Statistics

Problem Statement for "FactCount"

Problem Statement

Given a collection of facts, we would like to get rid of as much redundancy as possible. The facts involved in this problem are members of a transitive relation between uppercase letters. So each fact is a pair of uppercase letters such as AB meaning that A is related to B. A letter may or may not be related to itself, but transitivity holds: if A is related to B and B is related to C then we can infer that A is related to C.

Create a class FactCount that contains a method minFacts that is given a String[] known and that returns the size of the smallest set of facts that will allow us to infer everything (and only those things) that can be inferred from the facts contained in known.

Each element of known will contain 1 or more facts separated by a single space. The smallest set of facts may contain facts that can be inferred from known but that are not contained in it.

Definition

Class:
FactCount
Method:
minFacts
Parameters:
String[]
Returns:
int
Method signature:
int minFacts(String[] known)
(be sure your method is public)

Constraints

  • known will contain between 1 and 50 elements, inclusive.
  • Each element of known will contain between 2 and 50 characters, inclusive.
  • Each element of known will consist of pairs of uppercase letters ('A'-'Z'), separated by a space (' ').

Examples

  1. {"AA AA AA AB"}

    Returns: 2

    AA and AB capture all the content of the 4 facts in known.

  2. {"AB AC CA AA BC", "AD"}

    Returns: 4

    AB, CA, BC, and AD allow us to infer both AA (AB, BC, CA gives AA by transitivity) and AC (AB, BC gives AC by transitivity), and there is no smaller subset that allows us to infer all the known facts.

  3. {"AB BA BC CB"}

    Returns: 3

    The set {AC,BA,CB} allows us to infer exactly the same facts. Note that AC is not a fact contained in known, but these 3 facts allow us to infer exactly the same things that we can infer from the 4 facts contained in known.

  4. {"AB BC CA AA EE FG GA"}

    Returns: 6

  5. {"ZZ"}

    Returns: 1

  6. {"AX BX CX DX XA BC CD DB DE EF FD XY YZ ZY MO OM MK","KL LP PL"}

    Returns: 17

  7. {"PF MN LP PJ HD HC GL HC GG KP EE NC II CI NE GN HG", "FK AD KA PI IE JC ME JK DK JC FK HG JE BL PG OK EK", "GK KA LM DF CA LD KL CE GP DC PO CD NJ ON ED KF EI", "IM BH AG OO DO DD CA CC PK EB DN OP CD PA MI OJ AD", "CN JE OA GB KO AG KP PB ID DO BI KE EM AP NM NE HD", "HK KM LH EH HP CN OG LI CF MI KG EF AA IP OM JC AL", "CP OP JE PK EK LO LA HL LO MF OB PO BI AJ BK GG JF", "KD NL FH GA GI GO HF FH MI AE JD IF DO PJ CJ DH NF", "MI IH HD GP MI BD CP PP JL EB HC AG MG BA KO GE GC", "PM NK JO PI CL PC PG NG JC NN LF HB AB AB IF DK JG", "EH BL BO LD OK BO BH DO GD DB HC IO BE KA EN IP JO", "HA JG CF JA DL NN PF DB GF IH FB CN MB AL BM NI AF", "PD HN LO MD FK IN GL LG BE KA CH DI II LK AA CB MG", "OK BE LA PC GP IL EL GN AL BM FO KB HE FI AI KH DF", "OG DN EO PN HI HF LL IJ AJ EP AC MK EP FL GC BE JH", "HA HF EO PB HD JO AC PG LO AJ CH PI DC GL MC OE NH", "FD OB OC FO JP PF CP KG JO KJ DK EM EJ NI GL DD ED", "DF FP KE EP JB CL DM LK PD IL NF CO HL FI KK LK CH", "PB LL AI MD GL NI PJ JK ME HI LN JN PL DF HC BI JB", "EA KH FK HP JA AH EE LB FG CG HK AA JE FN FH BI BF", "OM HI BE LC ED NO AP CO BJ EM PL BM FH KG JB MD EN", "AG GD DC LO FB DN ML OE FB DI PC NB EA JH AC ND GC", "HK AE DH LK KE JG EB CL PH CJ EA JF AK GP PF EN KN", "BD FE DI JK HC HG PK GC OO KJ IE KD FI GF GA HB HE", "GA IB KP CE AJ OK BB CP GD NB NN KP CF LN AE DL HJ", "BK LK NE PE LA CO NC LK HL PF HM LE IM GD OF NK HD", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF", "PF"}

    Returns: 16

  8. {"KR QJ JK"}

    Returns: 3

  9. {"IG IB GA IA CM JB AC ME NE JE EL NI NN KJ IN LN FF"}

    Returns: 12

  10. {"AB BC CB"}

    Returns: 3

  11. {"AC BA BB AB AA BC"}

    Returns: 3

  12. {"EB EB DB BD AA CC EE CE BA EB DD DE CB CE BD AB CD", "BE EE EB BC DE DC AC EA DC CD BE EC EB CB DC DA DB", "EA BE EC BA BA CD CE BD DB CB EE BE DB BE BA"}

    Returns: 5

  13. {"TF JR EI VM SR QO NV UT SK CU FI NB TL LB KH CO HC", "IR LF IS PE KV KN MB BJ KC KR QT KS NC KV LC TN EN", "SB MC IE QT GC UM VO DL TQ RC UN MO KM KT UU GQ CK", "OT JT BP FI DD RR BH LR SL RD QD BK JN SU TK VV JN", "CB GS JF CR SV BA OL NK OT CU GD EI MG ER LO OJ CG", "IC MQ PV AT TM OH EA ID GI TB OQ MG SM EN OI VK KM", "IN VS RK BV KA LT HC VN UM AU JR DR VP TI BV PT BS", "HV IC QU VU QM RH RE NC CN LJ JH NO NA IT DD PI LC", "IE FV KL LG JM BH VA VR KB FN OS QD JQ LQ GT SE LD", "VM OH GB OK UF PQ LM QM DR GN BC TA DH CH SC GN DN", "SC GM KU VC BT IB EL GV NS IA LS QT RR HT LR GC QD", "RU AE NT HJ EI KD MU UR MK PA AU EJ FB HA FI MJ MC", "AV HR SK OE MQ QC SQ VS HG IV HN QH DC FB VG GV KG", "AE OQ IK MI OR LA AD SH NL GS GV FO RJ QG VA KN UM", "DT JU JI JV UD NO TS QK AC VR VP MM EN GI KN FA DF", "VV UM SU NT GA BH JD RN VJ CB HM SR UH OJ UN KG SK", "UA IE UV TS SP MU PI AE FP KL RN HK SA VV KF LC RO", "SD KP AU SB SS OR UU ME OI PF DU QN KF JJ MO HD TC", "VD PJ KQ GK EQ JG SH PR AJ SJ IS SE JQ OT BK ER EQ", "UM NI LD DH BK SF QC TG QS HB DO QA DQ ES IE MO VU", "TE SV UJ CL GG BP BE LV RP QO QA HB HL QI QJ EQ QT", "TJ FO II EU PK MF FS FF MB TD MV IK PB JT BD JF EB", "MK AP FU RQ IK GS KI CB AT TV VA US SB ED LT CT CA", "CF UV OL GP MK UJ PO FV OH RD NF AG HR II GP HG PP", "FA FD KG EU DA KC IS EI GE TR SL EK JL NF FQ SG BV", "LQ EO VP IB UP IP GE RG GV VQ QJ TS VM TT NB RP FC", "BT VK MH SA AS CB HF BN NL DN SH VK UV JA NH GK GL", "BM TS BB SN PI AI UM NK GO ED MC GK LM RR VC VF RK", "KS GK UQ UE JS MR AQ CD OC RD NJ JS AS HM GN VR MV", "KN IS RL QL RM VK NV VO IQ OU FF BL BS OH RI VA CS", "VB AB II DJ NV UD JP DB MP PE AN FO NQ RL RG BA SR", "RC CO DD NL UM VG TF FS TM DU OH HI IT VC TN PH AJ", "SK KQ KE JG SI NI DK BU NH GD DH KD GA LB QF SR GC", "RS BS LM GG CI NR BQ NM AA GF ML QJ LE EP ES VO VP", "BB AT VG PV RH SL UE IE ID MF IS AS MI UO EK ML EM", "UE CJ DQ JN FM EG LF HL PA HR AU OS LP VL UI RL DM", "EC HV QJ IJ DE LH CD BG HP UE QF QO VN MQ QC JP FF", "PD BT SB EU IE QE VJ IN BU IS RS HI DE RC LC MJ JI", "KU NO AI HF HA PN BJ SC RR BF LJ KQ VB CD GP OM LK", "GC UI GA FF TD TG GG QO UV DP VC JO KI LH AE KT TE", "OU FN SA BF GJ AA JH QH CD JO PP MJ RE OI IC PJ CI", "NN DB OS RC HV AP HD RI MG NQ DK VL IS GN AR VC JG", "LC QJ ME UV EC IA KO TH KQ HQ CL FS MO EJ PS JO EC", "KB DM EI LM LN IR CP AR JH UM BM GO TE HM EH ON RU", "KT CK LM VE FE SI BP LE HG RM JD JB IM EH DH RF FN", "RJ JE AI HB OU SS HO IH QA OT IB QO SS CM BG AP TA", "IS KI II JR IG PB GK NJ FN GH EV PS SV SD DM RP UB", "UF GH CU PG HO AV VN OV DH CH IM DS IN ES HI FJ MG", "PV KP BT LF KM BU RV NC TG VG KL RF FA CN OQ RI PV", "CA IB RK GK CS RT OH QN TC FF TR NK EC SJ FQ IU NB"}

    Returns: 22

  14. {"KC GL DI MJ OJ BD EJ PI FO LL IB BF IH CJ JL OM DL", "IL KK NI PF LL DA EJ GA NC OA JL OE LH CG HG HE PN", "PM IO JG HF LC FC JD LF JD EO MF MN EA HA KP KK HH", "OJ EE IP HH ND CI NM JD DC OE DL JM NG AI ON MG KM", "NM LK NK HO FP IP KG DJ BD NJ AN DJ LE AA LA BG DK", "BN BA KB LD MK NM LN IP CN EO KO FD FC FE MG AD DA", "NJ OP JB AO IG FJ JH DP JJ ID OH BN KB AC KA LO KM", "NP HC LJ IH EP OO DC II CK AI GI FM HF PH OM MI NM", "OH HL NP CL EB GG OH FD NH DJ DG JM FA AN AI JP PO", "DL PM JM BD FH IG DH IK FL NL ND PJ AG MK FJ KL BC", "FK KP KF GP JI OA IO LF GE CI JE MO CC ND DP BG IM", "BD PN EB DL OF CC CC AE EB CL JF GO OB EC FB LI EG", "CN CC CO NI GP ME NC IO CI LB FN NM NC KD KL FC AF", "LH GD AM JA BL IG FG JM OD ON GN HC BL PF OJ JK LG", "PG NE EC DP PJ BC CK GD BF AP LJ CK DO MJ JG GO MA", "EA IJ PC EC PH HJ PD MG LB FI BB NL CM CK NN JB GF", "LA HE KC AG LH AK LL AI CA"}

    Returns: 16

  15. {"DE GH EI FJ FI GI DB GC CJ AI AA DD FB BI JB FB JD", "HB IJ AD JA AH EB HD HJ IC IB EB AH HJ DH JC FH HB", "DB HD HH DH GI GI FE EF JB"}

    Returns: 10

  16. {"DF EF AC EF BF DD GG AB BE CC GA EG AG GG AC BG FA", "GF FF EB EG EE FA GC FE EC GA DF DB DA BB DF CE FA", "CB CB BC AA BD BE EG BB FC CB GC CA EE GB ED EG BE", "AC FC DA DC"}

    Returns: 7

  17. {"GP LN JA IC ML CO NJ AJ NE EE MC OJ KF IM BN PN QL", "PM DE"}

    Returns: 17

  18. {"AB BA AA AB AB AA"}

    Returns: 2

  19. {"GC AG DD FF DE BD BC GD GF GE EB AB FA GC GE EE BD", "GG FB GA EG AA ED DC DA AC DC FE DA AA EE EE CC CE", "BG AF EA CF BD GB EB DF CD BG CA GD"}

    Returns: 7

  20. {"KV SS LH BQ OW CQ WI FJ GH VW FS MJ TR QF LN TI QJ", "IL UB BI EW OH XD XM FA LB MI JU GB LE GP LF BN WO", "SR ND GL CE OK PJ ST SQ SH NF AX JN CX LW TE XG RD", "RX JI KE WP PD BL GP KR CJ FI FS IH NX RK HR ML IH", "RR TT UQ EP WM LS RL FS RX UH WU GC GU TQ XE XP KT", "QM LP SP FL WU DB RW BA BJ IS KU AV OC AU TU RB NU", "IR NI CE KC LX MA XQ IE RN UK BK EB AF NI IP PH HC", "QH SC DX FR IU QK FM GB KH HO RK NU UJ UK RA LO RP", "PR OI WD CG AL EM SK WW VF SQ TG KK KG HU IB KU ON", "OJ KI GL EO KR SM FG PE SQ OV VX MW OX TO PS DL PN", "UG HV WP KG RT SA QW FO AW HU XO AM QD OV TX NB AP", "LC UT RQ MC TJ WI AW AN MV QS LA SL BS QD VB LJ MF", "AG JD WX CG EF WL IO SP RP LX GB VL PO CJ"}

    Returns: 24

  21. {"AD BD AC AC DC DA BA CB CD CB DA AD"}

    Returns: 4

  22. {"AB CA AA BC AA AA BC"}

    Returns: 3

  23. {"CF EC HD EC CF EH GD BG GG"}

    Returns: 7

  24. {"BB BC CC CB BC AA CB AB BA"}

    Returns: 3

  25. {"CB CF CC CF CD FB DB AE EF BF DC BD AF CB CA EC EF", "DE EA AB BF DD DA BF CD BD DB EC AF"}

    Returns: 6

  26. {"FE FE DB AB AG AE EF DB FA GD EE CC EG GF DF EC BD", "EG BC DA EF FE BD DG DC DE DF AB DF CE BB FA DD EE", "BD GG DC DD"}

    Returns: 7

  27. {"BH IB FF KI IJ AC IA FD FF FL CJ AJ GC FM CL FB HI", "CL MH GF HK MC LL FL HK KI KI CG BL AI IC JG FF JL", "DE JA LF BH BB LM KK JG ED BG KM CA JE BD CK LI IG", "HK EI JB EB ML DF MF KC IK MM AC EB LE DB HK CM JJ", "EB AD AM LH GE LA HK FJ AB LA MI KD FE KC KB EE GG", "FD LA HM JC II AL DD GE KD GC FE HM FI AI BJ LI FC", "JC AA BM JB EK CL BG CI DI JB CB EC CA JB EA ME EC", "ED KF EC EC MJ HF KA HB AK CD AB HF CM HL JE AK JC", "MC MJ JH DL KK HM GA AA CF ME DJ KJ JD KA AI IK BD", "CD MC CA BG DD MB GH LI BJ KK HI IM IC CF LE EK GI", "LC JE BE BD DE HE EA HB CM BB BK LK JF JL BI AC FK", "MH JL LE ED KJ LD MF EK GE MF CK BI MB HB GM AH EI", "AA KA AE IL KE KJ KM MG ML GG GJ FL GM LE MJ LD HI", "CG CG GG JC IB AH KM ED ED HL EL FJ ED CG EF"}

    Returns: 13

  28. {"AA BD AC AD AC CD DB"}

    Returns: 5

  29. {"IE EM FF LI HM LI IC GC HM IJ EK BF FI BI HK GM FJ", "ID LM DJ EC EK CL HM GB LC MJ EL AD MB JF AH GA KD", "BM GG AJ IE DI LE CK JC JF DC FD JE MM GJ FB HK BK", "EH LB HB BG BD MD AB BF FG BK KE CF DE KJ IL LK MI", "AM AL CD ED EJ GE EH GC DH CI GK MI KE HG AF"}

    Returns: 13

  30. {"IG BB FG HE HD DI FH AA HD EC CD HC IE EA BC ID CG", "DE DH BF II EA AC CC AE CI BH HE ID FF HG DC DH DI", "AC IF BF DE FI DA GE EI DD HI FE GC CH IG FB AF HH", "CC BB DD GG AF IB AG"}

    Returns: 9

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

    Returns: 3

  32. {"AB CN BC GH LA HP DB MN OK LP BC JB PG OF FH DI ED", "OO AJ EG HN AP KE ME DG BA ML GH KF KP KL KK KJ ML", "BP DJ JP FL JK BH JP KJ EI GE HB MF HC BL FP KJ CP", "HC NE CN DI JH LJ JC LM PL EG NC AL KD BF DM CC KI", "PM PL PN AI GL KN KI DL BG MF OD IC OG DH HC LP AE", "FC EE BJ EH ID CO CG BO CF OC GD GJ EI OJ IL IK HI", "OM OF KC BN BO NA NE DD OM PG PM HE PL AD GJ MP FH", "PK GA KD HN FK HJ BG FC IC CF CF II PD NN CE ON HC", "DN GB OF PL AJ DP KF KK KJ AG MA GM AN PG AA HI KA", "AM LN PB JH BL GI MC AE CA DH PG FK LC NN KG FG FJ", "DP GK AG JA DA ME KC MB BP NA OC EN GI GL JG LB FF", "MG EI CG KA MF CP OA BG KA FJ FN CE CN NH IA JL LA", "LH HD"}

    Returns: 16

  33. {"DC DC BD AD BA DC DD CD CA DA AB"}

    Returns: 4

  34. {"BB BC CC AC CC AC CC BC AB AB CA AB AA AC CB AB AB"}

    Returns: 3

  35. {"QA HR RA MK QQ SM SP DG AD GQ DK IS KM DN MQ GG IQ", "II FO MR DG RG RQ BE CB KF JJ KC HS EB GA DH EC IJ", "JF IL EN FE QC DR QB MH JH SP JG LR DJ FF CB DF JR", "KG DN SD AD PK QJ II IE RH IK BG NR LL IS NI DO LQ", "NM ID EQ ED KR JQ MI OC AD IR CQ AE QP QM MM JM GB", "OE IE BI OP DK QD RP LL JL GQ QQ CS OR RI SG GE IP", "RI DI HB ON HE FG QR EJ AH OJ EN FL ER IA MF SN CA", "OD GI JL EI LN LI GO NO OM BP IK HQ HR EG IM GB EI", "QC NI BO IR DM KA PM HB MF MS RE QF JH LH QO QN HF", "NH EE BJ JN OK MN KN GN LL LK OJ DM CI MQ LQ LQ SO", "DN AR OK AG FF RH HS IN OO FG DH NE KD DK FP SS QQ", "DH MN RO CM BC MA GK EH BO SD RD AS RP IP FS QG KL", "ML HK AB KL NS NB QM MA RJ RD KL ER QD JI JD NJ QH", "SA QL DR QN IS LP HO AS MQ HL BB SI QQ FF CK OM QF", "OJ BM KO OH NE KP AO BR OF QC HD KO SK JJ CR FQ HH", "QD PE PK IH BH QB MM BA FH OK EG LD GM BD IS MS SB", "IN CB MJ MM QS BP FR LD EA EQ BI FE AH LM DF NP IO", "BB QL DA JC CA JA HI CH DK AQ RK IN PO QD CO DN PO", "DL EG NA LR QM ND DN EJ HE AS NB GF BO QC SP FO DG", "PS GO GA KJ MN FN AP BA HR JF BL FS GM SK AK QE JF", "IS EI FF EK BD FO MA RK DM"}

    Returns: 19

  36. {"AA"}

    Returns: 1

  37. {"AC BC DD AD EB EB BB ED DE BC AE EE DF CA DD AA FF", "FD CA FC DF BE DA FC AA"}

    Returns: 6

  38. {"FG FK BH NA NM AA GM FG KN DD MO LJ ID EA HP AN IL", "LB JD OG IN HH KK PF KB MI PO MO KA IG MM KN BP MH", "AI ME ML IC LG CA ED KI AA JJ PN DB CE CE KF OA NO", "IM EN GP IB IG OP IE EF GB NC KN AE MH LH LC EN HF", "JP DD LB FI HK FE GI IA AP CI AA DJ EE CE PE JF CF", "HJ PM PD EO MD FG NB IP AJ CA HA KM JJ JK OK PI OM", "BF KE LB KM CA ED NI NM HH KI LA IP JD CB CP CM EG", "JD EJ NC PA FI OI BP AP FJ HJ NG CM BJ MF LM AB BI", "IB BI HP HO HL CJ HN JK JB JI FO PL AI HD LJ IJ NK", "DH KH CI LA CF LF IA KM MK LE PK ME OD PC BP NC KM", "IE EJ LB OA CI DJ GM NK GA ML OJ BL EP OH PJ LP EC", "EB HI JO DA IF IL PK PJ ON HP KK LN OI MO GO AO OC", "KC ND IE AK EI CM KL FC JD PL BG EG CN FI BJ KC OE", "GF AC BK NP AN MH NG NM FL LK NJ EJ PI ED CD BO LM", "NG GM MF FB JN JF CD EN IG GA MI MB AJ BK MO EL"}

    Returns: 16

  39. {"FJ NA NF MJ AA HF IO JD GH BB NH DG JN LF ID LB GL", "JK OI DM CA DE AB JO NK NO EA KN JA CE OC DJ KL JH", "HM DB HE ND NC AO MD MC MH NG IA BH ND IK ML JN AF", "JB KO BM GA FA DO LJ GE BI NE JF OO DL BC NB NA JA", "AO JI CB EM JF MA EJ IK CK NL II BJ MC ND BN KI OB", "FH EC CE BO AJ CL EB OK JO KH GM LO NM FG GC ED CO", "CG MB ON CF NE KK CO OJ HM OE DN EE CA DF CA II BK", "LI KJ LJ MK HF OF LO NC EH HJ AA FI BM MD BA NA EB", "NB LM OF JC LM LL KL AM EL AO OE EM OK GH KO AF NB", "OI ED NE KI HE NF CM LK DO ME IO KD IK AF EJ EB JJ", "HN LC NC FJ KG GK IC EF KI LI FL NN CK LB OM AO IG", "EF LL AC EB HK FK AI KK DK HC IK LJ BI BD HJ IN AJ", "NN HF ME OH OE KN"}

    Returns: 15

  40. {"AH BJ KG HG HC KE FF BK EA JH DB IE KA AI DG EG IF", "HD FF JC GJ CJ DB CC DH HK EG DB BD FF AE HF HK GK", "JL JF KE FG LK GG IE IA AJ BD HI CA EE BG CH BJ KL", "GG KF FJ EC AB CH LB KI GC EJ LI HF AB BB KA GK FH", "EL EG KB JF KA KE KL HJ LJ"}

    Returns: 12

  41. {"IC KK JD EI KC CC DI FF BJ AC AA AH KE EJ KB HJ AC", "JI CH GH BB DE DG GG DH ID JG FC CH HF BH GB KE FC", "KG GB GD JJ GF BK EF KJ JI AA GG AJ KD EJ AC HH HJ", "CK FJ AI IA CE BG HB EA EE IJ CH FA ED AC CD HB EA", "BF BF FH JD BC CH CF AI DA HD DC DH BE GF DG AB KA", "AD KC DI EB CG AH IE HJ BK KB JB IF DG KC EH AG GC", "IA JH BB CJ AJ EI KB KK EH JH ED AF DE CC BA AB JB", "KC FH BB GA CC KJ AC DE IG BH BD FH EJ DD HF FF AB", "KH FI EE KH AA CJ JF HG DD KA CH JJ JH JH HB HG AE", "DK IF JJ FJ EK GG II CE DK BC JH BB BB GE DA GE BE", "GI AH AK JC FB JC FK KH JE GE HJ DK BK GF JG AK CB", "GE BD IC DI BC KD JH FG BH ED CB DK BB JG AE BE DF", "EI EA AC EF ID CF JG IF HJ"}

    Returns: 11

  42. {"AA AA"}

    Returns: 1

  43. {"BD NV RJ WM NF RU CM VH ET OS EO KE JT JJ JK HJ JH", "AA EE OJ IN KF JF VB BI TB GD UJ FT RS PG IT WU TP", "MI OH PP DL UQ HC NK AI SF NT WP RC DN LF ET AD DJ", "QH SI DE CA QW HE KN PD VD JA LH GE LJ WT AQ GW QQ", "EP AJ RM OP IP QU CJ MV TO WU IR MB OK QW SM UD FQ", "VI NP MQ TF KT ET QG FR NK NV PO NK JV NC QE LL OI", "OR FQ OQ UB EM KB LR CE OW ID UL UR DN UM UF BQ MC", "UV WR SU VM"}

    Returns: 23

  44. {"BA BB BB"}

    Returns: 2

  45. {"UB VI TJ OL SJ EQ DJ CV FI DT EC OB MB FH DP LH TI", "RT KU SV TH BH HI UU BV DJ DN CT IK BK MF SC CC PE", "VK PB BD LQ JG JR LA IA QD RN HN UF HU HD UD SL MH", "UJ QR CV JO DT MV JQ VJ NE SR NT NM GE NE PS UP MM", "BI QL JJ PP MD MM QT DR SM KC II TE KF JG GH MB DA", "IQ JU QV CQ BS JN EC EG JO KA TG SI HP KR AB GH HR", "LC KK GS RE GS KU BR RK LV IG DF JR AA OA TV TE JJ", "EH LQ VU QS FR OB UI LE VH BH NP EF RL ME CN TQ BC", "RD DV GG PE MK QI JQ DE NA OV JV QF BC FC RF VI FD", "FA EA KC ES CB GN CR FJ TT RO FG BB ST VO QG UD LC", "NH CG OI TP MG NT TN OQ FT QJ DU HJ BL LC NH GJ LM", "ME VU HC RQ DN IR PE NA AN AB LR HS FV LQ JT NR LB", "RO OI RQ KF AU PN IF QQ NG VT IC AE RE AE LD TK RS", "DA PT OS KO II UK DN NC PB EP PP SC DF UD EL RS SA", "PK OB EK UF FK HN JD PL KE ET VJ FP IA QD IB JK KD", "TR FQ OC TR OK EF MB MO DD JP AV LR DT KH MT OB PK", "NK VK UF BD VS DM FN KG HE CP VM RK KK FN EC KK RG", "DR ET RP LS MS TM NG SP DD UM PI SK MK CG DB EB UF", "HA UQ DR HE QA KD GQ HF UD BL LP FP IR LA BD HF NS", "AR HJ NI IM ND UV IA PL KM KO CS SI RD TA UD CN TN", "CD EO ER GH AU GQ PA DH UP RL MU LA BO MJ CT FH MR", "UP VS PR FJ TJ GO EM KA CD SS TC GD NR JN ID EB SL", "HE RB JU VA VM KB ND DC CH CA DC VH RI TD OP DM ON", "US RN IH CI DA UC HG UI JF NS TE BG JV BT HE NE JF", "MN MK AB RH NC AQ MC JG DN CP RH OC CQ SL HK LR VS", "SH JA AU LV IO EH UV OM CI CU SI IQ OC AE QR IO KL", "EG CI AP CC LA KK GO VH MB JR CD MA VL AH NV EQ NM", "DA TG DJ LA UM AJ QC MF LK JF NL ND AB DB PM NG GP", "SC JP JM IC EO BV UB CK OC BF AL HQ NR SC BH QV UP", "EI PL FB BE EH NT NM UP II LA VU SJ PE PG GF BE CS", "IF UC TT SJ MI IL CM BM CF JB PL IF VO CE GD UP ER", "FV LN KF VP OH TJ LG FT EB MN PP PR UP FM DK CG NT", "OO ID AP OJ CI QC LO SV BI PA VA JA HF HU LB IB FM", "AB JB AL PJ EQ UH BQ HA DO VF FB RM GH FH HJ HS DF", "AL RI DV FD RB AV"}

    Returns: 22

  46. {"AA"}

    Returns: 1

  47. {"BI KE HH KC KI HA HI CA IL KI KD KJ KA FH FE FJ GG", "FL EC"}

    Returns: 15

  48. {"EE CE CE AC BA BD ED DE CC ED AC AB CE BA EE DE CD", "BA EC BC BE BB DC BE DE BD DA EA"}

    Returns: 5

  49. {"IE FD GA EG DG HI DJ FI KI GC EG JH HG HK DA IF AH", "EC DG IG DB DK IC DC FH JK CG CK CB AG AE EE IH EB", "BB JI HA KJ FB DI BC KH JC HD FI IE KI CK ID CG IK", "EE HB EB IG GG HF CG JE AI CH JI KH EB DA II HA BC", "IK AG HE CI AG HJ GI KE AH DK FF HD HJ CI HG FH AE", "FD CG FK CA KC GG CD EA DJ FI KK JJ AF DD KH JC KD", "FG HC DB JI AG AG BH DF EC AE DH BK GC GB IE DE GB", "AA BJ DF IF HG EK JI AD KD FD CJ JJ BD FJ JC HH IE", "CA AI DG GG KK GD HF CJ KJ EA AB KG CG BD KA FJ GH", "FH HC EE HE KK HE HC KK GH IB FK KD AG BC GK KG DD", "HD BJ HK JE JI HC BB JG GH IK BB DG CE JK KK AD GK", "GB EH KG IJ EK KI EF EA IB CF AH KB EE IB DC CJ HH", "GG FK IF IE GH JK JB GJ AB IF DD IK HB GJ CF II AK", "FJ DC HF"}

    Returns: 11

  50. {"CD AG IB IQ HQ KA OI QK DL MK KD DG QA HJ HB MI BE", "RM PA EE GH NG AE FE CE PJ NO MD PM LK GR LL EC OD", "JJ CA NO OD MD EG ME HN JI BJ PC BL JG MC HD DA GA", "HQ GK IG QP IF BD MH HE OH IE QL AL QL LP AL JA LD", "BK LL JP NJ HO CI CN GG RN KH RB FH DR GN BM LI QI", "OH ME LA IN QQ GC DQ OJ QI RA JM PR BL KJ HM EO FF", "PP DA FG PC NB MH LQ IP RB RO DR IK RC KM MK HA PN", "JB PA LO MR OO HD NA RN HR AI PL BH CA OC FJ DO FF", "MR JJ CN QR FE EQ BG AQ MK ML GL QB FN FB DA JE EB", "BL JB BC FF HM CP AR EC KE BC AN JK MI JI JL GK IQ", "ON BB BA NB LJ EH PC LP MR DG QO RP KP OE RR EJ EK", "PG RP LG AH OP IG IH FF HE DD QP DA QB JH IM PM JF", "GN JH AB RG LC ED OE HH HB LR OQ JL IA EK DB KO JP", "DN MD AH KK NG DK KM QE KK OF EH AE CP RB FC CP EN", "CP KQ NN LR GP HL CB PO HE RF OR IK GR LH PB FM GG", "MC IO MO ML HM KP HI NE LQ BD AO CQ OL FJ GH RC HF", "EF EC FA FL MP DF KD AM LC MF IH BD BF OE IN MP RK", "PO CQ CJ GF JG EG PA ON GI LQ HP CO QA DA CF KL RO", "KH PI PF KG LC OQ DH MC BC HP DH EO LQ IP DK NK PL", "LG MH FC QL KH HI IG AM RH BH RN PP KO EQ AF QC IJ", "NO CA IN OI AO GR LI BR MK FG RQ HL QR EH QE FN KC", "GR QJ HB OH RB BJ AR HC FB HO NA DI IP RP OG NF DG", "IP OE LN JL IG FL AR NL IQ DD EJ FG NR MI NQ LN QH", "CE KH FA LO DN BQ CR FF HF QQ JK BK BO FR MB LK IC", "QI DL ML JC CG AK KN MC JI LK GK IA JA EA MF JI BI", "MH BD LB AA BB AF IA DA NJ OQ BK FF LL LI CD FP KP", "ME LR EG JP BP LH IF FK DE AF QN LI AE EF QB LE HR", "EO CE CO BI AB LO MG EM AR DP MP KH KD RO PM CQ FN", "BQ AD MJ DO PA AK OP HP AQ GR AG AD BL HK PH BE RC", "JD LC AM GC IN KC DO BQ NI QQ FG MA KH AL CH OD BN", "RK CC ID GB MG EO IL RJ FR PR CJ AN PP FM FI OA NM", "EK HI KF EJ OL IF OA KM PO OR BP PG OR EJ EO AR QA", "OJ QA BF KC KH CF FQ BR DA NH KC FM CO IC MD GR CG", "CM AA AR KO LD GK AR DO ID LE JI QH GD CN PD LB FO", "AL EQ AR AO MJ PM OA FK BL KR EG JQ QE PN RK HK DQ", "HH LK JF GH RQ BK DL IP GF KG BE PK KJ HL ND JO OM", "GJ DQ EG HN MC GM EF KB EJ LG AC LR II BF LD QH NM", "FA LH AF DR RN IQ NI LH PA BL EB"}

    Returns: 18

  51. {"FF DA DD DD BB CD CA CG DB BA CA BG EA FB DB CA EA", "DB FA BD AA EA GC ED AF FC CC FD FD BD DB GB AD AB", "CA GD DF AD BG GE CG GB GA CG BB AE FG GD CF DE GE", "EB GA BF EA CE BG EG FC EB GB CG DC AA BD CF GF BE", "EB BG FC BA DB DE BF"}

    Returns: 7

  52. {"AE DE FA EB FF BC BA BB AA EA AE CD AC DE FD FD BD", "EB FF DE FB CC BC FD DF AF EE CA"}

    Returns: 6

  53. {"CD NB DC BG JG CJ CE EB FJ FA KN IJ FC FJ CA EA IN", "EG HD FI JB BM KD II BA CA BC FL IH AB CF DL JC KD", "MA HK IH JA LE LK DJ JD IB LB BF DM HC GA KK EB KI", "DG GJ HJ BL AE JB BD IA JD BN FK HH FM CF GK JN FD", "LD FJ AG KF EH ML NL HN FE DC JE ML NB AF HH IG NI", "LI DK LH AB NC NM EG NI GC GM FI JG HE MF GI IK AN", "NF BD DI IG NC GL MI MH IN EA HM DF"}

    Returns: 14

  54. {"GD FD BC GD FE AI HE IB DD DI IG HF BH II EH DI HD", "IH HE CH"}

    Returns: 9

  55. {"HN AN NE IG LO EN OK AK BB FJ EI OO GO LF JN BC JJ", "DK KG EP KA MH PC DA FA FB GN OH FO MN BM DK OP KB", "BI JB LK PJ JC FF CN FL BB MM LG KJ IM LN LJ JL AH", "KB GA JH HP BP OD FF GC JP NL EN DB HF NL GC EF OF", "OH GO ND JN MA PB PF NH DJ NG PC BN AJ FJ GK EC AB", "BF CE DD NC OM MB EA NG AO LM OE JB EP NK MK KP FK", "KN KP GF PF DG HC OP CI DN CF AA FE OP IK BA EK FE", "GL BH PG LL HC JL FM JJ CJ PD LH NG OA LB IO EN GM", "GE EF PC BG CN LK CK MD HF IG BK JP JG OK PD MA HO", "NO LL CD CI PA KK LD FO JG MF AL LP CE NH OF GO IF", "IK EO DN EG DN FA FM BE OF HB JM IO DC OP CN MH DO", "DL JE GF IO HA JK PG CL NL CO AK IJ JL NF EL IE PJ", "FP IP JB NH BD AE DJ IJ EA IL FN JB DP EO OD LM MN", "JB AE OK KI JI OF OP FF JA PG DK EL AB AE FN JC CL", "KC PA AJ BF JH GG AK JJ HH DA DI DM HF OL AO MO KI", "GO LH PN HK DH PK LE BH FO PC BP MB JO MA IM IF GD", "CN MI DH II DL PM CN BH MD OH LP BE CD NM KN NF JD", "HF KL JL LN PK KN ND NJ PF DG EA LD GF FO LE CG LI", "FK PE KO AC LE FN MA JF CH PE AF GE LF DD EJ MP FH", "HH PD CE LI NK ML IK"}

    Returns: 16

  56. {"BI NI WG QB JQ WD EF ER LP WP JV TT MH TA TQ UI XB", "MV PA RU GM VG AT NN KK IH WQ UK NH DV II FO PT AF", "SA LM ON QJ WE XK DX PE HT HI DO LT BX SA TB MD CL", "BF LP VH UN AF UL RC AD KR JR GW LX HK JI VF UV RD", "DH HG DS CT IB JM ME HJ DT IE KW QI UD WF TK FK QQ", "KH KG RH SO TG XK TV NR GP JO QO HO DX EW CH AP LR", "DH DV AN UG WJ JH LF TL ME EB AO QA LV DF NP VG CA", "CB FD PO FN PV SO LO IU IE CG BE KS VI VM UC EE UH", "ED QK PJ HC MN CC BC HS BD LH AL FE DT FS EB LE TB", "LA JD GK OQ VD KS PB II RU XL NV CP TC XR LC NK FC", "GV AK MT PH II SN NB AQ LN RX IN CO JR CX WJ RU TV", "RU SB MQ WA FI DD SG RG PX AI WR FG CW CC EE DV MV", "VG BK JF TH WJ FL NT BX NV MQ HC ID VC QE TS WK PP", "IK EV CP KA VL CW MF NH PP US AC SF LQ OQ TW VH HE", "ES UD TT EC FE UU TK DJ IK WX HG QW JL HF MK KE NK", "GX FP QD BB FQ LL NL GN VX HJ EA IH FD WF DN KP EH", "UX UD KQ SF BF PR DB DN WS BK OQ LF IE IU PW SH EX", "MV WP AA RU HO KB KE BO VR HR TF PB VN RL LL RU VG", "WB TD HV RH IQ OS KJ UJ QI SB FK MT TK UQ HB CK RJ", "PE XE HP QM VT WG QG FQ TE AD TD SH RJ CK HU QV XG", "NL HT HH JB JB HD RM MR KP FQ KG OK GE JR KX RV NQ", "UP IG XB XW UN IB PH BC WP GS WH IS SF BN PN TH LX", "QF DI EK EI PE BX PJ DU LB HE KR ID BJ WC DD XW TA", "JB FB BP KP GG SX PL MO LN BM HQ HQ JB RQ UR LT MQ", "MW JH EX BB FR WP WE XX BQ JA OW GN RD WL XS SR GV", "ID CI QT DK EU UA WU XQ EO LX XJ IH CR BB VA HT AA", "HO VQ CW WA DW WK FA MX CP RD IB KX FM KB ET HC QU", "UU VK XF OT JE IN TP GR QH WM VQ RW MB HR AM II DT", "AJ LA KB EG FK XB UT PH WM ES OF RD GS XM EV VB PA", "HM SV TM WE TC HI UI VW VG SD DK DR JL QG NL NK WO", "DK JL JO TG TL JX VN DL RV XM ED JA OB QD AD EK IG", "MF AU UI VB TX TW CT GX QN TD TV FI KX DQ FD OE GQ", "RD IN RX FE MM HC OG EH OG EH PI GK KM WW RP EH OG", "OB SX FC KD EO ME VX PX PR QV SI BE CP UV RW VK HX", "VW FN LI IR VF QC MS AA FT IW ED NC LI TR BK RM FA", "SR RO EI EX BT IU DQ CO FW XV UC LN UN VS HD HB IT", "CC GO ON EW GI FM CK EW OP ST IR RE PH VB XM CV QP", "BA OD EH UK BB SD DI NE DD VO GE CM QS QH GN JC RS", "RE GS FP DD FU EK IB TL PJ OA KO KC ON GO AF SH LW", "WE FL XV HT MI UB PS RG XM SQ KM GB HM IH RU PD IP", "HQ CU WC HU LJ CK QA TE IO BV LR FU HR JM JA IJ BU", "HE TX JT KE IA PF PM PF NQ KH LI AK PF WJ RF GL KI", "VM VC NO GA TI WJ LA BC PQ GG PD VB SD IH SI AV WW", "QL RU WF XE ON QU BX NQ SR PS JM QQ JL BP UH SR WM", "QR GU IX RO KU RT JD LF GK PL MM AV XN KJ WB TQ PJ", "SR BD EP FN GB WF NG XA BS UV IK AN OA NS CL LB UP", "PN TU NC TG AS DA OP VV BO WF QE VQ EA BK GM KL GR", "SB WH FF NW TX PU OX JL OR LV SU HH CX VH IA RM ML", "EJ OT GV WI OK QF IX UE FM JB JC CQ VV IM EA WM LT", "EU KS LG PN AT JH EK KO HK WX UA AL II MR UK HJ SD"}

    Returns: 24

  57. {"AC AA CA BB CA BA AA BC BB BC BA BB BB BB"}

    Returns: 4

  58. {"DB AD CD DC AA CC DA AA DB BA CB BC BB CB DB DB CC", "DA BA AC CD DA DB BC BA DC BD AA DD DC BA CB"}

    Returns: 4

  59. {"AC BB"}

    Returns: 2

  60. {"AE GC JD EB IG FB FD CC EA GF IJ AD BI BI IH DF EI", "AE HB HE HF DG AI EC AB FH BE GG FB EA CA GE AC EC", "JA IE AF AF AG DG CD JE GF ED JG II FI FA FE EI DA", "CE IE IH IJ EJ JA IB JA AB DB FF CG DE DD IA AF EB", "CC BC II EF EH CC FC AA GJ DB HI CJ BH CJ BD CA JI", "BG FG JF HG CJ FA BF JI EJ HI FB DE BA CJ EG GE BF", "DE CI AJ II DB IB FB FH CI EH FE IA HB DH AE DA BD", "EF CE BD BC BE EE DJ FD JE GJ JJ CE IE EG DE FH JC", "AF DB JF JB EJ EH"}

    Returns: 10

  61. {"KF UK GR PT TH DK GI FB RA TL CB JR FV GF UR SD TG", "DT SI OI PF SH BO RQ DG HO FD HH BU MO CE UC CO ME", "FR TA MD PR JA JR KI RA NP NQ TV ES FD HK IC SP FH", "OK SN VG TA LF ED NF UT EN OJ KR DE JF HM CG DJ DL", "HV KU DD DM CS EF EV TO DF ID EO SB ET LF SL DC FV", "ER VA NB BB OJ AA CS ET RU QU UF IQ RI KH FA EB UB", "RE NT VN SP OS QM UG LS IJ VD LT BA JH PI TE SV BD", "NB UT DF JB OP KN OS DH NM UN VF MC GA HR ET EL PS", "FP KB DE IG EC BO RI RE KF CV BO AV DB LT ES VS VI", "GL OF FR SM JC OP MU DT DT PT VG PU CD IC CU MD MV", "RL NV BE PK AA SL BE JJ LG DC BT IP EG UG PC DK IM", "CF QC NM CH AL RJ CT ML VG KF CU EJ CM QS KI UM KO", "BL KV BO SD AA BV NM NK RC HK RV PS DA KN SI FN DE", "BV VF RP ES HP DF GB IJ QT BK TI EC"}

    Returns: 22

  62. {"ZZ"}

    Returns: 1

  63. {"AB","BC","CD","DE","EF","BA","FA","FC"}

    Returns: 6

  64. {"AB","BC","CA","AD","ED","DE","EF","FG GG GG GG GG GG HH GG"}

    Returns: 10

  65. {"AB","BC","CA","AD","ED","DE","FE","FG GG GG GG GG GG HH GG"}

    Returns: 10

  66. {"AB","BC","CA","AD","ED","DE","FE","FG GG GG GG GG GG HZ GG CF"}

    Returns: 10

  67. {"AB AE CE BC BE"}

    Returns: 3

  68. {"BC EF AD CB BE EE"}

    Returns: 6

  69. {"AB AC AD AE EE EA CA BA"}

    Returns: 5

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