbbbacdadbbdbbceebecdbbdddaeaeabecbdbeeedeaadbecaaebbedeccaddcaabacbecedecbadcdbbaaeaaebebadcabedbbecdaddaeaccddebaaccccebeddbddeeccddbbcaedbbebceeeedbdbbbaeebbddcbdaedbbddaeeaeeabeacbedbeddadeeebdebdbbcdeecbaddacaeedddaddbbdacaeeeacaabbdbdacdccbaedcccdaceaabbdbcbbeadbabedcdbcbbdcadeebbeebaaaaedbdccbaaadbecdbddaeebccbccacbbdbccbbbcebbaccceabebbcddccbeabacdddbeedbcdbbaacdbcbeadceadbbadcdaecbdbdbebcbdeadceaecbacacdbeaaaccabbeadcccbdedbcbaccedcabbeaeeeebcddcecaddbdadcbeaebeeaeeabcdcbbbbaeaecbcbeabdddebdaecddddddecebacecebaadebccbeadbaeaedbbadebddcbaecdbdaddcbbbcbbdcdbbcdbbddbdedebcadbbbecdeaeacaacdcedcaaaebeeaacdbaabecdddccbcdeabbdcdbedbadeedbaeaeaecaadebccbbcbdddeddeeedbebedbbdeadaebbdcbdabdaadacbcbeaaedebcdabeabbdadccbdddabcbaddeeebcadedacdbcecdbebbddcbcddcdbadbcecdbeebbdecaeaecdceacbcecbbecdbbbdddeeadaceeadecdaaccbabadbeadcbdbdadbbeabeaddacadbcaecadacadcdeabdededbeaebbdceeabcdaadecaddbdaeeecaaddceedacbcabaabbbaadbdbebdaadcdbbeedebecabcdadcebeaaebcdbdccbaacedacbcdbbbdbbaaccedcabceeceecdecaaecdcbceceaeddccbeeacdbcccddaedceeddaaceebadcabacceaaedbcacecbedddebabbcbaadbaaadbbedabdbddbeeccababbcbceddaeddedbadebedbadcdcbdebabbdcbaabcceddcdadbbcdbaeaacabbccbabaeeeeeedacebadceedaacbabaccaaadeeabbacebbebacececeabababacbaaaaddbcbccebbcbdabeeececaaeecdcbceedbdbbcccedbeaecebbaeebeaaccdeebbdbacebaecdabaeaecdebecadeecadeddebaeabababedcbcaadeadcddbcbaadabcaddecadbeceadecabdaeacbbeaadacbaaeeebbabdaaaacadddcadeaabcbcecdacbaebbbeeacccdabddedabcdabaeccdcaadabccecedccacbcadceadcaccebaabaaccecbdaebdaecbbbacebacedbbecbcaadedbdaccaaabaebbdcdcababcbcaebeceeecabdbaeebbdeaecdcdcbecdcebaeceaacacedbdbcbddbbeaadceabbbbeeababebbbdccceadabcdbddaceaabedbcedccabbdbebcaceaeebebdbaaaccdaeccbabedbccdadbaeeecbdccddeccadecbeccbaeadcdaccaddbbcadaecbaacbcdbcdacddecaaddbeccedeabccdcdddcadccaceecaeeaddbccebdebadcebdbdabbaedcecacbeaeabadcecebddbeadbbcabdbcdbcedcecaebeebdeadadccbdcaeaedddbcbabcccaeceaceddabddbaacdbeabebdbeadebabbbdbebacaaeacebeebdbbeccacddeabedebeabadcbedeeebbdcdaceadadbadadeedacacdddeedcccadcbcbaeadaddecedcacdecaacaabbebcccbcbddaaebacccabbccacceebbabbcadccecdacdeaaedbecbbeeeeadccadaaceceaddcaceaacabedccdabaeccebbcdbcaacccbadabcbeebdcadeaacadaeaaccebdabdedcacddadebedbccdcdcccceeeeeaaddcdbebebeadecbebdeabeabdaadedbdbbabaebadaebcbbcebeceaeaabbcbaddabddcbbdddeeeedbbaaabbdceecbabbdbdaeedabbdabcabaaebcbbaceacacbddaedebadcebbbccebebebabbeceebcbecdaedebdaedcacbdacdedbadaebacadedcdeacbacadebdbdeeaecccddcbcacdccadcaebcbadbedcabcbdebcdcdbbadebcddabccbaddddceacadddaaddadcddeaabeadbcbedeaeeebadbeddcddadcbcbecdbbdcbdacdeeaeeaaeacccadbbcccbbdcdabcacedccccdacadadceccbcdbbbddaabcaacacbabaccbacaddcdbeabcaaaddeaacbcedbabedbbcaaaedebdeebbcdbabaecdccdbeedcbcceaeebbdbbbddbeeabadaebdbcccdbbdbddaeadbcaccdadccbdebdbbadbadeeabaebabadebedcebbddecdbabbcbaccbbeeebbabdcacbcbcedbbedcbaebabaeaaaaaceeaccddbedccedcdbceceeebddddbcccacddcddaeebddcebadcaeeadeddbbdbeebddbdbccdedaccaedbaebbacededcebeccecdcdcaceaadacebebecabdeabccbddebededbbddccaacaacddacbcbeaceecbeebbcedbcccaabdcaecdeabaedbeabddbacccdddaddddabbcdadbebbcbddebececbbceccabdedbbdeddbcabdeaacebcadbaeaebdceeeeadbadbeaacacbdcbaebeaacddebdecedadcbaccacdebddaecabeebcbedeabadcaabaceceeadadbcecbaacaabcdaaeddedcacedceeabebcddcadecebdecddaddaddebbbcbcbeeedeabecbeeaddbcbcbcbacccabeabcbceeebdcdddadbdbcdebcacacbdceebecaccebbaebaaadebededebaddbeebbeeebdbbbdbaedeeaedabdbdcdbcdcebcabbbddeaaddebaacbcdebdccccaebbeabcacadccbaebbddbeabcbdbdddaeedaadecceeddebcceebdaaeeabedabedcddbdbbbbcacdbbbbcddeceddcdebcecaaddbbcbccbacbeecbeecadbaabdcccaeeacaedbeeadcbaecedbbcababedbececcaccaaccddaedbbadeedcbdebbcdeebceedaebceabcaecbcdcbecebbbcceeddaecaccdaaebdaebdabacbcedebeceeebcdebcaeacadeeeaaddbdbbdcaecbdbccaceebbbdbddcaccdaaccbcbcccdcadeccdaacbbadbadddeacbacaeadabccedccdeabdaaadebeeebdcbaebeccacebccaedbdccddabedcbcceadadbeaaaeedecedecdebbcbacdaccddaebadbcbcbcaeebdebcbdbdccabdaeabdbeccabedcddeaaedebaccddcbbeeadaccadeaddceecdccceaaabddcbbedeebeeccbdebacaececbaaaeeebbbebcccbbbaebcbcddecbbebadbcbddcdbbebcdbdedeadcacaeaaccabbeaaaccaccecddcaccebccdbbbeadeadededdeebdbacaeeddcedeabbedaaabacaadabecddddeeabadaddceeebbaceeaececbebebcaceaccadddcdcdccdccbbabcdcddbeccdcdccaebdaaeeaebecdddbbedcbeededcdebadabdeeadcceddadaeeaacbabbbbebaedadadbedbbdaaaccdeeabceabbbebdcbeccbbabebabdcebdaaeedebaabeceedcabcdcbdabbcbedabdaacccccaaabbcaacbeedebccecbeccedeebdedbdadeeeacacabdecbddeaadaacdddaeeacdadeaeeabacaecdcedbaabacebeecebeebebccbbabbdecbbdbeccbcdedeaabdacdabddecacdaebcdbddddeccdcadbdaaccedebdccddcbbedbdadbcebcadbebcaedcaecccdebccaebdadadaadbbaaabdeaebbbebeebabcacaadeaaeabedebcbbcceeecdcaddbeebaebcdcebccecddcabdebdbdbbaeaaadaecadcccdbccbddccdaccadcaceaaeaeedaaaadacaaaabedebeabbdcbaccbcbebcabedadebdadeeaccaabedadedebbcbbbaeaeedaaecacbebacacaeeedabbceecabcabbcabdebdecabaabeadbcdaccdaebabbecdcacadaeddddccedbceeebcbceacdedabcdeeedeaddeabbbeaacbaebedbcaceaaeabdecbcabdeaebdebcddbacdccddcaedececacbdbabeeccadaaaabdbcdeaebaabdccbcdaabbdcdbcaedccddbcddccdaebbdeeedeeeabbedaeaaceccaadbdabccdaddedcdedceeceaeebbaaccdcdabbdcebdaabaaeeaabecbbbcdececbeddcbaabeeddadccdcdcceabeeedabdddeabcbbedddabaacecbcabaadaecedddecbedecaaeaddabdccbbacebededeacddebdaaadeebbaeeaebaabccaaebaceccdcbddceeacceeeebccdacbbbbacdcdaaacdaeeaecebabbcadecbcacadabbbcddddadcbdccbcbececadddadcbceaeebdabbbadcbcdbaadeebeedbaddcdbecceddcdbdbbbbbebebbdcabbcdecdebdeebbdddadcebadecbaccdaaddecdddacbdadcedcaaaaedddeeccdabdddcdbbecceececddbeadcadcdeabbaeccededacbddecbccbdcdddacaeecacabdabaacceccbcdaddcbadceccdbcdabbcdbceedbdaadbbaecaaceabdadceedcaeacbddbbeeeeceeaeeadbbddbdbaadbedabbddacacdaeddceaadcbcabecbabcdaebbeedbbbccaabadceeedadbcddbdeacddeaddbbccaeceadbebddececbebddbddabeedeceebccdaeaeaaebcecaeeaaccbcddabcdaeececdbacdcdbbbbedcbdcadeebbaaddebdddeabedddddecdbceabecdecaddcebcceabcbeaddcdaecdeabaaaaadacaabcdaeaedacdceeeebaeeceaedaaaccaecceececcabdbdacbcadbaebecddceadcadadedacadaddddcbbbaccdaababeaeabdbccadacbdbbcdeeecdbcebbebecadeebdcbabadecbabbeeaecebbccddcbeacbacebeabaeebeabbcbdaabcebddaeabecaebdededcddedeeccdabceccaaeedcbebbaccaecbaacdbedeadaccacdeacbadbdbecabeeabeccededaccecccebbcbcbeeaddebebeeaddaceadbbacaaabeaacadacabdbedaccacbcadabbcebebdaedccecbdbedddbdbcbcdeaeadaeaaddceabbeddbcecbdbdebdddbccacedaebecdaddddbdcbcecdbbaebaabbddccdbdcbaeedacbddcdcddeebaaeabadeabeeecbcaebcdebabeeeabecddcdcccaebbbdbdecddddaecdeaeccedecabbaabbbdedceeeeededcacbbdddbaddaeccbcdbbdcbdbcaeccbdcedeaebdeedebbcbecabacabcaecdacdbeddacccbcebedabddaadaaabceeadeaecbdbedbdadbbedecaabaaeadedbadeedbecaecbdddadcacebbbadcebcdbcbcebabaebcedcdaeeccccbeaacabdbbddaebcabcabdaeeeabcacddcdcbbdbeeceddcbcdbaaeabdeacabbcedbeddcceabbbbadecadedeaeddacaeceedecabaaceacacacacbdcbdebbbcdecdaeececdddceedcbdedaadedaddcaddbabddacdbaecaceadaadccdeddbccccaebaacbacccbcaaaeeddedbedabebaecabcbbddacbedcceaebcbdebecebaaceadadeeedbbdadbedcaeeeeacabeeceddaadecdccbcacdaeacdcaeecdbcdeccbcceecbaadbbebbdeeacecbabdecadababdccebcabbeebbbdaabaececabaceebdbebaceeadcbbaecdebaceaacccedeaccbaebddddeaeceeccebdeeaaeaeadacdacccbdceddbcacddedcaaedacdceeacdeabaeceeaedcbbadabbcdbbcdebbceadeededbeeecddbdbdbbeeaaadcbbbccecbadbedcbbaddccebceebdeaacdceeacbdaeaaaacabadddaddcdbceaeebcebbeaaccdbcbcaeeeeceeddcabcdaeeaaaddbdbbcadabdabcbaaeeeecddccbebcbceaddadebaaaeedecbcceeecdcaaeaeddedaacdcdaaeeccaeccaeabcdabadbeccebbeeccbebbdaabdaccecadddaebcdacddcccddbebabeeedecebaceccbadeaccddabcaacecacaebaeecebcdbdbaadcaacdbeedeaacbddcbdccddedabcabcedbeeeecbcdcebaacecbeaacaacaeeeddcbccdabedaeacacdcddceadceaccaebedbcaeecdceabceeddcadceabddabeabacdedaebdcdcbeeaacaebbcacabbcabbadaddaccdccddbecccdedabaebabbeeeeeaacdddabedacececbdbcedbebacbacbeccdabdeadddaaccceebeddecaebaadccaadaddbeeedddaaebaaadbeacbaacdbcaebbbeaccdccdeadeeaeedeebdaedabedbeeeedcdccbdcabbeedbdebdceacebccbbcbceccdeadeceadeddeacabeaecbcbabacdbdaaacadceccddbdbaecddbebdcceedbaaeadbdbabdacaadebabdcdabacbcaeadedccacabadedcddaeebdbedecedbaeeeaaebaceddaeeeeecadaecbecaeabacacbdbbdcedcaabbacacebbbbededbdbceddbddabbcbaabccedcbdeababacbcababddeedeccbacbbdddbecaccdccbdeeadeceabbdccaebcbcdcdedcdeabcbacdbaaeddbadbddbaceddebbeededaddbebadeeeebaedcceaaebdbebcaebadebacecbccbccaedacedbcdabcdeaaebbebeeacbbbabcecdbbecdbeaaadecceecaeabdcecdbdbbcceecccebbebdbccceccbdeeceeeddedbcaedcddceaddaadcdccbebaceedecbeccaeeddaeaeeaaeecbcadceebbdbabceceebaebadbbabcddacceeeeebacabaedcbabcdabadcadbbedaaddaadcadeddcdccbccababceaebddaddcaddecebebcacbdebddeaeaedeabecebbdacdecedddccdbabeeaddaabbbbdadbdbcbaeeecaaacdaccbbeddccddebacdaeadbcddbddecdededabecebeadecacbbebbbabadbadedebeaadacdacacadaaadbdcdddcdaceecacecaebcdeabacaaddebecedeadeabccddeeeacdedcebcdcbbbebebbdccbaeacaabbaadedbeacaaaedebcddececcaddccdddceaddeedbdcdbcddebcdebeecbbbcaebaccbadccdaccdeaebccceaaeabebcbecadabcaacdecaabcbaacaeabedcdeaebeabdcbbebeadeacdcbcbcbdddbcdbaebbedbadedaeaeacbddcbcbecdbabacbccdedcddedaecbcbbabebcbecbbbeaebbeecbbaaeeceddededbcadabdeebeacbcdaacedddebbebbbeaadbcaebcdcaecbeecadaedaedeedabaaedaedbdbdbdcccaaeacabcdebbbeeeeeeaeabbdeebaaedcbdbbdddaccebdeddaaebddacedceddacdbebbecadacebebbceaaddcbcabeebcbbdbcaacedaaadaebecdadbeedabdbbccbcbebccdcadbadecdbaebaccdccececdddaaedbbebdbedabdceaabacbeadacdaadebdbbabbbecedadbecddbedbcababdcbcbeaceeeaceaabdcacebdbeebcdcbdaedababecaecbbeaddcaabbabbacadbaaaaddacbcbcccccbbbbcdeccaaddacdecebeeadcaeacaaeabbdbaaedbbadbeedcabaadeadedaebabcddbddeedcacdbcdadaeeaeabadccdabeeddeddadbbbdcdebbbcaaaecceedceeaebdabaddaacbabcecbbaaacabccaacdddbccbabcdbcbdedcbbbaaedbdcbcebbeabdbdebeacbaeeccddcbdddeeaabdaeacebeadeadacdacbecaeaadbeaddcbccbeecdbbbeeddddddcaeadbdeedbcbcedbecadbbcadcadeeecaeccadabeecadeebcadcbebaacccecebdbbccccbabececedcdbcbaeedeedceacdcdcdcadbeadaadcddbcacbaaeadcbeedccecccaabedaebdedaaddbedcedebaeacdaacacacaebaeecdeccbecaadceedbdeeaccccbdeabaecabcecdedaaedaebeccacbecdeacebbbeaddecaaddbabbadebaccccceacebabedbadebabaccaceccedecedeadcddbbcaaddcaabeccdecbcbacedbacedebeedbbaebadcdaedbcebdcbdeaeeeecbcdabaebbcbcdcbceacaeaceeeeaadcccaccdbcaebdbaeabacbadbaeeedcedbdabbcdbcceccceedeacdedddaceaceeccddabaedaadccdecccdccddceabbbdcbcdbeaaaabacddbdbabdedaedabddacbcdeaabcbbeaecebaebbabdcacdbdbadddebebdaadcddcebdbdebaeddbeeeddeacdeaccabbedcaebbdbbdeebdaaddeccbeecacecdbbdccebabbacdaddeceaebcabdbcaaceeededbbcdcaaabeaeebeabbbacabcaadecbbdddeddacdddecedabebececbaddbedecdaeeddeebdeddcecedcaebabedcccccebabecebdcdceebebadacaedcbecaeedbedaaecedcecadcaccccdaabcaecbdecdaeaeaddaccdbdceddccbbeaeeeaaaccdddaebabaddaebaabcddedcedbaadaaecbaaaacebdddbaacdbeccebdadcebbdbcadcbbbbaecbcacebcdcccabaedcdbceddceaebbcebadcadddbbbadedaadbdcaabcedbcdbdaedbeaeeddcdcdeabdbcebbecdabdacbcddceaeeedbdbbcbecbbdbaebabccdaabadcbecbdbdeeebdccdcdcebeccacedeabeeaceaccbddadddccaeabebabdcedecabcdcddadaaedeacdadbabaecececaebaadbdcaddacecaebdcebcbeeabbebcbbddcaccedaccdcddeaebecebdbbbaddbeccaceebbebeacbcdbdcbdcaaaaceeecebccbdebdeeaebbeceeccdcdcdeaddbbbacdecaadeeabdabbcceaecedccaaaeccdacbccbbdbeaddecbcacccbbddeaebbdddccebadaeaaabeaecbdecabbbdcbebbcedcbcccbedbebecbbaedcebabeadecebeabbacbbdeebddacaedcdebbbacdaccaeacdbdacedccbaeaebacbdabeeaaddbcdeceedebabdddadcbceebacedeaabbdaaeedeeebcdcaacbaaacaeeabecacdaebabcccaadaccdaccbaebdbacdbbdeaccbdbbecddceadbcdeceeddcdceebbcbeaabadcedeaebdddedeccdeeecabeccdbbddbdeabbadbbeacdecdbdddabcddabcbedadaebbacaeacdcbcacbcabcaaacbabdcabecdacbecddbacdccdeabcedcaebeaacacbadabbbcdbbecbdecadceaecacdaeaadadcdddddeedebdebcbeeecceccbaccbdacdddaeeaebcddbdaaabaccdcebeadbcdeebbbdacdbaabcccabbbdbcdcaeccbebeecacadadebcbeebcdceabbecbebbbeacaccabdedaadbdedeededadcbddbaebabcaceabceecdeacbabcbbbccdddcabdbbecdadbddcadbeacabbeddeaedeedceebebbabbceadcadcdecbaeceeedaabebedcebacbdaaaddbbebacbebdcadcabcaecdedbbcbeacbaebbbcdbcdcdaedbdaecdadccbdcecedcebbaaacecbbdedadebeeecacabaeaccbeeadceaaaebdbdaecbbbdccaeaededbccdbbacdcbbeabcebbecbcecbecededbbcdddeaebdbdcbaadaedbddcbaabcccdacbbebbcebcccaebdaababacbecedcacedbaccdedaeeccecccedaadccccacdbaccdacdbbdddcbebdeaddbbbbaccdbaabdadaeecdeadbbaeeadeedadcaabacedcdbacdddbcedddbecbebbdecabacbcdadcdadcceedccbdecabeccedadcaebbeeedbbebcbbedcabcaeaabcdadaaeebccbeedecbabadaedadebdecaebabcaceaddececbdacdcaeabdcaebdceccbcdaddddedaedabdceebdacaadedeacacdcddbcdabebedcebeccdaebaedddcacdcdaeebdebaccabcdaeaeccaaccedacaedcaeadbaeaababdadedaaaecceeaabcedeecdeabbaeeceaacabaccadcceecaabcddcadcabcbdebcecddecbedadbaaceeeddcdddddeaabacbebcebbeaaaedcdbadebeedbeeeabbebdacbaaaacbdccedadcecaecdecaceeacdecddddcbadcadaebbaddbddcdccebaceecddaeeceeadccdecbaacecaebbdaddaaeaeaacdccbcdabaacadeccbeedbcdeacbeeebdbceeacebabdbceebbbabdadeaebecacbbddeaddabccaccaeeacacbcebeeaaaccabcbedaadabdaeddacdacbbeabecdbbdeaeebceacdcdcadebdccedabdeaaccaabeeababbeaaabedecbbeabbbcbededbbecbbdecdcecaaeedbadceaacdeacdadeeecdbebcecccdeaecbeaaebbabeebcdbaabdececdeaaecaaedcceeeecaaedbeebdcccdddbbececcedecbbeebedccebcaceceecdedecebdedeaceeacddaadaebabadaabebacebeaedbddddeaededbabebcccacceeeaaeecdbdddadabdeababdbbaaaeaccbdcddccbedddacbadcbcaacecaddddeedcbddecceedbcdacdeedaeebcdbbeaababecbcbecbcaeccdcceaeedceecaaedeadedcebabaaababceeeacbdeceebdbececeacbaeeaddbcdddbabdcabbeaeadaccecbdaedcedbbeebebaccdcecdeadbdceaeacbceceaaaeeaebaaeabebebededababdecaacadeaccececdecbaeabcbbebdcbdeedbebeabedbccccdbbacecaddabebcddaeebddeabdcdacedcbbbbceaacbadaaeacaebdebceaccddadadabcbdddacbcbcbcdabbaeabecaeedacddaaeaeceebeceadbcccadedaedbeeeeadcacaecdbbbaecbbaaeaddbadcaeddccedcbcdabcdccaccadbeceabaabeecadcbaaedaadaeecbeaabacadabdabddedbbdbedaaabaaedbebedebdddedeedbecbdedaaecbbbcdddeebcecddebabeeecbbcbeeaeeddebcbdcccecacddcecddcbbebcccdcdddebedbbdeedecedecebabbccbdebadaaaaddbebaeebdaabcecbedcaddabeebbdebbabdeaaecebcdbddadedcbedbacbdaabedabcbbadddeeadcacdacacbadbaddeededdbaaadaddaccadeeaedcdcdbddcbcecceaedbcadecbddbdadaeabbecbbebadadcdbadbeddeedcbcdceaaedccecaaaeecebeecedeaaeaabebeadbbadadecbeadbdcdbcedabbadbacaacdddabbeeabedecdecbceeaeacedadbcadabbbcbeebaeedbabecaebbeccbeccbdebbdcdebeaddbcbebceeedcbadacdedcaaaebeaeeccccdabbbeaceadcbadaeaaadbeacecdbdbcbdbdbaeadaebbbbbaaeeaecdcddcaccdbcbceaedccacbacceacdddbedadbdecaceaabaccbdbcaeeabbaecdaaceeeccaeccadccacbcadcdcebeecedbabebdeabcececdaaeeeeaadcdaceaddacaadbadadbcadeedeeaebdbaebbabbeeccceedacbdcebcaddccacdecdbdbcbecdecbbceaeeedbababaeeacbcaddedadaebecbeaebdebcabbabeebcccaedabccbdcdcadcececebedccebbaccbbacecebacdeeeebedcddbbeeabdbdacccaddecedebeabaccdecdacadabaebebeccceabaaeeeedadcdecbbacdacaabbdcdededdaabccacbaddeebaccbeaeebebbebcaedabecceaaecdaebdabedeebceaabdaccadebbadccdeabdcceddabdeaacdebaeecdbcbceddbbadddbaecaeacecccccedccecdbdedeaaeebcdddeacebeccdcbbdaebcebbaaedaabeeedecbbebcddcdbcbcbabceedcbaccebccadaabaaecaeebeeaedaebdcedabbadccdbdaeedbeeedcacacceabeaeabeedabdeecbbdecddaeebeeddbbdedddddbabaaeeeddaedcadcaacdeeabbcbcdbceeebeccddcadbaeadddecbdebcadecdccbaecaaaabedecaedecdeeaeaebcbadaebaeeadcecbcaadbbdaeabbcacceadcecebabcabcedcbcacbecdeeaccdddbbdabedcdacceaeaecdedadcdcbdbdcacbdeaabdcbccedcdacedbcdadeecdbceceaaaeecdeaeecaecdcdeebdeeadeabeeebcdadceabdcdeaabdddcbaaaeeaaeadceddeedbbebecebcddddadbcedadbebcbbadbbaaedcbedaaceabdaccddcddbcebdcaebacceecccbbbedccaabdddaebeacddcadbbcdaebcaaecbabcdecedcaabecbdbeeacaedcdbcacdabacbbddbddcebcddcccdbddaabdabaeaeecbbcbcdedeaddedccdaeadbcdeeccaeddebaaaeceaacbcaabdaebeddaeadcabccecbdebddcdcdedcbdbacedcbceccceedebeebaadeceadcccbcedcabadbccdeadabaccbbdadddacebaaabcdcacccaabcaedcccbcabedaeabdcbedcacbdbeedcabcaddadedbaaddbcbbebccaedcbadeceeeaebbecddbdebeeeedaebccdebadccccdddedbddcbeacccdedabcbcbaeacdeeebdbecdaacabebaddaadccecbbccceacaaccceaccbadcbdabaeccacbbdedcaddbabbccbaadcadadbdebdbcebdcbddaddccebbbeacbbaecaaecceabbbeebbcadddddcccbdbcbccabcbddcceeebbaddbbcdadaebbbededeeacbcebbbdcbccedcbbbbbeeeadecdecbbebbccaacacbecbdaedbceeccbdccbeaccecbddacdbbbadcabaedbacbcaedcccddbaadececabceccadcbeedaccececebaadebcacdcdecdeadaccbeebeddbdddeecdeabbbccdcbabbbbaccddaeacdceccdeeddceddbbdeaceccedadeeaaaaaeaaadbddbacbaaaaceebaaecbdaeccbebaeeedadbdddeaaacbbbbbbbecdeeeeecadedbebcaaeedbcccabcedeaadacaaacebdaacaccbdeebbedccadcbaebaddceededbaaeacddedcdcacbadddbadddadbbccebeeaeaaabbccbaabcaebeccddddcadbeaaccdacdbbddcebcebcbbdccdeaaeadadeeabebaceadecdebccdedaadedccacddedbebeebcccdcedbbaadddbdceccbadabddccbcaabeaebaeaaaeccbebbbaacdccdaceabcedaacabadebaadecdededbbdcbcadabdaddbededbbdbadeaccebbbbacabbeeecbcccedaceddabbeacaebdbaeebbbeceaddbddabdbceeddacadccdcebcdccccdecbeebccaedebaadacaeadcbccbdcdddddecdaddccdcecaeabcacbbaaedbedacaceededebbdcbceaedaadeccdcadeecbceedabddeebecbcbbebcbeecdebccbdbebadebeccadbeddccbaaddbdaaabacabdbdcdacdbecaebccdaabebcdacaccbaededbeacacadebacdebacbeaecaebdceeebcedcbbeebdcedecedeadbadbedabdaabbacbdaacadebeebcbbaaacbbddddeebabaadbeecbdbdaecdbdaedceabbeebcbaaaeaceeeeaddaaadadbceaeccebdbeaccddecededcdcaccedbcecaceebbdbdebabbdbeceaabbcbedeacbeeabbccecadeeebcebeacbbdaacbaedcdbcbebdcbceeeadaebdacacabcaceadbebdbcbeebaacbbbccaecbeeecdbeeedeaccaadabeedaccbbebabeaeeddaadbbbdcaaddedaedbacdecbdbdcbaecddbbcaecdbabaacbbdeadaeaaeddaaabdbbadbbbedccacedecbabacbcaecebbcedcbebddcceccaecbbcecdbcebebbedccdcaecbdcceaebcdedddabceaebcdaccdaacecccbbaebdbebaccecdedcbadaeecbabcddaccdbbcbdbdeaabcdaabbebbedddadabbeeabeecbaaaaacecbaadedcbeebeeeeceaceeabdebeddcebceecbabbddbedeaaeeeaeedbbaacebababdbcdcedcbedebaebbeaeabebcdaabaddbeaacdeedbcabbdacbcbeeecdebdcadcbbadcbadbbbbcbedadcccadcdebdeaccddcebdacaaebebebcdaeaeceacdcccdbbbcdedecbeeabdadbaebbaeccbbeaecdcbaecebbabaabdecaccacabccbdebddebeddbdadcaedbbbeceaadddacebccededccdcbaeacbeaacbdddcabceeedababaaddaccaccbcdadedbaeebccecbeddecedadeabcbceddecdcdaabebcbacbbcedbedadbdadeacddecbaabebcaccdbdbdeeecdbccaadcdaadbaaadaaacbeceadaedeedbdacebaeeabacbaecebdeaceaaddacddddaceeeeccedcdbddaaebaeaeaddbeebaaddacedecaeeaeceddecaaacbbbbaeadecebabaceaccacaddcdabcdcdebeceecbbcebbcabeceddecbeadaadbdcccbbddcedbabebadadbeaddcbeeeacdaecccebacaaeeddbdbbdcbcdbcbaeecbcedbddcacdcddbdaeddbbbbbabdcbbaaceeeeccebacccceaecdcbbeaeadbccdadacbcdeeddcccaaaabeeeadaeacddbaebcececedebacadeedebbedbddcdccaeaebaeaecadeecdecbbcdccdbacbaacaddadcdababbdddebcaaeeeacbdeecdabbcbacbdaceeaeecaeebeedebcdcbabbabbaaeeecacbbaeccedbececdabedcdabccdaabcbdeebbdbcababaaaaeaebbcdbbcbceedcccbaacabdaddbebeeabbdbaabdaceadeedceacccdacdaebbbcedeaedabecddeeadcacbacceacedcbdddeccdeacaaeaccdbbeadeccacbceeeaaeccdcaddcbcecbdbadeeebabcbccdcabcacbdeddabeaadabccdadbbdbebeaeecbcaebdcabdbdbebdceaddbdaedddceddbbbcbdccdcbcdcaacadbcdbbaeedcadcebdebdadadbbeeadacdecadaadbbcbeabddcbbccdecdbcabdaadbddadbabaadeaceedcaaacebeadbbcdbdbddeddaedebaeeccedacddcaeacedcbbcecdcbdcaeedbedbbabdaeeceeabcebceedbcdecdddbcdaeaacdbbeccaaeadedeabeecdabceccdceebdecaeebededdbacecdcbaebebdecedbcececddbebbcbbcdcebbbaedcdddaaaccbbdaeaaceedbeebdaccdbbdadbceeaacecbdabcbdebeeedccababaccbcedbbecacdcddeecebcaaecadcccebdedbbaddadccbccddcdecaaaaabdaaedadaeecbbcadadaeaebdeeadacabdddcbbecacbeaeebbedeacaebdaaabebadecdadcabdcddddecbdbccdeeebecbdaaeabaebeecaddbaadaeadcabcbdcaecadbabeeccccbbbccbbebbcbaedaeebcdbbedebdedccebcdcebaecaadeadebddebebeccaeebebbceadbbaeccbaedbddaadcbddadceecaceebdadadadcbecbcedacceeccdeddaeaddacdabeecaaeedaecbdbaceeaaadccabcddbeccedcabaedcaeeaddbaaceaacddbaebdcdeccbeeddaeaccacacccaacdcaddcacaedcbdbcaededcdeedacedbbdccdbadbbacaaeeaeaaedaabdaeeecbdeaeabadbdbbebbeebedbddbceebabdcdebcbbebaeaddbdadbeabaadbdbaeacacbaadcbaacebbbcbedbbbdbedbbaecebcddeecbdddadeebbdbadbaaabeacbdcbcacccdcdecccbdeabaedcebeeabeddbdbeebbcbedeaabbeedaaaeaecbcacceeaadccbabbcabcececdeebbaabdddceddadddbddeaeeeceaaddacdceddbadbcdebcdcdbbeeabbedbcdcbbbeadbcbccadabdeabdcbaecaacebbcceadbbdbeadecdbcaeabcccdcebaaaccaaeebccaccdcdcababeedcebaecbbedbaeceeebddaecbaeeabcabbcacabebadccdcacccdcacebdbecbbecdceeedcaeddcedbeeabbbeccbcbedccacdbecaedddeeeecbdbbadbcdeaeceaadeaaeceabdcadbbcceacdbdcabcddcacaaabdbeccbabbbdadcdeacceceadbecdaaaacadcbdbbdbabcebaddedbcaabaabdccdcedddcbbeadcdaabbcaaeacaeabeacdbdcbceebacacadddcecdcddebcaacedebcdbdeccdecdccaaababcacddebadedecddacbaabdabcacadcabdaebaabedcdccaabbaacacbceddacbaaaadcaeacdbeccecddcddcabaeabbdbdcbaababdbdeedbcabbeaedeeddddbaceebaaecaccedcbeedabacbebddeaddebcaaccceaccbacdbdacdbbeadeabadeecebbeeededeaecdcdceaedbceedacbaabdeacdcabcdbeedeabaccbbabedddebadceecadcdacedbdadddeddedecabaabbadabaaeabaccdbcadecbbeddcbacccedcdaadcaaacedbeadbeecdedadedacdbeedacccdcdaaecdcdbbcdbccceadccdcbaeeebadaabecedbebeebccadacdaabaebbeabcbaeeeceebcebeebbddbdcbddbbcebadbcccbecddcbaeaeacdcebeadeedbdbaccbdbebaaebdaabdddbececbacdcccecadbbadbacecaaedcdcbbddbdedbddeabedeebbccaeeaaaebddbbacaebeacdaddccedbaebdcacbacaaedaecbbeabedaccbbdccddaecdadecdcaeaccaebddddabbebcbbdcdedcdaeeaadbbdebdcbabcbaceeccdbcbedaebccadeeebcbbedaaebaedcbcaeaecbdabacedbbaaacaaceebbbdecbbaeacebcecbbddccadabadcdddaadccebbdcadddbeeaccbebaadaaeeddebdddbaeaaeaabecadcabcecadcdaabceecabddebbadeeacecddecddabebedeedcaabacaaeaaccadbccceecdeabaeccbadbbaaeadbaacbccaabaabaadcdbebcaacdacbaaaedbaaadcbdcacdbdddbdcdeaebdbbadabcacbcdebeebbcabecaacaabbacbcbacbcdceaaeceaeaebcdcaaadccddaddbdabebebcbebbccbabedaeedbeccabdedbcbbaddebecebbecdaeebddcedbcdacddaddccbbecadcbbceedcbbcadaccdbdaeeecaacaccbabcacadddbadeadceaaddbeaabcbbdddaddedcaeadbbbeceeeebbaabeaececdcddbcdceadabdaadbaceabcdbebdaeaaceddacadaaaededdcddedbcabcbdebbdbdcdabadddecddcabcaaeaecabedbbbedbcadedadeeaeeadcacccebcbaacedbcbbbdebaebcdbcadeaceccbbbbacadacdabacedeebbbbabdbdadccbcdddbddebacebaabaaeedadaeceaecbcddaccdebebbbcacebbddccdbadcecbeaebcebccceaaaecceedcecadabddcbbbdcccdbceeaadaebdeddbebdcbdededcdadcdebaaeecdcdbbcedabcbebdbbecaedaddacabbeeeaebdabeaaddcecbaebbdebbaacbbebcbccaeaccaeeddbebedacaadbbbacbacbdebedbbddaabbecdbebbacdccaaadeaedebedbaecbeaddbedebbbdcaaaaadcacccdeeedabdecebebcbaccecaccedddeadccdbddecabaadbedadcddbdbdbdecbeebdeadadadebdeaccacaecadbceaebaedcacdbabbbeeedcbceebadcbdbccddceeaecbdcbcdcbaaedbcdbdebacaacaecdbccbbabeebcadaaaadddbccccaedecebeecdceeaeedbbdaeadcdddabbccacaebbaacccdeaecddebbaabcecaabdbbdacbeeebaedaedddabdaabdbddaeeebdccadeddddbbdcebcceacadbcaaabadabaceccdbecdebeaaedcaaeabcabccbeaeecbaabaabedeaabbebebedacdeeadaaaceccdececebadbaebaebcdcdeadebcebcdecdbcaaabdbbccdeebcbceadcceaadabbbdaaabdccceebcbeeeecaddbdcdeacaccceacdcccdaeeaeddebbadceedbdecabaadababbbeddbccbcebccadddaedcdebdaeaccebbcadcdaceaaabaebcbbebbcebccedeedbdbceeddcbdadceebeaeaadaaabeacbdadbcacbbbeabebccbedbdadbceceaaccbadbdaccbcbeacaecdeebdadabbebbbaeaccaadeecebcbbdaeaadcadaaecceebaecdddbeebccbadacadaceeaebebcdbcdcdadacaeeeccbeabaacdebdbabbcaccbacbcbbbadebcddbbebabadaedaebcbcbcaaccddbdbbbccbbebbdcbdbecbcbbcebadeeabeaacdbbedeceebebacceebebbedabddaedacbcddbadbabcbbcbeeaaeaebcaadcbeebedaaccdaaabbacaacdaaacdaaabbcbdaaaeebdeaecabeeebbbbccebecabdedebadacbdcbcabccbcadbacbabeeeabcecebcbdeaaaadcecebeaedceaababdebaeaeeeacecaecccaecbbbbadcaabaccaccabdbdcbeceeeccabeadbacdeacccedcadbcbccddabdbcdcebaeedacdaeaddeccecabeebbedacacbeabbeeaebdccbdebbdbdaccadcccadeabceeedbabdbbedbecacbeaabacdbcedaeaadcbcbccbaebabacdbedaaadeeeeaeeaeaaaaaebadccaaaebedececcbebeacceccdbcebbecaeddbdcaeacabdeeecebabecbaecbedaaebadadedecabaebedcbebddcaeedccdcaaddaaaadabdcddcebbadaaebbeabddaccedaedbebeacbabcedcbdcbaaeebeaaeaeadccbaacaeebbdabcdecbdbcccedbbbecaaadbddbbabdbaeadcedcbeadebcaedeabeebddcecdddcdcdabebecacdbaaedecacacbeecaabaeaaeeacbcaebcdbadacebedddbeeaecdeabaacddbaccceeddabeaadcdabeaaaedcabbaceaddceaeacebdbdacccbbeabeaedddcacaceaceaeebedbcccccdcebbeedbdddeecbeadcbceabecbcbdbdbbedbdadcebeaaddebabaceedccacabecbedaabaccbbcdddaeadaaccabebbccacaceaedbbdbebbbabbbebededbacbbaadeeaddabbdbebbceadabdbbcbabcecdcbccdebebabeedbcadadcbcadbbebeecabeadaadcebdeddeaecceeecdedbacccdbbdddccacccdcacadeacaaadcaedbcddbeecbceabdabcecdcbcecbaacaabcdceaadcccdddbcddaedcdecebdceebcdcababcbadbccadaadbbacacbdccbabebbebaccbaaeceeeeccabbebabceaecbbabdbebccecbaacccbcbabbcebcedeecbccdbddabacaacccbcedabebdbbaebecccaaaedbddedcedbeaebaedecedddadcebbabdadeeedbedbaaacacddcedeadbedccbaeeedcbdebebbdbddabcabaceeaccbcceadacaecaadcedbbbedaccecdcbeeccdbabcbbbbdcaebdebcabdbecbaecbdbaeeadcccbbacdbcddaeedcbeabececbacdadbdbcbcebabbdbcdebdeaabedbcdbbbaeaeaabeddeceedbccaedebbaeedecadcbeabccaebbebdddeeedbabaddebcbbcdddaceadcedaedececacbdcddabeeeabebdadbeedebccbeabebeeeaabebbaaeeeadbdddabaedcdcaaeabcbebdcbeadeabbdcdeccbceaeeddbccaedccaedcbddcdabaabbeedeadacaadeceabaacdbabcccaebcecadababccebbdcdadcadceeabdaeaaebabdbdebbedcceeecbaddbcdbacbbccceaeeabdbbacbcddccdaeacddaaddccdabcdcebbacdbeebeccaaebaaeadddaaccbebdebcaadbaecdcbcbddbeebdcbdbadedeceaacbaaaecdcdebedbecbdbebdeededcdbdaaabebdbeaccabceadbaecaecdbecdebcedaaeaabdeeecedadeabdedbaaaabbaccdbaeddbbaebdebdbcaebacacedaebcbadcdeadebaebceadccacaeaedceccaaccaccdeaadcacebbbdeeedaadbcebcbacdaeddeccbccadabddaeacedcbccaedaacbeeccbeceabeddeaadbdebbaecaadcebbbeacbcaebabdcdeeeddcbacedccdeaeacedaedaedabeeeaddddbdccbccecaaacedbaebdceccebdadccdeadecdbadabcadeaaceaadcdadddaeebbcacbedbedcceacabaecadbceccbcceeabdacacdaddbcadebeadbdecdcadbeddadcceaccebbeecbebdaedbadceccdcecabcaabdddceceecdccbdeadacddcedacaabaddebcbeaccaedacacbbabaaeccdcdcecbceaeeccbbeeabeeaeecddbaeeceeedccebdeecdebeaacccabebceebacacdecbebdddeabdcabebbbddadbeacaecdbbedeaeceeedbacabccdbdebdcccaeadcacbcddcbcadacbdceeadcececadacbbecaaccaddebababeecbacbccaaeccaeacddbebbbadcadccedddecccbabcdaecdbabebdcedccddddabcabaeabccbdcbcdccddceeedbaceaeaeeaeddadcecedeaededcbcdeaedcabbedddedebbeeaccbddabccaebebdedceabeebdeabdddaecdedadaaeabaeedcedeaacdbbceecedcbbabcedeecabbedacadbbebcecbdbadbbcdadcaadbeddeececabaaeecaddecdbabbcccbbaccdaeaacbecdabeaeccdcbecbacbeceeddeacbbaeeaaaececaacaaecbdcbcddaeacdecebeedacbacebbdbbedcbbebbacadebcdcabcedbbecdedccbcdadcebeceabbddcdddbacadaeaebcbceeebbeaeaecceddebaababdbaacddbbeeedeadcbdeceeeccdeebebeabbeeebbaddcebcbecddbeaccbeddcedbdbabecedccbdbbddbdedbcdddbabeadbdcddeadeddebadaeeaabedcbbdbcccaaabbdeacabaebccacdcabdccdbeeacdeacdbbeecccdccdebbbcbbbedadcbddaddadaeaeeeacdacaecaeceacecdbcdeaabccbddcdabecdbbabeaceaedccbbeeedccbeabebeabaedbeaeeccccaabadbcebcbacbebcddeababcdaddadbeaabeaecdaabbaeecbeddaccedcdbddacbbdcbabccdaebddeabedaebaaebcbdceddaaaeeaceaebcaaddeddccedcebababddeceeacdbbabbebaebdaeecdcccccdaabaccbcdcdedbcccacaecccbecadaaeebccbbbbaacceadcdcaaadabedeacabdadcdadbbaadbcacbcdedddaaaadceeeadcacabcbedcaacbbceccbcccdbeddcbaeddaeecaecacbbecaccbaccebeeacecaccccedaebedcbeccdabccccdddbdcbadcaccdbaacaaebdacdcddbcacdeceacedeccbeebdcbaacbacdccddbddeedababeeccdbeeabeabcdbbeeccecaaaabbbabddeecdccbdbcdbdedecadbcbebbbbcddccdeacadeebcabbedecaaacdccbeeeadaceaaddebabedecedececdceaddeecaaaacbcbadaceacaecceccdedbcdbccaabdeebdecbbcadbbbaccadebccdbeeeaeebaaacbcbddacececddeededdcbabbacbadbddeebddacbeeedbcdadebdcdbbaedbdcadabeecbcadcecadddcbcaddabceaabdaebdeeeddbccacbbbadbbadaebecdbcadabebececcabadecaccbbecbeededceaecebbeceebcaaedbdabcacecadbbccebcddbbcbcdedddedecaecdedaccdebdebaacecadecdedccaeecabbaecadabdcaccaeaabadceeadeaddcdaddeabeebdcdcaaaedaccdcccedbcbcaccaddaeeaecdddcdbdaacaddaaeaddcaebaaeaaeedbcedbbbdcbabccadcbcccedebceacbbbeeeadcaeaadaadaebcecaaebdacabddbcaebdecbcaddcabececdabacdeeaacbbcacdeddaeaabeecddaeceeebabababdcadbbcbcbbdedbcaedcbdeecacaededdebbcaacbcaabddedddbeadcacddbeceecaebdaddbbcdcabecbdeeaaabdbeedeaacaedadcdebdededbbccdcdeadcacecababbdceecabbbcddacdbddcaedbcacaccaacceeceadddedbebededecbbeccdbeeeeadaeacecabbaadecedcddbccaadadbddcaacdabbbbccceaeeddeccbcaacdbccbbdbedbbbaabaacdeeaacaeeecccecccecbbeeeeadecbebeedcdbbdadadaacdeeeeccdbaebaebeeeccdcbaebabbdcabbacabdccdbcbcdadaebdadbcccdcadecbbbdbaaaeabcebeccaabccabbbdebdbbeaacabbcdcecddaadcaaaadbebdccbddbbabebbedabcabebedccdbcbacbcacaecebcedbbddeebabddaaedacdebbacaddbeddecdceababaeeeccdadebeaaadacdadaeeeeadeacbbcdcbbeaaacedeebbcbeececbbeecaeecdceeebabbaeadbebbbecbbdadecadbebeadcdbcbedbcbebbbaccdcabdedabdbadddaaeeddcbdecdbeedeebdddbdeabdebbcddcbbabbeaccdbddbdeddeaedceceaeccddcaeaddeeeadeddebcdcdaeedbaaabecdbbdbadecdbbdbdadbdddedeedbacddbecddbdbbbcabbaecceabbbbdbeebadbdbdacdcedbabebdadbdcaeebcadacaeacabadcccdecdccdebceebbaedbaeaeaeaecbaaacaeccedbacebdeddeddbaacabbeabdecbbaddccddadddabedcdebeeaeadcdedaeaadecaeaebaaabbaabaecaaccdaadceeababcebeedcebccaadeaaaabcdeebccbcbccaebeeebcbaecebcceabcdadecdbbcabbceaedaadbbcdddeedbceeebeeeaebcedbbccaadcdeaddbddbceadabdcbccadebcddaabeabccebdaeecdcbaedebabbbdeedaccacdccaeceeaeddcedbccbaeaaeebebaedddaccedecdddeddcacbaebebbecedbcceadbaeeacdbadadedebbbcaebdcecaeaddbcaacccaadaeeaeeeedbcbbabddceacbcacecbdddbeabdecdddabcddcdbeaaacaceccedabddbbebeebcdebabadbbabbabaaeccbebacddebedcacccadddebdcbcedbbebdcbdccceaabcddedbededceeadebbcbabebcbeacabceeeceaaddbedeebceadcbecdabedadccdabbbecaededbecdaaebcacaeeacbbdbcbdbadadaaaebcceadbabcbcedacaabbdbeababdaaecaaeeaccbeddbbddbcbeddbeeeeadbcaccaedaebadeeebcbcddcaededdddacbddccacdacccdbceacbedebadbddbbcdccaeaeebcacdeccbebbaacdaaccabdecbadcddbeccaaeeddaadebddaddcaccdddeeababddeabeedaabaceaabdaaaaededbbdeceddceeccbaaadcedecbaaccaacceedacadbcdacecdccecebecbbebadaedecbcbcdaadebbdedeacbacdbcceacdaeccaadbdcaeeadaceacebdbeceabcdccceebaadaebdaccccdacddaedbdbabacaebebaacaecdccececbeaedbcedecceddabcbcbedbabeadabceadeedeeeeecdaacdebdedaaabcbbbddbebceeaabddccebdcbddedcccdddbdbaeadbaebdedbdbeebbbdaccccbabbcecbcaadbcdbccbcbdbdeebbaedccadddeacadadadbcaddcecbdaedabcaadcbeddaecbdbdbacdaeceeebaaaddcedaeebcaedceaebecaccbadbeecdcccdceebdadacbbccedbeccebeecaaabbcadcccaccbcdcdbcbcbeecabddddedbbecacdbdedecabcacbcdaccaddceadacceaccccbaecdadaeebcaacbadcbadbccacbeaeabdeecdbadbcddddaacdbabaedcbdddeacedadbabebbccbceabdcbcbecccbcbeedbdaeebbbadbbbabbebaaabbcdddbacacaeeabcaddebadbdaacbaebeccdbaecadbabbacbbbdcdaadbdaeccacdbdbdeacddadececedddaecabdeecbedbdaeecddbddceacdabccadbdaceabacdcaaebccceedbacaeedcceaccaeceeecdacccaddaeebabbeaaabaebedcdcddaaecedeeabaeaddedabdceedacbacabcebcadcbdbebbeaedaedbadbceadbdbbcaabddccdbceaeaabacddeacaabbeebdebdbdccabbedacdeeaeaecdbdbbdeeadabdebcdccaceeebdabeacedcebcecebeddcadccadbbbbacdcaebddedadadcdacaeedddbbdcacedbccdcdacceebedabdddcabeaedabcbeeaeabccbdbcaceeeabcceeececdbbaadcdcddcdaaadbeacedbaaecaebbebddecdabcaebadabceccdaabeaacdeaebdcdebacdeacdaccdccebadbacececcdcdcbbdbaceccaebabccebcedbccaaaedeabecbcdacdddaabdeebddcddadabddcadbeaeedbbdbaaaeeedcbcdcecbaccccaeccdaedcacaaabcbeeeeeeaabcbaddbdeecdaededbecccbbcbbcecbdebedcceaaadbbabaeededebaabebdecbeaaaeaaecbdbbecdacddaacbcdceaecaedccadcebdbceaebaedbadddbebddecdacedcdcedbebcecbdcbbacacecebcadbeecaccbbaeadcbeeededabcaddbdaababdaeeeaebedaacbaadcebccbbdcdbaabdccdceeabdedbcbbdecadbabcdecddacbacccadeeecccebeadceddcecdecddecadcdcaeaccabacbabaebbacaaabaedacccbdbbedbecabbddecdcdddcebbdadeeadaaebdebcabeaabbdabccaeedccaebdaedaccdcbaceccaebaaccebecdebccdccdeedbdcaccdcaccbeaeaddcbdeabddddcbdceabddabaaaecbbcaeebdcdcdbdedaececdccaebbebbdcdadcebeacadaabceaacbcacecebbaaabdcdcdccdedeeaddbecbedbeccbdddecaeddddedebeaabebbdcaadbbdcabbbbebebebeeaddacdbdeeeaccbcaecadaacedeeabbccbcabeecbeeaceeeeecbbcdadebdcbebdcdceebbebaeaeaaaadaaacdacdddbaadadbabacddbbbbeeeceaeeacdeccbdebccbbacadbbdebbbbaaebeabebdbdeabaeccdeddcbeecdebabaeadbddaaebdddccebcbbcbddbdbaabcaeceadabcadbccabedecbdecacaaabebeeceebaabcbceabababbcaacddddacdccbbbbabddaceddbdbeadccdcadcccbabceccbecaababcbbaceedbadedcacbdcdcceaaeadbdbdabbbbaeeadeadebadcddcadaccacdeaaddaddbacdaadabeadbcdaaaebeadbaaddedddbdbbddeedacceeeabdeaedbbceccddcdadecccaadebdedacbcdeccdecbabbcadbababcaddcaddcbedaeecddecbdadaaeccaecbedcdbcbeecabaaceabaaaeabdeabbcadeabdcacadcaceaeebabacdacddeeceeaddbeccdeeddcdaaaecbddcecbdcdaedcecabbedbacdccedeacaccddddbededaedecaccccbcbbedacbeeaecdeeedbdacdacaedababaadabccebaabeccddbddcecdebdeabccaeeddaebccedaadbaceabaeaeaaacdbbccbdaaeeeaebbdbcabedceeaedadacddcebecdbcbbdbdbdddceecdddbbcdaaedebcabaeaaccaebaabbeedabcbbadcaecdddbaaebaacaaccbddabdbedcdeedecdadedeaedebbdbcaaabadbbaebaedcbecdaabddbddaccddabebdbbabdcbebeadaabdbabdceeabbacaedccabecbcaeacaaadbddeeeebaabebececbeccbeaacadaecabbecadabbaaedeccaeeadabbcebecacddbebcbacebaacbaadcecebdabcbbddededeeaabcabbeeceeacaacbccceedebbcdbbadedabdccdcdddbbbabecdeaccaeadccdbbcbcdbbbdcdebabebadcbceccbcbababaadacacbdebedeebaccdeeedcdcbacdedbadacbcedddcaabcbecaaccbbadbebddddeaacccaadeadacddeddeeadbcadddddccdadcdaeceeebadcdcceeccbcbbaecdaeaaaadaccceacbbedbbecbbeaebabdacddaabadbadcaaaeeadbaacaabdecbcbdaedebadbecadcedbabbabeccbbbeaebbcceccbceedbaecdbeadcddbccdeaddcbdacbcadedcacdeebbaacdcccaacacbbbeecbcbbdceebbedccecaaccdbbcadebbdaabeaeeccadbdababccaedcbacaccdeeabecddeccbcccceebacbabbccbdcabbbdcadcbdcebedbbaddadcbaaebadabceccabbdebdcdeadcddbdaeccaeaacebaabcdcddecacacceceebbddabcebbceabccddcddadbaebddeacbebeccccbecedecacabbaaaeedaedeeddaeacdcacaeddcebebeadabecbebbeabdbdbdaebcdebaaaacdcecdbbecdcdbabccceeddeeeecdadadbbcabdebeddabcceceeddbbbcccbdaaddddceebdcebabddedeadcbddacbeeadeaeabedccdabaccdaccccadeacddbbaecdecceebdebaaedcbbdabdedbececeaaabeedaadbacbcedcbbedbeccecaaadaeaeceebdccbeeecdedadceedbecdabdeaaeceecbeaecbeecdbccccbebbaaedbeceebaaccecaadbccdaeedbddaddabbeaebbdadbecaeecdaabddccaabdbdeceedbaecdbcdeadceecabdcddebaabdecedeccebbbcddccdadddacbcadbbbddddcecdaddbeccccebecacaacedadabddacceeebbdacddbbeeeacdcecbaebdcacbabaaccaeeccdbedeeaebecabcddcdbdcbaecedecaadeecaaebdcecebbacdaaaaccccadeaebaebbebddbeaecadabbcbdabbcaecbdabaeaeaccbddcaadccabedcdeedadecdabeacadcbcbabedacabdcacbcecacdaeecabcecdcedeedbcecdbabdedcebaaeecbbaccbadbddabcdecaacdeeeacccabdcadcebaaacdeaddacbbbbccaebcbdaaaabdbebbdecacbdecaeeddcdecadeaababdeebebcedecdcedabcbcbbadccebeebdadbccaacedccbcbabebdcbeddcecacaddddaecaadebaeacdaaadbbdeedcddaaecbdedbccacbabbaaebbeecbbcabaaecdddccddbebbcbbbaddadbdebabbbdebabceaedaccadeeeccceabeecaeeedacbbbcecebcaedeedabeaadedeebccacadcbbeabdccbddabcdebdbdabbeeabececaddbcddaaadaebcdcccdaaeceebeebeebadadeaabceecaecedebecacadcdbbddaecddbdcacedececcaceaaaeccbcbcdaeaedcececabcddbccaeaecabcceeeacccdbbdabaebbaabbaaecbecccaaceddebdbdceeccadaceaeedcddcccceddaacddcebaacbbcaeabadedeaebebdbebdedceebdbccebccbbbccbbdbdadeccbaedecededccbecdbbdbacccebbbabaacebaebeabaaadbeedeaedaaecbdbaedceabceaadbcbbccddecccceecbbcedebacdeddabcccbceaebebebdebceeaedbeddcebecabddaabaebbeddeadeddbdebbddcaabcbdceacaabcdabccaeddddbdcbaaccbcddbddaeddddbacbdcbabacbcddaddebbeccebcadbbadeebcdddbdecdbaccaeeadedbabdebeaaebeddbccaebabcaadcabdcdaebeabbcabbdbdaecbadddcebcbcadbacbdeabccabccaaaaddcdaaabcbdcdeabeeacbcdebeabbdbbcaddbedbdeaeadecaabdedeedebcddbadecacbdcebdedecaacaeaddbaedaacaccdbbeccdaabbbabcbeecaaaaabcdeaeaacedaaacbabbabcebcdbacbcabdcaeeeaccaddbeadeabceaeaadbebbdbdeddebdbddacbcbdddedbaaaedbdecdacabacbabccbbedadbbbcaeebaeddebccbabadabdbdbcbbeabbbceeebbacbceccbdbacabdcaeababaaeebcdccdeecdcddcdcabcdedbadeebbebbeeddecbedcdcdcebdddacdedaeddecadcadbdadbcabdadbeebeaaeddeddddcdeceddacdddaddcaaadedcacdeceeaebbccbddecdaaeebdbdbbbabdbaacabbdbbccbedbbbedeadbedbdadbaeeaeadeabaacdbbceecadcbcacdcadeadbdcdcdeeadaeeeccceabcbeaedaecbabdedeadacebeceedceabedaaaccacedbaaaaabcbdbdaeddbceeabeaaacaceaababeeebeacdbaeeaacaeadbaccccabcabecaaabcdacdbebebcebaececbacadeaecdecaadacdeceecceabeedaeabbeebdedcdbdacaaabaeeaacbacaccaeabdebadbdebdcbebdeddcdecaadddbaeaddaeeccaabebbbcddbeedaacbdbaddabddceaceeaeabccacbabccbbadccbcddadedbeaedddabbebbacecdaaeceeaccdbbcddacabdccdcecdbebaadceaabecceecbcabaacaabdaaaceaadbaebacaeadedcdaddaccbbaeaeedaacaaeceddadcbdeedceeabdaedebcedcaecbcacecaadedebabadbaebdebaadcbeabdaddadcbaedeacacbbdceaaaebabadcbcaadeaccedcabaceacedcaccecadedeecacbacceeaabbebeebeeeceddcbdaebcbcbceabcbeeeadbadceebbbaeaabeaecabaebecebcbbaaaccddabbcceadebaacddaadeddcccababdeecbadcdbccdeecdeedbeadabcbeaaadbbedeaddebebeabedcbdbecaabdadcbeecbcaedccbddecacaecbcabbbeabdddcbadbbddbaaecbcdeccdcacdaabbdebbcadbdcaddbaeeabceaaaeddcdacaeeebabceebccdedccabbbbbcabcaebdbbedaacbaebacbbbcccacacdabbcbbaeadcadeecdeebaeecdadaddaeaadeaebcedcdadcdeecdddcddeedecdeddabdccabecacaedbdaeeeadbcdecaaebaecbccddbddeedaeaacadaeecedaeaebaabaaebebbadadaccddbebdaccacbcaebbabdaebaddabecaebecdebdbbaebeccbcebcbaebecbadbebaaddbceadccccdecdccbaededeaaeebdceccbecdcacdabdeebcdccbecceeaedebcbadebeeeaedeaeddeaacecbacacdbaacdacabecaddebdceccadddecbdbbeadaacdcbadadabdececacdedeeccdaadabeaedbecccbedeeedebadcceaacdbdeadcdbdeededaaaaddadeeaacdcbabaeddceecceaadaadabbccbdbaecbcdeaaddaeeedeaeebebaacadcccadacbbeccbbccbcdbaedaaddeccadcdeebaaddeaaebdadbabdbcebabdcebbccbcbeddadaedcbaeacdcccdebedbacedcaeeccddbddeaccdeaadcccaedeebdadabcdaaccdeebcdbabbabcecbcbedabeccabebeebdbdaeabecbcbdbcbebccaadaabdbedceeecdaedddccbdeaeddaddeebcadaacdaedccebeeaacadaebbeaaccbebbcceaddcbaeaddebccbbdcaaaeaaabdcedaaabbcaedeacbbbebadecdceedaeedececcbacbccdceddbbcadbdccceeeaabccceeecabdedaedcdbecdcddcaececcedcadbedededbdcccadcddebaceedbaecbacabdcdbbcecadcaaeddcaaecbaddaedeacbcdcabdeacdbdbcabbdecbcedcdeddcbbdceedecaeadcddcedacebdcbaeedcacaddebdabdbdabedcccadbabcabcdcebddcceedceaedddcacaadaceecbcaacbaaebbcbeebadddbeccaaebebeabcbadeedcdeaeeddcdccccaecedbcecadebcacbdaabbccaaadaeaeacbacbcecbaaaadcdbdbbdcddcbdcacddcceeeaecbaacedceedabebcedccdbcdbadddecbcbcadcacabaabaebeebaebaeeabdececaebbeccaeacbcbbdececeedeeeddddccebbdedbdcbdecddeceaceaabaebbdaccebcaadddccbcdcabadbeccbdcbabdbdbbeaacddcbacdecbeedbcecdabbeddcadbcbecccaeaccdaeccdeccdcdccbdeaedbacbadebbdcbceaccaeaecdadedaddaeebdaeecaeabbadadadacddcbbcceebaebabaedecddccbdddadcdcbbbecccddeaaebedbadcdbecbbcdccabbbdeaaaecdaedaeeeabcaddcebdebdedeadaccdcccbabaeaceebedceeecebbedbbcbbacdeadacdaeecedcbcceceedbebdebabccbdeadaaadbdcabbaaeebeaebbdddacddebbabeaabaaabceecebadebbecadaccbbaabbaceddeebcdeacdbecdbceadebabdbecaceeddcaabcecadceaebdacbedbebbedbcadbceaeecabaebddddddccedddcdcecaedcbcbadbbebceadecbbadcadecccebdeeddcbeddabebdedccabdacbaabbabccabdbbeeadedadddabbecccacedbdbaaabdccbbecaccebcddccadebceacdbbbdcbddcbecbcceceadebebbeddacdaeecdbecbabeeadcaeecaadccacebecbdceeecdcacbcbdcbdbcddcccccaedcebccaecaaabeddbdddeeaddaaacdcbdcdaeaeccccebdebdcbeaabacbbccaceccabeaeccababebdeaeccbabbbdeacccddbcacdbcbbeaccdcdecebbcdababdacccadaabdadecabdeeececbedeabdaaaebbebbcaedaddadabcdabcaaeebbcbbaeaaacdbbdadaeadedcebbcebbaaccacbdaeecdaedbddbcdbcaeecaaddecbbdacdbacadacbeedbeacecddececbedcbadeeceecdbceadacdaaddbdabbbecdbedbbcacddbadbebcadddeeabeccceacadccccaeaaeceebdbddedddbbeabddbacaabcbacdacdecddcaadceeddaaccbddacbaeecadbcaaceeadbebbccedbebbaaaaaaeddaabbccacbaadecdbebaadebedbecebecbbebbcbbbbdaacccecceeadaddcdcbcecebaadecdaacebebebcaccccecaacbaccddaeacceaaeaaabedbdeddccbbceeeadddcbcbdccbcadceebcdebdadebaabbdbbdbbcdceddeebeddbdeacedddbcaabbeecbcbedacadbbedeeceecdeeddddacddaaddccebcadadbecdddebbbbcbbedccdbdbcdeeeeacceaebbbbeecccbbbcdbaecbeecabaebddabeacbabcdbedaabebbaacecbdccccdcabbcbeacbddbabbeaadbebcbacecaddedcbaddcbeedbcbecadeaccbdeeeeadaecaeeecdcdbabaceddadccbbdbbbabdcaeabdededccdbcbcabddbcdeacbaacacecbbccdccbbdcedceedcedacdadbadeaedcaadbeceeecebaadedcacbdbaadbedeaceccadececaebecabaeeacbeddcbcabcdbbdaebecbdbcdccccccabbccbccdbadaeaebdecaebecbddcddccaccdecbecaeabddcbedbbdbadaaddcedcabdbcbdbbcedbacedeebcdadbedeeeecbbbadeebebcacacebeebacbcbdeaaabbaabaddaabedccebabccaaeabaaddabbccaccaacdceebacdebdcedacabddbbccdaddebcdaadbeeceaeecaabaddbcdedbadeeaeecddaaeebdbdbbabdcadbdadabebcbbacbeaacceaaaacedacebaaccbabebaaedcedacecbbbbdadbbcaacabacdeebccedabeabedeabbadcaabceeabcdbcbcbebadebeacecabadaedeeadbebacbbcabaeabebcbbddbcebbeeeceacaecabeabcebadaacddaeedbdecbbcacbceabdeecdcbcbbaeaceedeacceacddbbbaabbaacceadaecacbeebceeaaadebeddecabaddbeedeaaadedaceececbacbddcaadecbbddeabebbabadbddceedcdbbbbeeeccdaabdbdecbeeeccdcbebadebcaccbededaabaabdddceddcadbcaecededbaaedeccebdbbceacaaddcbcaeaecbabaabcccdccbeabbdecebbacbbedbeceadcbcebeacdaeacadbbdeaeeedeedaebaadbebbeacebbaeaacabadaacdbddddecbcbacebeaaabdecbdbceccaecbaeebdadcdeccceeeeccdbcdcdbdacaebdbdacbbbceeabcbebecbaaeddedaecdddcdbceecaceacaedabedbbeaacbbdceabccedcdecbcabcaddcbaebcaabedddedaaaecbccdcaceaaeddeacebecdbabddcdaededaacbddcecdcddcaaeeedbeeacadeaeaeccebbaedbceedeabdadbbaabdbaceedcedcdceaacbbdbbaddacaacceaceaeedaaaeaccabcbcccbacbeebeadbedddeabdbcacebcadcaaecceddeccbcecddeecbacabeabdeedaadebbedacdbbbabbcbaebddaaacecedbacadbdcedadecdababeebabeedddaecdcadedcccedeececeaadecbabdeadbbcdedcdcdcbccccdaedbdebecdcbbdcabadedebaecabcedaadaabadceebdacdebbdaadedeaabbbccadacbcedecbaabaacddcbabccadbbaaaadacbacebeeaacbebdcabccdbcedabcecbedcaadaadbbaabdacedeedebdeccbbdadaeaeeecacbaeebabcbacbecddbeadbbbdebcccaeebdbedbacccdccdabdbabadbadbdbaceebcbeccbaaacdedcdaaebbacbdacbcddaeddadadeacbaaebcabbbccabdcdaadaebbbbbcbcadaebabadbebaecabbaddbbcbcceeeaddbdaabaeaeedbcbdebdeeebcecccbdcbebeedbcaddcbceddbaecaeccadeabdecaebcecceaecdebabcdbcbdeeeeadcbcecddbdedeeabebbbceadeaccbcecdaaceacdabccddeedcecbdddcadbcabbdebccebeeaceeeaadcddbecaeeacbeedddbaabbdeddeecbdbceabaaabebdbdbebcdcebecccdedbdacbcdadeeebaaeaeedabdedaddaaccccbcdacacdbbbdedccedebeeedeaeddecbbbeeeaabbeadbbdabcabecabebbabaacbaaaedbecdcadabebcddebdadbbeaebbeebebbcedeecadcabedbadebdecbdeedcaddbaeedaacddabebabbadeacbcdbadddbbdcacddaaaeccecdbebdbbecabbaabccceaaebaaeddbbddedbabcacdbdbceacabecacdbbcdccbbbdecddaabaeebacacebdbbecbabebadbececaaeaadaecaeceddccbdaddcedeabedaadeadaccddedbabbaddadaeaedecdedadeacaeabaeddbddaabbaaaaedaecdedebbdbebddddceaceaababebeccdbaeeedebecdbddddaabcaedebddbbddeacccebbbecbacbeaabaaecbbebbedabeaecaabeaebbebbcbecdcadedccddceeedaccaedcbcadccceaddbbbcecdcecdedcbbccbdbeeddccecdedecdcaddeabcbeacdadbccbbacbeadecccddceceaccaedcbabdceceeebcaeadabdbcdbeeadeecdebbbeecbacccaebaceeecccddabadacbbbaedcdabeabbbcdeaeeebcaacacacbcdddecaaeeeccdbeabebaaecddaaaadecabeaeeabccbdeeededaeddadcadaaedabcedcbdccaabecccddbaaacbaccacdbcbdaeecbadedacbddaacdcdcaddaadeecdaaccdabdecebcdaaaeeecebaabebccccacdccbbadcdaabaecbbccedbabedbeedebcddaacbdadceddabdadebdbecbacdaaceddaedcaecbdebcdebccdcdcbeacbdcedbceeabcdeebbecbcebeacbdbcbaebbddcacdadddaeadccaceacadaaebdcebcecbdabaecdbbbddbeebdcaccdecadddbaddbebbddbeaedbaceadaaeecbccbaaaccaaeccdabcceebcdabdcabbecbecccaabccabbccaabcecbabbadcadaceeccacdabcadddcdecdaebecabededcceabcecdececdaedeebdbdaeedbdbaeceaedeacecbadebecaaeeacddbeebaadeceecbcbddedaabedacdccbbaaccbeccddcacdadebbdbadccecddcaacedcddcbeddddebeedbacaebeabddebbabbcdbddedcadacabebdadbdbaadeddbbdbddebaddbbcadbbdcbedbcbebbcbaeecccaddacecbeabbddbcabbccedabacacbaabedabaebeaccdbdebcccbbddccaabbecadbcbaaebccdaddeaceddddcbbbcaacdebeaebedacaebebdebccdbbdcccaeaadeabbcededaadeaaedaedaccbaadbaabbeccaedecddccceabbdabbbdcceddcedcedbdeeaeaedeaceaecebdabccbaebabaaeccaddaeddcdebedaabebebaeaacdbbedaecdcbdbbedcbebdecaaaedacaeddeeeaeadababebddddeaaaabecedeaabcbbaaeeebcdaadebdabaebaecaceddacdbeadcaeccbaadcadebeedbeaccaeeaaeecebbeeaeceadadbdbadebddadbdddecbabbcbdadeccbdbededdccaebaedcccebceedbbdecdbedcaeedcaebeedacabbacbdccdbebebdaacaeceadccaadecaeadeeaabaeadcecdebbeccaddeaebdadcdaebaaddeeabdaaeaaaaddcedaccbadccdceddacccaeededddadaebbcdedbabebbebbedacaadbdcbccdeaeacecbcedebdedddbdaeeecedddecdabaedcbaaeddacdacabbbcdeaaedaeddddcadccbcbdcdeacceeedccbbcedaebabeebdededeaebbdebccaeaacadcaaaecbbaeabbcebbbaddbadbcbdecabdeaebbcbbedbacbbbabcbddcabceeacebddabaadeacabbecaabdbbdbaeebdbceeaaeedaaaedacdbbcdccceedaadcedabaabccebecbbdddcbcedbaadcdcebcddedaccaeebbbbbebdaeaebecdbbededdbeabadccebaaaeeddbbbdaccdeebecdbaabaacecebebccadddddebaacddcedabdacdcebccddbabbcddccdbadddecbecbbcecbbabcbcbadeadeebbaccbcecddbddbcbdaadaaeabbcbbbddaddacabadcaacdceddebcdaeccceaecbdcccabaacacbacdbbababcbddcdcccdcbbacdaddccdcdaebbadadacdddeabbdaccddbdddbaaceaaebbabdbacecbedbeabecbbeadecdeadccdcdbcadaaabdcedbabdcbdbdaabaebcbbbecdbeaceaecebcadeeacaadccadaaaaabdeccedcaacbccacaeceebcdacbdecececdaacbdebcedbccebdeaabeceeedbadedbacbbeecaceaebbcaacbccabbbbdbcddaccbbbbacbaedaebecaccdadddbedebbeebeeaddaeeaaceddaddaeadacbadeeebeebbceaececcedbdccdebadbaaeadcbdbdceeacacabbdaacabbeaacbeeccacbbbdddccabcaecddbdaeaebbccedaeccbdbaecedacadcedbaeeebaccacdebcbceceeabacedddbebeabebcbccbbaecbceccceddaceadbaaebbebbacecccbdddbdbaeaacaeaadadbebeecbbecbecdaeaddadbaddabddbdbedccceecedeaecabdcdacceaacbdbdbaaaaabdaaecbaaaaeceaebceeeaccdacaabaaccbecbeadccaabeeaeabacaacebcbecddbadccceaddaddcceaabdcaacedeccecbacabedcaabcceadacbdcbcbddbccaceeaddbceeddddcbceeaccecdbbaaeabbaadbcddeacaeecdbcbcebebeeecbebacaeeaaaacbcbddceaabaaabdabacbddbbecbeeccacbbeabececcbbcceebababddecdecabbdebaacccadedbecdaceabedebaecbcabbdbdabbedbaceecdabebecdebceebbedcaeebcccdeebaaadbbccebeedbbbabaaebeabacadbaaaccbbdcebdabecaeabeadddabccbdeeecaacdecabdcdbbdeedbdcbbcbdeaaaacebcbcaedcdecabdceeaccecbeddaeabeacaeddaeecdaaccededaedbaabbbcbebedadaecdececebdadaaddeedbbedadebbcceebdddeceecbdcabedbbabebebeeeacdacdbbbedabceeeecdddbeacabddbabcbcbcbeeeebeabdbddbbcebddeebdbcaceacbbaedccbdbbbcdbbbadaacdbabdbbdbaebadadaebabadbbdbecbbeaaeadecaedaedcaaeddcdbcdccedbcadccdccadbdcdadddbaeedcedbcbdadbdecccebbadbdbbecdcdccaeedaecbcddebebbdadaacdbcdabeabbcbaeebcaeeceacdabdceccaedebdbdadaaaebbeaeedbddaeebcdbcbebbeabdbeaddcbcadedabadabeaddcddccdbeccdadadaecadeabcebcebbbaaecebcddedddbeecaceadaedeeadabcecddebdebbaebebbabdebddbedeadbabaecedbeedbcacaaeddddceeedbddabbadbbbacbbdbdbbbeabcbddaddeeceabaeebaaacecbdcbdbecacacebccbcdbadaeabbcbecdcdabbbdebdadabeebcabedeaeeccdbddcaceedddeaecbcbaeddbdeccdccbdccdebaeedaeedcdcbbaebaebbdadeaaddadaabedbecbbdddeecaedeebeecacadebddabbdcbaccdbdcbbabbebadaeadcaaddceaaabbcbbbceeadeeaccdadcadcebbbeaaadacdddcadcabaadebaeccbbaacbebebcdaaaecbddcebdcddbabdedaececeabccddaebeebecaebacaedddccaabbbaccacecceaccacbbbacaddaedbaedddbbedacaebbcaccecccaebddaaededbeeabbbbddebecabbbebdbaeaedecadcccdebadebbaccddbeedcddeabbeadcdeaecdbbcccbaadecedceeeeadeceddaacabbbbcdeebdcdbabdccbaedaabddeeabcdbecbcedeebedcebaeabacdcbcdccedbbecdeccebecdbeeeaadbcbddedacecdcebaadecbabeecdacdacddceaeecedebcbebebcacacadceecedccdbeddaeedcaccbdcddacccacbcecbdcccaadeddddeaabbeccacdddaddcdcdecbbdeabccccccbecccbececcbbdaedbebbccccaacbdbddecdbabaacadbcadcbcddebbccdedebcbeceecddadbbcceeebbecbdcddeabebedcdebacceacdabcebcdeaedbeaabeeddcdcadaadebecadddbabeccccbcceacaeabbeadbbaecacaceeedcbacbbbadbdcdeccdbebddbedbcadedcebeeabeeeddedabcadebbbaaecbaaccdecabcedededabddbaecbdccabdbceaadddaeaccbadebdbdabbcedccbcdbbebecaebcdcaaabacebbcaabadbbdeacabcbbbaadcbdddddbaabaececbbcbaadbecaebdcecccbbddcaeebaeddddcbbcaeabceaadbbedcdcaebaedbecbeecbebabcbeecabccaaebbeeaebddaeaccbaebadabbedbeedebaccdecacbdcabecdecebccacbcaacaabdaaacbdbcaeebbbcdeacabeeaddbeacbbebcaececcddadceecedcbbbeecceebedaabeaceeddeaaeadaaabcdbceaddacabbdeaeaceaedbccedbdadeabcdeaddadaaddbedecaadeabebedeeeadeccbacbecacabcbedbbbecdceaceddedbabdbccaabadceacbcdacbacebabcdcbebcdbccbeaeabdbaaeceebedaabcdebccdbcbebcaaceeadeeadcebebdddebaddebdecaccdedabadacceaeebeacbeebbbdeaeccdecceadcdaceacdccebaebdacacaeeeaceaababddaebadbcedebaccbdbdccdddeaaedadabbadeebaadbdecbbaaaaeaeebededbecbdbabdcadeaecdbabbbbbddcebcbeccbbabeedacadebcbcaebceabbaedeedbabaadebdeaddeeaaaeecdaedbacddcbcbddaebbaebdaabcdbdaeecacadbbbaebeebeddbbcecbcedcdedbcdbacdaddedebbabbbdeddcbbcbddecbddcbbebcbbbbeceaccbdeaabcacaaadbcaaeacbecaadcebecbbbbbeceaccdbeacbbddbdaecedbacaabbeabaabdbcddacabbabacbddcabcceeabaedceedaaddbcbaaaabeacacdeebabceddedcabbabbcacebbcdacbadaeaeebccdecbdddbeecbabcdbbedddcdebddadcbadaddcdccebaccbaaeaaaeebdceaaabddbbbdedceccbbcbaaeecaaeecabdedaabadacccaedebabcdaaccddbeebdddadecbcedaebcdbaccbbdabddcbeeecbcabcaeeeabdbacbabeadaabecdaccaaabeaedeeadceaaacebdcdeaedbdbeeeadaabdacccdbdaeeadadeeccccacbcbadbebbceecdaddaabbbddabcdebbaadacebbaadeaaeeceadbbaaeebcdeabcbdacdbecdbbaceceeeaababaecbceaddabbcadecedcdcdccdeadedecbcddbecaeebeadcebcccacedcacaebaecececcbadebcdaebbeecdadaeadaeeaadeaeeeceebdabdccaaaeeedabcedceccddbcbdaebeaeabebddbbcabedcabcaccbaabddddacadecbdedaddbdccbadabadedacdcabbabaacbacbeadcccadadceabddbccceaecccdcdaeddcccdaacbbccdbaaddeebadcaecaedbabaabbcdeabddddedeabdabdacabbdedbbbdabeebcdcbcdaceebeddcaacbbcaabdcdcbabbcdbeeaedbaaadcbaabbbaebbeabebcedeaeabbdecedbbcbdcabaaecdbedbaabacdadabebbcceecccebaedebddabdebbeaaadecadbcaccccbbbcbbebebcebebbbbaebeaeaddaceaacdcadcbccccadacabbaecdcceedcbeebaaaadcaedbdddcaaecccaecbdbbcdbddaacbacbbabaaedbedcbdcdabaebccdccdbcacdcbaadebadcbbeabacbaeaacbdadeadebbccebeaeadbebdcdcbebadaaeeccbbbbdccceaecbcaeabebcacecceadcccdadcecbbdcebeaaccbbcabbbdedbacbdaaccdeccbbbcebeaddcbdcbeeeeeaadcaaeaecdacacdeeeaedcdecebbcbaccaaceabeacadacedeecbaccedddabecaabdcabeddbbbcacaccabeedcbadeecaebbbeacaeaacebcbdddeddeecababceedaeaedeaeaecaabcbceaaecccccbbbeaadabebebccecacbbdacbbbeedbaaeeadaadacdaedcacdbaabddbdcdeaaaaeaccbbcdbeecbaecaaeeaccdbdceaaadecedbadabceacbdbcbbceabaddcedabadddddbccbbddebeeededaceddabdeacbdeaeeddbcabbddaaecbbbeedcdebdcaaccabdddaddccbeaccecdbbeccdebdadaaacbbdeeeedbcaccdccacaacbeccceceddaedebacacedbdbdbdcdbddaeaadecdaeeeedacdeeedaddaeedccbbcabdbeeaaebcdbbdbbeeadcdedbaaeddaedcabaeceecbaecbdbcccbaccceabcaacccebccbdcacbadbaaaddebcbbdecaaaeeedbeaddaedecddbeaddbebdbdbbabdabcbcedcecabeeebcbeadbabbcbbdecdbdaeaabbdcbdacaabacdbeaabceeddabdecebbcacbababdceadadaceebdcbdeaccabdeaadeaccdcccaccdedeacbdeeadeecedebbbcbcaaabdeebabadaaeacbabbcbbeaceaececbcccedabdebbbcdabeccdececdadecaeebbadcbeceabccbbecdeedeedbedacbdeebdcadbecaeddbcdeaedbddbbbcdddbdeacedabecbeecdaaddbabeeeadeebbdabaadabbddddbbaecceddaadccdaabbbdeeebccdecdbdddcdeddaeceddcaaeedcbbcbadabebbcdeecaacddbdaeddabaedcdeacceaddcadccabddbcbbcedbbcceebcccdcebdaaaaadeededabcdebadedeaedbabaddceeaaeadeceaeadbeeabccedaddcdeeabdcdddccdddbbaeaabdabdeaaeabddebcabdbaaaaebedbdeecaaeadcbeaebedebccceabdddadbeeceaddebabcdaeabdecbbeeeddabbcbadedcdecdbdcbccbcacbeeccdaeadeacacabeababbcbbcecbcedcdcccacbdebecdaceeaaaaccbacbadaeaaccacbedeaaedccdbdacebceaeabdecbcabeeccaaabbeddadedcdddecaadcedbbdbdcdcecdeaacebddddadcdcdbaaeeeecbabaddcabdeceececeddacdaeadddeedcedcadbbaeacdaebdcccceeecbbceeabeebebecbeaadaeebadcadeebadacdbaeabacbbbdeceebadbbcdebbcbddcaaaacadcdbddaaeeddcdaebebcabcacbacbeedccbdbbcbadeccbabcccdaecbcaaaecedebcdcdebdddeadcdaaebdaecedeeadcbaaedaebabaaeeceebcbbddbdbaeebccbabbccdeadccdccbaceacaecaececceaaebedebacdcdaeddcddebbbaeaecbaeeeeecaaadaebdeccaccedbaabcbcbeccecbdcebaaddbaabaaccabdedddabecaaeccdedcadeedaeccbbccabcdeededcebccdbceadecaebedcccdeaeabbaccbacaddbcdbccaecbaeccdaeecaeaccecdbbbeebbcededaeddaddaedcdbcecbbecbeaadebbdaecaeedaedceecdabcedadccbdcdcecddaeeaacadcbcbacecaccaccdcccdbedadadacabcceceadcbdbbdcdaadccbcddcbdacaeddadddbbcceeecddbebdbdabedbbacebddcbccbdeeedabcdebdcbdeadcadbadbbcaccddbdceadaecdaaabcdbbdebacacbeaacdbbbcbeadaabecddcadbbbbcdbbacccacceeebbedaecdcbaeddeddeceebaccaedcdaaadbcedbaadecbbcdeceaeaacbdadeacbaccebdeacbbccdbcddacbacaaedebbaeaecdceecdcaedbbcceedebebabecaaebdcbaedebcedccdcdedcaabdccaacadbbedacceabacebbdbdbadaacadbedbcacacaabdbbdbdaccbccdeacbbbdbabbadaadcdbbbedbcaacddbdcbaeabeaabdccadcdbabdeaaceeeceeaceebaecaecceaddcbeceadccabececaecbebcbdedddddbcaebaedecdbbddbeadccecabbdbdeebedcddcbacbeeadeeeaccdceeaccbdadcabbbcadedeacbceaabbaeddeddaceecdddebbaacacaeccebaadabeeccebddcdcbadeabedaebbedbbdcdeadaedcdcdcbcdaedecdeeeebbeaccabadbcadecbeebbadacdbeadbcdbbadbcdcbbadacebebceceabeccbbdbebcacaddccaeaeddbebdbcbaeeeedcdadbdcbcdbedceaecacdcdecccaaabdcccaeaddecaccddeddcaabdcbecbaedaeecbeabaeccdaacbcdbeaaeaebdedaeecebbeaceeebeaddcbdbdbcddbcabeedccacebeabaeaaeeeadcabaacdedabeebeddbacaaccebdacdacdcccaddbdcbcecbdddbeaceeedeeceeedcdaddacedabcddcbcddaecadcddbddeedcdcdacbaebebebdbbacccbeeaaebdbeabbddccbcbeeababbeaacadaccabaeadaaecdcdbdbabedaceadabadaaededaebbaecdbcaeacaebadeabeaaedceaddabdadcedeecebacddddeeebacbceeeddcabbdcececbdaaeabbdbbaccceddecbaaaeedbabcebabaebdceebcbddaadcdeeddadabaeaabdbaacccedebeeeaeebdcaedaaadccdabebeaccdcedebeaeaaadbacbdeebeababaaaeaedebbcacdecadeadedadaccebacbeaeeacdbbddaabdcddbdabcbbdccaabbecabeedcbdeeacaadbbabdcdaddaceaddcbbeddabaeececbbdaacbeaaacddbcabaddbcddcacdcedbbcabecdacaddcdaadeabcddbbbededabeaccebbececaabcbaccacedaaecedabbdcbeebdaecedbacdabacadabbbcecbaabeeccaccbaedcadaabbdceaabdbdaabbccdbadedbabebaaeaaacddeadaebecdeecacbdebdebcaabddccabedcbecedaaacbbdaccdeaeabdebdabdcddeabedadcacaeabdeebbedaadbdcaecddbcaccaaaaaedebbcedaddaaaccddddecbceaedbddacceeaeabbdabdcbeababbaeebaaebcbbceaabeccebdcaddaaccbdceecebccbaedeaaedededceaadbaaddebbbcccccaabcaeccadcabbbbbbeaaacaeddcabacabcebdddaeebeddacabcdebdadacdeaaecdbcccaabceaccdaaabebeecdbebcbebeaebabdcbeeacbcbedebdabbedaeddcacbecbecdbeadedabeddbaeabddabaecebaebaabacccedabccdeedbbdeeabebdbbcdcbeebccbbadabacaabbdbceeebeaadcdabaeabeeecaaaccebbedecebbdeeabbceaecdbdaddddcabedbedabecdecddbbdeaebeaeebacbabbbaebbbccceabedebdacdceedddabeeddacccecbadcbbadeebbcddcdebcdeaecaebebbacedcdaeedabeeedcdbcbeebccccbbcdceebdeddedaeccaeddcabaeacecceaaccadbecbbbbeadacdbdaebbdeabaacaabecdbccbcdeaacabccecbccdabaacbcaeaaedbbcddcaadeaebcdbcecdcedddcbbeaebeddcedddddceadaabaccdeadaeedcbddbedeeaeddaacdeaababaccbdebabbaedcdccdcacbebacdcccbcccedbaecdcbbadeceeeceadaebbeebaccdcaebaaecddbbdecebebdebddaddcabbacadaaabdbdcebcecdcbbdcebeaebdbdbeedeedaecdcdbcddcaceeeadadabeaaebaabbbcdbbaeaabcbadddbadceabcbccacacdbddcebcccabbcbeabbeedcdbcbabddcaeacdeaeabcbbbadcecaeebcdabbcabbddececddaceedddaeaabcdcbbdaebecacaabbbcbccbcbcaeeeeabecdccbdcedddcedeeceebabaaebbeaedebbccaeaaceeebcabbdeecddebedbcdaaaaabaabbdbbbadeaeeaeeedeceeabcabccadaccdaaaacbebbccceababbdbaacbceecbbecaaaaadedbcccbbabeeabdbedbdcbbdaaacbabdbcaddbbcbeaacadcabcdcaecbdcdcacdcdeabbbaaaaadebbbddaaecbcdaccadccddcabccdabcaedbbdaeeadaeccecadedaeebdbedbdcabacbeaceabbddcacebcedadbabacdbbcaceabbeebdcebceaebadabeedeccdebddceebaedccbecceabcebdcbbdcebccacaebadbbadaedeeceedabebabbcbaadcbaededccdbdcaceabbeccaaceaebababbdddccbbebbbcccebedecbdecaedbddacabcebcddaaebbdbeedaaebbdceedcecdcabccbdceceabdedbeaeeebdbdaceedebaceadccddcaaddadadaeeeaceededecccbcacaeadcabbeaceecbacdcabbbbddcabedbabbdaecedbadcdaecbaedbdbecebebdcdedadccdeaadccdcabbccebebdcebecebebebcbdecebcbcdceedcdeccdecaaccedddbcdabbababccdeccbacebbccdecdacdbbcebdbccaecdccbecadeceaaeaddcbcdaabedadaacbdaacbdaecbedcdaacbecaeeaedcebbcbadaeaebabbdabcdbadceedacecebcbedeceabdaccaebbaaaededbaedaadecceaeaaabddbdbacdaabaadcddeaadcbaaccbbeeeeedacbbebacdaeecdebeaccaedcccabeccbddcceaccecdeccbaebbdbccecabbbcadebebbdadcadaaacbaceebebcdddcceccceeadbcdbbbdebedcaaaeaaeaebddccececcdbbdceeebcbaedeceaaeeecbcacbeddbcebdddcbadceebabedacbaabaddcaebabbcbbaecaabbbaaacecbbaeecaaedecdabddaceebdbccbdedebbbabdcbeeabeddbeebaadadcddddaecabeedabcdbeeccebeccdebaaaeedabeaecaeadbcaaaedeaaebbbecacbecceadaaabebaaddbabdaebcedadcddbdeebdcacdbacdedaeecaeccccaedeaedddedccdbdadbaadbdcacabaadaddcabeccebdbccadaacdbcddcdccedaeceeeadbaaedeeaedbbdbdadaeeadeceabdebdcbcbdeeddcadeeddbabdaedddaceacbddaaabadbeaeeadbbbcdbcdcedecaaeecccaaceceaddbbcbebbdcdbdceacbbccecaaebccedddbedeebcbaaaddaacceaabbeababeacadbceacbdbbebaedeeddbadbabebadccbeddcbccbabbeccbceaceadeaedbbabbbeebebccdaeaddcdeedbebbddeaaacdbdacdccdcadbedcbbadeeeeeeebccbbebebabeadeaaceeedbacaebcbadddbaaabaadaeadedddcbaeeaeeaaedcdcbecbddcbedaecaeaaecddeccdcdadcadebdadedadecadebbebcbeaacecbdeababeddbdebbcacbbceeddbeaabacbbabdbecddbbcacdbbcabedeebeadcabecdaecdbddebeeeeedaaeeecceacabcdbcadddaeabaabcbcbdabdacedceecacaeebdbddabaeaabbbabaedeebdacbaaadeedeaaddbbdcdcabbbebbbaabaeccceccbcdaadeedbeaaaceedbdcbadbecdbbdeabdbacbaaeebdaaabebceabbdebdcabcbcccedcabecbcedddbdecacabdcaabacaedabadabeccdcdbabddecbdedabdecabbeedececeaddccbdceebdecbccdeebbacadbbdeabcbdccdbeedebcaddaedcdcaecbeccebedaaccccadbcbdbbdbaabcddcbdeedeeeaabcbedecdebdcddadebcaaddbeddbcbbdbaebcaaadebdebbdaeceeebeededbbdddcedcedbabedecccedecddaddabacbebaccddeacabedecbdbbcbcbbdeaacacbcdbaebbdedebcabccbaebdddedccbeeecacebbcbbaaedcadcbeeccaccdcbcabaccddebebdebccbecbcabbabeeaedeabebbcdddcedabbbbcaaebdbabdccedeedbebccadbedcceebbbcaaebebdedeceedeeebaeabbdacdbbaaaaacedbedccddadeabaabdbcdbabbeacbeccbcdbbbccddceaedddaaddeceeeebcbabaedbebbabcbcecacdacbdedcddbcdccbebbeecabececabddeacedddbeaddbbccaeaeeedebdbdcccbeabeedadaaeacdcbeeeabaecbbeabecddadcedadaedacaaddbedebccbabbacceccccdaaacbeaabaabeddccbeaacdceebeaaaacddceecdbbbbabcaebeebcbaaacbbaacaccdebccabdadbecbeacccdbedceedbddeeadacaaeaeebccebebccbbedceccbcccacbdabebaceecbcabdbeedcdbadabdbabdcaeebbadeaaaacbebceeacddcedebbeacbedaeacbaeaaddcccccbcdbdbbbecdcdbacaededecaecdbcbbedbeededeeedeceedeebbeedebbccaeebbbaebbdabdbeedaeadbbbaaabebeebdbcbdcdccebbecaedddecedccbcaeeabcbaaabababeeaeeaeeabaeabceddaaeeacdeadbebdecbdbbbadccbdcdeebaeddcbcdbeacaabddbcebbeeeabdebbbadbbdcccceacbeaccbbaddcebacabaaeaedbebbadabeddbdbdddbcbebdcabdbcaadcbcbbdadcedabeadacddebaccacaaecdaddccdaeacadabcadacbcaeaadbdbeeedcddbbaceacdcdcccbebdbddeaddacbdcadcdbbebbaecabcceedddcddaedcdbbaebcdaecdabeaecdbaeddebbedcaedaaeabbbabeedceccbcecccabeabbbbcbbdeccaacabccadecaebdecadcdddeedabeeccabdbcbcbbabbbbbecbeacadaceaeeebaabbcdabcedceebcbebcdbcccadbcdadadbdeddbddaeebeaabbaddbdedadececbacdeddcbdececeaabedcaebbcdeeccccbbabadddebcceccabccceadaadaddecaadacaebbddebbbecaeddadcaacaadcacddabbbcadacbdcdaadbbaebedbdbcbdbeadacddbceececeeccdecbaedbabadacebdbcdedbceccdecccaddcbbacbbccedaaddbeedddceeacbebbddeeeddaacdddcedccbcceccecabebddadbecbdaaebdecabdbdbeeecbeebbeddeccdbceebdcbcadeacbdcdcbdeedacbbdecdbbabdddbdddbeeaecddebceecbcaeaaceddeccdeeaeebeadbadcacaebcaeeebdceddabeabdaabdbcddddeddddddacbdcebdeaeeaaaaedbcbaacecbebbecdcdebacbeceaeadadbedcbbccdbdbeebbdbddbeecbedcceedbacbdadcadbceacbbdbbbeacadeeebdaeebdcbdcdceeebccccaaddaebeccecbecadccaddcdccbecddcecedbcebbcbbbbacabadeeabdcdaebccaaaeeecdbcedcdadbadcdceecebccbebbeeedbaabbdbbdebdcaacdeceaedbcddaecbeaebcbcecaebcecaedecaeaeccdbbccecebbdbaedcedcaedecedddaeeddcbebaecbdabdeceaddeaaeaaeaddbcdcaecbdeaebddecdceaaccceccdeabcacacdceadddebcabcecedbceaabdcdddcebaeadcaacbebdababcddcbaccedbbddcdbccaaadaabdebeadedadadbbdadaacbbdcbacaaababadbeeeeadbcdbacaccebbedeeedcbabaecbddcacadebaeabccebebccaeeaabbaaebededeebeabcdcdeacdcbbdddaeceebcabcbcdedceeeaeabedbaadbbdeadeedabcabcbccabdbacebadcbbcbbdadecbcebbbecdaedcebcaacabdaabddcecbdcccddbadbbabdcecdabcedecadbecedeebcbacabddbecbbacabcdbeccbaecaebdeeabcbeeaeebdcaeccecbddaecdabdbaedcaeceaaeadadeabeaadcadcbaebdcdceacbeddeabdaadbbbaeccedeebbcaadacbccadbeedccbdcbaedceaccbcbcaaeeabcaaeacbbdecceceeaaeacacacdbecbebccbaecacabdaddadbdaedabdbadadcbbebcacabbebeeebcbeecbbaeebcccccdcaceaabdacdbcdddccedbaccbecdaeedcbeddddaeddcdbdddadbbdddebbbdedcdbdadddaadabcceacedcebdcdaaeadddceedbcceabadcbeddcbebadecaaddecaacebdadaaececcaeeaaceebbaeaabebbbebbcaeadcbdabcebededdedebbdebaeeddeccddcbddeaaeebcddcaacebdcdceabdcebcdaccadebcabedaedaecbabeabadccedabecaedbcaaedaabdcebcaadbbcebaeccaeccbeacbddeaeedebabeccebacabcadaceeadceaabcdacbdbbedcddcbbabcbddeeabddbcebdceceaaaabaacecbbcdcdbebbbcebeaddcdedcdddbcadbcdbaaebddaddbcadedccdaddbdabebcdcdeaeebedcedaadeecddddbbcacdececbebeabccdaeecceddddeccddeceaebeecbbdaebddcbacdabccddcbcbdbdedeabeddaeabebcaebddddeadadbdbeebedceacecceadbbeeedecebcecbdeadeccaeadbbbceddebbdecadbabebbacbaccdaacadaeeebcccedeaeababdbddbededbddacabeaeaebcacabedecaaeeeeceebcacbcebcdaedeadcbabecadacbbcbdaeebdeeceddeadcddbbaadbcabeccaaaceddcadcbbcbeebedbaedebedbecbacabbbcbdcdbbaeebaedbcceabeaacccedbeacdadadddaedddebcdedcdaccbabeadbcccaaaaceaecaaaddbbcadcabedeccdcaebacaddaeaadbebdcdcedeccadbccbccdcdbebadcecccbcccabcadeecdaaccaedbbbddcddcddeeccabdaadccaecebeaecbbeeeadabebcebbeddedccbdadeebdddaecadcbadbbbbacddbcaaceedaacbbdabaceaacacedeabaaabddbbcaaadabaaaaecbdaceeececadaceaeceedadaeedebebedaebdcbaacedeabbdcaeaacaeaddbdedddcaedccebebcdabdadbebdbaaccdeacdeacaddeaebaacebaeeaacdeccdbdbbeceaacdcceacdedcabcacddaacddeaeabdbedceaeaeadeedbebececdcddaecaddebddeaabcadaedbbccddabbbcdcecaddaddadcaceaedcbcbcbcbeabbabbebebeaecbeaceeaeaeabbcdccaacadaeeaeceeacaeaebbecbdddbedbbbabbceaaeabdcbacbdebadcddbaecaeebcddaedeadadcceeebdcbaeddaccacbeddbbecaadeceebbaeadcceecdbaeedbcaecbebabbcbbccdacadbdaedecbbcdaadaadcccdebdcdacecebecebaaebddbaaddbeedbabeddedcbedcdccabadcecdedddeceadeeaddddedbaaaebdcbdbededbedbdbbadddaedbecbcbabcbebebcdbcaceaeebbbdbbaeaaddadabadbbaadebdaeeebaeececacedddeaddbdeebdcabbdcbbddddadeadaebcbabbaadaedbeaccebbedeaebdcbccdcbbcaecaceccdebdbdbdadceedccadaeabeedeccdcecacdeecddecbdddbedadedbeeabaeaaedadadadbdccbcbadabceeeabdcececcdddaeebcbedbccbbbaedabeadaecddcaedeebabeecdbaabeedaccddbeabacaeceaeeacbeebbadecaedcbdacbbaddecbddbbedaddeeaceaaedbcbaaeeaeabdbedbdcdeabbbebdbaebaceabeabeecdedeaadaaaaececedbcecacbeaaeaeceaabceeaeeabadaddbeeebcabbbdbdbdecccabbedaaacdeaaaddacbacbeddcceaaabcaecaabbdacababdedbcbeccbcddbbbabcbdcaadcabbcbbebbecacbbabadedbdeedbdecbcececebdceebdadcaaedcabcacbdbdeeddbdcbebbeeddeeddcbabbbceebbcdbaedceacbcbceeeacbbcecadddadcbbceecaadbdedaeebbcdddaedebbedacdbcbaacabadabbdbedebaeddbddcaeeeaadcbcaaedeaedcdeebdeadaeabadabdbaaaebcacedeecdbecdeceaeabcceecabeadaebcececaccddceeddabecceeabeddacccdedeedeebcbaddcdceacdcbbdcebaacdceaeebebedaabadecbecebdebccbceabaddecdadecaabeaddcebaddcddaabedbedaeeedebcbdececedabecbebdeecadddcdebebdbcbadcddacddbbdbdaadbeeaadadbceadaaeeaccaadcecececbeaaeecedbadbbcceaeebebcbdbbdeeceeadccaedbdabceeabbaccdbdcbbdecdbdadbabdeeddaacadeabaeaabdbdecbeacecccbebddabeacebaabddbecddbecaacbceaaacacaaecddaeebcdaabcdecaadebccccdacaacaddbecccabbdceecadeababceaebaddcceddecdcedebdbebaeccaeadcebceddcbdcbedbaadaedadaccadeaeaaacddedddbbdabedeaeedaecbdddabbaeaabcebacdcccbaaddecedaadcaadabcabebddbcbceeebaebbdbeccaacddbddbcaeadebacabadbccaccaceaeadaabbdebbdbaeadedeebceacdbcdcbdcdbeedabcbaecaadddccaccdebecacbdabacabccbedcaddacbeaacedcbdbdbeaeccadddaccdcccabadcbabbebbddaedaeaacadceaedcbdcdbdcbaaebedabbdceacbcaeaeaccbaabdacbcbdbbacadecaaddcbaadbaaaccddacdbcecbdcdcaacdcdadbebcdacccdaeaaccdeaaecbedcacadaaccbdaecccaaabaaadeebedbabeeedaebeaeaaecaedbcdaedadcccceddaaaecbbdaabddecdbddbddeedbcdcdebedcebbedaceecabebbeceaabddbeeeebbaeeedabaeddcddddbedeecadedeedecedbbeccdbeaebeceecdadebecddcacbccbedeadebdabbacdeeeaaacbecadeeeaeacbcbdbcaeceddccabbbaaacaaddbdadbeaebeabcdcdbacbcddeeabdadeceeebdeccbacacdbabaeedcddcaadaabeabdbaabdeadebbeccabcecdbbdbbeaccadddbccbbcbdeaeebeebbadbbbccceecdeaedeacadabeaeaeabcbacbdcedabecadedcccbcbccaabecaabadadadddbcabeaeebedbbdaceacacadadbacdacdebbeebdccccaacbbeacbabbdaaddeceaaeccbacebebadcbbdaecabbcabdbabbcbbbdaebdccdcbdccdbbeddbacadceddecddacadcdcaaaacdddadaeaadccaacedceeaebabaecabacaaeadabbcbaecacabcaaaebacdedccadeecadeddedbadbcecedbbbeaeedaabddccdccadbabacdecbeabdeecabccaecaadebaaddbaebccadacebceabcccdcdabeabeebbbdcbbdadeaebcacbecdbceebeacceddcebaabaaaebdecbeeaddeccedbaadbaddedabadccaceacbebcebcbeeebbbebcbdabaecaeebebccbdbbededbeceecebddbdbdaeebedeaceececeacedbbbcdcdedeacbccadadadebabdcceacceaabcccdaabacaadbdabccdeaabbcedcbbbababaaadbceaaebbcacbedbabaeadacaeedecddcaceccaadecaaadccdecadaadddddedcbbcbcedbaecbbbcceeccdcebbecaaeceacdedcecaeebebacbdaedcdeceddbbbbedcdaaaeacccbcdcceadbeedcbcedececdeebdaeecbececdaebebddbcdcdeecccdcdeadbaeecbddbdaeaeadebbedebadbaededaeebccbcdddeebaaeddccadedcbbedeceababcbcbeeccdabebaeedeaaebebbbedaaeacceadbcccccbaacedbcccadcbabbddebccebadeeaaeccaceacceebabedeadabbdabecbaadabbaaeaebaeeaeccbdbccdcebecaeecacddabdddcedeabbeddccddecadeacaaeeeabddaaaebccbadedbbaadbddbaebecdaeeabedabbabededcccbbdcedcebeaebdbadbabaeaddcebeabbcdcbcaccdddcaedbdacabcaacdccceeaccdbccceacccdbdbbdbbdaadcdbebecacaebcaacceddcdcbaddaddaddddbcbbcedddbdeadbbddbdeedacdedcabbeacddebdadebeadacdeecebaecacabceeacaadabcdaabbbcbaaccdbacbebcdddadceaeaabadbcacacaeddabbceaecabaadeeeaacccadcebdadcbdbaebbaaebeddacabccebabbcaaacdeebbeceaebbedaaecccadebcbbeadcaededceabbaadadcdeceddaabdcbecdecbddecedecbedbecedeabdecaecccbcaadeedaddebdeadadcecaccebbddeddadebbaebbddbaeaaaeababcacdebbdcceacbeeacabbbadeabbabaaecbcbdcccdbdceebbdccdebbeacbdddcaeabcebdbbdaaddbacbdaeccdbdcbddaeedcccddcaabdeacaeadeccabcebbbccbeddecdedabeaeabaacccceecaebdabeabdedbdbcbbdbaadacedbbeeaceecccdcdaaecdccabbccbeabeedbdeebcbeeadbdedaabcecaecbeebbdccadaecbbeaedceaabccdadcddbcdbcdbdedaddbadcacecbdcbdadbdadbebedddbabbbeddbddbececaeacadadadbeabecbaabecbdcaaaedaccdeedadaeabaeaaeeeeedadecadbabdcebbacaaebcbdcbecdaeecddddacbababedbbeceebbbeeaeabedebbaaedcadabadcedcdeccaceaaceecbdedbdeeebdadbecdbceecccdeacadbeedcacacbccebebaddacebdbdddcaceadebecbcaddedbbeaeeabbadadeaccbaadaceaabecebeaaaddbeacbddadabaeadebeabdcbbaaaaddeeebaecabbabbcdbebdbacbabcbddcedeacbcbecbdaddacecbebcbedadddbacdeddaaecdbcdaaddbceecdeeecdbadbdcabccbbebcabcdccdcbcdaababdaaebdebdedaaddbddecadbdecedccbeddabeeaaccaabdadcbbaeceecdbeabdcccbbcbcdddaedaeecdaebcdbadededbacdcaedbcdccaeaadadedbabeccdccbdaedccbabbbadecaacadddbcdeabeaaacdaddadecaeadadcaacecdcecbcdadebbadcbdedeadadbabbebaddceacaabababbdbedbeccaebcebcbcbedeacebdadbabaaadbeccbbcbbeabdeabeacbacdadbcabeabdcdcaeacabccdcadadbabdbeadeeeeeacaedbbebaadeaabdabdcaeecabaddebbcadeeeaebacdcacbeedeeddaecbbcdbbccdbbaaeabaabacedeeaebddabaabbeaeabdedeaaccaadaceedcbaaebdddaeeeadcbbcebedcbbedeceedcccdbececcacaeeacbccdcacaeacdddcccbabbdbedddcdcdbdcdddcbadedaaccddeebbcadcaadbcacaedeebbcdbceecdbcdaebceeeabeeaabaacceebedabbbbeeebadbedeebecabecebbabeadbaeceadedbbeacbbbdaebbbbddabbbcbbbbdcbbaeadbabeceeeebadcbebdebaadaeadaedbbeccebaedcaeadebdebeadbcaececcadebedbbcddaeaaccdebaaaedaccdbabcdcbcbdbdbcdddabbababeccbbabedecabababdddacacbeacaabebdbaebeaadecdcdeecdeacaecbcededceeaeebadaacaeecbeadadcbebaeedcebabcabdaadcaebacccebbedeeebccbdbbacbeecddcddebabcbddbdedcddbedcbddeeecbcabdadecbdecaabbeecabaeeddcdedcaeebceccceeaceedbcecccbcdaecdbbbdeebaecabcaeedcabbdebabdccecddceeabebbadcdaeeeebebdddceadbbddbebaebcceeabdceedcedaeabaceaeceaddeecbebbbbeaaabbebddcbbbdbaaedddedeabebbdcbddcacdaeccaccababaaaceebbdbcadbbcbacedbecdaabdddeadbdabdedccbdeabbbbdeebdabeeebdbacdbcddddebadaaeecabeacddeaccbcdeeeebcdecbaaedeecaecacbdadecceedaaacbbaccccdbeceeaeddaaaccdeaceaaeaebeaedcadcababcbcccaeadaecbdaedcaabababcaadaedddaaeddeaebbccabdcadeeeaeedceacaaedbcbbeabbebddbcaecbcbacddbccadadcedceebbedbacbeaacedebbcccbcedeacebeedaeaeabebcabebbababebdcadededeaabccccbaddbeebcceaebaeaeddbebbedaebceacacbdabcacdeecaebdcababadebeddbcdbbbcedcdcacdebdeecadbdeabbbbcdabacbedbbaeabcebbeaeeedabcabceeeaabbcbbaabaabbdaabacdabbbabcbdcbcabbacbbcebcabdceeabaedcbdcdedeeedccbababceceadbdedeccdabbddcabbadeddacaadbddbbbadececdbbedeedaedadbaccaaaabacaaeeeabdcebdadcdcadacaacedabccedacedceaebbdcebdcabdbaacaeacbcecdcadcebdddcecaadecbeceeedcabbeedacccecdcdeaabbcaabcbaaabeabaeedbbedceeacbaadbeeaddaabcdebabbaceaeeeabdceeceedddcbaaccbdeaaebaebeeaabeacecedaeccbedadaaceaabacdaaadecdaabedebbcaeeaaaeadacdeaeceabdeccaadbadccaddaccadabecedeeaaddadaaebabbbdbccacdacaccddbaeeebbdeceaedddcdddccbdeedacbccabbbbcbdcbbebeacdceebaadaebbdcaeedaecdeceabdbdbcadccdaeecbeacddadddebbabdddeddceedbdadcdbceadabeddbaacaceaaabcacadbacbdaeaddcddebbddeddccbeedbcdadebeadcceeabbdabdacbcdbedeeadbecaddcdeacaebbebeadeaebcdeccdaccdcbccceecdccacbeeddebdeaacceeeebcdcadbeebbeacbeeaccaceeaeccaedebdebceccbbdbabeeeebeaebeeaecbcdaddbaddccddecdabdbddbcccaccecccbadadadecdcabeebbccecebdbdadddedcbddbdbcbaeeadeebbbdaadebaecdcceabddabeadbdadbaaddbaaeededebeccabbcabeebbaadeedaddddeecabaabadccaccbacaeaccaedbabccdbdcddedebaddebaabaaccdacadecacadabbaabceecaabbdbabecddeebdadcabcbdaeccdebadbbaddaadcdcbcbadedbccaaddacaaeeadebedbddceabbedbabedbcadaaccabbcbddceaeedebeabecaeeeeacdcecaadaeebedaaeddaecaebbdbaabaeceeaddedbeeadeedecdbdecbbcaeedabeeeaeabdebaeebdaebbcaeedaeaaadbbeadcadacabcadbdbecddacccdbedacddabbedaabeeaaddecdadaaeedaecaaaeedaebbabaedbcbbeebaacdccacbecadeeecebabcacbbdbaacadecaeaddebdbeeacdceccecbcbceeeebdbbaaceadbcacbadbeeccbbcbdbccbbeacbabcaceaddeddbadcdeeabdadcbcabbebeabeaddebdcebccbebccbaaadcbedcdbeeceedaceabeecdecaadceddedbabebbedaeeecddaedccaedeaccecdedeadaeedececcaebcadbbcaedbcdedaebcbecadcdceccdccceecbbeaeeeaecadcdbeaddcccdadbbcddbbecaaabdbedeadddcaedebbaccbeadedaeaadacdaecadbdeadedeaaeecbecabcaeebbeabebcabadcaecbcbaacaeeeecbcecadabadadadbdeacdcdddedccacbcabacdecdaeeceaebeabeedeebaeacaccbcecdecbcabbdadacbdabdecaedccdabbabedaebcdbaecdedecbdcddeedeabdcbbedeacacccdbdaadaacbaedaebdabecdebbbdedecbeccaacbccdceadcdcadedccacbedbcaccbecacabeadadeadbdcbabedddccaececebdebbdccebcddaeddaceedebeedcdcebdeaabbdcbedecdabdaedbaadadddbebeadbbebdddeaabeecccbadceeacbddccdeaacadbdeabdbbaeccabaebcaeeadabbaceebebeecdacabcabbedbbdacaebceedabaeccebdbdbddaaccbaabcbaaccdcbeacccecbbbcedbaaaecdcbbbddbbbadaaacacbccabbdbacedadbedbeadeaddbaaededebddddddbcdbbaaeebaedccbbdcecbcecaccaaceecdddeabbdecbaeaedcdddddcceddbcabeaddeadccdceabebaadadbbddedaddccebadbacbcbdcbaccdadedccdcddcedceadcbadcbadbaebcaddcaddbbaacbedaccebbbaeedbbcaabddcdddcdeaddacddbbabeececeadaceedbeebcaecdaccacaecceebaccaccbbebaeaeaaedcedddbbcabeccbccbbeaceadebcdedededcddeaaaecadaaaeecabbeaaedaceddbbcccbebdecdbdabeeabecadbbeccbdabbddbacbabbbddbdcaeabcebdaedbdcceedcbaecbeeceeadcabcacbeaaaccaadcbdacddcabaceabbdcdddcacaabaebeabedebccdcbbcbcbbaebccecbedabcebcbaacbbadebebbaacabecbdceacebadebaedbdbdccbdcbdabaebbdeddacacebdbcadacbcecaadcbeebcadbabedeebecddadaccdedbbcbeebeeedebeaceacddbcebbabddadcdbcaaecbccabcaedaedddeebccdeadaacaadacbbbbbabcaeeaedcdeebddcbdbcecdedacdcbdcdaababacacaacbbacecdccacbbaeadbceeebbecaaadacbdcaaacaeadcadaddddcbceededdaacaccaaaddeddccadacdbcbeebabcdbdcdeeeaececacceeaadaabebaebeabaeadcecaeaeeaabeebdbedaecaecdceaedcdbebcccceacccccddbbaeeabeadadebacededccceccedbceddcbccebbaacadbcbacecdaacccdbaddeaeeccccccadddccdbbeecbaeeccadcadeeeeacebcdceeebddbaeacbbccddeeabbedabbaeeedaadebacabedbecbdeecccdbbbbacebbdccbabadaabceeceeceedabccdbaddbcccdbebcadcecebacaeeceddcecdcabeebdcbabedccaacddbebeeecdccaebdddcdeabccaaeaeeaacbcdbdadddeeadabcadddcacdccbdbbabaaeeddcdaacbddddcacedbaddacebbcaccebdabbeedabcccadbeebbabdcadcebccecabcebcdddebcadbacebdbcabdebadececeedcdaadbcceedacdeacadcbbabebccacaaeeadabaecbeabbdabbaceacbebdadeecceeaacdeccdbcaaebcbcabceaddceedbbaaaaacbaeaddcdbaaeeecedbddeeeeaacecaaecdabcaeecbdcbeccbcccdecdcdedcacaaeeadebbaadccaaaeedbebebabcceccbbaeddeeeebddaebbddabdaecbbdbbdeddbacadbedceeeeceebdcacbaaecacabdaecdabeabbeacaecccddababdadeccdbbcaecbaabbedabaedcecadcceabbdbaabbceebdbeecadddcbdecdbbabbdddbeccbeabadecdeacdedadaedbeadcbeeecdbbedaebeceddaccacdaecedbcecadeecdecebddeccdeeccddbedbaeeddcebaecbcbcbaecbdabeabdbcccbecabeceabecbbececaadacbcedcebeaeeaecbabbebdeabadbbeeeecacadadeadccedadeecebddbbedcbcedecbcddbdcadadaeeeedbcadcabbdbbeadbebdbcadcbedbdcdddbccccdabcdbdadbbadccbddaecbedcedbcdccabcbdebedccdeddcbebaaebdaaddccacccececceebdedcaacbebebbdabddbbadaabbbbadadabaadaaddaaadebeacdddbbcbbcaebdaeadedaceecccceadebebdddebcccacbdadddbeadcabdaceeaabcddaeeaeecbdaedbaeeacdeddcbcdcaadbeeeaaacecedeeaeebcceadedecedebaadceedadbcccdaaeedababcedaaebabbebaddadeaadddbdaeaecedeeacdddecadecacbbdbbecabdddcdbaddacadebbbaccbbbceaacdaacadaceadaaddcdcbececbabecebeecbebdccbddeccbdcdcabcecbdeedcdaeccebadccacdccebbdddccccbbbdcaebedebbcdaeededdeaaecaabaaabbaacebcaceccaadbbcdbcbdcddbcaabceaecbceddddbccdababdbdbbaaacdceedebaacaccdacadabeecccaceccaccdcdddedededcccbcbcbebebaeaadedeccadbebbeebdabbacdcddbbbbaebabaeabaaaeccdebddeadcdaeacadddebaeeebcadcebcdaabdbbdbecddcaebbbebaabbeeacdceedaadcbccccceaedbcdbdbadeeacdeacadaebddeaeaddcbeeabcdedbadcaaccbceaabbceecacdedbbedcacdaaeebbaacdbcebcddcaadbdbdbdeaeaadeceddadcdceaeaaadabebeeeeebccccadbacedbadebdbbbaadbdabdbdeccbbbbceebbaebbdcdabdcbcacbbdaaaeecceebeecebacbecaecebcdcddccceaaddcaeedcdcbdebccebeaecdbbbceabdeadcaeaaadebcdcdddceeeceebadaebdeedcbdcdacaadadeacddacdcbdebdccacbceccbebdbabccdcaedcabbccaceebabeeecbbacdbddccbbadeecbccaeacaedbbceaececddeaeebabecbbdcedeaedecbcacdeadaadbbacbacaccacdebcaaecdabcbcbbaeccdaaeebcaadcbdeddddccbaadbbeadeecaacdcccbaedaabecdcbbeaecbdcdcddbbebaaaddacbeadbaedcdddcbaeeabbadcbedddacededebbccabeaeceabdddddcbdebbaadcdcdebdaccdeebdebdcbdcdcbcaeecaaedcdaebebeaeaacaeaacebaabcdddedebcacaaadaebbaabeccdeadbecbeeedbddaeddccbeecadbedaeceaddbeddabdbbacdbecbbcaabbedcdcebcbbcbdedccadddabdbbcedecbbabedbbadebddabdcbbacacdbecbbaaabdbbdebddcdccdeaddbcdebcdacdababaacdbbadadcdadcabdcceacacbaddaabbbddabdaeaadbebecebabcdabcedccecaaabdbebadcebecbcaedbdeedcdcbbabdddcbeaecacedabacabbaeceaeebecabcdbaedcaccecddceadccbecbbcaeacdaddcacdaceebcddcdccdaabadcbddcbeeeaacdcabcddbaeddbabcdcbedcdccbcabadaecbccbeadecddbbebdcdddeeaadaeeabaebbedecdcadecdccbccadacccebdeccceeabdbeccbeacbdcdabeaaccadeacbbaeebcccaaebcacbdcbbeedacacbcdcdceaeeecbdacbdddbeabccdeecbbaebbdebbaaaebcecbaceacaaccaeacbbccdddacaacdaddeadaaabeddeacecadeecceebdeaeaccaebddacceeebdbceecbaaacdabcdaaadcbcbcaadcbaebaccabcbccdddaedbdbeeaaccaacbdedbadcbaeadebeabaceecbaeebbacddabaebaeebceadaaedeabeedcbedbaeedaddbdbdbbdadaaccbbeceabcbaccdbbeedcbeeaadbcecaabbcadccbeaebaecceacebbcdebcbeecbbbaccebdcdebdeddbbcbaccebeacbebbdedecbeebaaccccbeebcddecbddbacceaadbecdedccaaceecceeadedeedbddcdceeedaddbedadcbecceaaacdccaacebceddcabadedccbdcdaddebdcdbdeadbacdbcbdadbcdaacaadceabeeaaeddebaaecbecbbbacbdcbaccaecccaeaddeeabbeccbcbbeebabddbadaeaddeaeecbbbcbccabccdabddcacacbebcdccdcbbcabbadcbdcacceeeceebccebdcdacabaceeceeceebbcbeddaeeabaeaebdeedbcdedeccdeaedecaaceadcdaacdceecbeccddeceaebedbacedaacbeeeeeaeecccdabddabdbabbbbddccdabcdedeaabbbccebabbcaebbeaaccdbcdbcaabbccccecdebdcaaeabceadabbedaaacbeadddaecabaacdbcdccedecceaecaadadedbdaaaebeddbdceebedeecbbdebaeaddaaeebbbcecaacabceeddbedceaeeeacbeedabaebbbbccbbccdecbbaaaedcdbaedceaecacbacadaddeaeecdbbcbaaadacddcaebbedaeaecadeeecbcbbceecdcdcecddaaedbbbebaabececdaadedbceddeaeacbceceaedaadcbbbaddcdccaeaecaaacbbcccabdcbebababdeebabddbebdbdddedbcaaabcdcaeddccccbeececbdbdadbacaedeeaaceddeacdaadcadddabcdbbaedaccebdaddceeeebabbbbddddcadcededaceebbcdbbacbebebecdaeccdadbaedaaceebbbcaebdbcecdadcbabdeccedbdeabaeeeaebaccddbdbabaebccebeadcceeecabdaddeeeebddadbebbdeeeedbbdccdecbaaaadddddcccaceddcaedcdbbacbbeebdeeabcdcedeacaadcdddcededcdeebacdbcdcbeedcbebaedbdedeaabadeddbacddbcecababcecabbcededcaabaccabbdbbcabaeebcddddaedbebeccceccecdaabeceaeacabadbadecdbbbaedcabdcbbebabbcccdeeacbbbcecbabecccdbacabbdcbaacecadddcaecbbabcceaedededecebeccedceabbebcbeebdecddeeebeabebeeddcccdabebaebcbdcedcdeaedcebbaeddacbceddccddbecbcbeaebbaeaccaccbebbcbbaaaccdebeeddaaeccbecbdecababaecacbcedcbacdecceadabaadbdadbddeeacedacacbcceebcbdcaeddbabaabacbcbeecebdabbceebdedbcaacdecdebdbbecaeebebeddecadddeaacdebaadaeeeadbbbcbdeecbabbedbbeadbedacbdeebadcaaddadaacdceadbaabbebdbacaeeeaadeadceeeedeaddeaaddacdebaabbabbcecbdeddcdbeeaeedbbbcaedabacbdabedcdebadebdceabaaddaeeeeccdabaeabcacbecceeaabeedacddcddbbbaaeabbacccaadebccaedaddeedceabbcdcecebebccbaedcbcbbccdeabcabaeecdbabeeeaceaaacabaaaeecbabceedbdabdedeadcbaccbcaabdeeeacabceaccceaccbbbbbcecbddbaaebadaeadcdaeddbabdddbdceaabaebaeeeabdcaddcbedeeaabebcbdbeabdbbdcbbdcdcadeedcecebddcdcebeebaabaddceedeacabcdeeabedeaceacbeebbececececaaecddceebbbabeedcbaadaeccadbecedcdaeacaddadcaecbaeebdbaaadcbdcaeaabdceaedededdaeebadecadccedbcacdddddaaeababdcaaaabbeeaebeabbddbccdbbeccbabdcecabbeceacdcdadededadeaceeeedbadadeaecbaeaccccaabbbcaadcecceecddebdcaabecbbbacaabededbeeadaeaabaeeecaaebaddceceacaeebeecbeebcdeeeeeeebdaedccceccedddadcabcbbdeaebbcebbeddacaacaebdadbddbddbaaabcadcedeabacabbadeecbadeccdeecbaddedbeabdbcbedaaabaeaacaccdaceebdedcadbecdceaaeaadbbdaecdeccaebbecacbeadcbeacaeedccaadbedaaeddabbbccbddebbadaeecbebaecdeeaeeadeaccadbcdabcbdeeddcbaabcadbecadcddebdadeadbccbbecddadbceceaccebbdecdbdebcdaaaebabdaaacceceedcaadabcebcbccacdbbcdddacbccaaaabbacaacdeacbabecacececdeddadaaecbaeaaacaabbeeacabbbddaaaecabaedcabaceaaabcdcbbaacebbccdbbbdcacaacababededecacdbadedecbdbcdaedcadebeeadeedbaeaecbbeccbbccacbbeceaecbcbeabcaedbdaeeddebbedcbccadeaebabdabcedddedeecdbadcedaadcaaeedecebacedcbbeecceaecceaaebccbbeedabcabcbdacadacdbbadcdaecaeecaeaeaacbdbdceaabcaebacdcadbbaddebbeaacbdcbaacadbaeceeceabadacaccdecaeddaaaccbeacedbeeaeedacddabddacdcbacbdeadcddddaeaddcbaddaebdacdebbdeccbbabecdadbeecdecadaeadcacbebeccddeeabbcabbdaeaaedcaaeebeacddbbeaeededacadebbccabeceaacdaebbdadcacbddabceacceddbcbbaeeacddcceccdbacdebecedbbccedaccddcebcedacdcddaceddacabeeeadaccacbadeaedacdabdcbbdecadbdcabddedecbbdeaeaccaabeebbdeecacdbccccaebbbcdaccadbeaccdbebcbbdaccbdecdcbbdeceedcbcdaeedbeedacdbcedbecbadeaaebbcdaeeceeacecbcebdcdceacbebacebddeacccdbccaeeaccddbdccacaacddaccebabbdbabebccdbaadddbddbbeeeaaedeccabebbbabbdeadbdbbdacbdbacebcbdbaaadceeedbdcaebcccdcbaecdbabeccddeceaeeadbdabddcdaebadcbddbbeacebbdbcebbbecbeccaddbcceebeedabbddcbaaddcbaacecabeddddcebebadddaeebbbacccdcdabbbabdadabceacdbeaaacdaacbdcbceaecbdeedbeeedddbddadcdbbedadbdcedaaeceabbdeabccbbceedbcaaecaeeacdadbddeeddecdbeadeccabedebddcacddbbaddddaadcebadacabdeceddcbbacdabadbaadadcdbbcccbeecdceccdebdeeddaecdbdcdaeaeeabecddbbebadaebbeebcbedacbacbebdadbecbdbcdacdbedaeebddcecaeceeabebebebdbccbedcbddbebbddbdecadaceacccbaddeecccbcddaeadacccadeeaebeacbdbbecdeeacbeccacbdeedbbaaaddbeaeeaedcebdbcaacbcbcbbceabeacebbaeddddedecdbcebcacecddebdbeccaaeacaeacbacecbcedaaaccaebcdcdccbcccbbecddcacadbaebbaecbccdcbebeceedccecdeeddebdaedabeedbcebbecbddbedacdcbcebbdbdcbbeecbdaedcadacbedecaccbedacacadcdaeeaadedbadddccebdadccbbdbcaaacbabdadccccabedaeadbaeebdcecbcdaceeacbedebbcbbdaaabaeebcbebeaaeccbabdcedeaebecdeaaecabaacbdbcaadcbdaddeddcdeaadeaccbcbddcdbeddcacdbcbacdebeabbbdcacdbcddecdecccaaaeabcdaadbdcedccebabdcceceeabedebaeabbacbaccdbdccddebbcdcabceeadcedcedcccbadbbbbaedceceededbaaeeecedaedbbcbcdbddbeacbbedcbdaadecdbbbaacdeddadabebabadbacdbabbcccddebbaceabccadaeaeaaeabdddbbabeddeaabdcddeaceebbdeaaceadeecebedebdcceeceacbdbdbcebadaddeebbbaddcdcbacebbbbbeceeeeabbcdbeabdaaaebeccbeabceeabacaeeacbdceceaebeecbcbbeaaecbeecbddbacddbeeaccecccbcceeaedebebcdbdeaaebadeccbdbabeacdcceecbedadcddabdeedcebbeddadcbebccdbecbaadcdbceceececbbeebedabdddaaedddadccacdbeabbabcaceebcbdddaadeceddebbdeeddbbaddeabbbbbabcecdabadadbaeebbdebdebbcabedcebbbbeccdeadaebabdbaeceeeebecadcededcbcadecccdaabebadebeaeaeacebacbaaabceadeaedecabaebedbbbeeeddaabdaaccecdeceebbaadeccceeccababcaeaccaeccddbcbcbdbaeeebaccabaddcaaebadedacddacdceddeceaaccccccbeedadedbccdcacaccaddbebdeccdabdcdedddbbabcededaccdeaadbdecbaddeddecddbeddbbadbbececacbadbbbeabcebecdbbcceaeebedbaeededccecabeabadddecebbecebbaacacbebbcbdcdcaecdccaaaebededdeccdbccddcedbcbcdbcebdeabdcbdadacabdbcdaaeabbcaecccdcdaebceccabcbbdececbaecdeaedbeaadcaebcadccbedceaabdbbcdeabababdccaecdeecbcbccbcbddabdaeaaccaebddacbeccbcdeaddeecbdedddccaddceadbcadcedeeccabeeccbabecbcecaeddeabececdbeaabeeaadcadbdbeddbadababcbebdebccbaddeeeeddcbaabdbececaeeaeacbbbdedcddebecadabccdadadecbcbdbbbcdebaddecbcbbcccedcecccdeccacccadecbbabaacbebbddeacbcdbdbeceeedbccbadaebdcbaaedbeddadbadacccdbacbacbabbcbaeeedcaaeaabdcdaeecadeabdaeccdaeaeabbbdcecdcccbdbbaebacbccedceddcddcacadadeeaaebddccdaeeeedbcbaabaddcddbbbceacadcabcaadababecaaaebebabcbdbccdaeaddaebcecdaecddbbccdadaecceeaceaadbdecdcedbacdbeeecdcdcceecddcdebbcadebeaedcbdcdceedebdbdebcdedcbebaadbcabbebebbbeaebaedbedadeddeceaadbdcccabbedadcebccddcebabbcbbdcdcaaeacccbbacaadbeeaeddedeceadeabbbdaabacedeaeadebbcccaceeeecebabacdaabcbbbaacdebabaeddbddddeceabebcaebbdcbebbeecaeedbbedbcbddcdcbcedeeaeedacebdccaececcaeaccaaaadcdabbeeaeaaabbddcdccdcedddcbaaeabebebeedeaddccdccadabceedbbdabeaabdabadacccbadaecbeacecddaeaaadccbcaccbcaedaabbcbcdcbabddceccceebdaedeadbecdaeaceebdadbdedcdebabdbadcdbcbcdaaccdcceceddcceedaecddbdedccaebaeedaeebaaebdeeaadebbadbbedccacdebbdcecedbdeeaceacadadcbacdbacdeebdecbeadabbacbbbadaaadbaccacacbdedaabeecbbbcaabeceaceddccecadcadabbedeecceebbbcccbebadadcaabbebdcdccddadcadabdcdbeeceedcdbcddecabbeabdeddddbbcacbaaeacdaacebbdaeabdcbcbbeceecccbeccdcacabebdcabbdaaaecabacdcdaeecacdceddaadaedbcbbceabeacbbebcabcaccdacdeecebebbcabdedeaaaacaadedcbecceeeaeebecaabaeeeccacdcdbbeeaeaadeccaecbdabdadacbaaeaaeeabaacdbbdcebacdebaecedddaadabadeaacabacbbcbdeacdcceccddadbadcacbcddeaedcbcebebacecabadcededadcbdcabcdcdaccabdeeaccabadbaedeebbbacecaacdaedcdcbddeececeadbdeceeaeeaeedacaaccadddaadbebcacbbcebacacddbceebddbbdcaeecddbebebcedcbabbaeeeebeddbdebeeddcaaebccccadaacccebaacccaedabcbccceeccadaadbacdbdedecdaacdacbdcaeeebcccedaebadddebbecadbedbabdcadbdaeeebcbeccdadbbbdaacecaaaaebabcdabddaaceedbcdedeeabccbeacadedceaccbadabdadaedbdbaaceeaaebaceebdabceedececacbaecabbbdbdaeeecedccabacaabbdabbaedbedebcedaeecdabcbedccaaaceaccbababbdbcdacccddababadbceeaacaabecdbbcdeabacedccccbbebabdaaeddbcdabcecedaacdbedebaccceddcaaeebdcaeebbaebbbeaedcecceaacedadecedebeedbaecccdebeddebdabdbddddabdbabdbedbbdedaceebeeabcdeecabaddabdbedbabbcdceacdeabdcacdadcceeddbceddaaddbedbaddaadddeeeeecadbdbeccdaeeceadbdebacabbddcdadbdcbacddeddadddbeebeebecbdddccceccaabcceebaeaacecdccbacbcccbacbeeeaaaeabdcbddccedddeedeaadeedabeadeebacbdceaabecaadddcddecdbbdeeaabddbaadabcaebcbbebdadccbbaacaaabdcedeecdccaadbbbadedbcddadbadaaeabacadeccbbaecaeddacdbdeecddaddaeaccecacdaaeccacaceccbcccaaecadeeeabeeebedeaabbebacbceacdbeaeedbeaeebaaecbcddebeccdbeaddcddcbcacbaceaedbbdeaaadeceeeedabccecadadeebcdadaeaebceabedaceceaabaeabddacceecdbbeabbeaccebbbecbdceaabcbeaaeebbabcaedbdadeaccdacadadaabcddcaedebecedebadbcaeadbcaaebaaccabbaeecbdcdcbdebbaddbdbaebacdbbabebbdaacaebaabbacaeabacbeddeabdcaabccabddcececcaaabbcdebbdeabebdcbbeabcadeecaeeadaedaecbcabbdcacadabbceedeaeceedcaadbdbebebccabceaaedbeecacaaccddbecdacbbcbbeddacdebedecaeededacabbbcddcedabacedabecbdaacadcadbaeeebdebacdaadacbdaaacaabdaecddacabaecbdecaadddcecaccceebecadcbbcbdcabdabedacaccbebbbcebdbabeeaadecadceebdbbedcdebacdbaacaacebecadcecccbabbbebaccdabcabcbdbbdabebeeabddbdcacacadceecbbcedcdacebcddcdcaedeaeeeebbbcaacbeabccbdcddedcaedaccedaddbceeedbcdcddbbcdddeeeedaedcaeddecbbddbcebbabdcababeaabaebaaabeeadeadededdaebbccedcbeeadbdadbeddeabadceebbeaabcddccdadbabebcaccbcbeceabaaabacecedddadeddcdabbdedbdbbaaeecbdcacbbabaebeeaacaeecacddbababcbbbaacbebaceaedddbabbdaacdcaaacebbaaabbcbcbaeacdbaddcddaaabaebcacbeaeeacedcabdddbacbaaebecabdedcbeabcdbdcdaceeaebabecbccbbeeaabbebbccaebadbcdddeeeabdebbadedcecaedddcacaabdcbddbddbdddbebacdceecadaedaecadcbbccacccedbecbceaddecabeedeabdeaebebbdeacddccbbdeedcebdaabceeadaacdadbceaadeecebedaabacdacaecdddcccbaadceeacedcdbbcccebacebdccaeaebadbdbdaebcdacbdeeeacedaebdedccadadebebdbdacacdbececaadebaaeeddbdbbecaceccbeeeddbddedcebcedccdbbbeaabedebbdddcedecdacccecacdeaceaededcaeeadebcedbeebacbabaadbbcacebcabdbeabbdeceeadaadcceadbebceaaadbbabdcaaaddadeccebcddbcdcaabbadaeceeccacdedeeccbbaeaddbecaeaddaeecbbcbcecdacaedcedccaabcbadeacebcbdbdbaddaadbeeceeacecaeeebcdcaacbbcdddccbbdaaabcdceeabeeeecebbecdcbbecececaebdddceceacbcdbababdddbcacdeacbcccbceebcbcedcebcadabebcaccebecebbedaccbeadadecdddcabacadcbeccedecbaaeadbabeadbeabdedbabecbebcababeeaadbdadddecabbcbcabbebcabcaeebbedeeecccbebbddbeccdceabaebaaadebcbbadceccbdbcdeebedbdddbbbceeddbbaeddbaeaeeacaeebecdbabcbdbbbbbbbeadbecddabddaaccabcbdbdaadedcaebcdabcdabcbbeabcceaabcceadbdcadbcdcbcabaecccdacdadadeadacddabcbabdacecddaceeedebcceededababddcebbacdcdebcecdcedabaeeedbcbbdedbaccbbeadacaecdecbabedcbbecaabbcccbbeabbcccddbbbdeeeedddcdcacaaadbdadaaadaabaebdececceabdadbacbabdebccdebdddadbecabcacaebaadaaabadedadceaedbbdebbeebaabbbabecabbbaeeacaaebacdcbcdcbcedabddcadabbaacbcdadebadceeadcbbcddaabdeabedaeebcdeeadabcbabdbbdbeecaedcecaeeedbbedaccaeaaebecabcebacbdadedcdbceadaaaccbebcbadbaaadbdeadbbcadcccebcecadbdbacbdedaecbbdccceeecacdabeedcadededecababeaacaebcabdddcedeeecabaeeacceeadabcbbdbdbcdbccceecddeaceaeaccdedcddadeebeaceceaabdcbbbbdabebeebedddecdadebceddabbcdceabceeeadeabebcdccedaedacadcebdebcdabebececebcbbdadcdcddaeedebedddbaadecdebccbbbcaddabababbecbcdacaddccdcacdaaeedeebddeccdbeedbeaacabbacceacdbaababaacaebeceddecaaadeabdecadbdccbbebedcabeecdbadedecbcbaabeaeacebddbeadebddccddcbcceeddccbcceaaaabbabaebeeeabbbaacaecabbadbadbbcedceddacebbccedbcbdbdbaabdaebbebecedbbdcbdaabccccbdacddebdaddcaccaeaeacbbabbeccedaacbacadbbedccbcebbcacbdacedadebdaeeeaacbdaeceaeecacccebdbccccabbcdbdbbdbbacdebdcabcabcbaabeeaecbeaaccdaedcaabaababebaabedceacdbedbeadddaacedcdbeccadcbddaccacacccdceaeaabacbcdabedcaaeacdacbcebeecbeeaaceabccebbaddccccaedbadaedebdceeaecabccbdabaecadaaeabecadcecaddbbbbabdbdaeebbceecddaeaeaaeeedddccbaccdaeacaabbedaadabcbedeaaadeedbdadcbeedabbdbcebbceecaaedbaeecdabbbadceeeecaaecaabcdadaeedcecdbbdbcbdabadcebbedadbcbaedaaccbbccccadcdaebbccbcbbbeedadccdebedeabbebeabdddaaecabcbadcbadddcabebadcddedadaecddedeecabedbeaacccbaadedbaadadbddecbabbddbbbecbcaedacdbbdbaacddcceeacbebebcebacdadddcbdbbdeccddaaabeacbdedadbcdeedbdacceeabebdeecbeedebcdccdadeceacbeacbdbdabbdcaabeecaedadbbbcbbcdbdadceaaaaebaedbbebdbcccbeaddddcdcdbacbaacadbeddabdccadcaeacaacaccbdcecbdedadeebbbadabcddaedbaaebcaacdbecdcbcedcbddeebacacdeacabebcacaeacdcaabdceadaaeaecbdcdeaaaedcbbccbabdbeedaeaaacbacebacbbdadaeeabccbaacacddeeaceabcbaaadedaaeaacaddceebcacddddaebcadabcbaddedbebacedcbcdebbbbcbebecadcdabaaddaabaaaaaebcbecebbdcbcadecbcdaaccedbeaedbccbeaaebdababbdacbaecdcbbcedeeeaeaecdebbeabebdaabddbbbabeeedadecaaadeecedbdbebebdbebddbccbbeceaeeeedbcdcdbdbdbcbbaeeabeadddcedabeecbbebcdaaccedeacadebacadcdadaababecdbbbcabebcaebaecbbceabedbebbbdecaceccdacbeabbcceeaecabceeccabcaddacebdcacbbbabacecddceedccdabcdeabaabebcdeddbdadaeaeebabeeecddccdeeedacabacdbddceebeacaaedcdcdacecaeedcbdcbbbedcaadbbecacccccddbaadadebaeaddeebdeebabaebdeddaecdcccdbbbadddbbaedbcbdcbdbbcceebbebddedcbdeabeadeadabbbdcdbecebbcbcccacbaccbcacaedbdeabeeccdbeebadadaabeddccdcaebdcaeebccdbeddcdeecbbbcdddabdecbbcdcaeeacdbbaaaddeebdbcdecdbcebeaababeceebcaeddebcadbeacedabdaaeccdeccbcaacbcdcedbedabdadcdacaecabbdedddbdebaecdccdbdecbceeabcdabacbbcadcadddeaacdaebcdcbaabddaebbeddcbcdabcaeacbdebdbcdadeaaceecedcacecaedbeeceaaaaddaeeacecdaedcbcedebdeaaeeeeecbdcdebdacebaacebeadeecbaddaddaddcecbdabcddbcaecbabcedbeadccebccebedeceedcdedebdceacceadccbccaeadbbacddcebcadabdbcaddadbccbeeecdebdcebaaecbadbacecbcabaeaecdcaddcedeaacbdaaebeacabdcbccadbecdeddaeaabdadbcddbbaacadbcabadbeeababbedaaddbeedeacadbcdccacddbaebaaaebedcedbdcadceaebdececedecaaddacaccbeaeeeeabbeaccbeebdbccaeeccaccddebedabebbecdbcaeccdedcbdbddadadaecacbecabbabbdedcadbdddcccecceacbdbccadddedadcdbacbddaeacabbbecadaddaedaeeaebebebecadbbadecbedecbacbbeccaaeebeeeedcecddccecbedadceccaccdaeaacbcebccaeebbbaeabeccdbddbadbceecaadedcdbcaaeddededcecaabcbddcaceeaeccbbdaabceecadcdabdbbadebdcdaaecbeaeecabaebaabdbdbaadeeecebcdccaaacecdababcedbaabcbecabbcbabccadbbdaeccddceceeabdebcadececcbcccdbaeeaabcaddebbcabdacdabdacbbebabeacdedcdbacdbbcdccebccaebdcdadbaeeacceaabcebcbacaaeaaadbbedecbdeedaaeedccbbacebababeacceaeddaddcdbbdcbdbdbcacbeddcbbeaecbadcaadeabdcecadbbaacbdbacccaecebbdcaaadaeaaabcccecabddaaedecdceceacdebedecabbcebacccaacadceedaeeaeeeaaeaadddebbadcaabcabcaeeaccaeddadedaaebecabeedbacdbacdddeddcbeecbeeedccdaaeaaaeddedbadaaecaacceabedaaecdaedaeccccdeaacacacbeceeccdaeaecbdebcdadcacddaaceceeddbecccbdccdceacbbebebacbcabdbeeeaedeaacdeceaaebbebedadaaaacdaedbebaabaebcabebdeedcddedcecdeeeaaccbeaacbdedadbdeddbabdccabdebcddeddeacaeabccadcebdcdcdaaceaccbaccccdecaaacdddbcbccceaceceecdbccaebeeecbcdaeecbdaecbedebacbeabaaeabbabebabddaadecbeedcedabdbadacdeebcaaaccbcdcaecbaacccbbddaaebdacdadcceabaccbcecbccabbccdbcabdddcccdacacaaaecdabeadbdbabaadabaccdebbcccacedebadabdbbcaaedaccdeecebbaaebebcedbcddacacacceeacecbacbddedbbbcadcedeecebdaeabbcdccaadcdcabbdbbcecdebddadedcceccadbcbabcaaaedeceeceabbbcabaceeadcecebddddabaedbdcebecbdddcdbbdbdceaeebdedaedcdbaeadbdeacbdeddcbbcdcebaeacabccbbbeeaddaeebbdeeaeebbdabbcebbeeabcdddcbcdddeaececbbdaabbbedbcccedbbeeecbacbaaaaaecedaacbeedbbcdccbcedcdedddadedebbeacaccddadaabdeccbdabdccacaebdaeddeecdeaaececbedccbbaeecacbeeacedaaacdeddababdbacecbbabadbaaaedacdbeeaecacceeccdddabccdeedacdebbcababedecddeaacedbcdcacdaeebcdbaedeedbdaaaecbccbabedacadbabebecebcceaacadcaddedbcbcccaceeacecddebdedbadccebddbccdcdbbccecaecddcbcbcdeacacebebecebbbdeadaedeeaaeecacbbddaedeaaeeddebdaeadedddabadbeeaccecadcbbceeaedbaeddcbeeaeeabdbcdddbceabdbdabcbaaacabcbdbeadbacbebcacebeaddddabaabeebbeeebcbddcacbaeadcbcbbeaedebaeceebdedcaacadcbaacebdcabbeeccddbdddcdcdccbcecbcbbdbcdcbaaeaecadecebeaeeccadebbeeacceacdbbcccbadbaacdaccedcaebbabeceebabeaaebcaddacedcaabadccebaeddbdcbccecbbccdeebdbceeebbaedcbedccebcedbbccecdaddeedaeaceaaadbaedaabacdaddaaddacacaacebecbbddebbccddbddaaabaecbcddbebbaedbeeababaddbbabaeddaecdbbadddeeacaedaaaebbccbeabbdddaabedeabcbaaccecbaeebdbbbbbccedadcaabedaeacaaccdbbbabccaeaaabeccabcdceecadebaedcabceacdccbaaacbceadbdccbbeaaebbadcdbcdeaeddbebaabdcceeddacbaeadbeabeabceaccacbedcdacaaecacccbcbccdbacdcdbaaceddccbeddeecdceeabaccecdcacbbcacdbcaaeeabdacddcbcbabeabadaddebabeeaeedabdedeabbaceeacbceadbaaabbcbbebcddabedaeceaddecabbbdececceaecdedeacbebabdebdedcdabdccbbabeccbebabcaedbecebaddaaabeadcebedbaecdddcbdbccdabceabbbdeabcdaeccaabdaadccebebcdcaccdedaeadeaaeebedadadcaccdbdebebccaabedbaacaecedeeedbcaebaeadbcccbdbaecbeeeeecebcdcddccddbebadcccaceabbeaeabcbeadccedacdecccebecbbdbabeaeaadbaebdcccaddbdddacbcbebacbbdabebaccdbdbbcacdbddebbebecccbbcebccbeaeaaddceccccdaabbdcbecceabbdddaeeadeaccbbadbbeebbeeeecbdbdacbcbdecbacbceddedeccadacacedbeeaabaebdbeedddabcabaeacecabbebbbeadabaeceebdeddebebcdddebbacbbbebdbabccbdaabcbcabdaceacceebcdaaddcedbdcaaeaebccdaadebcdabaceccbedcacbedadbbcbdabaeddadadddbcabddbdeeeebaeabececeebbdbadedaebccdedcddabccabaaddcccbaabaedbccbcddabbedeceeeaebddbcbbeeeabbcbeecccdbdabaaddccadbecbbeecaeecbbdbddcebeedbaaeddddbcebeebdcbdbecedcbedabeddaebbeedaccebbecedecaeebdeedeccdaedbedbccecbeacecdedaebdcbccebbaaddadbdecdabdceaaeeaedacdbbccbaabdadeaeabaeeeaddabdccabaceddebcadacbcececcbddcacdadccbeebcbcbcdcadebbedbebecebebbcbbaabdbcdbdcececdbaedbdebeeeedbeceaecdabdbdaaabdbddbabdbacbbcdadeebadbdebcccddeedcccbacdbbedcbeceaeddecbbadceccbadbbcaaeaaaedbbaaeeacdeebdbcedceeeaceaadbebebcbcceeddddbaeddabacdedcabdeabcdedceceadeedccddebbedcedbababbeeabbbccdeabbccdbecdeebaeaddbbbebbaeeddbcdaddbaddbabbbdbccacbebeaaaaabaacbeccadccabcadbbdbbadbcceebeaccadcdbcbcccacbadadcbbdabeaabbedcaecedcebeaeaaadeaadaddadcddcacdcaaceeaedcbcaebadccecddbecdccdebeaeabeddabbcdbcccacebaeeaacbeacebdcbbbdceabdeecbdebdeecaaeeaadbeceadbabdbddeadbabaaababedcbcdedccbadbcaadceecedecdeabdbdacdeddecaabecbcbdcdbacccbaedceccaaeddedeaacaaecbaddbcccdebdccaacceaecdccbcaabbcbbadacadebdeaaacdcbaeccaccbedababbeacdeabaadcabbecbaeebcedccdabddbecabcebccecdaecbacbcbaaebbccedabbbbceebaedbaaaddcbbddacdecedbceeaabbdddedeccabdceeebebcccedaabddbddadaeecdcbcccccababadceaeecccdccbedaeebabeddbbbcbbdeededeadedbbddedaeacbdcbcaaadcacaecebebcbebbcdaabceeaeddcbcccbcdedaaacdabaaceeddacacbcbdceaadeebcbbcdccdbecdbaabeebebbdeeabbabaebcccaaaaecddaacddeecebbabebaddddbdabbebabeeeedabdbeaadaeabcabedabdeeebcbedbdceaccaeaecddaddbcaeccceaceaacbeaaadbdbbdeacbcaacddaadccbedbeedcdbecdadcdebdbbaeabaceecbcdceebececdbeaaecadccabaebbbedbecebdebacebdecdaaeebdaaaebcddbdecdccaaabdcebdcbebadeecbeebceaaabededbcbbdbacbcceededaceaacabdbacbcaaccccedaecacdeabccbbbcabdcebeedbbacecbadceebaebebadbcbaaeeebceabbddcedeaaedbcbadecaddbbebdadbcdeedbcadedabebeeaaceabbdaeddecaeeadddebcabbbedcbddbcabcaabaeaecadabebaaaabbdbdadbdbaebccddcaceddedcceebbeeebbcaecdcaaddbabaaececcccaedcacccdcebcaedddababbaccecbbacbeecaabbebadedcddeaebcecaceddacdbbbbdccccdbccbdeabeeaaadbbdeceebabbebedddbaddcecebebeeeaeeaebdbcbbccbaacbeebbeddecbcdedbeeddaccebadacabcedbcaeddaddeabbcccbdcaaabddeaaacecabaaadacebaeedaadaddbeebedaaeeeebdccbccbcabccdccddddcdaaccbdeddaaecacedbabcaadbdaaaedabaddcadeaabaddbabbcbbbbbbeeeacadedbbcdcaeaeaaddcdadccabddcacdcdedbbaaacaccbadedadceedddbacecbbbaeedeabdbcaccabcadebcddabbbdeabeebaeddbbebccadccbcacbccbabbbdbcbddceebccdacceedceebbeebabbedbccdcdaeaaabedcaabecadedcccddadeaeacbeeeedcdbdedeccaebaaaabacebdcdeedbcecacbaadacbcbecdceeaddaedecdbcddeecabbdbbdcdddecedbbadbecbcedeccbbaaeddaddcacbeaaeaccbbcabecccbaeedaadeaddddeeaeaaacedebcadeebcbacdbedcaeebdacaddcededadadbbacbbdaaccadaadcabbdbadeeceabaadedcbecacaaccccaadacbcdccbddedaeebebcbbaeebdeabbeebbabbabacbddbcadbdeaebebcaaeabdcdeeabacbbabccedceddcdcebebeaabddadaebcbbcabeecacbbaadacedbedeaacbdeeadbeceadcadbadbbcdadeaaacacbbaabbbbdcddbeebddaeacaedadaedeaabbcdedeaabddbaebedddcdcedddaeaddeaadebbdccbacaaeebcecaaecbdccbcaacecaeabdacadaabdeeadaaaecccabbccaabbbadcecbdcdaeedcddacccaecccebbbbdeabdecbeaababceeaebadeaaaaaccaaddaabbacbbcadaedadbcbbecaedbdceabdedadeebcabeedbccecacecdebbaaccddecdcedeaeaaecabbadbdbedccdadecbeebaedebceedddbbbabadabedcbdceaeddbbaaaccebbbdadbdcdabbddacbceaebeaadcbeabaecbeaeaddabecddacbbceabcbcdeaeaddeaabeaddbadcbbdaaacacaddcaceaaebabbcaebdbbdecdcadadcdddbeeacdddcaccaaccacdeabceacdbadecaaebeeececdebdccaebeabeeccccaeabddaeaaaeabdcddcaaebbdadddbecacebbbbbcbeadadbdedadabeacacbeeadeeebaccceebcccecaedbabaceceaddcabcbcdddcacccdeacdbbcababdebceedecaaeeaecabcaabbcaadcddbbcddaeccadccdedeabdeddcebeaadbbdccbebcbabdbceacbabbadbdddabdaabdaecbcebeddcabcbdebcedabadedbebaeccceabcacdddcedeebaacddbdcdcdeccdaececabedcdbcddacbbbccabedbabbbbbedccebeaaedbaceeadbabbaacdaacdeccccbacceeaaebabdcaedcbddeecacecabdbcabebedeeebeaaeabbeabeacddbbdbdcdecadcdaacdbaabdcedacedbcebbbeaadeceddacacedeeaedccbcdadacceecebcadddbdbedeabbdecbdaeacaadedcceecbbeebcacdcbcadceedabdebaeecaaacdbeaecbdbdaacddabbedebbddaebeaaabbddeecbcabdebeecddcbbdbddaeecaddbaedeacedcebbbceeeaecaeddaaececcbbbbeeedbcddebaadadeaccbdcbdddbbcaaccecdcbeacdcdadbbacabceecbaddcdaaeaabdbaaaaabeecbeecbdbdcceeeeecdcedcdeaadeebaaeebbdaeebeecbbeaacbdbdececbceceaeaaacbdecaacccbaaddcccaccebbdcbcbaebbacacebaeeacaacceaccaedccaebeaaacacecbadbcadbdcbebaaedcaebaaaedcaebbdbdcdddbabccdaeeeaecbcaadbacdaabddccdbdbdeccabcedbcddbdbdedabbeacaeeedacceabcccadcbebacddeeddedbeecdddaebbadeeebaedebcedcdcdeabdcbabbeeabeeaccdcebadecbeebcdedeaaaccdebddcddaddbbeacababbcbebeabdbbbcdeaecdebddceddadadccdbdcbacdeadccbadaedeeaedebcaddacebeacbbeaacacbcecdcccbebbebbcdbeeacedaaccacbadeaeeebddaebaaddabcebcceaecabdaadbadeaadcbccceeaedcaabbdebaceeaedaadcccecccaadebceadecdabcbacdabcbbeeecceeadaaaaedbcdadbdcdcabeebacedbaacebbdcbadeacbbecabccaccdcdcbecdeccaeedcbaddbcdebdeddebebbaaddbeebdbbeaabacebbabedcecabaecddabdebbdbbeebebdcbdecaaaeedecbebbbecddbcdbdceebdceaddcbbebdabdeedccaecebddcdbeadccaeadbcaceaabcbeaeecbebdeccdababaaddbcdeceeecddabcbabceababaacdcbeccecedddbeacddaddddcbebaadbadbbdbadeddeeaeeecdababceeabdccdbaaadcbcadecbadedaabaaabeddeaccccbaedadabeaecaebedabaeaacedccebbacabdcdacdbbdccdadeaacbccbbdeadaabdcbbaedcdaacdbcddaabbcdcecabbccdedbcbecacedcaceaabbcaabbdcceeaacaeecccaecbbceddabcdedadccccadddaeebccddeebaeaaaaddbecdbadaecaddcacdeaaddcebbcddbbbacabbebadadbcdceccddddaccccbcaecbbbcbddbdcedcacedceccebebeebbadeaccaabeebbcbbddbbdcaeccaaadabcbcbecaadbaeadeddeeaddeaeecebeadbbaccbdebadabbcdbbbadaebcaaabddbcebcdaebcdbebceeaebbdccdbdecbeaabdbbdcddebcbadcceeecbbbaababeeebddcbaeebbbcccedadccbddbbadaddbcacccaacdbabcdcdaadaeeeedbaeedadaeeabebcddbbbbcaebecbbceeeabcdaddaaeaabaaccccbedeceaecbdadeacebbadcddcabbcdcdcecedaeedeaebadcacbdeacebdccabbbcadedabdccbbacbebabbccbaaabddeaaeceebbcbbacbebedeababcaccedcdcadebcdcaeeceeeddbacebaedbababebccdddcecdbdbbdacedccdeaaacaecbbbdedeadbaadadddeaecebecabdebaeeedeaebeddadbedbdeccdacecdadaeaabbdddbabeccdcbadbbbbbcbbedbcabbeadbbccdabbdedbdaeddabcabaadabeecbedcdbdaceecbadcdceeecceeeebcceadbbedaceecdabeccadbeacbadbbcbaeccecacbeebbadcaacbbbeabadcbeddaedabbadccdebbebcbcacabaabeaddaddbcedcadecddcceecaadcdaaeaceabeddccaabcecccbbcedcacccbaccbbabedbcdbceacacdcdbddccbcddebbbcabdcbbeecdaecebaeadbeebbebedccaeaaddcbbbeeaaeaedddceecaadaccbeccddadabcbcededbebabdecadebcaeacdecceebbdacedeeacecedceceddddcdbadebdbbccebbcedceadbbaecdcbaecdeacacaecbcecbeadbeaeeabaaeabacadadbaeedaaacdebcdceeccccebbcdaebadccdaadecccaeaeabbcadddaadbedcbdbbacacbcababdceadbccbacaaedebaddccecdeebadabecaabdeababebccbacceeccaacadeeadabbbaebecacaabeceddbbdadaeeebbeceeccebaacdabcceeeedbdccaaccccdedccbedbeadaeebaedcadddeacecaaabceddedabdbebbedaebebcadecaacdeddedbecbbbcabddddbeaddabacaccbaecedcadadccaaeccaadacbccbbccbedcabbabcedcdeceebeebecaaddecdabceebabcdebebdbdceebcaceccdeadedcbdedbbcdbccdbbbdcadacbddaeeddbeebbbededeeaecabadcaecbecaddcaebeeeabaddbdededaacecdbadedceedbaaeaaeaccbddbcbdceabbdbbcbcddbbcaecbadcecbaadaeaccedacddecbbcdedcaabcbdceeacbeeaecbddbdbecdaebddaecbecbddccbccabdbededdeebacddedaedcebddacaaaeeccedeaaaacbcbccebbbabaceebbdebdbbabbcaaccabdbbbecbaccbbdbdcdcadbaebdeeddbaebedeacbbabaabdadbbadadbbadcbaabedbeeeebcdbbdadbceccbedbcaeecbbcbbadaadcdbeecabccccdebceebeecaeebebcbdcbcdaabecacccedbeabcbdcceeebeddebddbeebebcccadcbdcabdaeceededaacaabcaabdadcedbbdddcadebbebbddbdabbddbddbdcaeebcddcebcedeccdeccaebabacadcdcbdeabeebebaacbaabdddacadbebbbaeebbdabdeedceceacdebaeaeaaddaebaebddabcacaddbecdcecbdeacccedeeabeaecabbabcaabaeccbecadabcebccecdccebcebedaaaecdcddccbcbdaeeeeddeedeebedabedddeedadbdcedcadbaebebabceecbcbececcedecccaccdeaeddceacbbcccbddceddaadbdeeeeededbabaacaeeaaadecdedbbbadbbecaedcbdeeeeeebebbdcaeeaeeabccedadedaaceadbbaeddedbeceeebaddceeabeddeacacadaeccedaecccedcdcaadabaccdeaaedbeccdbdbedceddcddeaaadbedccdadadbcbabbdecbbdeaaddeabdcbbedccdbcaddeedaddccecbabaedbcdcbdbacddaccccdccaeebabeaddabaebcccdeacbdbbdcccccbabebcddcabdcedbcaacebdeeadcbaaeeedaaeddceacbbbbdccedebceebeebeeadabeecceeaddecbdaabdceadbcaedbddbabaaeebaebdbdbebabcacedcbdeebbcadcdbbbbcaeecbeaacddedadaabedaaeddedcaacabdadeceeccbbebdbcbadedcccdccedcdedacbbcecddeeaecdcddedccebccbbcddcaacdecedbedebeedebdbacddbeeaddcccdcdcbbbedeaacdebbccbedaeadcdceacbbcbaaeacdbdacaabbcaabecddadbdddbccabbbaeddedeabeebcbabdbccadcabdabadaeccdddebbdccdecaceabacdacdaacedaebbcccdedaaebbdaacaadbcedeacdeadbbaebdddeedbebbbcdebebcbbabbeeedbbddccacaebdeddbccdcadaeadaddadeecdbecbececdcaecdcdbceedecedabbedebbeaadbdadecaadbbcbbacdcbccdcadbbdabaccbaacaebbdbabcececaebeebcededcebbbbbeaeddcbacedebabcaeddbbaedebccddcdeadabbcaddcdabddcbbbbbddebadcaabddadcbcaecedeebbbebbdbcabacccaedeaeaaeedeaaadccbeaeacedbceeaddeddacebaadccdbdbbddacdcacadaeedaacaedecaecbabebdccaadecbacaddeebeddabaeecbeebedcdcaeabddaacaeeedaddbddcdcdaecccacbdcdbdcbdbbbdeebdeeaeedacedcadedadeadaadadcaeebbcacbbbbdbcaccbccdcdabcbbbaeabdcaabbdaebbecdeedecacdbeecabdbcdeaddcbeacbccceabdcdbcbeccacecbeaccceeeecccacdbecaeeddcedadadadedecdebecaadcabdbbedaedebddeacadbbbaecaeecaadeabeebedbddaceacbaebadeadaacdacceddadbeacbadecacdebabaaddcabdcdcbcdbedddecccbcbcaeabadceeeeeddacddddaacedaacdeddaeecdddeaccdeddaddadaadaadcabcddceebeaebddbbecacbbdbceeacdebecbbbebbeaddcdbdddddaddbcebeecaddeecdbebeebdeeddcdaacedcebbbdeeecceeededeaceedceaecbccbdccedbdccebcedbdadacdedeeacebdbdabacabcbbabdaacbddcacdbaeadeeceeadbedcadaccaaeeedbbbecdcdcaeeaecceddaddadbabbdeeadbebeaddecceaeccbcaccebccbacddaeddceaedbdbdbccdaebcedebeeeeeeabaccadbdeddeccabdecdeabeaecacabeacedeecddcacadeacedbcdeeccacbdcceaaebeadabeeaabddeabbedbadcaebaebaceebdcebbeeedaaccaaceadcaecaebadbdbccdbacaccedbaabdccbceaedcdaebdabeeececebdebebccbebcbedbbacdbdbcdccbebbedcdacacdbaceaaebabeebbbddbeacbeebbdbccbdeabaacbeabcbccbaaacadbddcadccdbcecbcedadcdadcaadccbbebeeebcaadbddbaacaebacdcdcaecaddacddacdabbededebaecdbebbecbeddececcaebeaaecbacccedbaaccacadbcdcdecebbeabaedbcdbdbaeabdcabaadbdeaecdbeecabcdaabbacabaeaddcedaaecbabbdbbdebdeedddeaadeebdecdaabaccbeebbedadbacaccedacbdedcdccaabbeadbbadceaebcebacabedbdebccabcdcbbebdbbaabeebaecbddccecbeadbceaaeeabaddccbbdcccddcccddaacdedaacecbcbecddcdeccdbeacceaebaedeceecdedecebaecaaadcadadbecabeaaeeecdecebadabccbcceaaeecbebdadaeaddddbaceddababdeccbaadcbbcbcddcabdddbbbbedacadedcaddbeaadeeeceabdaabecaeebcaecaaaceacbeaebeacaceabeaecaebeaaacdecaacadbceabcedaeadecacdadbeeabdadbdebbaceeedaccaeceaeebcabbdadceeeeeceaebdeebddedbeceacdbaedacedaaebacbaeeadebcbcddeeaaacbcbdbbbdecebdbebbcbccbaeddbaccebababdccccedbddeceeeededceeaecdbabbcdcbeccecbbdceeeeebdaedbccdaebdebcdddbacdadcaeabcecbccdbebbdaeaaacdbbaeecedbdcacebbebdecceebaaeceedabdabeaedccedebbabedacedebeebaeedecbceceabebeabcccccbbbadebaceabbccdeabeadabedcbbbdbcbbccbacedcaedcaccaedaadbbbabecccaabccebbdcbadcecebaadaededbbbbdbadddcccbcebdabedcbdaddeddabebbdaeebbbcaedbeaddaebadedabddcbebadddcbdddccdbcddcecbdaeceaabdddaaebcccbceceaedbbbdbebbdcccccaabbbaabaddbabcebeebcaaebdceaeabcddaacdccaaecbadaebacdaecdeddeabbceccdedeeabdebbeccddaecbcabcabcceebadabaccbbaedbddbacdaeeededbcdaabadeedabbeebddbebcdaaecdbbaaccbedbaeabbaabdbeedadebdcbbaaedcdacecbccbbdececbadebaddeeacdabdbbdabcacecedbaaaccdbdeecbeadccbadadbddcaeadcccadeeeceedacccabdbcccbacaabaaabcbccdcaccbdebaaceccecbcbdbacaceebaaedcdadaabcdaaeebbcceeeedccaaeaccbdeabbabdebaeecccdaeccabbbeaddacdecedeebebcadadbeadccedaceadbbcaabdbbdeddeadcdbddabacdebeccbecbdbabbbbdecacabedbeddceaceacccdebcaeaabdebedcaecabdeabeaeeaceacececeeaaeeceadeccecdcaebdebcbddcbdcaebbedaeddbbacacceadcaabccddaebecbebcacbbacabaaacbcbdecceacccedddbcaeceeedeeeeabccceedcecaedaadcacdcaabdebeaccacedbbdaddceaecadcccaadabdbcddcaedcaccbbbeaebdccedbdeacdeebaecdbabebbabecbeaeadcebcabccddbebbdbcbbabbbddbbdaeadbbbbddedddebbaaacddbbbaaacadaebcbdabbeadbeceeebbebaeabccdbeaacccbcabdaadeedbebbeadedcceaededdaebeeeebbbaecbeaececdaeceabaccabeedbacabcbaebabddddadbeaaaeaedadccdeadadaeccddadedaddacedabebabececbeaaebaecddbaebdabddadeacbbdadabcbecdccbaddcbcccecbcaddaebadbeadbeccddaebcedcccbdeeabcecebadadaeadcddbeaedcccbbacbbeabedceaadedaabddbcbddeaccbeabcbaabdcbaceddeaeabbddceacebccbebadcebddddbaaedbaccebdedddaedadabcdeeadcaaaaaadcbbdcceebedbbeeeadbdadeabcccdbcabdecabddeceaeacababbdcaeabdbeededcaccbcaaecaddbabacbbeecdaeacbebccacaaecdddebcdcddbbdcdbaacebddcecabcdebaaeddecbedccbddebecedcdeddccaaedecbbcccdbedddbabcdddeecebddebcceaaddbeaadeaddcddaccababcaceddadabdbaacceacedbaedcbcdbbaeadbdbdcacacdbbadeaddcbcdcaceddbdcceeeaadcacbbdcaccecbdbbadedebcbaccbeaaddeeeabeaebaaebacdaeeeebcccbbbccbbbaecaaeabccadcebbeddadaaddcbedcaacbcbaacabdccbaaadcedaaaaaabcdeaddbecbcaeedbaeacbebbdbebdcabdbebedcbabacdbddaecbabaeaadddcadcdbaeeacdcddbcebedcbaeaaadaacbcccddceebecabcdccbcdddccaedcbdeaccaceebebaecaaeadadacddbddddbbdeebcdbddacedcacdbcbbbeaaebaaddacecdeacbeddadcceeddbddcedcaeebbeccdcacadbaceaaeaaaedebbccdcaabecaddbdbbecbaddcdbcacdddecddcdcbcceacdcbeebabbdbceeceeeaabdcbabaeeebccecdacdbeebcabccecaacacabdaeaadcbaddaaedebbbadbbebbdbbbdddbdbaceedecacdddeaeaeaddaeadacdbcbbaaaacaddacddecbddbecabdeecaebbaadacbbcdabdccceececdaceabadbbacdecbebaddaecaebcaebaddbbaaceddcccdcbacbcebadeedbedcebdacbdcbbaadcbabdedeebedaddccceaddcddcbddbbaccbbaddcecbaedeaeccecbcedbbaedeeddbadeebdeecbaeabcbbbcaeccccddcbaaeeecbcecedcbcedeacddeeccacbcdadeacdddccecadbcdbebdddcadeaeeebebecbadcdbcbaeaedcceabeabbbdbdebbeebecbaaabedcaccdddecdbcebaeecaedbcaaaddedaddaebeeceddbccaadabdeeddbccebccaedeebbbeedceeedcdcdcdcdbbcbceabdacacbbbecbeadeecccbadebbdddcecaceedcebebecdbccaaaecadeeebaccabdbacdbbacdadaaceadcacbceaadecbecedacbaaeecdeaceaecbbebbddcadeebddaccbaebedaaccadcdbbabacbabbcccccebceababddceabecbbaadabcdaddddbdaabeadddbaacaebdaeabbcccddccbdeedddddeddabbcccabadbebedbbdacbeeabceedbeddaeeccbbacaadcadbccecaeabcacbaadecbdadaecaaccabdcbabcaabbcdedcceedadcbadaecccdbceedaaaeaeabadedeceebbcbadabccddceaeecdeacaededeebaecbadbcdcecedcedabdeeabbeeedbbaebbcceabdedceadbccdcadcdbeccacbaaeedaacadebcaddcbccebbaeddbecdcaaeedbeccdadbbcdcbccddcdbeeabacbaabcadebedebaedcedebdbcaadeeeabbeeccdecbeedcdecbaeedcacabeccdddcaacababedbcecacbdcadcddbadeccbdadbeaecaecebceeaceaebcbcdbdbceaceacdebaeddcbbacabedebeeccebecdbadeedbacebdbeebdddcccdeaaebcbebddebaebeeabcbaedcaccaebbccbbadebadbebabacedebaadcecbdcccaebabbbabadcdaabddceeeeacbdcdabdbddeecedcaadedbebceaedcdceaaabbbcccdebacbbdaadcbaecdbabccacbbcdebdeebadeeebbcadaeebbeddccaeccbaedabbccacbaccdeaebcaeccceebecadebcaccaccaedaedbebbbccbacabeaceddcdbdaebabadeaedcdbcbcbebbeeaebbaeecaaabdcdcaaceadbdebeabdbbcebeccecacaadbacedadbcdeddeeabedccdbabdadbdabeadebaaebdaebababbbbdcdbcbcadcebcbdbcdaeecacbadccaedababbcdeaeaaacedabaedeedcedaadadcbacdacddedbddadcaecabababbbcdbaccbadacbddebdababcdbbadbdbdcdedbedeedaeeadbbbebaabdbabbcdbaeeccabacdbbaaacdacbddbbaacdbecaaaebceaddbddbdcebeeacbabbcdbeddbdabdeacaeddbecabdbcbadecbdceebdaadaeddaadeeadbedaeadcbdadaadbdedbcaeecaaedddeebbddaebdabbcddabeceadedabadcbcacdddbbcddabaaecaaabdbbddaeebdacbdccaabccaeadddeebecbdddbeaaaeaceecddcdcdceadeeaaeeacaaebedbddadaacbcbbdadcdedbaaededbdccaecaeecccaeaedabcebddbabcacaecdebcdbbaaabcaeedacebabcdaaecbcecebaccbdccdbceceaebdbcdddcdbbcebedaeeddaddccdaaadceadedecceaadcadddedcdaacccdebbaecbcdaeaacdeacaecbbbcaeeeeeddeddbacbdedccebebdeaecdccadecabebddbcaacdaceabbeeabeaeeebceeceabaecbdeddcdcbbeddedbbbdadebcbaadedacbaedaeeecadacdbdcdbbabcbebbcbbacaacbddddebbbedecabadedacdccbadbcacddaccbcbadbebacaebeadbebdbdadebaaaabcdededaacedacdadccdacaacebaadedeaecbcccebdedcacddcdcddcddccbbdaacedaaecadeddbcebacbcccaeecabebecddcdaccdbcedeacbdbcbbcdcbeaccebdcabedcdeaaddcceccdaabdeaebeacebbbcddabacdababccbeedebaacaecbcbbdbcdcadbbbdbebdccabbbacbeecadcedaabeaeedecdcadccbbdddbecebdabdaabccdcdcedbbaebabdeecebbabececddacdadcdcbbcadedabecaddceddbdbcdaacacccdcaaebeebecbadedeadcaaaecadabdbcbeddedbcdcdddbeebbaccebaebdedbdbabdcdbecacebcecebdbccdeeacdacebdaaeebceabeaeabebcdabeaabcbdddbbceacbabaadeedeaabddeeeecaebedbdcabbceadbeeaacbbdcbbcdedccdbdedbdaebbbdbdeeebcceaaedebbcccdcedeebbaabecebddacdecaeeceedbdaecbccceebdddbcbabeecdcbdecdaccecaaebdbeaedcdaeaadacdebadbaedbeeebcabaceaecebccebaabdabdaebbacadbabeaddaceadaebededceeeeaeebdccadcadbcccadeeadbacaadcadcdedcebcaccdbdbebdaddbcedeebbcadaadaceecbcceccaceecbadabcbabbcbceaaeccdadbabcccdabeabdeddbaaeedacecedccebedcbdbebcdacbabeadeebecdeabaadeeabbccccdecebdeeecddbcbeebeebcaebddecedaabbdcbdcadccebccadaacbeaecaedadcebecdebeeeeeddbedbaabdadebbcdabcadecbbdeebbccecacddaaceceddebbdbdebdadadbeaaaeebbbdcdeddaceadaccccabadddbeacbedbeddaaebdbbcdedbeeddbbcbbedeeeeecbdcdbecdbebebdecdcabcacbdaadbeaeddececbbacabbdaacecbbaacedbbaebcbbadccebeeadececdeddbbeecbcacaadacdacbaabdbeedecbcbbddacecbeecbeebceedcbaccbdcaecbaeedbdcbbeaebccaccadeacbcedbbdcabbebeaecadabcbedcddcbcdcbacaebdbbbabbdbeedbacbcebbcbecadcadcaedbeebcadaaedbaaacadebaedbacbeacdaaadaebbbccaecccaebcabcbabeeececdbedededccdaaabebadeadbeedbddccbbacaebcbdbacaaacbdcbbdaaaceccecbbbecddaccddeaadaaaaedaedacdbaccdbbadeaedbbadececaeabbbcbccbbbaedcdeaccadedeebcbeaaedaaccebccdedbcebeddecabbbebacdbbdceecdeebbedbdeccdabedabedaaeabaacaadccccacdedccadaacbeebbaebcdbaebbaddcebccdeeaabdacbbececbdabdaaebacecccdeebeebeecdbcabcedbaadeadcddeeeddaaadceabcecbdebdcbdbabbedecaaecbededbbdcabacdaeeeeebcaecbcdeaecbeaecaabdeaaabaeadbdadcdebdababbbaeecedceadbbecbaabddbcbabdcecdbacdddebcabbacbbadcbbddbdcbedcacddacdbcbbcaccbcebaecccddaccabceececbbdaceeedaecccaaaabddaceabdddeabcdcbbcacbdeeeabbbccdbbbbedaeaacdecdaedeeabebccaccddeddebabdbdbcaedecdcebacbbadddcdeedaedbdcabaacddbcbccccdebbaaaaaaebcbcbdddebbeeacbeeccebecadceedabeebabcaeaadcedcabbebcbdbcaabdaaaabcdceeacbcbdecedbddbbdbbbdadebdaeebedccacaaadcbbeaeccabeedbaddcdaadbbbdcccdcddbbdebcbbbcbaaadceeadddddbcacbeadbedacbbdbbedaedbebbadcaceccdeeaecedeabacceebcebaaacabacccddbacbcacedaeaebbedcbddaeabdbbebcddebeddabbaabbbedaaddacecdbcbddcbecbbdaecdbdbaedebbbceaddaecabebceabedacdedeaedebedaebdbacbecbdcacecedadcdbdeeeccdbedddecebbbbeaedcabbddecaeacdbddeebbeaaeaddeadbcccbcbdcceecebecbcbbbeceaddcbddbddeccdbedbbedabeeacbdbddcadadeabdccaeceddcbdccbebdadeceeadebacccbdbdceedbcadecbbbbdecbaedbadcbddcabeadcadabbceaccdaaddebcedbdeccebdedebaaacadeeabdcccaedeeeaabddadccecbceceadaedcdcaaceaeceabcbbaedbcbaccdaeabacecdcedcceaeccecabaaebacacababcdcaccaaedabaccbbeacedddeebcddedebeedeaaaabceabacaaddedeeeebbabdbaaacdaadbcccadeecdccebcdaacdecbcabedbccbbdabaacbcecbebdbaebdbccbbddcdbbcbdedeecaecacebeebedcdecedaeaabaacebacdddcdcdedcacdedbdaaaeadcbedadbbaeababaedbccccddbceacccbaccdbddedcceedbbbdceccbcbebaebbebededaadcdbddcbaeebdbacadcaeebbbcaddedeeabcadbccdebaccddddbeceaebacabeebccedabddcaaaaeccacdddcaedceeadaabdacacaaabcadbaddccaaceadcadabdeceabddccdecbbeedccacbdbecbbcabecadaddcaedaabcceddbacddaebbaaebcabebeeceddbededcabaacadddbeadddcdbdbbbebeddbdbaaacdbaddeaeaabeacebbbcadeaedecdddaacebadaaeccccceabacdedbbaaaadbdecbdcabdacdbcbccaaedbacebbddbdaceeccabdedcdbbcdbbbdbbaabbcabbbadceacebddbededcabaabeddebacddbbecbdbbcdedaaecbdeadebececbdaebeabeeaccbdcecaeddacbcdbaecadbdeeeaabdeeccddadeeeccbadddedbdecdcaaececcccbecccadacebbbdaceabccecdbbddaeebbdeacbeaacbaaebbdbababdadcbeceeeeddadadbdeacbbbaaadccaccaadebabcbadbaedbeecedadadabeeeebabdeabeacbdadaabeaadceeaeeacebdaeaadedbcaceedeeeceaadeddbeaaddbabecdcebdcbacccebeddedaebeecddeeeaeeccbdbcecaabcdddeaaabeedbdccadcedacaeaabcdedcecbcbbcbebceacebaabedcbcadbaebeeabebdcdadbdeaedddbccaaaacaaaccdaecbdedbcbccaddbaddbecedeeecbdbdbddaaccdbaccbadeccbdddcabbccbcacdbecbaedececeddcaecaebccaecdeeaccbedeaabdacdcabbcaaedbedaadcbccebedcabeeebeeacaadbddaceebcdeeeacbcabddbcacbaccccbdcdaecbbdbdaaadbddbddcbcbebdaaeccedaaccebbeeabccbbdececcdbccabacaedcadeccacbceeeeeaaecbbcaddbcbddeadbdecbcbbebcacbedceeaaaadaebadcbaacdecbabdadadaccbeedbdeedcccdaebccecbebcbebecdcdcbdcbedccaaebebbaaccbedceacddccaceeceacccebcebeebbaeebbbddccbbdbacdccbddcecdbcadedeedbedbdbbbaeebeaedcdbaecacbaaeabccdaeededddadceedbeabccbeeabecaadcaceebebedbcdbabbabceeaceaebeedbaccebedcddbababeadeacccdcadabbaddabaeeedebdaaeeacdabacccceeabdababbbdcbdcbaceedabeeabcbaabcbdbddacbacebaeaedaaacbddcbdaeddceaedebadbbaebcacaaacedbeebbabedebcaeaaadcdcccdadbcdbdacdeaeedebebacabaaccdeeabcacbddcbeacedbcaddcbeceedeeaaeadccadbcacadebbbaceaccbdecbcaeaeadedcbdaacbeeeeccedaeeaabaeecdcbdecbacadebdeddadabdebeeeebdeeebddbceebacccadaabccaacbdeecbdabccedbeaaecebcedbbceadeeaeeccebaabceaaabbdbeaebadeccadabbdacbbcaaccabebeecdeedbdedcabbbeebecadcadbbeaadcdcacabcebedeabdeabecdbbeddbeaabaadeccdeadcadcbbbacddabdbbbbdcdeedbbedcbcabecabeedcbdacdadedabbadaededddaacbedeecadddbdabcaacbaaeecaccbcdecbaaccbebbaadddbaddddaaddbcbeeeabbaceaecadccbbcbdbbaeeebbdececcdaabbdbdecddaadedaedebaeaddebddaecdbabeccabcbeedadbacacacecaecddcbcebdacdccebdaebcacdbbeeddecddeecadcdadeecbbedbebdbeadaeadbbeadabebddadaccbcedccebbcadbcadabbbeccabaaaecbebcdcbabaecacbcbaecaeedaecbdcbeecadceabbdcddcacaacdebddbbdcdeccccdbdaccebdeeecbbadcaabddeacdbebcedcbcebbcbdadbeaacbdadaeebeeebdaecdaedbccabccdabdadcabbceaccebdcddaeddadeeecdacaebdddadaddbdbadacabdbecccaebebdaebcedacbdbdbcadedddabccccbbbecbaeadcbcbabdcdaccbeaccccebbebbbabcbbeaabcddeddbaadaedaceadccebcedeabaebbdbbcbadeadcaeaccabcecdbcccdcbcdebcdaccebbaabaaddadacbdcbdebebbedcedecdddecbeebbceadcedbcaabdcceceaddcecaebcddecabaeacddabbcbbeaccabbdadaeadbaebdecccebabdeabdbeacdcdeaaaaabaccbbecdbbcdceceabbdbbdadeedaabbbcaabeacbeebdaaabeaeddddcbdcddedaedbdbaedcaddbcacbbcadbdebaeeebaabcdcccdadbbdcaaaecdbcdcccbaabcceaabccbabddddedecadeacbecbdaaabcacceedeaeddeeecabdeceabedadbdadbedcecdbaedbcbebecdbbdcbeeebdaebdabaabbaccbadbcbabbabdcddcddbacddadddddeeccebbecbbbbdacebdbcceeecbeceaceabbeccadaedecabacedacdedbcddccbecdcbcedcdabcebcaacadbaeadcbbcedeccbadccbcceacceaacbbacadacaceedabaadabaadbeedebdccadaaedbaedeaacecbeacedbaedbbeecbadccecbebcbedcadeacadbbddacbadbcebcdeaecbadbcaaeebdabedeceabacbecddaaaadaadcaecaecacecabcacecaddecaeddaadbeedbacacbdcbdccdaaebeadcacaadbaccacbeaacdedcaaeceabcabdbbaeabecaeabdeeeadccdeccccbcdbbeddbacdcbedacedccadebdebdaeeecaedbadeecebcecedccaecdadbaaabcddeaeadeccbdcbdceebdeddcddbddcaeedbdcccccdcccdbebbeccdabdacecadeddbaebceebceeeebcaddeeccdabbcabdecbaceeabdcdbabbaceceaecbdeccccececcdbebbeaceaeaeabedcadcabedddeccdcedcdecddccacebccdacdddbeeedcbeeccaddadadcbcdebbadacdaccbbdbbdeeabbddbdaddadbaeeeddbeabbebaeedbeeddcecddbeabccedcdcbcccbbbacebccaabdabeeaeeecbaecaedadbbdabdbdeeaeadbbdbacdebcebcdbcdabaacbdceabbaabccdbceedcdaddacdbbdddbccdccbededaccaebdeeeeabbecdeabdcbaabeedabeaabeebbadccbcdeeedbdacbadeaadcccdeacdbaaeabcacabbdbdacedbbdaddcededccbddcebbbadaeeddadddbcabcadacecdbaacedbeadcacbdcacaecebbcdeaccbdbbabbeebccdbaecbeabdcaebbbdeeeeaebcebabbcebbdbbcdaaebbcddcbcaecaabaaebcadabbedabddbebedadddaaaceeedddebdbacacdaceedbbbaacadddeeaeccccdbcbdecbbacceeddaebdbedebeacbbbbeaeccdccccddacacdcaceedbbacaabaaaadabaaccceabcabcebabbbbbecaeceacbdacbabeeaacdeecbedadddccbaccacaaacaeddebcedabceabdabeeacdcdcadaaeaeadadbabbedeeecdaccbedbbdbebeeacceeddeaecbbbaeadbdacaedbcccdeceebcdcacbebcbcbaeaadddccdbcaaabccbccdbaabecababdecdaebbaeaacdeabcdabaebebaeceaeecabdbecdbdaeabddbbcedeccebcccadcbbbacecbebaaccabeddddaaabbbdeddcadaeadadcbddacdbbdcbceabdabecaaecbbbdbebdebbdeccedacbbbaabeecdebacbddecbededebcaccedcbbeebbbbabdbaadceaabcdadceadcadedadeedcedeecacebccadcaddaacbedebeabceacaacedacbccaaebeccdcaaadadedddaeecdabdeccddebeeacedbcddeceedebdbbacaddeebcdcaadabbeeeedcecacddcacecebebccbeaeadaecaeddebbaeedaeaddbccbeaebaddcabdbdaceeecccecdeebbcbccdbaaebeeadcaecdcceaeadceaabbbdbdebbccadbdabbeabedbbcadeaabbccbccabcceddddbcebcbdddddcbeabbbadcbbcadaceedccccedeecddacabedcadbcabbedceaacedebddaedecaaaeeadcdadbedcaaabebeccdeaddeceaaecdcaebccaabaeddcdacaadeeddbabbeeaaedeadaaaebcbedebbcebedcbbdcceadcedbbcdccbdabebaddebbedbacbacedbcdddadccbbdbceeaaecceacceeaeeeceaebcdbaeedcabcedebbbdccebcbbebeaeacdddabebacccaabbeeddbbebaddeeadcecdcdeeeecdbcedaadcbcbcbdadaebbcbaddbcaadccebaeacdbbaeabddccccbecdadcceecadaddccddbdebecadacabeecbdbcebcdbabdecbeeddcceaabdcdacbcbeccaeaedaadcbddecacaadccbedddbdededdaeaaeabceceebcacedcdbccdcbbaabdcaedbcbedddbceadcedddacebedabedcaaedabbcbaabddabdbbabdaeaacdcdeeaebeccaaadbcaddbdacdbebbcabacdccbeabdabedcbaaaadeebddbeaaedbedeeccadaeabdacaeadacdacdbbeeeabdeedbceacdbaeacaedcecdcbceadebedbaadaaeddeaddcdbcdbbbadaaeaeaebcadbaacdaaaedaebdcbcadecabadacdeeddcbebdcadcbcbdedadcdecdacbbdedeecbdedabdaeaedabcbcbeddbceaacdddeabceaeebeebacdbccaeddaacccecbadeeaceaededbdacadaaceeeeaebdedbecedabbaaaddaaaacebadddccebdddaeeacccaeceaadbcacdeeaedebecaacbcdcddddebddaaceeeccdcaabecedbdecadcbbbecbbdcebccacbaacaeeccbcbabdaabdadcdebbabdaabebbdeadaabdbddbdebbabadadebdbcebaddcecddebeceddcbcaedacbdcebadacbcbcbeacbaabbeabaacedaeecdcbaadbecebeeeddceadecbaabdccacbdeeadebedeeedbaaeccccabaaebdabbaeacbdaaedbecadcbadaaddadedabdcecbddaceabdccedcccbebadbaaedceecdcbebabecddbbeaaeacacabcccdbdeccddcbdcbaadbdadceeeecbbabbcdcdccccbccbaecddcbeeacdebedbbbeadadeadbedadaedcbdbeededbeeeeddbdcbaccebbbaddcebccdeacbcdebababbbaabbacbddcbeacbdccabdadaeddddeedaccddbdeecedbcddcdcbaddddceccceebbbcbcaaeebdbeaccdbaaaabeeeeecbdbecdabcbbcbebaebbbeceedbabddacedcdbdbaeaebdadbcaebcbbeaecebcacbaccdbcdaaeaebdaaedbadecccdbededbddbbbdbaaccacbacadbeccbcacdeacecccdadbbdceacbbbedcceacacececebbbbadcbedecedbebcdedbbcdcdeabcbdbdbbacdceacbcacbbcbceeaaaecaceceddedcdacaedcdbecdaddbcccdceaaacbcadaaccbbbcdeccddeabbcaeceeddecabdeebdaddabbccadcbcdecebcbeccbccacbedacdaadabcbebaeeaeeddbdaaaddebababcbeaeccbedaacddbbabddaccccedbbcaaecacabaecbcdebbadcecdcbeaabeadaeccaeeecdaeaaaabbbdaacdaacbbecceccdbeebdabddadcebdeeccebedbbbcaedaedaadacabcdaeabceadeedaeccaaeaadedccacadcdedabacdddceedbcdeebabcbeacecdcbedcbbacebbcddacabbccdaaadaebbcaccbeceddecbeaaeedbeadceadeadddadcdabacddcaedcccaabdbcaebcdedaddeecbbcaeeacebecaadbccebaeecabbcbcadadaebbdedeeaeabbedbbbcabcecddcebbadbacaececceeeeedaaabbadabeaecdcaaabbecdadbdadceabdceaeeacadddbceaceecebabebbcbeecbeebabaedcdbdbaeeaceccabbcdbcabedddbbbcddcbbabbebbcaaeadebcdabedeeccbebddbedbbcedeeebbcbcaebdcdeabbcadbddaaaeedbbddabcbadebadddcacadbeceaaaebbeaecaccbecaaacaaacbecadeecededeaacdebdbebcabbccdbedeccebbbbabeeadaddeacbdccddebdaceecabdddabebebbccadedacaddecbcdcaedddebdebaacbeaeaabbaabeaecbdcceeececcaaababebeabaeabdcadbdeedbaceabbaaeacecbbceeebdaebbbbbdddbabceedcbaecedaebccceacccccdebaaeedabcddeacebbcbacbbbaedaeadbceccedddcaaaaadaaaaaadbeaccededaacbeeedbbcddacddceacbbabdcbbaddeedcabeccaddacecbbabaabeaedebbddadddceeeccdacdacdbabbaddcbcbababcbeebcdeaeebadadcebdaebabbcbbdbcaeabcedeaadeceaecedbdcdebddacaaebcdbccebaedabacbadadeabdddbcaabccbcecabecbdadbceaeaccbbddbbbabeccbccbceebacbedaacdadedecbeacbbaebeeadcbaeaacaabdbebeadbdcaddccdeacdbeabcbedeebbcdbcdcdaadcaeaaaecbecdaccaecadebcbcaaedcbdbdccacedcebbbbbaeaeacdeaedcbeacbabbceaaebdddbeccdebbbeadaccddddabcdadbebdabbeebbdcbacaaddcceeeeeadcdccdbcdeebcabdcbecdebabadabecdcbddcaeaebcccaaeebeeecdebbedcdadebebeceadabeaebeabcddecdccdabeccbecdeeaddcdacbdbeebbbbdabcdbbedbedeabeecadcdceebcabddaaceecbccbadeceeaaaacccdeebeebdebcebecbddaeacadeabaaaaebeedeededdeeccbdababecdaebeeeebebdbdaccdccbbeacaebedecaeecbddacadabccbdbdbcbeccbceeccacdabccedebabeabedeaddcbcbabcdcdccddccebccccaabbeaeababcdeeeeeebdceacceceebebdbbdaddaeddabbebbbddccdaccbebccdbadcaddcedcebcebabddaabadbebbaecaeaaddabdddeeedddcdbbccebdddedbdbbdaccdbbaccddeeeeccacacdcdcbbcedbdecdbdbabcedaeebeebcccdcbecadbeedaaeabecbdcbcbeebdbbabdcdacdedeeedddccbdcbcadbbdceebaedaebcbcebeceebaabedaeecbecdadadbdedeedccabeebcabacbcaecaeecbeebecdaeabbcdaedcbadabbbbadabcbbcbcdecadebdeccdedeabbcbdeebdcababebbdcbcceebcadaacaaeeecbadceaaceaeceeacbebaedeccbbdddcddeaaabaeddbececbcdaddebeebadbaaebeaeecaebebbbdceaecaadbbedcdbceebbdbbbdccdedbcbdcaecaeaccbaccadeadeaeeedeeeebaabaebbbbaddddcdbddecbbdeaaadcddeceaeabaceddccbbcdbdcdcabebaecbbcbedaedacbbeecedcdacbdcddebddddcdeeebedeadbeecedccaeecccccdaccbddbebcbbecbeaeadadceececbeebdecebdcdaccdedbbecbeeaeecbacaaeaebeecdecaacaaeeeebbcabcbedacbdbcebeeebbdcecbcebdbcebeddadeebccebadaddccebedbecadbdcedacbdedabacdbbeadabaabeadecaeaceaebdeabebbedcabedacaabaeeaeecbeebaeabbaadcebaddaeacbcdddedaaededdbadeebcedbecaebababbcdebdceccdebbaeaeaeceecbccbacacbaeddceedccdbbeebaceeaceaaebacbcedcaeabdaaeddeadcaddbeccedecbddbadddbacbdbddadabcbeadaebbbdebdececbdebaeeedebbadeaddcbbaaddbcabbecbebbecebaaadaaadeeceaadbeadecdbeebcccadcddaabeaeacdacdebcacdecbaebbebddaccbdaebdddbdbcaecdabbdadcedabdcbbebaccaeeebadeeccebbecaaebceaddadcdabaaeaeadededccbecadbabcdbcbbbdabaaceeaaaeecededddedddbbcedeaaebcdcaaeebdcdebbcaddcdacddaeedbaccaebddbbcbdbcbbeddceecebbccbccbabbabeacececedeabecddecadabccddebcbbddecbecedbbacbbbeceaaadaaaacaebddceababaedeacbdacdbeedeebcdbdddbdbccecdbeecdcaecdceddeaabbaccbbbdeddbaceedadadeeaccbaaedeececbaacaaaccbedddeaeccbcbebedecbcdabdbedbaadeecdbaeabadeacbbbeabedaeaeaddcaecdebccbcdbbaadaebedcbabdeaabbaedbbcdeccdddbacabadcdccbaeaaaebbdaebddaeeececceeedcdcdcbeacbedbbcbcabdaceecaeedddaeabeaddcdacbdcadbbcbaddeeddabeadbadebdabcccebaeedbdbccddbbbddaaebbeedcecbbcbedbceecdceedeccdcbbcbdeaacdeecabbedcbcedcbceaeddeaccdddeebbccbaacabbbbeaaaeaeacaaeacdedeabeaacecdeaccedaddabaaeebaaadcbcabcaeaecdaddbaeabddadcaebacdceeacdcbeecdccedebdaadeeecdddcbedbedbdbbeddababaeabdabbdeadbacedaaeebdaaacedcccaacadeadaedebebdbaddbbceabeaaaedabdaddbbeaeaebdabeebaaecaecbddbedbcadbebcecbbbedbaaeaeabcbacaecdaaaddcbbccbdddecdeeebcdcaaecddbecccebeeabebdadbceacdcbaedeedcdccdbcadeeededaebdaeaacbcaaceebbbcacadbbdebadcbadeccaeebcacbcdeebeedbacedeccedcbeddaddcbbacecaecbaaedceecabdaecbbbbcbecccaaeaceebcaacbecceceeebdddeaeaeeebaaaaeecadbdeecebcdbeddabccaccdaebdddeebacdcdaedebcccecbbccabccabeeabaebbecbebecaaaaedebbebcbccebbaddbdddbcdceeeceabdadabededbcadbcdddcaedeadbdadecbcbbdcecebabaeacbddacdaebabdbbbcbbdbcceaebecbbdbebbaacbbadedddaeddeaebdeaeeaecdccacaedeebddeaaebcbeaaaaabeaeaeedbbaecccbddceebdebcadccbbbecdbadbbbbeecccbdaaccbdceaaeabaeadaacabdcdcdbdabaaecdbcabbdbdcdeadacbeccdaeceaaebaaddbcccabddbedcacbdadeddceedcbcbcbcdcbddaeeeaebeeddceaeebcadcdacbdaddbaebbdeadeddcacdbdbedeedaaabcbedcceebededbdedecdebcdecdacacdbcebedcaeecadacbcbaaacadccdcbccbaacaaebccacbaacaeebbbdcbadceebedaabcdaddaceccddcbdcedeacacdadaecbecdccaaebbeddedebaacaeeeabbbbeabbddaceedcebceeeaeedccbccbeeededbbcbeccdecaedcdabeabbcebeacaaaccaccacdcebebeabbcddcabddbaeaacdbdeabdaccdbddbbcabecdbbbbbebadecdddddecebeedcbeabcdbdbebebddeebacecacaeababdccddaababebaedecbabbbaeecaedaadacacdcedcdbccabecabbccdbbcabaeeebdcaeabddadceedeceddebaeaccedcabebaaedcdbbbbdcebbabeecadcbeaabbdeebeaaaccdeadbecaaeecebeaaaaebbbebeaccaccbaddaccebbbddecedadadbeabebbacceaeadadeccdcdaeacbacbbdeaaacccbaacebcdcaeaddcdceccecdaaddceeccbbbdabcacbbbebdcadaacabcebdddbdbcabbebeaeecceeaacacdceeeacaeeebadbbadaeccebcbccecaccbdeecebcacbdbebcebdecadedaedaeebdeebbacbcceaadbccddccdadeaaabeceeedcaeeaeabeebcdcddaadccadebbeaaadbadaeababedbadaedaddbbaeaeabdebbbaacaaebebaddaaacaacbbdbaeacccccabcaceecbdadbceeadebcaeacdcbabbaeaaaccbaddbceacdceaebcddbcbbdbebdbedcceaeaddebdbadedbbbdedecaeebceaabadcddbccaadcacdebcaddabccdadbcabbecbebaabebabbaaaeaaeedcbbadeebbeaceacaebaccadddaecaaaaaedaeddcaacbcddeaeaccdeedddaccccbeddebcbeedbedbdebcbbdbacabaeddecdabbeecdcbaeeebceccccbdddeceeccccbdcbebedddcbbcaadcbdbeeeacddbaecaadbdcaaabdcbdecbedeacaeaabdadeceaacbaeeeeddeaeadcdeecbbdeceadbcadebedaaebedaeadbeeecaddeeeeceaeaddaedceacdaaaadcdabcaabadcaaecbcabaccaddbaabcdbacecabdceeaeedcedbbbeeddcdaeebdbaacdcaecdbdaeacaedaadbcdbcbeaaaeccdedbbbaaaecbcaadddeadbbbdeaadcdadaaadaadebaadadaeadbaebecbcbaeeabeaaeaadebdbcaddceccaedddabbaeceebceeeabedecaceddeabdebeacdbeaaaebcdebabcecbedecdaaaceedbabadedddaccdaeeddcbcdebdbaeaeccdaeedecdedddbdccdeaacecebdebdbaeacebeaeebadcdbedacadccceaddccdceaabbdaeacceccdaabdabbeaabdbabbbaeaaeeecbaacaacedbdcdebddbbcbecccccaaeeaecaccbdcabeeaeceeadebdadebccbcddeababdaaadbebeebccecdacabadebaeaedcbbbccccdcbabbbdccadcbbabdecabdbbaaccebedadaacdeabacacabcbdbaebaeabebbaebebdbcadbacacaacbcdaaddceddccdbecdddbeecacbdcceaadbccdebdcdadeeebdccabdaebdcdbcdbddacdcdccdcbccbcadccbaaddabedeacbddbdadcebaebcaaddbabebcecedeeaabaebbdbcacebeaccceabacadadbcdeabbebabceedbddeadebbdbeadeeedabaeecebbbdbebdabbeeeaebcbdcdaaeddecebedcdeaabceabddaedceadeddcbbdcccaababdcbacdecaeabeaaadccdabbabedbcaedabdebadeeeccbcdcaabbacebeddebcbcdcabaeabddbeaccbeaaebeaedaeacbbaebbaaadeaaaeadbccdbeebcbbbeaabcbacbbceaaaecdcaeebdadcbbabcbaaddccddbcabcbcecaecbeebccabcacccdabaababcbdaedaedacacdcedeeaabceeeadcbbceadcacdeddaceacdbbccececeaaedccebedccaecbaeeedeedcccdaadadcbdecaaabdccdebebbbedceccadbcaccebdbcabaeeebecddddedcedaceabbbecdadbeaacbbaddcaabcabeabbdbaaeddacbebbabdcadeeeabcbdeeccaecbdeebeadbabaedcccbeaceeccbadbbacabdadbbdcbcccdbeddccbaecdebbcbacddbbaecbaaebabceeeddcedaaedecaaceaadcaaabbedcbcddeebeedbeaaeccbacacdebcbcbeccbadcdeedaeebbbaddbdacaebeadcceccdeedbdddcadbbbadadbcbcbdcdcbddbbaccebeabedceedacaceddccadcabdabcadbeaebaeedcddaeddbeadabbdecedebacdacaabaaacdadbaccbddcdcbaaeebbeabbbabbcdedbccbeebddbcbeadcbeaddeadbeabedbdbcebdccaeaaeadeebdbaacecacdeebccdcacaadddecbddedacbcdeaacecbdcadeaaebedaeabdbcdadaadbabddabaeacecdddbceeeadddaaaacbdcaeacbcccbecacaabecaeebcabadabadcdeeddaedbaccecdabccacbbdeadbebbddeeabcebebdbcdceeeebcaaebabecbaeccacabebeaaccdabcdbdedabeadcbaceddeccacabaccbcbdadbdeeaaabdbbeaddbdeaebdaceaedebdebbcbadcbcbecaadcdaeebbeddaceeeeadceddbacaddbecddbcaebeebdabbadcdcdaaebdccdcdaeedccccdaeccdaeddececacaaaabcebdebddcabcdeddbecdeabebccabcabebaebcaadbcbaccdcadcbaacacbcedaaddcaedaabcbdcebecbdebcbedcecdbdabaaadacebadeeccbdaaddaadbdaceacaadabaaeedebdbeaaedeccebccbdcdbeebbccdceedaacbbbaeddceaeadbebbabcdccdcabeeeaaaadccaedaacaacbcedcddddbacbcbdabebcebcbcabbcbcdbbdcabccbedbbeadbecbbacbeacdedccdcbbecddebddeeadaddabcdabeccbcbedbacabbebcdbddacebbceddecaceaebaecbecadaebcacbcbcedbbcdabdebcaaceeabcdcbedaaddcaeadedeecdedbadedbdcdedebdedabcdbccdbaabebdabbeecbdbbccdbabaaabdadeccbeaddbeebdbdeabeecaeecbeeaedbbdceddeabccbdadbdcddcaeedbbadddbcbdcbcbbbbaadceeebecbcaecdcbbeeacdacbbdcdebaccbbbddebdebabdacedaccbbccbddbbccecbeeecbddedeacddacabaeadceedeacedaeedbcdbeddccceebdeddddccebaadbbbbcecdcebedacceedacbdaaeecbcaabacabbbadbaccddcbeaeeaccceabaadedcabaeeebbbcbdeccbebcbeedabaedecaddacbbdaabdabdbccccacbaedaceddeadbbddbaddeabeabcbeeebdedcbcdbcbbbcaaabeaecdeaebdeccedcdbdbcacbaebeebcbaebcdccccbbcdeaeaaecacbcabaaecbccadeedcadadddcccdabacbbcdbbcdebecbbaadbbebadcedacddbbdeebebaebbbbccddcdabaabeaebbabebbedcddbcddbeaadceaabecbaabadeeaeaeaeeeaeedbcaabaaeeadbaceacbeaeebebaadbabcacdeaabccaeedebcacedeaedeaeaebbabddcccdabaeeaedbedcacaeacddccecdbdeecdeedeabdeadcadcacebdccbddbebeceacabadedabeddeeeecaabadbcaaebeecbbccbcaeeddcbcaadeecadcdbeaedecaceeedadbebaabadccddbeaaacaaaabacededaaeaacaddbcdeacebedddbabceadbdedaeceedecadbadcceddcdbddeaccbbaecaecadbccbbcabddbecebecadadebceabcedcccdcbbecabbceeadeddcccdecaecaaecbdddbcebbeeadceeeacaebaebabdccdaeaccbeaadcaeadabddccbbcaeddbdbddeddecedbbdeadcaeeaeeddbcdbbccbdbaceccaadbeecbdaeabeebbedaecadccbebccbdedeaacccddeaaebaaabaeaebceeaceadbbcdcebaecadcdddacbdeebaedeaedbaaecbebaaaeaacbeacacbdcdbdaadaeabbddeecbdeabeedaaacddebcbebdeedbdeadadadcbebdbeccceeacebcecdcdadaeeacedbecaebbdecaeeaccbbdbdededcaebeabdbedeabaaeaebbdcccadeadbcddcdeedcbaededaceeeceabeaaecadeacbaebecbaaaeccbedcceadcedbdbbdeaadcaeeabaeebbdbcaededeeedeedecceeccdaedadaacbedbcabadabeeeebbcebabcdbecedadacbcdabbcaaeadaeaeeeaedbbbcaebadbcdbecacaaecbebbcbecabacbbabdaababbaabbdbadbeccadebbcdacedebccdceaeeceecdeebcaddeeaaebabeddaedabeaaeaabebeceecbddeeedbedecdcccebbbeacadddadeebeabecdaabbdedebdadbeddecaaaaaaccaccbdadecccacbaeebcceccbceccdacddcedaaceceabacdebaddbbbdcbbaadabaebcbaacacdadecdacccbacabbbdddeaceaeeadcabedecbdcbcadaabddebdcccddebbeedbbbedacdccccbacecabcdbdcdaaabcbacbcaceaaabaeeaeceeeddccaacedaabacddeaebeaceabeecdbbeecacdbeedacbcbebaccebbdcceaceaedcddeaeedbeeabcddadadcecbebeabdebacaaaeabadcbdecbaaabcdeecccccdbaaddecbecbaedacaadccbecacdabdbedccbadbbcccacacedaabababcaebdacbbeaeeabedcbceededacebbdbcbcecbdcaaecbedabbacaeaddeabddabbbeddabcaabddabccbbcaebaddbabcbbdcacdbddacabcdceeeeeeccaceedccddadcddbabacaaaacaaaebbaecbbadacceeeabaedeecbdeaadebeeedaecdcbddacaedbabadaacaedeaedcaaeababddbcbecaeaebdbcecbbcacddacacedaabbacbadaddcdcdbeadaecebedecdadbdbdaeedadeebddbdbbaeaceccdbbedaebadbbcecdabcdebaacdcaccedccadccaebbbbddcecccccddbdeecadbaceeceaecacbcbabdcdcdacccedecabcddaaedbddaccdbeaaeccacaacacddeaccbeddcedadacecdaecbcddccbdbeebccadcabaadccabbabeeedcbecabebeccceabdabeaabeebcabcaeaabbcbacceeaeabcbeecbcadaeceeadababcbbcbeadcbeeabdabbcededbbedeacddabebeecbbeabacdbbbcddecdabbcdeebacdeaacdecdbdeedaccdeebaeaadcaaccecabdcaceeedcadbcccbbbcbdcaabbaeacecbbacdeecbdabaabdadedaabecbedcbcdceaeeedbcaadebabeebacadacdaebdadddadedaabececdddcbdcadaeabbbebebdaadedcdbabadbabbaecbbdbbecdaccbeaabcdeecbdcadedeccdedccdcbacbbaceabceedbadcbdddebacbcaeabaccdcedecaabecdaadeeadceccbebdcadabacacdddabbabcbbceebdbbdaaeeadecbbbbaccacadebedcaaaaddbdbbdcedcbbdddddcbeaccbbcbccdeabcddbeadecccbdaabbbebaccdcbcabaeddcdddbadeaebedddcaeecdbcbebaedadabddbbcbabbacceeeacbbaeadcebeaeaedeeccaccaaeadecadeaaeccedcdabaaaaaeabedabbacababecededeeebdeacbcebdccdccdecdbadcdddaaaaceddebbbddcceaddbbddbaebbadacdebeaabadeacbacdaddeeedcbeeeebcbbcadaebbbddbdddcceebdebabecdbedeceaaddaddcddecaabadbdaeaaedebbccddddbcbcacdebaacddddceaeceabedaaccedcadecbaacbebbadeeedcaaadbeddabecdcaabaecacadedcbceacaddacedbbbaacdaccaacbaababeddddbbeaccddecccdbcbcabeabaaaaaeeacdebcaabdbacdabaeecabcaaeeebebcbdaaaedccdbcccdceadeeddadddaedacdabaccbbeebdacdcabcbdecabbdacaddbeababaacbbaadcaeaceccbbdeaeeccdceddcbaebbdbebdaaaddebcadcedddcccabebbaccaabbaeaaaeedcbdddaecbdebdcabcaaeebccccedddbcceacbaceeedbbdeeebadabaaaeabbdcceaedbdecccbdaccceaccddedcdbbbeddccdeadaddebbcaeedcddacbeddbbeaaacadebeacdeaebececcddceedbbdcdaadeacdddedadaccbeeabcbeacecebcbcecbeccdaeabacbeedabbdbdcbedaddeecebbcdcaeceaabdbbdbbcedbcecdddbdbacceedbbbececcaececbbbabddabaebdbeabebbbeddedbbcdbaebabbccecabdeabaeeeccdccaeebecadebcecdecbbccaceabebadedbecaadbbbdcbbdcdcbbccedeebccdeeeeeebcebdcccdaccebcedccadecaaabbceecddeeaacdcdcccceacdbbbacbcdaadbecbabcccadbcbeecddebdccdabaedeabaebcadceceadcdeddeeeadbbeecdcceaeabedecbbdecdbcdcbdaeccbedaaaebeceeeaadceccabbcddaaebddaaacadbbdeabcacbbbddeaadeebeedebdedabacaecceabdeeeeacdcdecaceedabbbbdececbcaebeabddcaaabdcdccaededccdcadbcebbebccbbebbcaeebdcdcbdabcbbbabcadaadbdbdbccaeedcdacdaceeecebeeadbddedccbcbdabbeebededcbcccabbcdeaabcbcabedeeeeeeaddeeebadadabeecabdbadacceeadecdaabcccdadeadedceecccadabbcacbcbbdbabceabccdbcbabccacbcabcacbbbdaeeceddcbacedecadeeabbebdabcdebaeaeebaaddaedebdcdbcbddeccabdeabbbdbcaeeeaddbbdbeeacadcddccdebecdcaccdddadacbdbeadabdaecaaebbcdbeeccaecaeacdcdcdaaeadbecbaccabcbcacedddbdbebacaabbddccabedecacceedbbebaeadcdbccdcaadaeccbdcbbacbdddbcadeeeabbcbcdbbaaabcecbbceeecdcdcdadbebdcdddccbdbebaeadaccebdeedeccacceebececcebaaeddbdebedddebbaeaceddcbaedccacbaddbcdeedaddeeebaadaedaeaddbeaccbddcedbabaeadcaeaadccccecabbbacbbdbcdcecbcbdcedbdcddbcdaeccaceddbceabecedcdcdacdecaeaeceaebacbadeadeadeaddddeabbcedbdabbcebcabbbcbdedbedaeadcddddcccbcdebaabbebbccbcdcbdcdeeceacdbbaabdcdabbcaeabdeebcdbecbbebaccadbdeacdccdddbdbbcbeeadaeccdcceeeddaeadecdddcccbeddaacaeebeabbcdeaebdedbeeddeaacecadadaddcdedbaeecbeabbaecdedadbacebcaccadcdcaccaeadbaeabddbcabaaddebbccbbeeaabeebccbdbcaceddeddadabdeeecabbbedcedeaabeceacaddeeebebdcedbadbedebbbbddcebbceedaaceccedeabdebaadbaddcaedeccedabdeaccdbaacbeacdeebaeebacddcbaaaaabcadeeacceaceadbbacdebacaeceecadeceeddcdbeeaabaabccaaeaabcbbaccdecebbdbaacedceadcccecdceabbbbacdceebcbdaaadadcadabdddedeebedcbaadbbbdbdcadebaeadabcabeccbaeadcbeacadaadadeadadebdbbedaebcbbedcbdabadbbcdbaccbbaadecabbaaaebbdebdbcbbdeacaacaedcbaacbdebabbacbeadabeccececabaacddaacabbaddedaaccebcbabadceeebbabecaebcaaeabbccbcbecabdaacebeddaaecdaaecdecdbdcaeeaeedecbacadbccadabdbedbbacabcacecbcebebcaedaabcbebbbebcaebbddaabbaadebcdbccbbcbbaacaadccdcbadbaccedacbecdbadccacbeeaccbcbabeccdceedcaadcdaaebcbcceadcbcbdaaeeadbdecaaeddaacacbdbecbbceaebabbeaeacaceedaebabbbadbcbebeabeeaeddcebaaeabdbbaecddadeddcdbcccadcdcbdddbebeadbbdcebedddaebeccabddbdcebacdbabeeaedabcebbdbbcdeeaddecbcaaecaadeaedbabeeabacbeadceaaeedababeeeeadcedbbaebadeacbcbeedbbbbdbbbebaecaabbebeedecddcdeaeabedddcbccabedbeebeccacecabedcddcdeaabcababaddbaedecedbcacbdedcbdcbedacebeedbecaaeabcabdcdbbbccbdbbaccbcdbccdedebaeacabcdebdaebbbccceeebdbaebebcbadcbcecbaaadacbbbbbeeedeeababeeabdedeeedccaebbdbadeaceceecccbceabeecbecebabcbbceaecaeaaddaadbaeecbabdbdebeccebcceaaaaeeaeeaacaabdbdeabbbcaddeecbbbdcccddedbbeccbecdebebcaddbbcabccdddbdcaaebcbaaebacdeaadbeccbedddcaaddbbddeadbabbdccdedcbbebbbeccbbeedbeabcccabaecddcddacbeacccbedeceecbbcccecbccccedabacbecebcedecdecabbedabbeeecdbcdcacaaaaecdaabecaaacdacdeadbedebcebccdcdbabdcedbdccdcbdcaeaadeedccddaaacbbedadaabdcdbdddbabbabbdaaccaeedabdaeeceaecadaddbadaccdccacbeddedcccebdabaddacbacbddcddccddddeaedeabaadadccbddbdcddadedbcaadcacccaecdabebdaaeecacdedcbdbbeecaecebedaddeedebbbeeebccbbccabedaadcdeeaeebdccbdbbecabdeccbbeabccaacbbcccdeadbdceddadedacbcabddacebceeeaaadeeadedceacedacecbeddecceeccbceedadaccdbeedecadcdacdddbaebebbddbaaaadadacdddbbcdbbbcdcacebdbeebcdabeadcbaeeaaecdbdbdebaaebcabacadeadaeaaacdcdcddcacccceedcebaeadedceabacbbabeeddbbddabcecaeabbccedabdecdcebaedbbabadbccdabaadabeddecaaedcceacbebeeebecedcadcbdeacebacdcaacabbbbcdcdcdbbcbaccdecaabcbbaceddedbabdcacacaebabeacccccabacbaecabdcdbddcacedbbaccaecbddbadbedcbdbccdddbdbbdbecbcaaaddbdabacdeebeacdecbcbbddeaeeddbcebbbbedaebcdebbbbebeeccdbbbbcaddeccaeaacbbcbdcbcadaeedaddeecccebbdbbcbedbbebebcdadeadbabbbabddadaddaabddacceecdcdabbdcbbbeaccdbdbededeaecaaaeebeebcebdadddddabebcaaecebaadacbddbaedacacaccdccdcedbaebbcbdcbddeeecbeebbaababbbeadacaccabedcbebecbdbcdadbdcabcaedbaabdedbeebeccdbcdcebdaecdeceebaebcacadecbbcccdaaebcadbdbbceacedaacdcbbdabdeacacbedeaccbedbeeedabcbdcbedcbcaaadccebcaaacdcbaecebadcdecacccabedcacadacbedeaebecdbccabbcbdbbeececdddddddbeadabcecacbebdbeaabcceccbaccaaaabeddedecdddccbddcecaecbebbdbeecbddebbcebcbaddedcaeaadcaaddbcdedbcbebedaccacabdccabcbdcbdcbbccaaeddaacdbbaeccdabaedddbadacdebeaaacbaadeccecedeaeaccdcccddbcadeebeadedeccadeadaeaecbdadbbecdbceebdeabdadeaddbdadbacceebaddddcdebbbcebddecbadbbcadcbbaaaedaecceebdcabbebdadbdcabdaccdbaabadabcedbdacddbbdcaeacedebeabecebdadaebedabcdbbbccaaebddbeddacccdceddeebbdaeddcabacacdbcdcacbddbcbdebcabdacadcbbbbbccabcdabadacaaacdbbacdaccddbceebdcbcdaebcaacadceebbaecaaacbbebeecedaedeebdccdacceeeccbcaecdbddddebbcdeccaadaaceedbbceaacdbeeaccccdccdecadeaeeadccbdabaccdceeccecdadeabcbebbcdbdeaaaeadbdbaeabbebddbcebeeadeeebadbebacaddeebdeaeeaaceecdcccaecbaecddcaadddeababacbdeeccebebebccdddeaaedceacccadbeaedcdaaaccadddaabcbebbeebdacadaadcbadacbbdeccaaabeadcdbcbcabbeaccacdccaaddacedccdcaeaeebdaeaddadcadebdaeecccecbedbdecbcaebbaceadbbabcdccaddbaaebbcdaecddceedbcaecccbdebbddacaacaadaadcbebdedacdecbeaeedcdbaadebaaebdbdaaccaaaeadaebcedcbcccacaaddddeeebebceeceaecccaeeedddbceeeeedeeeabadccabeacbcabdacaacbebccdedacbbecceaabddcaddaaebaaddddcdedcabbeecacaceecbcabebdcbaddadedaaebdbabbebcadabbacdcbbbebdbcbaabdebabdacbceaccbedcedceacbdaadedebbdccebeaedbcbbaebaeebeccaaeaebbabccabccddbacddeaadbcbdacabdbcaebbdbdaecbaddbdbaadbdedacebaadbcbdceabaaabcbacdeaeecdeebdbdaeeeadceeacdceccabcbedcabddaaccdabcecddcaabbcdaaadadbdcedaaaadbdeaacdebdecbeaadcecbdeeceaceeecccbccaeabecdbabdebdebdcaabaabbebeababbdddbbbabeaebcaadccbabababbebcdceecacadaddceebabdcbdabbdddeaecdceebeebaccaacbcdaeabcbbdaeadecedddebbbeadceaeedeacabdeeeabdacacecddcbdcdbdaeecebbecaabeadedebebddcbdbeaebddaaaccbdeabcbdbbcdaebcaedbcddcbcecaeeaccbadadcebccdcbaaaeeeabcebedecbdcbcbcecadcdaacedbbccdcbdeaeababbbceadccccdbacbecaacdaeecceeedbebddcccaacacabdaabdaedaccebcbbdbbbcaddeccdddcadedeeaebbdcddaebddbdcaccdececbdbacdaaadddbdecddececbbaceeaccaecdeeaecabbebecbdacabbabadecabcdbbaeaabbebacbbbbbdbbacaacbceedccaabcdcdebddccbbcdccaeacdccccadbeeabaeeedcbacdeddbcecdcdccceacdbbddebcdcebaaecabbeacbbeeaaeacebedddebbdcadccdcceacaaaabbabaedcaebaaabecaebbacbaadccdbcedeeeaabcebdddcdbcbeeccecdccbebcdbebbbdeeacdeeeacecadbbbdeecbdbeecabdedebaaaabedbabdacabeaaeacdaebbdccabbeedbaecdcbebdceabedecceccabeecdbccaebaeaedcbaecbbcceacbdbedeaaceebbeaaceaeaaaebeacdddeadbebbaaccaceaeddbdbeededdaddeeaadaaaeeddaadecaaadabadaabaeadcbdbbbecbacdecbdadadacadbaacbaacbababdbcadbdaeddaebbcbdaaebccbeeebbddbecaeaacdededbaedcacacbbeaeaeabccdaadecaeedeaadecebceecbbdeaddddedbddeacbdacccccddecaeeddccbdbdaddbdbeedccaebcabeeadaceeddbcacabeecddbbddbeabeacabaacdbcecabdbcbbaadccdebacabcbbeecbbcbdcdeacdebceedbadadebaeebdbecbbdbacedbdbdbabbeddbcaecedbbcdcbeaddbbebabdeebdaabcdccbcdbaadacecccddedbebacbaabcaccebacedadbacadcbbdbdeeebaabedacadabedadcebdeeceadaabacaebeadbaebceeebebdcccaceecdecedaedebddddebecdccaadcdaceddcdeaaaecbcbbecccceedbeabcdacadbcaddccdbadeedcdbeedceaacbcdbeeeceedbbceebdceeaecedeaeaadbdacbbeeedcedbddcabdadabccdbedabbceabbedbdedceddcdedcbedecccbbdeaacccceccbaebbacdbbbbedcbecbbcecbdccdacbadbbcebdcaedbdbeaaabeebeabdddbdbacbbdbcdcaedbeeacbbdebadeaacddbbbebaedeebeacdaceaabcacddbebcdbecddbbaddcbaabcdddbadbebaaadeacdecddadecceeacaddeadababdabdebbbadcddaccddccadcbcccdbeebebecadcccaebddddbaaacdbadedbeaeedabeebcbcbebbbebcdcecbadcaaccbddbecabcdbbbdebaadcceedcbdbeadbacdaaacabaeeaacebeecdbdbbaecaeaeaeababaaaccebbabedbebdbcbbbdccbcbceadbcccdabacedacecaeabcedbbddbeeddadbecdcaddcaaeabeaabccadcaeddacaaaacecbddedccbedbbaaebbabdccbccddaceddcacabbdabcbdcebbcddbbbdacdcaaeadadcbcccbaddebdbbaebcdcdcbbebcddcbecabbaecddaecabaedcadeaadaeadcbddccaaeabbebbeddebddecbbbcbdeedcbddacdbebddadaadccbdbddcccdabeadaeaadaadecbadabeaacadabeeadddeebcbccccddcbeaddccceacdaadcdbbbeccabbacddedbcaddbaaacbdabaddddedeceebbbbadeceecbbcbbebddcbcbccadecccaebaddbebbebecceecbcabeababaadbadbbcddaeaecdeeddadcddaeadcabeedbcaaabacededcccdeeaeaeeddbabebdcedbacebdebeaddaaccbecbcccabddabedbbbcdbeadedbccaeacdabdcaddbeedadeedaaeecedcdaababaccdadedbdbaddaddeadbadbedeeddecadcbcaaedebeeacbbeebbadeadbcdabaaeacdebbaddccecadbaaeaabcaabeeabbdecdacdaceedaddeecadedeeeabaeecaadbbadcddeabdbedbaaaeabcbcbaecdbceddecacbbabebdceabbcceebbbbcbddbaecdebdbaaabcebbcccbcdcadaabbaecacaaedbadccebbebbbeabadaebaacbadabcaabbbcbcbdcbededcbccedccdceaccbadccacabccecdecebadedacdeedecccaeedbdbdaaeccdddaceedaecddadcedbabacbebedcdeedbcdacdaecdcdeaccacbebacdeedbceaecececaaebddeebeaeccabaecabadbdaebacacaeacaabcdedbebeaaddbbceebeecbacebebdcaedcddbdbbeeeebedeaccdecaeedccbadbdbcbdcbeecbddddeacdeddecccaebdabacbdbadecabccddebbabaedabbbddaecbecacbabbccdebdcbaebdccbceedbdbddeaeaebddbcadaedbaeceeaadecdbebbedddbbccaaedcacbcbdcdaeaaadabbabeaaaabceaaedecbebabecdbebcdbabababbdbcdaacbdecdaabecdaaebdccccaeeeddbeaccecbacecaaedcaaadececeacaaeecdaccebddbbcdbdcdadbacabaaabceabbaaedbbbebbbbacadcceadaaddaddeecbabadddbdcddbeacddccadddadcebabcababcbeceeaccdeddbeadbdbcacbabeaaecbdacedabdaadebedbbbeaebdddccbccbdbebccaeabeccabdcdddcacacbcaaeebbddeeadbdbdbabccbacbedbdaaaaaeedbedccebdaedebeeedebceeddabcddadceecddebbdedccebbdddccbdeeacdaedbcabdbccecbaeabbebdeaabedacaabbdaebddeeaccbaacadccdcbeeceacdbaacebbdeadeacebeaadddaccedabebddbcaaaadeeeaaeeeadaeaccbdaadddabbebacaaaacabbcebebbaaccccbcbacbdedeabebaeececaedceacddcabcaccdbaccbadecaccccbaecdbcabceebbcdaaedeeadceeedcdbaedbedcbaadcbddbcabcdecebdbadeedcccccadbbcabdddcbcbbddcacdccebeaebceeedceacdcbaaeacbbaaadabecaabdeacdececbabebdeeeccabcbdabadaeabcddaabddeebcbecbbddbcdbcbeabedeaeedbaabdcaabbcbbececeeaceacaaabdcececdbbcccaccacddccddcccdcaaaedabacbdcbaccceedaaccbbedbcaecdaeedcadeadedbdeeaebcaaeceeaeacabdcbadcbbcacbebccaceeeeedacbbebdcadeaccdbdaeccdbadbbeccaabaceddbcbccabbdaeadaceceebdbbcaabaaabcbcceabaeacdedbccbebcbbeacbaaceaccceebadcbbeacbddbbbbbbebecdeeeddbbcaaedbcbbcdcacbdcadaecbbcedcedeeedbeadadbedceadaaccecdcddaebbccedaddeabebadacbaddaadcabeccecbededbecedaebdcededdaeeeebeeccebbbedcdcacdcacaecaaeecdbaccbabaedddedcbacabdeccbacbaaabdaddcdbeacedeeaddadbddbaeecababacbdcbdccbdaddbcedceacdaacdabbedcebadcbeedcccbcddcedebacdbaaddacdecbdabacbebeeccbdbecadbeeaccdecdaeeeaaceaebdcaabebbedadcdadaceebeebebbbaeddaaacbebdcdedecdeeacceacbcdbacaabddbbcbeaedcbbdbbaebbcedeeaabdeeabcededdabcaeeacddcceebdeaabdeccedcbabbcabdbecdbabeaebdbcdedccdbcddcaedeecaadcdeaeacdddeeeccdeabdccbacedaaeedcbeddcdacacdedcaedbcedaacdeecbaddcbaacdcdadadabbbaaadbacaebccdaeecaaaceabdbcccaacbeabdcdcaaababcdedbcabbaaabacadbedabdedddcdcbacedbceacabecbcbeaecbdbaaebebaabaebdcdcabddbebcbededbddbacabcccbdeeebebacbdeaebcedecdcedcdaebcbcbddcbcbbaeeeeecbcbebeeeebadcbecaddcabcbbaecdecdabaeabbbcbaddacacabebccccdddcddeedaabbcbdebdcdacaecaecbcdecdbdeaaeceaddbdbdeabbcaaeeacadddaeeebeadeabecadbddceadaacdebaccbccadabaeccdcbaddbceabeedbaedcdcdcaddecdecaddeabdadccdaeedcecbbaacaaeabddaccecaaaeaaaeaaddbdcabbdbeabcadadeeeadaaaeaeaebcabacdaeacddcccbeecaddeddceaeededbdbacbaabdacdeeeaeeacedbdbbecdcadaaddedbecaaaebaebbcdeaecdbedabeacbebeeeedacdddacceacddeecaebdecdbaebbcbedcabcddeeeeecaaeebcebccbedeebbcdcedeeebdbddcecebaceeeedabebcbdcedaaecdcdbbcbcebdddbdbcacceaabbcaabdeaeaeecedbebbeccadedcebcabbabbbccbccecddedebecbebdbbbcabbcbbdbeaeebbdcdecbcaddddacbcdcbeedcbeddadaeebbbcbabdaaeaceabdbedabbeeaccbeeebceccbddbcddbbbecbdbceedbeddcecbccddbbdbdeddcedadbcaeddeeeccabdedcddcadcbebeedaebabdecceccbdacbaeaadbaadabccebbceaddedeacbcbecadbabedddbcbeaadebbceaadebeadccacbdbccbcacabbbecdcdbecddadeaadadbdcaebdbdebaaceaeeebeeaadacbedccaddebecdedaccabdccaabcacdccabdccacaedccdcdeebabecdbaaaadddbdaebecdacecabcacebebccccdebebeddebbacdcebabaecbbcdaeeeaaeaeebdbeaddaacdbdededdeacaadbcccebaccbcebcbcebbeecaabaaaacdbcdceceadecbcdaeaeebdedcdeaecacdecacbaacbcbbbcecdccabcddeabbeddecadaeeeceddcdbbebbeabcacdeadcddbacaadbdabbedecdeecceddebbbaadedeaacceaadbadaeeccdbbedbeedcedaccdbecbedbecbeaddabbeacebaadeebbbedbadaebcabcebbdcaddeadaaecbaebacaedccbcbddbdaebccbbacdbededacbdacacaecbbaadaaedaadbddebeaccecbceaddbcbcecebbecaaeaebcbeebebbeccaeadbaddeabacdccbdbccabccaeaaddabeddacecddeacabbdbbdadcceadadcadcbaceeaaeeaabeedadbeeaabaccacdaedbccdccbbebacdebcbebdedecceaadcbcacbaebccdddaeeabeeabccebabcbcdacddbdcabbebcbcbeccbdeabbcebbccaeeeacdeeedadcdacccccdbaadcdececbcccceebccddebadbddbdbbdcbbbbdadbdadacbdeabbbbcbdeecceaebbcebbeaaaecccebabdcbbbecbdccceccdddaecaaeaabecebbeaeeecdceadbadccacbdbbbcdbdaddeaadeabbaebcabbcadddcccceccbccdabcddddcbceaaacddadaddbaccaaaeabacaeceebbbbeaceaeeaacbabbcbddabbacdbeaaabceaadecbecaccdadacedaeddadbbcbdcccaebdeeebddbbadeecbedeeeacbbebaebaeeeecbcbdcceccaebebdaaddbebeaaadadbaabbcccecdebcbeaaccbbdeeacdccedeedbabddedecdeeceeeaaeeeabecdceacdecbcdacbbebcbbdebbdbaecedeceeeceadeebadddecdeecedcaedcabeeabacacadcecacdbbcebaddebcebdabdcccabccbacabdeaaaacaadabceedabedbeaceecaadbaedcedcaddedacecebebcdbaebacddedaeedceeeebeedabaebbcaedcccdaadbaceababeeadbccdbdcaaebaaaaebaeebcdcbaedbdcbbedbceccaeebbbddcceebbbbbecbdddbaacbbaebceccceccbcebdbecabaacccbccedbdbddcbcbbadcacbabdaacdebdbceccadcaebdcbdeeacbddaeaaedeadcebbbeedcdaebcceaaeebbdeccbdadcdcdddccbdaccccbaebbadccaedceeceddbccaeccadccbbbdcccacdbdadbbcbcccccbeacacedebdeebccdabdceddebdaaebeeccacdbaecaedadbeccbdabeeadeadcdcbcdcdacdaaceecbbcabcceacbdbdcaeedcceaabdadbcbabccaeaabcdbcdcbeadbedcadbadbdeeaaeadcbbcdadacecbcbacebedaaeceeebcbaeccadaaceacebacbebceecdacabbdbbcccceecababbcaceebadbdbabaaddbeaeebabcbbddecbabbeadacdccedebbbcdadbebbcaebeacabeedcaedddbebeadbbbbdeeeddadeedecbdcebdccceacddeaeddecdcaabeebbbeeaecabddcdeededbedbaabbdebedbccedebdddeeddeeadcebddaacceabdaaadebcdddceedebebedbaedceadeacaecceebebcaadeecaeeaacbdceebcacddeeeaaedacedbddeeadcbbcbeadacbaddaeecbeccbaccceaacebeabadbbdbbeeccaadcacbceadbcaadcbebabddadabebaeabbccebbbcadbebdbcabcebaacbaabcdeabdbeecccbbdeebedbcaedebbbacceaaaceedbacdadbbeceaebbbeabcbabacbbdeaecbabbddddeccbebacbaeaedecceebccdcbdbaeeedecaabbddeccacceadaecdbceecebbcaabdaaeadccaedeabceaabdeedbbbaaabaaaeebbbecedbaeedededbaceeacdcccdddcbaccacedcbebcebddbaeacbdcdcbeedcbdebaaadbaadeececdbcecdecddcdeabbcedbbbadbbccdecbacbcacaccdedaeddaddeebbdebaaabcddacceabadedababecdebddebdaacdbddeeecbbcbcacacdddaddcedaeadeaebededcdceadebebcbddaeaacadddabccbaedecaabdadaebedcbccaeacababcabbaaceaddeedebdcadeecbdcedbaeebcedbecbcecbeaddbccbcabeeaaedcbcbacbabadccbcecdbeebebbcdaccecdbebeabdacdaecbedcccbddbdbdabeaadadcdbaaacadebbabdcbdbccbdeceddddaecbddddddbbadddddbabecceaecbeadedbdccebeaacbdcbeedbccddabadcbacceacbdaebbaaebadeeddcebdaaaaedaccaeddacabaccdcbbdccdcbbdcdbcdbaecceacaaebcaadecddcdcacdecbbccebdcebccebeacceaaadadbdbedcaeedaaaebaadeddcabeaeacaccddecdebecabaadceadacecdedbbdaedcdcbabbddabceadbdcbecedeabbecbebaddebeccccdbeeadbdadceeeadeaeaeabdbccdeeeceeddbdeceaeeceedcebeccbacbbaaedeacdebebbbadeedbeeacdeabedceabddacbedebbacababebddcbdcbadbdeddbbddbdbedecadeebcecabaababeabaadabcdaccbedcabceabbccebadccaaadebadcedbdaaceedebceabebeecdeeeaeedcdadcddbeccceebbececadeaedbecdcdcaeabeddbaeaebeedaeacbecbebacdbbdecbdbcdaedcaaecdbccceedaeceeeacedaeeacababcbbebceaabaeddbdadbacbbeeebcaeacebabdceaaeedacdaecceaecceebeccebebcdeabaeacddcdaddcacebedceabbebbeabacbddbadadbceedeccbadcbbeddaadeaecebabcabcbcdecaacccdacabdccdcabbeeaadbbcaecaebcbcbbadedcadadeeecccdaebecdcebacbdeecbbcecbaedbdbcbceaaccaeabbeaadeddbcdcbdbabcdbbeddbaebccccdbcaebadebbbdabccbaacedaceceeebcbedbbecadbedabcdbabbebcbeaeedadcccdcceecabbbbabadececbbecdcbeeebbacdbccaacdcedebabacbdcbdcedbabdadadabacbeabebdebabeedaadadaadcbdccabdabcebcadeebabcdedcbdaeccdbbccdecbddeeccbaceabbceaddcdabbceebeabadedeaacaabddeabbbeebcabbebedaeeacddebeaebceeedadcacadbbbcecdbbadbedeeebbecadcdedbddebaccdbaacaceacdaebeedbddcccdcacebeebdedbeedaecadaeacccbeaadbcabddcaeecadeaddebeacbaadabcdcadcbedddccdbbcaecececacbcadadbdddcddeeebbadbedabdbadcebcdcaddaabcbbdcdeeabebdaecdacbaddbdcbbecaaebddeeacacaeaebbaaddcdeecaacadeabcecbaeedababdadcbcbcdeeeababedbbbdecbdddcbceeadedcdedcacdcdabecdabcacaceebadddeecdaeaebcabadceeeaaceabaaebdacddacedecdddbdbaebdbaacecabaddbaabdedeedaadacdedcaabeabbacdacaebaccdbbdcbedaadcacbadeecdccbdadaccdedcdbdcabeccadaedecaabdcaabbaceecccadcddcdaecccdcbebbabaacecaebceacaeecacdbabadeeaccdcdbbbcbeeabbcaccdeaeecbdaeeebbdddeebdaaaceccbdbbccdbdbcdaeeceacdbbcbededabcccaeeebebecbccbcccebadbabccdecadabeacaeaaedaabedcdeeabaceaedecabecacdbcecababbaaaeecabceeeeeecabebeaddacbaceaaeadaabdecbcccebbbeceadcdeeecdbbcbeceebaaacedbcbccaeaeceeecaeebdaeaabedabedbcddaeacacaeaacededadccceabacbeaaeebecdcbddaceabcbedebceaaddcdbecdaadaceaeedaeebaaadddddbadabbceedcbaeccdacbdeaebeaabdddeacecebddeebebbebeeeebabcaebadbaaaadeadddadbaddadeeeaacaedbbdcdadbceeeacdcceaacbaceccccbdabbcabdbeaecbacdceadcccabcaedeebddddbedbeaccbbdadddbaeabbdbdebeeaedadddbaddeacadbcddcaabceeeacedecaeabcdbadcceabbdabaeebedcededddacebacecaebdbaecbbabddeddaaacdeceaeabaccdcacbeaecceedeebcbebaebacaedeadbcbceaabddababcccddcdcccadcbcbbcccdabcbceecdddbcccceadeadbadeeaaaddbbdcdcdbabaaadebbbdaaebbedbacccceeadaccbaeecdcecdeabebbebcccceadbcadddedceaecabcaecdacabdebecdeaceaddbbcdacaccaebdcbdbbdbcbcbaeeeddcdeebaaecebcacabeadcccdcbdccdbcadbcebceeadaedcdccaebddeaceceecaeccdcceededcabcdceeeedebaeeeebabaecdececddeadcadadcecdedddeeedeeadbcbeedbbcbdddbeeaabbdceddeebdcedbdadebabeadbeeedcbbaadbeeedacbaacadadaabeeaadcacbdcdaabccaadedecebcbbacaddaaaaeeeacbcbeddadcaecaabcbeaddabeaecabbdaadddebbaaeceeeedcbbcdbbbdaeebcabccadedecbccdbeabbbbcdccbdcaceebbbacaeeaebcdaecceeebecaaacacbaddbdebbcddaeadacbdccdcaaceabdacaadbdedabbcadeacbadbbbbcaccddaaadaabeeacededcdbbadbddbbaeceeddabadddcebdbbebddbdeabeebbbdbcaeaadcedbabaedbeaeeebeadaedebbdccadabbdbdeaaaecacadccedaeadeebddcccadbdbcedeacceedeaababbdadbdedacddcbcbbcadbbacaccadbabcccaedcdceecdbadcbebaabaedadbaeabcddcedddabcbeeccbcbaacbbecccdaadacaeccadacbccdecdaedcccebdddaeeebcdeedaceaebcbdaeeabaeddeedeaadcaebbabacccdcbebbcbdbbdaeedeeedddcdedceaaeebecbeeedabbddaeeeaacdabeecadddaecbecacaadedccdacecbeebedbdeceaabdcccaaacdcaabaaadcaadbecadadecacbecebcddeeceaaacbaedadebeacceeebbebdcaabbeeaacbdaeceddbdcbaaeebaebccbcaebcdbcbdaadeaddbdbbbccecbbadecdbeedbdabcccebaaddbcbbaedcbaceededcbcbbdbdadcbccccbbcbaaceecbaeacceebeedddabccbdbcbbdcbbeabbeecabdeaeadadbecdcaeecaadabbdcadecedbbcedabbddebadaadaebecaddcdaeeeceeaebeedeaeeeebabdddcabbbbdcaabdcbededacdcdececebeebbbacadadbabddeadedddadcdccedbaacbdaeaeeeedcaadacaabbccddbbdcadadbdcebbaabccccddabdcaeeaabcabccdecebabbbdbcdcdbeababaacdacecdbcecddacadcbddcdaedecdaabaccdcbbbebcaaaabccaedececbcdbccbdecdacbdabbcddedcaeacabdaceedaacadadccdaebbebddbbcbcbddbbccdeaadcbeddadeccdaceaecdcdceaeebdbdebeaaaadccdcaeabbbbcdecedaeeaeececddcacccecbcccbbbaceccaeddbecedcbdeebbdadeababeaedcebaadbbadaabceeaeeaccaeedaebebeacaccbaeabbadacecaedeabcadbeadaccdaaaabdeeccaacdbdeaaccdabadebcecaeeaaceccddbedaeabdecaccdeeabdbadcacbedbeacececcbceddcddddededbbdbbbacaecaebbcbacabbbdddacedddeaccdeaedeeddeeadcddeabcadcdebdbadedadedacbeaeebdeaacedbbececbcaccbdcabeaccdecbcadcdeacbabebecbbaecacbcacdbcbcaadcbbdeebdeddedeeaaddcebabcacbaaeebbeadeecddceeaeeddceabccdedabaeeabbcbaaaedaeededddecaaacccdccecceddcecbcebeaaecabdcccacebedadbbcdaceaeacdbeedddceabdaacadcedbbdebbecbcabaebdebbbcebecbedcbbabceabeedddbabbaedecdecedbdbaedabddabbbacedbecbacecceadcadaaccceacddcddccedbedbcbedcddbbcbdebdbdcaddeddbbcddcbbcbbacdebdaeebcbeeedaabeaaccaaeacbabceceeabddcbaaaedeabbbaacedcbabdbaddbebecdddbecccbaedadbceaebabcdeacbaaeecceecaabeccaadadbeaddaeedecceccccddadcaccedcbceaeabecaaedaaedebddbabccceadeeaeeeaadbeecdeceaedbdecabaeedeebdedbdbedcceebdcaaedeebcbbebabbdbdccbcbcbcdcedbaddaeaedbddebaaccbcebbaeecabbeabaedbaaddbaaadbdbeddddabcadeebededbabcbcaacdecccdeacabaeaccdeecdaaaabaabdddacaacbbceccccddbdbaeeddbdebebddbddcbeddecebeedacabbceacdeaaaccbbabbebabbecddaeaacdbdeabeddabedcbdccebdddebdbececcdeebeaecbdecacbebbaecadcbbabdcccecaeacdccbedaebccceedcabacbbbeccaccebcdacbcebabcbbbbcabdacbdeaaccdecacebeadbacdebbbdecacbeebaadeadddeeccebecdebbddbcbedadeabdaaaddecbeebaaeaccdaeaecbcbddedabaddccddaedcecccdcccdbebdccddcccdbcaecccaeeedbdbaecebdbedaedecbccbcdaeabedecdcdbcabbebcaadcbddbeecaacbedbeaabebddadbbebdbbccbdbeaeacdbbeaeadaaeaccebbdecdadedbccebbdbcdebdececdccccbbdadbceebccdbdceedeaeedcacbbceccebcdcbeaeecbaabeedbbadbedbddedceddacebddeabcdeacccdbbcbbdcaabcdbeebdaaacbcacacdceacdcaebdebddadabeaccaaacdbadddbdbabebceadedcdeddcbdacaceeceaabccdaabdcdebbddecbbcedbcedaecceceebdbeebeaceaeacabdddeadddaaaebbdeddecaceaeccdaaebcaecbcdaaebdaeacecbcdbdcaacdcdcdacacbdeaeecaaeecedacceaeebbaaeeaaceecebdeedaccabdababeccaabdcaabaaddcabbadaaeddeeaeadcaddaccecbdacaaeddbccebcbdceadaaeecbbeabccebdbaaecbabeeeaebabcaccabbdeceecddccbebcebeaaeadbccabceabaeeadcbccbccebccecdadbedabeecddcbccabadbaeaacdaccdaeeedbaeadcccebddcccacdeaccadbbdbdedecaedeecadddadeeeaadeaebacaaaddacccddeaecadecccadedecaeddebedceebdcdccbbeaaebebdecbebbbacaddabcadedbbbdacdcdaabccccbddecbdacdeeccdcdeccbaccabeedecdceccddacedacbcbceabbaedcbdbdaeeeaddebdadccaccaadeacedbdecbccaadbeaeececcedddadbccdecdaaddedeeeeacadaaabcceacabebaddcbaadcdecddbabababbbabcaadeadadaeacebaeeadcbeadcdcdbbddedacecbbdcedcdcebbbaceeebebdaceecdaceeeeadacacedaecdecaaaeddccbbaccbeacaededccceadaebddecbdaeaeebdeecacbedadeddaadddcbbacbabbcdeeedcededdabaddddbcbdbcdebcbddeaaddcceedcbcdaabbdbeebebcceadcadabbecedbacdeaedbeacbdeddeacbaedbcccdbaeabecbddaacdcaccbdcbcbbbdaaacdcecacbddaebdbedbaeeedceebbdacedccebeddaaaaeaaaacbecbecaabcedceceaabbbbabedbedbdebcbbecdedbbbbcbeacddebabddcaddcdcdecaaaaeeabdbeeaadacadeebbbccadaecdecedeabcaedadceabecbbeedeceabdabccdcabadebebeeaccbeedcaacdacaacabbdddecbbbbcbacbcbcccadbdbaededaacbdddaeabeeaaecadedbaabedaedeceabdedcbeeccabaccdeebeeceddbdbccabdddaebeaecbdbedaaadaabbdabdecbcedacbbaacaddbaabbacdbedbdbaedbcacbcddaecdcdcabadaaeacecccaeeddaddddbdeedceeebccdbccedddbadcabbeedbaccdddabceeedbbcecadedeedbcdbbdcadccaaadeddaaaaebacbabeabdedcdbaadeacdeaacbdcdbbcdaccebdbaaabaaabcabdbbbbaecaeaddcabeaeedebeecdddeadecdcaccceaebdadacadbbbceacceacecbeddaecbeacedddadeddabeaeabbbebaeeecaaeedbcceaedecabeccaacecedbacdadcbcabadacdaececbccadecbcbaccaacedeedaeaeeceeeeadcdedeeacdeadabbdebececbeeebdedaeacceccdacebedceebacaebeebdacabceeccacbbdbaccaadaaeaadcbddacebceaeaedddcddeabecbbdcdcadcecedddcedebeddebbddcdbdbeeaebeeadcceeccaacadbabbecdbdcbacaaccddeabbddaeebdbaabbbdccbdddddcdcbaacccbddebacadebadccbdaecdabcabbdeadbddedabcdcbbdddbadaaaedcdaeeebccaeebedccedccaeabccbcdcebeabceeeabeabaaebcbcbeccddabdaeaddbeedcaacddababcddadbcabbddcacacacbcdaabccdcecedeadadedbaaadbdcecceaacceadcaadcceebcbebeaabdcdedaceccdadceedcebedbecbeddbaebdbbaacedbcaeeaceaabbadeedbcbeccaecbbdccaacdcaeccdbeabedbbcdbdebdbdacecbdcdbccaceebcdedadeccdddadbcbdceaccbbbacddbddcebbbcbdaadecebcaebaedadaadebeeeccbdeaeebdecddbdaccebcccbaacbcedeeaebdacabcaacdecdecbbdcbceddddbdacddaceeddccbbabebbdeedccbcdceaaaaeeedddedddcbedacaaeaeddcbaaaecacecbddaccbeceebcbdbaddbddebeecbadbcdacdbbebeadbaaabadccbabccbdcbadedbcbaaedcedabaacdeaecdeeececdbbecdbdecbcddcecdcedbcacbeadaecebddacccddacaaeaeecceecbbceaaadecccddeadcebeadeaecabeabeaaddebaebbbcccbcbadacbbdcccabbaaaccbacbcbadddacdabeadcdeeedbeabbdcaaadccebdacaccbeadbaaeeecddaecdcadddcdbaddadccadcdeedacdacacbcbebacaebbbdecbcebacccbdbddcddbbcecdaabddadbdabaddeabadddbcbcaaeeadaeccadedcedcedbcebdacbabeabacaacbabcbdbdddbeecddecbcbadbeeedaebdaeebddaeaddbccdeeadbbbcacbabbbccdebdedeaaedeaadecbbadbddacaedcaaaecccbdbbebadebcbdbbaedacdecddadcceebacdccedcbdbacaebbdbebaddccaebcdbedccebdbccdceecdebccaebeedcabbaaaeccadadadbcaeadacebddabeaadbdacbceadccecbebedaceeaecbecaeabdceccbbebbcbceaacdbbabeecbbbbadddeecbdeebeeaccdebbabaedceeedeeccedcecbacebeccbacabedcabdcecdcaeeedaccbbaadabbaeebacadeccdbbebeccaedcaeaceebaebddbadbacaabebdcaeabbdebdecdcceccdbaddbcceccccbcabacdebcccbebbaebcabccbdaaceaeaadbaeaaddadecdccdbcddaaccbdcecbceeeaeebbebaeaedccacaecdbbecbdcccddbddeabcdeaccbbeddbaddccdedaddabedbeebcccbcaebebedbaacbdbaddcceeddeaccbceebbdedbbbeeabbccabcadddeabaddadeedaecccbebcddaabdbbbdcddeaeaebcabccdcccbcbaabaccecacaeccceaacebeedbbaedacecdddaadceadeebbceeddbbcdebdbccbcacaecebdaeabcbadddaaaeadbaddbededabaadbbcbeaaaabaaaedeeaecdeeacdbddcdebdcaebacbbebcaededbdaebeeaaceacccacbeddbcabaaebbacbbdecdccbbdbbcaaccdbdcacebeabcdaadeabadbbbeebaeabbecaddeeebcebdbbcbddbcbebddaecbbdbdddcedceedeaaccadbbadccedeaeaabedbcbceaacadaeeeeaddeacdbaaaeceacecbcdccccacabedddbdbcabeedcbdcbdaabbbecacdadbbcdaebcadaebeaaaedacaadedbeaedcdabdccbbaebceccbabccadbecaeaadbdcedebabbcbddeaccdeedbedaeebcdeecabdbaccababdeecadecbbbacceaaeccebcbaeeaebbdbbeedebaacadceddebaacebcaaebeeecbdccdbdbddaeaeacbddeeacbcbecaddcdecaccaabdecccaddbbeecacbccbdabcdddecaeeadeeaabedeeecddbdcbeecabcadcaeebcebbeaaaebbbeaddbdddeebdedddedcdebcdbaddeaeaddecbbcdaeddacdadaeadeaeecbcbbebcdedebccbeecaddaaacbaedbbaddecdbdcbcbbdebbeaccacddbceddeaeddedcddeabcecebeeabaadeabccaaceeebeeebeceadbebdcdbbeadcaeedbaadeecddadcdeadebebadbcceebedacbeabbcacdebbcebddebdcaccebaecaaabeedbbacbcebacbdcdbabbbbadaddebaadabacbdaaceeacabcbdededdbbaabeabedaecdcedbddecacdddddeabdcbabeccaeeddabaddabaeaddeeddeecbaeaadbbbdedcbcdbcabbdbbdbcccbcccabcbedaaebdecdebdeebaeaadebdbcbdaeebddcdceeccdbcdabcddbbcabccbabdedbbedbcbaedeaeeedcbbdcdaaadedbabaedbaeecdbddbecdacaacbedbebecdeceeacbeeaccbcaddbdbabbbcebbddcdaceeeecbaacbeabddceeeeeeecadcecdcaacabedbaacceabbedbdbecdeceddeebeaeacbcebccddceaceabdbbabcbcdcebaeabebbecaccdeadbeacadecaaaacaceacbadceceabecccbcacebdeebecbaaaedcdcecacbecddbabddbceeebcdbcdddbdbebcbebeacbbccaebcaaecaeaeeaacddeacebaeebebecaadacaeecbbccacbbbecbbbdbeedbbaacbaabbddcececaebbedcaabebdacabdcbcdcdecbdbeeaddacaabcabdabecdaeadcbbdbbebebbabddeddbebbcedcabeccaaadddbaeeddbddedbdbaceebdedaabdcaeedbcdceaabebaababcdccdcdaebacbbededdabaaaecabdbbadbaccdbcdbbabdaebcccdbbdddeebbebbbbbddddabaacdeaaecbcbededaadcbebedaaebcedbcddeeaedcbccacccadddaacabbdbeeeaaedcdaacbeaebaccdcaabdaccedbdcecaeebbadacddbebeadaddedcbaabbbbccadcbadcbdcacddbaaceaaecbccdbaaddbcbcacbeacbedbbdceabdadaeddaebcbbacdacebceabdddaedeecabcdadddccdbaebbcdbdcdccceebbdcbbebcbddddcadeedecbedbddbaccccdcacebeabbadabaecdbccddadebccedceecdabbdeeaebacabbcedeeedccdedcedcaccdacbbebebebaebccdeecddeddcacaeabaeedcdcceaecacbaabdadbbccabbccacbeaeedbadebadeececbadecbdaeabdaecbceddebccaedcecdcdeaabcbeaadddbadddeadbedeecceeabdbbeabcbbdcccebdceaececedddebdbdeecbdbdcddbaeacebbcedeeabbecabbbccecabcacddaabacebecbdeaddcacaceadceecacceadbeacbccdcadcceaeeeacbcdedecdbbcebbddccadecbbcbbcbdeeccabbceddaccceaebdbceabddedebadbdecdddeddedbdedcebccbebddbedbbdcccdbceecceccacceceadcadedebbecbcacecaaacabaadeabecbaaecbedeeebedeeeaedadabcdcbecacddbbccbacdbdaedbaeacdbcbecedbddebaaaedeabccaabcbdbebeedceaaadaecedbddbaeeabdbbdaeeaaeacaaaadcbbbcdbdbcdebcecccdaadcdcabaaddadccdbedcbccbecdbbcedbeeceebaaebcbbedaadbedaabcaadcbdcbdababaeacbdceddebcbbbeccdaabaaeecceadbcabdedcdadccacabebdbbeedcddcdcbccecdaccdaaedbcaaedadecbbbdbabaaeabbaebbadcadbdcdcedcecdbdbebdbbcaabbbadadebbcdacbaabcbaedbaaaaddacdeecebedcabebacbebbacaabeddabbccadcbdcebbcdeecbaaebcacddeddeabaccdeebcedcddcddaeacecaaebadabddebdadbcbbaedcdaebcdabdeedcaddbeadaadeceeacadabbacccbdbebabacdcceeccbcbbaeabcdbddabeacbabbcacaaacdedecdebaceebdecbbddacedbcabbcabaadbeaaeacccabaabadecadddabdecdecaadeeacbdecbbaaeedebedabeacdbeabebebdecbadcddbddeacedeaebcdcdcacdaacabcedbcbeabcceaedaeabcdaacdbebeacbddbeccacbcdbdbdedabcbcdbcabcbdebcbdacddbcceebbaeebbabcccdbddccebbdeccdbacbddccbecbdaccceccaebacbebedacdaaeaccdcdddccdabddcbeabbcdcbcebdedaaeccbdbceebbcabababdeacccdaeebbaadcbcabddbdacbbaebccecbeaecdeeccdeebdadccadcbebbcdbaabcebceeeaceaedcbdbebeeebcbcdcceaaededbcbdaacbaddabbbceadcbabcbcceebdeccccdbecdceadcecbbcabbacaacddaacddacdecdeddebdbeeeeaaabcdccecccbbcdcedddaaedadaeceacdcccadacdacceecddbdabbddcdceaddbdeeaabecbaaadebacbeabeedaebddddabbccbddebeacedabaddeabddcabacabbaadcbeacbabccaabdeacaccaccbdcadbccdbacbcaababdcaaacccedaececdcddcddaaceddedbadbdcddeaccabaaaadabaabaaaeeaedeacacdbacecbdecbedbdaacedccecdeccbbedabeabadadbbccebdbbecebbebaeaeeedddddacacbadebdddedaadceeaaeeeecbceaaaaebbbaaaaecaebbabaeaecdeacbadabedcddddeccecbccadcdbcebbcadadcecdedbebdaddbceebebdbaabecdcabdeacebabecaabaeadadbedeeadcbebdceebedaaacbeabcacceddccccdaeeabdbdbebacbcdcddbbdbacddaccccabecadebdeacceeccdacbbdeccbabdbaecadbdaabcbcbecedcdacadcaddddeccaeeeccebaedbceadcacccaeaeabdcecbccdbdadecebcdbbccaddeecedabddcdccedaedaaacaceadeecdacdcdddbcbdeecedabdbaabbccdabbccaaadebdeeddcbedeedceabdedebaabdedbcbcaabeebcaabadabaeecbeaecbaecbbddedccadbabedecccbabbadceabcacbcccacaaccaabcececebcbabdeccbcddadbbdbcabcecdabaacdcdddeeeceedacaeaaececdadedbcbcdcabcbebbbcaaeadeeaadaadbcdaccaeaeabdcaeedbebebbcbccadaaaabebdbaeccdceadadcedaaabeaadcbdabbdbdcdecccebbabedaebcaeaabdbcaeaeadbceecaededadcbdedecbbdeabdbacdbeecbdeccdcbaeaeedddddddcceeddededbacddbbaaaabbdacebaabaacacbccaaaeaaeeabdabcebaddeeeccecdadebccaeebcbecdecadbabebaddccdbacdccdbbdaccedbcebdbcbbdabeaecceabedeadeaeddcaaeaebcdcaaecddeaeebababcbbcbbcdaebcbbeeeabdbeccecedccbaacaedabecaecaaeadbebabecababaeacbdbcdeceaedbadcebcaeeeeedbbbcaebbbddeddabeedeaedbeedeaeabcdeacddceaaddbceaedbbdbacecebaccdaabbadeaabadacaeeabbaecebedadddbcdceacbaaeddceabbbebdcdebabbeecdacabdaccaedeedbaeeabaedcbbbdcdbbccdbcdcdaebbcaecccccdaceebdaadcdaedbcaeaeeacedebdabbcccccbbeacbbbeecbaeeedcdaaebddacdbecbcabddbccaeeddaacdddeddabddbbcddcedaaecebbeaabdbdddbbaddebeebacbbdcebbcadeaadbbbbebaaaebdcbebeeeddbcbbcadcaadeddbcccbcaaeebbcdbeadccbadccccedaadbadddbabaedabcaeebccaadecdaabdbaecdaaaadadecabaacebedacdcbadddbceaacebcbcbcdabaaedddbcbdaabbceeeddbadaaadcdaebccbdbbecadaaddbeacaaedecddcaceacbdcdebcdbecdbccdbeceaaaabcebedcdcaadebccbeaeabedbabeaeabdcbcdacdcadcaeaabddabaddacacebccbccdacdddabbdbedaeebdcbbbecbecedddeaebccbebdbbaceeacedebdcbaabdbdaebacbbddadbaabaebbbecabeedbeabbdaebcaccbabaccbaceeeeaaabadbaeabeaebcddbaedbcadadedcddeaacadbcbbaaddbdcbbcaeccaacdceebaabdcecececdbbadcabcabeeeddacbeaecebceeaaddbadccaaaddaeeebcccedcbcbaecabdccebaddcaabeddadbbedcbcaaacbdeecabecebadcbceceeedaecdeecadabbdabdaecdbdedadcbaaecbeacbdabbeebbaadaebacdeadacdbaebdbbebcbedeacddbdbbacdeabebacabaededdcaebbcaddaacceebddadbcecbacdeedbcacdceeebceddcacbbadebaebeeddabaddcacededcbdccbeccbdebeceedacaadbadbcaededeaaeeeaeecadddbecbecceabaceeceeadeedabecdaedecdbccecdbdcedaaceeaaddacaeedbdbbdaddcdaaeccbaaccadcbcdbbebaaedbcdcdcededebadcbadebabdeaacaeacceabccebbcdbddedbeaaeebaaaceccecacbcccebcaedddacdcdaceacadabbdacceeeabecccaaadacaacccbadabeeeaeedcdebadccaaeecbaaedabdbddeebbbcadccabebcebcbebbabbaacdaddebaadbbeccecbdcaddedcdcccbeeededeaaaeaecdbdcdaceaababeeadcebcaecabbedcbaaedbeaedddbeacbebdcbeabbccebccabcadebdcadbabacbecbdcacbbbbacecdecbdccceebdecadeaddedbaaebaccddaaedeedadaabcdddaccaeddcccbbdacabccadcdbdddeeeacabedbaadaccdeebbaeebbeedbaebbadaedcedbaaabaaecdccdbccedeeebbeccdabbecadddacceeeeaeeebaabbbbbaebdcaccadeceaadcdeceaaddeccebacddeadcbdaeddeaaddddccbdbbaaecadadeedbddebebabdcbecbbdcecdbaacdbadbddcaabcbcceeecbddccdbcedabaaacbbaeadeececccdabbddecdceddbedbdbadccdbbdebeeaebccbeabbccdbcbbaebacabdcdaeccadddeebedeececdbbadbcabcdcaccaddeedbcdcbadcaeebedbdbeccdeacccbbbcdcabbedaadbdedddbaeadcbcdcaebcddeedaeeaaddbbcbddcccaaddbecedbadcdaccccddbdeceebcadddeeacabedebdbbdeccdecaadeccdcddcedccbebccaeddacabebeeaeacddacceebdedbcdcbabaeaaccccdcbaeaabcddaacdaedadbdedbdcaaecdceaabbaedeeabaebdbcccbdaebdadcbedebaeaabdcadcbeeaadacceacdeecdcabdbbccabcebceaccceedcacbbccacccedbdcecdcabcceebddccadbdaeebbccacbcbddcaceddedeeebbbdcddebceaeddbadaecedacabaaedcabadceacedddbbecbecedebaadebcdeccebecadeddbdcdbddbabaeebccdaabdecaaaaaadbedbbddcebeebdedbedccccceecaacdcdaaddcbbbbbaaebecedcacabaebaabaaeebbaadeddbceaacaaaaaaeddbabeccedbedecbdaacdbdaadcddaacddabdaaddddeaaadaadbeeeadebeaaceddbedddeaeddeaeaaeaeaaaeabaecdacbcaaccdedceecacadebabdceecdbabaeebaacaacaaeaedeabdadaddebacaacdadeaabcdadbbcaddaacebdecbecceceebcaccdddcaceccdaccddbadadcbdbdadaadbdabcedabdbecbdeabeadccaecddaebdbacdacddbdbadbabeebcebeeaccaccceabbcbaebeaebbdbcecceeecebeaaceddebabbebadbcdeabcebccbaabcbcedbbadcebcbdecebedcbadebbadadcccdbededbdcadcebaaeedbccaedeaeaaaadadaecaedebebebcecddccbddacdcacaecacddceeedeaccbdcedebeabbacbceedeadcceeeecbbabcbcebdaaebbaeceeedbaeecbbedadceeeeaacdacacdabbcaaecaeadccebccdaaecceeeccadaedddbcbedecccdaeacaeebcaaaebdcecddebdcbadddeadecdbeaddecdabcbbaecacececcdcbacbdeecbedcedaeabeadceaeeccdbbcbddbaaaababeceaebcadaedaaaadccbbeeacaedbbcebdebebeccecdbbacceeedbeedcddcaacdbabecdbdccdecebeaaeecedaeeaccddbeaeabdcaeceaddbacdcaeebecbceebedabeeebeabceabbccbedcaabdbcbcdddaacccdaedbadcceeeabeacbcbdecdadecbeabccedcaeeecdbdbdaecbccababaeadccdbdebdeecbadbdabdbdbdcbcdeacbdbceeebdbbdbeaaebadedaacceadebedddecebeacbebbcebccbdddbecddeadabbeacbaecaabaaadbabaaddaaebccbeacdabdccebcccddcdddaebbbbdaddaeacccaeadcaabebcacbcacdeeedcccccbbecbdedebeeeeaadadcdcdbdecbebededebcbdbdadcdaadabcbbaccabecdbbccdcdeaccdeacbabddadaedeadabecabceabecaeeddaeacaeabebadedeabbaaaeabbceadadccaceeedceddebebeaeebcbdacedbeecabdecdecceeecdecacadceecebabaaeeaaecdebabaebaadadedeedcabcaadecdedceeaebbaeaedceadabbecccdaedaeabebebeaedebaedccaecbdabdbbcedaecaedeadabbedbceabcadbaedebdddaeccddbedacedbaccceaeaeebaebcccccedcdaadaaeabbcbdaebbcebbccdeacbbebedabecaeceebdcaeddbcbcadbbdeedabedddcbbdeabaabbbadbaeeccacbceaedcdebedbbecddaddcdadcebecaedbebbadcbdbccbedcaabadccceeaeaeacaeedcaddaedbeeacecedbdadebeebbdbbceaababbedcbdbeecbcedcedddbdcbdbbeceadcacaebceeddeaacabbebadbeccdeeddeebadbbbdddbdaedacbcdcbacaebbccdebeeadbcdbecbeebddaabeecdedcabcbaabcceeaaeeeccdacbeaaeceabbbcdaeaacecdcdacdcaaeaabbcbacdecedcadcaccecdcedbbcbdeeaaedabbcadaccdaddedeeeabaeedeaddaeedaedbdcbebbbebabadaeccdaddacebeecdcbcaeebceabdbaaeacacaaaddbccdddadbdaaaeaecbbeabcaacbddceaddedeeeccaadcacccddccaeebbadadeedeadbcaeacebcbbcdbcedaebabdacaedaacbaceacbcbeaceeedccebeedaddcaeaceebedbbccecdbcddebbbccebbaeacbcebedaccccdebeadcbccaaeacdeeacceceecbcedbabcbcbecedddabebeeebedabcbabeaeebdecddedaacebeeddaadabbeeeecdcddaaedecbcabbcddcbacdddddaadaeddaccaebbbdacdbdddcaceccedceaccbabaedbaccedceddaaceaebaaadbcacebaaebcbeedaddcbbeaacadbbccedbccdadcbaeebbebaddebebacadcadccddaeccbbabceddacbddeaeddabcbeccacbdabceccaaeeddaeeabdeaccddbdeaacbebeaddcbaddebbcbeeceecdbaccaeaaecbcbbbaccabddccbbabaacdadcaecbeabebadabeaedaeedabacaeaeeeabbebaaaecebacbecaaeabbaeeaeaecddababbcdbeccceddacccdaceabbdcbcaebbabcdcddaedaceedeccebbbadbaedeeadaecadcddbcddeeadacdcccabacaeeccbbcbbbadcbdcabcdbdeeeaaaadabbabbcdbcbabeaaeeddcacadbddeeeadcedaaadcecaddebbdaaacccacaddddcceedbcebebdeecaeddcdccbdabbcadcbabcceabbdbabdeabdeaecbcbaecaccbceeaebbcbadccaaccebacabbeddbaceecebcadeddcabbdbeaeedacdedddeecdbedbdbdbdebbabedabbebbbcaeaecaccdaadacabccbbcdeeaccdabceececbecebbeacdebcdacaddaeaaceecceaaacabcdbbaeabbcccaadabccebeebbaaceadcbcdcdeacbdbbbcecbecedbdbbaeadcabeacbacaededcbdaedceceadceadabbdbdddbccceceedaedaadebabaeeadbaeadaabacddbaaedcadaabdebaebdcecdcadebaebbddbdedeacbcdbceecabcebdaaddbedccdbeddaababeaadaebadbddcdeedbeebeaeddedcbccaacedecbaaedeaecdabaeaadebddbedabddeecbdaecebacacdeddccbabcecbeecaaccdebccedbadbceebebdbacedbdceddcaccdbadcdedbdeebccaebdaecbabaaeddadecebcdacacaddbdeaccedcadadccbbbaccedecdecaeaeabeacadeedcceccbcedddddedcaacbdecbddbbeaaadbbdecdbbeababbdcdecaadcbcbaeedbadeebecadcabcdbeaeaaacaddcbcceaeeebeebabecacaeabbaeaeacdbdcccebdceebbbecddcbaeddbdcdabcabbaaabccebdddeeaecbdeeabeacbbcbcaaedeebabdeddbdabaccdbceccdaacebeedbccacbebcbbdddedcdcaddcbeacacaebcecbbdecadaeccacbcdcedbabddabeccbdabecdbcbaecacebceeadcdbbcecedadaeeababcacaadbdcdacabcadbcddabbeaccaedeacaaaedaeeececcbddcabdebedcdccbdbadacabdbedeebcddbcdcbcdbcddaddaeaccbebeddcdebeadbbdaedeaebeeaaecdacbdcbeeecaaadccecccdbdbadbeacaeedaaabcdabcdcabacacdccbecdcbdecbcbceadcabeacccebcceabdddddacccaccccbebdbabaeadcccbddcdbcecdeacdbaaacebbbdcecaccacceadcaaedaeeacedaebbddcbdaecbbabecceaebcdabdbeaececcceacaaaddbeceeabceebbedadbbbebaaceedcbbdedaeacbcbadadeabbbbeaacbebabcbdcecbebeddbddbebebaebeeeacdcdcbdbaaabcaaeabcbecdceeeeabadbdbccedaedbbabbceacbddcdacbacbcbceeeecadddcedeeedaacdccbdcbacebacbedddbdbbbbeaddacbcdeaacadeaabdbacbbadeceeddddbcdbaacabbededadadbeddeacdbcbeabcbacdbbcbeeebaadbdccbbaedeedeecdecdcdcebcaaebaccabbbccabdadadcccbadebbbadcceaaecbceedacbcccddcacadaabacdbaacedeedaaeaadacaceaabdcddccacadeacbdcceccabcaedccdaaeaaddaaecdbccdeaacdccddeedcdacbcbddaacddbdbcebecebaeabedccabcdbbdebeeabdaabbadebceebcabbdbbeaacecabdeddaabeeecaebecdbcebcbbbadeebdccaecddcbcedbacbaedbaebbbdddbcebceacbdbceecbbdbcbdebabdaebcdebebdaeeadccddddaddcebdcaceacdcddbddadbcbbcbeeeaeddcdbeeaacbecccbeaeeeccacadbbaebecddacabaeecebcececbcadedaccbdcecebedcacbadcebdecbdcbedcaadeabaaaddcebeebaadbcdcaddaedbcdddabacdabaeaaebacdaeaadbebdcbddaeadbdccaadccadabadaaaccbdabbcddccaddeedbedcdcecbabaaaeccdcaceaaadcdcedccebbeacdaebcddaceaeadccbadeacbdceddcbdadaedeeccaeaaacdbcaceeaeaeeebebeabeecdbbbdbeaeeaeebcadaaaaadedebabeabdccceaabccbacbaaeeddedabcdcbaeaadaabbddbebcecccceceacbedadacdedbbcecaecaeaadecabedadacdecebceadaeaaabeccbeadbdaeaeacdaaaeeeacbaeedbebbbccedbecddeaacaddcbdadcabaeddcaddbdccccceccbdbabacbddeebeecacdabecddcdbaacccaceddccbebabeaedceccabebcbbdcdedeaaeaeeebdeadeccacedacaeeebcaeecdecbbdbecddddeceaeaabedcbebdccdecabbedcceaacddeaeeaaeddbaddbebcacbadaaddcabdbbaedcbcadedcababcceebecaababcacceedecaabcbdaedeaeedcbaaadbbceddbdcacabeeaceaaedabaacaaaebdeddaddecacdbaedecdceedceadacceadbdcedecddcdabceadcbbaacddebcdcbdadceeadbbadcbcbeedcbdecceabdbcdabccdedbcdcbacdaeaabcdbccaeaccbbbceaccebbdcedddbdbdcdcecebdedccaeeecaebacdcadccdccaccaccecbbcebdcbecbdabaceaecdcceedcecdaaddcdabdeaabaaceedecccccbdedccbddecddbdcdeddbdabdaaeeeddcadcdccedcbdacbaadbdabcdaddbeccaaabedcdbaadebaaeaeeeaabceadeebaebedbbabeabaeaacaebabedcabcadbbaeeceadbbaeebcdbbeabaebacabdabacbccbbddeacbdecebaeeecaebbabdedbeaaaaebacdbebaabadddabcdccbdbccdcacebaebaeacabddcbdbbeaacbbeaaecdbedeebedbacedadccbbdcbcdeaeabaadacddadcaecaceebbbaddcbceecbbecdaecbcbcbababdcbbccbdacccaaaccdbeeaedadaabecacacbacccdacccbadecbcabddceadceebdebbddcbdeaddccaddddabedeabeccbeaeadedceebbcaaddeadddcecbbdadbabbebaecdcceeaebbccccacacbbbeeabcedbeedcdcdebedddcaedebbcacccdcabecbacbccbccbeddcecdbcdccedabaadababdeaababcaeebbbbcadacdaddedcebaebcdacccdedabbcbeedcccccecaabbdddccdebacddeaededaceacebacdaadeaddcdeabcccebbbebddadcbaaccedaebdadddbcbcdaabcdcdeedccabbeaedebbbaceaceedbecacedcedeaeadcaedededabebbbadbdbcabbcbeeddedcddeaddacbbccdcbdeccabeadcceccdebcdbccddcdcabcceacdaeaeedaabeaebbabdbabacccabcedbdadeceabcdbddbceddbbdbddbedeadceaceedebcecacadedceebcdaadaeeeacedadbebbccbdcccceaeeedabeacedcbbbedeebceeeeecbabcaabceaaeeadadabdbddcddecabcecdaebcdabedebbddcceabaecaaeebbecbdeaacdbeecdbeaadbcdcdaccedbcccccbaabeccaaaedbcdcbdabdbdbcebdccecadbddcdebecbcedeaebcbeebaddcaabaceaedebaeaaeaccaaaccedebccddcdcdbccdedccecdccadbdeeaacacdecdeeceeaeeddaeadeadeebecdbcdabbdabceeacddeebacbdbbddabaacecbeebaddcebeaedddaecacdbceedbeaadbdbcbbecedbabbeaadccddcacdaeddecbdadacdeedaaeadcdabebcbaceaaccbaaecededbcabcdecaadbbaddeabaaeedaabebccdecebadeedbbceebadbabececeeacdbbbaeccdecbddaecacadcadbccabdadceaedcccdabbacaecbbbcccaeacccbdabbbacdabaceacdababeebbebcbaaaadedebdcabcdeacabdadabbdcdecaaedddbdcebbdedadcacceeecbebacdeebcedbccdacbaeedccabbceceeaaaecdbecaababdaaaaededbcdebdceebceaabeabbaeacbeadeacbdbabdadccdedcbddbbcbcebebddcddeedddbdebbcacabdebbdaedaebeaacbacccedcbbaaaebdeccaeaadcecbccbeebdbebdcdbcdeadccaabdaabdaaadaeccacebbccccaabedbadcbdebedebeacbabaacdceebabadbbbaadecbdcbabbabbdecdddbacaadeaddcddbcedadcbeedddabdbbdcdaedaaababbddaebaededbddcbcedaadddbccbdacdcdabbaccdbeecedcabecdedbadddbeeaeaabdaacadcbaeeebedbeeccaaaaddadaaebeaacaeeedbcdaddceaecbeadcaddaaeabccbecaebddadbebbccbcceedbdaabdadabcaadebdbbcaecedeacbcbabeecbedcdeabbbedbabceceacedceaacaeeebcccccaeccabedabdadcaeaadddddadbedeeeeceddbaebcdecaeddccaacbdbaeecaeeccaeddbbbbcdaeebbabeadbbcdbbdbbabdebbbecbacbbcecebddcbaeedbdceaaabcccddcdecccaebadecebcbdcceecbebeeccedbabeeddcbecccaabdbbcbaabdbbdaecccedaeacabacdbaaaaadecebadacecdbbcbcaabadcceceacdaabcddcaaaeeabceaadcdcbbebbddbeddcadeeebadecaabbdbcdeaaccdcdccecaacebbabeeeacccdcdceccdebdebaaaadbeaebadcdcdecabecaedbbeebddecbecabbeaeaabacddaceebabceeeacabecddebbbdecbdddccacaaccdbabdddaadbaaeacacbdebecebbdcdddbaaaebcdbabaaacaaeccccbaadedabdadceedccebbedbbdddedeeaabbecdabaebcdbebbedbaaecaddccebdcbeddbbedecaadabebbdbbcaabeebdaabeecdbcbcbddcbbabcdbaedcabdaecdceedbecedeeadceeedcaedbebacbeccdcbebcdcdbdcacdaecbdebeccbabddcbcaaeaecbebedcdeaabbdaaacddcddeedddcabdceabacabcabdebaeebbbeeabaadbcdedbbebeedaceacebecdabcaddadbbacaebeabdacbedcccdbadecedacebaceaaaeaabcaeaeecbecedeaccdbdccdeacdaabdadaabdbebbbbddbaaaaddddbbaaaebabacaaecbeacecbaedacdbeeddaccedddcbdbbcdcacdaaeedeeccdabbbececabdabeedabdceccaabcacbdbeaaecaeeececedbcabdbcdbbadbcdbeeabbddcdadbcddcbeeaaddbadeccdbccdbdbeeccecbabdbeacdccabbcbbccebbebabaeebbedbceabcaecdbcdbacaecdcceaaddbeebecaabebecccdeeeacbbbccdbcaecedaaedcbcabbdddddddaecbebccedababaaaadebbedebcdabbaebdceaeedbaaeadecbbedbaadaccadbeacabebbcebdcbeabbeacdbedbcbdedbedbebddaacdcaccaebedeeebbbeecbcddaacaadcebceeeaeaeddabbacaedbdaabbcdeeccaedddbadbedbcecececedeadbabbdaaccadcabaeeceabeccbdccacbbaabdeeecceeedeaccaccccddbadccabceacaeaacbbcecabeedbdbdcecdbbaebceaebbcddeddddbbcdbcdebcbccabcdeeeeabebdbcdeedebccddbcccaccedcbdcedaebaeacabbebddaddbccecbcdeebeccedceacbccdabacbadedaaeebbcdedaecbcdeedacabdbeabdbdecaedeabdeddbedcddaecacaaadbdecdbbedeeebaaacbeadcaeccaabbadaceaedcbdeeeccacbaaebddeaebbbdbcebdebbcdabaeeaecdccddadeeadccabdedebbcaebeabcecbccaddeccccaccacbaaceadadbebacbbacbecbecdbceceddadbbaeeddcecbacbbaeaecebdbacbdcaebaacdbdeabdeabbbbcabaeeaedecbebbeabedadeebabeabecbabcecccddaccaadceeaaaedbadbcedeabebadacaeaeaecdcecaadaacbceaddcceedcdeedaceaebbdaaeadadbbebbddbabaaaebeddcaaccbcdacdaaeeeabddbddaacabdbeacacdcbbddecccaceedaabbabccdbcceaaeeebbebacaeabeebbbbceeceecaedeaeeccbacaecbbdcedecbcabebbcbabddcddacedaeddebddebbcecaeebeeadbcecccbdaddedccdaadabceabdcccadedcdceebadaaedebabccacecbcbecddcbdccadadcbadcdcbcecbbeeedcacadcacebebdbacdceedabddecdbcbbaaeccbacaadbceadacadecadcedbcbecdeedcccaeadbcdbddccbebedddaedcbabdcbaadadcdbbacadaabbacedbcbbbababeccdcdbbecbcbddeeadaaeaddbacdbbadaaccbabacaaaeaaadbdecdbcbaacacaecbdbdcbecaaaaedeedcdbbeeeeaebacadecbbcdaebaacbbeccadbbacdbebeccbcbdbeadccdaeaaadaebaaeccabcdaecdcbdcaedeacacaacddcdabdcddcedbebbbababeeabecabbcdbbbebdaecbeedcaedadeedceecddbbaadcbeaeaeaaaaccddadebadbcedccaadaecedddddaabcbbbaeececbaadaeccdcdbbccebdbeadaddeaeaebcdaceecbecadcacdcaaccdabcceaeddcdcbcceaeebbadabbacddbbdaecdacedbceddddccdbedeecbbaacdbdaceccccaabaeebdcececaccdbcdcbadbddbeceaabcebdcababcaaacbbceacdddbccbccecdbddbddceacdebbeebcdbdbbbbcbcbaddbddedaddeaaeccdbdecdccddddecebdaabaccbceaebddcddaebbaaaeedbbacdaacaaeddccdecaccdbbdaabcbdabbabcaddcadbbebacebbaedaaedbcaeeaaabaecdaaeecdaeaaabaaedeebcabdaccaaaecabdbedebcecdcebecbdcaeeeedcacaaadbeeddeadaaabccbecabebdaeabedaaaecbdbdaeaaebbcaaecdebaebccebeeecedccabbdbedceedadddeabbceabbecdbdebecacaabdebbaecddbccecdcedbaedccbaceedcabcdcbdeeececcccaecadeccddeedadacbabdadaeeaddaacaaecadabaeacbcadebeddebeccdcdceeaaaceaedeaacadaaaecaaeedebbaabcdaabaaeeaceeaedddadceecebdbaaedaacecabcaccaacacdccecbacceceaabbecddabcbebacdedbedaccecbecaceeebeccbdcaeecaecaabcbddbedaacbabddaaddcbaaddecdebcbccdbecddbaaecdcdaacbaaecccebeeccccadeebbacdeecdcdacaceaabeedaeebaeccbbdaadeceebbecaecebdbcecddbdcdabeabccacebdebbedbdbbadabaecdabbddecbdeeabadcbdcbddddcedabdeaedebdcaacbcdceeacdaaebdaadcdbdebacebceeaecbcbbddeeacaedecabeadaadbaeddecaeeebeaeaeeabdaddbcadccadcdcadaaeceadcebeeddeabbadceeeaeaadbcdebbbcbcdccdcedababdcdceacaccceacaabbdbcbcbbcaaaeebddabbeabebbdceeccaabbacceabdbcddcbadedcaeaaaececcacaecabdedbaecbebdadcceeadddecddbebebedbbdedbaceaddadcdebddabebdaaabedddadcaacaeceecdadecbbbeaeaccdaebaddbcdceddcdadcceacccedeacaddadeadebdccaacdecddacaeeadabaabddbddbaaadebbbdceabedbecdaccdceedadaabaabaaaeccbaebbeecbdcedaecbedbaebddceaaeaaccacbadaedbdeadbdeeceaeebdccecaaddedccabadabaccdddccaaecceeadabaccbdbbaecbdbdebeadacdedcacacadaeadcebddaeddeeeebceeebbddecdcdeccddacbacbcdadbdcbeaaaddebebabbcdedeecdbdaccaabdbabdbdbbcedbdeabcbbaccaaaaeaceacabcadcecbdeceeabbadeeaebdadaedecaabaacdaddccaebaeddaddabebaaceabbccbccbbbcdbcdbadadbadcadacbeaecdadebeebaddbdcbccaecadcdeacaeaddaeccaedcbbdbeacabaceacbdedcabddddedcdeceecdedadeaabecbbeeeabeeeabbeceebdcaacebceabdaebeadccbbdaaacaaeadbcbdaadcdddccaeccecabcaecdbcddcaedcddbedebebdacbbbdbcedacbecdcbebbbedbdcdbbedddbbbdabaddedbbbccebedabedebbcededaeceaebaeabaaccbaeebdcbecddeededddaadbbaacdedcaaaccbddeaebbeeebdeedabedebaaebdaccecbdeeaadeedaebcabceebebcdecdaabedcadcdecceecdeacaaaeddaddbebddeacedebccbbaddddbaecdbacdbabceabdeedeedadadbbbbbbbbdaccbebceebdaebbddedebcbcbbecbddccdddceebecaadabcebbdacbbaeddcecaeddccaecdbacabcdeddabecbaddbdecabadbaccdadaeabbbabaeabecddacedeeaccdbbeeacadddbadaeedbadbdccccbebbecceedbccbcaadeaaceebacdabdbabbaedcaecbbebabbabdbeeaaaadaccbdeecbaabbeedadabccdcaadadccdadcbaabebdeaeeecddaebdeedcbeedcceddaaababeabdaddcbcaceeaadacbddbeaccebaabdbdcaadaecaddeaeacceeeeaadbbcecbeaaedbcbaadccaaceadddbdaebadcebcececcceaeadccebeaddadddccecdeababcdbbcacbecbabeebebcceabcbabcdddbececacbbebadecddcabdeabcccacdbcbdcdaebbbabbddecbceddceeecbebbbbccdddbcdcbdecdedebeedddcaadbbcaaeadebaebacaadbebaeaaaeaeedeadebedcddededcbbadcedabedaaabcedabdacabaedbdbdbcdadacaedaceceadbebeddebacdccdbccadbbdcedbedebadbeddabebaeeceabebcdcbacdaadbdceeebcdcabdacaebdacccbdacaaecbdcdadacedbabddadecdceebbbaabeccbbaceddaddadbcddaaaddadcbaaaaaabbedaeccadeccbbacaceacddbaaacabcedceddaaebdbbacdeaeeacdaacebbaebbeecbaadeabbaebacbccdcdcccaaddeeedbbdccbadeacbaabecbcebbeaebddbcbacaaabbbdbecccddabbaedebaddabcabecdabaaddcbbebbbcaacbeceaaeaabebeadceebddabcbadccecacdccdbbdddeceeacdaabacaceaddeeeaaedeeaaaadddbdbeaaabeecabaeecddcbaceaebbaeaebbaaebddbbbacadaacddcaaeaddddabdadceaabecababdcdeecbcebaabcebadbdeaaabbaedbdebcdcdaddcdeebacedeadcaaebcccedbacdebecdbaeeeccacebedbecaeeaebabdaddbdddaaccbccececebddddbeebdaacbdccbbeebbeadcdbdedabbceebebbbbadaccaeaeadedadebaabaadaddbbbcdddaceeaecbddacdeebdaeaaaaacdaaeedecadaadcbbaccebddceadabbacccdeaabeababcecddacadddbeaaddaceaabbaaeaccdbcadcadccaedcbedaabceebdbaaacadedbcdbcacdcbbdeccddedeabbcadbdcddecdeaedbabcdbdabdeabdbbcebaedeedbebccaedeacebaabcbcaedebedbaccaecccdbeeceabbbcabcadeecadacebdeacabbdaabacdccccaabaeabcdacebedaccedaadbbeecacbcbccadbcebaabdcddcaaeacbbaabcaeeabdaceeabccbdebeacdeaaceccebddbcdacecccaebedeeedbceddbbccdaeacacabaddaaabcbcebbaaaddcabdabcaabdddaecebadceddcdbecddebeecaacbcedcabaecdedbedcdedacabbbbbeeabecdebaecebeaeacacadcbebdacbdcacaebcedccdabcaedcceedcbddcaeebeacabeeddacbaacaddeeaaedaacbddeeadbebabdcbdaddcdcedbaadbbbdaccdcabcabeaeacbaeebdbebdbcdaeaeadcbdcbdeedabcdbadcbecceeccaeaebadeebdaadcbdbcadaeeddeaeaebdceccbdaeaaeacadedaaaccbabaccdeacdaabeecbddeeedbcabedabebdedebbaaccedaeadccdbeaabcecbebbcdcbaaaadebcdecbabacbdddcdadadcdcccccebdcdaaebccdbccceddbdbeedbcadabadbceecbdddeedacccdcbebccacaadeebeccadcedabbdcacbaeddaddbbbdcdbcdbddabadecbbeaacddbbdbeabbccdabbecbbceeacebaebabaeabccdadbcbdcdbacddaccbbbcbcdecbddebedcacbbedcdaeaabcaadabddebbcadeeeaeceedeedccadddeadcaccddebaebaacacbadedacebbebbbedbecbcaacaddeadeacaeabacdaeebccdbbbbedabebaeeadcaeeeadbbeeddeebbadadccaeccaeddecdabaceecebceedbaabdcaabeccdcaecbbbabaacbcbcbbebaaeaeceaecdeddddbaceddcaaedcdbbccbdcadcdaeeecddecaedebbecdeeccaecdbacaeecbccccdbeaddaceaecbbacaeaeadebabaebbedbeacadecdbccbcceacdeabdadaaabeacbbbadeedcdedaaceaadaedebedcaaabeebccadabbdeabedbcddeebecdadaaacecdeaabbcbbbaceabedccdccdcbbabbacdeccdbecbadaceddcccbeecaaaeadaedcbdbbadbcbccbdbadebeecccbebacaccaddabdcbddddadaebaeeddacbacdbacbecabeeaacccaaaccbadbceaedccdbbbaacdeaaaebdedeebaedeacbccadcccadcedecdedaaedcceaccdcbdbeeccdbdeedcccedebdbddacebdbdeebdaebeedadcedddecabbedaadabaceabbeaaeabeaaecaedccedbedccbabceecbabadcbababbcdeacaebebdedecbdbbdaadccaaedecebcddbebaeaaebedeadebdbaadacadaeaeebabdaacddbaeaebdbaabdcabeabbaccdbeebbbceedabadebcedabcecaebaddbeaddddadcdeabdcaedaaddbecaeceebecdcdbcdaadddbdbedaddeeacecbdaababcebedcccabdccdbbebeaccdaacdaaeaddcdddeecbabcbbeedaddddedcebebbdecdbbcbeccabcdbabbceeeeadcdbdcecccbedaccdaddeeacccadedcdcdeabddbebbedbdbaacaadddacdabcaddbaaebedbdeeadabedadcabbccddeceeabcadecaaddadcecaccccddadeecbbdddedeeaabbdcddcdbcabbccecbeeddadceeedacdadadceeccacdccbecdbaeddbaacaebdaaddeebbecdbbdeaaccedeacebebeecebdaedaccddecbcbbedeccabaeddadcbbcccadeebaeabcbcdabdcbddbdecebdeacccdcecdcdcaebddeaeeabdacebacaaaaaddbeabedeababbceaccabaeebdeaabcdcbbeeabdeeccceaaedbbdaecaaeaccbceecdeccedcdbdcebdeaacebeaeccdcddbdacbdecebaedcdbdceaeaecedadabdbcddeccbecdbabcaadaeebebaebbcebccebabbacdbbebbeebbbaaedeccebbdbebdacccecaedcadcecbbbaaabdadaedccedbcdeeecdeabbccdbedbdcbccccbccadccdeadccdcaadddeabaadaaaaedcacdedecebcbdbbbbabbebedaabcbdddedcdbbdcabdcbabcecadbbbbdecddceedcdedaaeadcccbaaaeabbeeadbdeddadccaeebdbbbcebcdddabeaeaeebdcbebaebaceabecbedcadbdcbecccbebeceadcbacedcbcbbdcbcceecdbcdedebccdbebccbaaaabeeaccbebacbececaecabbccccdadcdcbbdebecaedcbacebbcdbaeededdcebcebabdedadeeddaebeddcaabbabecdbbdbcbbecddabeedbbcabbeceeacbabdcbedccacbbebaabbaacebaaddabaaeeacadaedcaedcbedbbeddabadadbabaecdcacbceecadcebbbbccabbeecbeeddbbeeecbeaabdadeababbeadeaedbebdaacbaabcbbceacedcbcedcdaecddebeacdccddedcddebddddbebebeddceddbacbedaeccabbdcdcaabacaacedeededaeadcdeccbedaabcdecadbbdebeaeecdebdedebeddaaddbdebbedcceadddddacdedeceabcceaabaeccaacebadcbbebbaccaceddecbabaaebbaadaabedbcaaaaecddcddbceecccbeeedaeabcdaeaecaccbdbecbcddadbedadaabcdedebceeaeaadabaaccadaaeadbddbcaecdcecbcbdbaaccabbbbcceebebbaacdbdbadbdccaddcaadbdebcaaaaedadaaecccdacaeeeedaddecdbbbebacaeeedcbbdeaccdcdadddbaddddaaaeceecebbbcaabadecbdeaecbbbeabeacbcbcbeedaebacceaeebeadbaeaddacedeebccaddcedcdecaeabedaaaddadaadebcdcecbdcdadcacbabebecadeeedaaabeadaabbdcbaeabbeeacceccdeccdacccbccbebcdbcebceacddcedceeedaccbdbbedaedcaaccdebdcebbaabeabeabdcdbccdcddbccbaaeaadeaeeaeaeacbedcbbbcacadaebadccaabddbbddcadcadbdbcdebedcceacdadaecbbacadacacaeabeaceaeaeeeebcacdabeaccdbaabaaacdbeaddcbeadeabaadbaaebccdcaceeecadedbadbecddacbdcaaababdabdccbcebaaeedeeadeceedcbcebeeabdabddaeedeecaedcbaddddaabebbdabcaeeecdcbcaceccaeebbbebebaecdaaddeccadaebddebaeaebeceeaaedcadcedebddedecebbeebbdcaabcbcccecdcacedcdaedecabccbcedaccbdeaeeadeddccbeedddbedcbcaeeaedcbecbdbdeccadcabbdaacbccaedeeababcebadeeadadacdbceacedcdbaeadddadaceeebeeadabadaeacadedacebbcedaedbabbadeeceacdcaeababacccbebbaedeabaacbcccdcaccdeecaddcdbccbebbceababbbcdadcabbbaceecaeaeaccecaccbebedbcaadaeeedaccaeedcbbbaacddebadbcdebbebededeeceddceecaeeddaedbecdaeceebbebcabeeedccdedbbebeecbdccecbaaedacddaacebdeebaceeaecedeaeccbdcccbdcebeeeccdaabaacaacbbbebebeaadcaebcdaadcbcecddcaddaccabbcdebeacdcdddbabeebdddeaeececabebddebabbccaceeccebdecdcebbcaacceecdecdbdddbbbbbdacdedbceaeaeeaaadcdabbedabeaaadbcdeeaceeacdadbdcecdbdeddbdecebddacbadcaabbeccecbeaedbcadabbcdeecdaebaecbcdeaddeedabbaeeaebbbdbababbeccdeecdadbbeabaaccddceecdbabadbcddbaaebaabbeeccdccbdbabbccdcabbdddabdcbcadecccbedeadebdecdeedeeeeebedbcedddedaaddabccdcccbbacbcecbeebbdbbcadbcecadbaebbeebeebbdcbeccdbaaadeaabecacdbbebedcacccbcdddcdeeaaabbaaeacadcceccbeebcbcbeccabcbbaeedcbabecccebaecedcbeabdddebeccebaadecbebbbbcccdbeebabdeccdebdadceecbabebcbaebacadcaaedabacaedeeababaaccaabebdcabdbadccbdadbbeaabbebdcccaecaabeadecbadedbbbccdababebaacadcbcedaaacbabecbbceadbedbacdaceadbabdbebebddcdbbeeecdcbdeeaecccaaaadebacdcbcdcacceebcceeadecaddbcecaadbaddebebccbcbabacececcdbecaebccbbbebebeaadadcbababcaaeeecaebbaccabdeeabddbbecebaceeebbeaddeccccacdeebbbccceabccdeaaaeadbbeacadcceebeeeeaacaacedeedaeecbecaedcccbccecdbbbacaccdcdceebeaaedeeabaabbdaddaccdbbccdceebecedddabbdbbcbedcceedaacbeccbadeeddbbeceeaededaaddaaedadaceacdececebddeecbbabacbbeadacaebdbeeaabcecddceededdcbbdedcbadcbaaedaabcdbdcebdeedddddaeccbcbebbeacbdedeeacceaadbdebbabbbcadeabbeedeecbcceeeadbacbcdbedceadcdebcdadaccccaddcaddedccebceecaaceacdbbdcbdbcabacadabedbbcaaceeeecbecadbaebbcaecadbcaebbdaeabecbdaaededcaaabcdceecaedbbedbaceeabdbeccbcbebdcbebdaeeedccebeaecaebeceadbdedbebadeedccabaeacaeedbbbdeccddedccccaaaaaadceeceadcadcadebaadecceeeeeabcadeebdeeaccebabebcecddaedddaebdebbbbcbdbbbbcadebbbebcdaecadcaadbbcabcecadbabebbabdeebeebebcbbcdebadccdbebdcbceacccdedcdbdabbbcbbbeeeedcecdacebebddbcabbaaddcecaebeeddbbbbbebeaddabbacabddeeababbdeacbcadddcaebaabcbbedbbeedadebbabcdeedcbccaacccbddbeaaedddcdecaaeecebdcadedcacccbbaadeabbacddabeaacebdbedadededabacedabbbdaaddccadddccadbdadadcbbcadcabbeecbeeeeabebbaaccdeccdbaaaddbcdbeadadebbcddcecaaedcadbaacaeeeccacaabdeabdecbcccbeadaaaececacadddcebccebcaeabaadcdedeadebadaadaceadcbeabeecaeddadeaaabbedbedcaeddbcaeecdeebebbadecabbcdcdeddbebedadabcaebccebcbbeeccdddceecebcacdadaeedeecdebebebebbbeabbdaeaabcdbcbaddeeaccecacceabbbabcdeecabbbcdcbcacedacadeebabddebadcacdedaaddbaeeaaebecdbadeabdbccaacbcebdecddbedcdcaedddabdadbbdddbbccbaaaeadbaddcedbdeadacbaebbdcacaeeeebbbabcacaeaeacbcdecccbeeabbdbccabdedccacaeebdcbacaeaedeaaabadbddbceabbcdcdbdebdebaabeeeebaadebcbeaaaddcacedddcbecdcbadcdcaaceabbbeecdaebbdcdbedcedadbaddadaccdeecbcdbdbaaecccdcccbcdaaaaddeeebeadebdcdbeddecadcecbdccdeacaacbadabaabecbaaaceaeeddceabaabbbadbebccebdbcecacceebdbcccabaeddabdceeabcabdebbddbccbabcbdaaeadeecdeacabbddceccbddbbadecbcddaccceadcebceceacedabcedababadabbaceeebaceeeabebcadcaabbcddddceeceadccbcdecbecacdabcddabdecabbabdebdbbdeceeaebcdddecbedadebcbcccabedcdbeeabcceeccbaedceadebeacddcadcdeccacebcebbedeaabeabdabadcaadeabccdeabcdababccbbaacecbbccecaadabababecebcdcdedeebbdeabbcbdaabbbbbaceecdbbebbddccaaacaeceaccaaabadddbdacbedeebebdcdcddcdadbadbbadadaaeaeacccedccbecbbbecdeabcdbeaebdcbbcbedeaababadacbccddcbdecabadecdddaacecabedaedcebbadbeebbdadaceebbbeababdbabccecdecabcceabdbccebbccdaedceacaeaacdaacdcdadabbdedecacedbeabaaebcaccceaaedacdadbccdebbabdcedbbebbeeadecdedadddeedcdbcbcbdabadbeedcbceeadeeebdcbededbabaacebcddbbaeababbabdaaecacdeceeaedebccabebddebbcdeecdeebbbcbaeaebbeaecacccbcdaadcdbabaadbddcdcdcaeaaaccbaeaecebdbbcdcdcdccbaddecadecbbdecdbdbcacccdaaabbbcacbadaeaacbbdbacebbbccedeccdaeebeedbbdbddabdbddaaeedcbeeabdaadabbddebaddedcceecbdbcecceadcaeacbebecbdeedaabaedcaadbbbedcdebedbdeadcbdcbddcdddccbedadecbccacedcdddbdbdebcbdaaccceaceadbdbeecaaaabdbacbcbbdceaeacdacbdaedbbccaabdcbebeebbbccedcadbcbdcebaaddaeaacabedabeccecbabacecbbbeebabcbaaccacdbcddebddcdcdabaacdaeccabdeabdcdebcabbebbddcdeddcaadcdadbdaceceecaabeceabbddedbdacaebabeccdcaebaebbcaaddcbbdbcacedccdeeadbcadadbadaebedcddddbbbbddecadcedabbaddeaadcdecabaecaaddaceabcbdaccbbaeaadabcbddebccbaccabbeabbddbbdeaaecccbdccdcbedeaeebbbdcedbdeabeceaeeddedabeedaadbcacdbddaaadcbadeacebaebdcecbbbeebcadcdccabcceecbbccdbdbbbedcdaedadbdaaceeabacbdbcbbadbabbdbeeabddbcaadccacedabecceabdedeceedabaedbebabbddbacdeccbdaaaceabeacadcebbdabaeaccebeadbbaebccaeeceeaabcacddbceadeebcecaeaaddcbacbaeedbedaaedaacddcecadeddcaccbeacebdeccebdabebdaaaaedbbcbcedbdaeaeecaddaaccadbacccbbabeeabaecccadcbbedeacbbbdcbbdcdbebbebecbebddecbedaaddeadceddaedceeeeacacdaaadaacdeabecebabcdcedccdacddccadedcecebabcbdadacaebedbcceaabbddebdbdbebbcbdbadacadababacaaecbcbdabbccadadbdeecdaddbdebdabdabdacdcbbdccaceaddadbbdacadbadceaecdaeeabededbdabddbecbabbcedccdebbdbdaecaabeaceeeadbaeadbabdcacdacddbcccbccdebcbbecccbbedbedadeabbbaadbdaeeecebdddeacbcccddabdbaabeeeabebebccedcebadbccabbcceeedccbadaccddacedaecddbdbdeadceeedbbeccbcacdeedeededecadacdeccdadedcaceebbdedbbcedabdabeadacdceedeeedebbedecddcccacbbbdddadadcbbbbdceccdebadbeedcdbbeabacdebcaccdbabbcbbabebbdaceebbececdeadddaeeaaecaebadacaececbbecedbebdceaabbeedcedadeeaabbddeebcabcdeebdebeaabedbaddadadabcbcceaaddebccdccbeeeaaeacacebecdabebbcadbebbbccbaadcdccbbabdcdbdabeecceacdbbbaadaabbcdcbadccececdebccaedadeaeeadabcbdcdadbeeeabccbdbebddcaecdccdcdacbdabaeadcbbbddedaaaadeeaceedbaeebeeabdceeebceeabcdaabedccdbddbcdebbbcadebbcecacbcdbeaabceaddabbcceedeeccbeecdbbbcddddcbeaeccacbebdddeedcbdebbedadcabeacbbaabebaeacaabaaccedceaabebbccacbbabaacbbadbdacbebccebebecdbdddcaadacbaecbececacceeccbbbedebacaaabacaacbdddaabeacabdcdededaeaabaebeebaabaaacaceecbcbdbecedceaceaeaceeebbcdcbbceebbeddebcdceadcbeadbdcbeabaddadaeeaadabacaaccadeebdbdcacacbbadcabaddcbacccdabaeedeccaebaeecdbadceccbeebacdcdbcdbecaebdbdeedbdddaeaceedcbeebceddbbebbbaeeccbcadccadeaeecaacadcadcddbbdeecdbeebbdccdcdabaccaacaeaaaaedbebceacedbcaebdbebaeacadeaeeaeacaeedabbbaeccedeceaeadbbeadccdaacbebcaddbeaebabaddbcdacaaddbcecaecbcbccabdebceeaaddcbaacabeabaccecaacdaeceebceecceebbaaadeceabedbccaccdababcbabaaddcdddbabceecbdcdcceebbcaceeaeeebecdbcaedbacabecaeebbaabcedbedeccabbdaaddcbbecaaaacaabcddbbecbedbceedcacdcdbecebbeecbaccaedeebdbcbccbdcbdbecdcdedebbbcbdabebcceaacbaddecabedcceddecdcaababdecceadeaeeddaddeacebdaabecbcccbedadddeddbabccbbdecabbddcaebadcaadaaeaacccbadbdabedcbabeeeceaebceaeedaaeaebcaeedcdabbaecbebbeebdecccddaaabeacaedbedeaeeeabdddbeaddeceadacdcbdedadcbaccbdccacabaecbadbddbeadcbdbccbddcceaaedebabddaacedbcceeebbcdcacbdaacadeaeacbccdcedcebacdaadcbddccacdecacddbdedcbbaececcebbeaadcddaeeeeedcebaedacdabcebaddcaabedecebaeebeeedaaeadebaeabebeedccbbcbdabcccdbadcabeedcececceeeedcadcabaedbcacddaadedaacdaeecdeddcdbcbaedabbddeddebecccceeaebbeadedbaddbaeebbdbadbddbaebdaadbeebecbbbdabacbaebbdebbdbebdbcaecdddabbadbebddcccabccbcaecbaaccadbdbdbccbeaaaadddbbaabddbbcdedacedcdebddeedcedbdaecdcabbdceaabcaaacecddbadddebcbeecdecbcaacaaedaaeccdaedebaddbecbaaebdcebbeaecbcebeccdbaeaeecbdcebcdcddaaedccddeeeeedecccddbddaadecebabcadcedcedbbdbeaddeaebcacbaccadcadedabbebaddeeabdcaeeeabccddecdbdcddcaceededabeebedbacbebaebabdabcdedbecaaaeecadbeabaebedbbaddaabbeaaacedcdcccdaaaebbbedabdcbcecaccaedecacbcbdbdabebcaddacdcdbddbeebccbaacbebccddcbbddddedeceeacecaadabebbebdcbeadabceebaceebdaacbbeecbadabbeebbcdeeecdedccddecdbbbcceededcababdceaecbbaeaadcbbaaaeecbaacdbbabbbcdbeeecbebeabbedddeceededbadcceceaeccebccccbcadaaeaceaadbacceceabdeccceaaaedadedeebbacdbcedadaebeedededbdaaabbdaeaeddddbadbbbbddbdabdcbcceccdabeaddbadaacabeaaebdbaedbeeaeebbecebeecbacaededcecdbcdacaaecccaaaeacdaadeabbcccbbceaabdddcceaebcbecabececdbcabdaaacebbdbbbecbbdecbccaeadddcacbcbeedddbcebbcaddbdacecddeeaeeaabcbcddceecbebecbecbebbbbdaababbbccceeeadedccadacdbdbebeaceaabeabdaeacbbdeddadeacceacdacbededadbcaceddcdbccdebdaadcacbacdadaeddcadbccaacacdebbbdcbecedaedccbddccbccebdbdeaddcbedaceeddeadebbccdeacadaabaddadbbbbcaadacdbcbacaddcbdcccddaccbddccbecdbdeaedcbacdaceebdbebccbebdcdccbeabbadabeadbbbabccaeeccbacaadcaaadaadcdeaacbbcbeacadedbabcaeebaaaeabdccddebdebbedecdbcaaddedabceddbcaceeaaacaececbceaedeacbaadcaedbccedcadebbcabbdaeacaaabbabcdadedacccbdcebdebaaedeeebebceaeaddeecddcdceecdcbcccabbeabebeccabcacaecabdbdabbcabbdeeabaeccaddcedececdddadadabdedcdcbdceabdeeedacebbdbcaccddbdbccbedbeaecadbdbebaebdededabcadecacddbbedacddbcdcedccdacbcdbbaebcbcebdccccdaedaabdaacbcadaebcbadbacacbcbedeccabdbcebcacaaeddceeebcdcbabcabcbcbabbddcddcceadaaececbdceeabeebeadaeccecebcabbeebbdccabbdeaabddecabecebaaacbabeabeecaeaedededacdbabebdbdccddcacaeacceacdeedeacbbabcacaceecdecbbddcedaaaddadcadeddddcabeddcbdadcbedbcbccbcbbacaebcedceabbeacaadcdbceabdeebecddceececdeceecbdeddbbbddeeaacdaaebbabbbbbeacaeacbcebcccdecadabbeabcccdbcabccddbdedaaaacddbddeecaaccdbbecbabdbceceaecabaecadaccabacebedbbdbdcceacbedcdbbcdbebbbcdbaabbedadbbcccdcebdebcacdecaeceebaaeaaeaceedbbaedaaaadcdadcdbeaccbbedadeaedccadecadbebcaccecaeddcdaecadaecebddeaebabebecadcdcddeacedaecddbebecdbddaaaeaeccbbbaeeddcedcdaebdddbbeacabbccdcebaaecedcdebbddeeccebcbcecdbbdecdbecabcccebbcbcabadbdbeadaceedcbeccbbdcbcaadceccdacabcdcebcddaadbaedeaadbaaeaeceadbabeecddbdaecedbcababaebabadbdbdeeeeedeedaeaabeeadebbaadcedaeabbecdeaedcbbbbbadebbaccdcbdbeabeadeceeccccdebdaebddddcceddcdbcdaeecadbedbbaaaacebdbadceedcedcdbebecaaeacbcedecaeedbbcaabbddeacdebdbcdacbbacbbaabdaebeebeaebcccedcaacdaacebbbcdbeacebcaddeccdbaecbaeecccbabbdeaeccdabbccddbdcceacdbaeeaebbbcadbaccddacebbbdaebccbbcddedaabcbdedbaddececaacbddabecbdbeeaddadeadcbadbcddaebedddcceeaeaebcbbaeecabdaeaddbcacacdbcdacbaaedababcadcadabddccbaecddaaceaaceecbbdcadbcdccabeebbbeddeaeeadaabeddcdedebddccbebeebabadbdddebeedaeadebbecdebedbddbeecceccaaeadbbbeacbaaedaacdcccabcecdcbeeebbceddcccdeddcbddcaadbbdadeedbccdcdeccebedbcadadbdeeceeabcbaaedaaebabdbecacabbadcddbaedbdacaebadcceedadeadcaedbdbcbcdeadbbbacedebbeebcbdbcedceecdeabeaddbbbaebcddcdcadbbbeeedcccacbdbbaebebaeedbaddccbcaeaaaeddcdebdeeebbdebbbeeebccaeecaeebadeeedeadadcbbdadbaeeeaeddeacebececeaaedeadbcdccbaecbacaebebbeeabedccaededbedcaeeddeaebbccdbbaebbdcabecddcabaddeeeaaecccebeceaaecaadbeebdcddabbdbdcdccacabebcbbaecdbcddaedaadcdeebdecdaececeedacbaeaeacdcbbbacccdacbbbbbabacadcdbdcebbcecbdbebaecbcbaddddbbaaeeaececebadaabeebeeacacbdcceeeddbaaeeaeebadaebcaeeebbaedaecedcceaadaeaeeebbbdbeeabececabdbdbcbcaaeabedccbdaecbcdbdbcbeccebdbddeceedceeceabebedecbbbebbaabaeaaedcaeadedebcedcccdacbdccaaadbadedceebccaecdbeecccdccbaadaadeddbbeacacddceebbbabdebcbbddedbacdcadaaeaabeabadbaeccebdcbccdeaaedcdbeccadccecbdeeaabebcebbeabdeaebaedddceccbbecbbbbacebebebadaaeeeccddbdabbdcceccacadeedcecaeeacdcbcdaceacdaaccaebccedbbbabbebedcabceaccbeeeccbabecedeeeaabdebceedebeebedbedbccadcdbacabbccdaccebbecebdcbacaedededbdbbdecbcededddaccaeaedcddbeddbeaeebaadacbbaeeedcdceecadbbcedcbcaccccbadacacbbebdaebedbebbaebccebbddcdedacbdebabbbdddbdbeabdaadcaccdeceacbbeccdccbdedecbbbcbcdadcbccaeeccabcaaedaecbabbeeecabcabacbdbcceebeaddcbaddaceecedaeedebbeadbadaddbbadacaaabacbbebdccceedbaabebdadcdacaeaddbcebbcedaecdbccebeedcebceabbcebababadbabdbcddbdbaeabbbbcdbbdcdacbddcabacdbadeecaceecdadbddbcdcaedabadaaeccaeceeceecbaeadeedadedcdbeeddacbcccddebaddadaea