{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 7 1 2 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36894 "with(linalg):\n\n charform :=\n\n # Written By M. K. Bos\n # This procedure calculates \+ the character formula for X lower N upper r with\n # specialization (s ).\n proc(X,N,r,s)\n\n local funkyfin,Xfin,Nfin,Ndual,rdual,imadim, comat,delta,flag,S,K,P;\n\n P:=init(X,N,r);\n\n \+ Nfin:=P[1];\n\n rdual:=P[2];\n\n imadim:=P[3 ];\n\n comat:=P[4];\n\n delta:=P[5];\n\n \+ FunkyAcase:=P[6];\n\n S:=s;\n\n if Funk yAcase \n\n then K:= Agenhits(comat,S,rdual,delta,imad im,Nfin); \n\n else K:= genhits(comat,S,rdual,delta,im adim,Nfin);\n\n fi;\n\n K:=reduce(K);\n\n \+ d:=vectdim(K);\n\n print(eval(K));\n\n \+ print(d);\n\n # P:= Product( product((1-q^(d*k-i))^eval(K[i ]),i=1..d),k=1..infinity);\n\n # print(eval(P));\n\n end;\n \n \n\n init :=\n\n \n\n proc(X,N,r)\n\n local Xfin,Nfin,Ndual ,rdual,imadim,comat,delta,FunkyAcase;\n\n FunkyAcase:=false;\n \n if X = A then\n\n if r = 1 then\n\n \+ Xfin := A;\n\n Nfin := N;\n\n Ndu al := N;\n\n rdual := 1;\n\n imadim := 0;\n\n comat := comatA(Nfin)\n\n else\n\n if N mod 2 = 0 then\n\n FunkyAcas e:=true;\n\n Xfin := B;\n\n Nf in := 1/2*N;\n\n Ndual := 2*N;\n\n \+ rdual := 2;\n\n imadim := 1/2*N;\n\n \+ comat := comatA2(Nfin);\n\n else\n\n \+ Xfin := B;\n\n Nfin := 1/2*N+1/2;\n \n Ndual := 1/2*N+1/2;\n\n rdu al := 1;\n\n imadim := 0;\n\n \+ comat := comatB(Nfin)\n\n fi\n\n fi\n\n \+ else\n\n if X = B then\n\n Xfin := C ;\n\n Nfin := N;\n\n Ndual := 2*N-1;\n \n rdual := 2;\n\n imadim := N-1;\n\n \+ comat := comatC(Nfin)\n\n else\n\n \+ if X = C then\n\n Xfin := B;\n\n \+ Nfin := N;\n\n Ndual := N+1;\n\n \+ rdual := 2;\n\n imadim := 1;\n\n \+ comat := comatB(N)\n\n else\n\n \+ if X = D then\n\n if r = 1 the n\n\n Xfin := D;\n\n \+ Nfin := N;\n\n Ndual := N;\n\n \+ rdual := 1;\n\n im adim := 0;\n\n comat := comatD(Nfin)\n\n \+ else\n\n if r = 2 t hen\n\n Xfin := C;\n\n \+ Nfin := N-1;\n\n Ndua l := N-1;\n\n rdual := 1;\n\n \+ imadim := 0;\n\n \+ comat := comatC(Nfin)\n\n else\n\n \+ Xfin := G;\n\n \+ Nfin := 2;\n\n Ndual := 2;\n\n \+ rdual := 1;\n\n \+ imadim := 0;\n\n comat := coef fG\n\n fi\n\n fi\n \n else\n\n if X = E then \n\n if r = 2 then\n\n \+ Xfin := F;\n\n Nfin := 4; \n\n Ndual := 4;\n\n \+ rdual := 1;\n\n imadim \+ := 0;\n\n comat := coeffF\n\n \+ else\n\n Xfin := E ;\n\n Nfin := N;\n\n \+ Ndual := N;\n\n rdual : = 1;\n\n imadim := 0;\n\n \+ if N = 6 then comat := coeffE6\n\n \+ else\n\n if N = 7 then\n\n comat := coeffE7\n \n else comat := coeffE8\n\n \+ fi\n\n \+ fi\n\n fi\n\n else \n\n if X = F then\n\n \+ Xfin := F;\n\n Nfin := 4; \n\n Ndual := 6;\n\n \+ rdual := 2;\n\n imadim \+ := 2;\n\n comat := coeffFrev\n\n \+ else\n\n Xfin : = G;\n\n Nfin := 2;\n\n \+ Ndual := 4;\n\n rdua l := 3;\n\n imadim := 1;\n\n \+ comat := coeffGrev\n\n \+ fi\n\n fi\n\n fi\n\n \+ fi\n\n fi\n\n fi;\n\n delta := getdelta(X,N,r);\n\n RETURN(Nfin,rdual,imadim,comat,delta, FunkyAcase)\n\n end;\n\n \n\n getdelta :=\n\n \n\n proc(X,N,r) \n\n local delta;\n\n if X = A then\n\n if r = 1 then delta := vector(N+1,1)\n\n else\n\n \+ if N mod 2 = 0 then delta := vector(1/2*N+1,2); delta[1] := 1\n\n \+ else delta := vector(1/2*N+3/2,2); delta[1] := 1; delta[ 2] := 1\n\n fi\n\n fi\n\n else\n\n if X = B then\n\n delta := vector(N+1,2); \n\n delta[1] := 1;\n\n delta[2] := 1; \n\n delta[N+1] := 1\n\n else\n\n \+ if X = C then delta := vector(N+1,1)\n\n else \n\n if X = D then\n\n if \+ r = 1 then\n\n delta := vector(N+1,2);\n\n delta[1] := 1;\n\n \+ delta[2] := 1;\n\n delta[N] := 1;\n \n delta[N+1] := 1\n\n \+ else\n\n if r = 2 then\n\n \+ delta := vector(N,2);\n\n \+ delta[1] := 1;\n\n delta[N] \+ := 1\n\n else delta := vector([1,2,3])\n\n fi\n\n fi\n\n \+ else\n\n if X = E then\n\n \+ if r = 2 then delta := vector([1,2,3,4,2])\n \n else\n\n \+ if N = 6 then delta := vector([1,1,2,3,2,1,2])\n\n \+ else\n\n if N = 7 t hen\n\n delta := vector([1,2,3 ,4,3,2,1,2])\n\n else delta := vec tor([1,2,3,4,5,6,4,2,3])\n\n fi\n \n fi\n\n \+ fi\n\n else\n\n if X = F then delta := vector([1,2,3,2,1])\n\n \+ else delta := vector([1,2,1])\n\n fi\n \n fi\n\n fi\n\n \+ fi\n\n fi\n\n fi;\n\n RETURN(delta) \n\n end;\n\n \n\n\n\nAgenhits :=\n\n \n\n proc(C,S,rdual,delt a,imadim,Nfin)\n\n local i,j,t,k,c0,p,q,modulo,dim,L,powers,s,C0; \n\n t := coldim(C);\n\n s:=vector(t,0);\n\n f or i to t do \n\n s[i] := eval(S[i]+1) \n\n od;\n \n modulo := dotprod(delta,s,orthogonal);\n\n dim := m odulo*rdual;\n\n L := vector(dim,0);\n\n powers := eva lm(C &* s);\n\n k := vectdim(powers);\n\n L[dim] := Nf in;\n\n for i from 1 to Nfin*Nfin do\n\n for j from 0 to 1 do\n\n p := j*modulo+powers[i];\n\n \+ q := (j+1)*modulo-powers[i];\n\n \+ L[p] := eval(L[p]+1);\n\n L[q] := eval(L[q]+1)\n \n od\n\n od;\n\n for i from Nfin*Nfin +1 to Nfin*Nfin+Nfin do\n\n p := powers[i];\n\n \+ q := dim-powers[i];\n\n L[p] := eval(L[p]+1) ;\n\n L[q] := eval(L[q]+1);\n\n od;\n\n \+ L[modulo] := eval(L[modulo])+imadim ;\n\n for i to dim do L[ i]:=eval(L[i]-Nfin) od;\n\n RETURN(L)\n\n end;\n\n \n\n ge nhits :=\n\n \n\n proc(C,S,rdual,delta,imadim,Nfin)\n\n local \+ i,j,t,k,c0,p,q,modulo,dim,L,powers,s,C0;\n\n t := coldim(C);\n \n s:=vector(t,0);\n\n C0 := delcols(C,t .. t);\n\n \+ for i to t do \n\n s[i] := eval(S[i]+1) \n\n \+ od;\n\n k := rowdim(C);\n\n c0 := matrix(k,1,0);\n\n C0 := augment(c0,C0);\n\n modulo := dotprod(delta,s,o rthogonal);\n\n dim := modulo*rdual;\n\n L := vector(d im,0);\n\n powers := evalm(C0 &* s);\n\n k := vectdim( powers);\n\n L[dim] := Nfin;\n\n for i to k do\n\n \+ if C[i,t] = short then\n\n for j from 0 to rd ual-1 do\n\n p := j*modulo+powers[i];\n\n \+ q := (j+1)*modulo-powers[i];\n\n L[p] \+ := eval(L[p]+1);\n\n L[q] := eval(L[q]+1)\n\n \+ od\n\n else\n\n p := powers[i] ;\n\n q := dim-powers[i];\n\n L[p] := \+ eval(L[p]+1);\n\n L[q] := eval(L[q]+1);\n\n \+ fi\n\n od;\n\n if rdual <> 1 then\n\n fo r i to rdual-1 do L[modulo*i] := eval(L[modulo*i])+imadim od\n\n \+ fi;\n\n for i to dim do L[i]:=eval(L[i]-Nfin) od;\n\n \+ RETURN(L)\n\n end;\n\n reduce := proc(K)\n\n \n\n local T,A,i, j,k,l,p;\n\n T:=eval(K);\n\n k:=vectdim(T);\n\n \n\n i := 1;\n\n while i < vectdim(T) do\n\n if type(k/i,integer)\n\n then A:=vector(i );\n\n for j to i do A[j]:=eval(T[j]) od;\n\n p:=0;\n\n \+ j:=1;\n\n while p=0 and j<=i do\n\n l:=j+i;\n \n while p=0 and l<=k do\n\n p:=eval(p + abs (A[j]-T[l]));\n\n l:=eval(l+i);\n\n od;\n\n \+ j:=eval(j+1);\n\n od;\n\n if p=0\n\n t hen T:=A;\n\n fi\n\n fi;\n\n i:=eval(i+1);\n\n od;\n\n \+ \n\n RETURN(eval(T));\n\n end;\n\n comatA2:= proc(N)\n\n \n\n local i, j,k,iCurr, C;\n\n iCurr:=1;\n\n C:= matrix(N*N+N,N+1,0);\n\n for i fro m 2 to N+1 do\n\n C[iCurr,i]:=1;\n\n iCurr:=iCurr + 1;\n\n od;\n\n for i from 2 to N do\n\n for j from 0 to N + 1 - i do\n\n f or k from 0 to i-1 do\n\n C[iCurr, j+k+1]:=1;\n\n od; \n\n iCurr:=iCurr + 1;\n\n od;\n\n od;\n\n for i from 1 to \+ N-2 do\n\n for j from N-i by -1 to 2 do\n\n for k from N-i by -1 to 1 do\n\n if k>=j then C[iCurr,k+1]:=1\n\n \+ else C[iCurr,k+1]:=2\n\n fi\n\n od; \n\n C[iCurr,1]:=1;\n\n iCurr:=iCurr + 1;\n\n od; \n\n od;\n\n for i from 1 to N do\n\n for j from 1 to N-i do\n\n \+ C[iCurr,j+1]:=2;\n\n od;\n\n C[iCurr,1]:=1;\n\n iCu rr:=iCurr + 1;\n\n od;\n\n RETURN(evalm(C));\n\n end;\n\n \n\n comatA: = proc(N)\n\n \n\n local i,j,k,iCurr, C;\n\n iCurr:=1;\n\n C:= matrix( N*(N+1)/2,N+1,0);\n\n for i to N do\n\n for j to (N+1)-i do\n\n \+ for k from 0 to i-1 do\n\n C[iCurr, j+k]:=1;\n\n o d;\n\n iCurr:=iCurr + 1;\n\n od\n\n od;\n\n for i to N*(N+1) /2 do\n\n C[i,N+1]:=long;\n\n od;\n\n RETURN(evalm(C));\n\n \n\n e nd;\n\n comatB:= proc(N)\n\n \n\n local i,j,k,iCurr, C;\n\n iCurr:=1; \n\n C:= matrix(N*N,N+1,0);\n\n for i to N do\n\n for j to (N+1)-i do\n\n for k from 0 to i-1 do\n\n C[iCurr, j+k]:=1;\n \n od;\n\n iCurr:=iCurr + 1;\n\n od\n\n od;\n\n for i \+ to N-1 do\n\n for j from 0 to N - i - 1 do\n\n for k from \+ i to N do\n\n if k <= (i+j)\n\n then C[iCurr ,k]:=1\n\n else C[iCurr,k]:=2\n\n fi;\n\n \+ od;\n\n iCurr:=iCurr + 1;\n\n od;\n\n od;\n\n for i t o N*N do\n\n if C[i,N] = 1\n\n then C[i,N+1]:=short\n\n el se C[i,N+1]:=long\n\n fi;\n\n od;\n\n \n\n RETURN(evalm(C));\n\n \n \n end;\n\n comatC:= proc(N)\n\n \n\n local a,i,j,k,iCurr, C;\n\n iCur r:=1;\n\n C:= matrix(N*N,N+1,0);\n\n for i to N do\n\n for j to (N +1)-i do\n\n for k from 0 to i-1 do\n\n C[iCurr, j+k]: =1;\n\n od;\n\n iCurr:=iCurr + 1;\n\n od\n\n od;\n\n f or i to N-1 do\n\n for j from 0 to N - i -1 do\n\n for k from i to N-1 do\n\n if k < i + j \n\n then C[iCur r, k]:=1\n\n else C[iCurr, k]:=2\n\n fi\n\n \+ od;\n\n C[iCurr,N]:=1;\n\n iCurr:=iCurr + 1;\n\n od; \n\n od;\n\n \n\n for i to N*N do\n\n a:=1;\n\n while C[i,a] \+ = 0 do\n\n a:=a+1\n\n od;\n\n if C[i,a] = 2 or a = N\n\n then C[i,N+1]:=long\n\n else C[i,N+1]:=short\n\n fi ;\n\n od;\n\n \n\n \n\n RETURN(evalm(C));\n\n \n\n end;\n\n \n\n co matD:= proc(N)\n\n \n\n local i,j,k,iCurr, C, CF;\n\n iCurr:=1;\n\n C: = matrix(N*N-N+1,N+1,0);\n\n for i to N do\n\n for j to (N+1)-i d o\n\n for k from 0 to i-1 do\n\n C[iCurr, j+k]:=1;\n\n \+ od;\n\n iCurr:=iCurr + 1;\n\n od\n\n od;\n\n \n\n for \+ i to N-2 do\n\n for j from i to N - 2 do\n\n C[iCurr, j]: =1;\n\n od;\n\n C[iCurr, N]:=1;\n\n iCurr:=iCurr + 1;\n\n \+ od;\n\n \n\n for i to N-3 do\n\n for j from 0 to N - 3 - i do\n\n \+ for k from i to N-2 do\n\n if k<= i+j\n\n \+ then C[iCurr, k]:=1\n\n else C[iCurr, k]:=2\n\n fi\n\n od;\n\n C[iCurr, N-1]:=1;\n\n \+ C[iCurr, N]:=1;\n\n iCurr:=iCurr + 1;\n\n od\n\n od; \n\n CF:=delrows(C,2*N-1..2*N-1);\n\n for i to N*N-N do\n\n CF[i,N +1]:=long;\n\n od;\n\n \n\n \n\n RETURN(evalm(CF));\n\n \n\n end;\n\nc oeffE6 := array(1 .. 36, 1 .. 7,[(26, 3)=2,(28, 3)=2,(6, 7)=long,(7, 4 )=1,(26\n\n , 5)=1,(34, 7)=long,(30, 6)=1,(21, 7)=long,(31, 3)=2,(15, \+ 7)=long,(10, 2)=1,(2\n\n , 4)=0,(6, 6)=0,(32, 1)=1,(15, 6)=0,(1, 4)=0, (11, 3)=0,(26, 6)=1,(36, 1)=1,(7, \n\n 6)=1,(3, 1)=0,(3, 5)=0,(12, 6)= 1,(29, 7)=long,(3, 3)=0,(8, 2)=0,(22, 3)=1,(18, \n\n 5)=0,(30, 2)=1,(3 6, 4)=2,(18, 7)=long,(22, 4)=1,(13, 2)=0,(34, 1)=1,(35, 5)=1,(\n\n 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\n\n , 1)=1,(33, 1)=1,(14, 6)=0,(8, 3)=1,(9, 5)=0,(20, 1)=1,(25, \+ 4)=1,(18, 2)=1,(32\n\n , 3)=2,(26, 7)=long,(8, 5)=1,(18, 3)=1,(7, 5)=0 ,(15, 3)=1,(16, 1)=1,(36, 3)=3,(\n\n 21, 2)=1,(29, 5)=1,(32, 6)=1,(35, 4)=2,(5, 2)=1,(19, 5)=1,(31, 4)=1,(31, 7)=\n\n long,(14, 3)=1,(23, 4) =1,(14, 7)=long,(23, 1)=1,(4, 7)=long,(30, 1)=1,(4, 2)=0,\n\n (33, 7)= long,(17, 1)=0,(10, 6)=0,(32, 2)=1,(20, 4)=0,(8, 7)=long,(18, 6)=1,(20 \n\n , 7)=long,(36, 2)=2,(23, 6)=1,(2, 6)=0,(3, 2)=0,(31, 1)=1,(1, 5)= 0,(11, 7)=long\n\n ,(13, 6)=0,(15, 5)=0,(32, 5)=1,(28, 5)=1,(28, 6)=0, (34, 2)=2,(5, 7)=long,(6, 3)\n\n =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\n\n ,(19, 2)=1,(29, 2)=1,(3 4, 4)=2,(5, 5)=0,(19, 4)=1,(35, 2)=2,(3, 6)=0,(5, 6)=0,(\n\n 33, 2)=2, (27, 5)=1,(5, 3)=0,(14, 4)=0,(20, 3)=1,(20, 2)=1,(21, 4)=1,(22, 7)=\n \n long,(27, 2)=1,(13, 4)=1,(5, 1)=0,(3, 7)=long,(30, 4)=1,(15, 4)=1,( 22, 1)=0,(24\n\n , 7)=long,(15, 1)=0,(17, 6)=1,(36, 5)=2,(18, 4)=1,(1, 7)=long,(23, 2)=1,(26, 1)\n\n =0,(35, 3)=3,(21, 6)=0,(7, 3)=0,(30, 3) =2,(6, 4)=0,(17, 2)=0,(16, 5)=0,(36, 7)=\n\n long,(10, 4)=0,(8, 4)=0,( 27, 4)=1,(26, 2)=1,(29, 1)=0,(31, 2)=2,(1, 6)=1,(17, 5\n\n )=1,(24, 1) =0,(28, 1)=1,(29, 4)=2,(14, 2)=1,(30, 5)=1,(33, 5)=1,(33, 4)=1,(4, 1\n \n )=0,(16, 2)=1,(2, 2)=0,(14, 5)=1,(27, 6)=1,(34, 5)=1,(10, 5)=0,(29, 3)=2,(11, 4\n\n )=0,(11, 6)=0,(19, 3)=1,(25, 1)=1,(5, 4)=0,(27, 7)=lo ng,(7, 1)=0,(9, 2)=0,(1, 2\n\n )=0,(35, 7)=long,(17, 4)=1,(15, 2)=1,(1 6, 7)=long,(34, 6)=1,(32, 4)=2,(7, 7)=\n\n long,(25, 3)=1,(12, 3)=1,(1 6, 6)=0,(16, 4)=0,(6, 5)=0,(25, 6)=0,(30, 7)=long,(\n\n 22, 6)=1,(23, \+ 5)=0,(9, 4)=1,(12, 7)=long,(34, 3)=2,(8, 6)=0,(4, 5)=0,(9, 1)=0,(\n\n \+ 24, 4)=1,(10, 1)=0,(29, 6)=1,(19, 6)=0,(21, 5)=0,(24, 6)=0,(6, 2)=0,(1 0, 7)=\n\n long,(24, 3)=2,(24, 2)=1,(3, 4)=1,(9, 7)=long,(20, 6)=0,(28 , 2)=1,(17, 7)=long,\n\n (28, 4)=1,(4, 3)=1,(22, 2)=1,(26, 4)=1,(1, 1) =0,(2, 7)=long,(8, 1)=0,(33, 3)=2,\n\n (2, 3)=0,(13, 1)=0,(25, 7)=long ,(12, 2)=0,(25, 2)=1,(4, 6)=0,(13, 3)=1,(36, 6)=\n\n 1,(13, 7)=long,(2 3, 3)=1,(27, 3)=1,(31, 5)=1,(21, 3)=1,(35, 6)=1,(16, 3)=1,(9, \n\n 3)= 1,(28, 7)=long,(20, 5)=1,(32, 7)=long,(22, 5)=1,(18, 1)=0,(33, 6)=1,(1 3, 5)=\n\n 1,(19, 7)=long,(17, 3)=1,(10, 3)=1,(12, 5)=0,(23, 7)=long,( 12, 1)=0,(21, 1)=1,(\n\n 25, 5)=1]);\n\n \n\n coeffE7 := array(1 .. 63 , 1 .. 8,[(30, 5)=1,(5, 6)=0,(44, 7)=1,(3, 8)=long,(1, \n\n 1)=1,(26, \+ 4)=1,(33, 1)=1,(53, 6)=0,(58, 8)=long,(27, 5)=1,(50, 2)=2,(52, 8)=\n\n long,(22, 4)=1,(24, 8)=long,(43, 1)=1,(45, 8)=long,(59, 6)=1,(27, 7)= 0,(13, 8)=\n\n long,(28, 8)=long,(42, 6)=0,(20, 4)=0,(40, 3)=2,(52, 4) =2,(34, 8)=long,(35, 3)=\n\n 2,(44, 8)=long,(32, 7)=1,(11, 6)=0,(33, 2 )=1,(49, 8)=long,(35, 7)=1,(61, 1)=1,(\n\n 3, 4)=0,(24, 5)=1,(52, 7)=1 ,(58, 2)=2,(6, 6)=0,(20, 5)=0,(17, 5)=0,(46, 2)=2,(\n\n 61, 5)=2,(11, \+ 1)=0,(15, 2)=1,(32, 2)=1,(3, 3)=0,(38, 7)=1,(51, 6)=1,(63, 1)=2,(\n\n \+ 41, 5)=1,(14, 5)=0,(48, 3)=2,(15, 1)=0,(19, 7)=0,(46, 7)=1,(48, 2)=1,( 58, 1)=1,\n\n (61, 3)=4,(1, 3)=0,(22, 7)=1,(52, 6)=1,(3, 5)=0,(38, 8)= long,(51, 2)=2,(53, 7)=\n\n 2,(59, 2)=2,(9, 1)=0,(12, 7)=0,(20, 6)=0,( 29, 4)=1,(26, 2)=1,(18, 1)=0,(23, 2)=\n\n 0,(26, 3)=1,(17, 4)=1,(36, 8 )=long,(8, 5)=0,(28, 3)=2,(45, 2)=1,(63, 5)=2,(41, \n\n 7)=1,(57, 1)=1 ,(1, 7)=0,(16, 6)=0,(37, 4)=1,(51, 7)=1,(47, 6)=1,(58, 3)=3,(34, \n\n \+ 6)=1,(49, 5)=2,(54, 4)=2,(51, 3)=2,(29, 7)=1,(12, 5)=1,(2, 7)=1,(42, 7 )=1,(10, \n\n 7)=0,(12, 2)=0,(54, 7)=1,(8, 1)=1,(57, 8)=long,(22, 6)=0 ,(49, 6)=1,(33, 8)=long\n\n ,(51, 5)=1,(55, 3)=2,(61, 4)=3,(26, 8)=lon g,(55, 7)=1,(56, 2)=2,(1, 5)=0,(9, 7)\n\n =1,(14, 2)=1,(36, 2)=1,(46, \+ 4)=2,(33, 7)=1,(12, 3)=0,(23, 7)=1,(24, 2)=1,(25, 7\n\n )=0,(20, 1)=1, (61, 8)=long,(32, 4)=1,(19, 3)=0,(36, 6)=1,(5, 7)=0,(6, 3)=0,(49\n\n , 7)=1,(50, 3)=3,(29, 5)=1,(49, 2)=1,(14, 4)=0,(42, 4)=1,(43, 6)=0,(46, 3)=2,(\n\n 27, 4)=1,(60, 8)=long,(1, 8)=long,(42, 5)=1,(52, 1)=1,(61, 2)=2,(28, 7)=1,(6, 5\n\n )=1,(27, 1)=1,(33, 6)=0,(13, 7)=0,(31, 6)=1, (55, 4)=2,(15, 8)=long,(40, 6)=0,(\n\n 13, 2)=0,(40, 8)=long,(2, 6)=0, (43, 8)=long,(49, 1)=0,(53, 2)=2,(30, 7)=1,(42, \n\n 8)=long,(50, 7)=1 ,(8, 4)=0,(9, 8)=long,(16, 5)=0,(2, 5)=0,(21, 8)=long,(43, 2)=\n\n 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,\n\n (7, 7)=0,(18, 2)=0,(29, 3)=1,(30, 3)=1,(55, 8)=long,(51, 4) =2,(56, 3)=3,(58, 5)\n\n =2,(60, 5)=2,(21, 1)=1,(63, 6)=1,(34, 5)=1,(4 8, 1)=1,(16, 4)=1,(39, 8)=long,(23\n\n , 8)=long,(38, 5)=1,(21, 3)=1,( 38, 2)=1,(1, 6)=0,(10, 8)=long,(57, 3)=3,(21, 7)\n\n =0,(25, 6)=1,(32, 8)=long,(34, 4)=1,(5, 8)=long,(59, 5)=2,(15, 6)=0,(39, 7)=1,(\n\n 40, 2)=1,(56, 4)=2,(9, 5)=0,(24, 4)=1,(31, 4)=1,(2, 4)=0,(11, 3)=1,(20, 3 )=1,(\n\n 37, 7)=1,(23, 3)=1,(34, 1)=1,(34, 2)=1,(19, 4)=1,(7, 4)=0,(1 1, 4)=1,(20, 7)=1,(\n\n 63, 7)=2,(32, 1)=1,(9, 3)=1,(14, 8)=long,(36, \+ 4)=1,(56, 7)=2,(31, 3)=1,(51, 8)=\n\n long,(29, 6)=0,(31, 8)=long,(41, 6)=1,(47, 8)=long,(40, 4)=2,(48, 4)=2,(2, 1)=0\n\n ,(6, 1)=0,(27, 3)= 1,(50, 6)=0,(41, 4)=1,(54, 1)=1,(16, 1)=0,(31, 5)=1,(5, 3)=0,\n\n (20, 8)=long,(21, 4)=1,(2, 2)=0,(4, 8)=long,(54, 3)=3,(60, 6)=1,(7, 1)=0,( 11, 2\n\n )=0,(7, 2)=0,(8, 7)=0,(49, 3)=2,(52, 5)=2,(63, 3)=4,(18, 3)= 1,(19, 2)=0,(39, 2)\n\n =1,(7, 8)=long,(36, 1)=0,(45, 1)=0,(46, 5)=1,( 23, 6)=0,(32, 6)=0,(33, 3)=1,(32\n\n , 5)=0,(56, 6)=1,(30, 1)=0,(14, 3 )=1,(48, 7)=1,(60, 3)=3,(11, 8)=long,(6, 8)=\n\n long,(16, 3)=1,(24, 1 )=0,(25, 3)=1,(8, 8)=long,(24, 3)=1,(58, 4)=2,(1, 4)=0,(13\n\n , 1)=0, (22, 8)=long,(57, 2)=2,(8, 2)=1,(11, 7)=0,(7, 6)=1,(43, 3)=2,(39, 4)=1 ,(\n\n 10, 1)=0,(32, 3)=2,(9, 2)=0,(30, 8)=long,(10, 2)=1,(21, 5)=0,(6 , 4)=0,(6, 7)=0,\n\n (29, 8)=long,(56, 8)=long,(41, 8)=long,(12, 1)=0, (17, 3)=1,(17, 8)=long,(35, 6)\n\n =0,(26, 5)=0,(36, 7)=1,(61, 6)=1,(7 , 3)=0,(22, 2)=1,(46, 6)=0,(11, 5)=0,(25, 5)\n\n =1,(14, 6)=0,(10, 3)= 1,(58, 7)=2,(47, 5)=1,(33, 4)=1,(50, 5)=1,(17, 1)=0,(28, 5\n\n )=0,(35 , 5)=1,(43, 4)=2,(59, 4)=3,(24, 6)=0,(31, 1)=0,(57, 5)=2,(35, 1)=0,(47 , \n\n 4)=1,(52, 2)=1,(62, 8)=long,(18, 4)=1,(53, 5)=1,(14, 1)=1,(17, \+ 7)=0,(45, 6)=1,(\n\n 36, 5)=1,(60, 7)=2,(4, 5)=0,(59, 8)=long,(28, 1)= 0,(62, 2)=3,(28, 6)=0,(49, 4)=\n\n 2,(53, 1)=1,(26, 7)=1,(27, 2)=1,(28 , 2)=1,(62, 3)=4,(15, 3)=1,(17, 6)=0,(44, 3)\n\n =2,(45, 4)=2,(4, 2)=0 ,(45, 3)=2,(21, 6)=0,(34, 7)=0,(50, 8)=long,(56, 1)=1,(42\n\n , 2)=2,( 38, 6)=0,(16, 8)=long,(25, 4)=1,(35, 8)=long,(4, 1)=0,(44, 2)=1,(55, 2 )\n\n =2,(37, 6)=0,(54, 6)=1,(62, 4)=3,(62, 7)=2,(41, 3)=2,(44, 5)=1,( 47, 1)=1,(2, 8)\n\n =long,(40, 1)=0,(45, 5)=1,(46, 1)=1,(57, 6)=1,(60, 2)=2,(19, 8)=long,(33, 5)=1,\n\n (61, 7)=2,(15, 4)=0,(21, 2)=1,(5, 4) =1,(36, 3)=1,(27, 8)=long,(38, 3)=2,(16, 7)\n\n =1,(23, 5)=1,(15, 5)=0 ,(14, 7)=0,(39, 5)=1,(44, 4)=1,(15, 7)=1,(10, 6)=0,(12, 8\n\n )=long,( 37, 1)=1,(62, 1)=1,(4, 6)=0,(19, 1)=0,(12, 6)=0,(47, 3)=2,(52, 3)=2,(3 7\n\n , 8)=long,(16, 2)=0,(1, 2)=0,(58, 6)=1,(29, 1)=0,(54, 5)=1,(19, \+ 5)=1,(41, 2)=1,\n\n (3, 7)=0,(26, 1)=1,(30, 6)=1,(57, 4)=2,(63, 8)=lon g,(6, 2)=0,(39, 3)=1,(62, 6)=\n\n 1,(25, 2)=0,(29, 2)=1,(30, 2)=0,(47, 2)=2,(48, 6)=1,(53, 3)=3,(22, 3)=1,(37, 5)\n\n =0,(50, 4)=2,(19, 6)=1 ,(25, 1)=0,(22, 5)=0,(37, 2)=2,(38, 4)=1,(55, 5)=2,(23, 4\n\n )=1,(40, 5)=1,(22, 1)=0,(10, 5)=0,(18, 8)=long,(38, 1)=1,(10, 4)=0,(17, 2)=1,( \n\n 18, 5)=1,(18, 7)=0,(60, 1)=1,(4, 3)=1,(4, 4)=0,(47, 7)=1,(53, 4)= 2,(59, 1)=1,(\n\n 53, 8)=long,(25, 8)=long,(43, 7)=1,(5, 2)=0,(13, 5)= 1,(9, 4)=0,(63, 4)=3,(46, 8\n\n )=long,(55, 6)=1,(3, 6)=0,(3, 2)=1,(12 , 4)=1,(30, 4)=1,(39, 6)=1,(51, 1)=1,(54\n\n , 8)=long,(55, 1)=1,(20, \+ 2)=1,(28, 4)=1,(56, 5)=1,(60, 4)=3,(62, 5)=2,(18, 6)=0\n\n ,(2, 3)=0,( 42, 3)=2,(59, 7)=1,(57, 7)=1,(54, 2)=2,(26, 6)=0,(50, 1)=1,(24, 7)=0\n \n ,(40, 7)=1,(43, 5)=1,(13, 3)=0,(4, 7)=0,(5, 5)=0,(37, 3)=2,(45, 7)= 1,(13, 6)=1,\n\n (34, 3)=1,(42, 1)=1,(63, 2)=3,(23, 1)=0,(39, 1)=1,(8, 6)=0,(44, 6)=1,(48, 8)=\n\n long,(35, 2)=1,(44, 1)=1,(27, 6)=0,(3, 1) =0,(5, 1)=0,(35, 4)=1,(41, 1)=0]);\n\n \n\n coeffE8 := array(1 .. 120, 1 .. 9,[(10, 6)=0,(103, 1)=1,(81, 4)=2,(42, 9)=long,\n\n (103, 3)=3,( 49, 3)=1,(87, 5)=3,(47, 8)=0,(106, 9)=long,(10, 9)=long,(14, 3)=1,(\n \n 42, 8)=1,(10, 3)=0,(86, 5)=3,(2, 5)=0,(23, 1)=0,(83, 7)=1,(73, 5)=2 ,(6, 3)=1,(\n\n 85, 9)=long,(26, 9)=long,(17, 5)=1,(77, 6)=2,(108, 7)= 1,(29, 4)=1,(6, 2)=0,(49\n\n , 2)=1,(49, 6)=1,(45, 7)=1,(82, 8)=1,(31, 6)=1,(117, 8)=3,(73, 4)=2,(106, 8)=2,\n\n (105, 5)=4,(11, 4)=0,(11, 9 )=long,(114, 1)=1,(118, 2)=2,(92, 5)=3,(112, 3)=3,(\n\n 73, 9)=long,(5 8, 4)=1,(105, 3)=3,(13, 1)=0,(57, 1)=0,(86, 6)=2,(94, 1)=1,(120, \n\n \+ 7)=2,(5, 7)=0,(84, 4)=2,(34, 4)=1,(46, 3)=1,(32, 9)=long,(103, 6)=2,(1 18, 5)=6,\n\n (107, 7)=2,(40, 2)=0,(37, 4)=1,(74, 5)=2,(2, 4)=0,(67, 7 )=1,(57, 2)=0,(22, 7)=0\n\n ,(78, 2)=1,(28, 3)=1,(66, 1)=0,(15, 9)=lon g,(96, 3)=3,(81, 1)=1,(36, 9)=long,(\n\n 97, 4)=3,(3, 3)=0,(81, 2)=1,( 18, 5)=1,(33, 7)=0,(33, 8)=1,(25, 5)=1,(61, 7)=0,(\n\n 52, 7)=1,(86, 2 )=1,(22, 6)=0,(53, 2)=1,(119, 7)=2,(58, 5)=2,(27, 3)=1,(8, 1)=1,\n\n ( 42, 1)=1,(106, 4)=4,(59, 8)=1,(50, 8)=1,(50, 7)=0,(65, 9)=long,(60, 8) =1,(67, \n\n 8)=1,(58, 3)=1,(35, 3)=1,(110, 2)=2,(77, 2)=1,(96, 8)=1,( 69, 6)=2,(111, 4)=4,(\n\n 58, 1)=0,(46, 8)=1,(40, 8)=1,(95, 7)=1,(46, \+ 5)=1,(72, 3)=1,(53, 6)=1,(1, 9)=\n\n long,(3, 2)=0,(39, 2)=1,(45, 2)=0 ,(95, 2)=2,(67, 5)=2,(9, 8)=0,(78, 5)=2,(39, 1\n\n )=0,(35, 2)=1,(35, \+ 5)=1,(60, 5)=2,(47, 6)=1,(8, 7)=0,(64, 4)=2,(18, 6)=0,(19, 9\n\n )=lon g,(104, 6)=3,(7, 3)=0,(60, 2)=1,(115, 5)=5,(4, 6)=0,(13, 7)=0,(18, 2)= 0,(\n\n 112, 1)=1,(115, 4)=4,(78, 3)=2,(37, 3)=0,(27, 6)=1,(84, 7)=1,( 83, 4)=2,(101, 5)\n\n =4,(58, 7)=1,(91, 4)=2,(18, 7)=0,(64, 9)=long,(6 8, 8)=1,(39, 5)=1,(9, 9)=long,(\n\n 46, 2)=1,(116, 6)=4,(113, 5)=5,(78 , 1)=1,(19, 2)=0,(100, 8)=2,(36, 8)=0,(95, 4)\n\n =3,(104, 2)=2,(15, 2 )=1,(104, 4)=3,(24, 7)=1,(67, 2)=1,(57, 4)=2,(42, 5)=1,(25\n\n , 7)=0, (118, 9)=long,(107, 6)=3,(7, 7)=0,(84, 2)=2,(33, 1)=0,(111, 5)=5,(44, \+ 5)\n\n =2,(104, 8)=2,(41, 6)=1,(81, 3)=1,(9, 3)=0,(105, 8)=2,(32, 7)=0 ,(29, 5)=0,(94, \n\n 7)=1,(13, 9)=long,(11, 1)=0,(110, 7)=1,(92, 6)=2, (79, 9)=long,(70, 2)=1,(34, 3)\n\n =1,(82, 1)=0,(67, 9)=long,(51, 7)=1 ,(56, 7)=0,(53, 8)=1,(88, 1)=1,(45, 6)=1,(\n\n 104, 1)=1,(33, 5)=1,(11 9, 8)=3,(77, 9)=long,(114, 2)=2,(103, 4)=3,(14, 8)=0,(92\n\n , 9)=long ,(105, 7)=1,(53, 3)=1,(90, 5)=3,(99, 4)=3,(62, 8)=1,(34, 9)=long,(113 \n\n , 1)=1,(70, 4)=2,(37, 9)=long,(20, 2)=0,(49, 7)=0,(68, 3)=2,(85, \+ 3)=2,(30, 8)=1\n\n ,(9, 7)=1,(84, 8)=1,(110, 1)=1,(12, 1)=0,(33, 2)=0, (16, 7)=1,(66, 7)=1,(59, 5)=\n\n 2,(15, 6)=0,(116, 2)=2,(26, 6)=0,(21, 7)=0,(109, 4)=4,(65, 3)=1,(81, 6)=2,(89, \n\n 6)=2,(20, 5)=1,(48, 3)= 1,(92, 1)=1,(33, 6)=1,(63, 8)=1,(71, 5)=2,(96, 1)=1,(105\n\n , 2)=2,(1 3, 5)=0,(88, 8)=1,(78, 4)=2,(100, 5)=3,(118, 6)=4,(102, 4)=3,(77, 3)=1 \n\n ,(44, 3)=0,(21, 6)=0,(31, 2)=0,(45, 8)=1,(107, 2)=2,(71, 1)=0,(19 , 3)=0,(13, 8)\n\n =0,(66, 6)=1,(117, 5)=6,(50, 4)=1,(109, 1)=1,(41, 3 )=1,(17, 2)=0,(31, 4)=1,(72\n\n , 7)=1,(113, 3)=3,(83, 6)=2,(3, 6)=1,( 114, 5)=5,(79, 2)=2,(58, 6)=2,(44, 8)=1,(\n\n 117, 7)=2,(10, 1)=0,(21, 5)=0,(3, 7)=0,(74, 9)=long,(29, 9)=long,(53, 4)=1,(43\n\n , 3)=1,(20, 4)=1,(91, 8)=2,(43, 7)=0,(11, 5)=1,(49, 4)=1,(99, 1)=1,(81, 8)=2,(\n \n 98, 9)=long,(111, 6)=3,(76, 4)=2,(3, 1)=0,(51, 1)=0,(112, 6)=3,(113 , 4)=4,(37, \n\n 1)=0,(31, 8)=0,(28, 4)=1,(76, 2)=1,(62, 3)=1,(7, 8)=0 ,(99, 5)=4,(98, 7)=1,(59, \n\n 9)=long,(80, 5)=3,(70, 9)=long,(1, 8)=0 ,(54, 6)=1,(38, 9)=long,(42, 3)=1,(12, 4\n\n )=1,(99, 9)=long,(8, 8)=0 ,(43, 6)=1,(29, 8)=0,(89, 1)=0,(7, 5)=0,(55, 2)=1,(110\n\n , 9)=long,( 17, 7)=0,(98, 5)=4,(28, 5)=1,(53, 7)=1,(65, 5)=2,(93, 9)=long,(30, 7\n \n )=1,(9, 4)=0,(4, 7)=0,(48, 4)=2,(90, 4)=3,(88, 9)=long,(107, 5)=4,( 107, 9)=long\n\n ,(22, 3)=1,(97, 7)=2,(10, 7)=0,(94, 9)=long,(90, 8)=2 ,(42, 6)=0,(67, 4)=2,(81, \n\n 9)=long,(113, 8)=3,(80, 1)=0,(22, 4)=0, (46, 1)=0,(38, 8)=1,(55, 3)=1,(85, 2)=1,\n\n (72, 4)=2,(81, 7)=1,(68, \+ 2)=1,(33, 4)=1,(3, 5)=0,(73, 2)=1,(4, 9)=long,(68, 5)=\n\n 2,(6, 6)=0, (116, 5)=6,(116, 8)=3,(71, 8)=1,(13, 2)=0,(64, 8)=1,(109, 8)=2,(102\n \n , 2)=2,(45, 9)=long,(47, 7)=1,(9, 6)=1,(5, 5)=0,(86, 3)=2,(5, 8)=0, (60, 6)=1,(\n\n 15, 5)=0,(72, 1)=1,(71, 4)=2,(24, 8)=0,(89, 3)=2,(7, 4 )=0,(61, 6)=1,(20, 1)=0,(\n\n 89, 9)=long,(8, 4)=0,(48, 2)=0,(74, 7)=0 ,(41, 8)=1,(56, 6)=1,(23, 7)=1,(38, 4)=\n\n 1,(32, 6)=1,(91, 5)=3,(51, 4)=1,(44, 1)=0,(99, 2)=2,(73, 1)=1,(101, 9)=long,(31\n\n , 5)=1,(78, \+ 9)=long,(107, 1)=1,(99, 3)=2,(54, 8)=1,(37, 8)=1,(120, 4)=5,(4, 1)=\n \n 0,(68, 1)=1,(49, 8)=1,(104, 9)=long,(45, 5)=2,(82, 5)=3,(17, 9)=lon g,(71, 9)=\n\n long,(21, 3)=1,(119, 6)=4,(41, 9)=long,(40, 4)=1,(45, 1 )=0,(64, 2)=1,(30, 3)=0,\n\n (28, 8)=0,(28, 9)=long,(74, 6)=1,(52, 5)= 2,(60, 4)=1,(101, 3)=2,(2, 8)=1,(21, 4\n\n )=1,(36, 3)=1,(1, 2)=0,(117 , 1)=1,(43, 4)=1,(52, 1)=0,(50, 3)=1,(69, 9)=long,(\n\n 120, 9)=long,( 7, 2)=1,(19, 1)=0,(99, 6)=2,(20, 7)=0,(116, 3)=3,(56, 5)=2,(113, \n\n \+ 7)=2,(55, 4)=2,(19, 6)=1,(31, 3)=1,(96, 9)=long,(56, 2)=1,(114, 6)=4,( 48, 9)=\n\n long,(66, 4)=2,(49, 9)=long,(87, 8)=1,(90, 6)=2,(63, 6)=2, (38, 1)=0,(70, 6)=2,(\n\n 50, 5)=1,(44, 4)=1,(109, 3)=3,(92, 2)=2,(96, 2)=2,(117, 4)=5,(77, 8)=1,(58, 9)=\n\n long,(72, 6)=2,(12, 2)=0,(101, 6)=3,(52, 9)=long,(107, 4)=3,(19, 7)=0,(68, 7)=0\n\n ,(46, 4)=1,(83, \+ 3)=2,(119, 2)=3,(26, 4)=1,(1, 5)=0,(48, 6)=1,(58, 2)=1,(7, 1)=0\n\n ,( 6, 9)=long,(14, 6)=0,(109, 5)=4,(86, 8)=2,(51, 6)=2,(14, 9)=long,(34, \+ 7)=0,(\n\n 51, 2)=0,(16, 4)=0,(54, 2)=1,(22, 8)=0,(78, 6)=2,(28, 2)=1, (61, 4)=2,(55, 1)=0,\n\n (30, 4)=1,(76, 1)=0,(74, 2)=2,(63, 3)=1,(27, \+ 9)=long,(95, 9)=long,(8, 6)=0,(83\n\n , 5)=3,(63, 5)=3,(102, 3)=2,(85, 7)=1,(70, 8)=1,(94, 8)=2,(85, 4)=3,(12, 6)=0,(\n\n 54, 7)=1,(119, 9)= long,(80, 7)=1,(82, 9)=long,(4, 5)=1,(38, 5)=1,(115, 8)=3,(18\n\n , 8) =1,(16, 9)=long,(120, 6)=4,(34, 6)=0,(110, 5)=5,(64, 6)=2,(87, 3)=2,(6 7, 6)\n\n =1,(31, 1)=0,(120, 8)=3,(51, 9)=long,(39, 6)=1,(13, 4)=1,(80 , 8)=2,(10, 5)=1,(\n\n 56, 3)=1,(23, 2)=0,(44, 9)=long,(115, 2)=2,(13, 6)=0,(75, 9)=long,(80, 3)=2,(24\n\n , 3)=0,(21, 1)=0,(89, 5)=4,(107, \+ 8)=2,(27, 5)=1,(62, 5)=2,(19, 8)=0,(9, 5)=0,(\n\n 32, 3)=0,(99, 7)=1,( 93, 7)=1,(77, 5)=3,(101, 1)=1,(81, 5)=3,(77, 1)=1,(51, 8)=1\n\n ,(69, \+ 2)=0,(90, 2)=1,(64, 1)=0,(40, 7)=0,(108, 3)=3,(66, 9)=long,(91, 7)=1,( 87\n\n , 9)=long,(57, 7)=1,(43, 2)=1,(94, 2)=1,(88, 7)=1,(20, 8)=0,(12 0, 5)=6,(92, 7)=\n\n 1,(25, 1)=0,(51, 5)=2,(79, 4)=2,(69, 5)=3,(48, 1) =0,(112, 7)=1,(117, 3)=3,(80, \n\n 4)=2,(74, 3)=2,(91, 2)=2,(44, 2)=0, (14, 5)=0,(118, 8)=3,(15, 1)=1,(24, 2)=0,(65\n\n , 8)=1,(18, 4)=1,(87, 4)=3,(71, 7)=1,(31, 7)=1,(113, 2)=2,(63, 2)=0,(37, 7)=1,(\n\n 120, 2) =3,(14, 7)=0,(108, 9)=long,(11, 2)=0,(50, 2)=1,(89, 8)=2,(116, 1)=1,(1 6\n\n , 1)=0,(41, 1)=0,(75, 1)=0,(6, 8)=0,(6, 5)=0,(97, 3)=2,(39, 7)=1 ,(119, 4)=5,(\n\n 100, 2)=2,(1, 3)=0,(87, 2)=1,(86, 4)=2,(65, 2)=1,(4, 8)=0,(43, 9)=long,(26, 8)=\n\n 1,(64, 7)=1,(106, 6)=2,(35, 6)=1,(57, \+ 9)=long,(83, 2)=1,(78, 7)=1,(83, 1)=1,(35\n\n , 1)=0,(39, 3)=1,(35, 8) =0,(12, 5)=1,(55, 5)=2,(79, 7)=1,(48, 5)=2,(79, 3)=2,(4\n\n , 3)=0,(54 , 3)=1,(52, 6)=1,(100, 7)=1,(55, 8)=1,(6, 4)=0,(98, 6)=3,(89, 7)=1,(\n \n 65, 7)=1,(98, 3)=2,(12, 3)=0,(22, 5)=0,(97, 5)=4,(14, 2)=1,(101, 8) =2,(20, 9)=\n\n long,(27, 7)=0,(57, 3)=1,(26, 7)=0,(115, 1)=1,(21, 2)= 1,(52, 2)=0,(28, 6)=0,(32\n\n , 8)=1,(93, 1)=0,(26, 5)=1,(113, 6)=3,(3 0, 1)=0,(38, 7)=1,(77, 4)=2,(109, 9)=\n\n long,(119, 1)=1,(61, 3)=2,(7 4, 8)=1,(53, 5)=2,(71, 3)=2,(75, 2)=1,(41, 7)=0,(38\n\n , 3)=1,(35, 9) =long,(116, 7)=2,(40, 5)=2,(120, 3)=4,(73, 7)=1,(96, 6)=2,(61, 1)\n\n \+ =0,(84, 3)=2,(90, 7)=1,(56, 1)=1,(16, 8)=0,(17, 3)=0,(40, 6)=1,(92, 3) =2,(90, 3\n\n )=2,(103, 9)=long,(47, 9)=long,(1, 6)=0,(79, 5)=2,(87, 7 )=1,(8, 2)=0,(60, 1)=1,\n\n (8, 5)=0,(42, 7)=0,(28, 1)=0,(103, 7)=1,(7 5, 7)=1,(19, 4)=1,(37, 5)=2,(109, 2)=\n\n 2,(105, 9)=long,(59, 1)=0,(5 , 6)=0,(91, 1)=1,(33, 3)=1,(106, 3)=3,(80, 2)=1,(27\n\n , 2)=0,(99, 8) =2,(43, 1)=1,(27, 4)=1,(83, 8)=1,(114, 8)=2,(118, 3)=4,(106, 2)=2\n\n \+ ,(54, 1)=1,(100, 4)=3,(35, 4)=1,(93, 2)=1,(111, 9)=long,(108, 6)=3,(5, 9)=long,\n\n (114, 4)=4,(60, 7)=1,(111, 3)=3,(48, 7)=0,(94, 3)=2,(9, \+ 1)=0,(90, 1)=1,(90, 9)=\n\n long,(68, 4)=2,(5, 2)=0,(66, 3)=2,(73, 3)= 2,(56, 8)=1,(32, 2)=0,(57, 8)=1,(59, \n\n 4)=2,(60, 9)=long,(96, 4)=3, (16, 2)=0,(55, 9)=long,(104, 7)=2,(102, 5)=4,(32, 4\n\n )=1,(55, 6)=1, (111, 7)=2,(58, 8)=1,(108, 2)=2,(36, 7)=0,(24, 6)=1,(23, 3)=0,(52\n\n \+ , 3)=1,(112, 9)=long,(36, 5)=1,(54, 9)=long,(26, 1)=0,(4, 2)=0,(94, 4) =3,(5, 1)\n\n =0,(103, 5)=4,(17, 8)=1,(23, 4)=0,(103, 2)=2,(60, 3)=1,( 36, 2)=1,(115, 9)=long,\n\n (110, 3)=3,(82, 6)=2,(72, 9)=long,(115, 3) =3,(50, 1)=1,(110, 4)=4,(98, 2)=1,(76\n\n , 8)=1,(101, 2)=1,(79, 6)=1, (75, 8)=2,(94, 6)=2,(93, 8)=2,(24, 9)=long,(101, 7)\n\n =2,(118, 4)=5, (38, 2)=0,(52, 4)=2,(70, 1)=0,(34, 1)=0,(40, 3)=1,(69, 3)=1,(108\n\n , 1)=1,(93, 6)=3,(28, 7)=0,(25, 2)=0,(116, 4)=4,(91, 3)=2,(118, 7)=2,(7 2, 5)=2,\n\n (74, 1)=1,(17, 1)=0,(65, 6)=2,(11, 3)=0,(117, 6)=4,(12, 9 )=long,(11, 7)=0,(82, \n\n 7)=1,(30, 2)=0,(103, 8)=2,(15, 8)=0,(32, 5) =2,(29, 3)=1,(91, 6)=2,(78, 8)=1,(16\n\n , 5)=1,(40, 9)=long,(108, 5)= 4,(65, 4)=1,(98, 4)=3,(2, 1)=0,(102, 1)=1,(76, 6)=\n\n 2,(71, 6)=2,(82 , 2)=1,(66, 8)=1,(39, 9)=long,(15, 4)=0,(62, 9)=long,(95, 6)=2,(\n\n 5 5, 7)=0,(85, 6)=2,(41, 4)=1,(61, 9)=long,(71, 2)=1,(111, 8)=2,(108, 4) =4,(26, \n\n 3)=1,(85, 8)=2,(93, 3)=2,(29, 2)=1,(76, 3)=2,(91, 9)=long ,(16, 3)=0,(120, 1)=2,\n\n (6, 7)=0,(114, 7)=2,(30, 9)=long,(92, 4)=3, (21, 8)=0,(49, 1)=0,(14, 1)=0,(22, 9\n\n )=long,(10, 8)=1,(36, 1)=1,(5 2, 8)=1,(47, 5)=1,(2, 7)=0,(59, 7)=1,(47, 4)=1,(98\n\n , 1)=1,(24, 1)= 0,(35, 7)=0,(23, 6)=1,(63, 9)=long,(83, 9)=long,(10, 4)=0,(95, 5\n\n ) =3,(18, 9)=long,(106, 7)=1,(79, 1)=1,(112, 5)=5,(104, 5)=4,(5, 3)=0,(1 05, 4)=3\n\n ,(100, 3)=3,(114, 9)=long,(59, 2)=1,(98, 8)=2,(102, 9)=lo ng,(115, 6)=4,(62, 2)=\n\n 1,(117, 9)=long,(59, 6)=1,(97, 8)=2,(86, 7) =1,(97, 9)=long,(3, 4)=0,(23, 8)=1,(\n\n 37, 2)=0,(51, 3)=1,(113, 9)=l ong,(67, 1)=1,(72, 2)=1,(44, 6)=2,(29, 6)=0,(39, 4\n\n )=1,(32, 1)=0,( 53, 9)=long,(68, 6)=1,(106, 1)=1,(80, 9)=long,(2, 6)=0,(36, 6)=0\n\n , (95, 8)=2,(5, 4)=1,(43, 8)=0,(18, 1)=0,(79, 8)=1,(95, 3)=2,(1, 7)=1,(6 6, 5)=2,\n\n (64, 3)=1,(25, 3)=0,(92, 8)=1,(67, 3)=1,(2, 3)=0,(112, 4) =4,(11, 6)=1,(12, 8)=0\n\n ,(53, 1)=0,(44, 7)=1,(27, 8)=0,(108, 8)=2,( 102, 8)=2,(8, 9)=long,(26, 2)=0,(48\n\n , 8)=1,(80, 6)=2,(112, 8)=3,(8 5, 5)=3,(64, 5)=2,(110, 6)=3,(45, 4)=1,(63, 1)=0,\n\n (114, 3)=3,(88, \+ 2)=2,(27, 1)=0,(76, 7)=1,(47, 2)=1,(22, 1)=1,(89, 2)=1,(69, 1)=\n\n 0, (29, 7)=0,(95, 1)=1,(20, 6)=0,(88, 3)=2,(94, 5)=4,(115, 7)=2,(100, 9)= long,(\n\n 96, 5)=3,(76, 5)=3,(42, 4)=1,(22, 2)=1,(70, 7)=1,(3, 9)=lon g,(12, 7)=0,(54, 4)=\n\n 1,(24, 5)=1,(25, 4)=1,(97, 1)=0,(23, 9)=long, (47, 3)=1,(1, 4)=0,(16, 6)=1,(3, 8\n\n )=0,(30, 5)=1,(11, 8)=0,(40, 1) =0,(110, 8)=2,(61, 8)=1,(21, 9)=long,(63, 4)=2,(\n\n 34, 2)=1,(104, 3) =2,(117, 2)=2,(72, 8)=1,(118, 1)=1,(70, 3)=1,(47, 1)=1,(57, 5)\n\n =2, (75, 3)=1,(107, 3)=3,(75, 6)=2,(77, 7)=1,(89, 4)=3,(62, 4)=2,(62, 7)=0 ,(18, \n\n 3)=0,(54, 5)=1,(102, 7)=1,(2, 9)=long,(66, 2)=1,(43, 5)=1,( 37, 6)=1,(69, 4)=2,(\n\n 100, 6)=2,(8, 3)=0,(25, 6)=1,(86, 9)=long,(85 , 1)=0,(101, 4)=3,(116, 9)=long,(\n\n 20, 3)=1,(23, 5)=1,(56, 4)=1,(17 , 6)=1,(88, 4)=2,(36, 4)=1,(112, 2)=2,(39, 8)=0\n\n ,(9, 2)=0,(106, 5) =4,(75, 5)=3,(45, 3)=1,(1, 1)=0,(68, 9)=long,(100, 1)=1,(42, \n\n 2)=1 ,(15, 7)=0,(62, 1)=1,(74, 4)=2,(86, 1)=1,(62, 6)=1,(65, 1)=1,(50, 9)=l ong,(\n\n 87, 1)=1,(76, 9)=long,(10, 2)=0,(70, 5)=3,(88, 6)=2,(14, 4)= 0,(73, 8)=1,(97, 2)\n\n =1,(19, 5)=1,(69, 8)=2,(46, 6)=1,(31, 9)=long, (69, 7)=1,(41, 5)=1,(73, 6)=1,(46\n\n , 9)=long,(88, 5)=3,(29, 1)=1,(1 11, 1)=1,(24, 4)=1,(49, 5)=2,(15, 3)=0,(84, 6)=\n\n 2,(56, 9)=long,(87 , 6)=2,(109, 7)=2,(46, 7)=1,(50, 6)=1,(61, 2)=1,(2, 2)=0,(30\n\n , 6)= 1,(6, 1)=0,(25, 9)=long,(119, 5)=6,(105, 1)=1,(84, 9)=long,(34, 5)=1,( 41, \n\n 2)=1,(33, 9)=long,(59, 3)=1,(13, 3)=1,(119, 3)=4,(63, 7)=1,(7 , 6)=0,(4, 4)=0,(\n\n 96, 7)=1,(75, 4)=2,(82, 3)=2,(102, 6)=3,(84, 1)= 1,(17, 4)=0,(105, 6)=3,(61, 5)=\n\n 2,(109, 6)=3,(57, 6)=2,(93, 4)=3,( 93, 5)=4,(7, 9)=long,(38, 6)=1,(34, 8)=1,(25\n\n , 8)=1,(111, 2)=2,(84 , 5)=2,(97, 6)=3,(82, 4)=3]);\n\n \n\n coeffF := array(1 .. 24, 1 .. 5 ,[(15, 2)=1,(22, 5)=long,(8, 2)=1,(3, 4)=0,(2, 2\n\n )=0,(6, 4)=0,(24, 5)=long,(22, 2)=3,(13, 4)=1,(1, 4)=1,(12, 2)=1,(15, 5)=long,(\n\n 21, 4)=1,(10, 3)=1,(23, 1)=1,(6, 5)=short,(13, 3)=2,(1, 1)=0,(18, 5)=long ,(16, \n\n 5)=long,(15, 4)=2,(3, 5)=long,(16, 1)=1,(22, 4)=2,(7, 1)=0, (22, 3)=4,(14, 4)=1,\n\n (19, 1)=1,(8, 5)=long,(4, 5)=long,(17, 1)=1,( 4, 1)=1,(20, 3)=4,(23, 4)=2,(6, 2)\n\n =1,(9, 4)=1,(23, 2)=2,(18, 3)=2 ,(9, 1)=0,(5, 1)=0,(1, 3)=0,(5, 5)=short,(10, 5)\n\n =short,(11, 2)=1, (16, 2)=2,(9, 5)=short,(4, 4)=0,(6, 3)=1,(16, 4)=0,(7, 2)=1,(\n\n 20, \+ 5)=long,(19, 2)=2,(9, 3)=1,(19, 5)=short,(20, 4)=2,(17, 2)=1,(4, 2)=0, (2, 5\n\n )=short,(6, 1)=0,(11, 1)=0,(10, 1)=1,(4, 3)=0,(11, 3)=2,(21, 1)=1,(9, 2)=1,(5, \n\n 3)=1,(20, 1)=1,(3, 1)=0,(12, 4)=0,(5, 4)=1,(23 , 5)=short,(17, 5)=short,(11, 4)=\n\n 2,(12, 5)=long,(12, 3)=2,(8, 3)= 0,(10, 2)=1,(7, 5)=long,(13, 5)=short,(24, 1)=2\n\n ,(5, 2)=0,(21, 2)= 2,(8, 4)=0,(14, 5)=short,(18, 1)=1,(20, 2)=2,(13, 1)=0,(1, 2)\n\n =0,( 2, 1)=0,(19, 4)=1,(3, 2)=1,(21, 5)=short,(7, 4)=0,(2, 3)=1,(16, 3)=2,( 24, 3\n\n )=4,(8, 1)=1,(1, 5)=short,(14, 1)=1,(23, 3)=3,(24, 4)=2,(11, 5)=long,(15, 1)=1,\n\n (7, 3)=2,(18, 4)=2,(22, 1)=1,(19, 3)=2,(14, 3) =1,(3, 3)=0,(10, 4)=0,(17, 3)=2,(\n\n 24, 2)=3,(2, 4)=0,(12, 1)=1,(17, 4)=1,(18, 2)=2,(21, 3)=3,(13, 2)=1,(15, 3)=2,(\n\n 14, 2)=1]);\n\n \n \n coeffFrev := array(1 .. 24, 1 .. 5,[(10, 4)=1,(22, 1)=2,(14, 2)=1,( 8, 5)=long,(\n\n 9, 3)=1,(9, 5)=short,(14, 5)=short,(23, 4)=1,(13, 2)= 2,(3, 5)=long,(24, 2)=4,(\n\n 15, 3)=1,(15, 4)=1,(5, 1)=1,(20, 5)=long ,(11, 3)=1,(23, 3)=2,(7, 4)=0,(18, 5)=\n\n long,(9, 1)=1,(22, 3)=3,(20 , 3)=2,(1, 1)=1,(10, 1)=0,(15, 1)=2,(17, 1)=1,(18, 4\n\n )=1,(4, 1)=0, (8, 2)=0,(11, 2)=2,(21, 1)=1,(18, 3)=2,(12, 3)=1,(20, 4)=1,(22, 2)\n\n =4,(19, 1)=1,(6, 2)=1,(23, 5)=short,(19, 5)=short,(20, 2)=4,(24, 5)=l ong,(9, 4)\n\n =0,(5, 2)=1,(12, 2)=2,(13, 3)=1,(3, 4)=0,(16, 5)=long,( 7, 2)=2,(24, 1)=2,(10, 2\n\n )=1,(15, 2)=2,(17, 2)=2,(8, 4)=1,(20, 1)= 2,(4, 2)=0,(11, 4)=0,(17, 4)=1,(21, 2)\n\n =3,(5, 5)=short,(1, 4)=0,(1 5, 5)=long,(12, 4)=1,(19, 2)=2,(14, 4)=1,(10, 3)=1,(\n\n 11, 1)=2,(17, 5)=short,(22, 5)=long,(17, 3)=1,(4, 3)=0,(6, 3)=1,(24, 3)=3,(13, \n\n 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)=\n\n 0,(18, 1)=2,(23, 1)=2,(16, 3)=2,(1, 3)=0,(19, 3)=2,(10, 5)=short,(22, 4)=1,(2, \n\n 5)=short,(18, 2)=2,(8, 3)=1,(21, 4)=1,(16 , 2)=2,(7, 3)=1,(3, 1)=0,(23, 2)=3,(11\n\n , 5)=long,(13, 5)=short,(12 , 5)=long,(6, 4)=0,(6, 5)=short,(3, 3)=1,(16, 4)=1,(\n\n 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\n\n , 1)=0,(5, 3)=0,(1, 5)=short,(3, 2)=0,(21, 5)=short,(2, 3)=0,(8, 1)=0 ,(24, 4)=2\n\n ,(4, 5)=long]);\n\n \n\n coeffG := array(1 .. 6, 1 .. \+ 3,[(6, 3)=long,(5, 1)=1,(2, 3)=long,(5, 2)=2,(3, 1\n\n )=1,(3, 3)=shor t,(4, 1)=1,(5, 3)=short,(1, 1)=0,(6, 1)=2,(4, 2)=3,(1, 3)=short,\n\n ( 3, 2)=1,(2, 1)=1,(1, 2)=1,(6, 2)=3,(4, 3)=long,(2, 2)=0]);\n\n \n\n co effGrev := array(1 .. 6, 1 .. 3,[(5, 3)=short,(6, 2)=2,(1, 1)=1,(3, 3) =short,\n\n (6, 1)=3,(2, 3)=long,(4, 1)=3,(1, 2)=0,(1, 3)=short,(3, 1) =1,(2, 1)=0,(6, 3)=\n\n long,(4, 2)=1,(3, 2)=1,(4, 3)=long,(2, 2)=1,(5 , 1)=2,(5, 2)=1]);\n\n" }}}}{MARK "0 0 0" 36894 }{VIEWOPTS 1 1 0 1 1 1803 }