day12.py

import marimo

__generated_with = "0.9.26"
app = marimo.App(width="medium")


@app.cell
def __():
    data = """SSSSSOOOOOBFFJJFTFBBBBBBBBPPPPPPPPBBBBBBBBBBBSSDDDDDDCCCCCCCCCCCUUUUUAAAAAAAAAAAAAAAUUUUUUUUUUUUUUUUUUUUUUDDDDDDMMMMMZZFFZZFFFFFFFFFFFFFFFII
    SSSOOOOOFFFFFFJFFFFBBBBBBBPPPPPPPPPBBBBBBBBBSSSSSSSSDDCCCCCCCCCUUUUUUUUAAAAAAAAAAAAAUUUUUUUUUUUUUUUUUUUUUUUDDDDDMMMMZZZZFZZFFFFFFFFFFFFFFFII
    OOSOOOOOFFFFFFJFFFFBBBBBBPPPPPPPPPPBBBBBBBBBBSSSSSSSDCCCCCCCCUUUUUUUUUUUUAAAAAAAAAAUUUUUUUUUUUUUUUUUUUUUUDDDDDDDDDDZZZZZZZFFFFFFFFFFFFFFFFII
    OOOOOOOOFFFFFFFFFFFHBBBBBBPPPPPPPPPBBBBBBBBBBSSSSSSSDCCCCCCCUUUUUUUUUUGGUAAAAAAAAAUUUUUUUUUUUUUUUUUUUUUDVDDDDDDDDDDZZZZZZZZFFFFFFFFFFFFFFFII
    OOOOOOOOOFFFFFFFFFFFFBBBBPPPPPPPPPPPBBBBBSSSSSSSSSSSDXXCYCCCUUUUUUUUUUUUUAAXXAAAAUUUUUUUUUUUCUUUUUUUUUUDDDDDDDDDRDHZZZZZZZZFFFFFFFFFFFFFFFII
    OOOOOOOOOOFFFFFFFFFFFFFFBPPPPPPPPPPPBPPPBBSSSSSSSSXXXXXCXXCCUUULUUUUUUUUUUAXXXAAAUUUUUUCCCCCCCCCSUUUUUUDDDDDDDDFRRFZZZZZZZZZZZFFFFFFFFFFFFII
    OOOOOOOOOOFFFUFFFFFFFFFFIPPPPPPPPPPPBBPPBBSSSSSSSMMMXXXXXXWUUUUUUUUUUUUUUCXXXXXXXWWWUUCCCCCCCCCCSUUUUUDDDDDDDDXFFFFZZZZZZZZZZZFFFFFFFFFFFFII
    COOCOOOOOOKFFUFUUUFFFFFIIPPPPPPPPPPPPPPPPPSSSSSSSSMXXXXXXXUUUUUUUUUUUUUUUUUUXXXXXXXWWWCCCCCCCCCCSSSUUUUUDDDDDDFFFKFFZZZZZZZZFFFFFFFFFFFFIIII
    COCCCOOOOOKFUUUUUUFFFFFIIIIPPPPPPPPPPPPPPIITSSSSSIXXXXXXXXUUUUUUUUUUUUUUUXXXXXXXXXWWWWWCCCCCCCCSSSSSSSSUUDDDDDFFFFFFZZZZZZZZFFFFFFFFFQQQIIII
    CCCCCCCOKOKKUUUUUUFFFFFIIIIPPPPPPPPPPPPPPIIIIISIIIIXXXXXXXUUUUUUUUUUUUUUUXXXXXXXXXWWWCCCCCCCCCGSSSSSSSSSUDDDDFFFFFFFZZZZZZZZMZFFFXFSQQFQQQII
    CCCCCCCCKKKKKKUUUUFUUKKIIIIPPPPPPPPPPPPPPIIIIIIIIIIIIIXXXXXURUUUUUUNUNUUXXXXXXXXXXWWWWCCCCCCCCSSSSSSSSSKKDDDDFFFFFFZZZZZZZZZZZXFFXFFFQQQQQII
    CCCCCCKKKKKKKKUUUUUUKQKKIIIIIPPPPPPPPPPPPIIIIIIIIIIIIIXXXXXURUKKUUNNNNUXXXXXXXXTXXWCCCCCCCCCCCISSSSSSSSKKKKDDSFFFZZZZZZZZZZZZZXXXXFQQQQQQQQI
    CCCCCCCCKKKKKKUUUUUUKKKKKLLIIPPPIPPPPPPPPPIIIIIIIIIIIIXXXXXXRSSSUUNNNNUNXXXXXXZXXWWCCCCCCCCCSSSSSSSSSSSSSKKKDSSZZZZZZZZZZZZZZZXXXXFFGQQQQQQQ
    CCCCCCCCCCUKKKUUUUUUUUKKLLLIPPPIIIPPPPPPPIIIIIINIIIIIIIIXXXXSSSSNNNNNNUNXXXXXXZXXXCCCCCCCCCCCSSSSSSSSSSSSKKKSSSZZZZZZZZZZZZFFFFFXXFFFQQQQQQQ
    CCCCCCCCCUUUUKUUUUUUULKKLLLLLIIIIIPPPPPPPIIIIKKNIIIINIIIISXXSSSSGGGNNNNNNNXQZZZZZXXXXCCCXCSCCCSSSSSSSSSSSKKKSSSSZZZSZZZZZZZFDFFFFFFFWQQQQQQQ
    CCCCCCCCCUUUUUUUUUUUULLLLLLLLLLIIIPPPPPPPKIIKKBNNNNNNNNSSSUXSSJGGGGGNNNNNQQQZZZXZXXXXCCCXXSSSSSSSSSSSSSSSKKSSSSSZSSSZSZZZFFFDFFFFFFFQQQQQQQQ
    CCCCCCCCCUUUUUUUOULLLLLLLFLMLLIIIIPPPPPKKKIEEKKNNNNNNNNSSUUSSSJJGGGNNLNNNQQQQZZXXXXXXXXXXXXXXSSSSTSSSSSKKKKKKSSSSSSSSSSZZJFFDFFFFFFFFQQQQQQQ
    CCCCCCCCCUJJJJJJUULLLLLLLLLLIIIIIIPPPKKKKKEEKKKNNNNNNNNNSSSSSSSGGGGNNLNNNQQQQQXXXXXXXXXXXXXXXTSSSTSSSSSKKKKKSSSSSSSSSSSZZFFFFFFFFFFFFQQQQQQQ
    CCCCCCKKKUUJJJJJJJLLLLLLLLLLLIIIIIIPKKKKKKKKKKKNNNNNNNNNSSSSSSSGGGGGGLLLNQQQQQQQXXXXXXXXXXXXXTSTTTTTSSSKKKKSSSSSSSSSSSSSSSFFFFFFFFFFQQQQQQQQ
    CCCCFFFFFFJJJJJJJLLLLLLLLLLLLLIIIIPPKKKKKKKKKKNNNNNNNNNXXXSSMMMGGGLLLLLLNQNQQQQQXXXXXXXXXXXXXTTTTTTTTTSHKKSSSUSSSSSSSSSSSZFFFFFFFFFFQQQQQQQQ
    CCCCFFFFFFFJJJJJJLLLLLLLLLLLLLIIIHHPPKKKKKKKKKKKNNNNNNNNXXXSMMLLLLLLLLLNNNNNQQQQQXXXXXXXXXTXTTTTTTTTTTTHKSSSSSSSSSSSSSSSSSFFFFFFFFFQQQQQQQQQ
    CCCCFFFFGFFJJJGJJJJJLLLLLKKLLLIIIHHKKKKKKKKKKKKKNNNNNNNXXXXSMMMLLLLLLLLNNNNNQQQQQQXXXXXXXXTTTCCTTTTTTTHHHHHDSSLSSLSSSSSSSSFFFFFFFFFQQEEQQQQQ
    CCFGFFFFFFFFGGGJGJJLLLLLUEELILIIIKKKKKKKKKKKIKKUNNNNNNXXXXXXXLLLLLLLLLLLQQQQQQQQQQQXXXXXXXXCTCTTTTTTTTTHHHHHIILLLLSSSSSSHHHFHFFFFFFEEEEEQEQQ
    CCFFFFFFFFFFGGGGGJJLLLLLUEESIIIIIIDDKKKKKKKKUUUUNNNNNNXXXXXXZZLLLLLLLLLLLQQQQQQQQQQQXXXXXXJCCCCTTTTTTTTHHIIHIIIWLLSSSQQSHHHHHHFFFFFFEEEEEEQQ
    XFFFFFFFFFFFGGGGGGJHLLLLUEEIIIIIIIDDDDKYKKKKKUUUUNUUNNCXXXXXXZZLLLLLLLLBLMBQQQQQQQQQXXCCCXCCCCCTTTTTTTHHHIIIIIWWQQQQQQQSSHHHHHFFFPPFEEEEEEQQ
    FFFFFFFFFFFGGGRGGPHHLHHLLEEEIIIIIDDDDDUYYKKKKUUUUUUUWWXXXRXXXKKKKKKLLLBBBBBQQQQQQQCCXXCCCCCCJCCTTTTTTTTHFIIIIIIWWQQQQQQJHHHHHHHJJPEEEEEEEIEQ
    FFFFFFFFFCFFFGRRPPHHHHHELEEEEEEIDDDDDUUUYYYKUUUUUUUWWWWWXXXKKKKKKKLLLBBBBBBQQQQQQQQCCCCCCCCCCCCFTTTTFTTFFFIFIWWWWQQQEQQJJHHHHHJJJJJJXEEEEEEQ
    FFFFFFFFFFRFRRRRPPHHHHEEEEEEEEEEEDDDDUUUUUKKUUUUUUWWWWWWXKKKKKKKKKLLLBBBBBBQQQQQQQCCCCCCCCCCCCGFFFFFFFTFFFIFIWWWWEEQEQQJJJHJJJJJJJJJJJREQQEQ
    FFFFFFFFFFFFFFPPPPPHPEEQEEEEEEEEEEDEUUUUUUUUUUUUUUUWWWWWWKKKKKKKKKKLLBKBBBBBBQQQQCCCCCCCCCCCCCCAFFFFFFFFFIIFIIIWWEEEEQJJJHHJJJJJJJJJJJJJJQEQ
    FFFFFFFFFFFFPPPPPPPPPEEEEEEEEEEEEEEEUUUUUUUUUUUUUUUWOXXXXKKKKKKKKKLLLBBBBBBBBBBQQCCCCCCCCCCCCCCCFFCCCFCFFFFFFFFWWEEEEEJJJJJJJJJJJJJJJJJJJQQQ
    FKFFFFFFFFFFFPPPPPPPPPEEEEEEEEEEEEEEUUUUUGUUUUUUUWUWOVVXXKKKKKKKKKLBLBBBBBBBBBQQQCCCCCCCCCCCCCCCFCCCCCCFFFFFFFFWEEEWWEJJJJJJJJJJJJJJJQJQJQQQ
    KKFFFFFFFFFFFPPPPPPPPPPEEEEEEEEEEHELLLUUUGUUUUUWWWWWOOOXXXWWKKKKKILBBBBBBBBBBOQQQQCCCCCCCCCCCCCCCCCCCGCFFFFKKKAWWWWWWWWJJJJJJJJJJJJJJJJQJQQQ
    KKKKKFFFFFKFPPPPPPPPPPEEEEEEEEEEEELLLLLGGGGUUUUWWPWOOCOOOXWWKKKKKIBBBBBBBBBBBOOQQCCCCCCCCCCUUUCCCCCGGGGFFFKKKAAAAAWWWWWWJJJJJJJJJJJJQQQQQQQQ
    KKKKKFFFFFKKKPPPPGGGGPIEEEEEEEEEELLLLLLLGRRRUCUPPPPOOOOOOOWWWKKKIIIBBBBBBBBBBBOQOCCCCCCCCCUUUUUCCGGGGGGFCEAAAYAAAAWWAAWWJJJJJJJJJJJJJQRQQQRQ
    KKKKKKFFKFKKPPPGGGGTTEEEEEEEEEEEELLLLRRLLRRRRUUNPPPVOIORROWXXXMKKXXBBBBBBBBBBBOOOOOOCCCCCUPUUUUUUGGGGGCCCAAAAAAAAAAAAAWWNJJJJJJJJJJJJQRRQRRQ
    KKKKKKFKKKKKKPPGGGGGGGSSSSEEEEEQUUUURRRRRRRRGGGPPPVVPPKRRWWXXXMKXXXBBBBBBBBBBBOOOOOOCCCUUUPUUUUUUUGGGGGCCAAAAAAAAAAAAAANNNNJJJJJJJJJQQRRRDRR
    KKKKKKKKKKKKKGGGGGGGGGGSSSEPEEEQUUUUUURUUUUUGGPPPPVPPNRRRRRXXXXXXXXXBBBBBBBBBBBBBOOOOOUUVUUUUUUUYYGGGGRCCAAAAAAAAAAAAAANNNNNNJJJJJQQQRRRRRRR
    KKKKKKTKKTKKTTSSGGSGSGGSSSPPFEZUUUUUUUUUUUUUPGPPPPPPPPBRRRRXXXXXXXXXXBXBBBBBBBBBBBOOOOUUUUUUUUUUUUAAGGRCAAAAAAAAAAAAAAAGNNNNNJJJJJQQRRRRRRRR
    KKKKTTTTTTTTTTSSGGSSSSSSSSPPFPZUUUUUUUUUUUUPPPPPPPPPMPRRREEXXXXXXXXXXXXBBBBBOBBBOOOOOUUUUUUUUUUUUAAGGGGAAAAAAAAAAAAAAAAANNNNNNJJJJJJRRRRRRRR
    KKKKKTWTTTTTTTTSSSSSSSPSPPPPPPUUUUUUUUUUUUUUPPPPPPPPPKRRREXXXXXXXXXXXXXVBBBOOOOOOOOOOUUUUUUUKUUUUAAGVVVVAAAAAAAAAAAAAUUUNNNNNNJJJJJRRRRRRRRR
    KKKKKTTTTTTTTTTSSSSSSSPPPPPPPPJUUUUUUUUUUUUPPPPPPPPPPPPPPEEXXXXXXXXXXXXXXFBEEOOOOOOOAUUUAAUUUUUDAAAWYVYAAAAAAAAAAAAAAUUUNNNNNNNRRRRRRRRRRRRR
    KKKKTTTTTTTTTTTSSSSSSSPPPPPPPPPURUUUUUUUUUPPPPPPPPPPPRPPPEEEEEXXXUXXXXXXXFFEEOOOOOOOAUUUAAUAUUUAAAAWYYYYYAIAJAAAAAUUUUNNNNNNNNNTRRRRRRRRRRRR
    KKKKTTTTTTTTTTSSSSSSPPPPPPPPPPSSUUUUUUUUUUUPSPPPPPPPPPPJPREEEEXXXUUXXXXXCEEEOOOOAOAAAAAAAAAAAUAAAAAYYYYYYQAAAAAAAAUUUUUNNAANNIITTRTRRRRRRRRR
    KKKKKTTTTTTSSSSSSSSPPPPPPPPPPPPPPUUUUUUUUUGPPPPPPPPPPPJJJRRRRRXXXOUUUXXXCEEEOOOOAAAAAAAAAAAAAAAAAAAYYYYYYYYYAAAAAAUUUUUUUATTTTTTTTTRRRRRRRRR
    KKKKKTTTTTTSSBSSSSSSSPPPPPPPPPPPUUUUGGUUUGGGGGPPPPPJJJJJRRRRRRRRUUUUUSXCCEEEOOOGAAAAAAAAAAAAAAAAAYYYYYYYYYBYYBBAAUUUUUUUUUTTXTTTTTTTTRRRRRRR
    KKBKBBTTTTBBBBSSSSSSSSPPPPPPPPPPPUUGGGCGUGGGGGPPPPJJJJJJJRRRRRUUUUUUUUXUEEEEEEEGGAAAAAAAAAAAAAAAAYYYYYYYYYYYBBBBUUUUUUUUUTTTTTTTTTTBBBBRRRRR
    KBBBBBBTTBBBBBSSSSSSSSPPPPPPPPPPPPUJGGCGGGGGGGGPXPPJJJJJRRRRRRUUUUUUUUXUVEEEEEEGGGGAAASAAAAAAAAAAYYYYYYYYYYBBBBBUUUUUUUUUTTTTTTTTTTBBBBRRRRR
    KKKBBBBBTBBBBBSSSSSSSSPXPPPPPPPPPSSGGGGGGGGGGGPPPPZZZZJJZZNRRRUUUUUUUUUUUEEEEGGGGGIIIIAAEUUUUAAAAYYYYYYYYYYBBBBUUUUUUUUUBBBTTTTTTTTTBBBRRRRR
    KKBBBBBBBBBBBBBSSSSSPPPPPPPPPYPSPSSSGSGGGGGGGGPPPZZZZZJZZNNNRRRUUUUUUUUUEEEEEEGGIIIISAAAUUUUWAACYYYYYYYYYYYBBBBBUUUUUUUUBBTTTTTTTTTBBBBRRRRR
    KKKBBBBBBBBBRBBBBSSSSSPPPPPPPPSSPPSSSSGGGGGGGGPPZZZZZZZZNNNUUUUUUUUUUUUUUEEEEEEEEEIIIIAAUUUIWAAYYYYYYYYYPBBBBBBBBUUUUUUUBBTTTTTTOOTBBBBRRRRR
    OOKKBBBBBBBBBBBBSSSSSSPPPPPPPPSSPPSSSSGGSGGGGGGZZZZZZZPZNNNUUUEEUUUUUUUEEEEEEEEEEIIIIAAIIIIIIIIIIIYYYYYYPBBBBBBBBBBUUUBBBBBBYYYYOONNNBRRRRRR
    OOOOOOBBBBBBBBBBBBSSSSPPPKPMPPSSSSSSSSSSSGGGGGGZZZZVVZZNNNNNNEEEUUULUUUULLEEEEEEEIIIIIIIIIIIIIIIIIYYYYPPPBBBBBBBBBBBBBBBBBBBYOYYOONNNNPRRPRP
    OOOOOOBBBBBBBBBBBFVSSSPMMMMMMMSSSSSSSSSSSGGGGGGCCZZVZYZNNWWNWEEEUULLULLLLLEEEEEEEIIIIIIIIIIIIIIIIIYYYYQPPBPBBBBBBBBBBBBBBBBBBOYOOOONVVPPPPRP
    OOOOOOOBBBBBVVBVTVVSSVMMMMMMMSSSSSSSSSSSGGGGGXCCCCZZZZKKKKKKKKKKELLLLLLLLLEEEEEEEIIIIIIIIIIIIIIPIIIUUPPPPPPBBBKBBBBJJJBBBBBOOOOOOOONVVPPPPPP
    OOOOOOOBBBBBVVVVVVQVSVMMMMMMMSSSSSSSSSSSSVGGGXXCMMZZZZKKKKKKKKKKELLLLLLLLEEEEEEEEIIIIIIIIIIIIIIPPPPPPPPPPBBBKBKKKKBJJJBBBBOOOOOOOOONVVPPPPPP
    OOOOOOOOOBXVVVVVVVVVVVVMMMMMYSSSSSSSSSSASVVAGXCCMVZMZMKKKKKKKKKKELLLLLLLLLEEEEEIIIIIIIIIIIIIIIIPPPPPPPPPCBBKKKKKKKBJJJBBBBOOOOOOOOOOXXXXPPPP
    OOOOOOOOOXXXVVVVVVVVVMMMMMCMSSSSSSSSSSSVVVXGGXMMMVMMMMKKKKKKKKKKQLLLLLLLEEEEIEIIIIIIIIIIIIIIIIIIIPPPPPPPCPBCKKKKKKJJJJJJJJOOOOOOOOOOXXXXXPPP
    OOOOOOOOOZXXVVVVVVVVVMTMCMCCSSSSSSSSSSSVVVXXXXMMMMMMMAKKKKKKKKKKLLLLLLLLLLIIIIIIIIIIIIIIIIIIIIIIPPPPPPPPPPBBKKKKKKJJJJJJJJJJJJOOOOOOXXXXXXMM
    OOOOOOOOOXXXVVVVVVVVVVVVCCCCCSSSSSSSSSVVVXXXVVMMMMMMMMKKKKKKKKKKLLLLLLLLLKIIIIIIIIIIIIIIIIIIIIIHPPPPPPPPPPBBBKKKKKJJJJJJJJJJJJOOXOOOXXXXXXXM
    OOOOOOGOOXXXXXVVVVVVVVVVCCCCCCSSSSSSSSVVVVXXVMMMMMMMMMKKKKKKKKKKLLLLLLLLLKIIKIIIIIIIIIIIIIIIHHHHHPPPPPPPPPQQQQKKKKJJJJJJJJJJJJXXXXXXXXXXXXXM
    OOOOOOOOOXXXXXVVVVVVVVVVCCNNCCSSSSSSSSSVVVXXVVMMMMVMMVVVVWWWWWWWLLLLLLLLLKIIKKKIIIIIIIIIIIIIHHHPPPPPPPPPPWOQQQQQQQJJJJJJJJJJJJOSAAXXXXXXXXXM
    OOOOOOOOOOXCECCCVVVVVVVCCCNNNCSSSSSSSVVVVVVXVVVMVVVMMVVVVVWWWWWWLLLLLLLLLKKIKKKIIIIIIIIIIIIHHHHPPPPPPPPPXOOQQQQQQQJJJJJJJJJJJJSSWWXXXXXXXXXM
    OOOOOOOOOOCCCCCVVVVVCCCCCNNVNSSSSSSVVVVVVVVVVVVMVVVVVVVVVVVLWWWWWLLLLLLLLLKKKCCCCCICIIIIIIHHHPPPPVVVPCCPPOOQQQQQQQJJJJJJJJJJJJSSWWWWXXXXXXXX
    OOOOOOOOCCCCCCCCCVVVVCCCCNNNNNNSSSSVVVVVVVVVVNNZZZVVIVVVVVVLLLWWLLLLLLLLOODKKKCCCCCCIIIIBIHHHTTPPOOOCCPPPOOOOOQOXQJJJJJJJJJJJJJSWWWWWXXXXXXX
    OOOOOOOOOCYCCCCCCVVVCCCCNNNNNNNSSSSSVVVVVVVVVVNZZZZZIVVVVVVLLLLLLLLLLLLLLDDDDCCCCCCIIIIIIIHHHTTPPFOCCCOOOOOOOOOOXQWWWJJJJJJJJJJSSWWWWXXXXXXR
    OOOOOOOOYYYCCCCCCVVCCCCNNNNNNNNNNNVVVVVVVVVVVVNNVVZIIVVVVVVLLLLLLLLLLLLZZDDDZCCCCCCCIIIIIIHHHHHPPFOCCCOOOOOOOOXXXXXXWJJJJJJJJJJSWWWWWWXXXXXX
    OOOOOOOYYYYYCCCCCCCCCCCNNNNNNNNNCOVVVVVVVVVVZZNSGVVVVVVVVVVLLLLLLLLLLLLLZDDZZCCCCCCIIIIIIHHHHHHFFFOOOOOOOOOOOOOXXXXXWJJJJJJOSDSWWWWWWWXXXXXX
    OOOOOYYYYYYYCCCCCCCCCCCNNNSNNNNNCCVVVVVVVZZVVZFSGGGGVVVVVVVMLLLLLLLLLLLLZZZZZCCCCCCCTIIITTTHHHHFFFOOOOOOOOOOOOOOOXXXXXWXXXOOSDWWWWWWWWWXXXXX
    OOOYOYYYYYYYCCCCCSCCCCCCCNNNNNNNCCCVVVVZZZZZZZSSSGGMLVVVVVHMMMMMMLLLLLZZZZZZZZCCCCTTTTITTTTBFFFFFFOOOOOOOOOOOOOXXXXXXXXXXXOOOWWWWWWWWWWXXXXM
    OOOYYYYYYYYYYGGCCSSSSCCCNNNNNCCCCCCVVZZZZZZZZZZZZMMMLVVVVMMMRLLBLLFFFFFFFFFFZZCXCCCTTTITTTTBBFFFCFOOOOOOOOOOOOXXXXXXXXXXXXXOOXWWWWWWWWWWWMXM
    OOOYYYYYYYYGGGGCCCCSSSCCCNNNNNCCCCKVVNNZZZZZZZZZZZKMMVVVVMMMRLLLLLFFFFFFFFFFZZCCCCZATTTTTTTBFFFCCCOOOOOOOOXXOXXXXXXXXXXXXXWXXXSSSWWWWMMMWMMM
    OODBYYYYYYYGGGGGSSSSSSSCCCCCCCCCCCCNNNNNZZZZZZZZZMMMMMMMVMMMMMLOLZFFFFFFFFFFZZZZZZZAATTTTTTBBFCCCOOOOOOOOOOXXXXXXXXXXXXXXXXXXXSSSSWWMMMMMMMM
    OBDBBBBBEYSGGGGGSSSSSSSSSCCCCCCCCCNNNNZZZZZZZZZZMMMMMMMMVMMMMMMMMZFFFFFFFFFFZZZZZAAAATTTTBBBFFCCBOOOOOOOOOOOOODDDXXXXXXXXXXXXXSSSSWHHMMMMMMM
    BBBBBBBBBGGGGGGSSSSSSSSSCCCCCCCCCCCCZZZZZZZZZZZZMMMMMMMMMMMMMMMMMZZZZZZZZZZZZZZZZAAAAAATTBBBFFBBBIOIZZOZZOOOOOODDXXXXXXXXXXXXXSSHSSHMMHHHMMM
    BBBBBBBBGGLGGGGGSSSSSSZZCCCCCCCCCCCCCCZZZZZZZZZZZMMMMMMMMMMMMMMMMZZZZZZZZZZZZZZZAYAAAAATBBBBBBBBBIIIZOOZZZZOODDDDDXXXXDXXXXXXXSSHSHHMMHHMMMM
    BBBBBBBBGGGGGGAASSSSSSSSCCCCCCCCCCCCCCZZZZZZZZZZZMMMMMMMMMMMMMMMZZZZZZZZZZZZZZZAAAAAAAATTBBBBBBBBZIZZZZZZZZOODDDDDDDDDDDQQQXXSSSHHHHHHHHMMMM
    BBBBBBBBBGGGFFSSSSSSSSCCCCCCCCCCCCCWCCCZZZZZZZZZZZZCMMMMMMMMMMMMZZZZZZZZZZZZZTZAAAAAAAAAAQQBBBBBZZZZZZZZZZZOOODDDDDDDDDQQQQXXSHHHHHHHHHHHYYM
    BBBBBBBBBBBBBSSSSSSSSSCCCCCCCCCCCCCWCCCZZZZZZZZZZZZMMMMMMMMMMMMMZZZZZZZZZZZTTTZAAAAAAAAAAQQBBBBBZZZZZZZZZZZZDODDDDDDDDDQQQQQXXHHHHHHHHHHHLYY
    BBBBBBBBBBBBBBSSSSSSSSCCCCCCCCCCCCWWCCZZZZZZZZZZZZZYMMMMMMMMMMYZZZZZZZZZZZTTTTTWBAAAAAAAQQQBBBBBWZZZZZZZZZZZDDDDDDDDDDDQQQQQQHHHHHHHHHHHHYYY
    BBBBBBBBBBBBSSSSSSSSSSSCCCNNCCCWWWWWYYYZZZZZZZZZZYYYYYMMMKMKMMMKKZZZZZZZZZTTTTXBBBAAAAAAQQQBBBBBBZZZZZZZZZSZDDDDDDDDDDDQQQQQQQHHHHHHHHHHHYYY
    EEBBBBBBBBBBSSSSSSSSSSSCCNNCCCZWWZWYYYYYYYZZZZZZZYYYYAMMMKKKMMKKKZZZZZZZZZKKKBBBBBVBAIAQQQQBBBOOZZZZZZZZZZZYDDDDDDDDDDDQQQQQQQHHHHHYHHHHYYYY
    EEBBBBBBBBBBSSSSSSSSSSSSCNNCGCZZZZZZYYYYYYZZZZZZZYYYYAAMMKKKKKKKKKZZZZZZZZKZKBBBBBBBBBQQQQQQQBBBBZZXZZZZZZDDDDDDDDDDQDDDQQQQQQBHHHHYYHHHYYYY
    EEBBBBBBBBBBSBBSSSSSSSSSSSNNZZZZZZZZYYYYYYYYZZXXYYYYAAAAMKKKKKKKNNNZZZZZZZZZBBBBBBBBJJJQQQQQQQXZZZZXZZZZZZFFFFDDDDDDQDDDDQQQBBBBYYYYHHYYYYYY
    EEEBEEBBBBBBBBSSSSSSSSSJJJJJZZZZZZZYYYYYYYYYAXXXYYYYAAAEEKKKKKNKNNNNNZZNZZTBBBBBBBBBJJBQQQQQQQXXXXXXXXXZZFFFFDDDDDQDQDDDDQQQQQBBBYYYYYYYYYYY
    EEEEEEBBBBBBBBBSSSSSJCSJJJJPZZZZZZZYYYYYYYXXXXXXXYYYXXDEEEEKKNNNNNNNNNNNNBBBBBBBBBBBBJBSOQQQVQXXXXXJJXXJZFFQQQQQDQQQQQDQQQQQQBBBYYYYYYYYYYYY
    EEEEEEZEBBOOBBBSSSJBJCCJJJJJZZZZZZZYYYYYYXXXXXXXXXYXXXXEEEEKKNNNNNNNNNNNNNNBBBBBBBBBBBBOOOQQVXXXXJJJJJJJJFQQQQQQQQQQQQQQQQQQBBBBYYBYYYYYYYYY
    EEEEEEZEOBOOBOBSSOJJJJJJJJJJJZZZZZZZCCCAAAAXXAAXXXXXXEEEEEEKKNNNNNNNNNNNNNNBBBBBCBBBBOOOOOQXXXXXYJJJJJJJJJQQQQQQQQYYQQQQQQQQBBBBBBBBBBYYYYYY
    EEEEEEEEOOOOOOBOOOJJJJJJJJJJJTZZZZCCCCCCCAAAAAKXXOXOEEEEEEEKKNNNNNNNNNNNNNNNBBBCCCCOOOOOOWYYYYYYYJDDJJJJJJWQQQQQQQYYQQQQQQBBBBBBBBBBBBYYYYYY
    EEEEEEEEOOOOOOOOOJJJJJJJJJJJJJJJFGCCCCCCCCCAKKKQXOOOEEEEEEEKKNNNNNNNNNNNNNNNNBCCCCCOOOOOOOYYYYYDDDDDJJJJJJWWQQQQYYYYYYQQQQBBBBBBBBBBRBYYYYYY
    EEEEIEOOOOOOOOOOOJJJJJJJJJJJJJZZGGGGCCCCCCCKKKKKKOOEEEEEEEEEECCNNNNNNNNNNNNNNCCCCCOOOOOOOYYYYYYDDDVDDDJJJJWWQQQJYYYYYMMMMMMMMMMJJJJJRBYYYYYK
    EEEIIROOOOOOOOOOJJJJJJJJJJJJJJJZGGGGZZCCUUKKKKKKKKOOHPPEEEEEECCNNNNNNNNNNNNNCCCCCCOOOOOOYYYYYYYYDVVVDAJAWWWWQQQDYYYYYMMMMMMMMMMDJJJJJOYKYKKK
    ERRRRRRROOOOOOOOOJJJJJJJJJJJJJJZZGZZZCCCUUUKKKKKKKOOHHHPEECCCCCCNNNNNNNNNNNNCCCCYCOYYOOOYYYYYYDDDDVVDAAAAWWQQWDDYYYYYMMMMMMMMMMJJJJJJJYKKKKK
    ERRRRRRRRROOOOOOOOJJJJJJJJJJJJJZZZZZZZZZZUUUUKKKIIIIFHPPPECCCKKCNNNNNNNNNNCCCCYYYYYYYOYYYYUUYYYDDDDDAAAAAWWWQWDDDYYYMMMMMMMMMMMJJJJJNYYKKKKK
    RRRRRRRRRROOOOOOOOOJJJJJJJJJJJJZZZZZZZZZUUUUUUKGGGIIHHHHPKKCKKKKNCCNNNNCCNNNCCCCYYYYYYYYYYUUUTADDAAAAAAWWWWWWWWWDDDOMMMMMMMMMMMJJJJJJLLLKKKK
    RRRRRRRORROOOOOOSOOJJJJJJJJJJVZZZZZZZZZZUUUUUUKGGIIIHHHHPKKKKKKKKKCCCCCCCCNCCCCCCCCCHYHHYUUUUAAADAAAAAAAAAWWWWWDDDDOMMMMMMMMMMMJJJJJJLKKKKKK
    ZZRRRRROOOOOSOOOSOOOJJJPJJJJVVVZZZZZZZUUUUUUUUUIIIIIIHHHPKKKKKKKKKKCCCCCCCCCCCCCCCCHHHHHHHUUNAAAAAAAAAAAXAWAWWWDDDDOMMMMMMMMMMMJJJJJJJJKKKKK
    SZRXXROOSSOSSSSSSSOOOPJPJJJJVVVZZZXXXUUUUUUUUUUIIIIIIHHKKKKKKKKKKKKCCCCCCCCCCJCCCHHHHHHHHHUUNAAAAAAAAAAAAAAAAAWDDDDOMMMMMMMMMMMJJJJJJJKKKKKK
    ZZZXXZOSSSSSSSSSSSSSSPPPPJJJVZZZZZZXXVVVVUUUUUUUIIIIIHBBKKKKKKKKKKKCCCYYYCCJJJCCHHHHHHHHHHCCAAAAAAAAAAAAAADAAIWDDDDOMMMMMMMMMMMJJJJJJJKKKKKK
    ZZZZZZOSSSSSSSSSSSPPPPPPPPJVVVVVVZXXXCXXVUUUUUUUIIIIIHHBBKKKKKKKKKKCCYYAYCCJJJCCHHHHHHHHHHCHRRAAAAAAAAAAAAAAAAADDDDOMMMMMMMMMMMJYJJJJJKKKKKK
    ZZZZZZZSSSSSSSSSSSPPPPPPPPPPPVVVVZXXXXXXVUUUUIIIIIIIIIZZKKKKKKKKKKKKCYYYYYCJJJCCCHHHHHHHHHHHHRRAAAAAAAAAAAAAAAIIIDCCLOOMMMMMJJYYYKKYKKKKKKKK
    ZZZZZZZZSSSSSSSSSSPPPPPPPPPVVVVVVVVXXXXXUUUUUIIIIIIIIIZZKKKKKKKKKKKKYYYYDDJJJJJJJIIIHHHHHHHHHRRAAAAAAAAAAAAMMLLLLLLLLOOMMMMMYYYYKKKKKKKKKKKK
    ZZZZZZZZASSSSSSSJSPPPPPPPPPPVVVVVVXXXXXXXXUUUUIIIIIIIIIZZKKKKKKKEEDYYYYYYDJJJJJJJJIIJHHHHHHHHRRRRRARARRARRAAMLLLLLLLLOOOOOJYYYYYKKKKKKPKKKKK
    ZZZZZZZZZZSSSSSSPPPPPPPPPPVVVVVVVVVXXXXXXXXUUUUIIIIHIIZZZZZZKKKKEEDYYYYYDDDJJJJJJJIIJJHHHHHHHRRRRRRRRRRRRRRAALLLLLLLLOOOOOJYYYYFFFKKPKPPPKWK
    ZZZZZZZZZZZUSDSSSPPPPPPPPVVVVVVVVXXXXXXXXXXUUUUUUIIIIIZZVVZKKEFEEEYYYYYYDJJJJJJJJJJJJHHHHHHHHFFFRMMMMMMRRRRRLLLLLLLLLOOOOOJYFFFFFEKPPPPPPKWK
    ZZZZZZZZZZZZDDDSSPPPPPOPPPPVVVVVVXXXXXXXXXXXUUKUUIIIIQVZVVVTKEEEEEEYYYYYDJJJJJJJJJLJHHHHHTHHHFFUMMMMMMMMMMRRRRLLLLLLLLOOOOOOOFFFFFFGPEEPPWWK
    ZZZZZZZZZZZZZDDDSPPPPPOOEPVVVVVVVVXXXXXXXXXXUKKKKKIIIQVVVVVTTEEEEEEETTYYYJJJJJJJJJJHHHHHHHHHHFFUMMMMMMMMMMRRLLLTLLDLARAOOOOOOHHFFFXPPEEPPPPK
    ZZZZZZZZZZZZDDDDDPPPPOOOOOOOOVVVVVXXXXXXXXXUUKKKKKKIQQVVKVTTTEEEEEEETTTTJJJJJJJJJJZZHHHHHHHHFFFMMMMMMMMMMMMRJTTTTTAAAAAOOOOOOOHFFFFFPPPPAPPA
    ZZZZZZZZZZZZDDDDDPPPPOOOOOOOOVVVVXXXXXXXXXUUKKKKKKKIIKKAVVVVTTEEEEEETTTTTTJJJJJJJJZZZHHHHHFFFXXXXXXXXXMMMMMJJTTTTTTAAAAAAOOOOOHFFFFFPPPAAAAA
    ZZZZZZZZZZZIZDDDDDDPPOOOOOOOOVVVVBXXXXXXXPKKKKKKKKKKKKAAVTTTTTTTEEEETTTUUUUUUJJJJJJZZHHHHHFFFXXXXXXXXXXXXXXXJJJTTTTAAAAAAOOHOOHFFFMPPPSPPPAA
    BZZZZZZZZZZZZZDDDDDPDOOOOOOOOOOVVBLXXXXTXXKKKKKKKKKKKKKKTTTTTTTTTEEETTUUUUUUFJJJJJJJHHYHHHHFXXXXXXXXXXXXXXXXJJTTTTTAAAAAAOAHHHHHPFFPPPPPPPAA
    BZZZZZZZZZZZZZDDDDDDDDOOOOOOOBBBBBLXXXXKKKKKKKKKKKKKKKKKTZZTTTTTTEEETUUUUUUUJJJJJJCCCCFFHHFFXXXXXXXXXXXXXXXXJTTTJTTAAAAAAAAAAAAPPPPPPPPPPPAA
    BZBBBZWWZZNZDZDDDDDDDDDDOOOOOLLBBBLLXXXXRRRRKKKKKKKKKKKKTZZTTTTTTTTTTUUUUUUUUJJJJJCCCCFFFFFFXXXXXXXXXXXXXXXXTTTTJTTAAAAAAAAAADPPPPPPPPPPPPPA
    BBBBBBBBBWWNDDDDDDDDDDDDODDOOLLLLLLXXXXRRRRNNNNNKKKKKAAZZZZTTTTTTTTUUUUUUUUCCCJJJVVVFFFFFIIIXXXXXXXXXXXXXXXXJTTTJJTAAAAAAAAAAPPPPPPPPPPPAAAA
    BBBBBBBBWWNNDDDDDDDDDDDDDDDDDDLLLLLLXRRRRRRNNNNNKKKKKKZZZZZZTTTTTTTUUUUUUUKKVCCJJVVVCFFFFFIIXXXXXXXXXXXXXXXXTTJJJJTAAAAAAAAAAAPPPPPPPPPPPPAA
    BBBBBBBWWWNNDNDDNDDDDDDDDLLLLLLLLLLLLRRRRRRNNNNNKKKKKZZZZZZZTTTTKKTKAUUUUKKKKCCCJVVVCCFFCFIIXXXXXXXXXXXXXXXXTTJJJJTTTAAAAAAAAAZPPPPPPPPPPPAA
    BBBBBBBRWWNNNNNNNNDDDDDDLLLLLLLLLLLLLLRRRRRNNNNNKKKZZZZZZZZZZNNNNKKKUBUUUKKKKCVVVVVVCCCFCCCIXXXXXXXXXXXXXXXXTTTJJKTTTAAAAAAAAAZZPPPPPPPPPPPA
    BBBBBBBBBNNNNNNNNDDDDLLLLLLLLLLLLLLLLLRRRRRNNNNNKZZZZZZZZZZZZNNNKKKKUUUUUKKKKCVVVVVVCCCCCCCIXXXXXXXXXXZZZZKKKKKJJKKTTTTAAAAEAAZZZZPZPPPPPPPA
    BBBBBBBVNNNNNNNNNDDDDDDLWWLLLLLLLLLLRRRRRRRNNNNNZZZZZZZZZZZZZNNNNKKKUUKUKKKKKCVVVVVVCCCCCCIIIIIIZZZZZZZZZZKKKKKKKKKTTTTTAAAEAZZZZZZZZZPPIITA
    BBBBBBBBBLNNNNNNNDDDDKKWWWLLLLLLLLLLLRRRNNNNNNNNNNZZZZZZZZNZNNKNNLKKUKKKKKKKKCVVVVVVCCCCCCCVILIIZZZZZZZZZZKKKKKKKKKKKTTTAAAEEGGZZDDDDZPPITTA
    BBBBBBBBBLLLNNNNNNDKKKKKWWWWWLLLLLLLRRRRNNNNNNNNNNNNZZZZZNNNNKKKKKKKKKKKKKKKKKVVVVVVKCCCCCCCLLLIZZZZZZZZZZKKKKKKKKYYTTTTTAEEGGGZDDDDTZZZTTTT
    BBBBBBBBLLLLNNNNNNKKKKKKWWWWLLLLLLLLRRRRNNNNNNNNNNNNZZZZZZNNNNKKKKKKKKKKKKKKKKVVVVVVVVVVCCCCCCLLIITZZZZZZZKKKKKKKKYYYYTTTGGGGGGDDDDDTTTTTTTT
    BBBBBBOWLWLLLNNNKNKKKKKKWWWWLLLLLLLLLRRRNNNNNNNNNNNNZZZZZZNNNNKKKKKKKKKKKKKKKKVVVVVVVVVVKKCQQFLLLTTZZZZZZZKKKKKKYYYYYTTTGGGGGWWWDDDDDDTHTTTT
    BBBBBLWWWWWNNNNNKNKKKKKWWWWLLLLLLLWLLRRRNNNNNNNNNNNNZZZZZZZNNNNKKKDWWWKKKKKKKRVVVVVVVVVVKKVQQFFFFCCZZZZZZZKKKKKYYYYYTTTTGGGGGGWDDDDDDDTTDLTT
    BBBBBBWWWWWNCNNNKKKKKKKKWWWWLWLWLLWLLRRRNNNNNNNNNNNNZZZZZZZNNNNNKKDWWWKKKKKRRRRRRQVVVVVVKKKQQFQFFFCZZZZKKKKKKKKKKYYYYTTTGGGGGGGDVDDDDDDDDDDD
    BBBBBBBBWWWCCKKKKKKKKKKKWWWWWWWWLWWWRRRRNNNNNNNNNNNNZZZZZZZNNNNNOWWWWWKKKRRRRRRRRRKKKKKKKKKQQQQQCCCCCCKKKKKKRKKKRYYYYTGTGGGYWDDDDDDDDDDDDDDD
    BBBBBBBBHWWHKKKKKKKKKKKKKWWWWWWWWWWWRRRRRNNNNNNNNNNNEEEEZZNNONNNOOOWWWKKKKRRRRRRRRKKKKKFKKKQQQQQKCCWWCKKKKKRRRRRRJXXXTGGGGGYYDDDDDDDDDDDDDDD
    FBBBBBHHHHHHKKKKKKKKKKKKKWWWWWWWWWWWWRRRRNNNNNNNNNNNEEEEZZNNOOOOOOOWOWKKKRRRRRRRKKKKKKKFFFFQQQQQQWWWCCCKKKRRRRRRRXXXXXGGGGYYODYYDYYDDDDDDDDD
    BBBBBBBBHHHHHKKKKKKKKKKKKWKWWWWWWWWWWWRRRNNNNNNNNNNNOOEEEZNNNOOOOOOOOWWUKKCCRRRRKKKKKKKKQQQQQQQQWWWWCCCCCKRRRRRRXXJJJYYGGYYYYYYYYYYYYDDDDDDD
    BBCBOBECCCHHKKKKKKKKKKKKKKKWWWWWWWWWWWRRRRRRRRRROOOOOOEEEZZNSOOOOOOOOUUUCCCCRRRIIIKKKKKKQQQQQQQQQQCWWCCCCRRRRRRRXXIYYYYGGYYYYYYYYYYYYYYYYYDD
    CCCCCCCCCCCKKKKKKOKKKKKKKKKWWWWWWWWWWWRRRRRRRRROOOOOEEEEEZZSSOOOOOOUUUUCCCCCCCIIIKZKKKKKKKQQQQQQQQCCCCCCWWWWRRRXXXIYYYYYGYYYYYYYYYYYYYYYYYDD
    CCCCCCCCCCKKKKKKGGGGKKKKKKKWWWWWWWWWWWRRRRRRRRROOOOOEEESSSZSSOMMOOOOCCCCCCCCCIIIIKKKKKKKKIQQQQQPPQQQCCCCCWWRRRXXXIIIYYYYYYYYYYYYYYYYYYYYDDDD
    CCCCCCCCCCCKKKKKGGGGKKKKKKWWWWWWWWEWWRRRRRRRRRRROOOOOOSSSSSSSMMOOOOOOCXCCCCCCIISSSLLLKKKIIQIIIICCCCCCCCCCWWRRRXXXIIYYYYYYYYYYYYYYYYYYYYYDDDD
    CCCCCCCCCCCCCKKGGGGGGGKKKKWKWWWEWWEEEGGRRRRRRRUOOOOOOOSSSTSSSMMOOOOOOOOOCCCCCIISSSSLLKKIIIIIIIIICCCCCCCCCCCXXXXXXXIIYYYYYYYYYYYYYYYYYYYDDDDD
    CCCCCCCCCCCCCCTGGGGGGGGGKKKKEEWEEEEEEGPRPPPRRUUOOOOOOOSSSTSSSMOOOOOOOOOOOCCCCIIISSSSSIIIIIIIICCCCCCCCCCCCCCXJXXXIIIIIYYYYYYYYYYYYCCYYYYDDDDD
    CCCCCCCCCCCCGTTGGGGGGGGGKKEEEEEEEEEEEPPPPPPRUUOOOOOOOOOOSOSSSOOOOOOOOOOOOOIICCISSSSSIIIIIIIIICICCCCCCCCCCCCJJJXXIIIIIIIYYYYYYYYYCCCYYYDDDDDD
    CCCCCCCCCCCGGGGGGGGGGGGGKKEEEEEEEEEEEEEPPPPRUUOZOOOOOOOOSOSSSOOOOOOOOOOOOOOIIIISSSUSIIIIIIIIIIICCCCCCCCCCCJJJJJJIIIIIIIYYYYYYYYYCCYYYYYDDDDD
    CCCCCCCCCCCCGGGGGGGGGGGGKKKEEEEEBEEEEPPPPPPPPOOOOOOOOOOOOOOUOOOOOOOOOOOOOOOOIIIIVVIIIIIIIIIIIIIIICICCCCCCCCJJYYJYIIIIIIYYYYYYYYYYYYYYYDDDDDD
    CCCCCCCCCCCCGGGGGGGGGGGGGKKKEEEEEEEEEPPPPPPPPOOOOOOOOOOOOOOUOOOOOOOOOOOOOOOOOOIIIIIIIIIIIIIIIIIIIIICCCCCCCCYYYYYYIIIIIIIYYYYYYYYYYYYYDDDDDDD
    CCCCCCCCCCCCGGGGGGGGGGGGGKKKKKKKEEEECPPPPPPPOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOIIIIIIIIIIIIIIIIIIIIICIICCCCCYYYYYYYYYYYYYYYYYYYYYYYYYYYDDDDDD
    CCCCCCCCCCCGGGGGGGGGGGGGGKKKKKKKEEECCCCPPPPIOOOOOOOOOOOOOOPOOOOOOOOOOOOOOOOOGGGGIITIIIIIIIIIIIIIIIIIIICCCYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYDDY"""

    data = [list(d) for d in data.splitlines()]
    m, n = len(data), len(data[0])

    def count_regions():
        dirs = ((-1, 0), (0, 1), (1, 0), (0, -1))
        seen = set()

        # returns area, perimeter
        def dfs(i, j, prev): 
            if (i < 0
                or j < 0
                or i >= m
                or j >= n
            ):
                return 0, 1
            if prev != data[i][j]: 
                return 0, 1
            if (i, j) in seen: 
                return 0, 0

            seen.add((i, j))
            area, perimeter = 1, 0
            for i_off, j_off in dirs: 
                dir_area, dir_perimeter =  dfs(i + i_off, j + j_off, data[i][j])
                area += dir_area
                perimeter += dir_perimeter
            return area, perimeter

        res = 0
        for i in range(m): 
            for j in range(n): 
                area, perimeter = dfs(i, j, data[i][j])
                res += area * perimeter
        return res
                    
    # 1434856
    print(count_regions())
    return count_regions, data, m, n


@app.cell
def __(data, m, n):
    from collections import Counter 

    def count_regions_with_sides():
        dirs = ((-1, 0), (0, 1), (1, 0), (0, -1))
        corners = ((-0.5, -0.5), (-0.5, 0.5), (0.5, 0.5), (0.5, -0.5))
        
        seen = set()

        def is_in_bounds(i, j): 
            return i >= 0 and j >= 0 and i < m and j < n        
        def rotate_right(x, y): 
            return y, -x
        def rotate_left(x, y): 
            return -y, x
        def vsum(v1, v2): 
            return v1[0] + v2[0], v1[1] + v2[1]
        def halfscale(v): 
            return 0.5*v[0], 0.5*v[1]


        # returns area
        corner_tracker = Counter()
        
        def dfs(i, j, prev_letter): 
            if not is_in_bounds(i, j):
                return 0
            if prev_letter != data[i][j]: 
                return 0
            if (i, j) in seen: 
                return 0
                
            seen.add((i, j))


            # add 4 corners
            for corner_i, corner_j in corners:
                corner_tracker[(i + corner_i, j + corner_j)] += 1

            for direc in dirs: 
                perp = rotate_right(*direc)
                diag = vsum(direc, perp)

                d1 = vsum((i, j), direc)
                d2 = vsum((i, j), perp)
                d3 = vsum((i, j), diag)
                
                if (is_in_bounds(*d1) and is_in_bounds(*d2) 
                    and data[d1[0]][d1[1]] == data[d2[0]][d2[1]] == data[i][j]
                    and data[d3[0]][d3[1]] != data[i][j]
                ):
                    corner_tracker[vsum((i, j), halfscale(diag))] += 2

            
            area = 1

            c = 0
            for direc in dirs: 
                next_i, next_j = vsum((i, j), direc)
                
                if (is_in_bounds(next_i, next_j) 
                    and data[i][j] == data[next_i][next_j]
                ):
                    # remove corners if necessary
                    corner1 = halfscale(vsum(direc, rotate_left(*direc)))
                    corner_tracker[(i + corner1[0], j + corner1[1])] -= 1
                    corner2 = halfscale(vsum(direc, rotate_right(*direc)))
                    corner_tracker[(i + corner2[0], j + corner2[1])] -= 1

                dir_area = dfs(next_i, next_j, data[i][j])
                area += dir_area

            return area

        res = 0
        for i in range(m): 
            for j in range(n): 
                area = dfs(i, j, data[i][j])
                # num sides == num corners
                res += area * sum((+corner_tracker).values())
                corner_tracker = Counter()
        return res

    # 891106
    print(count_regions_with_sides())
    return Counter, count_regions_with_sides


@app.cell
def __():
    return


@app.cell
def __():
    return


if __name__ == "__main__":
    app.run()