with(linalg): charform := # Written By Maegan K. Bos # This procedure calculates the character formula for X lower N upper r with # specialization (s). proc(X,N,r,s) local funkyfin,Xfin,Nfin,Ndual,rdual,imadim,comat,delta,flag,S,K,P; P:=init(X,N,r); Nfin:=P[1]; rdual:=P[2]; imadim:=P[3]; comat:=P[4]; delta:=P[5]; FunkyAcase:=P[6]; S:=s; if FunkyAcase then K:= Agenhits(comat,S,rdual,delta,imadim,Nfin); else K:= genhits(comat,S,rdual,delta,imadim,Nfin); fi; K:=reduce(K); d:=vectdim(K); print(eval(K)); print(d); # P:= Product( product((1-q^(d*k-i))^eval(K[i]),i=1..d),k=1..infinity); # print(eval(P)); end; init := proc(X,N,r) local Xfin,Nfin,Ndual,rdual,imadim,comat,delta,FunkyAcase; FunkyAcase:=false; if X = A then if r = 1 then Xfin := A; Nfin := N; Ndual := N; rdual := 1; imadim := 0; comat := comatA(Nfin) else if N mod 2 = 0 then FunkyAcase:=true; Xfin := B; Nfin := 1/2*N; Ndual := 2*N; rdual := 2; imadim := 1/2*N; comat := comatA2(Nfin); else Xfin := B; Nfin := 1/2*N+1/2; Ndual := 1/2*N+1/2; rdual := 1; imadim := 0; comat := comatB(Nfin) fi fi else if X = B then Xfin := C; Nfin := N; Ndual := 2*N-1; rdual := 2; imadim := N-1; comat := comatC(Nfin) else if X = C then Xfin := B; Nfin := N; Ndual := N+1; rdual := 2; imadim := 1; comat := comatB(N) else if X = D then if r = 1 then Xfin := D; Nfin := N; Ndual := N; rdual := 1; imadim := 0; comat := comatD(Nfin) else if r = 2 then Xfin := C; Nfin := N-1; Ndual := N-1; rdual := 1; imadim := 0; comat := comatC(Nfin) else Xfin := G; Nfin := 2; Ndual := 2; rdual := 1; imadim := 0; comat := coeffG fi fi else if X = E then if r = 2 then Xfin := F; Nfin := 4; Ndual := 4; rdual := 1; imadim := 0; comat := coeffF else Xfin := E; Nfin := N; Ndual := N; rdual := 1; imadim := 0; if N = 6 then comat := coeffE6 else if N = 7 then comat := coeffE7 else comat := coeffE8 fi fi fi else if X = F then Xfin := F; Nfin := 4; Ndual := 6; rdual := 2; imadim := 2; comat := coeffFrev else Xfin := G; Nfin := 2; Ndual := 4; rdual := 3; imadim := 1; comat := coeffGrev fi fi fi fi fi fi; delta := getdelta(X,N,r); RETURN(Nfin,rdual,imadim,comat,delta,FunkyAcase) end; getdelta := proc(X,N,r) local delta; if X = A then if r = 1 then delta := vector(N+1,1) else if N mod 2 = 0 then delta := vector(1/2*N+1,2); delta[1] := 1 else delta := vector(1/2*N+3/2,2); delta[1] := 1; delta[2] := 1 fi fi else if X = B then delta := vector(N+1,2); delta[1] := 1; delta[2] := 1; delta[N+1] := 1 else if X = C then delta := vector(N+1,1) else if X = D then if r = 1 then delta := vector(N+1,2); delta[1] := 1; delta[2] := 1; delta[N] := 1; delta[N+1] := 1 else if r = 2 then delta := vector(N,2); delta[1] := 1; delta[N] := 1 else delta := vector([1,2,3]) fi fi else if X = E then if r = 2 then delta := vector([1,2,3,4,2]) else if N = 6 then delta := vector([1,1,2,3,2,1,2]) else if N = 7 then delta := vector([1,2,3,4,3,2,1,2]) else delta := vector([1,2,3,4,5,6,4,2,3]) fi fi fi else if X = F then delta := vector([1,2,3,2,1]) else delta := vector([1,2,1]) fi fi fi fi fi fi; RETURN(delta) end; Agenhits := proc(C,S,rdual,delta,imadim,Nfin) local i,j,t,k,c0,p,q,modulo,dim,L,powers,s,C0; t := coldim(C); s:=vector(t,0); for i to t do s[i] := eval(S[i]+1) od; modulo := dotprod(delta,s,orthogonal); dim := modulo*rdual; L := vector(dim,0); powers := evalm(C &* s); k := vectdim(powers); L[dim] := Nfin; for i from 1 to Nfin*Nfin do for j from 0 to 1 do p := j*modulo+powers[i]; q := (j+1)*modulo-powers[i]; L[p] := eval(L[p]+1); L[q] := eval(L[q]+1) od od; for i from Nfin*Nfin+1 to Nfin*Nfin+Nfin do p := powers[i]; q := dim-powers[i]; L[p] := eval(L[p]+1); L[q] := eval(L[q]+1); od; L[modulo] := eval(L[modulo])+imadim ; for i to dim do L[i]:=eval(L[i]-Nfin) od; RETURN(L) end; genhits := proc(C,S,rdual,delta,imadim,Nfin) local i,j,t,k,c0,p,q,modulo,dim,L,powers,s,C0; t := coldim(C); s:=vector(t,0); C0 := delcols(C,t .. t); for i to t do s[i] := eval(S[i]+1) od; k := rowdim(C); c0 := matrix(k,1,0); C0 := augment(c0,C0); modulo := dotprod(delta,s,orthogonal); dim := modulo*rdual; L := vector(dim,0); powers := evalm(C0 &* s); k := vectdim(powers); L[dim] := Nfin; for i to k do if C[i,t] = short then for j from 0 to rdual-1 do p := j*modulo+powers[i]; q := (j+1)*modulo-powers[i]; L[p] := eval(L[p]+1); L[q] := eval(L[q]+1) od else p := powers[i]; q := dim-powers[i]; L[p] := eval(L[p]+1); L[q] := eval(L[q]+1); fi od; if rdual <> 1 then for i to rdual-1 do L[modulo*i] := eval(L[modulo*i])+imadim od fi; for i to dim do L[i]:=eval(L[i]-Nfin) od; RETURN(L) end; reduce := proc(K) local T,A,i,j,k,l,p; T:=eval(K); k:=vectdim(T); i := 1; while i < vectdim(T) do if type(k/i,integer) then A:=vector(i); for j to i do A[j]:=eval(T[j]) od; p:=0; j:=1; while p=0 and j<=i do l:=j+i; while p=0 and l<=k do p:=eval(p + abs(A[j]-T[l])); l:=eval(l+i); od; j:=eval(j+1); od; if p=0 then T:=A; fi fi; i:=eval(i+1); od; RETURN(eval(T)); end; comatA2:= proc(N) local i,j,k,iCurr, C; iCurr:=1; C:= matrix(N*N+N,N+1,0); for i from 2 to N+1 do C[iCurr,i]:=1; iCurr:=iCurr + 1; od; for i from 2 to N do for j from 0 to N + 1 - i do for k from 0 to i-1 do C[iCurr, j+k+1]:=1; od; iCurr:=iCurr + 1; od; od; for i from 1 to N-2 do for j from N-i by -1 to 2 do for k from N-i by -1 to 1 do if k>=j then C[iCurr,k+1]:=1 else C[iCurr,k+1]:=2 fi od; C[iCurr,1]:=1; iCurr:=iCurr + 1; od; od; for i from 1 to N do for j from 1 to N-i do C[iCurr,j+1]:=2; od; C[iCurr,1]:=1; iCurr:=iCurr + 1; od; RETURN(evalm(C)); end; comatA:= proc(N) local i,j,k,iCurr, C; iCurr:=1; C:= matrix(N*(N+1)/2,N+1,0); for i to N do for j to (N+1)-i do for k from 0 to i-1 do C[iCurr, j+k]:=1; od; iCurr:=iCurr + 1; od od; for i to N*(N+1)/2 do C[i,N+1]:=long; od; RETURN(evalm(C)); end; comatB:= proc(N) local i,j,k,iCurr, C; iCurr:=1; C:= matrix(N*N,N+1,0); for i to N do for j to (N+1)-i do for k from 0 to i-1 do C[iCurr, j+k]:=1; od; iCurr:=iCurr + 1; od od; for i to N-1 do for j from 0 to N - i - 1 do for k from i to N do if k <= (i+j) then C[iCurr,k]:=1 else C[iCurr,k]:=2 fi; od; iCurr:=iCurr + 1; od; od; for i to N*N do if C[i,N] = 1 then C[i,N+1]:=short else C[i,N+1]:=long fi; od; RETURN(evalm(C)); end; comatC:= proc(N) local a,i,j,k,iCurr, C; iCurr:=1; C:= matrix(N*N,N+1,0); for i to N do for j to (N+1)-i do for k from 0 to i-1 do C[iCurr, j+k]:=1; od; iCurr:=iCurr + 1; od od; for i to N-1 do for j from 0 to N - i -1 do for k from i to N-1 do if k < i + j then C[iCurr, k]:=1 else C[iCurr, k]:=2 fi od; C[iCurr,N]:=1; iCurr:=iCurr + 1; od; od; for i to N*N do a:=1; while C[i,a] = 0 do a:=a+1 od; if C[i,a] = 2 or a = N then C[i,N+1]:=long else C[i,N+1]:=short fi; od; RETURN(evalm(C)); end; comatD:= proc(N) local i,j,k,iCurr, C, CF; iCurr:=1; C:= matrix(N*N-N+1,N+1,0); for i to N do for j to (N+1)-i do for k from 0 to i-1 do C[iCurr, j+k]:=1; od; iCurr:=iCurr + 1; od od; for i to N-2 do for j from i to N - 2 do C[iCurr, j]:=1; od; C[iCurr, N]:=1; iCurr:=iCurr + 1; od; for i to N-3 do for j from 0 to N - 3 - i do for k from i to N-2 do if k<= i+j then C[iCurr, k]:=1 else C[iCurr, k]:=2 fi od; C[iCurr, N-1]:=1; C[iCurr, N]:=1; iCurr:=iCurr + 1; od od; CF:=delrows(C,2*N-1..2*N-1); for i to N*N-N do CF[i,N+1]:=long; od; RETURN(evalm(CF)); end; coeffE6 := array(1 .. 36, 1 .. 7,[(26, 3)=2,(28, 3)=2,(6, 7)=long,(7, 4)=1,(26 , 5)=1,(34, 7)=long,(30, 6)=1,(21, 7)=long,(31, 3)=2,(15, 7)=long,(10, 2)=1,(2 , 4)=0,(6, 6)=0,(32, 1)=1,(15, 6)=0,(1, 4)=0,(11, 3)=0,(26, 6)=1,(36, 1)=1,(7, 6)=1,(3, 1)=0,(3, 5)=0,(12, 6)=1,(29, 7)=long,(3, 3)=0,(8, 2)=0,(22, 3)=1,(18, 5)=0,(30, 2)=1,(36, 4)=2,(18, 7)=long,(22, 4)=1,(13, 2)=0,(34, 1)=1,(35, 5)=1,( 7, 2)=0,(11, 1)=1,(2, 5)=1,(19, 1)=0,(6, 1)=1,(11, 5)=0,(1, 3)=0,(35, 1)=1,(27 , 1)=1,(33, 1)=1,(14, 6)=0,(8, 3)=1,(9, 5)=0,(20, 1)=1,(25, 4)=1,(18, 2)=1,(32 , 3)=2,(26, 7)=long,(8, 5)=1,(18, 3)=1,(7, 5)=0,(15, 3)=1,(16, 1)=1,(36, 3)=3,( 21, 2)=1,(29, 5)=1,(32, 6)=1,(35, 4)=2,(5, 2)=1,(19, 5)=1,(31, 4)=1,(31, 7)= long,(14, 3)=1,(23, 4)=1,(14, 7)=long,(23, 1)=1,(4, 7)=long,(30, 1)=1,(4, 2)=0, (33, 7)=long,(17, 1)=0,(10, 6)=0,(32, 2)=1,(20, 4)=0,(8, 7)=long,(18, 6)=1,(20 , 7)=long,(36, 2)=2,(23, 6)=1,(2, 6)=0,(3, 2)=0,(31, 1)=1,(1, 5)=0,(11, 7)=long ,(13, 6)=0,(15, 5)=0,(32, 5)=1,(28, 5)=1,(28, 6)=0,(34, 2)=2,(5, 7)=long,(6, 3) =0,(12, 4)=1,(14, 1)=0,(9, 6)=0,(31, 6)=0,(24, 5)=1,(4, 4)=0,(11, 2)=1,(2, 1)=0 ,(19, 2)=1,(29, 2)=1,(34, 4)=2,(5, 5)=0,(19, 4)=1,(35, 2)=2,(3, 6)=0,(5, 6)=0,( 33, 2)=2,(27, 5)=1,(5, 3)=0,(14, 4)=0,(20, 3)=1,(20, 2)=1,(21, 4)=1,(22, 7)= long,(27, 2)=1,(13, 4)=1,(5, 1)=0,(3, 7)=long,(30, 4)=1,(15, 4)=1,(22, 1)=0,(24 , 7)=long,(15, 1)=0,(17, 6)=1,(36, 5)=2,(18, 4)=1,(1, 7)=long,(23, 2)=1,(26, 1) =0,(35, 3)=3,(21, 6)=0,(7, 3)=0,(30, 3)=2,(6, 4)=0,(17, 2)=0,(16, 5)=0,(36, 7)= long,(10, 4)=0,(8, 4)=0,(27, 4)=1,(26, 2)=1,(29, 1)=0,(31, 2)=2,(1, 6)=1,(17, 5 )=1,(24, 1)=0,(28, 1)=1,(29, 4)=2,(14, 2)=1,(30, 5)=1,(33, 5)=1,(33, 4)=1,(4, 1 )=0,(16, 2)=1,(2, 2)=0,(14, 5)=1,(27, 6)=1,(34, 5)=1,(10, 5)=0,(29, 3)=2,(11, 4 )=0,(11, 6)=0,(19, 3)=1,(25, 1)=1,(5, 4)=0,(27, 7)=long,(7, 1)=0,(9, 2)=0,(1, 2 )=0,(35, 7)=long,(17, 4)=1,(15, 2)=1,(16, 7)=long,(34, 6)=1,(32, 4)=2,(7, 7)= long,(25, 3)=1,(12, 3)=1,(16, 6)=0,(16, 4)=0,(6, 5)=0,(25, 6)=0,(30, 7)=long,( 22, 6)=1,(23, 5)=0,(9, 4)=1,(12, 7)=long,(34, 3)=2,(8, 6)=0,(4, 5)=0,(9, 1)=0,( 24, 4)=1,(10, 1)=0,(29, 6)=1,(19, 6)=0,(21, 5)=0,(24, 6)=0,(6, 2)=0,(10, 7)= long,(24, 3)=2,(24, 2)=1,(3, 4)=1,(9, 7)=long,(20, 6)=0,(28, 2)=1,(17, 7)=long, (28, 4)=1,(4, 3)=1,(22, 2)=1,(26, 4)=1,(1, 1)=0,(2, 7)=long,(8, 1)=0,(33, 3)=2, (2, 3)=0,(13, 1)=0,(25, 7)=long,(12, 2)=0,(25, 2)=1,(4, 6)=0,(13, 3)=1,(36, 6)= 1,(13, 7)=long,(23, 3)=1,(27, 3)=1,(31, 5)=1,(21, 3)=1,(35, 6)=1,(16, 3)=1,(9, 3)=1,(28, 7)=long,(20, 5)=1,(32, 7)=long,(22, 5)=1,(18, 1)=0,(33, 6)=1,(13, 5)= 1,(19, 7)=long,(17, 3)=1,(10, 3)=1,(12, 5)=0,(23, 7)=long,(12, 1)=0,(21, 1)=1,( 25, 5)=1]); coeffE7 := array(1 .. 63, 1 .. 8,[(30, 5)=1,(5, 6)=0,(44, 7)=1,(3, 8)=long,(1, 1)=1,(26, 4)=1,(33, 1)=1,(53, 6)=0,(58, 8)=long,(27, 5)=1,(50, 2)=2,(52, 8)= long,(22, 4)=1,(24, 8)=long,(43, 1)=1,(45, 8)=long,(59, 6)=1,(27, 7)=0,(13, 8)= long,(28, 8)=long,(42, 6)=0,(20, 4)=0,(40, 3)=2,(52, 4)=2,(34, 8)=long,(35, 3)= 2,(44, 8)=long,(32, 7)=1,(11, 6)=0,(33, 2)=1,(49, 8)=long,(35, 7)=1,(61, 1)=1,( 3, 4)=0,(24, 5)=1,(52, 7)=1,(58, 2)=2,(6, 6)=0,(20, 5)=0,(17, 5)=0,(46, 2)=2,( 61, 5)=2,(11, 1)=0,(15, 2)=1,(32, 2)=1,(3, 3)=0,(38, 7)=1,(51, 6)=1,(63, 1)=2,( 41, 5)=1,(14, 5)=0,(48, 3)=2,(15, 1)=0,(19, 7)=0,(46, 7)=1,(48, 2)=1,(58, 1)=1, (61, 3)=4,(1, 3)=0,(22, 7)=1,(52, 6)=1,(3, 5)=0,(38, 8)=long,(51, 2)=2,(53, 7)= 2,(59, 2)=2,(9, 1)=0,(12, 7)=0,(20, 6)=0,(29, 4)=1,(26, 2)=1,(18, 1)=0,(23, 2)= 0,(26, 3)=1,(17, 4)=1,(36, 8)=long,(8, 5)=0,(28, 3)=2,(45, 2)=1,(63, 5)=2,(41, 7)=1,(57, 1)=1,(1, 7)=0,(16, 6)=0,(37, 4)=1,(51, 7)=1,(47, 6)=1,(58, 3)=3,(34, 6)=1,(49, 5)=2,(54, 4)=2,(51, 3)=2,(29, 7)=1,(12, 5)=1,(2, 7)=1,(42, 7)=1,(10, 7)=0,(12, 2)=0,(54, 7)=1,(8, 1)=1,(57, 8)=long,(22, 6)=0,(49, 6)=1,(33, 8)=long ,(51, 5)=1,(55, 3)=2,(61, 4)=3,(26, 8)=long,(55, 7)=1,(56, 2)=2,(1, 5)=0,(9, 7) =1,(14, 2)=1,(36, 2)=1,(46, 4)=2,(33, 7)=1,(12, 3)=0,(23, 7)=1,(24, 2)=1,(25, 7 )=0,(20, 1)=1,(61, 8)=long,(32, 4)=1,(19, 3)=0,(36, 6)=1,(5, 7)=0,(6, 3)=0,(49 , 7)=1,(50, 3)=3,(29, 5)=1,(49, 2)=1,(14, 4)=0,(42, 4)=1,(43, 6)=0,(46, 3)=2,( 27, 4)=1,(60, 8)=long,(1, 8)=long,(42, 5)=1,(52, 1)=1,(61, 2)=2,(28, 7)=1,(6, 5 )=1,(27, 1)=1,(33, 6)=0,(13, 7)=0,(31, 6)=1,(55, 4)=2,(15, 8)=long,(40, 6)=0,( 13, 2)=0,(40, 8)=long,(2, 6)=0,(43, 8)=long,(49, 1)=0,(53, 2)=2,(30, 7)=1,(42, 8)=long,(50, 7)=1,(8, 4)=0,(9, 8)=long,(16, 5)=0,(2, 5)=0,(21, 8)=long,(43, 2)= 1,(59, 3)=3,(31, 7)=0,(9, 6)=0,(13, 4)=0,(48, 5)=1,(8, 3)=0,(31, 2)=1,(7, 5)=0, (7, 7)=0,(18, 2)=0,(29, 3)=1,(30, 3)=1,(55, 8)=long,(51, 4)=2,(56, 3)=3,(58, 5) =2,(60, 5)=2,(21, 1)=1,(63, 6)=1,(34, 5)=1,(48, 1)=1,(16, 4)=1,(39, 8)=long,(23 , 8)=long,(38, 5)=1,(21, 3)=1,(38, 2)=1,(1, 6)=0,(10, 8)=long,(57, 3)=3,(21, 7) =0,(25, 6)=1,(32, 8)=long,(34, 4)=1,(5, 8)=long,(59, 5)=2,(15, 6)=0,(39, 7)=1,( 40, 2)=1,(56, 4)=2,(9, 5)=0,(24, 4)=1,(31, 4)=1,(2, 4)=0,(11, 3)=1,(20, 3)=1,( 37, 7)=1,(23, 3)=1,(34, 1)=1,(34, 2)=1,(19, 4)=1,(7, 4)=0,(11, 4)=1,(20, 7)=1,( 63, 7)=2,(32, 1)=1,(9, 3)=1,(14, 8)=long,(36, 4)=1,(56, 7)=2,(31, 3)=1,(51, 8)= long,(29, 6)=0,(31, 8)=long,(41, 6)=1,(47, 8)=long,(40, 4)=2,(48, 4)=2,(2, 1)=0 ,(6, 1)=0,(27, 3)=1,(50, 6)=0,(41, 4)=1,(54, 1)=1,(16, 1)=0,(31, 5)=1,(5, 3)=0, (20, 8)=long,(21, 4)=1,(2, 2)=0,(4, 8)=long,(54, 3)=3,(60, 6)=1,(7, 1)=0,(11, 2 )=0,(7, 2)=0,(8, 7)=0,(49, 3)=2,(52, 5)=2,(63, 3)=4,(18, 3)=1,(19, 2)=0,(39, 2) =1,(7, 8)=long,(36, 1)=0,(45, 1)=0,(46, 5)=1,(23, 6)=0,(32, 6)=0,(33, 3)=1,(32 , 5)=0,(56, 6)=1,(30, 1)=0,(14, 3)=1,(48, 7)=1,(60, 3)=3,(11, 8)=long,(6, 8)= long,(16, 3)=1,(24, 1)=0,(25, 3)=1,(8, 8)=long,(24, 3)=1,(58, 4)=2,(1, 4)=0,(13 , 1)=0,(22, 8)=long,(57, 2)=2,(8, 2)=1,(11, 7)=0,(7, 6)=1,(43, 3)=2,(39, 4)=1,( 10, 1)=0,(32, 3)=2,(9, 2)=0,(30, 8)=long,(10, 2)=1,(21, 5)=0,(6, 4)=0,(6, 7)=0, (29, 8)=long,(56, 8)=long,(41, 8)=long,(12, 1)=0,(17, 3)=1,(17, 8)=long,(35, 6) =0,(26, 5)=0,(36, 7)=1,(61, 6)=1,(7, 3)=0,(22, 2)=1,(46, 6)=0,(11, 5)=0,(25, 5) =1,(14, 6)=0,(10, 3)=1,(58, 7)=2,(47, 5)=1,(33, 4)=1,(50, 5)=1,(17, 1)=0,(28, 5 )=0,(35, 5)=1,(43, 4)=2,(59, 4)=3,(24, 6)=0,(31, 1)=0,(57, 5)=2,(35, 1)=0,(47, 4)=1,(52, 2)=1,(62, 8)=long,(18, 4)=1,(53, 5)=1,(14, 1)=1,(17, 7)=0,(45, 6)=1,( 36, 5)=1,(60, 7)=2,(4, 5)=0,(59, 8)=long,(28, 1)=0,(62, 2)=3,(28, 6)=0,(49, 4)= 2,(53, 1)=1,(26, 7)=1,(27, 2)=1,(28, 2)=1,(62, 3)=4,(15, 3)=1,(17, 6)=0,(44, 3) =2,(45, 4)=2,(4, 2)=0,(45, 3)=2,(21, 6)=0,(34, 7)=0,(50, 8)=long,(56, 1)=1,(42 , 2)=2,(38, 6)=0,(16, 8)=long,(25, 4)=1,(35, 8)=long,(4, 1)=0,(44, 2)=1,(55, 2) =2,(37, 6)=0,(54, 6)=1,(62, 4)=3,(62, 7)=2,(41, 3)=2,(44, 5)=1,(47, 1)=1,(2, 8) =long,(40, 1)=0,(45, 5)=1,(46, 1)=1,(57, 6)=1,(60, 2)=2,(19, 8)=long,(33, 5)=1, (61, 7)=2,(15, 4)=0,(21, 2)=1,(5, 4)=1,(36, 3)=1,(27, 8)=long,(38, 3)=2,(16, 7) =1,(23, 5)=1,(15, 5)=0,(14, 7)=0,(39, 5)=1,(44, 4)=1,(15, 7)=1,(10, 6)=0,(12, 8 )=long,(37, 1)=1,(62, 1)=1,(4, 6)=0,(19, 1)=0,(12, 6)=0,(47, 3)=2,(52, 3)=2,(37 , 8)=long,(16, 2)=0,(1, 2)=0,(58, 6)=1,(29, 1)=0,(54, 5)=1,(19, 5)=1,(41, 2)=1, (3, 7)=0,(26, 1)=1,(30, 6)=1,(57, 4)=2,(63, 8)=long,(6, 2)=0,(39, 3)=1,(62, 6)= 1,(25, 2)=0,(29, 2)=1,(30, 2)=0,(47, 2)=2,(48, 6)=1,(53, 3)=3,(22, 3)=1,(37, 5) =0,(50, 4)=2,(19, 6)=1,(25, 1)=0,(22, 5)=0,(37, 2)=2,(38, 4)=1,(55, 5)=2,(23, 4 )=1,(40, 5)=1,(22, 1)=0,(10, 5)=0,(18, 8)=long,(38, 1)=1,(10, 4)=0,(17, 2)=1,( 18, 5)=1,(18, 7)=0,(60, 1)=1,(4, 3)=1,(4, 4)=0,(47, 7)=1,(53, 4)=2,(59, 1)=1,( 53, 8)=long,(25, 8)=long,(43, 7)=1,(5, 2)=0,(13, 5)=1,(9, 4)=0,(63, 4)=3,(46, 8 )=long,(55, 6)=1,(3, 6)=0,(3, 2)=1,(12, 4)=1,(30, 4)=1,(39, 6)=1,(51, 1)=1,(54 , 8)=long,(55, 1)=1,(20, 2)=1,(28, 4)=1,(56, 5)=1,(60, 4)=3,(62, 5)=2,(18, 6)=0 ,(2, 3)=0,(42, 3)=2,(59, 7)=1,(57, 7)=1,(54, 2)=2,(26, 6)=0,(50, 1)=1,(24, 7)=0 ,(40, 7)=1,(43, 5)=1,(13, 3)=0,(4, 7)=0,(5, 5)=0,(37, 3)=2,(45, 7)=1,(13, 6)=1, (34, 3)=1,(42, 1)=1,(63, 2)=3,(23, 1)=0,(39, 1)=1,(8, 6)=0,(44, 6)=1,(48, 8)= long,(35, 2)=1,(44, 1)=1,(27, 6)=0,(3, 1)=0,(5, 1)=0,(35, 4)=1,(41, 1)=0]); coeffE8 := array(1 .. 120, 1 .. 9,[(10, 6)=0,(103, 1)=1,(81, 4)=2,(42, 9)=long, (103, 3)=3,(49, 3)=1,(87, 5)=3,(47, 8)=0,(106, 9)=long,(10, 9)=long,(14, 3)=1,( 42, 8)=1,(10, 3)=0,(86, 5)=3,(2, 5)=0,(23, 1)=0,(83, 7)=1,(73, 5)=2,(6, 3)=1,( 85, 9)=long,(26, 9)=long,(17, 5)=1,(77, 6)=2,(108, 7)=1,(29, 4)=1,(6, 2)=0,(49 , 2)=1,(49, 6)=1,(45, 7)=1,(82, 8)=1,(31, 6)=1,(117, 8)=3,(73, 4)=2,(106, 8)=2, (105, 5)=4,(11, 4)=0,(11, 9)=long,(114, 1)=1,(118, 2)=2,(92, 5)=3,(112, 3)=3,( 73, 9)=long,(58, 4)=1,(105, 3)=3,(13, 1)=0,(57, 1)=0,(86, 6)=2,(94, 1)=1,(120, 7)=2,(5, 7)=0,(84, 4)=2,(34, 4)=1,(46, 3)=1,(32, 9)=long,(103, 6)=2,(118, 5)=6, (107, 7)=2,(40, 2)=0,(37, 4)=1,(74, 5)=2,(2, 4)=0,(67, 7)=1,(57, 2)=0,(22, 7)=0 ,(78, 2)=1,(28, 3)=1,(66, 1)=0,(15, 9)=long,(96, 3)=3,(81, 1)=1,(36, 9)=long,( 97, 4)=3,(3, 3)=0,(81, 2)=1,(18, 5)=1,(33, 7)=0,(33, 8)=1,(25, 5)=1,(61, 7)=0,( 52, 7)=1,(86, 2)=1,(22, 6)=0,(53, 2)=1,(119, 7)=2,(58, 5)=2,(27, 3)=1,(8, 1)=1, (42, 1)=1,(106, 4)=4,(59, 8)=1,(50, 8)=1,(50, 7)=0,(65, 9)=long,(60, 8)=1,(67, 8)=1,(58, 3)=1,(35, 3)=1,(110, 2)=2,(77, 2)=1,(96, 8)=1,(69, 6)=2,(111, 4)=4,( 58, 1)=0,(46, 8)=1,(40, 8)=1,(95, 7)=1,(46, 5)=1,(72, 3)=1,(53, 6)=1,(1, 9)= long,(3, 2)=0,(39, 2)=1,(45, 2)=0,(95, 2)=2,(67, 5)=2,(9, 8)=0,(78, 5)=2,(39, 1 )=0,(35, 2)=1,(35, 5)=1,(60, 5)=2,(47, 6)=1,(8, 7)=0,(64, 4)=2,(18, 6)=0,(19, 9 )=long,(104, 6)=3,(7, 3)=0,(60, 2)=1,(115, 5)=5,(4, 6)=0,(13, 7)=0,(18, 2)=0,( 112, 1)=1,(115, 4)=4,(78, 3)=2,(37, 3)=0,(27, 6)=1,(84, 7)=1,(83, 4)=2,(101, 5) =4,(58, 7)=1,(91, 4)=2,(18, 7)=0,(64, 9)=long,(68, 8)=1,(39, 5)=1,(9, 9)=long,( 46, 2)=1,(116, 6)=4,(113, 5)=5,(78, 1)=1,(19, 2)=0,(100, 8)=2,(36, 8)=0,(95, 4) =3,(104, 2)=2,(15, 2)=1,(104, 4)=3,(24, 7)=1,(67, 2)=1,(57, 4)=2,(42, 5)=1,(25 , 7)=0,(118, 9)=long,(107, 6)=3,(7, 7)=0,(84, 2)=2,(33, 1)=0,(111, 5)=5,(44, 5) =2,(104, 8)=2,(41, 6)=1,(81, 3)=1,(9, 3)=0,(105, 8)=2,(32, 7)=0,(29, 5)=0,(94, 7)=1,(13, 9)=long,(11, 1)=0,(110, 7)=1,(92, 6)=2,(79, 9)=long,(70, 2)=1,(34, 3) =1,(82, 1)=0,(67, 9)=long,(51, 7)=1,(56, 7)=0,(53, 8)=1,(88, 1)=1,(45, 6)=1,( 104, 1)=1,(33, 5)=1,(119, 8)=3,(77, 9)=long,(114, 2)=2,(103, 4)=3,(14, 8)=0,(92 , 9)=long,(105, 7)=1,(53, 3)=1,(90, 5)=3,(99, 4)=3,(62, 8)=1,(34, 9)=long,(113 , 1)=1,(70, 4)=2,(37, 9)=long,(20, 2)=0,(49, 7)=0,(68, 3)=2,(85, 3)=2,(30, 8)=1 ,(9, 7)=1,(84, 8)=1,(110, 1)=1,(12, 1)=0,(33, 2)=0,(16, 7)=1,(66, 7)=1,(59, 5)= 2,(15, 6)=0,(116, 2)=2,(26, 6)=0,(21, 7)=0,(109, 4)=4,(65, 3)=1,(81, 6)=2,(89, 6)=2,(20, 5)=1,(48, 3)=1,(92, 1)=1,(33, 6)=1,(63, 8)=1,(71, 5)=2,(96, 1)=1,(105 , 2)=2,(13, 5)=0,(88, 8)=1,(78, 4)=2,(100, 5)=3,(118, 6)=4,(102, 4)=3,(77, 3)=1 ,(44, 3)=0,(21, 6)=0,(31, 2)=0,(45, 8)=1,(107, 2)=2,(71, 1)=0,(19, 3)=0,(13, 8) =0,(66, 6)=1,(117, 5)=6,(50, 4)=1,(109, 1)=1,(41, 3)=1,(17, 2)=0,(31, 4)=1,(72 , 7)=1,(113, 3)=3,(83, 6)=2,(3, 6)=1,(114, 5)=5,(79, 2)=2,(58, 6)=2,(44, 8)=1,( 117, 7)=2,(10, 1)=0,(21, 5)=0,(3, 7)=0,(74, 9)=long,(29, 9)=long,(53, 4)=1,(43 , 3)=1,(20, 4)=1,(91, 8)=2,(43, 7)=0,(11, 5)=1,(49, 4)=1,(99, 1)=1,(81, 8)=2,( 98, 9)=long,(111, 6)=3,(76, 4)=2,(3, 1)=0,(51, 1)=0,(112, 6)=3,(113, 4)=4,(37, 1)=0,(31, 8)=0,(28, 4)=1,(76, 2)=1,(62, 3)=1,(7, 8)=0,(99, 5)=4,(98, 7)=1,(59, 9)=long,(80, 5)=3,(70, 9)=long,(1, 8)=0,(54, 6)=1,(38, 9)=long,(42, 3)=1,(12, 4 )=1,(99, 9)=long,(8, 8)=0,(43, 6)=1,(29, 8)=0,(89, 1)=0,(7, 5)=0,(55, 2)=1,(110 , 9)=long,(17, 7)=0,(98, 5)=4,(28, 5)=1,(53, 7)=1,(65, 5)=2,(93, 9)=long,(30, 7 )=1,(9, 4)=0,(4, 7)=0,(48, 4)=2,(90, 4)=3,(88, 9)=long,(107, 5)=4,(107, 9)=long ,(22, 3)=1,(97, 7)=2,(10, 7)=0,(94, 9)=long,(90, 8)=2,(42, 6)=0,(67, 4)=2,(81, 9)=long,(113, 8)=3,(80, 1)=0,(22, 4)=0,(46, 1)=0,(38, 8)=1,(55, 3)=1,(85, 2)=1, (72, 4)=2,(81, 7)=1,(68, 2)=1,(33, 4)=1,(3, 5)=0,(73, 2)=1,(4, 9)=long,(68, 5)= 2,(6, 6)=0,(116, 5)=6,(116, 8)=3,(71, 8)=1,(13, 2)=0,(64, 8)=1,(109, 8)=2,(102 , 2)=2,(45, 9)=long,(47, 7)=1,(9, 6)=1,(5, 5)=0,(86, 3)=2,(5, 8)=0,(60, 6)=1,( 15, 5)=0,(72, 1)=1,(71, 4)=2,(24, 8)=0,(89, 3)=2,(7, 4)=0,(61, 6)=1,(20, 1)=0,( 89, 9)=long,(8, 4)=0,(48, 2)=0,(74, 7)=0,(41, 8)=1,(56, 6)=1,(23, 7)=1,(38, 4)= 1,(32, 6)=1,(91, 5)=3,(51, 4)=1,(44, 1)=0,(99, 2)=2,(73, 1)=1,(101, 9)=long,(31 , 5)=1,(78, 9)=long,(107, 1)=1,(99, 3)=2,(54, 8)=1,(37, 8)=1,(120, 4)=5,(4, 1)= 0,(68, 1)=1,(49, 8)=1,(104, 9)=long,(45, 5)=2,(82, 5)=3,(17, 9)=long,(71, 9)= long,(21, 3)=1,(119, 6)=4,(41, 9)=long,(40, 4)=1,(45, 1)=0,(64, 2)=1,(30, 3)=0, (28, 8)=0,(28, 9)=long,(74, 6)=1,(52, 5)=2,(60, 4)=1,(101, 3)=2,(2, 8)=1,(21, 4 )=1,(36, 3)=1,(1, 2)=0,(117, 1)=1,(43, 4)=1,(52, 1)=0,(50, 3)=1,(69, 9)=long,( 120, 9)=long,(7, 2)=1,(19, 1)=0,(99, 6)=2,(20, 7)=0,(116, 3)=3,(56, 5)=2,(113, 7)=2,(55, 4)=2,(19, 6)=1,(31, 3)=1,(96, 9)=long,(56, 2)=1,(114, 6)=4,(48, 9)= long,(66, 4)=2,(49, 9)=long,(87, 8)=1,(90, 6)=2,(63, 6)=2,(38, 1)=0,(70, 6)=2,( 50, 5)=1,(44, 4)=1,(109, 3)=3,(92, 2)=2,(96, 2)=2,(117, 4)=5,(77, 8)=1,(58, 9)= long,(72, 6)=2,(12, 2)=0,(101, 6)=3,(52, 9)=long,(107, 4)=3,(19, 7)=0,(68, 7)=0 ,(46, 4)=1,(83, 3)=2,(119, 2)=3,(26, 4)=1,(1, 5)=0,(48, 6)=1,(58, 2)=1,(7, 1)=0 ,(6, 9)=long,(14, 6)=0,(109, 5)=4,(86, 8)=2,(51, 6)=2,(14, 9)=long,(34, 7)=0,( 51, 2)=0,(16, 4)=0,(54, 2)=1,(22, 8)=0,(78, 6)=2,(28, 2)=1,(61, 4)=2,(55, 1)=0, (30, 4)=1,(76, 1)=0,(74, 2)=2,(63, 3)=1,(27, 9)=long,(95, 9)=long,(8, 6)=0,(83 , 5)=3,(63, 5)=3,(102, 3)=2,(85, 7)=1,(70, 8)=1,(94, 8)=2,(85, 4)=3,(12, 6)=0,( 54, 7)=1,(119, 9)=long,(80, 7)=1,(82, 9)=long,(4, 5)=1,(38, 5)=1,(115, 8)=3,(18 , 8)=1,(16, 9)=long,(120, 6)=4,(34, 6)=0,(110, 5)=5,(64, 6)=2,(87, 3)=2,(67, 6) =1,(31, 1)=0,(120, 8)=3,(51, 9)=long,(39, 6)=1,(13, 4)=1,(80, 8)=2,(10, 5)=1,( 56, 3)=1,(23, 2)=0,(44, 9)=long,(115, 2)=2,(13, 6)=0,(75, 9)=long,(80, 3)=2,(24 , 3)=0,(21, 1)=0,(89, 5)=4,(107, 8)=2,(27, 5)=1,(62, 5)=2,(19, 8)=0,(9, 5)=0,( 32, 3)=0,(99, 7)=1,(93, 7)=1,(77, 5)=3,(101, 1)=1,(81, 5)=3,(77, 1)=1,(51, 8)=1 ,(69, 2)=0,(90, 2)=1,(64, 1)=0,(40, 7)=0,(108, 3)=3,(66, 9)=long,(91, 7)=1,(87 , 9)=long,(57, 7)=1,(43, 2)=1,(94, 2)=1,(88, 7)=1,(20, 8)=0,(120, 5)=6,(92, 7)= 1,(25, 1)=0,(51, 5)=2,(79, 4)=2,(69, 5)=3,(48, 1)=0,(112, 7)=1,(117, 3)=3,(80, 4)=2,(74, 3)=2,(91, 2)=2,(44, 2)=0,(14, 5)=0,(118, 8)=3,(15, 1)=1,(24, 2)=0,(65 , 8)=1,(18, 4)=1,(87, 4)=3,(71, 7)=1,(31, 7)=1,(113, 2)=2,(63, 2)=0,(37, 7)=1,( 120, 2)=3,(14, 7)=0,(108, 9)=long,(11, 2)=0,(50, 2)=1,(89, 8)=2,(116, 1)=1,(16 , 1)=0,(41, 1)=0,(75, 1)=0,(6, 8)=0,(6, 5)=0,(97, 3)=2,(39, 7)=1,(119, 4)=5,( 100, 2)=2,(1, 3)=0,(87, 2)=1,(86, 4)=2,(65, 2)=1,(4, 8)=0,(43, 9)=long,(26, 8)= 1,(64, 7)=1,(106, 6)=2,(35, 6)=1,(57, 9)=long,(83, 2)=1,(78, 7)=1,(83, 1)=1,(35 , 1)=0,(39, 3)=1,(35, 8)=0,(12, 5)=1,(55, 5)=2,(79, 7)=1,(48, 5)=2,(79, 3)=2,(4 , 3)=0,(54, 3)=1,(52, 6)=1,(100, 7)=1,(55, 8)=1,(6, 4)=0,(98, 6)=3,(89, 7)=1,( 65, 7)=1,(98, 3)=2,(12, 3)=0,(22, 5)=0,(97, 5)=4,(14, 2)=1,(101, 8)=2,(20, 9)= long,(27, 7)=0,(57, 3)=1,(26, 7)=0,(115, 1)=1,(21, 2)=1,(52, 2)=0,(28, 6)=0,(32 , 8)=1,(93, 1)=0,(26, 5)=1,(113, 6)=3,(30, 1)=0,(38, 7)=1,(77, 4)=2,(109, 9)= long,(119, 1)=1,(61, 3)=2,(74, 8)=1,(53, 5)=2,(71, 3)=2,(75, 2)=1,(41, 7)=0,(38 , 3)=1,(35, 9)=long,(116, 7)=2,(40, 5)=2,(120, 3)=4,(73, 7)=1,(96, 6)=2,(61, 1) =0,(84, 3)=2,(90, 7)=1,(56, 1)=1,(16, 8)=0,(17, 3)=0,(40, 6)=1,(92, 3)=2,(90, 3 )=2,(103, 9)=long,(47, 9)=long,(1, 6)=0,(79, 5)=2,(87, 7)=1,(8, 2)=0,(60, 1)=1, (8, 5)=0,(42, 7)=0,(28, 1)=0,(103, 7)=1,(75, 7)=1,(19, 4)=1,(37, 5)=2,(109, 2)= 2,(105, 9)=long,(59, 1)=0,(5, 6)=0,(91, 1)=1,(33, 3)=1,(106, 3)=3,(80, 2)=1,(27 , 2)=0,(99, 8)=2,(43, 1)=1,(27, 4)=1,(83, 8)=1,(114, 8)=2,(118, 3)=4,(106, 2)=2 ,(54, 1)=1,(100, 4)=3,(35, 4)=1,(93, 2)=1,(111, 9)=long,(108, 6)=3,(5, 9)=long, (114, 4)=4,(60, 7)=1,(111, 3)=3,(48, 7)=0,(94, 3)=2,(9, 1)=0,(90, 1)=1,(90, 9)= long,(68, 4)=2,(5, 2)=0,(66, 3)=2,(73, 3)=2,(56, 8)=1,(32, 2)=0,(57, 8)=1,(59, 4)=2,(60, 9)=long,(96, 4)=3,(16, 2)=0,(55, 9)=long,(104, 7)=2,(102, 5)=4,(32, 4 )=1,(55, 6)=1,(111, 7)=2,(58, 8)=1,(108, 2)=2,(36, 7)=0,(24, 6)=1,(23, 3)=0,(52 , 3)=1,(112, 9)=long,(36, 5)=1,(54, 9)=long,(26, 1)=0,(4, 2)=0,(94, 4)=3,(5, 1) =0,(103, 5)=4,(17, 8)=1,(23, 4)=0,(103, 2)=2,(60, 3)=1,(36, 2)=1,(115, 9)=long, (110, 3)=3,(82, 6)=2,(72, 9)=long,(115, 3)=3,(50, 1)=1,(110, 4)=4,(98, 2)=1,(76 , 8)=1,(101, 2)=1,(79, 6)=1,(75, 8)=2,(94, 6)=2,(93, 8)=2,(24, 9)=long,(101, 7) =2,(118, 4)=5,(38, 2)=0,(52, 4)=2,(70, 1)=0,(34, 1)=0,(40, 3)=1,(69, 3)=1,(108 , 1)=1,(93, 6)=3,(28, 7)=0,(25, 2)=0,(116, 4)=4,(91, 3)=2,(118, 7)=2,(72, 5)=2, (74, 1)=1,(17, 1)=0,(65, 6)=2,(11, 3)=0,(117, 6)=4,(12, 9)=long,(11, 7)=0,(82, 7)=1,(30, 2)=0,(103, 8)=2,(15, 8)=0,(32, 5)=2,(29, 3)=1,(91, 6)=2,(78, 8)=1,(16 , 5)=1,(40, 9)=long,(108, 5)=4,(65, 4)=1,(98, 4)=3,(2, 1)=0,(102, 1)=1,(76, 6)= 2,(71, 6)=2,(82, 2)=1,(66, 8)=1,(39, 9)=long,(15, 4)=0,(62, 9)=long,(95, 6)=2,( 55, 7)=0,(85, 6)=2,(41, 4)=1,(61, 9)=long,(71, 2)=1,(111, 8)=2,(108, 4)=4,(26, 3)=1,(85, 8)=2,(93, 3)=2,(29, 2)=1,(76, 3)=2,(91, 9)=long,(16, 3)=0,(120, 1)=2, (6, 7)=0,(114, 7)=2,(30, 9)=long,(92, 4)=3,(21, 8)=0,(49, 1)=0,(14, 1)=0,(22, 9 )=long,(10, 8)=1,(36, 1)=1,(52, 8)=1,(47, 5)=1,(2, 7)=0,(59, 7)=1,(47, 4)=1,(98 , 1)=1,(24, 1)=0,(35, 7)=0,(23, 6)=1,(63, 9)=long,(83, 9)=long,(10, 4)=0,(95, 5 )=3,(18, 9)=long,(106, 7)=1,(79, 1)=1,(112, 5)=5,(104, 5)=4,(5, 3)=0,(105, 4)=3 ,(100, 3)=3,(114, 9)=long,(59, 2)=1,(98, 8)=2,(102, 9)=long,(115, 6)=4,(62, 2)= 1,(117, 9)=long,(59, 6)=1,(97, 8)=2,(86, 7)=1,(97, 9)=long,(3, 4)=0,(23, 8)=1,( 37, 2)=0,(51, 3)=1,(113, 9)=long,(67, 1)=1,(72, 2)=1,(44, 6)=2,(29, 6)=0,(39, 4 )=1,(32, 1)=0,(53, 9)=long,(68, 6)=1,(106, 1)=1,(80, 9)=long,(2, 6)=0,(36, 6)=0 ,(95, 8)=2,(5, 4)=1,(43, 8)=0,(18, 1)=0,(79, 8)=1,(95, 3)=2,(1, 7)=1,(66, 5)=2, (64, 3)=1,(25, 3)=0,(92, 8)=1,(67, 3)=1,(2, 3)=0,(112, 4)=4,(11, 6)=1,(12, 8)=0 ,(53, 1)=0,(44, 7)=1,(27, 8)=0,(108, 8)=2,(102, 8)=2,(8, 9)=long,(26, 2)=0,(48 , 8)=1,(80, 6)=2,(112, 8)=3,(85, 5)=3,(64, 5)=2,(110, 6)=3,(45, 4)=1,(63, 1)=0, (114, 3)=3,(88, 2)=2,(27, 1)=0,(76, 7)=1,(47, 2)=1,(22, 1)=1,(89, 2)=1,(69, 1)= 0,(29, 7)=0,(95, 1)=1,(20, 6)=0,(88, 3)=2,(94, 5)=4,(115, 7)=2,(100, 9)=long,( 96, 5)=3,(76, 5)=3,(42, 4)=1,(22, 2)=1,(70, 7)=1,(3, 9)=long,(12, 7)=0,(54, 4)= 1,(24, 5)=1,(25, 4)=1,(97, 1)=0,(23, 9)=long,(47, 3)=1,(1, 4)=0,(16, 6)=1,(3, 8 )=0,(30, 5)=1,(11, 8)=0,(40, 1)=0,(110, 8)=2,(61, 8)=1,(21, 9)=long,(63, 4)=2,( 34, 2)=1,(104, 3)=2,(117, 2)=2,(72, 8)=1,(118, 1)=1,(70, 3)=1,(47, 1)=1,(57, 5) =2,(75, 3)=1,(107, 3)=3,(75, 6)=2,(77, 7)=1,(89, 4)=3,(62, 4)=2,(62, 7)=0,(18, 3)=0,(54, 5)=1,(102, 7)=1,(2, 9)=long,(66, 2)=1,(43, 5)=1,(37, 6)=1,(69, 4)=2,( 100, 6)=2,(8, 3)=0,(25, 6)=1,(86, 9)=long,(85, 1)=0,(101, 4)=3,(116, 9)=long,( 20, 3)=1,(23, 5)=1,(56, 4)=1,(17, 6)=1,(88, 4)=2,(36, 4)=1,(112, 2)=2,(39, 8)=0 ,(9, 2)=0,(106, 5)=4,(75, 5)=3,(45, 3)=1,(1, 1)=0,(68, 9)=long,(100, 1)=1,(42, 2)=1,(15, 7)=0,(62, 1)=1,(74, 4)=2,(86, 1)=1,(62, 6)=1,(65, 1)=1,(50, 9)=long,( 87, 1)=1,(76, 9)=long,(10, 2)=0,(70, 5)=3,(88, 6)=2,(14, 4)=0,(73, 8)=1,(97, 2) =1,(19, 5)=1,(69, 8)=2,(46, 6)=1,(31, 9)=long,(69, 7)=1,(41, 5)=1,(73, 6)=1,(46 , 9)=long,(88, 5)=3,(29, 1)=1,(111, 1)=1,(24, 4)=1,(49, 5)=2,(15, 3)=0,(84, 6)= 2,(56, 9)=long,(87, 6)=2,(109, 7)=2,(46, 7)=1,(50, 6)=1,(61, 2)=1,(2, 2)=0,(30 , 6)=1,(6, 1)=0,(25, 9)=long,(119, 5)=6,(105, 1)=1,(84, 9)=long,(34, 5)=1,(41, 2)=1,(33, 9)=long,(59, 3)=1,(13, 3)=1,(119, 3)=4,(63, 7)=1,(7, 6)=0,(4, 4)=0,( 96, 7)=1,(75, 4)=2,(82, 3)=2,(102, 6)=3,(84, 1)=1,(17, 4)=0,(105, 6)=3,(61, 5)= 2,(109, 6)=3,(57, 6)=2,(93, 4)=3,(93, 5)=4,(7, 9)=long,(38, 6)=1,(34, 8)=1,(25 , 8)=1,(111, 2)=2,(84, 5)=2,(97, 6)=3,(82, 4)=3]); coeffF := array(1 .. 24, 1 .. 5,[(15, 2)=1,(22, 5)=long,(8, 2)=1,(3, 4)=0,(2, 2 )=0,(6, 4)=0,(24, 5)=long,(22, 2)=3,(13, 4)=1,(1, 4)=1,(12, 2)=1,(15, 5)=long,( 21, 4)=1,(10, 3)=1,(23, 1)=1,(6, 5)=short,(13, 3)=2,(1, 1)=0,(18, 5)=long,(16, 5)=long,(15, 4)=2,(3, 5)=long,(16, 1)=1,(22, 4)=2,(7, 1)=0,(22, 3)=4,(14, 4)=1, (19, 1)=1,(8, 5)=long,(4, 5)=long,(17, 1)=1,(4, 1)=1,(20, 3)=4,(23, 4)=2,(6, 2) =1,(9, 4)=1,(23, 2)=2,(18, 3)=2,(9, 1)=0,(5, 1)=0,(1, 3)=0,(5, 5)=short,(10, 5) =short,(11, 2)=1,(16, 2)=2,(9, 5)=short,(4, 4)=0,(6, 3)=1,(16, 4)=0,(7, 2)=1,( 20, 5)=long,(19, 2)=2,(9, 3)=1,(19, 5)=short,(20, 4)=2,(17, 2)=1,(4, 2)=0,(2, 5 )=short,(6, 1)=0,(11, 1)=0,(10, 1)=1,(4, 3)=0,(11, 3)=2,(21, 1)=1,(9, 2)=1,(5, 3)=1,(20, 1)=1,(3, 1)=0,(12, 4)=0,(5, 4)=1,(23, 5)=short,(17, 5)=short,(11, 4)= 2,(12, 5)=long,(12, 3)=2,(8, 3)=0,(10, 2)=1,(7, 5)=long,(13, 5)=short,(24, 1)=2 ,(5, 2)=0,(21, 2)=2,(8, 4)=0,(14, 5)=short,(18, 1)=1,(20, 2)=2,(13, 1)=0,(1, 2) =0,(2, 1)=0,(19, 4)=1,(3, 2)=1,(21, 5)=short,(7, 4)=0,(2, 3)=1,(16, 3)=2,(24, 3 )=4,(8, 1)=1,(1, 5)=short,(14, 1)=1,(23, 3)=3,(24, 4)=2,(11, 5)=long,(15, 1)=1, (7, 3)=2,(18, 4)=2,(22, 1)=1,(19, 3)=2,(14, 3)=1,(3, 3)=0,(10, 4)=0,(17, 3)=2,( 24, 2)=3,(2, 4)=0,(12, 1)=1,(17, 4)=1,(18, 2)=2,(21, 3)=3,(13, 2)=1,(15, 3)=2,( 14, 2)=1]); coeffFrev := array(1 .. 24, 1 .. 5,[(10, 4)=1,(22, 1)=2,(14, 2)=1,(8, 5)=long,( 9, 3)=1,(9, 5)=short,(14, 5)=short,(23, 4)=1,(13, 2)=2,(3, 5)=long,(24, 2)=4,( 15, 3)=1,(15, 4)=1,(5, 1)=1,(20, 5)=long,(11, 3)=1,(23, 3)=2,(7, 4)=0,(18, 5)= long,(9, 1)=1,(22, 3)=3,(20, 3)=2,(1, 1)=1,(10, 1)=0,(15, 1)=2,(17, 1)=1,(18, 4 )=1,(4, 1)=0,(8, 2)=0,(11, 2)=2,(21, 1)=1,(18, 3)=2,(12, 3)=1,(20, 4)=1,(22, 2) =4,(19, 1)=1,(6, 2)=1,(23, 5)=short,(19, 5)=short,(20, 2)=4,(24, 5)=long,(9, 4) =0,(5, 2)=1,(12, 2)=2,(13, 3)=1,(3, 4)=0,(16, 5)=long,(7, 2)=2,(24, 1)=2,(10, 2 )=1,(15, 2)=2,(17, 2)=2,(8, 4)=1,(20, 1)=2,(4, 2)=0,(11, 4)=0,(17, 4)=1,(21, 2) =3,(5, 5)=short,(1, 4)=0,(15, 5)=long,(12, 4)=1,(19, 2)=2,(14, 4)=1,(10, 3)=1,( 11, 1)=2,(17, 5)=short,(22, 5)=long,(17, 3)=1,(4, 3)=0,(6, 3)=1,(24, 3)=3,(13, 4)=0,(16, 1)=0,(9, 2)=1,(21, 3)=2,(2, 4)=0,(14, 3)=1,(19, 4)=1,(1, 2)=0,(2, 1)= 0,(18, 1)=2,(23, 1)=2,(16, 3)=2,(1, 3)=0,(19, 3)=2,(10, 5)=short,(22, 4)=1,(2, 5)=short,(18, 2)=2,(8, 3)=1,(21, 4)=1,(16, 2)=2,(7, 3)=1,(3, 1)=0,(23, 2)=3,(11 , 5)=long,(13, 5)=short,(12, 5)=long,(6, 4)=0,(6, 5)=short,(3, 3)=1,(16, 4)=1,( 6, 1)=0,(2, 2)=1,(12, 1)=0,(14, 1)=1,(5, 4)=0,(13, 1)=1,(7, 5)=long,(4, 4)=1,(7 , 1)=0,(5, 3)=0,(1, 5)=short,(3, 2)=0,(21, 5)=short,(2, 3)=0,(8, 1)=0,(24, 4)=2 ,(4, 5)=long]); coeffG := array(1 .. 6, 1 .. 3,[(6, 3)=long,(5, 1)=1,(2, 3)=long,(5, 2)=2,(3, 1 )=1,(3, 3)=short,(4, 1)=1,(5, 3)=short,(1, 1)=0,(6, 1)=2,(4, 2)=3,(1, 3)=short, (3, 2)=1,(2, 1)=1,(1, 2)=1,(6, 2)=3,(4, 3)=long,(2, 2)=0]); coeffGrev := array(1 .. 6, 1 .. 3,[(5, 3)=short,(6, 2)=2,(1, 1)=1,(3, 3)=short, (6, 1)=3,(2, 3)=long,(4, 1)=3,(1, 2)=0,(1, 3)=short,(3, 1)=1,(2, 1)=0,(6, 3)= long,(4, 2)=1,(3, 2)=1,(4, 3)=long,(2, 2)=1,(5, 1)=2,(5, 2)=1]);