| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/rcwa/data/3ctsgroups6/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 22.8.2025 mit Größe 369 kB |
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Quelle database.g Sprache: unbekannt |
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## #W database.g GAP4 Package `RCWA' Stefan Kohl ## ## Data library of the groups generated by 3 class transpositions which ## interchange residue classes with moduli <= 6. ## ## `grps' is the list of the groups in the database, and the following ## relations hold: ## ## 1. mods = List(grps,Mod); ## 2. sizes = List(grps,Size); ## 3. TriangleTypes() = List(grps,G->List([[1,2],[1,3],[2,3]], ## ind->CTPairProductType(GeneratorsOfGroup(G){ind}))); ## where CTPairProductType is the component of the record returned by ## the function `LoadDatabaseOfProductsOf2ClassTranspositions'. ## ## Given a group G which is generated by 3 class transpositions with moduli ## <= 6, Id3CTsGroup(G,grps) is the position of the group G in the list ## grps of groups in this database. ## ## The lists `abelian' and `metabelian' are lists of the indices of those ## groups which are abelian and metabelian, respectively. ## ## The list `solvable' is a list of the indices of those groups which are ## known (or strongly supposed) to be solvable. ## ## The list `freeproductcandidates' is a list of the indices of those groups ## which are possibly isomorphic to the free product of 3 cyclic groups of ## order 2, thus whose generators possibly do not satisfy any further ## relations. Only one index per class in 'conjugacyclasses' is given. ## ## The list `freeproductlikes' is a list of indices of groups ## whose generators do not satisfy 'short' relations. ## ## The lists `stabilize_digitsum_base2_mod2', ## `stabilize_digitsum_base2_mod3' and `stabilize_digitsum_base3_mod2' ## contain indices of groups which stabilize the digit sum of an integer ## in base 2 modulo 2, in base 2 modulo 3 or in base 3 modulo 2, ## respectively. ## ## The list `abc_torsion' contains an entry [ <group number>, <order of the ## product of all 3 generators> ] for every infinite group in the database ## for which the product of all 3 generators has finite order. ## ## The lists `spheresizebound_4', `spheresizebound_6', `spheresizebound_12' ## and `spheresizebound_24' contain the indices of the groups for which ## the sizes of the spheres about the identity are bounded by 4, 6, 12 ## and 24, respectively. ## ## The list `redundant_generator' contains the indices of the groups for ## which one of the generators is redundant. For the obvious reasons, ## such groups are dihedral. ## ## The list `D0pos' contains the indices of the groups which are isomorphic ## to the infinite dihedral group. ## ## The list `D0xC2pos' contains the indices of the groups which are isomorphic ## to the direct product of the infinite dihedral group and the cyclic group ## of order 2. ## ## Descriptions of the following components can be found in other files in ## this directory: ## ## - `equalityclasses': equalityclasses.g, ## - `samegroups': samegroups.g, ## - `conjugacyclasses': conjugacyclasses.g, ## - `subgroups': subgroups.g, ## - `supergroups': supergroups.g, ## - `chains': chains.g, ## - `growthsequences': growthsequences.g, ## - `abelianinvariants': abelianinvariants.g, ## - `compositionfactors': compositionfactors.g, ## - `intransitivemodulo': intransitivemodulo.g, ## - `partitionlengths': partitionlengths.g, ## - `degrees': degrees.g, ## - `orbitlengths': orbitlengths.g, ## - `permgroupgens': permgroupgens.g, ## - `respectedpartitions': respectedpartitions.g, ## - `finiteorbits': finite-orbits.g, ## - `shortresidueclassorbitlengths': residueclassorbitlengths.g, ## - `cyclist': spheresizecycles.g, ## - `trsstatus', `trsstatuspos' and `trsstatusset': trsstatuspos.g, ## - `orbitgrowthtype': orbitgrowthtype.g, and ## - `non_abc_cycle_orbitcounts': non_abc_cycle_orbitcounts. ## ############################################################################# return rec( ############################################################################# ## #S Utility functions. ////////////////////////////////////////////////////// ## ############################################################################# Id3CTsGroup := function ( G, grps ) local gens; if not IsRcwaGroupOverZ(G) then return fail; fi; gens := Set(GeneratorsOfGroup(G)); if Length(gens) <> 3 or not ForAll(gens,IsClassTransposition) or not ForAll(gens,g->Maximum(List(TransposedClasses(g),Mod))<=6) then return fail; fi; return First([1..Length(grps)],i->gens=GeneratorsOfGroup(grps[i])); end, TriangleTypes := function ( ) local triangles, triangle, cts, ctpairs, cttriples, data, ctptypes, mods, sizes, i; cts := List(ClassPairs(6),ClassTransposition); ctpairs := Combinations(cts,2); cttriples := Combinations(cts,3); data := LoadDatabaseOfProductsOf2ClassTranspositions(); ctptypes := data.CTPairsProductType; data := LoadDatabaseOfGroupsGeneratedBy3ClassTranspositions(); mods := data.mods; sizes := data.sizes; triangles := []; for i in [1..Length(cttriples)] do triangle := List([[1,2],[1,3],[2,3]],ind->Set(cttriples[i]{ind})); triangle := List(triangle,edge->ctptypes[PositionSorted(ctpairs,edge)]); Add(triangles,triangle); od; return triangles; end, 3CTsGroupsWithGivenOrbit := function ( orbit, maxmod ) local cts, stab, perms, gens, gensp, indcombs, grps, grpsp, trsinds, start; start := Runtime(); orbit := AsSet(orbit); Info(InfoRCWA,2,"Setting up the list of class transpositions ..."); cts := List(ClassPairs(maxmod),ClassTransposition); Info(InfoRCWA,2,"Elapsed time: ",Runtime()-start); start := Runtime(); Info(InfoRCWA,2,"Determining which class transpositions stabilize ..."); stab := Filtered(cts,ct->orbit^ct=orbit); perms := List(stab,s->Permutation(s,orbit)); Info(InfoRCWA,2,"Found ",Length(stab), " class transpositions which stabilize."); Info(InfoRCWA,2,"Elapsed time: ",Runtime()-start); start := Runtime(); Info(InfoRCWA,2,"Forming the list of triples of class transpositions ", "which stabilize ..."); indcombs := Combinations([1..Length(stab)],3); gens := List(indcombs,ind->stab{ind}); gensp := List(indcombs,ind->perms{ind}); Info(InfoRCWA,2,"Forming the list of groups ..."); grpsp := List(gensp,Group); Info(InfoRCWA,2,"There are ",Length(grpsp)," groups to check in total."); Info(InfoRCWA,2,"Elapsed time: ",Runtime()-start); start := Runtime(); Info(InfoRCWA,2,"Filtering the groups for transitivity ..."); trsinds := Filtered([1..Length(grpsp)], i->IsTransitive(grpsp[i],[1..Length(orbit)])); grps := List(gens{trsinds},Group); Info(InfoRCWA,2,"Found ",Length(grps), " groups which have the given orbit."); Info(InfoRCWA,2,"Elapsed time: ",Runtime()-start); start := Runtime(); return grps; end, ProbablyFixesDigitSumsModulo := function ( g, b, m ) local n, B; if b <= 1 then return fail; fi; if IsOne(g) or m = 1 then return true; fi; B := 100 * Mod(g); n := 0; repeat if Sum(CoefficientsQadic(n ,b)) mod m <> Sum(CoefficientsQadic(n^g,b)) mod m then return false; fi; if n >= B then return true; fi; n := n + 1; until false; end, ProbablyStabilizesDigitSumsModulo := function ( G, b, m ) return ForAll(GeneratorsOfGroup(G), g->~.ProbablyFixesDigitSumsModulo(g,b,m)); end, ############################################################################# ## #S The groups. ///////////////////////////////////////////////////////////// ## ############################################################################# cts := List(ClassPairs(6),c->SparseRep(ClassTransposition(c))), grps := List(Combinations(~.cts,3),Group), groups := ~.grps, # synonym for `grps' ############################################################################# ## #S Data lists. ///////////////////////////////////////////////////////////// ## ############################################################################# mods := [ 6,6,12,12,12,0,12,12,0,12,0,0,30,30,30,30,30, 30,30,30,30,30,6,6,6,6,6,6,0,0,6,6,6,0,6,0,0,0,0, 0,6,6,0,6,0,6,0,6,0,0,12,12,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,6,12,12,12,0,12,12,0,12,0,0,30,30,30,30, 30,30,30,30,30,30,6,6,6,6,6,6,0,0,6,6,6,12,6,0,0, 0,0,0,6,6,0,6,0,6,12,6,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,12,12,12,0,12,12,0,12,0,0,30,30,30, 30,30,30,30,30,30,30,6,6,6,6,6,6,0,0,6,6,6,0,6,0, 0,0,0,0,6,6,0,6,0,6,0,6,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,4,4,0,4,4,0,4,0,0,20,20,20,20,20,20, 20,20,20,20,12,12,12,12,12,12,0,0,12,12,12,24,12,24, 24,0,0,0,12,12,0,12,0,12,24,12,0,0,24,24,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,4,0,4,4,0,4,0,0,20,20,20,20, 20,20,20,20,20,20,12,12,12,12,12,12,0,0,12,12,12,0, 12,0,0,0,0,0,12,12,0,12,0,12,0,12,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,4,4,0,4,0,0,20,20,20,20, 20,20,20,20,20,20,12,12,12,12,12,12,0,0,12,12,12,0, 12,0,0,0,0,0,12,12,0,12,0,12,0,12,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 4,0,4,0,0,20,20,20,20,20,20,20,20,20,20,12,12,12,12, 12,12,0,0,12,12,12,24,12,24,24,0,0,0,12,12,0,12,0, 12,24,12,0,0,24,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,4,0,0,20,20,20,20,20,20,20,20,20,20,12,12,12,12,12, 12,0,0,12,12,12,0,12,0,0,0,0,0,12,12,0,12,0,12,0, 12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,20,12, 12,12,12,12,12,0,0,12,12,12,0,12,0,0,0,0,0,12,12,0, 12,0,12,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10,10,10,10,10,10, 10,10,10,30,30,30,30,30,30,0,0,30,30,30,0,30,120,120, 0,0,0,30,30,0,30,0,30,0,30,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,10,10,10,10,10,10,10,10,30,30,30,30, 30,30,0,0,30,30,30,120,30,0,0,0,0,0,30,30,0,30,0,30, 120,30,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10, 10,10,10,10,10,10,30,30,30,30,30,30,0,0,30,30,30,0, 30,0,0,0,0,0,30,30,0,30,0,30,0,30,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,10,10,10,10,10,10,30,30,30, 30,30,30,0,0,30,30,30,0,30,0,0,0,0,0,30,30,0,30,0, 30,0,30,0,0,120,120,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 10,10,10,10,10,30,30,30,30,30,30,0,0,30,30,30,0,30,0, 0,0,0,0,30,30,0,30,0,30,0,30,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,10,10,10,10,30,30,30,30,30,30,0, 0,30,30,30,480,30,0,0,0,0,0,30,30,0,30,0,30,480,30, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10,10,10, 30,30,30,30,30,30,0,0,30,30,30,0,30,120,120,0,0,0,30, 30,0,30,0,30,0,30,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,10,10,30,30,30,30,30,30,0,0,30,30,30,0,30,0, 0,0,0,0,30,30,0,30,0,30,0,30,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,10,30,30,30,30,30,30,0,0,30,30, 30,0,30,0,0,0,0,0,30,30,0,30,0,30,0,30,0,0,480,480, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,30,30,30,30,30,30,0, 0,30,30,30,0,30,0,0,0,0,0,30,30,0,30,0,30,0,30,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,6,6,6,6,0,0, 6,6,6,12,6,12,12,0,0,0,6,6,0,6,0,6,12,6,0,0,12,12, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,6,6,6,0,0,6,6,6, 12,6,0,0,0,0,0,6,6,0,6,0,6,12,6,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,6,6,6,0,0,6,6,6,12,6,0,0, 0,0,0,6,6,0,6,0,6,12,6,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,6,6,0,0,6,6,6,12,6,12,12,0,0,0,6,6, 0,6,0,6,12,6,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,6,0,0,6,6,6,12,6,0,0,0,0,0,6,6,0,6,0,6,12,6, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,6,6, 12,6,0,0,0,0,0,6,6,0,6,0,6,12,6,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,6,0,6,0,0,0,0,0,6, 6,0,6,0,6,0,6,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,6,0,6,0,0,0,0,0,6,6,0,6,0,6,0,6,0,0,12,12, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,12,12,0,0,0,6, 6,0,6,0,6,0,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,12,0,0,0,0,0,12,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,6,6,0,6,0,6, 0,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0, 0,0,12,0,0,0,0,12,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,12,0,0,0,0,12,0,12,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,6,0,6,0,6,12,6,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0, 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12,96,12,96,0,60,60,60,60,60,60,60,60,60,60,12,12,12, 12,12,12,0,0,12,12,12,0,12,0,0,0,0,0,12,12,48,12,0, 12,48,12,0,0,24,24,0,108,0,0,0,0,0,0,0,0,72,0,0,72, 0,12,0,12,12,96,12,0,0,60,60,60,60,60,60,60,60,60,60, 12,12,12,12,12,12,0,0,12,12,12,0,12,0,0,0,0,0,12,12, 0,12,108,12,0,12,24,24,0,0,0,0,0,0,0,0,0,0,0,0,0, 72,0,72,0,0,12,12,0,12,0,0,60,60,60,60,60,60,60,60, 60,60,12,12,12,12,12,12,0,0,12,12,12,0,12,0,0,0,0,0, 12,12,24,12,36,12,24,12,24,24,0,0,0,0,0,0,0,0,0,0, 0,0,36,36,0,72,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0, 12,0,0,60,60,60,60,60,60,60,60,60,60,12,12,12,12,12, 12,48,0,12,12,12,0,12,0,48,0,0,0,12,12,0,12,0,12,0, 12,0,0,24,24,0,108,0,0,0,72,0,0,0,0,0,72,0,0,0,0, 12,0,0,60,60,60,60,60,60,60,60,60,60,12,12,12,12,12, 12,24,0,12,12,12,0,12,0,24,0,0,0,12,12,0,12,0,12,0, 12,0,0,0,0,0,36,0,0,0,36,0,0,0,0,0,72,0,36,0,0,0, 0,0,7680,0,0,0,0,0,0,0,0,48,0,0,0,0,0,0,0,48,0,0, 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6,12,6,12,12,0,0,0,0,0,0,0,0,0,0,0,0,36,36,0,0,0, 6,6,6,0,0,6,6,6,0,6,0,0,0,0,0,6,6,12,6,18,6,12,6, 12,12,0,0,0,0,0,0,0,0,0,0,0,0,36,36,0,0,0,6,6,0, 0,6,6,6,0,6,0,0,0,0,0,6,6,12,6,18,6,12,6,0,0,12, 12,0,0,0,0,0,0,0,0,0,0,36,36,0,0,0,6,12,0,6,6,6, 0,6,0,12,0,0,0,6,6,12,6,18,6,12,6,6,6,6,6,0,18,0, 0,0,36,0,0,0,0,36,36,0,36,0,12,0,6,6,6,0,6,0,12,0, 0,0,6,6,12,6,18,6,12,6,6,6,6,6,0,18,0,0,0,36,0,0, 0,0,36,36,0,36,0,0,12,0,12,0,12,0,6,0,0,0,12,12,6, 6,36,12,6,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,72,72,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,6,0,6,0,12,0,0, 0,6,6,12,6,18,6,12,6,6,6,6,6,0,18,0,0,0,36,0,0,0, 0,36,36,0,36,0,6,0,6,0,0,0,0,0,6,6,12,6,18,6,12,6, 0,0,12,12,0,0,0,0,0,0,0,0,0,0,36,36,0,0,0,0,6,0, 12,0,0,0,6,6,12,6,18,6,12,6,6,6,6,6,0,18,0,0,0,36, 0,0,0,0,36,36,0,36,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0, 0,6,6,12,6,18,6,12,6,6,6,6,6,0,18,0,0,0,36,0,0,0, 0,36,36,0,36,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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0,0,0,0,12,0,0,60,60,60,60,60,60,60,60,60,60,12,12, 12,12,12,12,24,24,12,12,12,0,12,0,0,24,0,0,12,12,0, 12,0,12,0,12,0,0,0,24,0,0,36,0,72,0,36,0,0,0,0,0, 0,0,36,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,60,60,60,60,60,60, 60,60,60,60,12,12,12,12,12,12,24,24,12,12,12,24,12,24, 0,24,0,0,12,12,0,12,0,12,24,12,0,24,0,24,0,0,108,0, 0,0,72,0,72,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 7680,0,0,0,0,0,0,0,48,0,0,0,0,0,0,0,0,0,0,0,0,0, 48,0,0,48,0,0,0,0,0,0,0,0,0,0,48,0,0,0,0,0,0,0,0, 144,0,0,0,0,0,0,15,15,15,15,15,15,15,15,15,30,30,30, 30,30,30,0,0,30,30,30,0,30,60,0,0,810,0,30,30,0,30, 0,30,0,30,0,60,0,0,0,0,0,0,1080,0,0,0,6480,0,0,0,0, 0,1080,15,15,15,15,15,15,15,15,30,30,30,30,30,30,0,0, 30,30,30,60,30,120,0,120,810,0,30,30,0,30,0,30,60,30, 0,120,0,120,0,0,270,0,0,0,1080,0,1080,0,0,0,0,0,0, 15,15,15,15,15,15,15,30,30,30,30,30,30,0,0,30,30,30, 60,30,60,0,0,270,0,30,30,0,30,0,30,60,30,0,60,0,0,0, 0,0,0,0,0,0,0,1080,0,0,0,0,0,0,15,15,15,15,15,15, 30,30,30,30,30,30,60,60,30,30,30,0,30,0,0,60,0,0,30, 30,0,30,0,30,0,30,0,0,0,60,0,0,0,0,1080,0,6480,0,0, 0,0,0,0,0,1080,15,15,15,15,15,30,30,30,30,30,30,120, 120,30,30,30,120,30,0,0,60,270,0,30,30,0,30,0,30,120, 30,0,0,0,60,0,0,0,0,0,0,1080,0,0,0,0,0,0,0,0,15, 15,15,15,30,30,30,30,30,30,30,30,30,30,30,30,30,30,0, 30,0,0,30,30,0,30,0,30,30,30,0,30,0,30,0,0,270,0,0, 0,6480,0,6480,0,0,0,0,0,0,15,15,15,30,30,30,30,30,30, 0,0,30,30,30,0,30,120,0,60,270,0,30,30,0,30,0,30,0, 30,0,120,0,60,0,0,810,0,6480,0,6480,0,1080,0,0,0,0,0, 6480,15,15,30,30,30,30,30,30,60,60,30,30,30,0,30,0,0, 0,0,0,30,30,0,30,0,30,0,30,0,0,0,0,0,0,270,0,1080, 0,1080,0,0,0,0,0,0,0,1080,15,30,30,30,30,30,30,30,30, 30,30,30,30,30,30,0,30,810,0,30,30,0,30,0,30,30,30,0, 30,0,30,0,0,810,0,6480,0,1080,0,0,0,0,0,0,0,6480,30, 30,30,30,30,30,0,0,30,30,30,0,30,0,0,60,0,0,30,30,0, 30,0,30,0,30,0,0,0,60,0,0,0,0,0,0,1080,0,0,0,0,0, 0,0,0,6,6,6,6,6,0,0,6,6,6,12,6,12,0,0,18,0,6,6,0, 6,0,6,12,6,0,12,0,0,0,0,0,0,36,0,0,0,36,0,0,0,0, 0,0,6,6,6,6,6,6,6,6,6,6,6,12,0,12,18,0,6,6,0,6,0, 6,6,6,0,12,0,12,0,0,18,0,36,0,36,0,36,0,0,0,0,0, 36,6,6,6,0,0,6,6,6,12,6,12,0,0,18,0,6,6,0,6,0,6, 12,6,0,12,0,0,0,0,0,0,36,0,0,0,36,0,0,0,0,0,0,6, 6,0,0,6,6,6,12,6,0,0,12,0,0,6,6,0,6,0,6,12,6,0,0, 0,12,0,0,18,0,0,0,36,0,0,0,0,0,0,0,36,6,0,0,6,6, 6,12,6,0,0,12,0,0,6,6,0,6,0,6,12,6,0,0,0,12,0,0, 18,0,0,0,36,0,0,0,0,0,0,0,36,12,12,6,6,6,12,6,6,0, 6,0,0,6,6,0,6,0,6,12,6,0,6,0,6,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,6,12,6,6,6,12,0,0,0,0,0,6,12,0,6,0, 6,6,12,0,0,0,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,72, 12,6,6,6,12,0,0,0,0,0,6,12,0,6,0,6,6,12,0,0,0,0, 0,0,0,0,0,0,0,0,72,0,0,0,0,0,72,6,6,0,6,0,0,12,0, 0,6,6,0,6,0,6,0,6,0,0,0,12,0,0,18,0,0,0,36,0,0,0, 0,0,0,0,36,6,6,6,12,0,12,18,0,6,6,0,6,0,6,6,6,0, 12,0,12,0,0,18,0,36,0,36,0,36,0,0,0,0,0,36,6,6,12, 0,12,18,0,6,6,0,6,0,6,6,6,0,12,0,12,0,0,18,0,36,0, 36,0,36,0,0,0,0,0,36,0,0,0,0,0,0,6,0,0,6,0,6,6,0, 0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,72,12,0,0, 18,0,6,6,0,6,0,6,0,6,0,12,0,0,0,0,0,0,36,0,0,0, 36,0,0,0,0,0,0,0,6,0,0,12,0,0,12,0,12,0,12,0,6,0, 6,0,0,36,0,0,0,72,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 36,0,12,12,0,12,0,12,0,0,0,6,0,6,0,0,0,0,72,0,0,0, 72,0,0,0,0,0,0,0,18,0,0,18,0,18,0,18,0,0,0,36,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,6,0,6,6,6,0, 12,0,12,0,0,18,0,36,0,36,0,36,0,0,0,0,0,36,0,6,0, 6,0,6,0,0,0,12,0,0,18,0,0,0,36,0,0,0,0,0,0,0,36, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,6,6,6,0,12,0,12,0,0,18,0,36,0,36,0,36,0,0,0,0,0, 36,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 6,6,0,12,0,12,0,0,18,0,36,0,36,0,36,0,0,0,0,0,36, 0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,72,0,12,0, 0,0,0,0,0,36,0,0,0,36,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,6,0,0,36,0,0,0,72,0,0,0, 0,0,0,0,72,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,72,0,0,0,72,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,36,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,36,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,12,12,0,12,12,0,12,0,0,60,60,60,60,60,60,60,60,60, 60,12,12,12,12,12,12,0,0,12,12,12,48,12,48,0,0,0,0, 12,12,48,12,0,12,0,12,48,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,12,0,12,12,0,12,0,0,60,60,60,60,60,60, 60,60,60,60,12,12,12,12,12,12,0,0,12,12,12,0,12,0,0, 0,0,0,12,12,0,12,0,12,0,12,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,24,12,12,24,12,12,12,60,60,60,60,60, 60,60,60,60,60,12,12,12,12,12,12,0,24,12,12,12,0,12, 24,0,0,36,36,12,12,24,12,36,12,0,12,0,0,24,0,36,36, 36,36,36,72,72,72,36,36,36,36,72,72,72,0,12,12,0,0,0, 0,0,60,0,60,0,0,60,0,60,0,0,12,0,12,0,0,24,0,12,24, 0,12,0,0,0,0,0,0,12,0,0,0,12,0,0,0,0,24,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,12,0,12,0,0,60,60,60,60, 60,60,60,60,60,60,12,12,12,12,12,12,0,48,12,12,12,0, 12,0,48,48,0,0,12,12,0,12,0,12,0,12,0,0,48,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,12,12,24,24,60,60,60,60,60, 60,60,60,60,60,12,12,12,12,12,12,0,0,12,12,12,24,12, 0,24,24,36,36,12,12,0,12,36,12,0,12,24,0,0,0,36,36, 36,72,72,36,36,36,72,72,72,72,36,36,36,0,0,0,0,960, 60,0,60,0,0,60,0,60,0,0,12,0,12,0,0,0,0,12,24,0,12, 0,0,0,0,0,0,12,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,60,60,60,60,60,60,60,60,60, 60,12,12,12,12,12,12,0,24,12,12,12,24,12,24,24,24,0, 108,12,12,24,12,0,12,0,12,24,0,24,0,108,0,0,0,0,0,0, 72,0,72,0,0,0,0,0,12,0,0,60,0,60,0,0,60,0,60,0,0, 12,0,12,0,0,0,0,12,24,24,12,0,0,0,0,0,0,12,0,0,0, 12,0,0,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,60,960,60,0,0,60,0,60,0,0,12,0,12,0,0,0,0,12,24, 0,12,0,0,0,0,0,0,12,0,0,0,12,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,15,15,15,15,15,15,15,15,15, 30,30,30,30,30,30,0,0,30,30,30,60,30,60,0,0,0,0,30, 30,60,30,0,30,0,30,60,0,0,0,0,0,0,0,38880,0,0,0,0, 0,0,38880,0,38880,38880,15,15,15,15,15,15,15,15,30,30, 30,30,30,30,0,0,30,30,30,120,30,120,0,0,0,0,30,30, 120,30,0,30,0,30,120,0,0,0,0,0,0,0,0,0,0,0,38880,0, 38880,0,0,0,0,15,15,15,15,15,15,15,30,30,30,30,30,30, 0,0,30,30,30,120,30,60,0,0,90,90,30,30,60,30,90,30,0, 30,120,0,0,0,90,90,90,180,180,180,180,180,180,180,180, 180,180,180,180,15,15,15,15,15,15,30,30,30,30,30,30,0, 120,30,30,30,0,30,0,120,120,0,0,30,30,0,30,0,30,0,30, 0,0,120,0,0,0,0,0,0,38880,38880,0,0,0,0,0,0,0,0,15, 15,15,15,15,30,30,30,30,30,30,0,60,30,30,30,60,30,0, 0,0,90,90,30,30,0,30,90,30,0,30,60,0,60,0,90,90,90, 180,180,180,180,180,180,180,180,180,180,180,180,15,15,15, 15,30,30,30,30,30,30,0,30,30,30,30,30,30,30,30,30,0, 0,30,30,30,30,0,30,0,30,30,0,30,0,0,0,0,6480,0,0,0, 6480,0,0,0,0,1080,0,0,15,15,15,30,30,30,30,30,30,0, 60,30,30,30,0,30,0,60,60,0,0,30,30,0,30,0,30,0,30,0, 0,60,0,0,0,0,0,38880,0,0,0,0,0,0,38880,0,38880,38880, 15,15,30,30,30,30,30,30,0,120,30,30,30,0,30,0,60,60, 90,90,30,30,0,30,90,30,0,30,0,0,120,0,90,90,90,180, 180,180,180,180,180,180,180,180,180,180,180,15,30,30,30, 30,30,30,0,30,30,30,30,30,30,30,30,30,0,0,30,30,30, 30,0,30,0,30,30,0,30,0,0,0,0,1080,0,0,0,0,0,6480,0, 0,6480,0,0,30,30,30,30,30,30,0,0,30,30,30,0,30,60,60, 60,90,90,30,30,60,30,90,30,0,30,0,0,0,0,90,90,90,180, 180,180,180,180,180,180,180,180,180,180,180,6,6,6,6,6, 0,0,6,6,6,12,6,12,0,0,18,0,6,6,12,6,18,6,0,6,12,0, 0,0,18,0,0,0,36,0,0,36,36,0,36,36,36,0,0,6,6,6,6, 0,0,6,6,6,12,6,12,0,0,18,0,6,6,12,6,18,6,0,6,12,0, 0,0,18,0,0,0,36,0,0,36,36,0,36,36,36,0,0,6,6,6,0, 12,6,6,6,12,6,6,6,6,18,18,6,6,6,6,18,6,0,6,12,0, 12,0,18,18,18,36,36,36,36,36,36,36,36,36,36,36,36,6, 6,0,12,6,6,6,12,6,6,6,6,0,18,6,6,6,6,0,6,0,6,12, 0,12,0,18,0,0,36,0,0,0,36,0,36,0,0,36,0,0,6,0,0,6, 6,6,12,6,0,12,12,18,18,6,6,0,6,18,6,0,6,12,0,0,0, 18,18,18,36,36,36,36,36,36,36,36,36,36,36,36,0,12,6, 6,6,12,6,6,6,6,0,18,6,6,6,6,0,6,0,6,12,0,12,0,18, 0,0,36,0,0,0,36,0,36,0,0,36,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,12,12,6,6,12,0,0,0,36,0,12,12,0,12,36, 0,0,12,6,0,6,0,36,0,0,0,72,0,0,72,72,0,72,72,72,72, 72,6,6,0,6,0,12,12,0,18,6,6,0,6,0,6,0,6,0,0,12,0, 0,18,18,36,0,36,36,0,0,36,0,0,0,36,36,6,0,6,12,0,0, 18,18,6,6,12,6,18,6,0,6,0,0,12,0,18,18,18,36,36,36, 36,36,36,36,36,36,36,36,36,6,6,12,12,12,18,0,6,6,12, 6,18,6,0,6,6,0,6,0,0,18,18,0,36,36,36,0,36,0,36,36, 0,36,36,0,0,0,0,0,36,0,12,0,12,0,12,0,12,6,0,6,0, 0,36,36,72,72,72,72,0,0,72,0,72,0,72,72,12,0,0,18, 18,6,6,12,6,18,6,0,6,0,0,12,0,18,18,18,36,36,36,36, 36,36,36,36,36,36,36,36,6,6,0,36,0,6,6,6,0,0,0,6,0, 0,0,0,0,36,36,72,0,72,72,0,0,72,0,0,0,72,72,6,36,0, 12,6,6,6,36,12,0,6,0,0,0,0,36,0,0,0,72,0,0,72,72, 0,72,72,72,0,0,36,0,12,6,6,6,36,12,0,6,0,0,0,0,36, 0,0,0,72,0,0,72,72,0,72,72,72,0,0,18,0,18,0,0,18, 18,0,0,0,0,36,0,0,0,0,36,0,0,0,0,0,36,0,0,0,0,0, 18,18,36,18,18,18,0,18,36,0,0,0,0,0,0,0,36,0,0,0, 36,0,36,36,0,0,0,6,0,6,0,6,0,6,0,0,12,0,0,18,18, 36,0,36,36,0,0,36,0,0,0,36,36,6,6,18,6,0,6,12,0,12, 0,18,18,18,36,36,36,36,36,36,36,36,36,36,36,36,6,0,0, 0,6,0,0,0,0,0,36,36,72,0,72,72,0,0,72,0,0,0,72,72, 0,6,0,6,12,0,12,0,18,0,0,36,0,0,0,36,0,36,0,0,36, 0,0,18,0,0,0,0,36,0,0,0,0,36,0,0,0,0,0,36,0,0,0, 0,0,0,6,12,0,0,0,18,18,18,36,36,36,36,36,36,36,36, 36,36,36,36,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,12,0,12,0,18,0,0,36,0,0,0,36,0,36,0,0,36,0,0, 0,6,0,0,36,36,72,72,72,72,0,0,72,0,72,0,72,72,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,36,0,0,0,72,0,0, 72,72,0,72,72,72,72,72,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,18,18,0,0,36,36,0,0,0,0,0,0,36,36,18,0,0,0,0, 36,0,0,0,0,36,0,0,0,0,0,0,36,0,0,0,0,36,0,0,36,0, 0,0,36,36,36,36,0,0,0,0,0,0,36,36,36,36,0,0,0,36, 36,0,0,0,0,36,36,36,36,0,0,0,0,36,36,36,0,0,0,0,36, 36,36,36,36,36,0,0,0,36,36,0,0,0,36,0,0,0,0,0,0,36, 36,36,4,0,4,4,8,4,0,0,20,20,20,20,20,20,20,20,20,20, 12,12,12,12,12,12,0,0,12,12,12,0,12,0,0,0,0,0,12,12, 48,12,0,12,0,12,0,48,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 24,24,24,0,4,4,8,4,0,0,20,20,20,20,20,20,20,20,20, 20,12,12,12,12,12,12,0,0,12,12,12,0,12,0,0,0,0,0,12, 12,48,12,0,12,0,12,0,48,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,24,24,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,4,0,0, 20,20,20,20,20,20,20,20,20,20,12,12,12,12,12,12,0,0, 12,12,12,24,12,24,24,0,0,0,12,12,0,12,0,12,24,12,0, 0,24,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,8,0,20, 20,20,20,20,20,20,20,20,20,12,12,12,12,12,12,0,0,12, 12,12,24,12,0,24,0,0,0,12,12,0,12,0,12,0,12,48,0,0, 24,0,0,0,0,0,0,0,0,24,24,24,0,0,0,0,0,0,0,0,160,0, 160,0,0,0,160,0,40,48,0,24,48,0,0,0,0,48,24,48,96, 24,96,0,0,0,0,0,96,96,48,0,24,48,48,0,96,96,96,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,20,20,20,20,20,20, 20,20,20,20,12,12,12,12,12,12,0,0,12,12,12,24,12,0, 24,0,0,0,12,12,0,12,0,12,0,12,48,0,0,24,0,0,0,0,0, 0,0,0,24,24,24,0,0,0,0,0,160,0,0,80,160,160,0,80,80, 40,48,0,0,48,24,0,0,0,48,96,48,0,24,96,96,0,0,0,0, 24,0,48,0,24,96,48,96,96,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20, 60,60,60,60,60,60,0,0,60,60,60,480,60,240,240,0,4860, 0,60,60,0,60,0,60,0,60,960,960,240,0,0,1620,0,0,0,0, 0,0,4320,720,4320,0,4320,4320,720,20,20,20,20,20,20,20, 20,60,60,60,60,60,60,0,0,60,60,60,240,60,240,0,0,0,0, 60,60,960,60,0,60,240,60,0,0,0,0,0,0,0,0,0,0,0,0, 720,0,4320,0,4320,720,0,20,20,20,20,20,20,20,60,60,60, 60,60,60,0,0,60,60,60,240,60,240,0,0,0,0,60,60,0,60, 0,60,0,60,0,960,0,0,0,0,0,0,0,0,0,0,4320,0,720,0, 720,720,4320,20,20,20,20,20,20,60,60,60,60,60,60,0,0, 60,60,60,0,60,0,0,0,0,0,60,60,0,60,0,60,240,60,960, 0,240,240,0,0,0,0,0,0,0,0,0,720,720,0,720,0,720,20, 20,20,20,20,60,60,60,60,60,60,0,0,60,60,60,0,60,0,0, 0,0,0,60,60,960,60,0,60,240,60,960,960,480,960,0,0,0, 0,0,0,0,0,0,4320,4320,0,720,4320,0,20,20,20,20,60,60, 60,60,60,60,0,0,60,60,60,480,60,0,0,0,0,0,60,60,960, 60,0,60,480,60,480,0,480,480,0,4860,0,0,0,0,0,0,4320, 0,720,0,720,4320,0,20,20,20,60,60,60,60,60,60,0,0,60, 60,60,0,60,240,240,0,1620,0,60,60,0,60,0,60,0,60,0, 960,0,480,0,4860,0,0,0,0,0,0,720,4320,0,0,0,720,4320, 20,20,60,60,60,60,60,60,0,0,60,60,60,0,60,480,960,0, 0,0,60,60,960,60,0,60,0,60,0,0,480,480,0,0,0,0,0,0, 0,0,4320,720,0,0,4320,0,4320,20,60,60,60,60,60,60,0,0, 60,60,60,0,60,480,480,0,4860,0,60,60,0,60,0,60,0,60, 960,0,240,480,0,0,0,0,0,0,0,0,0,4320,4320,0,4320,0, 4320,60,60,60,60,60,60,0,0,60,60,60,0,60,0,0,0,180,0, 60,60,0,60,0,60,0,60,0,0,0,960,0,180,0,0,0,0,0,0, 120,120,120,0,120,120,120,12,12,12,12,12,0,0,12,12,12, 24,12,24,24,0,108,0,12,12,48,12,0,12,24,12,48,48,24, 24,0,108,0,0,0,0,0,0,72,0,72,0,72,72,0,12,12,12,12, 0,0,12,12,12,24,12,48,0,0,108,0,12,12,48,12,0,12,24, 12,48,48,0,0,0,0,0,0,0,0,0,0,72,0,72,0,72,0,72,12, 12,12,0,0,12,12,12,24,12,24,0,0,0,0,12,12,48,12,0, 12,24,12,48,48,0,0,0,0,0,0,0,0,0,0,0,0,72,0,24,24, 24,12,12,0,0,12,12,12,24,12,24,24,0,0,0,12,12,48,12, 0,12,24,12,48,0,24,24,0,0,0,0,0,0,0,0,0,72,72,0,72, 0,72,12,0,0,12,12,12,24,12,0,48,0,0,0,12,12,48,12,0, 12,24,12,48,48,48,24,0,0,0,0,0,0,0,0,24,24,24,0,72, 0,0,0,0,12,12,12,24,12,0,24,0,0,0,12,12,48,12,0,12, 24,12,48,48,24,48,0,108,0,0,0,0,0,0,0,72,72,0,72,72, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,12,12,0,12,0,0,0,0,0,12,12,48,12,0,12,48, 12,0,0,24,24,0,108,0,0,0,0,0,0,0,72,72,0,0,72,72, 12,0,12,0,0,0,0,0,12,12,48,12,0,12,24,12,0,48,24,24, 0,0,0,0,0,0,0,0,0,72,0,0,24,24,24,0,12,24,24,0,108, 0,12,12,0,12,0,12,0,12,48,48,48,48,0,108,0,0,0,0,0, 0,72,0,72,0,0,72,72,0,0,0,0,0,0,24,48,48,24,0,0,24, 0,48,192,96,0,0,216,0,0,0,0,0,0,0,144,0,0,0,144,144, 24,24,0,108,0,12,12,0,12,0,12,0,12,48,48,48,48,0,36, 0,0,0,0,0,0,72,72,72,0,24,24,24,24,0,0,0,24,48,48, 24,0,24,96,24,0,48,96,96,0,432,0,0,0,0,0,0,0,144, 144,0,144,288,0,0,0,0,24,24,48,48,0,24,96,24,0,48,0, 0,0,0,0,0,0,0,0,0,0,0,144,0,144,0,144,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 108,0,432,108,0,36,432,108,0,0,216,432,0,0,0,0,0,0,0, 0,0,72,72,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,12,0,12,0,12,24,12,0,48, 24,24,0,108,0,0,0,0,0,0,72,72,0,0,0,72,72,48,12,0, 12,0,12,48,0,24,24,0,0,0,0,0,0,0,0,24,24,24,0,0,0, 72,48,0,0,48,0,0,192,0,192,0,432,0,0,0,0,0,0,144, 144,0,0,0,288,0,0,12,0,12,0,0,24,24,0,0,0,0,0,0,0, 0,72,72,0,0,72,0,72,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,12,48,48,0,48,0,108,0,0,0,0,0,0, 24,24,24,0,72,72,72,0,48,0,96,0,0,0,0,0,0,0,0,0, 144,144,0,0,288,0,144,48,48,48,0,0,108,0,0,0,0,0,0, 72,72,0,0,72,72,0,0,48,48,0,0,0,0,0,0,0,0,864,288, 0,0,0,144,144,48,48,0,0,0,0,0,0,0,0,0,144,144,0,864, 0,288,24,0,0,0,0,0,0,0,0,144,0,144,0,432,144,288,0, 0,0,0,0,0,0,0,144,0,0,0,144,144,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,72,0,72,0,0,0,0, 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12,0,12,24,12,0,0,24,0,0,0,0,0,0,24,24,24,0,0,0,0, 0,0,0,4,0,0,20,80,20,0,0,20,0,20,0,0,12,24,12,0,0, 0,0,12,24,0,12,0,0,0,0,0,0,12,0,0,0,12,48,24,24,48, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,20,80,20,0, 0,20,0,20,0,0,12,24,12,0,0,0,0,12,24,0,12,0,0,0,0, 0,0,12,0,0,0,12,48,24,24,48,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,60,60,60,60, 60,60,0,0,60,60,60,0,60,480,0,0,1620,0,60,60,480,60, 1620,60,240,60,0,240,0,0,0,0,0,0,2160,0,0,0,2160,0,0, 0,4320,4320,0,20,20,20,20,20,20,20,20,60,60,60,60,60, 60,0,0,60,60,60,0,60,0,0,0,0,0,60,60,240,60,0,60, 480,60,0,240,0,0,0,0,0,0,0,0,0,0,0,0,2160,2160,4320, 0,0,20,20,20,20,20,20,20,60,60,60,60,60,60,0,0,60,60, 60,0,60,240,0,0,60,60,60,60,240,60,60,60,240,60,240, 240,0,0,60,60,60,60,60,120,120,120,60,60,60,60,120,120, 120,20,20,20,20,20,20,60,60,60,60,60,60,0,480,60,60, 60,0,60,0,0,0,0,1620,60,60,240,60,1620,60,0,60,480,0, 480,0,0,0,0,2160,0,0,0,0,0,2160,0,0,0,0,0,20,20,20, 20,20,60,60,60,60,60,60,0,240,60,60,60,0,60,0,0,0,60, 60,60,60,240,60,60,60,240,60,240,240,240,0,60,60,60,60, 60,120,120,120,60,60,60,60,120,120,120,20,20,20,20,60, 60,60,60,60,60,0,240,60,60,60,0,60,240,0,0,0,0,60,60, 240,60,0,60,480,60,0,0,0,0,0,1620,1620,0,0,0,0,0,0, 0,2160,2160,4320,0,0,20,20,20,60,60,60,60,60,60,0,240, 60,60,60,0,60,480,0,0,1620,0,60,60,0,60,0,60,0,60,0, 240,240,0,0,0,0,0,2160,0,0,0,2160,0,0,0,0,0,4320,20, 20,60,60,60,60,60,60,0,240,60,60,60,0,60,240,0,0,60, 60,60,60,240,60,60,60,0,60,0,0,240,0,60,60,60,60,60, 120,120,120,60,60,60,60,120,120,120,20,60,60,60,60,60, 60,0,480,60,60,60,0,60,0,0,0,0,0,60,60,0,60,0,60, 240,60,0,240,240,0,0,0,0,2160,0,0,720,0,0,2160,0,0,0, 0,0,60,60,60,60,60,60,0,240,60,60,60,0,60,240,0,0,60, 60,60,60,240,60,60,60,240,60,0,0,0,0,60,60,60,60,60, 120,120,120,60,60,60,60,120,120,120,12,12,12,12,12,0,0, 12,12,12,0,12,24,0,0,36,0,12,12,24,12,36,12,24,12,24, 24,0,0,108,0,0,0,36,0,0,72,36,0,36,36,0,72,0,12,12, 12,12,0,0,12,12,12,0,12,24,0,0,36,0,12,12,24,12,36, 12,24,12,24,24,0,0,0,0,0,0,36,0,0,72,36,0,36,36,0, 0,72,12,12,12,0,24,12,12,12,0,12,24,0,0,36,36,12,12, 24,12,36,12,24,12,0,24,24,0,12,12,12,36,36,24,24,24, 36,36,36,36,24,24,24,12,12,0,24,12,12,12,0,12,0,0,0, 0,36,12,12,24,12,36,12,24,12,24,0,24,0,108,0,108,36, 0,0,72,0,0,36,36,36,72,0,0,12,0,0,12,12,12,0,12,0, 0,0,12,12,12,12,24,12,12,12,24,12,24,24,24,0,36,36, 36,12,12,72,72,72,12,12,12,12,72,72,72,0,24,12,12,12, 0,12,0,0,0,0,36,12,12,24,12,36,12,24,12,24,0,24,0,0, 108,0,36,0,72,0,0,0,36,36,36,72,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,24,24,0,0,24,0,0,0,72,0,24,24,48,24, 72,24,24,24,48,48,24,0,0,0,0,0,72,0,0,432,72,0,72, 72,144,144,144,12,12,0,12,0,0,0,0,36,12,12,24,12,36, 12,24,12,24,24,24,0,0,108,0,36,0,0,72,0,0,36,36,36, 0,72,0,12,0,12,24,0,0,36,36,12,12,24,12,36,12,24,12, 0,24,24,0,12,12,12,36,36,24,24,24,36,36,36,36,24,24, 24,0,12,24,0,0,36,0,12,12,24,12,36,12,24,12,24,24,24, 0,0,0,108,0,36,72,0,0,36,0,36,36,0,0,72,0,0,0,0,0, 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24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,24,24,24,0,0,0,0, 20,20,20,20,20,20,20,20,20,60,60,60,60,60,60,240,0,60, 60,60,240,60,0,480,0,0,0,60,60,0,60,0,60,0,60,240,0, 0,0,0,1620,0,0,0,2160,0,0,0,0,0,4320,0,2160,0,20,20, 20,20,20,20,20,20,60,60,60,60,60,60,0,480,60,60,60, 480,60,0,0,240,0,0,60,60,0,60,0,60,0,60,480,0,0,0, 1620,0,1620,0,0,0,0,2160,0,0,0,0,2160,0,0,20,20,20, 20,20,20,20,60,60,60,60,60,60,0,0,60,60,60,240,60,0, 240,240,60,60,60,60,0,60,60,60,0,60,240,0,0,0,60,60, 60,120,120,60,60,60,120,120,120,120,60,60,60,20,20,20, 20,20,20,60,60,60,60,60,60,240,0,60,60,60,0,60,0,0, 240,0,0,60,60,0,60,0,60,0,60,0,0,0,480,0,0,0,4320,0, 0,2160,0,0,0,0,0,0,0,2160,20,20,20,20,20,60,60,60,60, 60,60,240,240,60,60,60,240,60,0,0,240,60,60,60,60,0, 60,60,60,0,60,240,0,0,240,60,60,60,120,120,60,60,60, 120,120,120,120,60,60,60,20,20,20,20,60,60,60,60,60,60, 240,0,60,60,60,240,60,0,0,0,0,0,60,60,0,60,0,60,0, 60,480,0,0,240,0,0,0,0,0,0,0,2160,0,0,720,0,2160,0, 0,20,20,20,60,60,60,60,60,60,240,0,60,60,60,0,60,0, 480,480,0,0,60,60,0,60,0,60,0,60,0,0,0,240,0,1620, 1620,4320,4320,2160,0,0,0,0,0,0,0,2160,0,20,20,60,60, 60,60,60,60,240,240,60,60,60,0,60,0,240,240,60,60,60, 60,0,60,60,60,0,60,0,0,0,240,60,60,60,120,120,60,60, 60,120,120,120,120,60,60,60,20,60,60,60,60,60,60,0,0, 60,60,60,0,60,0,240,240,1620,0,60,60,0,60,1620,60,0, 60,240,0,0,480,0,0,0,4320,0,0,2160,0,0,0,0,0,0,0, 2160,60,60,60,60,60,60,0,0,60,60,60,0,60,0,240,240,60, 60,60,60,0,60,60,60,0,60,240,0,0,240,60,60,60,120,120, 60,60,60,120,120,120,120,60,60,60,12,12,12,12,12,24,0, 12,12,12,24,12,0,24,0,0,0,12,12,0,12,108,12,0,12,24, 0,0,0,36,36,0,0,0,36,0,36,72,0,0,72,36,36,0,12,12, 12,12,24,24,12,12,12,24,12,0,0,24,108,0,12,12,0,12,0, 12,0,12,24,0,0,24,36,0,36,0,72,0,36,36,0,0,72,0,36, 0,36,12,12,12,0,24,12,12,12,24,12,0,24,24,36,36,12, 12,0,12,36,12,0,12,24,0,0,0,12,12,12,72,72,12,12,12, 72,72,72,72,12,12,12,12,12,0,24,12,12,12,24,12,0,0, 24,0,108,12,12,0,12,108,12,0,12,24,0,0,24,36,0,36,72, 0,0,36,36,0,0,72,0,36,0,36,12,24,0,12,12,12,24,12,0, 24,24,12,12,12,12,0,12,12,12,0,12,24,0,0,24,36,36,36, 24,24,36,36,36,24,24,24,24,36,36,36,24,0,12,12,12,24, 12,0,24,0,0,0,12,12,0,12,0,12,0,12,24,0,0,0,36,36, 0,0,0,36,0,36,0,72,0,72,36,36,0,24,24,24,24,24,24,0, 24,48,0,0,24,24,0,0,432,24,0,24,48,0,0,0,72,0,72,0, 0,0,72,72,144,144,144,0,72,0,72,24,24,24,24,24,0,48, 0,0,0,24,0,0,24,0,0,0,0,48,0,0,0,72,72,0,0,0,72,0, 72,0,0,0,0,72,72,0,12,12,0,12,0,24,24,0,0,12,12,0, 12,0,12,0,12,0,0,0,24,0,36,36,0,0,36,36,0,0,72,0, 72,0,36,36,12,24,12,0,0,24,36,36,12,12,0,12,36,12,0, 12,0,0,0,24,12,12,12,72,72,12,12,12,72,72,72,72,12, 12,12,24,12,0,24,24,0,0,12,12,0,12,108,12,0,12,0,0, 0,24,0,36,36,0,0,36,36,0,72,0,0,72,0,36,36,0,0,48, 0,0,432,0,24,0,24,0,24,0,24,24,0,0,48,0,72,72,144, 144,72,72,0,0,0,0,144,0,72,72,0,24,0,36,36,12,12,0, 12,36,12,0,12,24,0,0,24,12,12,12,72,72,12,12,12,72, 72,72,72,12,12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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2026-03-28