Statistics

Problem Statement for "FoxAndGemstone"

Problem Statement

Fox Ciel has a collection of bags. Each of those bags contains some gemstones. You are given the contents of the bags as a String[] bags. Each element of bags represents one of the bags. Different characters represent different gemstone types. For example, if bags[2]="ABAC", we know that bag 2 contains two gems of type A, one gem of type B, and one gem of type C.

There are at most 16 different types of gems. Gems of the same type always have the same weight. Gems of different types always have different weights. Each weight is some positive real number.

Fox Ciel wants to identify the heaviest of all her bags. (It is possible that multiple bags are tied for being the heaviest. In that case, Ciel wants to identify any one of those bags.)

Ciel has only one tool she can use while solving this task: a tiny balance scale. The scale is so small that the only thing she can do is to compare the weights of two gems. I.e., in each weighing she will take two gems of different types, place each of them onto one of the pans of the scale, determine which type of gems weighs more, and then she'll return both gems to their original places. Ciel can use the scale arbitrarily many times.

You are given the String[] bags, but you don't know anything about the weights of the gems. Return "Possible" if you can be sure that Ciel will be able to identify the heaviest bag. Otherwise, return "Impossible". In other words, return "Impossible" if there is some combination of weights of gemstone types such that Ciel won't be able to determine with certainty which bag is the heaviest one.

Definition

Class:
FoxAndGemstone
Method:
isPossible
Parameters:
String[]
Returns:
String
Method signature:
String isPossible(String[] bags)
(be sure your method is public)

Constraints

  • bags will contain between 2 and 50 elements, inclusive.
  • Each element in bags will contain between 1 and 50 elements, inclusive.
  • Each character in bags will be one of the first 16 uppercase English letters ('A'-'P').

Examples

  1. {"AB", "AC"}

    Returns: "Possible"

    Ciel just needs to compare a gem of type B and a gem of type C. If B is heavier, bag 0 is the heaviest bag. Otherwise, bag 1 is the heaviest bag.

  2. {"A", "BC"}

    Returns: "Impossible"

    This is an interesting situation. For some combinations of weights Fox Ciel will find the heaviest bag. For example, if she discovers that A < B, she can be certain that the bag "BC" is heavier than the bag "A". However, there are some combinations of weights for which Ciel won't be successful. For example, suppose she weighs the gems and she finds out that A > B > C. Given the above information, it is possible that A > B+C, but it is also possible that A < B+C. In this situation, Ciel has no way of telling which bag is the heavier one.

  3. {"A", "B", "C", "AB", "AC", "BC", "ABC"}

    Returns: "Possible"

    Here Ciel doesn't need the scale at all, she can simply choose the last bag.

  4. {"AB","AC","AD","BC","BD","CD"}

    Returns: "Possible"

  5. {"AB", "CD"}

    Returns: "Impossible"

  6. {"A", "A", "A"}

    Returns: "Possible"

  7. {"AB","CD", "AC", "BD"}

    Returns: "Possible"

  8. {"EPOGJJEMJGPFHNBNDMFGDBIHNMIAJIBGOBAEPAJPCOJEACMNAF","JBEBLBMBPNGKIFAJDGDJCDIEBIBIKFKBGICNJJLEDMPPDLEAJC","EOHANDDMIGAJPJBOFEMLPFEOAFBCHHNOCECKJMNMECMMMFGILG","ELEFFBDAGANJLKCNKJIHKEBPPJDOEIMJMPCOGCJLHIMEMDCFKM","KAJAOFKMEDFGFFLLIJJGINDGGECACJAAEAFHJMANKKGAIICJIH","LAOHKGMCJFLHOGPBFMDDLNEPDEFAAAPHGIFFHDGDLKBFMKNEEH","BFBFBICFCCBFOJMGILJLNOMGJAEKFEKDGJLPILBGBGKNDMKAMD","AJPDKBHBNLMPICDEKFNKKAGGDCODJBJBBJADGIBGLBNKDGHDKM","HBPKKCDJFODAKCKGDLBEPIBBIDMGCJJPJBLJPMMNEDPGJEEBOH","NHFNJFELOMPGJKJIOMBKIBBLLMLPADMPCDNOJKBMKGNKDDHCLH","IFKAJLJGOFNOJPBOJIKFEMIKJIHFPKMIDFJBBPNPPJGBIPLJLF","KFBJIMCOMEDFNPFIFBNABLLKHMOEIBNMCAHFIECAAAFIDLGFHK","IOBKNJMDMMEPNGEFGANPGBNAMODABKFHCLODLBPIJIGMDCENIO","INCJGEBBGLEPJEHEKHLABPPLAKBFIOOOBJJJIOBBAMJIOOCMDO","LEEGBNFFDIICGPGHKIIMJCADJCDLIHJMNFFKODIKGDCIJEHPHC","IPNHPBBPPPEKEBCALJGDDBGCMJPFMFIKKEMNNHMHBPOOLMLINK","KDIJFALOKHKOPOGINAMELAPAMEAIAGLLGDIEMHOOKJNBELFMCH","JJOCOHNDAKJGHIFNCHLNDOGIMBHKKMHHPBEFCKDDGBGBHOHFPE","LMOIKGCOOMOCGIHACNAPOLKHEHHFBOBDJLMIACFNBJFIIAALOH","NCABHAICCMPKHJAIICCLJANPCNOIFKKLPABOJEDJNBBLDJGNIH","GAMENGHIENFHCGOOIIDANGJCOKHLNPBOEANFOBFCFACHHMANHI","FBANCJLOBGHEKOOEKCBBFMNGIKLCBOLHOEENJAIEEOFDMNLIAO","EBGKFGOLCPBEIFGCPFOHBEGKPIGIFKEIHMGECPMBHPFMADIKMP","FEOMEMMIOOGLEGNCGKCPCCDOGCAGMHAMAALJKFIENGPHAJCJAC","CJABKAKDKMBPKGALKIIIBDKIPBNAHKBDJHONBEDFGEKAEEJNIK","FOCMKBIHHPDBGOAGONMBNONDIAJFDMFHEDOCKPAAAJHJACADLB","NGHOCLHEOOABNOKCNIPHDOEKPCPBBGEKAJPHGBLNFJCDBAGNPI","KAOAEJECILHKHFBEBBHBMAAFNCGLHDCHBMEGIMMHHBNCAGAOJJ","PKDPEHPKCGIDJHGMECDEMEHLBGEBLILDEOAPINOHCFLNDNMAFA","GPGKHCPCPHONEGOGIMKMPGJJNNDKNDPGAMOMJKOOOBMGJKPDOJ","CDDDOFAECMHFIDBHHDPNAFNGEFHBADOFELONEJJDEOGPJBCPKM","NPDIHPBPGNKJLANJCDHCIIFDILJHPHDBLJCBHNANONBIIEKFAO","PMEDEOLMOKFADEHGNMNBICJHKLKLEPEKNDFGLFPCFBPDJNJFPO","HEFPHAAOONBPHPNBNJBNDJAHKBFDNPFKJFGFBKNKIBLEAMLBKI","ICKNKHHPGLKHBBPOPLCDDHMANDKBPEBIMACFLCKACOMELNHMJA","JIHMLAAIMAONAECPIHDFKJLPCJLGJBOOMCLCAIFABEFEBILNIC","KADAPHEAOJKMINAJEELNDJNDMIMKMENGDEOAKJMGHFAFOPIGKC","OMJGFKJHPFDAPGIIJLLDJHKCCHPDEELIBJCFHODHPNJJEDNNKI","HBBLMFHKELOMCKBFKGIGJBJALGENIONHBMBPOGKDDGMJCDLIOO","JMELIEBMBOPKFJJIGOLIBFKDPFEAIGFJFBOAMEFIGBNKIKJBPH","FNBENOBPLGAFJDHJDMACMNHKJILCOECJOCLALKMCEAGFKPKJEG","DJMLEPBINACOOFAABDKMJEIBEFHMADNNHHEOOPKJJOBBKLGOIK","JHMEPIFHJOLBDMJIJCAKMFIIMMNIEGDGCBMGKLNFHMFGJDJIIP","EKDECBAJPACEMFCLHJJJEBJDDIFCHDEJOPGKLCAJOBNMKCMHJM","PIICGCHPIBPJKLONJIOHBLPDHBEBCKHIGMNPDLJOLIGDOIJBPC","BLAOFENLOPAOABKKGIJGMJKMHIFLOEDJBEMJFANDJFGNBIJHDH","KFPHILIJNDCFFOMIPKHPKIKBFPKCCFPCKEBHNBOPCFHENHMBKP","LMIKCLMKDNOMIEAMKDLMJNGDKENIHHJCHCDGCDDMBLNJGGBJBD","HCADFLJNGPNMDKCKOJPJKKFFJMNNGMBALIBCDGLAJCPEFBLMOO","JOLELHAGLOOILCKNFKKNMNBKLOPCJCDMBFGIIJEOJKNIFFMPKP"}

    Returns: "Impossible"

  9. {"AB", "CD", "AC"}

    Returns: "Impossible"

  10. {"AB", "CD", "AC", "AD"}

    Returns: "Impossible"

  11. {"AC", "AD", "BC", "BD"}

    Returns: "Possible"

  12. {"A", "BC", "AB"}

    Returns: "Possible"

  13. {"AAA", "BBB", "AAB", "BBA", "ABA"}

    Returns: "Possible"

  14. {"AAAA", "BBB"}

    Returns: "Impossible"

  15. {"AAAA", "BBB", "AABB"}

    Returns: "Impossible"

  16. {"AABB", "ABCD", "CCDD"}

    Returns: "Impossible"

  17. {"AB","PB","AC","PC","AD","PD","AE","PE","AF","PF","AG","PG","AH","PH","AI","PI","AJ","PJ","AK","PK","AL","PL","AM","PM","AN","PN","AO","PO"}

    Returns: "Possible"

  18. {"CB","AE","EE","DD","EC","AA","CB","BB","CA","BC","EB","DC","CC","BB","AD","BC","DB","CE","EC","EA"}

    Returns: "Possible"

  19. {"GD","HH","EM","LA","AL","FL","KD","IF","CE","FI","KC","GG","JB","FK","DA","HD","JK","AF"}

    Returns: "Impossible"

  20. {"DL","JC","IJ","HJ","EF","IL","JK","HJ","JL","KB","LE","GC","KA","CE","EE","JC","JC","CK","JG","IJ","LJ","KA","IA","IK","EL","DA","HC","KF","GC","FJ","LJ","GH","GA","CJ","GF","FF","EI","JG","JF","AJ","GK","AF","LL","KD","EL"}

    Returns: "Impossible"

  21. {"CA","AB","CB","AA","CC","CB","AC","BC","BC","CA","CA","CA","CB","CA","AC","AB","CC","CB","BC","AA","AA","BA","AB","BC","CA","CA","CB","BC","BA","AC","CA"}

    Returns: "Possible"

  22. {"LO","GF","OF","LE","DN","NO","OJ","CE","KA","DD","MN","IE","AI","DD","LA"}

    Returns: "Impossible"

  23. {"IJ","HJ","CC","CI","JI","HA","BI","IF","BG","EC","FC","GI","GC","DF","CJ","GE","IB","BC","JB","GH","JC","CF","AA","JD","IB","JB","DF","FC","FC","GI","HH","CC"}

    Returns: "Impossible"

  24. {"FJ","BI","EA","LB","FK"}

    Returns: "Impossible"

  25. {"AB","AB","AC","BB","BB","BB","BA","CB","BA","BC","BC","AC","BA"}

    Returns: "Possible"

  26. {"EB","GK","HL","FC","CM","BK","GH","GM","KA","HE","DF","BK","BG","BG","KG","EC","AL","FA","GE","HC","EK","MC"}

    Returns: "Impossible"

  27. {"AC","EC","EE","EE","EC","AD","CC","CD","AD","DD","AC","AC","CD","EC","AC","ED","CD","BB","CD","DA","BA","CC","BC","AE","AC","ED","AA","DA","AB","CB","AA","EA","EA","AE","EB","CD","BB","DD","EB","ED","CE","CA"}

    Returns: "Possible"

  28. {"GD","HH","EM","LA","AL","FL","KD","IF","CE","FI","KC","GG","JB","FK","DA","HD","JK","AF"}

    Returns: "Impossible"

  29. {"DL","JC","IJ","HJ","EF","IL","JK","HJ","JL","KB","LE","GC","KA","CE","EE","JC","JC","CK","JG","IJ","LJ","KA","IA","IK","EL","DA","HC","KF","GC","FJ","LJ","GH","GA","CJ","GF","FF","EI","JG","JF","AJ","GK","AF","LL","KD","EL"}

    Returns: "Impossible"

  30. {"CA","AB","CB","AA","CC","CB","AC","BC","BC","CA","CA","CA","CB","CA","AC","AB","CC","CB","BC","AA","AA","BA","AB","BC","CA","CA","CB","BC","BA","AC","CA"}

    Returns: "Possible"

  31. {"LO","GF","OF","LE","DN","NO","OJ","CE","KA","DD","MN","IE","AI","DD","LA"}

    Returns: "Impossible"

  32. {"IJ","HJ","CC","CI","JI","HA","BI","IF","BG","EC","FC","GI","GC","DF","CJ","GE","IB","BC","JB","GH","JC","CF","AA","JD","IB","JB","DF","FC","FC","GI","HH","CC"}

    Returns: "Impossible"

  33. {"FJ","BI","EA","LB","FK"}

    Returns: "Impossible"

  34. {"AB","AB","AC","BB","BB","BB","BA","CB","BA","BC","BC","AC","BA"}

    Returns: "Possible"

  35. {"EB","GK","HL","FC","CM","BK","GH","GM","KA","HE","DF","BK","BG","BG","KG","EC","AL","FA","GE","HC","EK","MC"}

    Returns: "Impossible"

  36. {"AC","EC","EE","EE","EC","AD","CC","CD","AD","DD","AC","AC","CD","EC","AC","ED","CD","BB","CD","DA","BA","CC","BC","AE","AC","ED","AA","DA","AB","CB","AA","EA","EA","AE","EB","CD","BB","DD","EB","ED","CE","CA"}

    Returns: "Possible"

  37. {"FK","LK","LA","GH","JA","KK","HJ","CJ","HJ","IB","IH","KC","ID","BF","FH","EE","EK","KC","DH","LD","EJ","IG","HI","HI","FC","BA","KK"}

    Returns: "Impossible"

  38. {"AF","HG","EL","IB","IJ","HF","CB","AA"}

    Returns: "Impossible"

  39. {"AA","EB","BA","AC","AD","BB","CB","CB","BC","BE","CB","CC","BC","BA","ED","AE","CE","AB","CD","EE","CE","EC","DC","DC","AB","DC","DA","CD","BE","AB","AE","AB","EB","DA","DA"}

    Returns: "Impossible"

  40. {"CB","CF"}

    Returns: "Possible"

  41. {"BA","EC","EB","BF","HH","GG","FD","GA","DA","BA","BA","AD","CC","EB","HA","HB","AA","CF","FB","BG","CB","ED","CE","HH","FA","FA","FH","AH","FE","EF","DB","FD","AB","GF","FB","DH","AF","BA","HA","EG","ED","CD","CC","HH"}

    Returns: "Impossible"

  42. {"DC","JI","GB","CA"}

    Returns: "Impossible"

  43. {"BD","AH","AK","FO","DP","OP","PK","AA","IL","DB","IJ","GK","OJ","BH","IB","MB","EN","OO","DB","IM","PA","DK","PN","HH","JA","NP","HM","ID","NP","PJ","JJ","OE","MA","OF","IC","CC","LN","EG","LM","PI","CD","OB","NN"}

    Returns: "Impossible"

  44. {"FD","EB","DA","CC","BB","FD","EB","FC","CA","DF","CC","EA","CC","DB","DE","EE","DB","EF","FA","AE","EA","EC","FE","DD","DC","BD","ED","AE","EE","DD","AC","CE","AD","CB","AF","AE","BF","EB","CE","EA","FC","AF","EF","FD","DE","AB","DE","AC","FC"}

    Returns: "Possible"

  45. {"DG","DA","DD","FB","AA","BF","FC","CC","CF","CF","BE","FH","FD","FB","EC","AD","HF","HD","HC","AE"}

    Returns: "Impossible"

  46. {"CB","CA","DA","BD","DD"}

    Returns: "Impossible"

  47. {"AH","BH","CH","DH","EH","FH","GH","AI","BI","CI","DI","EI","FI","GI","AJ","BJ","CJ","DJ","EJ","FJ","GJ","AK","BK","CK","DK","EK","FK","GK","AL","BL","CL","DL","EL","FL","GL","AM","BM","CM","DM","EM","FM","GM","AN","BN","CN","DN","EN","FN","GN"}

    Returns: "Possible"

  48. {"ABC","ABD","ACD","BCD","ACE","BCE","ADE","BDE"}

    Returns: "Possible"

  49. {"ABC","ABD","ACD","BCD","ACE","BCE","ADE"}

    Returns: "Impossible"

  50. {"ABC","ABD","ACD","BCD","ACE","BCE","ADE","BDE"}

    Returns: "Possible"

  51. {"ABC","ACD","BCD","ACE","BCE","ADE","BDE"}

    Returns: "Impossible"

  52. {"ABCEFG","ABDEFG","ACDEFG","BCDEFG","ABCEFH","ABDEFH","ACDEFH","BCDEFH","ABCEGH","ABDEGH","ACDEGH","BCDEGH","ABCFGH","ABDFGH","ACDFGH","BCDFGH","ABCFGI","ABDFGI","ACDFGI","BCDFGI","ABEFGI","ADEFGI","BDEFGI","ABCFHI","ABDFHI","ACDFHI","BCDFHI","ABEFHI","ADEFHI","BDEFHI","ABCGHI","ABDGHI","ACDGHI","BCDGHI","ABEGHI","ADEGHI","BDEGHI","ABFGHI","ADFGHI","BDFGHI"}

    Returns: "Possible"

  53. {"ABDEFG","ACDEFG","BCDEFG","ABCEFH","ABDEFH","ACDEFH","BCDEFH","ABCEGH","ABDEGH","ACDEGH","BCDEGH","ABCFGH","ABDFGH","ACDFGH","BCDFGH","ABCFGI","ABDFGI","ACDFGI","BCDFGI","ABEFGI","ADEFGI","BDEFGI","ABCFHI","ABDFHI","ACDFHI","BCDFHI","ABEFHI","ADEFHI","BDEFHI","ABCGHI","ABDGHI","ACDGHI","BCDGHI","ABEGHI","ADEGHI","BDEGHI","ABFGHI","ADFGHI","BDFGHI"}

    Returns: "Impossible"

  54. {"AB","AC","BC","AD","BD","CD","AE","BE","CE","DE","AF","BF","CF","DF","EF","AG","BG","CG","DG","EG","FG","AH","BH","CH","DH","EH","FH","GH","AI","BI","CI","DI","EI","FI","GI","HI"}

    Returns: "Possible"

  55. {"AB","AC","AD","BD","CD","AE","BE","CE","DE","AF","BF","CF","DF","EF","AG","BG","CG","DG","EG","FG","AH","BH","CH","DH","EH","FH","GH","AI","BI","CI","DI","EI","FI","GI","HI"}

    Returns: "Possible"

  56. {"ABCDEFGH","ABCDEFGI","ABCDEFHI","ABCDEGHI","ABCDFGHI","ABCEFGHI","ABDEFGHI","ACDEFGHI","BCDEFGHI"}

    Returns: "Possible"

  57. {"ABCDEFGH","ABCDEFGI","ABCDEFHI","ABCDFGHI","ABCEFGHI","ABDEFGHI","ACDEFGHI","BCDEFGHI"}

    Returns: "Possible"

  58. {"ABCDEFGH","ABCDEFGI","ABCDEFHI","ABCDEGHI","ABCDFGHI","ABCEFGHI","ABDEFGHI","ACDEFGHI","BCDEFGHI","ABDEFGHJ","ACDEFGHJ","BCDEFGHJ","ABDEFGIJ","ACDEFGIJ","BCDEFGIJ","ABDEFHIJ","ACDEFHIJ","BCDEFHIJ","ABDEGHIJ","ACDEGHIJ","BCDEGHIJ","ABDFGHIJ","ACDFGHIJ","BCDFGHIJ","ABEFGHIJ","ACEFGHIJ","BCEFGHIJ","ABCDFGHK","ABCDFGIK","ABCDFHIK","ABCDGHIK","ABCFGHIK","ABDFGHIK","ACDFGHIK","BCDFGHIK","ABDFGHJK","ACDFGHJK","BCDFGHJK","ABDFGIJK","ACDFGIJK","BCDFGIJK","ABDFHIJK","ACDFHIJK","BCDFHIJK","ABDGHIJK","ACDGHIJK","BCDGHIJK","ABFGHIJK","ACFGHIJK","BCFGHIJK"}

    Returns: "Possible"

  59. {"ABCDEFGH","ABCDEFGI","ABCDEFHI","ABCDEGHI","ABCDFGHI","ABDEFGHI","ACDEFGHI","BCDEFGHI","ABDEFGHJ","ACDEFGHJ","BCDEFGHJ","ABDEFGIJ","ACDEFGIJ","BCDEFGIJ","ABDEFHIJ","ACDEFHIJ","BCDEFHIJ","ABDEGHIJ","ACDEGHIJ","BCDEGHIJ","ABDFGHIJ","ACDFGHIJ","BCDFGHIJ","ABEFGHIJ","ACEFGHIJ","BCEFGHIJ","ABCDFGHK","ABCDFGIK","ABCDFHIK","ABCDGHIK","ABCFGHIK","ABDFGHIK","ACDFGHIK","BCDFGHIK","ABDFGHJK","ACDFGHJK","BCDFGHJK","ABDFGIJK","ACDFGIJK","BCDFGIJK","ABDFHIJK","ACDFHIJK","BCDFHIJK","ABDGHIJK","ACDGHIJK","BCDGHIJK","ABFGHIJK","ACFGHIJK","BCFGHIJK"}

    Returns: "Impossible"

  60. {"ABCDEFGHIJKLMNO","ABCDEFGHIJKLMNP","ABCDEFGHIJKLMOP","ABCDEFGHIJKLNOP","ABCDEFGHIJKMNOP","ABCDEFGHIJLMNOP","ABCDEFGHIKLMNOP","ABCDEFGHJKLMNOP","ABCDEFGIJKLMNOP","ABCDEFHIJKLMNOP","ABCDEGHIJKLMNOP","ABCDFGHIJKLMNOP","ABCEFGHIJKLMNOP","ABDEFGHIJKLMNOP","ACDEFGHIJKLMNOP","BCDEFGHIJKLMNOP"}

    Returns: "Possible"

  61. {"ABCDEFGHIJKLMNO","ABCDEFGHIJKLMNP","ABCDEFGHIJKLMOP","ABCDEFGHIJKLNOP","ABCDEFGHIJKMNOP","ABCDEFGHIJLMNOP","ABCDEFGHIKLMNOP","ABCDEFGHJKLMNOP","ABCDEFGIJKLMNOP","ABCDEFHIJKLMNOP","ABCDEGHIJKLMNOP","ABCDFGHIJKLMNOP","ABCEFGHIJKLMNOP","ACDEFGHIJKLMNOP","BCDEFGHIJKLMNOP"}

    Returns: "Possible"

  62. {"ABCDEFGHIJKLMNO","ABCDEFGHIJKLMNP","ABCDEFGHIJKLMOP","ABCDEFGHIJKLNOP","ABCDEFGHIJKMNOP","ABCDEFGHIJLMNOP","ABCDEFGHIKLMNOP","ABCDEFGHJKLMNOP","ABCDEFGIJKLMNOP","ABCDEFHIJKLMNOP"}

    Returns: "Possible"

  63. {"ABCDEFGHIJKLMNP","ABCDEFGHIJKLMOP","ABCDEFGHIJKLNOP","ABCDEFGHIJKMNOP","ABCDEFGHIJLMNOP","ABCDEFGHIKLMNOP","ABCDEFGHJKLMNOP","ABCDEFGIJKLMNOP","ABCDEFHIJKLMNOP"}

    Returns: "Possible"

  64. {"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA","AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"}

    Returns: "Possible"

  65. {"AABBBBAAAAABBAAABBAAABABBBBBBAABAABABBAABAABABBABB","BBAAAAAABAABAABABAAABABBAAABBABAABABBABBABAABAAABB","BABBAABABAAABAABAAAAAABAABBABAAAAABABBABBBBAABBABA","BBBBABABABABBBAAAAABAAAAAAABBABAABBABBBABBABBBBBAA","BABABAAABBABBABAAABAAABBBAABABBABBBBABBAABABAAAAAB","BAABABAAAAABBBAAABABBAABBBBBAABABABBBABABAABBBABAA","AAAABAAABBBBBBBBAABBAABAAAABABAAAAABABABABAAAABBBB","BAAABAAAAABBBABBBBBBABBABBAAAABBBAAAAABBABABBBAAAB","BBBBBBBAAAAAABBABBABABBBABBABBBBBABAAABABAAAAAABBA","ABBBBAAABAABABBAAABBBABBABAAABAAABAAABABBBBBAABAAB","ABBBAAABAABAABABBABBBBABBABBBABBAAABAAAABBBABBBBBB","BBAAAABBAABBBAABBBBABAABBBAAABAAAABAABBAAABAABBAAB","BBBAABAABBABAABBAAAAABABBAABABABBABABBBABAAABBBBAA","BAAAABAABABBBBBABBBAAAABBABBBBABABAABBBBBBAABABAAA","AABAABBBAABBBABAAABBAAABBBABBBBABAAAAABBAABAAABAAB","ABABBABBAABBBBBBABAABBBBBAAAAAABBBBBABBBABABBBBBBB","BABABBBAAABABBBBBBAABAAABBABABABAABBABAAAAAAABBAAA","BAAAAABABBABBBABBBBBABABABBBAABBBBBAAAAABBBABAAABB","BBBBAAAABBBAABBAAAABABAABAABBABBBBAABAABABBABABBBB","AABBBAABABBBABBABBBAABBBBBAABBAAAAABABBBBBABBABBAA","BBBABAABBBAABBBABBBABABABAABBBBBBABAAAABBBBAABABAA","ABABBBAABBBBBBBBBBAAAAAAAABABBBAAABBABAABAAABBABBB","BBBBBABABBBBBAABABBABAABABBBBAABBAAABABBABABABABBB","ABBABBAAABABBBABAAABAAAAAABBAABBAABBAABAAABBBBABBA","BABBABAABAAAAAAAABAABABBBBBAAABAABBABBBBAABBAABABA","ABBBBBBABBAAABBAABAAAABAABAABBABAAAABABABBBABAABBA","ABBAAABBAAABBBABABBAABBAAAABABAAAAAABABAABAABAABAA","AAABABBABBAAAAABBAABABAABBAABABABBBBABBABAABAAAAAB","AAAAABABBBBBBABBBBBBAABBBBAABAABBBBBABBAAABABBBBAB","BAABBABAABAAAABBABAAABAABBAAABBBBAAABABBBBAABABABB","AABABBBBBABBBABABBAAAAABABBABBBBAABABBBBABABBAABBA","AAAABAABABBBAABABBBBBBABABBAABBAAABBAAABABAAABAABB","BAABABBBBBBAAAAABAABBABBABBBABAABBAAAAABABAABAABAA","BBBBABABABAABAAABBABBABBAABBABBAAAAAABAAABBBAABABA","BABBBAABAAABBBBBAABABAABABBBBBAABAAAABAABBAABBAAAA","BBBABAAABBBABABBAAAABABAABAAABAABBBBBBABAAABABBBAB","BABABBAABBABAAABBAABABABBBABBBBBBBABBAABABABBAAABA","AABBAABBAABBABBAABBBBBBBBABBABBAABABAAABBBBABAABAA","BBBBAAAABABBAAABBAAAAABABBBABAAAAAABBBAAABBABBABBA","ABAABABAAABBABBAABBAAAAABBBBBAABABBBAABAABAAABABAA","ABBABABAAAAABBABABBABBBBBAABBBAAAABBBBAABBAABAABBB","ABBBBABABABAABABAAAAABAABAAAAABBAABBAABAAAAABBAABA","AABBBBBBBAAAAAAAABABBAAAABBAAAABBABBBABBBAAABAABBA","BABBBABABBAAAAABABBBABBAAAAAABBABBBAABAAAAAAABAAAB","BAAAAAABBAAABAAABABAABBAAABABABBBAAABBAABAABAABBBB","AABBBBBABAAAAAAABBBABABAABBABBAABBBBABABBBBAAAABAA","AABBABABAAABABBABBAAAAABAABBBAABABBBBABAAABBBAABBB","AABBBBABBBBABAABABABBBBBBBAAABBBABAABABBBAABABABAB","BBABBBAABAABBBBBABBAABBBAAAABAABBABAABBABAAABBBBBA","BABBAABBABABAABABBAABAABABBBBAABBBBAABBBAABABBBBBA"}

    Returns: "Possible"

  66. {"ABACCCBCCCBBBABCCACBCCBBCABAAABBACBBCCBBACBBCAABCA","ABCABAABBBACBCACAAABBBCBCCBBCABBBCBAABCCBABABBABCC","ACCBBAAAAAABCBACABBBBACBCCBBCAAAABBCBBABBBACBCCBBA","CABABBCCABBBCBBCABABAABCCCBBACACCCCCBACBACCCAABBBB","ACAABAABAAAAACBBCBABCBAABACCCCBBACACCBAACCCABBCACB","CBBACBCBABBABCACABCAABBACBBCCABCCACCCBBAACBACCBBBC","BACBAACCACCCACCBABACBCCCCACACCBACCCACABABBABBCBAAC","CACCBBCBCABCAACBBCAACBBACAAABCCCBCBABCABBBABAACCAB","CBCCCABABCCABCCBACCBACACBBCBCBAAACAAACBBCACACBCAAB","CCABABBABBCCCBABCCABBACABACBBBCACCCCBAACBBAABCCCBA","AAACAAABBCCACABCBBABBBABBBCCCBBCAABCCAAACBBBACCCAB","CAABACABAACBCBCBACABBBABCBACCBACBCAACCAABAAAABCAAA","BBBCCBCABCCAABAACBBBCBACACCAACBBBCACCCCAACAACCCCAB","ABBABCCABCCAAABCBCABCBCCBCBABACAABBABAABAAACBCACAA","CABBBCBBABCCAACCBABABBCABCCBBCACAABCBBCABBACACCCAB","BCAAACCBAABACBBCCACAABCAAABACABBCABBCCCCCAACCCCCBA","ABCABBCCACBCCBABBACABABCBBBAABCCAACCCCCCBACCBAACBC","ACACBCAACACCACCCABABBAACBAACACCAACBAABACACACCBBACB","BCCAABBCBBBCBCBBCAAACBAACBBCBABCABACACCBAAACAACABB","BCCACCBCBCACBCAACACAACABCBBBBCCCCCABACACBBAACBCBCC","BCBAACBACACCABBCABACCBAABCBAACBACBBCBACCAABBACCCCB","AAABCAACABBBACBCCAABCCBABCBABCBBABBBBACABCACACCACB","BCCBCCACABCCACCCCBBABACBBCAACACAACBBBBAAACACAACACC","ACBBABBCBBCBAABCBABABABCBACCBACBAACACABAACCBCBBACB","AABBBBCAACBBCBBBBBCCCACBABCBBBAACBCCCABABCCABACCAC","AAAABACABBACCCAACACAAAACBBBABBCABABCBACBBAAABBBAAA","ACCCBACCCABBABACABBBBBBCCACBBCBCBAABBBAABBACACAABA","ACCCCACCCCCCBBCCACBCAACAAACACBCBCBAAAABBCACAAABBCB","BABACBCBABBAABACBCABCCACCBBBCCCBBBCCCABCACACBACCBC","BBBBBCCCABCACACCAACCABCCABBBCBCACAACBBBBACACBACBBB","AABABBAAABCACCABBBAABABCBBAABACBBBAACAABACACCBAACC","AACCABCABACCCBAAAABBACABCCBCAAACCCBAACACABBAABAACC","AABCACBCCCBAAAABCACACBAACACBAAABACCABBCCBBBABBBACA","CABCBABCBABCCBACBBCABBCACBCCACAABAAACABABBCBBCACBA","CABBACBABBACAABBBABABCCABACBAAAAAAABACBCBACCBCBAAA","AABCBACBBBACBBCABCCCABCBABAAABBCBCCCACCAABACAACBCB","CBBBAACBABACBABCCCCAAABBCBCAACCBACBACCCBCACACCCAAC","BBACABBCCACBACCCAABCBCBACABBCACABACCBAACBCABACBBCA","ABBBABBCBBBCCBBCABCBCCAACCBCABACABBCBAAABBBCACCACB","ACBACCAAACCCCCAAAABCBABCABCACBACAABBBBAAAACBABBACB","CABACAAACBAABAABCCBCCCCBACAACACCBCBBCAABBAABBBBBCC","AACABBBBCAAABBCCCCACBAACCAABBABABABACACACAAACBCABA","ABCABABBBBACBABCCCCAABAABCABCBABCBACCABBCCCCAACBAA","AABCBBBBCCAAAAAAABCCCCAABACCBABBCBABBCCBCACCBABABB","BAAACBABCBBCAABCBAACACBCABBBAACBCCBCABCCCCBABAAABC","ABCBBCCBCCBCCAACAACBCABCBAAACBCACCCABCBBBBCCBCCACC","CBCCCABBABCACBACACCCBBBAABCBACBCAABABBCBCACCACCABC","CCCCABBABBAACCBCABBBCACBCACCBAABAABBBCAABBACBCBBBB","CBBBBBBBBCBCACCAABBCAAAACACCBBACABACAABBAAAACBCBAC","CCBBBACCCACABBCBCABBACABBCABCBAACAAACCBBCCBABACBBC"}

    Returns: "Impossible"

  67. {"PBPFJKBCFEBCDCHGKCIEFECHLJPNIFHMPEGGFNLDEBELHKJMJK","AHNMBHKCKPGFEIHAADCBPMHJACNHOEKLFFIGFAFOGHOKKLKFID","KFDAKDBEFPIIBKOGGJGFECBJCKOBDFMDIMGFINHHPAEBDDAHOK","AMIDJEFFOGCAEGCJMBCLMGENJLHHPFBMLIGOANFPALOFPJLJEJ","FPEIKAIBCGGJBADAGHGLHAACHACOMMPBAOEOLJEENHHICIEDNP","FGNJGAKHOMBIOFCBCDGHKGPAOGNPHACCDBMLNNMBPOMPDLCDOJ","KFHGNAFOJKIDIMPJOMGNMIPNMPIBHICFDGHGDODKFKFLDIBIFK","OBDAOCPCAOFEAPHCMAACBLHBAFCAKMCOINEJMMCLPKIEMFKLLA","PCACKDLBDEGGCFNOCNANGIFGNHOFCHDEFMFBFGJJEHOIDHGING","CKLFHGOEOMPBDKPCPADENJEJEMOIBDANHDBBNMOOMBLCEGPNOA","DPBKCKHOKGLGHPOFICBMHEBNFBJONNDBDKKLAHEOPGKOGAFHDC","BOJLFHIGJACLILDPDFJFEBEKGMIJFHFOMLCHMNBPKCADPLBKPJ","GLHPEPKLIMOKIMLBMJOKBPNBMECCHENGFPOHIHAHHFJKPBENIF","AIBONGNFKAKHDKHBFGCAJGCKLBJKDNGOMKMOJKGFOFLFEHGDJL","KIHOJHPADDMPIDLBIAAGGFNGELGCEICPGIODPPJAOACAFMBCGO","GAIPFADEHDPOPOPPPHCGDBMKJFMMBJKCGFGPNPGPCMPDAOJKFJ","ADMDHJHOBBNEBPLOPDIMPCGLJGLEMHMCONGICEEKCECHCEJDML","EJODEMNEIMBDFFBLNKAKALIICDLDDNGAAPNLMBLHFMGAGMNLIE","DDJILCKLAHFMJLNDDIELINODDKJGGODCKBILDEJFDGKHEAODOH","CCBHEAGCBAPPAJOBPEMIPEFALBHJEJGICFGIDPANMDJBJBBLEP","KGBFOFPFHFBEAIDNKGGEODKPONDOIHEHKHGJIDMDOGLHOAIICN","EKNCMDBCEILENBCMLBNHHHBNNBOEPFGLEDEFCBJILNAHAGDALD","BJJEIBCKOKPCBOBGDHCPGFABFKHNGABCKLKEDHHMOGPGCNLFLD","HLCOMCCENJODLILJNMFBKMOGBOIEOOOACJHKCJMGLKBDBPBJJG","APMENBHJHAJCPBPJLHFHEBLLMGKKHHLKELFNHMDLBCADCIJKKB","OKODHGPELINLGJCOMDAPLPIOMLEDFONJJCFOHBNADIDHFCMLOH","OMOAJBKLMNPAFDCFAIBFDLBMLBMMEHNDPIIICJDGHMINFLPHLL","JDDOMLMLJHOIEPFKBBDFCNNNMLBFKCMBDFECOELCKNMGDIGBEA","BBAEEGGPKMCCOEGKAOIOKJFIPLNOEBKJFKFBMNBBKFGEEJMDHM","LIBDHGOLDCONOCEBKGBDICBFFGIDCKAHCEDAPMBOJLEAINHECM","GHMBGIEPALOEBBJHIBCPMGIHCEIGGGAKOHKJGAACMPEBGMMKHD","AIKNHHIKCBKJDGFGAJHEKBPFPGMKCBCGGJNCFAIANFHDNPPICH","DKBAIJLHMHOPKKCIHCAHDHKMCPACHPLEIJLNLCHDHPHKJPBLDK","IPNHIGNPIFEAFGANAMGPMGJCEGMDFPENKLKMKEBMNAKOEKAGNG","KCFNGOPFGPDNLJAMNBBPBIPJKHPBICCIGLONFNPCNGCBFAKFKA","JMFMKHAJEAIDNIMDLBMBCDKJPDNHDNIMLNONKLHPPCHNEBFMEA","JEOOGNOEIGNPJGONMFFNGAGDJGNPPLNACPDCHGMGLFLKPGAMHH","IDEMFEJIOCNMFJOJIBGMCLIGPIFNJGPEJPOGOMBHOENGBEKMMH","OHIEEFNFODOFLAGCCGGMKCDHDNBACMIJMLGKLHGKGPGBIELFIK","LJACPHLEEGOJOEIOMBHMMPEPLCKHHJDFFDDFLMBPEDEDOHJOMI","KCDPBGDNKEBBGELNCHPEJEDAICKLCIIEDHPOLAJGFENAIDHAKK","CGBDMKBBLBOLLIKEKLMMBGNBLIGLOBNMGLKKFABIHGLOCPBPIB","LPFCLGGFGLGCPHMPLHFAEKHNKDDLKBHIDCJCNMAHAHPNNKKOFG","EGMBPJPIPOCPJNGMENDAEDEAIJPLHCEEOCDCNMBMEPPANEOIJF","AGJEGPCDIOKBJNGJBBCDFJODCCPJCEPNHLLGILNPAELMLNMKKH","CAKLOMKIONBCNHPGOHMPOEKKKKCILOHJBLFKIIPKMIHAEDMLLA","GADEPNHOFGCIPMOALMOPHNDDNBKGPJFLENCNIEIPGKKBHAIBBK","DOGECHOGKLMFBNJNNMBJODEINKGOJENOKEMHANOKAAONKFPNJN","AFDBMLEEIAGEPNAPBAMGCABDLDFNGCAPPIPHAJDCEEDFHHJGGJ","LOPMENHNFADCGCGDJHKCAJKMCIGDNMDMOJPOOEEJENDLKPJNBH"}

    Returns: "Impossible"

  68. {"ABC","ABD","ACD","BCD","ABE","ACE","BCE","ADE","BDE","CDE"}

    Returns: "Possible"

  69. {"ABD","ACD","BCD","ABE","ACE","BCE","ADE","BDE","CDE"}

    Returns: "Possible"

  70. {"ABCD","ABCE","ABDE","ACDE","BCDE"}

    Returns: "Possible"

  71. {"ABC","ABD","ACD","BCD","ABE","ACE","BCE","ADE","BDE","CDE","ABF","ACF","BCF","ADF","BDF","CDF","AEF","BEF","CEF","DEF","ABG","ACG","BCG","ADG","BDG","CDG","AEG","BEG","CEG","DEG","AFG","BFG","CFG","DFG","EFG"}

    Returns: "Possible"

  72. {"ABC","ABD","ACD","BCD","ABE","ACE","BCE","ADE","BDE","CDE","ABF","ACF","BCF","ADF","BDF","CDF","AEF","BEF","CEF","DEF","ABG","ACG","BCG","ADG"}

    Returns: "Impossible"

  73. {"ABC","BCD","ABE","ACE","BCE","ADE","BDE","CDE","ABF","ACF","BCF","ADF","BDF","CDF","BEF","DEF","ABG","ACG","ADG","CDG","AEG","BEG","CEG","DEG","AFG","CFG","DFG","EFG"}

    Returns: "Impossible"

  74. {"ABCDEF","ABCDEG","ABCDFG","ABCEFG","ABDEFG","ACDEFG","BCDEFG","ABCDEH","ABCDFH","ABCEFH","ABDEFH","ACDEFH","BCDEFH","ABCDGH","ABCEGH","ABDEGH","ACDEGH","BCDEGH","ABCFGH","ABDFGH","ACDFGH","BCDFGH","ABEFGH","ACEFGH","BCEFGH","ADEFGH","BDEFGH","CDEFGH"}

    Returns: "Possible"

  75. {"ABCDFG","ABCEFG","ABDEFG","ACDEFG","BCDEFG","ABCDFH","ABDEFH","ACDEFH","BCDEFH","ABCDGH","ABCEGH","ABDEGH","ACDEGH","BCDEGH","ABCFGH","ABDFGH","BCDFGH","ABEFGH","ACEFGH","BCEFGH","ADEFGH","BDEFGH","CDEFGH"}

    Returns: "Impossible"

  76. {"ABCDEFG","ABCDEFH","ABCDEGH","ABCDFGH","ABCEFGH","ABDEFGH","ACDEFGH","BCDEFGH","ABCDEFI","ABCDEGI","ABCDFGI","ABCEFGI","ABDEFGI","ACDEFGI","BCDEFGI","ABCDEHI","ABCDFHI","ABCEFHI","ABDEFHI","ACDEFHI","BCDEFHI","ABCDGHI","ABCEGHI","ABDEGHI","ACDEGHI","BCDEGHI","ABCFGHI","ABDFGHI","ACDFGHI","BCDFGHI","ABEFGHI","ACEFGHI","BCEFGHI","ADEFGHI","BDEFGHI","CDEFGHI"}

    Returns: "Possible"

  77. {"ABCDEFG","ABCDEFH","ABCDEGH","ABCDFGH","ABCEFGH","ABDEFGH","ACDEFGH","BCDEFGH","ABCDEFI","ABCDEGI","ABCDFGI","ABCEFGI","ABDEFGI","ACDEFGI","BCDEFGI","ABCDEHI","ABCDFHI","ABCEFHI","ABDEFHI","ACDEFHI","BCDEFHI","ABCDGHI","ABCEGHI","ABDEGHI","ACDEGHI","BCDEGHI","ABCFGHI","ABDFGHI","ACDFGHI","BCDFGHI","ABEFGHI","ACEFGHI","BCEFGHI","ADEFGHI","BDEFGHI","CDEFGHI"}

    Returns: "Possible"

  78. {"ABCDEFG","ABCDEFH","ABCDFGH","ABCEFGH","ACDEFGH","BCDEFGH","ABCDEFI","ABCEFGI","ABDEFGI","ACDEFGI","BCDEFGI","ABCDEHI","ABCDFHI","ABCEFHI","ABDEFHI","ACDEFHI","BCDEFHI","ABCDGHI","ABCEGHI","ABDEGHI","BCDEGHI","ABDFGHI","ACDFGHI","BCDFGHI","ACEFGHI","BCEFGHI","ADEFGHI","BDEFGHI","CDEFGHI"}

    Returns: "Impossible"

  79. {"AC", "AD", "BC", "BD" }

    Returns: "Possible"

  80. {"AB", "BA" }

    Returns: "Possible"

  81. {"AFBLDDOELDGDPDFJKEFOKGAFLNABNLCCJAJNHEOOGFFGHHJJHM", "HOJMKENLCEFAEEAFPBFCMHMGPEMLEHFGGAPFJOHGLAIPBNBDOA", "NMPDCAJFKIFIPMECIIKAPMMJDPGGICIDFBFLGHOHGPEOICDNKD", "HHJMMKBKGOHEHPKNBFHAGMGKKJONFKMAPGIPJCIJAGBIMHKIOI", "KMFGOLMBEOFJKNBBGPIJENPPLDCEHKLAMPNMEEECHNMOAIOAHN", "NEJNANOONKLNOKLEJLPNDMDBEJDHAAIBDFIJLOLIBLMMABNBHM", "PIHOFCGOMOJHFLLHGHBKOPOFBGALMNGAAJFFLPIOIFAKDFPEKD", "PNPHHKELBDEFAFFDKEBBJMIGFPFBPKNLPGJKCFMJDGBAHECBOG", "HKOHKEJPJOLIPOCBPJBOGAJFNLIJOPCMKJJGNDNKBBAHMIOEJP", "OIMPHOHHKHFKHIKKCKKKIINBFPNMHDKMJNCNNAGFKPBBGGFEGO", "LPMFIJOIMKGONLLKDDGKABBJFHIHNPEBLHNMCAGPDGKJEAMMID", "DLKOFNENDFDMAGDMIMECEGNBJIKEHIAMDPFOFOGPEEFCCNAONH", "BKOAOGCKJDKFIFAKFIPAIFPHHEKMLNJDMEAHGNNKCAOPPAICLG", "AALACGIPBHLLMAENNAHNPNCFKADJDOMEDAOFKGJFJCAKNBFJHK", "HKNDBDGCDNGBJMJINCHGIHPFEELKMPALHLFJHPLINANCMAPBHJ", "CBIIEKONKGHNPFDEEJHMFFAMEMPEEGPIINPPEIEAHNNBHIIJLA", "MHKAHEKFDPGALJIICINFJMOHNHFAADCJDLCNDHBFPCNMMPHIEB", "HFEHMOPNGDNICHEIHNLLMFBKCJMOOEMHGMECDKOHCNGGJAKCAL", "NCHAKLNBIKNKCJKPHEANNGDBPKHCBGDLHMKMCKKPLOAEIODFNG", "PDCFLBIGKJGAJMOLDEHBFCAPDLEBBHANMOGKAPMBALIMEEALBH", "JHHEHIGJFCKFAFMLPHODLICDIFPHFFMJDPGMBMPDBALLFFNBFM", "FPFBMEANLKFAAOKHOFGFALFFNBDNGPLDNFMLFECPGOJKFKLIPC", "ANNCINFNFEOPIKBPCLNOIJICBDOHIKOHHFNCGDGKJNHAJPJCCL", "HLDLLKJCIGDHHKNAACOCNKEGPENIEKHKHPDPJJFMHIEFLCANFI", "CGOKDNMPMLIBAIBLCFEFFICBANOHNFAPIJBLAFDDEAMBNMJAEE", "CEECJJDPADHNMBBOPFNLDGHCKGKIIFKLOAIHLOMEPHHJEKABCO", "LBNCAIDNOGBBBLJKHMCCFEDELMDHCMIBBJOKPMGHCFFAMAIOJD", "NAANIFHJFDCOGKBCDAGKLACGFLILELBINFGPIPJFMGAKAGCDEM", "COKNOAPMNBKACDMLPAOJNFDIKBLKOJNINDOKMEBHKDKAJJENMC", "CECPIPBKEDABEJLCEGJFKOFKPMLMBDKGNFLNPHDIGOFIHOIKKN", "DJGCLFNLEHEFPBHHEKOOLBBHLHCFIMIDCLMJIOGHJGKKNJMADJ", "IDBGLMJKKKBLNFIEIBEOCBMCFAFINFLPLEPKKALILFCMHMODHC", "DLBHDNEFNDHHCHABOPAMBGONIGJAFABIAEKDGEKCHOGEAKFLBN", "FHBELHKIGOHHLBIGDFBHPCBPALLPOEJPFMFEKHHHBKOKMCLECJ", "JHBPABAKIOCACBODNHOOGMBNPBOGKMGNCMDAACDJCPKKHPFFCC", "COBNPDNBCBPKKNAFGMELEKHLKMFNHBMLBAEELPHJPDOIPAIGGK", "CDEBENILJKDAGGBDDALDAHJJEAEDEGBHKEOKOLJOFDBLHECMLC", "BGBIHMMCLDOMFCLOFOGONHBOFIIJKGOLHMIPGHKPLCKAKGOIPA", "MOEBMPCIDOIJGKDDCCEGANHCHEGBFLLPGCPBOHDIFHPLBPPFPM", "IAJGLKCCGMGHGCIDCKMFIPKJMNHAIHIAKGHHILJBIKOBLJKPEC", "EGNHDEFBOONBPGPIFEBCLFDKBHAJOIOBIFEMDBCDGHDBGBGCDH", "BCKJMAOLMFHDKFECIJMGHIFPMCLEMJGOHHIMBDPGCBACBNJONK", "CKOHILLHBPEBCCJEOFMACJEEJNLGDGLFAELJBJJIKKNAPIAMNA", "CKDDNJNCJHHNMNAAPJDNLCELCMEJNILKIFHOPCFNCFFKLLBLEL", "BKKGPDHJGGENPKAIMACAFAPDCCMOIONHDJGBDCGAPPKCBBFGBB", "IJFJJILFKKJNIFJDBPDONPJCKDBEPKABFKHNJGMFKPHGLICOBA", "GPFCDPOKILHBPNBGPCJMFPMKKOJELNOHDEEKGCLBIKDBOHEHPE", "BOHONNDCOEMBLOPNHJJCIIOJIDPMMNCHAEANMHMNDGKGKKAMOI", "DLCBHJPOIJNGHJGEJDHCNBIJAADPOHKHCLCCJNEENFPINBJEGL", "KPNMMICHNHPCKGKEGNJFDCFEODFHGEKLGLJEBJAIBFFEIMLGGA" }

    Returns: "Impossible"

  82. {"AAA", "BBB", "CCC", "ABC" }

    Returns: "Possible"

  83. {"AB", "AC", "BD" }

    Returns: "Impossible"

  84. {"AAA", "BBB" }

    Returns: "Possible"

  85. {"AB", "BC", "CD" }

    Returns: "Impossible"

  86. {"A", "B", "C", "D", "AB", "CD" }

    Returns: "Impossible"

  87. {"AB", "AC", "DE", "FG" }

    Returns: "Impossible"

  88. {"AAABBB", "BBBCCC", "CCCAAA" }

    Returns: "Possible"

  89. {"BFJAOEDDCCDGMHAEDNMEKDEBBCMLJMOADPJBNPBCJJFHPEAOBP", "LPDKBJNJCKJPEMBIBLDHJGEOHJFLIODCPDPGEABHLEBBIDABLA", "EFDOEPPPDHCKOOCIFBOHOJAOCINMBJFMLKAGEEEPPIOFKMIBKB", "JHOPDKKIJHEFOAIFFGMGCFEPIBAKAKFGJBEMPONKMGPLENIJJM", "JHOAPCIFKMKIAKKGMIIEBLAAGOMNAOCCDEGGJGHCJJIGOIEMFK", "IAKOMFLLNMALKGINNHBAAFDNBFFLHDGLMPGJAAJOCANFAMGPIC", "FOKIJMFJMGPJDAEDBJGFBAGHGPHKLIEGHFMLEGGMGAAEALCKPI", "KBGEEMNNEOHPACFMGPMLCLIBEOJOFNLBBGPNCIOELKLFGLKHFB", "HLDJGDOMNNKKGKGEEJFGHLADFOGLKJBIDAFNKGHNGDGKELBPAM", "BCCCCOHMBBIFDDHHGELPCJGMCGPDNGDFICPMJHHDLEKPLHIHEL", "DNAHLAPJNFLPABPCKCGOIFNGFGIDPJAEBLIKOGNHMJFEBKDOBC", "JMKEBCMFBKMPMDJACLFNBNOGOPHOEONNHOPMKHDIFEILFDEJCI", "IBEMEPOICCMDOAINIJHJMGJFOPOOCMFGLJNMDHNEHMJHENNIBI", "IIDKFIDEJHDLAEGHOLDJLCHDCMBLLFABHHCEFPNCJFMLIBPHIN", "JLPEJJKAKPIDIGEKGOHMLAODPOEBEMMLOFKBJFDBANDMMCIOPF", "PBGMFCGKNIPKAIEFLFOHFPBDAEFAMDOMFCOMFCMHMAIEMMNNDG", "KGJMLDACCJLOIJJKPKJNPIGKKJLMPGLCPGOADOPKDKNMAKMBAB", "BBAKAKEJIALKNAIOOJEMDCHBGMGMBPNOLIMDKJKFJMGPMMEBFI", "IBDLDKEGIDOHLJMFOPELMCBPGDKBEDEENHIKINADHIMCIDLBKH", "FOIPFFALGJKEDEIHEJPHOOBADBHDEKHJBAOJIMIBLKPLPOENNA", "IGFAOEEJPNKDLJCKKJFEBLAGAOBGLALDJHNFGIACBIDBPBEPJF", "MPFFBDHLGKENLHDJMLBMEOLOCAHBAIDMJMINOPNBLPOELLOMHI", "EGEDKDHPJDDKLDKGBAGHIEIPBKOOGLHALEIALJKGBDCFPLIEKA", "ONPNEIDFAIHJOBKFMJNNIFMEHMHNOPPKBOOPLKEGGDEAJCHEEP", "PCEMGJGLLIFNKIFBHCDBFEKIEMECPMBJBHPLFLIOKJNOBMPFBK", "IDKECACEBKGJDEMOPFFJBLDNAIOHMDGCAINHGBHFPMOPPLFNNI", "MHKHNMBBNHDDENCAKPMIFKNABFFDDHJICJBELGJPPJMDOABEJB", "BEIHNLACEBHGLMFCJIBCPPCPEFKDKFKGBPFIPBOFEDJOGHOBOJ", "HKNENODGOKDJFNGJECENIMGEOHNGMIGEFMJEFLNHPPHOIPECBJ", "LAJGGLEODPFNKBMINDDIINLLMBOMJJLKPPDFHJHEEIKBABJBIK", "FBAPGAOMGOKHODFIGHBLJAIECKFFMOPMDEAPGKHFIHNCGIMMIN", "JKKNCMELLPHNMAJGHPMJGELPLOHJLMJLEFENMKCHAMAGPJEGLA", "OPGPCHJLMMAIOGBHIODGLHMPMABMMGAIBLFAEAEBPOOIGKINEI", "PMGMCKLCDFBOIPBFNDGEEHGMIDKJCNHNIJAFGOCKCGKPPDHCJO", "HENHABGNKIDGIBADFNIAIDBGBDEEFBCDICPFBDEIOCAHMJJJJI", "AHONINJPCLGGMLDKPBFJFDKBBEJFHEDGIJNPHEJGKAMLOIOBNP", "OMAENPPCMONDOGKDNPDOKFLICHBAIHHHGLLLBJHILCCBBPODPB", "BHFNJKENEHBGLHHGLBHEBHDJAPMAMJGMMMMKAAIJKGNNOFHBGE", "DBGEIJNKJGGNCCLCDEGGNJHEKNBOIOKAGKKLHOMINLPBBEOAKM", "ALJIMKPJLJPFAJKMPOIABCJHMEPMEHJEINELLEDNEPFGODGHOO", "JCHFLHKNKPGEOFJMDIBIKLPGHOEGGEHALNGMNCCLFFDOEKPOAP", "FOJDIGBMPDAMCEDFDHANEIDDNOENDMIEGJEOJMPJNJLHFFFJPN", "ADJHINCLBNNEFECABJFFGBLMAGGIPDMGEOIKGKDHDLFLOGOGEO", "NFAFLPDEKMHPCKFHNKNGLKAGIEPIELDDKFKCJCPLBDIPAHANEK", "IHEFMJAOBHKLKDCOACBKKKFDNANAGCCEDMCNCCNOPADNMCHGCM", "PCNFAAELGFEDBKAJKNIEEFDFGDCMJNDGEDBEEAJBGBBOIANEEL", "MANKDDPFEHEPGPCGGLIOBNACDHGBINFACOJJPHEMCFPCJEODPF", "HBGBGONBIJHFPPFFOKLPBPKOHEEBBOMPIJKMKMAHKFOKPPEALA", "JELGEGKCCMPCEGFOHEGOBCBABOHIGFJAICIHHPIGPGPEOEJEHA", "EFCENBMHMPJHKCAOJKNPLBMHMNLAOPPFMJOHKPAFBMKGPEDDNE" }

    Returns: "Impossible"

  90. {"BCBCDCADBCDCBBCD", "BCDABACCCAADABBD", "BBADDDABBDACAACA", "DBCCDDBCDBDDBCDC", "BBBDDDBACACBBABA", "AAAAAAAAAABBBBBBBBBBCCCCCCCCCCCDDDDDDDDDDDFF", "DBADCADDCCBBBCAA", "CABDAADCDADDBBAA", "DABABBCACBCDCDBB", "BABAACCBCBBDADDA", "ADCDCDDAAACCDBDC", "BBAABDCDACCDADAD", "AAABBDDDCCABCAAA", "ABCDDBDACABDBDAD", "DABAADADCCDBDADA", "ADACCACAACDDCDCD", "BCACADDDBBDCDAAB", "ACDDDCBBDDCBCDAC", "ADABDDABBCBACBBC", "DCBBDCCCDADCBDAC", "DDDDBADCCAACBCDC", "CBBBCBDBABBABBCC", "DACACDDAABADACAA", "ADBADAABBBBDDCCC", "ABBCCCCCCBDBCABB", "CDADCDACCCDBCABC", "ACAACCCCDAACCABB", "BBCADBABBCCBCBCD", "BADBDBCDCCADCCDD", "ADACDDBDADBCBCCC", "BDCDDCBACBCACAAA", "BABADCBABDABCCAA", "DCBCADACADBBDABD", "BBCBABACCACCBCCB", "CADADACDAACCDDCB", "CADBBCDDDBACDDCB", "DADABCBBBBBDBDCD", "DACBCBCDDBACBDBD", "CBCBDDDADDDDDDCA", "CDAADBDBDDACCCDB", "ACCDCDACACDDBCDB", "CAABBDCDADDBDBCD", "BAACBCDBCBDCDBBB", "CAACBBDBBDCAAADB", "CABABDCDCBDDDBDD" }

    Returns: "Possible"

  91. {"A", "BB" }

    Returns: "Impossible"

  92. {"AABB", "CCDD" }

    Returns: "Impossible"

  93. {"BC", "AD", "AB" }

    Returns: "Impossible"

  94. {"AAAA", "AACC", "CCCC" }

    Returns: "Possible"

  95. {"AB", "CD", "AE", "CE" }

    Returns: "Impossible"

  96. {"AA", "BB" }

    Returns: "Possible"

  97. {"AD", "ABCD", "ADEF" }

    Returns: "Impossible"

  98. {"AAA", "ABBB" }

    Returns: "Impossible"

  99. {"AAA", "BBB", "AB" }

    Returns: "Possible"

  100. {"A", "B", "BC" }

    Returns: "Impossible"

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