| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/rcwa/data/ctproducts/ (GAP Algebra Version 4.15.1©) Datei vom 22.8.2025 mit Größe 330 kB |
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Impressum ctprodclass.g Sprache: unbekannt |
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Spracherkennung für: .g vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen] #############################################################################
## #W ctprodclass.g GAP4 Package `RCWA' Stefan Kohl ## ## This file contains a classification of all products of two different ## class transpositions which interchange residue classes with moduli <= 6, ## by ## ## - intersection relations between the two times two residue classes, ## - order, and ## - cycle lengths. ## ## The list `CTPairsProductClassification' has an entry for any of the 17 ## possible intersection types. Any of these entries are lists, as follows: ## ## - The first entry is a list of four integers in the range 0 .. 4, which ## specifies the intersection type. Let cl1 and cl2 be the residue classes ## which are interchanged by the first class transposition, and let cl3 ## and cl4 be the residue classes which are interchanged by the second ## class transposition. Then cl1 and cl2 are disjoint by definition, and ## the same holds for cl3 and cl4. The first entry of the list specifies ## the intersection relation between cl1 and cl3, the second entry speci- ## fies the intersection relation between cl2 and cl3, the third entry ## specifies the intersection relation between cl1 and cl4, and the fourth ## entry specifies the intersection relation between cl2 and cl4: ## ## cl1 cl2 --> transposed by first class transposition ## | \ / | ## 1| / |4 ## |/2 3\ | ## cl3 cl4 --> transposed by second class transposition ## ## The meaning of the entries is as follows: ## ## 0 = equality, 1 = subset relation, 2 = superset relation, ## 3 = disjointness, 4 = general intersection relation. ## ## - The subsequent entries are lists, one for each possible order of the ## product, as follows: ## ## - The first entry is the order <ord> of the product. ## ## - The subsequent entries are lists, one for each possible cycle type ## of the product, provided that it has order <ord>: ## ## The first entry of such a list is the cycle type. The cycle type ## is a list of length 2. The first entry is the set of cycle lengths. ## All of them occur infinitely often. The second entry is the number ## of fixed points which stem from fixed points of non-identity affine ## partial mappings. ## ## The subsequent entries are the corresponding pairs of ## class transpositions. ## ## The function `CTPairsIntersectionTypes' has been used to determine the ## 18 possible intersection types. These are the 17 which occur in the list ## `CTPairsProductClassification' and [0,3,3,0], which stands for two equal ## class transpositions. The list returned by this function is ## ## [ [ 0, 3, 3, 0 ], [ 0, 3, 3, 1 ], [ 0, 3, 3, 3 ], [ 0, 3, 3, 4 ], ## [ 1, 1, 3, 3 ], [ 1, 3, 3, 1 ], [ 1, 3, 3, 2 ], [ 1, 3, 3, 3 ], ## [ 1, 3, 3, 4 ], [ 1, 4, 3, 2 ], [ 1, 4, 3, 3 ], [ 1, 4, 3, 4 ], ## [ 3, 3, 3, 3 ], [ 3, 3, 3, 4 ], [ 3, 3, 4, 4 ], [ 3, 4, 4, 3 ], ## [ 3, 4, 4, 4 ], [ 4, 4, 4, 4 ] ] ## ## Given either 2 class transpositions or a 4-tuple of residue classes where ## the first and the second respectively the third and the fourth are ## disjoint, the function `CTPairIntersectionType' returns the corresponding ## intersection type, as described above. ## ## The function `CTPairIntersectionTypeNumber' takes the same arguments as ## `CTPairIntersectionType' (or alternatively also a list of two lists of ## length 4 of integers as returned by the function `ClassPairs'), and ## returns an integer in the range from 1 to 18, denoting the number of the ## intersection type. Here, the intersection types are numbered roughly by ## increasing "difficulty": ## ## 1 = [ 0, 3, 3, 0 ], 2 = [ 3, 3, 3, 3 ], 3 = [ 0, 3, 3, 3 ], ## 4 = [ 1, 1, 3, 3 ], 5 = [ 3, 3, 3, 4 ], 6 = [ 1, 3, 3, 3 ], ## 7 = [ 0, 3, 3, 4 ], 8 = [ 0, 3, 3, 1 ], 9 = [ 1, 3, 3, 2 ], ## 10 = [ 1, 4, 3, 2 ], 11 = [ 1, 3, 3, 1 ], 12 = [ 1, 4, 3, 3 ], ## 13 = [ 1, 3, 3, 4 ], 14 = [ 3, 4, 4, 3 ], 15 = [ 3, 3, 4, 4 ], ## 16 = [ 1, 4, 3, 4 ], 17 = [ 3, 4, 4, 4 ], 18 = [ 4, 4, 4, 4 ]. ## ## Given either 2 class transpositions or a 4-tuple of residue classes as ## described in the last sentence, the function `CTPairProductType' returns ## a list [ <intersection type>, <order>, <cycle type> ], where the entries ## have the meanings described above. ## ## The list `CTPairsProductType' contains the precomputed values of ## `CTPairProductType' for all pairs of class transpositions which ## interchange residue classes with moduli <= 6. More precisely, we have ## CTPairsProductTypes = List(CTPairs,CTPairProductType);. ## ## The entry at position (i,j) of the matrix `OrdersMatrix' is the order ## of the product of the i-th and the j-th class transposition in the list ## List(ClassPairs(6),ClassTransposition);. ## ## For the description of the components CTProds12 and CTProds32, see the ## files ctprods12.g and ctprods32.g, respectively. ## ############################################################################# return rec( CTPairs := Combinations(List(ClassPairs(6),ClassTransposition),2), CTPairsIntersectionTypes := function () local types, modV4, subsetnormal; modV4 := type->Set([type,Permuted(type,(1,2)(3,4)), Permuted(type,(1,3)(2,4)), Permuted(type,(1,4)(2,3))])[1]; subsetnormal := function ( type ) local i; if 2 in type and not 1 in type then for i in [1..4] do if type[i] = 2 then type[i] := 1; fi; od; fi; return type; end; types := Tuples([0..4],4); types := Set(types,modV4); types := Filtered(types,type->Intersection([type{[1,2]},type{[3,4]}, type{[1,3]},type{[2,4]}], [[0,0],[1,2],[2,1]]) = []); types := Set(types,subsetnormal); types := Filtered(types,type->Number(type,n->n=1)<3 and (Number(type,n->n=1)<2 or Intersection(type,[0,4])=[])); types := Filtered(types,type->type{[1,2]} in [[0,3],[1,1],[1,3], [1,4],[3,3],[3,4],[4,4]]); types := Filtered(types,type->not type{[1,3]} in [[0,1],[1,1],[1,4]]); types := Filtered(types,type->type[1]<>0 or not 4 in type{[2,3]}); types := Difference(types,[[3,4,3,4]]); return types; end, CTPairIntersectionType := function ( arg ) local cts, cls, type, indices, pair, equivalentsV4, equivalentslist, i; if Length(arg) = 1 then arg := arg[1]; fi; if Length(arg) = 2 and ForAll(arg,IsClassTransposition) then cts := arg; cls := Concatenation(List(cts,TransposedClasses)); elif Length(arg) = 4 and ForAll(arg,IsResidueClassOfZ) then cls := arg; cts := List([cls{[1,2]},cls{[3,4]}],ClassTransposition); else Error("usage: CTPairIntersectionType(<2 class transpositions>|", "<4 residue classes>)\n"); fi; type := []; for indices in [[1,3],[1,4],[2,3],[2,4]] do pair := cls{indices}; if pair[1] = pair[2] then Add(type,0); elif IsSubset(pair[1],pair[2]) then Add(type,1); elif IsSubset(pair[2],pair[1]) then Add(type,2); elif Intersection(pair[1],pair[2]) = [] then Add(type,3); else Add(type,4); fi; od; equivalentsV4 := Set([type,Permuted(type,(1,2)(3,4)), Permuted(type,(1,3)(2,4)), Permuted(type,(1,4)(2,3))]); type := equivalentsV4[1]; equivalentslist := [[[0,3,3,2],[0,3,3,1]], [[2,3,2,3],[1,1,3,3]], [[2,3,3,2],[1,3,3,1]], [[2,3,3,3],[1,3,3,3]], [[2,3,3,4],[1,3,3,4]], [[2,3,4,3],[1,4,3,3]], [[2,3,4,4],[1,4,3,4]], [[3,4,3,4],[3,3,4,4]]]; for i in [1..8] do if type = equivalentslist[i][1] then type := equivalentslist[i][2]; fi; od; return type; end, CTPairIntersectionTypeNumber := function ( arg ) local cls, type, types, indices, pair, equivalentsV4, equivalentslist, i; if Length(arg) = 1 then arg := arg[1]; fi; if Length(arg) = 2 and ForAll(arg,IsRcwaMapping) and ForAll(arg,IsClassTransposition) then cls := Concatenation(List(arg,TransposedClasses)); cls := List(cls,cl->[Residue(cl),Modulus(cl)]); elif Length(arg) = 4 and ForAll(arg,IsResidueClassOfZ) then cls := List(arg,cl->[Residue(cl),Modulus(cl)]); elif Length(arg) = 2 and ForAll(arg,l->IsList(l) and Length(l) = 4 and ForAll(l,IsInt)) then cls := [arg[1]{[1,2]},arg[1]{[3,4]},arg[2]{[1,2]},arg[2]{[3,4]}]; else Error("usage: CTPairIntersectionType(<2 class transpositions>|", "<4 residue classes>|", "<2 lists of 4 integers>)\n"); fi; type := []; for indices in [[1,3],[1,4],[2,3],[2,4]] do pair := cls{indices}; if pair[1] = pair[2] then Add(type,0); elif pair[2][2] mod pair[1][2] = 0 and pair[2][1] mod pair[1][2] = pair[1][1] then # IsSubset(pair[1],pair[2]) Add(type,1); elif pair[1][2] mod pair[2][2] = 0 and pair[1][1] mod pair[2][2] = pair[2][1] then # IsSubset(pair[2],pair[1]) Add(type,2); elif (pair[1][1]-pair[2][1]) mod Gcd(pair[1][2],pair[2][2]) <> 0 then # Intersection(pair[1],pair[2]) = [] Add(type,3); else Add(type,4); fi; od; equivalentsV4 := Set([type,Permuted(type,(1,2)(3,4)), Permuted(type,(1,3)(2,4)), Permuted(type,(1,4)(2,3))]); type := equivalentsV4[1]; equivalentslist := [[[0,3,3,2],[0,3,3,1]], [[2,3,2,3],[1,1,3,3]], [[2,3,3,2],[1,3,3,1]], [[2,3,3,3],[1,3,3,3]], [[2,3,3,4],[1,3,3,4]], [[2,3,4,3],[1,4,3,3]], [[2,3,4,4],[1,4,3,4]], [[3,4,3,4],[3,3,4,4]]]; for i in [1..8] do if type = equivalentslist[i][1] then type := equivalentslist[i][2]; fi; od; types := [[0,3,3,0],[3,3,3,3],[0,3,3,3],[1,1,3,3],[3,3,3,4],[1,3,3,3], [0,3,3,4],[0,3,3,1],[1,3,3,2],[1,4,3,2],[1,3,3,1],[1,4,3,3], [1,3,3,4],[3,4,4,3],[3,3,4,4],[1,4,3,4],[3,4,4,4],[4,4,4,4]]; return Position(types,type); end, CTPairProductType := function ( arg ) local result, cls, cts, g, intertype, order, cycletype, CTPairIntersectionType; if Length(arg) = 1 then arg := arg[1]; fi; if Length(arg) = 2 and ForAll(arg,IsClassTransposition) then cts := arg; cls := Concatenation(List(cts,TransposedClasses)); elif Length(arg) = 4 and ForAll(arg,IsResidueClassOfZ) then cls := arg; cts := List([cls{[1,2]},cls{[3,4]}],ClassTransposition); else Error("usage: CTPairProductType(<2 class transpositions>|", "<4 residue classes>)\n"); fi; if IsBoundGlobal("CTPairIntersectionType") then CTPairIntersectionType := ValueGlobal("CTPairIntersectionType"); else CTPairIntersectionType := LoadDatabaseOfProductsOf2ClassTranspositions().CTPairIntersectionType; fi; intertype := CTPairIntersectionType(cls); g := Product(cts); order := Order(g); cycletype := Set(ShortCycles(g,[-1000..1000],20),Length); if Density(Support(g)) = 1 then cycletype := Difference(cycletype,[1]); fi; if IsSubset(cycletype,[1,2,3,4,5,6,7]) then cycletype := PositiveIntegers; elif IsSubset(cycletype,[1,3,5,7]) then cycletype := ResidueClass(1,2); elif IsSubset(cycletype,[2,4,6,8]) and Density(Support(g)) = 1 then cycletype := ResidueClass(0,2); elif IsSubset(cycletype,[2,4,6,8]) and Density(Support(g)) < 1 then cycletype := Union(ResidueClass(0,2),[1]); elif order = infinity then Add(cycletype,infinity); fi; cycletype := [cycletype,Length(ExcludedElements(Support(g)))]; return [ intertype, order, cycletype ]; end, CTPairsProductClassification := [ [ [ 0, 3, 3, 1 ], [ infinity, [ [ [ infinity ], 2 ], [ ClassTransposition(0,2,1,2), ClassTransposition(0,2,1,4) ], [ ClassTransposition(0,2,1,2), ClassTransposition(0,2,3,4) ], [ ClassTransposition(0,2,1,2), ClassTransposition(0,2,1,6) ], [ ClassTransposition(0,2,1,2), ClassTransposition(0,2,5,6) ], [ ClassTransposition(0,2,1,2), ClassTransposition(1,2,0,4) ], [ ClassTransposition(0,2,1,2), ClassTransposition(1,2,2,4) ], [ ClassTransposition(0,2,1,2), ClassTransposition(1,2,0,6) ], [ ClassTransposition(0,2,1,2), ClassTransposition(1,2,4,6) ] ], [ [ [ 1, infinity ], 2 ], [ ClassTransposition(0,2,1,4), ClassTransposition(0,4,1,4) ], [ ClassTransposition(0,2,1,4), ClassTransposition(1,4,2,4) ], [ ClassTransposition(0,2,1,4), ClassTransposition(1,4,0,6) ], [ ClassTransposition(0,2,1,4), ClassTransposition(1,4,4,6) ], [ ClassTransposition(0,2,3,4), ClassTransposition(0,4,3,4) ], [ ClassTransposition(0,2,3,4), ClassTransposition(2,4,3,4) ], [ ClassTransposition(0,2,3,4), ClassTransposition(3,4,0,6) ], [ ClassTransposition(0,2,3,4), ClassTransposition(3,4,4,6) ], [ ClassTransposition(0,2,1,6), ClassTransposition(0,4,1,6) ], [ ClassTransposition(0,2,1,6), ClassTransposition(2,4,1,6) ], [ ClassTransposition(0,2,1,6), ClassTransposition(0,6,1,6) ], [ ClassTransposition(0,2,1,6), ClassTransposition(1,6,4,6) ], [ ClassTransposition(0,2,3,6), ClassTransposition(0,4,3,6) ], [ ClassTransposition(0,2,3,6), ClassTransposition(2,4,3,6) ], [ ClassTransposition(0,2,3,6), ClassTransposition(0,6,3,6) ], [ ClassTransposition(0,2,3,6), ClassTransposition(3,6,4,6) ], [ ClassTransposition(0,2,5,6), ClassTransposition(0,4,5,6) ], [ ClassTransposition(0,2,5,6), ClassTransposition(2,4,5,6) ], [ ClassTransposition(0,2,5,6), ClassTransposition(0,6,5,6) ], [ ClassTransposition(0,2,5,6), ClassTransposition(4,6,5,6) ], [ ClassTransposition(1,2,0,4), ClassTransposition(0,4,1,4) ], [ ClassTransposition(1,2,0,4), ClassTransposition(0,4,3,4) ], [ ClassTransposition(1,2,0,4), ClassTransposition(0,4,1,6) ], [ ClassTransposition(1,2,0,4), ClassTransposition(0,4,5,6) ], [ ClassTransposition(1,2,2,4), ClassTransposition(1,4,2,4) ], [ ClassTransposition(1,2,2,4), ClassTransposition(2,4,3,4) ], [ ClassTransposition(1,2,2,4), ClassTransposition(2,4,1,6) ], [ ClassTransposition(1,2,2,4), ClassTransposition(2,4,5,6) ], [ ClassTransposition(1,2,0,6), ClassTransposition(1,4,0,6) ], [ ClassTransposition(1,2,0,6), ClassTransposition(3,4,0,6) ], [ ClassTransposition(1,2,0,6), ClassTransposition(0,6,1,6) ], [ ClassTransposition(1,2,0,6), ClassTransposition(0,6,5,6) ], [ ClassTransposition(1,2,2,6), ClassTransposition(1,4,2,6) ], [ ClassTransposition(1,2,2,6), ClassTransposition(3,4,2,6) ], [ ClassTransposition(1,2,2,6), ClassTransposition(1,6,2,6) ], [ ClassTransposition(1,2,2,6), ClassTransposition(2,6,5,6) ], [ ClassTransposition(1,2,4,6), ClassTransposition(1,4,4,6) ], [ ClassTransposition(1,2,4,6), ClassTransposition(3,4,4,6) ], [ ClassTransposition(1,2,4,6), ClassTransposition(1,6,4,6) ], [ ClassTransposition(1,2,4,6), ClassTransposition(4,6,5,6) ], [ ClassTransposition(0,3,1,3), ClassTransposition(0,3,1,6) ], [ ClassTransposition(0,3,1,3), ClassTransposition(0,3,4,6) ], [ ClassTransposition(0,3,1,3), ClassTransposition(1,3,0,6) ], [ ClassTransposition(0,3,1,3), ClassTransposition(1,3,3,6) ], [ ClassTransposition(0,3,2,3), ClassTransposition(0,3,2,6) ], [ ClassTransposition(0,3,2,3), ClassTransposition(0,3,5,6) ], [ ClassTransposition(0,3,2,3), ClassTransposition(2,3,0,6) ], [ ClassTransposition(0,3,2,3), ClassTransposition(2,3,3,6) ], [ ClassTransposition(0,3,1,6), ClassTransposition(0,6,1,6) ], [ ClassTransposition(0,3,1,6), ClassTransposition(1,6,3,6) ], [ ClassTransposition(0,3,2,6), ClassTransposition(0,6,2,6) ], [ ClassTransposition(0,3,2,6), ClassTransposition(2,6,3,6) ], [ ClassTransposition(0,3,4,6), ClassTransposition(0,6,4,6) ], [ ClassTransposition(0,3,4,6), ClassTransposition(3,6,4,6) ], [ ClassTransposition(0,3,5,6), ClassTransposition(0,6,5,6) ], [ ClassTransposition(0,3,5,6), ClassTransposition(3,6,5,6) ], [ ClassTransposition(1,3,2,3), ClassTransposition(1,3,2,6) ], [ ClassTransposition(1,3,2,3), ClassTransposition(1,3,5,6) ], [ ClassTransposition(1,3,2,3), ClassTransposition(2,3,1,6) ], [ ClassTransposition(1,3,2,3), ClassTransposition(2,3,4,6) ], [ ClassTransposition(1,3,0,6), ClassTransposition(0,6,1,6) ], [ ClassTransposition(1,3,0,6), ClassTransposition(0,6,4,6) ], [ ClassTransposition(1,3,2,6), ClassTransposition(1,6,2,6) ], [ ClassTransposition(1,3,2,6), ClassTransposition(2,6,4,6) ], [ ClassTransposition(1,3,3,6), ClassTransposition(1,6,3,6) ], [ ClassTransposition(1,3,3,6), ClassTransposition(3,6,4,6) ], [ ClassTransposition(1,3,5,6), ClassTransposition(1,6,5,6) ], [ ClassTransposition(1,3,5,6), ClassTransposition(4,6,5,6) ], [ ClassTransposition(2,3,0,6), ClassTransposition(0,6,2,6) ], [ ClassTransposition(2,3,0,6), ClassTransposition(0,6,5,6) ], [ ClassTransposition(2,3,1,6), ClassTransposition(1,6,2,6) ], [ ClassTransposition(2,3,1,6), ClassTransposition(1,6,5,6) ], [ ClassTransposition(2,3,3,6), ClassTransposition(2,6,3,6) ], [ ClassTransposition(2,3,3,6), ClassTransposition(3,6,5,6) ], [ ClassTransposition(2,3,4,6), ClassTransposition(2,6,4,6) ], [ ClassTransposition(2,3,4,6), ClassTransposition(4,6,5,6) ] ], [ [ [ infinity ], 0 ], [ ClassTransposition(0,2,1,2), ClassTransposition(0,2,3,6) ], [ ClassTransposition(0,2,1,2), ClassTransposition(1,2,2,6) ] ], [ [ [ 1, infinity ], 0 ], [ ClassTransposition(0,2,1,4), ClassTransposition(1,4,2,6) ], [ ClassTransposition(0,2,3,4), ClassTransposition(3,4,2,6) ], [ ClassTransposition(0,2,1,6), ClassTransposition(1,6,2,6) ], [ ClassTransposition(0,2,3,6), ClassTransposition(2,6,3,6) ], [ ClassTransposition(0,2,5,6), ClassTransposition(2,6,5,6) ], [ ClassTransposition(1,2,0,4), ClassTransposition(0,4,3,6) ], [ ClassTransposition(1,2,2,4), ClassTransposition(2,4,3,6) ], [ ClassTransposition(1,2,0,6), ClassTransposition(0,6,3,6) ], [ ClassTransposition(1,2,2,6), ClassTransposition(2,6,3,6) ], [ ClassTransposition(1,2,4,6), ClassTransposition(3,6,4,6) ] ] ] ], [ [ 0, 3, 3, 3 ], [ 3, [ [ [ 3 ], 0 ], [ ClassTransposition(0,2,1,4), ClassTransposition(0,2,3,4) ], [ ClassTransposition(0,2,1,4), ClassTransposition(1,4,3,4) ], [ ClassTransposition(0,2,3,4), ClassTransposition(1,4,3,4) ], [ ClassTransposition(1,2,0,4), ClassTransposition(1,2,2,4) ], [ ClassTransposition(1,2,0,4), ClassTransposition(0,4,2,4) ], [ ClassTransposition(1,2,2,4), ClassTransposition(0,4,2,4) ], [ ClassTransposition(0,3,1,3), ClassTransposition(0,3,2,3) ], [ ClassTransposition(0,3,1,3), ClassTransposition(1,3,2,3) ], [ ClassTransposition(0,3,2,3), ClassTransposition(1,3,2,3) ] ], [ [ [ 1, 3 ], 0 ], [ ClassTransposition(0,2,1,6), ClassTransposition(0,2,3,6) ], [ ClassTransposition(0,2,1,6), ClassTransposition(0,2,5,6) ], [ ClassTransposition(0,2,1,6), ClassTransposition(1,6,3,6) ], [ ClassTransposition(0,2,1,6), ClassTransposition(1,6,5,6) ], [ ClassTransposition(0,2,3,6), ClassTransposition(0,2,5,6) ], [ ClassTransposition(0,2,3,6), ClassTransposition(1,6,3,6) ], [ ClassTransposition(0,2,3,6), ClassTransposition(3,6,5,6) ], [ ClassTransposition(0,2,5,6), ClassTransposition(1,6,5,6) ], [ ClassTransposition(0,2,5,6), ClassTransposition(3,6,5,6) ], [ ClassTransposition(1,2,0,6), ClassTransposition(1,2,2,6) ], [ ClassTransposition(1,2,0,6), ClassTransposition(1,2,4,6) ], [ ClassTransposition(1,2,0,6), ClassTransposition(0,6,2,6) ], [ ClassTransposition(1,2,0,6), ClassTransposition(0,6,4,6) ], [ ClassTransposition(1,2,2,6), ClassTransposition(1,2,4,6) ], [ 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PositiveIntegers, 2 ] ], [ [ 3, 4, 4, 3 ], infinity, [ PositiveIntegers, 0 ] ], [ [ 0, 3, 3, 3 ], 3, [ [ 1, 3 ], 0 ] ], [ [ 0, 3, 3, 3 ], 3, [ [ 1, 3 ], 0 ] ], [ [ 0, 3, 3, 3 ], 3, [ [ 1, 3 ], 0 ] ] ], OrdersMatrix := [ [ 1, infinity, infinity, infinity, infinity, infinity, 4, infinity, 6, infinity, 4, 4, 2, infinity, 4, 4, infinity, infinity, 4, 4, 4, 6, 2, 4, 4, 4, 4, infinity, infinity, infinity, infinity, infinity, infinity, 4, 4, 4, infinity, infinity, 4, infinity, 4, infinity, 4, 4, 4, 4, 4, 4, 4, 4, 4, infinity, infinity, infinity, 2, infinity, infinity, 4, 4, 2, 4, 4, infinity, infinity, infinity, 4, 4, 4, 2 ], [ infinity, 1, infinity, 3, infinity, infinity, infinity, 6, 15, 12, infinity, 12, infinity, infinity, 4, 6, infinity, infinity, infinity, 30, 12, 6, infinity, 4, 12, 4, 12, infinity, infinity, infinity, infinity, infinity, infinity, 30, 12, 6, 12, infinity, infinity, infinity, 3, infinity, 12, 30, 30, 12, 6, 12, 4, 6, 10, 30, 6, infinity, 6, infinity, infinity, infinity, 30, 12, 4, infinity, 6, 6, 6, 30, infinity, 6, 12 ], [ infinity, infinity, 1, infinity, 3, 3, infinity, infinity, 4, 12, 12, 6, infinity, infinity, 4, 12, 6, 6, infinity, 30, infinity, 12, infinity, 4, 6, 4, 6, infinity, infinity, infinity, infinity, infinity, infinity, infinity, infinity, 12, 12, infinity, 12, infinity, 6, infinity, 30, 12, infinity, infinity, 3, infinity, 3, 12, infinity, 6, 12, infinity, infinity, 6, 6, 30, 30, 6, 4, 6, infinity, infinity, infinity, infinity, 6, 2, 6 ], [ infinity, 3, infinity, 1, infinity, infinity, 30, 30, 15, 6, 6, 30, 6, infinity, 4, infinity, infinity, infinity, infinity, 30, infinity, 4, 12, 4, infinity, 4, 12, infinity, infinity, infinity, infinity, infinity, 12, infinity, infinity, 12, 6, 6, 6, 6, 3, 6, 30, 12, infinity, infinity, 6, 12, 4, 12, 20, 12, infinity, infinity, infinity, infinity, infinity, 30, 30, 12, 4, 12, infinity, infinity, infinity, infinity, 12, 6, infinity ], [ infinity, infinity, 3, infinity, 1, 3, infinity, 12, 6, infinity, infinity, 12, 12, 6, 4, infinity, infinity, 6, 30, 12, infinity, 30, 6, 4, infinity, 4, 6, infinity, infinity, infinity, infinity, infinity, 12, 6, 12, infinity, 6, infinity, infinity, infinity, 6, infinity, 30, 30, 30, 6, 3, 6, 2, 12, 6, infinity, 12, 6, 12, infinity, 6, infinity, 30, infinity, 4, 6, infinity, infinity, infinity, 12, infinity, 3, 6 ], [ infinity, infinity, 3, infinity, 3, 1, 6, 6, 6, 12, 12, infinity, infinity, 6, 4, 12, 6, infinity, 30, 30, 30, 30, 6, 4, 6, 4, infinity, infinity, infinity, infinity, infinity, infinity, 12, infinity, 12, 6, infinity, infinity, 12, infinity, 6, infinity, infinity, 30, 12, 6, 2, 6, 3, infinity, 12, 12, infinity, 6, infinity, 6, infinity, 12, 30, 6, 4, infinity, infinity, infinity, infinity, infinity, 6, 3, infinity ], [ 4, infinity, infinity, 30, infinity, 6, 1, infinity, 3, 3, infinity, 3, 6, infinity, 12, 6, infinity, 6, 6, 12, 4, 4, 2, 6, 4, 4, 6, infinity, infinity, 30, 6, infinity, infinity, 3, 3, infinity, 3, infinity, 6, 6, 12, infinity, 6, 12, 4, 6, 4, 4, 6, 6, 6, 6, 6, infinity, 6, infinity, 6, 6, 12, 6, 6, 2, infinity, 6, infinity, 6, 2, 6, 6 ], [ infinity, 6, infinity, 30, 12, 6, infinity, 1, 3, 3, 3, 3, infinity, infinity, 6, 30, 12, 6, infinity, infinity, 12, 30, infinity, 6, 4, 6, 6, infinity, infinity, 6, 12, 12, infinity, 6, 6, infinity, 6, infinity, 12, 6, 20, 6, 12, 12, 30, 3, infinity, 3, 3, 6, 3, 6, 2, infinity, 20, 12, 6, 12, 60, 6, 2, 2, 12, 12, 12, 30, 6, 6, 2 ], [ 6, 15, 4, 15, 6, 6, 3, 3, 1, infinity, 3, infinity, 12, 6, 4, 4, 12, 12, 12, 6, 6, 12, 6, 2, 4, 6, 4, 15, 6, 15, 6, 4, 6, 3, 6, 6, 6, 12, 12, 12, 4, 6, 12, 6, 6, 6, 6, 2, 6, infinity, 3, infinity, 3, 6, 12, 12, 12, 12, 6, 4, 6, 4, 12, 12, 6, 12, 6, 2, 6 ], [ infinity, 12, 12, 6, infinity, 12, 3, 3, infinity, 1, 3, 3, infinity, 6, infinity, 30, infinity, 6, 12, infinity, 30, infinity, 6, infinity, 4, 6, 6, 12, 12, 30, infinity, 6, 6, 6, 3, 6, 2, 12, 12, infinity, 6, 6, infinity, 30, 30, 3, 6, 2, 2, infinity, 6, infinity, 6, 12, 20, 12, 12, 60, 12, infinity, 3, 3, 12, infinity, 6, 30, 6, 6, 2 ], [ 4, infinity, 12, 6, infinity, 12, infinity, 3, 3, 3, 1, 3, 12, 12, infinity, 30, 12, 12, 30, 12, 30, infinity, 6, 6, 4, infinity, 6, 20, 12, 10, 6, infinity, infinity, 6, 6, infinity, 6, 12, infinity, 6, 6, infinity, 60, 30, 30, 2, 6, 3, 2, 6, 2, 6, 3, 6, 12, infinity, 6, infinity, infinity, 6, 3, 2, 12, 6, infinity, 12, infinity, 6, 3 ], [ 4, 12, 6, 30, 12, infinity, 3, 3, infinity, 3, 3, 1, 12, 6, 6, 30, 12, infinity, 30, 60, 30, 30, 6, 6, 4, 6, infinity, 12, infinity, 6, 12, 12, 6, 6, 2, 6, 3, infinity, infinity, 6, infinity, 6, 12, 12, 12, 2, 6, 2, 3, infinity, 6, infinity, 6, 6, 12, 12, infinity, 12, infinity, 6, 2, 3, 12, 12, 12, infinity, 6, infinity, 3 ], [ 2, infinity, infinity, 6, 12, infinity, 6, infinity, 12, infinity, 12, 12, 1, infinity, 3, 3, infinity, infinity, 6, 6, 12, 6, 2, 6, 6, 4, 4, infinity, infinity, 6, 12, infinity, infinity, 6, 12, 12, 20, infinity, 3, infinity, 3, infinity, 6, 6, 12, 6, 6, 4, 4, 12, 12, 20, 20, 6, 2, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 2 ], [ infinity, infinity, infinity, infinity, 6, 6, infinity, infinity, 6, 6, 12, 6, infinity, 1, 3, infinity, 3, 3, infinity, 6, 60, 12, infinity, 6, 6, 4, 6, infinity, infinity, 6, infinity, infinity, infinity, infinity, 12, 12, 12, infinity, 6, infinity, 6, infinity, 12, 12, 12, infinity, 3, infinity, 3, 12, infinity, 6, 12, 3, 6, 2, 2, 60, 4, 6, 6, 6, infinity, infinity, infinity, 60, 6, 2, 6 ], [ 4, 4, 4, 4, 4, 4, 12, 6, 4, infinity, infinity, 6, 3, 3, 1, 3, 3, 3, 6, 4, 12, 4, 6, 4, 6, 6, 6, 3, 6, 3, 6, 6, infinity, 12, infinity, 6, 6, 6, 3, 6, 2, 6, 6, 4, 12, 6, 2, 6, 2, infinity, 6, 6, 20, 3, 3, 3, 3, 6, 4, 6, 4, 6, 6, 6, 6, 6, 6, 2, 6 ], [ 4, 6, 12, infinity, infinity, 12, 6, 30, 4, 30, 30, 30, 3, infinity, 3, 1, infinity, infinity, 12, 12, 6, 4, 6, 6, 2, 4, 6, infinity, 12, 6, infinity, 12, 30, 6, 30, 30, 30, 6, 2, 6, 3, 6, 12, 12, 6, 4, 6, 4, 4, 30, 30, 30, 30, 6, 3, 6, 6, 12, 12, 6, 6, 2, infinity, infinity, infinity, 12, 4, 6, 6 ], [ infinity, infinity, 6, infinity, infinity, 6, infinity, 12, 12, infinity, 12, 12, infinity, 3, 3, infinity, 1, 3, 12, 6, infinity, 30, 6, 6, infinity, 4, 6, infinity, infinity, 6, infinity, infinity, 6, 6, 12, infinity, 6, infinity, 6, infinity, 6, infinity, infinity, 6, 60, 6, 3, 6, 2, 12, 6, infinity, 12, 2, 6, 3, 2, 12, 12, infinity, 6, 6, infinity, infinity, infinity, 60, infinity, 3, 6 ], [ infinity, infinity, 6, infinity, 6, infinity, 6, 6, 12, 6, 12, infinity, infinity, 3, 3, infinity, 3, 1, 60, 12, 60, 30, 6, 6, 6, 4, infinity, infinity, infinity, 6, infinity, infinity, 6, infinity, 12, 6, infinity, infinity, 6, infinity, 6, infinity, 12, 6, infinity, 6, 2, 6, 3, 12, 12, 12, 12, 2, 6, 2, 3, infinity, 6, 6, 6, infinity, infinity, infinity, infinity, 12, 6, 3, infinity ], [ 4, infinity, infinity, infinity, 30, 30, 6, infinity, 12, 12, 30, 30, 6, infinity, 6, 12, 12, 60, 1, 3, 3, 3, 6, 6, 6, 12, 6, infinity, infinity, 30, 12, infinity, infinity, 6, 60, 12, 12, infinity, 6, 12, 6, 60, 3, 3, 3, 6, 6, 6, 12, infinity, 12, 30, 30, 12, 6, 60, 60, 2, 2, 6, 6, 6, 12, 60, 60, 2, 6, 6, 6 ], [ 4, 30, 30, 30, 12, 30, 12, infinity, 6, infinity, 12, 60, 6, 6, 4, 12, 6, 12, 3, 1, 3, 3, 6, 6, 12, 12, 4, 30, 30, 30, 30, 30, 30, 12, 30, 12, 60, 6, 6, 6, 4, 12, 3, 2, 2, 6, 6, 12, 12, infinity, infinity, 12, 60, 6, 6, 12, 4, 3, 3, 6, 6, 12, 6, 12, 4, 2, 6, 6, 6 ], [ 4, 12, infinity, infinity, infinity, 30, 4, 12, 6, 30, 30, 30, 12, 60, 12, 6, infinity, 60, 3, 3, 1, 3, 6, 12, 4, 6, 4, infinity, 12, 30, 30, infinity, 30, 4, 30, 12, 30, 60, 12, infinity, 12, 60, 2, 3, 2, 6, 12, 4, 6, 12, 30, 30, 30, infinity, 12, 60, 12, 3, 2, 6, 12, 4, infinity, 60, 12, 3, 6, 12, 6 ], [ 6, 6, 12, 4, 30, 30, 4, 30, 12, infinity, infinity, 30, 6, 12, 4, 4, 30, 30, 3, 3, 3, 1, 12, 12, 6, 6, 4, 4, 30, 6, 30, 12, 12, 4, 60, 60, 12, 12, 6, 30, 4, 30, 2, 2, 3, 12, 12, 6, 6, 30, infinity, infinity, 30, 30, 6, 30, 12, 2, 3, 12, 12, 6, 30, 30, 12, 3, 12, 12, 12 ], [ 2, infinity, infinity, 12, 6, 6, 2, infinity, 6, 6, 6, 6, 2, infinity, 6, 6, 6, 6, 6, 6, 6, 12, 1, 3, 3, 3, 3, infinity, infinity, 12, 6, 6, infinity, 6, 6, 6, 6, infinity, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 2, 2, infinity, 2, 6, 6, 6, 6, 2, 2, 2, infinity, 6, 6, 6, 2, 2, 2 ], [ 4, 4, 4, 4, 4, 4, 6, 6, 2, infinity, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 12, 12, 3, 1, 3, 3, 3, 6, 3, 6, 3, 2, 3, 6, 3, 2, 2, 3, 6, 3, 2, 2, 6, 6, 12, 3, 2, 2, 2, infinity, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 2, 6, 2, 2, 2 ], [ 4, 12, 6, infinity, infinity, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 2, infinity, 6, 6, 12, 4, 6, 3, 3, 1, 3, 3, 12, infinity, infinity, 6, 6, 3, 2, 2, 3, 2, infinity, 4, 6, 6, 6, 6, 12, 4, 2, 3, 2, 2, 3, 2, 3, 2, 6, 6, infinity, 6, 6, 12, 3, 2, 2, infinity, 6, 6, 6, 3, 3, 2 ], [ 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, infinity, 6, 4, 4, 6, 4, 4, 4, 12, 12, 6, 6, 3, 3, 3, 1, 3, 4, 3, 4, 2, 3, infinity, 6, 6, 6, 6, 3, 4, 2, 2, 3, 12, 12, 6, 2, 2, 3, 2, 3, 2, 2, 3, 4, 4, 4, 4, 12, 12, 2, 3, 2, 3, 2, 3, 12, 3, 2, 3 ], [ 4, 12, 6, 12, 6, infinity, 6, 6, 4, 6, 6, infinity, 4, 6, 6, 6, 6, infinity, 6, 4, 4, 4, 3, 3, 3, 3, 1, 12, infinity, 12, 6, 6, 3, 6, 2, 2, 3, infinity, 4, 6, 6, 6, 6, 4, 4, 2, 2, 2, 3, infinity, 6, 6, 6, 6, 4, 6, infinity, 6, 4, 2, 2, 3, infinity, 6, 6, 6, 2, 3, 3 ], [ infinity, infinity, infinity, infinity, infinity, infinity, infinity, infinity, 15, 12, 20, 12, infinity, infinity, 3, infinity, infinity, infinity, infinity, 30, infinity, 4, infinity, 6, 12, 4, 12, 1, infinity, 3, infinity, infinity, 6, 30, 12, infinity, 12, infinity, 6, infinity, 4, infinity, 30, 12, infinity, 12, 4, 12, 4, 30, 6, 6, 30, 6, 6, 6, 6, 30, 30, 12, 6, infinity, infinity, infinity, infinity, infinity, infinity, 4, 12 ], [ infinity, infinity, infinity, infinity, infinity, infinity, infinity, infinity, 6, 12, 12, infinity, infinity, infinity, 6, 12, infinity, infinity, infinity, 30, 12, 30, infinity, 3, infinity, 3, infinity, infinity, 1, infinity, 3, 3, infinity, 6, 6, 12, 12, infinity, 12, 6, 4, 6, 12, 30, 30, 6, 4, 6, 4, infinity, 12, 12, 6, infinity, infinity, infinity, infinity, infinity, 30, 6, 2, 6, infinity, 6, 6, 30, 6, 4, 6 ] , [ infinity, infinity, infinity, infinity, infinity, infinity, 30, 6, 15, 30, 10, 6, 6, 6, 3, 6, 6, 6, 30, 30, 30, 6, 12, 6, infinity, 4, 12, 3, infinity, 1, infinity, infinity, 12, infinity, 6, 12, infinity, infinity, infinity, infinity, 4, infinity, infinity, 30, 12, infinity, 4, 12, 4, 12, infinity, 12, 6, infinity, infinity, infinity, infinity, 12, 30, 12, 6, 12, infinity, infinity, infinity, infinity, 12, 4, infinity ], [ infinity, infinity, infinity, infinity, infinity, infinity, 6, 12, 6, infinity, 6, 12, 12, infinity, 6, infinity, infinity, infinity, 12, 30, 30, 30, 6, 3, 6, 2, 6, infinity, 3, infinity, 1, 3, 6, infinity, infinity, 12, 12, 6, infinity, infinity, 4, 6, infinity, 30, infinity, infinity, 4, 6, 4, 12, infinity, infinity, 12, infinity, 12, infinity, infinity, 30, 12, infinity, 3, infinity, 6, infinity, 6, 30, 6, 4, 6 ], [ infinity, infinity, infinity, infinity, infinity, infinity, infinity, 12, 4, 6, infinity, 12, infinity, infinity, 6, 12, infinity, infinity, infinity, 30, infinity, 12, 6, 2, 6, 3, 6, infinity, 3, infinity, 3, 1, 12, infinity, 12, infinity, infinity, 6, 12, 6, 4, infinity, 30, 12, infinity, 6, 4, infinity, 4, 6, 12, 12, infinity, infinity, infinity, infinity, infinity, 30, 30, 6, 3, 6, 6, 6, infinity, infinity, infinity, 4, infinity ], [ infinity, infinity, infinity, 12, 12, 12, infinity, infinity, 6, 6, infinity, 6, infinity, infinity, infinity, 30, 6, 6, infinity, 30, 30, 12, infinity, 3, 3, infinity, 3, 6, infinity, 12, 6, 12, 1, 3, 3, 3, 3, infinity, 12, 6, 6, 12, 60, 12, 30, 6, 6, 4, 6, 3, 6, 2, 6, 12, 20, 12, 12, 30, 60, 2, 6, 2, infinity, 6, 12, 12, 6, 2, 6 ], [ 4, 30, infinity, infinity, 6, infinity, 3, 6, 3, 6, 6, 6, 6, infinity, 12, 6, 6, infinity, 6, 12, 4, 4, 6, 6, 2, 6, 6, 30, 6, infinity, infinity, infinity, 3, 1, infinity, 3, infinity, 6, 6, infinity, 12, infinity, 6, 12, 4, 2, 6, 4, 4, 3, infinity, 3, infinity, infinity, 6, 6, infinity, 6, 12, 6, 4, 4, 6, infinity, infinity, 6, 6, 6, 2 ], [ 4, 12, infinity, infinity, 12, 12, 3, 6, 6, 3, 6, 2, 12, 12, infinity, 30, 12, 12, 60, 30, 30, 60, 6, 3, 2, 6, 2, 12, 6, 6, infinity, 12, 3, infinity, 1, 3, 3, 6, infinity, infinity, 6, 12, infinity, infinity, 12, infinity, 6, 4, 6, 6, infinity, 6, infinity, infinity, 12, 6, 6, 12, 12, 3, infinity, 3, 6, infinity, 12, 12, 6, 2, 6 ], [ 4, 6, 12, 12, infinity, 6, infinity, infinity, 6, 6, infinity, 6, 12, 12, 6, 30, infinity, 6, 12, 12, 12, 60, 6, 2, 3, 6, 2, infinity, 12, 12, 12, infinity, 3, 3, 3, 1, 3, 6, infinity, 6, infinity, infinity, 12, infinity, 30, 6, infinity, 4, 6, 2, 6, 3, 6, 12, 12, infinity, 6, infinity, 30, 3, 6, 2, 12, 12, 12, 60, infinity, 3, 6 ], [ infinity, 12, 12, 6, 6, infinity, 3, 6, 6, 2, 6, 3, 20, 12, 6, 30, 6, infinity, 12, 60, 30, 12, 6, 2, 2, 6, 3, 12, 12, infinity, 12, infinity, 3, infinity, 3, 3, 1, 12, 12, 12, infinity, 12, 30, 12, 30, 6, 6, 4, infinity, 6, infinity, 6, infinity, 12, infinity, 6, infinity, 60, 30, 2, 6, 3, 6, 6, infinity, infinity, 6, 3, infinity ], [ infinity, infinity, infinity, 6, infinity, infinity, infinity, infinity, 12, 12, 12, infinity, infinity, infinity, 6, 6, infinity, infinity, infinity, 6, 60, 12, infinity, 3, infinity, 3, infinity, infinity, infinity, infinity, 6, 6, infinity, 6, 6, 6, 12, 1, infinity, 3, 3, 3, 12, 12, 12, 6, 6, 6, 4, infinity, 6, 12, 6, infinity, 6, infinity, infinity, 60, 4, 6, 2, 6, 3, 2, 2, 60, 6, 6, 6 ], [ 4, infinity, 12, 6, infinity, 12, 6, 12, 12, 12, infinity, infinity, 3, 6, 3, 2, 6, 6, 6, 6, 12, 6, 6, 6, 4, 4, 4, 6, 12, infinity, infinity, 12, 12, 6, infinity, infinity, 12, infinity, 1, infinity, 3, infinity, 6, 6, 12, 2, 6, 6, 4, infinity, infinity, 12, 12, infinity, 3, infinity, infinity, 6, 6, 6, 6, 4, 6, 6, 6, 6, 2, 6, 6 ], [ infinity, infinity, infinity, 6, infinity, infinity, 6, 6, 12, infinity, 6, 6, infinity, infinity, 6, 6, infinity, infinity, 12, 6, infinity, 30, 6, 3, 6, 2, 6, infinity, 6, infinity, infinity, 6, 6, infinity, infinity, 6, 12, 3, infinity, 1, 3, 3, infinity, 6, 60, infinity, 6, 6, 4, 12, infinity, 12, 12, infinity, 6, infinity, infinity, 12, 12, infinity, 3, infinity, 2, 3, 2, 60, 6, 6, 6 ], [ 4, 3, 6, 3, 6, 6, 12, 20, 4, 6, 6, infinity, 3, 6, 2, 3, 6, 6, 6, 4, 12, 4, 6, 2, 6, 2, 6, 4, 4, 4, 4, 4, 6, 12, 6, infinity, infinity, 3, 3, 3, 1, 3, 6, 4, 12, 6, 4, 6, 6, 6, infinity, infinity, 6, 6, 3, 6, 6, 6, 4, 6, 2, 6, 3, 3, 3, 6, 6, 4, 6 ], [ infinity, infinity, infinity, 6, infinity, infinity, infinity, 6, 6, 6, infinity, 6, infinity, infinity, 6, 6, infinity, infinity, 60, 12, 60, 30, 6, 2, 6, 3, 6, infinity, 6, infinity, 6, infinity, 12, infinity, 12, infinity, 12, 3, infinity, 3, 3, 1, 12, 6, infinity, 6, 6, infinity, 4, 6, 6, 12, infinity, infinity, 6, infinity, infinity, infinity, 6, 6, 3, 6, 2, 2, 3, 12, infinity, 6, infinity ], [ 4, 12, 30, 30, 30, infinity, 6, 12, 12, infinity, 60, 12, 6, 12, 6, 12, infinity, 12, 3, 3, 2, 2, 6, 6, 6, 12, 6, 30, 12, infinity, infinity, 30, 60, 6, infinity, 12, 30, 12, 6, infinity, 6, 12, 1, 3, 3, 6, 6, 6, 12, 12, infinity, 60, 12, infinity, 6, 12, 60, 3, 3, 6, 6, 6, infinity, 12, 60, 2, 6, 6, 6 ], [ 4, 30, 12, 12, 30, 30, 12, 12, 6, 30, 30, 12, 6, 12, 4, 12, 6, 6, 3, 2, 3, 2, 6, 6, 12, 12, 4, 12, 30, 30, 30, 12, 12, 12, infinity, infinity, 12, 12, 6, 6, 4, 6, 3, 1, 3, 6, 6, 12, 12, 12, 30, 30, 12, 6, 6, 6, 12, 3, 2, 6, 6, 12, 6, 6, 12, 3, 6, 6, 6 ], [ 4, 30, infinity, infinity, 30, 12, 4, 30, 6, 30, 30, 12, 12, 12, 12, 6, 60, infinity, 3, 2, 2, 3, 6, 12, 4, 6, 4, infinity, 30, 12, infinity, infinity, 30, 4, 12, 30, 30, 12, 12, 60, 12, infinity, 3, 3, 1, 6, 12, 4, 6, 30, 30, 30, 12, 60, 12, infinity, 60, 2, 3, 6, 12, 4, 60, infinity, 60, 3, 6, 12, 6 ], [ 4, 12, infinity, infinity, 6, 6, 6, 3, 6, 3, 2, 2, 6, infinity, 6, 4, 6, 6, 6, 6, 6, 12, 3, 3, 2, 2, 2, 12, 6, infinity, infinity, 6, 6, 2, infinity, 6, 6, 6, 2, infinity, 6, 6, 6, 6, 6, 1, 3, 3, 3, 6, infinity, 6, 6, infinity, 6, 6, 6, 6, 6, 3, 3, 3, 6, infinity, 6, 6, 2, 2, 2 ], [ 4, 6, 3, 6, 3, 2, 4, infinity, 6, 6, 6, 6, 6, 3, 2, 6, 3, 2, 6, 6, 12, 12, 3, 2, 3, 2, 2, 4, 4, 4, 4, 4, 6, 6, 6, infinity, 6, 6, 6, 6, 4, 6, 6, 6, 12, 3, 1, 3, 3, 2, 3, 3, 2, 3, 6, 3, 2, 6, 6, 3, 2, 2, 6, 6, 6, 6, 3, 3, 2 ], [ 4, 12, infinity, 12, 6, 6, 4, 3, 2, 2, 3, 2, 4, infinity, 6, 4, 6, 6, 6, 12, 4, 6, 3, 2, 2, 3, 2, 12, 6, 12, 6, infinity, 4, 4, 4, 4, 4, 6, 6, 6, 6, infinity, 6, 12, 4, 3, 3, 1, 3, 2, 3, 2, 3, infinity, 4, 6, 6, 6, 12, 2, 3, 2, 6, 6, infinity, 6, 3, 2, 3 ], [ 4, 4, 3, 4, 2, 3, 6, 3, 6, 2, 2, 3, 4, 3, 2, 4, 2, 3, 12, 12, 6, 6, 3, 2, 2, 2, 3, 4, 4, 4, 4, 4, 6, 4, 6, 6, infinity, 4, 4, 4, 6, 4, 12, 12, 6, 3, 3, 3, 1, 6, infinity, 6, 6, 3, 4, 2, 3, 12, 12, 2, 2, 3, 4, 4, 4, 12, 2, 3, 3 ], [ 4, 6, 12, 12, 12, infinity, 6, 6, infinity, infinity, 6, infinity, 12, 12, infinity, 30, 12, 12, infinity, infinity, 12, 30, 3, infinity, 3, 3, infinity, 30, infinity, 12, 12, 6, 3, 3, 6, 2, 6, infinity, infinity, 12, 6, 6, 12, 12, 30, 6, 2, 2, 6, 1, 3, 3, 3, 6, 12, 6, infinity, 12, 60, 6, 6, 4, infinity, 12, 6, 30, 2, 6, 6 ], [ 4, 10, infinity, 20, 6, 12, 6, 3, 3, 6, 2, 6, 12, infinity, 6, 30, 6, 12, 12, infinity, 30, infinity, 3, 6, 2, 2, 6, 6, 12, infinity, infinity, 12, 6, infinity, infinity, 6, infinity, 6, infinity, infinity, infinity, 6, infinity, 30, 30, infinity, 3, 3, infinity, 3, 1, 3, 3, infinity, 12, 6, 12, 60, 12, 6, 6, 4, 12, 12, 12, 30, 2, 6, 6 ], [ infinity, 30, 6, 12, infinity, 12, 6, 6, infinity, infinity, 6, infinity, 20, 6, 6, 30, infinity, 12, 30, 12, 30, infinity, 2, 6, 3, 2, 6, 6, 12, 12, infinity, 12, 2, 3, 6, 3, 6, 12, 12, 12, infinity, 12, 60, 30, 30, 6, 3, 2, 6, 3, 3, 1, 3, 6, infinity, infinity, 12, infinity, infinity, infinity, 6, 4, 6, infinity, 6, 12, 3, infinity, 6 ], [ infinity, 6, 12, infinity, 12, infinity, 6, 2, 3, 6, 3, 6, 20, 12, 20, 30, 12, 12, 30, 60, 30, 30, 2, 6, 2, 3, 6, 30, 6, 6, 12, infinity, 6, infinity, infinity, 6, infinity, 6, 12, 12, 6, infinity, 12, 12, 12, 6, 2, 3, 6, 3, 3, 3, 1, 6, infinity, 6, infinity, 12, infinity, 6, infinity, 4, 6, 12, infinity, infinity, 3, 6, infinity ], [ infinity, infinity, infinity, infinity, 6, 6, infinity, infinity, 6, 12, 6, 6, 6, 3, 3, 6, 2, 2, 12, 6, infinity, 30, infinity, 6, 6, 4, 6, 6, infinity, infinity, infinity, infinity, 12, infinity, infinity, 12, 12, infinity, infinity, infinity, 6, infinity, infinity, 6, 60, infinity, 3, infinity, 3, 6, infinity, 6, 6, 1, infinity, 3, 3, 12, 12, 6, 6, 6, infinity, infinity, infinity, 60, 6, 2, 6 ], [ 2, 6, infinity, infinity, 12, infinity, 6, 20, 12, 20, 12, 12, 2, 6, 3, 3, 6, 6, 6, 6, 12, 6, 2, 6, 6, 4, 4, 6, infinity, infinity, 12, infinity, 20, 6, 12, 12, infinity, 6, 3, 6, 3, 6, 6, 6, 12, 6, 6, 4, 4, 12, 12, infinity, infinity, infinity, 1, infinity, infinity, 6, 6, 2, 6, 6, infinity, infinity, infinity, 6, 6, 6, 2 ], [ infinity, infinity, 6, infinity, infinity, 6, infinity, 12, 12, 12, infinity, 12, 6, 2, 3, 6, 3, 2, 60, 12, 60, 30, 6, 6, infinity, 4, 6, 6, infinity, infinity, infinity, infinity, 12, 6, 6, infinity, 6, infinity, infinity, infinity, 6, infinity, 12, 6, infinity, 6, 3, 6, 2, 6, 6, infinity, 6, 3, infinity, 1, 3, infinity, 6, infinity, 6, 6, infinity, infinity, infinity, 12, infinity, 3, 6 ], [ infinity, infinity, 6, infinity, 6, infinity, 6, 6, 12, 12, 6, infinity, 6, 2, 3, 6, 2, 3, 60, 4, 12, 12, 6, 6, 6, 4, infinity, 6, infinity, infinity, infinity, infinity, 12, infinity, 6, 6, infinity, infinity, infinity, infinity, 6, infinity, 60, 12, 60, 6, 2, 6, 3, infinity, 12, 12, infinity, 3, infinity, 3, 1, 12, 6, 6, 6, infinity, infinity, infinity, infinity, infinity, 6, 3, infinity ], [ 4, infinity, 30, 30, infinity, 12, 6, 12, 12, 60, infinity, 12, 6, 60, 6, 12, 12, infinity, 2, 3, 3, 2, 6, 6, 6, 12, 6, 30, infinity, 12, 30, 30, 30, 6, 12, infinity, 60, 60, 6, 12, 6, infinity, 3, 3, 2, 6, 6, 6, 12, 12, 60, infinity, 12, 12, 6, infinity, 12, 1, 3, 6, 6, 6, 12, infinity, 12, 3, 6, 6, 6 ], [ 4, 30, 30, 30, 30, 30, 12, 60, 6, 12, infinity, infinity, 6, 4, 4, 12, 12, 6, 2, 3, 2, 3, 6, 6, 12, 12, 4, 30, 30, 30, 12, 30, 60, 12, 12, 30, 30, 4, 6, 12, 4, 6, 3, 2, 3, 6, 6, 12, 12, 60, 12, infinity, infinity, 12, 6, 6, 6, 3, 1, 6, 6, 12, 12, 6, 6, 3, 6, 6, 6 ], [ 2, 12, 6, 12, infinity, 6, 6, 6, 4, infinity, 6, 6, 2, 6, 6, 6, infinity, 6, 6, 6, 6, 12, 2, 3, 3, 2, 2, 12, 6, 12, infinity, 6, 2, 6, 3, 3, 2, 6, 6, infinity, 6, 6, 6, 6, 6, 3, 3, 2, 2, 6, 6, infinity, 6, 6, 2, infinity, 6, 6, 6, 1, 3, 3, 6, infinity, 6, 6, 3, 3, 2 ], [ 4, 4, 4, 4, 4, 4, 6, 2, 6, 3, 3, 2, 6, 6, 4, 6, 6, 6, 6, 6, 12, 12, 2, 3, 2, 3, 2, 6, 2, 6, 3, 3, 6, 4, infinity, 6, 6, 2, 6, 3, 2, 3, 6, 6, 12, 3, 2, 3, 2, 6, 6, 6, infinity, 6, 6, 6, 6, 6, 6, 3, 1, 3, 2, 3, 3, 6, 3, 2, 3 ], [ 4, infinity, 6, 12, 6, infinity, 2, 2, 4, 3, 2, 3, 6, 6, 6, 2, 6, infinity, 6, 12, 4, 6, 2, 3, 2, 2, 3, infinity, 6, 12, infinity, 6, 2, 4, 3, 2, 3, 6, 4, infinity, 6, 6, 6, 12, 4, 3, 2, 2, 3, 4, 4, 4, 4, 6, 6, 6, infinity, 6, 12, 3, 3, 1, 6, infinity, 6, 6, 2, 3, 3 ], [ infinity, 6, infinity, infinity, infinity, infinity, infinity, 12, 12, 12, 12, 12, 6, infinity, 6, infinity, infinity, infinity, 12, 6, infinity, 30, infinity, 3, infinity, 3, infinity, infinity, infinity, infinity, 6, 6, infinity, 6, 6, 12, 6, 3, 6, 2, 3, 2, infinity, 6, 60, 6, 6, 6, 4, infinity, 12, 6, 6, infinity, infinity, infinity, infinity, 12, 12, 6, 2, 6, 1, 3, 3, 60, 6, 6, 6 ], [ infinity, 6, infinity, infinity, infinity, infinity, 6, 12, 12, infinity, 6, 12, 6, infinity, 6, infinity, infinity, infinity, 60, 12, 60, 30, 6, 3, 6, 2, 6, infinity, 6, infinity, infinity, 6, 6, infinity, infinity, 12, 6, 2, 6, 3, 3, 2, 12, 6, infinity, infinity, 6, 6, 4, 12, 12, infinity, 12, infinity, infinity, infinity, infinity, infinity, 6, infinity, 3, infinity, 3, 1, 3, 12, 6, 6, 6 ], [ infinity, 6, infinity, infinity, infinity, infinity, infinity, 12, 6, 6, infinity, 12, 6, infinity, 6, infinity, infinity, infinity, 60, 4, 12, 12, 6, 2, 6, 3, 6, infinity, 6, infinity, 6, infinity, 12, infinity, 12, 12, infinity, 2, 6, 2, 3, 3, 60, 12, 60, 6, 6, infinity, 4, 6, 12, 6, infinity, infinity, infinity, infinity, infinity, 12, 6, 6, 3, 6, 3, 3, 1, infinity, infinity, 6, infinity ], [ 4, 30, infinity, infinity, 12, infinity, 6, 30, 12, 30, 12, infinity, 6, 60, 6, 12, 60, 12, 2, 2, 3, 3, 6, 6, 6, 12, 6, infinity, 30, infinity, 30, infinity, 12, 6, 12, 60, infinity, 60, 6, 60, 6, 12, 2, 3, 3, 6, 6, 6, 12, 30, 30, 12, infinity, 60, 6, 12, infinity, 3, 3, 6, 6, 6, 60, 12, infinity, 1, 6, 6, 6 ], [ 4, infinity, 6, 12, infinity, 6, 2, 6, 6, 6, infinity, 6, 6, 6, 6, 4, infinity, 6, 6, 6, 6, 12, 2, 2, 3, 3, 2, infinity, 6, 12, 6, infinity, 6, 6, 6, infinity, 6, 6, 2, 6, 6, infinity, 6, 6, 6, 2, 3, 3, 2, 2, 2, 3, 3, 6, 6, infinity, 6, 6, 6, 3, 3, 2, 6, 6, infinity, 6, 1, 3, 3 ], [ 4, 6, 2, 6, 3, 3, 6, 6, 2, 6, 6, infinity, 6, 2, 2, 6, 3, 3, 6, 6, 12, 12, 2, 2, 3, 2, 3, 4, 4, 4, 4, 4, 2, 6, 2, 3, 3, 6, 6, 6, 4, 6, 6, 6, 12, 2, 3, 2, 3, 6, 6, infinity, 6, 2, 6, 3, 3, 6, 6, 3, 2, 3, 6, 6, 6, 6, 3, 1, 3 ], [ 2, 12, 6, infinity, 6, infinity, 6, 2, 6, 2, 3, 3, 2, 6, 6, 6, 6, infinity, 6, 6, 6, 12, 2, 2, 2, 3, 3, 12, 6, infinity, 6, infinity, 6, 2, 6, 6, infinity, 6, 6, 6, 6, infinity, 6, 6, 6, 2, 2, 3, 3, 6, 6, 6, infinity, 6, 2, 6, infinity, 6, 6, 2, 3, 3, 6, 6, infinity, 6, 3, 3, 1 ] ], CTProds12 := ReadAsFunction( Concatenation(PackageInfo("rcwa")[1].InstallationPath, "/data/ctproducts/ctprods12.g"))(), CTProds32 := ReadAsFunction( Concatenation(PackageInfo("rcwa")[1].InstallationPath, "/data/ctproducts/ctprods32.g"))() ); ############################################################################# ## #E ctprodclass.g . . . . . . . . . . . . . . . . . . . . . . . . . ends here [Seitenstruktur0.634Druckenetwas mehr zur Ethik2026-06-18] |
2026-07-27