[TASK] Solved Day 8

functions/src/day8.ts

@@ -0,0 +1,166 @@
+import Day from "./day";
+import Utils from "./utils";
+
+const FULL = "abcdefg";
+const SIGNAL_DISPLAYS = [
+  "abcefg", "cf", "acdeg", "acdfg", "bcdf", "abdfg", "abdefg", "acf", "abcdefg", "abcdfg"
+]
+
+class Day8 implements Day {
+
+  part1(input: string[]): number | string {
+
+    const signals = input.map(line => Signal.parse(line));
+
+    return Utils.sum(signals.map(s => s.outputValues.filter(o =>
+      o.length === SIGNAL_DISPLAYS[1].length ||
+      o.length === SIGNAL_DISPLAYS[4].length ||
+      o.length === SIGNAL_DISPLAYS[7].length ||
+      o.length === SIGNAL_DISPLAYS[8].length).length));
+  }
+
+  part2(input: string[]): number | string {
+
+    const signals = input.map(line => Signal.parse(line));
+
+    return Utils.sum(signals.map(s => s.decode()));
+  }
+
+}
+
+class Signal {
+  readonly inputValues: string[];
+  readonly outputValues: string[];
+
+  constructor(inputValues: string[], outputValues: string[]) {
+    this.inputValues = inputValues;
+    this.outputValues = outputValues;
+  }
+
+  static parse(line: string): Signal {
+
+    const split = line.split(/\s*\|\s*/)
+    return new Signal(
+      split[0].split(/\s+/),
+      split[1].split(/\s+/)
+    );
+  }
+
+  decode(): number {
+
+    const values = [...this.inputValues, ...this.outputValues];
+
+    // mappings maps the signal values to all possible correct wires (we'll filter this later on)
+    const mappings: {[key: string]: string} = { "a": FULL, "b": FULL, "c": FULL, "d": FULL, "e": FULL, "f": FULL, "g": FULL };
+
+    // First, we use the "easy" (EZ) numbers. We know that every value of length must map to:
+    // 2 is a 1: cf
+    // 4 is a 4: acdfg
+    // 3 is a 7: acf
+    // 7 is an 8, but that doesn't give any additional information (since it maps to everything anyway)
+    for (const nr of [1, 4, 7]) {
+      const ezSignal = SIGNAL_DISPLAYS[nr];
+      const ezCoded =  values.find(v => v.length === ezSignal.length);
+      if (ezCoded) {
+        for (const ezCodedSymbol of ezCoded) {
+          mappings[ezCodedSymbol] = Signal.intersect(ezSignal, mappings[ezCodedSymbol]);
+        }
+      }
+    }
+
+    // 0, 6 and 9 all miss one bar (length of 6). The only bars that can be missing are:
+    // 0: d
+    // 6: c
+    // 9: e
+    // So we can use this to deduct that the missing element in every number of length 6, must map to either d, c, or e
+    const lengthSixValues = values.filter(v => v.length === 6);
+    for (const value of lengthSixValues) {
+      for (const codedSymbol of FULL) {
+        if (!value.includes(codedSymbol)) {
+          mappings[codedSymbol] = Signal.intersect("cde", mappings[codedSymbol]);
+        }
+      }
+    }
+
+    // 2, 3 and 5 all miss two bars:
+    // 2: b, f
+    // 3: b, e
+    // 5: c, e
+    // So this means that the two missing elements in every number of length 5 must map to either b, c, e or f:
+    const lengthFiveValues = values.filter(v => v.length === 5);
+    for (const value of lengthFiveValues) {
+      for (const codedSymbol of FULL) {
+        if (!value.includes(codedSymbol)) {
+          mappings[codedSymbol] = Signal.intersect("bcef", mappings[codedSymbol]);
+        }
+      }
+    }
+
+    // By now, we probably know some mappings for sure (only one possibility), so we can remove the sure ones from the mappings:
+    let toClean = FULL;
+    let cleanedThisRound = "xxx";
+    while(toClean.length > 0 && cleanedThisRound.length > 0) {
+      cleanedThisRound = "";
+      for (const codedSymbol of toClean) {
+        if (mappings[codedSymbol].length === 1) {
+          const decodedSymbol = mappings[codedSymbol];
+          Object.keys(mappings).filter(cs => cs != codedSymbol)
+            .forEach(cs => mappings[cs] = Signal.removeMapping(mappings[cs], decodedSymbol));
+          cleanedThisRound += codedSymbol;
+        }
+      }
+      for (const cleanedSymbol of cleanedThisRound) {
+        toClean = toClean.replace(cleanedSymbol, "");
+      }
+    }
+
+    let res = 0;
+
+    for (let i = 0; i < this.outputValues.length; i++) {
+
+      const codedValue = this.outputValues[i];
+      const scale = Math.pow(10, this.outputValues.length - i - 1)
+      res += SIGNAL_DISPLAYS.indexOf(Signal.sort(this.applyMapping(codedValue, mappings))) * scale;
+    }
+
+    return res;
+  }
+
+  private static intersect(map1: string, map2: string): string {
+    let res = "";
+    for (const char of map1) {
+      if (map2.includes(char)) {
+        res += char;
+      }
+    }
+    return res;
+  }
+
+  private static removeMapping(mapping: string, decodedSymbol: string): string {
+    return mapping.replace(decodedSymbol, "");
+  }
+
+  private applyMapping(value: string, mapping: {[key: string]: string}): string {
+
+    let res = "";
+    for (const codedSymbol of value) {
+      res += mapping[codedSymbol];
+    }
+    if (res.length !== value.length) {
+      throw Error("Mapping is incomplete for signal: " + this.inputValues.join(" ") + " | " + this.outputValues.join(" "));
+    }
+    return res;
+  }
+
+  private static sort(value: string): string {
+    let res = "";
+    for (const c of FULL) {
+      if (value.includes(c)) {
+        res += c;
+      }
+    }
+    return res;
+  }
+}
+
+export default Day8;

functions/src/index.ts

@@ -9,6 +9,7 @@ import Day4 from "./day4";
 import Day5 from "./day5";
 import Day6 from "./day6";
 import Day7 from "./day7";
+import Day8 from "./day8";
 
 
 // // Start writing Firebase Functions
@@ -32,6 +33,7 @@ export const day = {
   5: functions.region("europe-west1").https.onRequest((request, response) => { processDay(new Day5(), request, response) }),
   6: functions.region("europe-west1").https.onRequest((request, response) => { processDay(new Day6(), request, response) }),
   7: functions.region("europe-west1").https.onRequest((request, response) => { processDay(new Day7(), request, response) }),
+  8: functions.region("europe-west1").https.onRequest((request, response) => { processDay(new Day8(), request, response) }),
 
 }
 

input/day/8-example.http

@@ -0,0 +1,15 @@
+POST http://localhost:5001/advent-of-code-2021-911a8/europe-west1/day-8
+Content-Type: text/plain
+
+be cfbegad cbdgef fgaecd cgeb fdcge agebfd fecdb fabcd edb | fdgacbe cefdb cefbgd gcbe
+edbfga begcd cbg gc gcadebf fbgde acbgfd abcde gfcbed gfec | fcgedb cgb dgebacf gc
+fgaebd cg bdaec gdafb agbcfd gdcbef bgcad gfac gcb cdgabef | cg cg fdcagb cbg
+fbegcd cbd adcefb dageb afcb bc aefdc ecdab fgdeca fcdbega | efabcd cedba gadfec cb
+aecbfdg fbg gf bafeg dbefa fcge gcbea fcaegb dgceab fcbdga | gecf egdcabf bgf bfgea
+fgeab ca afcebg bdacfeg cfaedg gcfdb baec bfadeg bafgc acf | gebdcfa ecba ca fadegcb
+dbcfg fgd bdegcaf fgec aegbdf ecdfab fbedc dacgb gdcebf gf | cefg dcbef fcge gbcadfe
+bdfegc cbegaf gecbf dfcage bdacg ed bedf ced adcbefg gebcd | ed bcgafe cdgba cbgef
+egadfb cdbfeg cegd fecab cgb gbdefca cg fgcdab egfdb bfceg | gbdfcae bgc cg cgb
+gcafb gcf dcaebfg ecagb gf abcdeg gaef cafbge fdbac fegbdc | fgae cfgab fg bagce
+
+###

input/day/8.http

@@ -0,0 +1,205 @@
+POST http://localhost:5001/advent-of-code-2021-911a8/europe-west1/day-8
+Content-Type: text/plain
+
+gfeabcd adecfb gcedb cef efgdc decabg cbfg edfga fdegcb cf | fc faedg fdage fec
+bcfegd fdceg ecgfadb fdae af cdeagf afc abdgc gcadf gfbace | cefdbg afgedc bcagd gedcf
+gbf bagdec fgdbae cfbd bgacd fb fbcaegd dfgbac gbfca gecaf | gadcfb abgcf bdcgea gbf
+eagcf cdgbaf cbadg fbcdgea cebfad fb fdgb abf gcdbea cgabf | bfdg dgacb gacef bafcg
+bgface cfadb gfc gcfba febg aedcgfb bceag cdgaeb adfecg gf | acfdb fabdc efagdc facbd
+bfegac adbfg ebagf beafgcd gfeadc age cgedbf gfceb eabc ae | acbe gfcbea aefgb abdgf
+bfeag cbae cbg bc cbaefg cfdga fgdbec ebadgf eacgfdb gabcf | bfgcea eabc eagfb bc
+abdcfg aebfd fbcade cdbge cfae eafcgbd dcabe bca degfba ca | ecfa fcadegb edbfag abc
+dfcgea efcbg ecda fadgbc fac bdacegf ac feabgd afgde ceagf | fdgae abgdfc egcfa fagde
+gfd gdcab fgdcae ecdfb bfdgc dacbef fbeg fg fdcgbe cdagbfe | bacgd cfdbea efacdg bcaefd
+eb afbgd gafbe bef gacdfb gdecfab aecfg egdb defgab bdaefc | gacfbd bfaecd gabfdc bef
+ecfb cbdfeg fgbadec fgcdb egf cefdg eagdc fbcdag fe gadbfe | fbgade bedfag gafbdc ecfdg
+bafcdg gbd dbcgef ecgdf cbged cgabe faebgcd cgfeda db debf | bdg efdgc fbed gbcde
+gdfceab afced decafb gadfc fg agdbc befcga fegd cgf cfegad | egdf ecafbg gbcda dcagf
+eca ea efda cfbda badgcf dbcea edcfab abfcdeg bagfce cbdeg | efad fedcba fgcbea adfbce
+gdefbca cf acbfg cegbda begca fbc gfebac afce gbdfa bdfgec | cbf bfc gecbaf cbafg
+afcebd agebfc fbcea eadfbg bdf cdfa dfecb df cbdfgea becgd | ceagbf fcda becfd ebfac
+ecb adgfeb fedbgca efac cfdegb egbaf ec bgcda gefbca cgaeb | afbdgce bec ec feca
+eacdb dfcabe dg fdabgc cdg gaed cbaged gecdb ebgcf dagefbc | debgc dgaceb gcd fdebca
+cega gdbefac gfdcb efbgca ga afg cgbaf aecfb ceabdf edgbaf | fedagb dbafce ga ga
+efbadc acgde fagcde fe dcaebg edfg acgef cbagf fae acfebgd | ef badcef dfge gecfa
+cbgfa cbae dabgef ba bag fcgea fdcage gfbcd cgbdaef gfecab | aefbgd bfgac gebacf bgfac
+dgfbce fgc bfcda egdfa gc fgedab acgdf acedgf aegc fbcgade | dfagc bgdafe aegfd egfda
+dgfa bedfc badcf agfbcd af eadbcg bfegca bfa cgabdef bgadc | bgdacf dcfba fcbda gbedafc
+aceg gdaef fcbegda dcefab afcedg abgdfc cadef agf degbf ag | bdgfe bacfgd cadfe fcgeabd
+bgefcd edg acdegb edcba cbdefa cfaeg beacgfd egcda dg dbga | efagc abcdegf adfceb dg
+faedbc gabde becfgd caebf acfg eacbg cgabfe cdebfga gc gcb | cdgebf cefab abdfce gdcefb
+de cgdfb edbg dbacfge cdfeg cebdgf agcef afbcgd dce dbfcea | beadfgc gbcadf dgcef degb
+egcafb cgadfbe gdace fd bafce cedabf bgdefa dcfb afd ecafd | gaefbd dfcb aebcf gcabfe
+cb beafcd bdgacf cdb bgac edgbfac cgfed bcgfd bgfdae gdabf | bafdg gcba fbgcd cegdf
+fceba ag degafbc bfcga bcafeg agf bafedc gace bfdcg fedbga | bdefca fcgbd cbafe cgbdf
+cafbge ce fbcea fecgdab aec adbcgf fbgca bgec baedf fegdca | defab bcfae ecgb aec
+dgbc dagfcb acfgbde bad adcfg dabfc gacdef aebdgf cabef bd | acfdb defgca dbegfac gfdca
+ecdf degfb adbge fcbgea dbgfec gfd df egfcb gacdebf cdfgba | cgbdfe gfd cfegab gfabce
+defcbga fcade efbac fb gacdbe abceg abcdgf egbf fcbgae bfa | befg cabdge eafcb bf
+cfbdae cg decbfag egfab fgdc dcbfe fegbc gce gdebca bfdgec | dcfg eadgcb ebdfc gfdcbe
+eagcdf cfaeg dgfe bdcefa gcabfed cgbda cegfab dae cagde de | dae adbecf edfcga fdge
+egfa gfbeac cfbag af fcgbe egbdfc abf cgbda ebfadc gbaedfc | cagefb edcbgf gebfc egcfb
+gda ga bcadge gfea dcbgef adcfb fdebg cgbfdae gfdaeb fabdg | fegbd egaf dafgeb gda
+gefad fegbad adecbfg db bed eacgb fcdgeb agdbe adbf acgfde | fabedcg bed gfadeb gedafc
+fb cbefa baf dfbgca edfac gefbac eadbgc efbg gfecbad aecgb | dbacfeg degabc fgacbed febg
+cbgfad eabcfgd cfdeg fbd adegb fb cfeb egbcfd fbegd agdefc | fdaegc febc fb ebgad
+dbfgc badc cfdabg fgaceb degfab facegdb dgb efgcd fcagb db | gfbca cgfbd gacfbed fbgdc
+efgcbd efbdc ef febdag dagfbc fcge bfdcg dabcefg edf ecdba | cbdegf defabg dcgabf bcade
+ecdfbga cbdeaf bfgdc fca eagdfc eafdb bdfca ca caeb gfeadb | cbae dcbfa acf fgcbd
+gdefcba bafd efcdab gecdbf fdc becfa gceda fd cafde baecgf | dfaec cabedf abcfeg df
+cfb daefb bgfcde dgacb edfcagb acfe fdbcea dcafb cf febagd | fecdba dfcageb fabcd ceaf
+adgbec fcgb badgecf dagcb bagefd fdb bf dcbfa bfadgc cfdea | fb efdac cfdba gadcb
+afcgd bac gdebfca bcgaed afbcd ecdfgb dcfbe ba befa eafdbc | dcgfa dgbfce ab afcbed
+gbcdaf fdgac bagde cgdbaef eabgcf bf gecdfa gbafd cdfb fgb | aecgdf bdega gafebcd aefgbc
+gfeb cadfg bdfga aefgdb bgd bagdcfe bgeacd gb cebdfa efbda | dafebc bfadge dgb adcfg
+cda dageb fgebda bfcdage dcbeag cgade cefbad ca cbga cfdge | gbadec febcad beadg cfbdea
+gdabf eadgf fe defagcb abef feg gabcdf cedag dafgbe edgcbf | abgfde gedafcb cgeda adgec
+fbd gfeba fgecad edafgbc dfcbga abdgf cadfg cgdb bd aecfbd | agfcbd ebacfd bafdg dagcf
+cadefb cgde eg aebfcg fdbagce afdceg fbagd aeg dfage aedfc | gdaef fedca eg ecabdf
+dgbeaf fcbdga ae agfcd egabdcf deac dcgfae acgfe fbceg gea | aecd dace gcbfe gcfea
+dafeg fcg degbac gcdbe dcgef bdegcf gedbcfa cf ebfacg bcfd | agfebdc cegdf cf cf
+bdfcea bdgae ecbga dbg fegbda bdefa dg dbacgf geafbdc efgd | bdg gefd cagbe debga
+aegfdb afcbd cdaebfg dgafbc cagb ba dcefb fba cdagf fgadec | fedcb acbg bfcdga gfcaed
+bfagcd agfb afcdg fcegadb dfgecb gb adbec gabdc efacgd gbd | eacbd adcfg fbgadc dbgca
+fcedg dfgbea ea fcbadeg ade agefdc afcdb egca ceadf fegcdb | dfgce efcgdb dgecbf cfabd
+dfea ed agdfebc eabfc bcdgfe edc cdbga ecbda aefdbc acfgeb | bdaec abfec gbedcf acbde
+dgefcb fbcaeg fbcga bgfcaed bfgda dcbfag fgd cfda edbga fd | bgcfae abgdf acfgbe abegd
+dgabfc cgdfe afd fdcae af agfe decba fcebdg dgfcbea dgfcae | fcaed fcabdg eafg fa
+gafce debca gdfeca dfag dacbfeg fcbedg ceagbf fdc fd cadef | ecfad gcbefa begacf edbcgf
+daceg efdcbg fcgad dbeca bdface bcfagde abge ged aecgdb ge | ecgdbf egcad eg aebg
+fdbace debagc cgbef degba bacfedg gfda afb edfgba gbefa fa | fbdgcea befacd cdaebg fbaegd
+fgbdea dg gdfb gfcebad abfeg afecgb dagbe edcgfa cdeba edg | egd fbgd dge eacdb
+ge agdcfb fdcag fcbgaed degcf eadg bdcef acefdg bcfaeg gfe | aecfdg eg dcgfa caegbf
+bcgef gfdb bgfcae fcadbge cedbg edafcg dg dcebgf bacde dge | agefbc bgefcd bedfcg dg
+fga ga dcgfb dgeabf beadfgc eadfc gbca dcagf fadcbg bcgfed | ga dgcfba agcdf befcdg
+dbag cafgbe cdfgaeb gabcde eabdc fdace bd bgcea gdecbf bcd | afdec abegfc gebacf edgabc
+fcde cbadefg gdcefb bcdagf bcgef fdg abgcef edbfg df eabgd | egabd dbega gfcadb dbega
+bfdag adbefc efdgcb fceab dbc cfdba egafbc dc ceda beacdfg | dbfcge cd fbcea efacb
+dgaeb cgbeadf afbeg gdbfae ebadcg gdfb acgedf fg abefc gaf | fcdgbae gf bgaed fbaedg
+cfdbeg dcfaeb cagbe cfgabde afdc fbaed cfe bfaec bgadef fc | fcaedb gbeac cfdgbe afdc
+ceg dgecfa abecfg agcdfbe gcdae gfdcab fdec gbead ce acfdg | cgfad fgebca adbfgc dagcf
+dcf cgebfa dc gdcaef eacgbdf cdefgb cebd dagfb cdgbf cfgeb | cd bgadf dbfga dgfba
+gebac caefd bf bgacedf ebfdgc dbaf cfb bfeca agcedf dbcfae | debgcf adcefb befgdc gaecfd
+abec bafgc fcebg fbaceg dcefgba degfb gec acdfeg ec fgdbca | dbgfe gdbfe ecgbf bcea
+egafbd egdbc bdc cbfdag fcde ecbdfg fgbde ebcag debgafc dc | cdbeg fabedgc fgdecba dc
+ecdgfa ag badcegf gaecb eabgfc adecbf cag acebf fbag dbceg | ebgac bfag dgacef edgacf
+afgeb adgcbe efdb fgeacbd ceagf gbdefa eb bea dacfbg dabgf | eab bgfdea abfge bdfcage
+egbdac aefdb fgdeb dabfc ea dae dbacfeg cagbdf caef eabdfc | cadbf ae dafcgb beadf
+egcadbf gbce debac dge adfebc ecgad gdcfa dgcbea gdafeb eg | dgbfae ge adcegb bdfega
+fecag dc fgecd dgcb edc fbedca dbcfeg gbedaf gfdbcae ebgfd | dce gbdc edgbfc fedcba
+cafebdg adcfge debfac dgcae gec fbdegc ge cgdab faeg ceafd | gafe bagcd edfac cbagfde
+dc bgcaf gdcebaf ecgdab cagdf efabcg dgc dcfb fgeda cgbafd | gbcfea dacebg bgfdcea dc
+afedc ebfcg dgfbac adbe eafbdcg fdbce bd fbd bdafec afcdge | baed cfgade becdf dbcfea
+bdae fbdac deafcb badcegf bcefga badfgc efcgd eb dcebf ecb | bcafdeg eagfcb dcbfag fcdbga
+gb dafbce feagd bdegf bdcgafe fdgebc acdgbf cfbde ebcg bgd | adgfcb cgeb bceg dgbcfe
+cbdfge bdceag fc edbgc dgfae bcdf fce bcefdga dgefc ebgafc | cdfge bgecaf fdgce cf
+ba fcgae gecbfd cefbd cba afdbce aecfb beda fagdcb facdbge | ebad ecagf ba deab
+ba baf ebacgf fcgad fbcdeg bgcef gadbecf ecfadb acbgf geab | cgdbfe ba dbceaf adbecf
+cdfga efd efagcb egbd ed gacedfb fbdeca decgf gbcef gfbdce | cfedg bedcfg gecbf gbfce
+fegbca ega egfdca gfeba afbec fadbg defacb gcbe eg dfagecb | ebacdf bdgeafc dfabg efabc
+fdb efcbad bdaeg fbgade gfbe egacfdb adfgc bf dcebag badfg | dfcga bfd adfcg dgbaf
+ead agbcd de bcgeda gedb agced cdafgeb bfcgda adefcb fecag | cbgead acdgb edacbf dfeabc
+cagdfe egfca geacd dg gbaecf ged agfd cebda edcbgf decafbg | gbaefc ecgaf cgbaef gcfdbe
+fd agcfedb adgfb cdaf degab bfacg cebgfa bdgfec fbd dcgbaf | abdgcef dgacbf cfda cedfgba
+cafbd fgcb bgcad gdfcba eadbf adecgb cfa efgadc agcdefb cf | fc fdbcag fgeadc fegdca
+dgcf eadcg fg dabfe gdefa efg cegabd fadecg gadfbce facbeg | aecbgd gceda gdecab abcgfe
+ebfdca agbdcf gfadc bfc afgb cdgaef egcdb gbedfac fb dgbfc | ecbfadg baefdc bf dbgec
+fabcge cafged beg abfdge aegdf dabg fgbacde bg fdebg bcfed | efgda dgefba gaefbd bagd
+gbfda afbcgd acefdg adb bd gbfae dfcga acegdb acfdegb cbdf | dbfc abd bd dcabfg
+ecgdf abcedf gfcdba eadb ecb fdcab fecbagd be eacgbf ebfdc | gdbcfa ecfdab deba efbagc
+ca fcda efbdgc ebgda bgefacd cea cdebf bdefca efagbc ebcda | fgebca egabd edcbaf acfd
+agebd dcge ed gaebc fegacb cfaebgd bcedfa gfbad dbe cdgeab | dbega fbeacd gaebcd gfcabe
+bg edfagb daecgf bgafdce bdeag cgbdaf ebgf ebdac bga edfag | dabcgf cbaed ecdba abg
+efdcg afbd bfdeg bgf fgdaecb dagceb fb gcbafe abgdef egbad | fbeagd bcdafge gdbfe fgdbe
+becfa fg dgfe dfaegcb cedfbg begdca fgceb facbdg bfg gebcd | fg gebdcf dcbega cdegb
+edgacb cb cefdba gcaefd adcbg cdb cbge efgdcab gdeca fadbg | gcabfed cb acgdbe gbafd
+cfgbde eagdbc cegdb ebcf bdf fb fbgde facedgb eafdg dcbgfa | cdfagb cfbgde bf dfegcb
+gedcfab ebfcda ecdbf gfced fcebdg gcd gdeaf cg cdbgae fgcb | cedafb gdfecb cg gc
+fbe edbfca feadbgc cbefga fb dfaeb abdge eacdf gfedac fbdc | fadeb acbedf fbdae daecf
+dgacbef efgba dgbfe fecabd bgaefd bde dfcbg de aedg bfgeca | bdfcg ebfdac eagfb gdae
+efbgcd aedgcf acd cafbd gbfdaec bagc bcfgd ca gdafcb dbfae | bcadgf beadf ca fgcadb
+edgfba fbged aed gadcb bdgae ea efga cdbefa cbefdg dcabgfe | dfbcae bfceda ae gbaed
+gdc dfgbeac adcf bfecg abgfd bcdfg dabfgc cd fbgdae dbeacg | gcbfd fdgba afgdcb gbdcae
+ca acd ecfbdg fcdeb cdfbea gcabfde afdce cbaf afedg cgadeb | cdbef ca dbecf agfed
+gfceab ed fgecd fdgaec gdbfc eacfg cdegfba dcae deabgf efd | eagdfb ed cefag aced
+baced dg deabfg dga adcge gcfd acgefd acegf acbdfge fabgce | egfdac becad aebcfgd gcdae
+ed dec cdabgf acefb ecbfdga becagd gdbac cedbgf adeg edcab | bdagc acebd bdfgac gdfbcae
+gefbca edbfc agdf bgadce fegadc ceagf gafdbce ecfgd dg gcd | gdfaec bfecagd gacefb acgbefd
+cdega fcdbga gbfceda gafbde adgcb egfcd ceba dea badecg ae | aebgdc dfbage badfge edgcf
+egcdfba ebcga gfe adgcef gdbf bedgaf gabfe dbefa fg cbdfea | gdfaec dfbg abedf gcdfae
+feabc gdfeab ebgdafc fa cebga cadgeb gafc fbgeac ebcfd fea | gcabe cbgea febadg fcag
+afdb agdfe bdcafge fdaegb aegbd gefdc abdecg aecfbg afe af | fae adfgbe af degab
+fdg cdafgb fg cdbef bgfde gfea edbag ebadgc bgaefd adfcegb | befgd dfbgca baedcg gedba
+aedgfc afegbcd ag bcedga bedafc aedbc agd gbcda baeg gfcdb | edabc gaeb afedgbc agfdce
+eafdc db fcgbe dbac dcbfaeg ecfbad bdf bfced beafgd aedcfg | cdba bd cbafed db
+cf fcebgad adfeb afdbce afgcde debgc cbdfe cafb cfd dafgeb | bdecg aegdfc cf dbcegfa
+dfceab cebgad fgcbade dae ecdgb bgae dagec fdbgce ea dcagf | eagb ceabdf dcfeab badgce
+dgf agcfed gacf afcde dgcef dgaefb efdacb egbdc fg bdeafgc | acdef afgc gdeafcb fdegab
+abc aegfcb bc aedgbcf abdce eagdc gdceaf bdfae dcbg aedgbc | fbacge cadgbe gcaedf fdeba
+ebdagf ac gcbfe agc aebgc gcbfeda cbdgfa edabg dcae acbdge | cbgfad cag dgfbca abfegd
+cdafbge bgf afgd adcebg acefb gf dbgca agdcbf gacfb cfdgeb | dagf dacgb cfabe dbgfce
+ebgfacd eafgcd dbcafg ebcafd gdeac afeg eac bcgde afgcd ea | fdbgac dfgca ceafbd gfbacd
+gfeb gcdbfea dbecg edacgf fbdac efcdb fbdgec acbedg efc fe | cedbg bcfad ef fec
+gfbecad faegb gcdfea cfg gc bceg bagfc fagdeb bacdf fcabeg | aefgcb cfg dafbge agbfdce
+bfcedg decba agcf abegfd bdceagf bgacfe cg cbgae efgab ceg | fbceag eabgfc gc abgfec
+adebcf agbef abegdc bedgf cfbadeg bedcf fgcd gd bcdfeg gdb | cbafgde dbefc gdb abefg
+aeg cdabeg cgfadb aebgd ge ecafgdb edbfa acgdb gafedc gecb | cbge agefdbc cgdafb fdabe
+febag ceba ceagf dabfge gce cabedfg cadfg efbcga ec fbdceg | edgcbf bgefa fecag afcgd
+faecdb cea dabfgc dfagceb baed dgfcae caebf ebgcf ae bdacf | ae fbaecd ebcgf bcfda
+gefc efbdga ec bdgfe fcbeda ecadgbf cbgde cedgbf bce bcgda | ce bec ecdbg gcbad
+dbaegcf dbgaf agbde dcebfa gfdc fcabg gcfbda df ceafbg dfb | becdfa dbf egafcb bfagd
+gfdae gbfec egcdf afbceg bcdf acgdbfe dabcge cfegbd dc cde | fcdgeb dbagec cafbeg gacebd
+fg edcgafb fcadb bdgae fgbda ebdfac fabcgd gecfdb gfd gafc | cefgadb fg cbfged gf
+bdfea fceba fc agbce ecdgfab gcefad fec aebdgc bcegfa cfgb | dbfae efc ecbfga gdceaf
+cdfgb gefcda abdgce beagd ec bcae dbgfeca ecg ebdgc abfedg | dgabe adgcfe fdcbg ec
+fbedc egfabd gadcf dcfeg aecdbgf gcea eg dafgec fcdagb fge | bafedgc eacg ecdfg deafgb
+faegdb fdb bgfdec bcgda agfebc gcebdaf cedf gdfcb cfbge fd | dbegacf cfaegb gfcaeb befgac
+gbacdfe fdgcba befgc fabe bcf edcbg cgfeab cfaeg fb acdfeg | cfeag bcgde ebaf fgcdab
+gef dceg edfbc baedcf bdagef eg cfegb bfacg afgbced decfbg | dfegba cfegdb eg gacfb
+cba adgcfeb abfdce dgecbf ca ebdacg becdf adfc fbeac fabge | fbaeg gfbceda fceba bdaecf
+cb adefc egcb abc bedgac ecdab bdfgca eabgcfd edagb dabfge | bfdega fagcbd abcde agdeb
+dgfbae efgbacd gcdf bdg gd bcgdfe bgcde bedac cgbefa bcgfe | gbd aedcb ecfbg ecdbg
+gcafedb ecdbfa fedcg dcefga dfgca gbcde gfae ef fec bdfcga | fdgcabe cbadef fcgda ebdgc
+eca ea fbadec debcg agef edcga caedgbf fadgc dgafec cfbgda | cbdeg cedgbaf aecdfb dcgea
+afc gbafec egbdfca ca eagbfd aecgf abfeg gcba abedfc dfgec | gafbe cedafb afbeg cagfe
+agbde eabcgd fe dcfgb efd becdgfa dfageb fdebg fdcage bfea | def edgfb acfedg bgead
+gbdec facbgd ag gba bgceda aedcbgf eagd cgabe bface fbdecg | eagbc gcbdfa bafcgde eacbf
+dbacfge cagfdb geba cefgda bgc eacgf caebfg cbdef bg fcbge | bg abcegf efgca cfdeb
+gaefc cgefdab fdcaeg aegfdb gb badfc gbf bcfag gbfeac gceb | bdafc aefgdb gfcae dfcab
+dbceg bcafgd cfabde cfabdge aed ae deacb face egfbda bfdac | cgabdf fgeadb ade dcbge
+dfbgcea fbeca cefbg dfgc bgaefd dbecga gfe fg efdgcb cdbge | gcbfed cfbeg gdfecba gecbd
+gaced bd edfcag aecdfgb bgad edcbg debfca deagbc bdc egfbc | bdc cdb efcbad dagb
+egfca bgea adebfc gfceab cfebg cdefag dgfbc bgadecf ceb eb | dcefag facgeb edbfca eacfg
+fged bcaeg fcgbde gdfacb fcadbe bfcge ebfcd fcg edabgcf gf | gfbdac efcdb gfceb fgdceb
+fgbdeac facdb agcf fc bfegcd bedfa gbcda bcdfga fcb degacb | bgecad cf dcgbfea gfca
+dafbgc cfdga dgafeb db cfdage bcfaedg fbgec bdf dcab cdbgf | cfdgb befadg ebgfc acdbfg
+eadgf gdefab ebacd fc eafgcd caf deafc egcf dacbegf bfdagc | egadcfb agfdcb debca fdcagb
+dgaecb efd gbecdf fgdcae geaf faecd dfcab bcfagde egcda ef | fe ecagd efd fed
+dbaf bf bfg ebfcga degba cedfg adfcgeb edgfb begafd daecbg | cbegda cbeadg fbg cgfde
+gdebcfa cbfad ecgfd fbeg dgfbc bg gfcade gdb gdbecf gdbeac | fdcgbe begf acgedb cbdfg
+acfdge cadgbf gecfd dbefc fg agcebfd cfg gedac adcbge efag | egaf cbdgeaf gfc bdfgca
+fbgad eabg bcdafg bde edcfab fdgec degbfca badgfe dbgfe be | egbdf bgadf bfdge edgfc
+gfceab acf ceafbd cagdbe bdaf dcfae af febacgd fgdec daebc | cegfd dacfbe faebcd adfecb
+bgefcda facgb bcg fgec cgebad gc efagcb bdgaf fecba dcfbea | bfeac acgfb ebcaf bgadf
+eagbd abcgde afedc gcbe bac debcafg bgacdf bc dbcae gadbef | cba adcfbeg efdac cb
+fbead gdebfa cabge adfbgce dcb dc aebdc dacfeb dcfa gbfecd | decfba cd dc edcgfb
+gcbae ecfbag gebcf edabg efagcd cga ac beagcdf bcfgde fbac | fgecb gdabe agc ca
+dfgacb fadbg afebdg acbgefd gdbc cgafd efgac cd beafcd fdc | daebfgc cebfad bgdeaf dcf
+cfdeab efgadc cfbag ef cagbed dbcea ecfab cfe befd gecdfab | fgecdba cabde abefc dbcae
+fadec cbgade acbfe df cdf acfdeg afdg gabcfed acged bfdcge | efcda ebfca ebgcfad dcage
+cdfgeb eabgcdf faegc facgbd gdc efbdac fdbca fdgca gd badg | dfbceg cfdba cfgda bcadf
+cdeafg ecfbgd cb eabc aegdcfb cdfba bfc cdfeba edfac dagbf | ceafdg feadc fbegdc beacdfg
+acfbde agc cabgf cfdba gfecb bgadce bcgfda fadg cebdgfa ag | cbfad cebfagd agdcbf dcabf
+dfeag fgbedca dfceg fcgaed egdcfb edbcga aefc gfadb aeg ae | gefda gabfd egacdf dfbgec
+gfbec bdcaegf cdb bdacgf dgcbae gdcaf cfdage bd badf dbfcg | gaedbc dcb fcgdb afdbgc
+cgdef geafc fd fdgbac degbc dgcefba cfeabg dfae cafdge dcf | egbcfa defa df dcf
+cafed gdbfa cbfade cfgead cb gecbfd gdbcfea bcea cfb bacfd | bcea afdbg cbegdfa afdcbge
+ac fcdgeba gdfec bdgefa fedab eac fadce aecbgf dbac aedcfb | efgabdc cafde bacefd cfeagb
+begcf eagcdbf cfg bdcfea bfeca cfdagb bfged caeg cg acfegb | bgfde dgafceb dcfeab dgacfb
+gbdfca fadbg fbc cb bdfgae abgcf feacg dfabceg dabc cfgdeb | cbf fcgdeb eafgc bdfgea
+fcaegbd abgdce fdcgab gf bfgcae bfg gbfea abgce fgce ebadf | fdabgc gcfabe aebgdfc gbdcae
+cdagbe gedbacf efbcad ebdag be gbcfad gbdac ebcg ebd egfda | efgda ecgb gbecda bdfgca
+bfdgac gdecb abcde daefc efbgcd ecdbga agbe dab ab cfgabde | ebga ab cgbfad eacdb
+efgda ac acf dfgbec dfeac edfbc ecfdgba fceabd bfdcga aecb | ecadfgb abcedf cefad cabe
+
+###