> restart; > with(LinearAlgebra): interface(rtablesize=infinity): with(linalg): > H:=Matrix([ > [1,1,1,1,1,1,1,1], > [1,-1,1,-1,1,-1,1,-1], > [1,1,-1,-1,1,1,-1,-1], > [1,-1,-1,1,1,-1,-1,1], > [1,1,1,1,-1,-1,-1,-1], > [1,-1,1,-1,-1,1,-1,1], > [1,1,-1,-1,-1,-1,1,1], > [1,-1,-1,1,-1,1,1,-1] > ]): > n:=8; Omega:={seq(i,i=1..n)}: n := 8 > A0:=IdentityMatrix(n*n): > A1:=Matrix(n*n,n*n): > for x1 in Omega do > for x2 in Omega do > y1:=x1: > for y2 in Omega minus {x2} do > A1[(x1-1)*n+x2,(y1-1)*n+y2]:=1: > end do: end do: end do: > A2:=Matrix(n*n,n*n): > for x1 in Omega do > for x2 in Omega do > y2:=x2: > for y1 in Omega minus {x1} do > A2[(x1-1)*n+x2,(y1-1)*n+y2]:=1: > end do: end do: end do: > A3:=Matrix(n*n,n*n): > for x1 in Omega do > for x2 in Omega do > for y1 in Omega minus {x1} do > for y2 in Omega minus {x2} do > if H[x1,x2]*H[y1,y2]*H[x1,y2]*H[y1,x2]=1 then A3[(x1-1)*n+x2,(y1-1)*n+y2]:=1: > else end if: > end do: end do: end do: end do: > Hnn:=MatrixAdd( MatrixAdd( MatrixAdd( A0, A1 ), A2 ), A3): > for i from 1 to n*n do > for j from 1 to n*n do > if Hnn[i,j]=0 then Hnn[i,j]:=-1: else end if: > end do: end do: > orth:={}: > for i from 1 to n*n do > for j from i+1 to n*n do > orth:={op(orth), add(Hnn[i,y]*Hnn[j,y], y=1..n*n) }: > end do: end do: orth; {0} > for i from 1 to n do > for j from 1 to n do > B[i,j]:=SubMatrix( A3,[(i-1)*n+1..(i-1)*n+n],[(j-1)*n+1..(j-1)*n+n] ): > end do: end do: > Equal(B[1,1],B[1,1]); Equal(B[1,1],B[1,2]); true false > C:=Matrix(n,n): > entry11:={}: > for i from 1 to n do > for j from 1 to n do > if Equal(B[1,1],B[i,j]) then entry11:={op(entry11),[i,j]}: > else end if: > end do: end do: entry11; {[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8]} > entry12:={}: > for i from 1 to n do > for j from 1 to n do > if Equal(B[1,2],B[i,j]) then entry12:={op(entry12),[i,j]}: > else end if: > end do: end do: entry12; {[1, 2], [2, 1], [3, 4], [4, 3], [5, 6], [6, 5], [7, 8], [8, 7]} > entry13:={}: > for i from 1 to n do > for j from 1 to n do > if Equal(B[1,3],B[i,j]) then entry13:={op(entry13),[i,j]}: > else end if: > end do: end do: entry13; {[1, 3], [2, 4], [3, 1], [4, 2], [5, 7], [6, 8], [7, 5], [8, 6]} > entry14:={}: > for i from 1 to n do > for j from 1 to n do > if Equal(B[1,4],B[i,j]) then entry14:={op(entry14),[i,j]}: > else end if: > end do: end do: entry14; {[1, 4], [2, 3], [3, 2], [4, 1], [5, 8], [6, 7], [7, 6], [8, 5]} > entry15:={}: > for i from 1 to n do > for j from 1 to n do > if Equal(B[1,5],B[i,j]) then entry15:={op(entry15),[i,j]}: > else end if: > end do: end do: entry15; {[1, 5], [2, 6], [3, 7], [4, 8], [5, 1], [6, 2], [7, 3], [8, 4]} > entry16:={}: > for i from 1 to n do > for j from 1 to n do > if Equal(B[1,6],B[i,j]) then entry16:={op(entry16),[i,j]}: > else end if: > end do: end do: entry16; {[1, 6], [2, 5], [3, 8], [4, 7], [5, 2], [6, 1], [7, 4], [8, 3]} > entry17:={}: > for i from 1 to n do > for j from 1 to n do > if Equal(B[1,7],B[i,j]) then entry17:={op(entry17),[i,j]}: > else end if: > end do: end do: entry17; {[1, 7], [2, 8], [3, 5], [4, 6], [5, 3], [6, 4], [7, 1], [8, 2]} > entry18:={}: > for i from 1 to n do > for j from 1 to n do > if Equal(B[1,8],B[i,j]) then entry18:={op(entry18),[i,j]}: > else end if: > end do: end do: entry18; {[1, 8], [2, 7], [3, 6], [4, 5], [5, 4], [6, 3], [7, 2], [8, 1]} > Sigma:={}: > for i from 1 to n do > for j from 1 to n do > Sigma:={op(Sigma),[i,j]}: > end do: end do: > Sigma minus entry11 minus entry12 minus entry13 minus entry14 minus entry15 minus entry16 minus entry17 minus entry18; {} > for i from 1 to n do > C[ entry11[i][1],entry11[i][2] ]:=A11: > C[ entry12[i][1],entry12[i][2] ]:=A12: > C[ entry13[i][1],entry13[i][2] ]:=A13: > C[ entry14[i][1],entry14[i][2] ]:=A14: > C[ entry15[i][1],entry15[i][2] ]:=A15: > C[ entry16[i][1],entry16[i][2] ]:=A16: > C[ entry17[i][1],entry17[i][2] ]:=A17: > C[ entry18[i][1],entry18[i][2] ]:=A18: > end do: print(C); [A11 A12 A13 A14 A15 A16 A17 A18] [ ] [A12 A11 A14 A13 A16 A15 A18 A17] [ ] [A13 A14 A11 A12 A17 A18 A15 A16] [ ] [A14 A13 A12 A11 A18 A17 A16 A15] [ ] [A15 A16 A17 A18 A11 A12 A13 A14] [ ] [A16 A15 A18 A17 A12 A11 A14 A13] [ ] [A17 A18 A15 A16 A13 A14 A11 A12] [ ] [A18 A17 A16 A15 A14 A13 A12 A11] > print(Hnn); > for i from 1 to 4 do > for j from 1 to n do > print( [i,j], B[i,j] ): > end do: end do: [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [1, 1], [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [0 0 1 0 1 0 1 0] [ ] [0 0 0 1 0 1 0 1] [ ] [1 0 0 0 1 0 1 0] [ ] [0 1 0 0 0 1 0 1] [1, 2], [ ] [1 0 1 0 0 0 1 0] [ ] [0 1 0 1 0 0 0 1] [ ] [1 0 1 0 1 0 0 0] [ ] [0 1 0 1 0 1 0 0] [0 1 0 0 1 1 0 0] [ ] [1 0 0 0 1 1 0 0] [ ] [0 0 0 1 0 0 1 1] [ ] [0 0 1 0 0 0 1 1] [1, 3], [ ] [1 1 0 0 0 1 0 0] [ ] [1 1 0 0 1 0 0 0] [ ] [0 0 1 1 0 0 0 1] [ ] [0 0 1 1 0 0 1 0] [0 0 0 1 1 0 0 1] [ ] [0 0 1 0 0 1 1 0] [ ] [0 1 0 0 0 1 1 0] [ ] [1 0 0 0 1 0 0 1] [1, 4], [ ] [1 0 0 1 0 0 0 1] [ ] [0 1 1 0 0 0 1 0] [ ] [0 1 1 0 0 1 0 0] [ ] [1 0 0 1 1 0 0 0] [0 1 1 1 0 0 0 0] [ ] [1 0 1 1 0 0 0 0] [ ] [1 1 0 1 0 0 0 0] [ ] [1 1 1 0 0 0 0 0] [1, 5], [ ] [0 0 0 0 0 1 1 1] [ ] [0 0 0 0 1 0 1 1] [ ] [0 0 0 0 1 1 0 1] [ ] [0 0 0 0 1 1 1 0] [0 0 1 0 0 1 0 1] [ ] [0 0 0 1 1 0 1 0] [ ] [1 0 0 0 0 1 0 1] [ ] [0 1 0 0 1 0 1 0] [1, 6], [ ] [0 1 0 1 0 0 1 0] [ ] [1 0 1 0 0 0 0 1] [ ] [0 1 0 1 1 0 0 0] [ ] [1 0 1 0 0 1 0 0] [0 1 0 0 0 0 1 1] [ ] [1 0 0 0 0 0 1 1] [ ] [0 0 0 1 1 1 0 0] [ ] [0 0 1 0 1 1 0 0] [1, 7], [ ] [0 0 1 1 0 1 0 0] [ ] [0 0 1 1 1 0 0 0] [ ] [1 1 0 0 0 0 0 1] [ ] [1 1 0 0 0 0 1 0] [0 0 0 1 0 1 1 0] [ ] [0 0 1 0 1 0 0 1] [ ] [0 1 0 0 1 0 0 1] [ ] [1 0 0 0 0 1 1 0] [1, 8], [ ] [0 1 1 0 0 0 0 1] [ ] [1 0 0 1 0 0 1 0] [ ] [1 0 0 1 0 1 0 0] [ ] [0 1 1 0 1 0 0 0] [0 0 1 0 1 0 1 0] [ ] [0 0 0 1 0 1 0 1] [ ] [1 0 0 0 1 0 1 0] [ ] [0 1 0 0 0 1 0 1] [2, 1], [ ] [1 0 1 0 0 0 1 0] [ ] [0 1 0 1 0 0 0 1] [ ] [1 0 1 0 1 0 0 0] [ ] [0 1 0 1 0 1 0 0] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [2, 2], [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [0 0 0 1 1 0 0 1] [ ] [0 0 1 0 0 1 1 0] [ ] [0 1 0 0 0 1 1 0] [ ] [1 0 0 0 1 0 0 1] [2, 3], [ ] [1 0 0 1 0 0 0 1] [ ] [0 1 1 0 0 0 1 0] [ ] [0 1 1 0 0 1 0 0] [ ] [1 0 0 1 1 0 0 0] [0 1 0 0 1 1 0 0] [ ] [1 0 0 0 1 1 0 0] [ ] [0 0 0 1 0 0 1 1] [ ] [0 0 1 0 0 0 1 1] [2, 4], [ ] [1 1 0 0 0 1 0 0] [ ] [1 1 0 0 1 0 0 0] [ ] [0 0 1 1 0 0 0 1] [ ] [0 0 1 1 0 0 1 0] [0 0 1 0 0 1 0 1] [ ] [0 0 0 1 1 0 1 0] [ ] [1 0 0 0 0 1 0 1] [ ] [0 1 0 0 1 0 1 0] [2, 5], [ ] [0 1 0 1 0 0 1 0] [ ] [1 0 1 0 0 0 0 1] [ ] [0 1 0 1 1 0 0 0] [ ] [1 0 1 0 0 1 0 0] [0 1 1 1 0 0 0 0] [ ] [1 0 1 1 0 0 0 0] [ ] [1 1 0 1 0 0 0 0] [ ] [1 1 1 0 0 0 0 0] [2, 6], [ ] [0 0 0 0 0 1 1 1] [ ] [0 0 0 0 1 0 1 1] [ ] [0 0 0 0 1 1 0 1] [ ] [0 0 0 0 1 1 1 0] [0 0 0 1 0 1 1 0] [ ] [0 0 1 0 1 0 0 1] [ ] [0 1 0 0 1 0 0 1] [ ] [1 0 0 0 0 1 1 0] [2, 7], [ ] [0 1 1 0 0 0 0 1] [ ] [1 0 0 1 0 0 1 0] [ ] [1 0 0 1 0 1 0 0] [ ] [0 1 1 0 1 0 0 0] [0 1 0 0 0 0 1 1] [ ] [1 0 0 0 0 0 1 1] [ ] [0 0 0 1 1 1 0 0] [ ] [0 0 1 0 1 1 0 0] [2, 8], [ ] [0 0 1 1 0 1 0 0] [ ] [0 0 1 1 1 0 0 0] [ ] [1 1 0 0 0 0 0 1] [ ] [1 1 0 0 0 0 1 0] [0 1 0 0 1 1 0 0] [ ] [1 0 0 0 1 1 0 0] [ ] [0 0 0 1 0 0 1 1] [ ] [0 0 1 0 0 0 1 1] [3, 1], [ ] [1 1 0 0 0 1 0 0] [ ] [1 1 0 0 1 0 0 0] [ ] [0 0 1 1 0 0 0 1] [ ] [0 0 1 1 0 0 1 0] [0 0 0 1 1 0 0 1] [ ] [0 0 1 0 0 1 1 0] [ ] [0 1 0 0 0 1 1 0] [ ] [1 0 0 0 1 0 0 1] [3, 2], [ ] [1 0 0 1 0 0 0 1] [ ] [0 1 1 0 0 0 1 0] [ ] [0 1 1 0 0 1 0 0] [ ] [1 0 0 1 1 0 0 0] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [3, 3], [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [0 0 1 0 1 0 1 0] [ ] [0 0 0 1 0 1 0 1] [ ] [1 0 0 0 1 0 1 0] [ ] [0 1 0 0 0 1 0 1] [3, 4], [ ] [1 0 1 0 0 0 1 0] [ ] [0 1 0 1 0 0 0 1] [ ] [1 0 1 0 1 0 0 0] [ ] [0 1 0 1 0 1 0 0] [0 1 0 0 0 0 1 1] [ ] [1 0 0 0 0 0 1 1] [ ] [0 0 0 1 1 1 0 0] [ ] [0 0 1 0 1 1 0 0] [3, 5], [ ] [0 0 1 1 0 1 0 0] [ ] [0 0 1 1 1 0 0 0] [ ] [1 1 0 0 0 0 0 1] [ ] [1 1 0 0 0 0 1 0] [0 0 0 1 0 1 1 0] [ ] [0 0 1 0 1 0 0 1] [ ] [0 1 0 0 1 0 0 1] [ ] [1 0 0 0 0 1 1 0] [3, 6], [ ] [0 1 1 0 0 0 0 1] [ ] [1 0 0 1 0 0 1 0] [ ] [1 0 0 1 0 1 0 0] [ ] [0 1 1 0 1 0 0 0] [0 1 1 1 0 0 0 0] [ ] [1 0 1 1 0 0 0 0] [ ] [1 1 0 1 0 0 0 0] [ ] [1 1 1 0 0 0 0 0] [3, 7], [ ] [0 0 0 0 0 1 1 1] [ ] [0 0 0 0 1 0 1 1] [ ] [0 0 0 0 1 1 0 1] [ ] [0 0 0 0 1 1 1 0] [0 0 1 0 0 1 0 1] [ ] [0 0 0 1 1 0 1 0] [ ] [1 0 0 0 0 1 0 1] [ ] [0 1 0 0 1 0 1 0] [3, 8], [ ] [0 1 0 1 0 0 1 0] [ ] [1 0 1 0 0 0 0 1] [ ] [0 1 0 1 1 0 0 0] [ ] [1 0 1 0 0 1 0 0] [0 0 0 1 1 0 0 1] [ ] [0 0 1 0 0 1 1 0] [ ] [0 1 0 0 0 1 1 0] [ ] [1 0 0 0 1 0 0 1] [4, 1], [ ] [1 0 0 1 0 0 0 1] [ ] [0 1 1 0 0 0 1 0] [ ] [0 1 1 0 0 1 0 0] [ ] [1 0 0 1 1 0 0 0] [0 1 0 0 1 1 0 0] [ ] [1 0 0 0 1 1 0 0] [ ] [0 0 0 1 0 0 1 1] [ ] [0 0 1 0 0 0 1 1] [4, 2], [ ] [1 1 0 0 0 1 0 0] [ ] [1 1 0 0 1 0 0 0] [ ] [0 0 1 1 0 0 0 1] [ ] [0 0 1 1 0 0 1 0] [0 0 1 0 1 0 1 0] [ ] [0 0 0 1 0 1 0 1] [ ] [1 0 0 0 1 0 1 0] [ ] [0 1 0 0 0 1 0 1] [4, 3], [ ] [1 0 1 0 0 0 1 0] [ ] [0 1 0 1 0 0 0 1] [ ] [1 0 1 0 1 0 0 0] [ ] [0 1 0 1 0 1 0 0] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [4, 4], [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0 0] [0 0 0 1 0 1 1 0] [ ] [0 0 1 0 1 0 0 1] [ ] [0 1 0 0 1 0 0 1] [ ] [1 0 0 0 0 1 1 0] [4, 5], [ ] [0 1 1 0 0 0 0 1] [ ] [1 0 0 1 0 0 1 0] [ ] [1 0 0 1 0 1 0 0] [ ] [0 1 1 0 1 0 0 0] [0 1 0 0 0 0 1 1] [ ] [1 0 0 0 0 0 1 1] [ ] [0 0 0 1 1 1 0 0] [ ] [0 0 1 0 1 1 0 0] [4, 6], [ ] [0 0 1 1 0 1 0 0] [ ] [0 0 1 1 1 0 0 0] [ ] [1 1 0 0 0 0 0 1] [ ] [1 1 0 0 0 0 1 0] [0 0 1 0 0 1 0 1] [ ] [0 0 0 1 1 0 1 0] [ ] [1 0 0 0 0 1 0 1] [ ] [0 1 0 0 1 0 1 0] [4, 7], [ ] [0 1 0 1 0 0 1 0] [ ] [1 0 1 0 0 0 0 1] [ ] [0 1 0 1 1 0 0 0] [ ] [1 0 1 0 0 1 0 0] [0 1 1 1 0 0 0 0] [ ] [1 0 1 1 0 0 0 0] [ ] [1 1 0 1 0 0 0 0] [ ] [1 1 1 0 0 0 0 0] [4, 8], [ ] [0 0 0 0 0 1 1 1] [ ] [0 0 0 0 1 0 1 1] [ ] [0 0 0 0 1 1 0 1] [ ] [0 0 0 0 1 1 1 0] > for i from 1 to n do > for j from 1 to n do > E[i,j]:=SubMatrix( Hnn,[(i-1)*n+1..(i-1)*n+n],[(j-1)*n+1..(j-1)*n+n] ): > end do: end do: > print( E[1,2] ); print( E[1,3] ); print( E[1,4] ); print( E[1,5] ); print( E[1,6] ); print( E[1,7] ); print( E[1,8] ); print(H); [ 1 -1 1 -1 1 -1 1 -1] [ ] [-1 1 -1 1 -1 1 -1 1] [ ] [ 1 -1 1 -1 1 -1 1 -1] [ ] [-1 1 -1 1 -1 1 -1 1] [ ] [ 1 -1 1 -1 1 -1 1 -1] [ ] [-1 1 -1 1 -1 1 -1 1] [ ] [ 1 -1 1 -1 1 -1 1 -1] [ ] [-1 1 -1 1 -1 1 -1 1] [ 1 1 -1 -1 1 1 -1 -1] [ ] [ 1 1 -1 -1 1 1 -1 -1] [ ] [-1 -1 1 1 -1 -1 1 1] [ ] [-1 -1 1 1 -1 -1 1 1] [ ] [ 1 1 -1 -1 1 1 -1 -1] [ ] [ 1 1 -1 -1 1 1 -1 -1] [ ] [-1 -1 1 1 -1 -1 1 1] [ ] [-1 -1 1 1 -1 -1 1 1] [ 1 -1 -1 1 1 -1 -1 1] [ ] [-1 1 1 -1 -1 1 1 -1] [ ] [-1 1 1 -1 -1 1 1 -1] [ ] [ 1 -1 -1 1 1 -1 -1 1] [ ] [ 1 -1 -1 1 1 -1 -1 1] [ ] [-1 1 1 -1 -1 1 1 -1] [ ] [-1 1 1 -1 -1 1 1 -1] [ ] [ 1 -1 -1 1 1 -1 -1 1] [ 1 1 1 1 -1 -1 -1 -1] [ ] [ 1 1 1 1 -1 -1 -1 -1] [ ] [ 1 1 1 1 -1 -1 -1 -1] [ ] [ 1 1 1 1 -1 -1 -1 -1] [ ] [-1 -1 -1 -1 1 1 1 1] [ ] [-1 -1 -1 -1 1 1 1 1] [ ] [-1 -1 -1 -1 1 1 1 1] [ ] [-1 -1 -1 -1 1 1 1 1] [ 1 -1 1 -1 -1 1 -1 1] [ ] [-1 1 -1 1 1 -1 1 -1] [ ] [ 1 -1 1 -1 -1 1 -1 1] [ ] [-1 1 -1 1 1 -1 1 -1] [ ] [-1 1 -1 1 1 -1 1 -1] [ ] [ 1 -1 1 -1 -1 1 -1 1] [ ] [-1 1 -1 1 1 -1 1 -1] [ ] [ 1 -1 1 -1 -1 1 -1 1] [ 1 1 -1 -1 -1 -1 1 1] [ ] [ 1 1 -1 -1 -1 -1 1 1] [ ] [-1 -1 1 1 1 1 -1 -1] [ ] [-1 -1 1 1 1 1 -1 -1] [ ] [-1 -1 1 1 1 1 -1 -1] [ ] [-1 -1 1 1 1 1 -1 -1] [ ] [ 1 1 -1 -1 -1 -1 1 1] [ ] [ 1 1 -1 -1 -1 -1 1 1] [ 1 -1 -1 1 -1 1 1 -1] [ ] [-1 1 1 -1 1 -1 -1 1] [ ] [-1 1 1 -1 1 -1 -1 1] [ ] [ 1 -1 -1 1 -1 1 1 -1] [ ] [-1 1 1 -1 1 -1 -1 1] [ ] [ 1 -1 -1 1 -1 1 1 -1] [ ] [ 1 -1 -1 1 -1 1 1 -1] [ ] [-1 1 1 -1 1 -1 -1 1] [1 1 1 1 1 1 1 1] [ ] [1 -1 1 -1 1 -1 1 -1] [ ] [1 1 -1 -1 1 1 -1 -1] [ ] [1 -1 -1 1 1 -1 -1 1] [ ] [1 1 1 1 -1 -1 -1 -1] [ ] [1 -1 1 -1 -1 1 -1 1] [ ] [1 1 -1 -1 -1 -1 1 1] [ ] [1 -1 -1 1 -1 1 1 -1] > for i from 1 to 8 do > print( [i], add( E[1,i][2,y]*E[1,i][3,y]*E[1,i][4,y],y=1..8 ) ); > end do: [1], 8 [2], 0 [3], 0 [4], 0 [5], 0 [6], 0 [7], 0 [8], 0 > for i from 1 to 8 do > print( [i], add( E[1,i][2,y]*E[2,i][3,y]*E[3,i][4,y],y=1..8 ) ); > end do: [1], 0 [2], 0 [3], 0 [4], -8 [5], 0 [6], 0 [7], 0 [8], 0 > print( E[3,1] ); print( E[3,2] ); print( E[3,3] ); print( E[3,4] ); print( E[3,5] ); print( E[3,6] ); print( E[3,7] ); print( E[3,8] ); print(H); [ 1 1 -1 -1 1 1 -1 -1] [ ] [ 1 1 -1 -1 1 1 -1 -1] [ ] [-1 -1 1 1 -1 -1 1 1] [ ] [-1 -1 1 1 -1 -1 1 1] [ ] [ 1 1 -1 -1 1 1 -1 -1] [ ] [ 1 1 -1 -1 1 1 -1 -1] [ ] [-1 -1 1 1 -1 -1 1 1] [ ] [-1 -1 1 1 -1 -1 1 1] [ 1 -1 -1 1 1 -1 -1 1] [ ] [-1 1 1 -1 -1 1 1 -1] [ ] [-1 1 1 -1 -1 1 1 -1] [ ] [ 1 -1 -1 1 1 -1 -1 1] [ ] [ 1 -1 -1 1 1 -1 -1 1] [ ] [-1 1 1 -1 -1 1 1 -1] [ ] [-1 1 1 -1 -1 1 1 -1] [ ] [ 1 -1 -1 1 1 -1 -1 1] [1 1 1 1 1 1 1 1] [ ] [1 1 1 1 1 1 1 1] [ ] [1 1 1 1 1 1 1 1] [ ] [1 1 1 1 1 1 1 1] [ ] [1 1 1 1 1 1 1 1] [ ] [1 1 1 1 1 1 1 1] [ ] [1 1 1 1 1 1 1 1] [ ] [1 1 1 1 1 1 1 1] [ 1 -1 1 -1 1 -1 1 -1] [ ] [-1 1 -1 1 -1 1 -1 1] [ ] [ 1 -1 1 -1 1 -1 1 -1] [ ] [-1 1 -1 1 -1 1 -1 1] [ ] [ 1 -1 1 -1 1 -1 1 -1] [ ] [-1 1 -1 1 -1 1 -1 1] [ ] [ 1 -1 1 -1 1 -1 1 -1] [ ] [-1 1 -1 1 -1 1 -1 1] [ 1 1 -1 -1 -1 -1 1 1] [ ] [ 1 1 -1 -1 -1 -1 1 1] [ ] [-1 -1 1 1 1 1 -1 -1] [ ] [-1 -1 1 1 1 1 -1 -1] [ ] [-1 -1 1 1 1 1 -1 -1] [ ] [-1 -1 1 1 1 1 -1 -1] [ ] [ 1 1 -1 -1 -1 -1 1 1] [ ] [ 1 1 -1 -1 -1 -1 1 1] [ 1 -1 -1 1 -1 1 1 -1] [ ] [-1 1 1 -1 1 -1 -1 1] [ ] [-1 1 1 -1 1 -1 -1 1] [ ] [ 1 -1 -1 1 -1 1 1 -1] [ ] [-1 1 1 -1 1 -1 -1 1] [ ] [ 1 -1 -1 1 -1 1 1 -1] [ ] [ 1 -1 -1 1 -1 1 1 -1] [ ] [-1 1 1 -1 1 -1 -1 1] [ 1 1 1 1 -1 -1 -1 -1] [ ] [ 1 1 1 1 -1 -1 -1 -1] [ ] [ 1 1 1 1 -1 -1 -1 -1] [ ] [ 1 1 1 1 -1 -1 -1 -1] [ ] [-1 -1 -1 -1 1 1 1 1] [ ] [-1 -1 -1 -1 1 1 1 1] [ ] [-1 -1 -1 -1 1 1 1 1] [ ] [-1 -1 -1 -1 1 1 1 1] [ 1 -1 1 -1 -1 1 -1 1] [ ] [-1 1 -1 1 1 -1 1 -1] [ ] [ 1 -1 1 -1 -1 1 -1 1] [ ] [-1 1 -1 1 1 -1 1 -1] [ ] [-1 1 -1 1 1 -1 1 -1] [ ] [ 1 -1 1 -1 -1 1 -1 1] [ ] [-1 1 -1 1 1 -1 1 -1] [ ] [ 1 -1 1 -1 -1 1 -1 1] [1 1 1 1 1 1 1 1] [ ] [1 -1 1 -1 1 -1 1 -1] [ ] [1 1 -1 -1 1 1 -1 -1] [ ] [1 -1 -1 1 1 -1 -1 1] [ ] [1 1 1 1 -1 -1 -1 -1] [ ] [1 -1 1 -1 -1 1 -1 1] [ ] [1 1 -1 -1 -1 -1 1 1] [ ] [1 -1 -1 1 -1 1 1 -1] >