#!/usr/local/bin/python3
def rk(M,n):
 M=[r[:] for r in M];r=0
 for c in range(n):
  p=next((i for i in range(r,n) if M[i][c]),-1)
  if p<0:continue
  M[r],M[p]=M[p],M[r]
  for i in range(r+1,n):
   if M[i][c]:
    for j in range(c,n):M[i][j]^=M[r][j]
  r+=1
 return r
def dt(M,n):return rk(M,n)==n
def iv(M,n):
 A=[M[i][:]+[int(i==j) for j in range(n)] for i in range(n)];r=0
 for c in range(n):
  p=next((i for i in range(r,n) if A[i][c]),-1)
  if p<0:return None
  A[r],A[p]=A[p],A[r]
  for i in range(n):
   if i!=r and A[i][c]:
    for j in range(c,2*n):A[i][j]^=A[r][j]
  r+=1
 return [q[n:] for q in A]
t=4;n=6;bits=3
L=[[(bits>>j)&1,1-((bits>>j)&1)] for j in range(t)]
E=[(i,j) for i in range(t) for j in range(i+1,t)]
for m in range(1<<6):
 W=[[0]*t for _ in range(t)]
 for k,(i,j) in enumerate(E):
  if m>>k&1:W[i][j]=W[j][i]=1
 if not dt(W,t):continue
 F=iv(W,t)
 # U basis l1,l2 for bits3: (1,1,0,0) and (0,0,1,1)
 u1=[1,1,0,0];u2=[0,0,1,1]
 q=sum(u1[i]*F[i][j]*u2[j] for i in range(t) for j in range(t))% 2
 K=[[(F[i][j]^(i==j)^(sum(L[i][a]*L[j][a] for a in range(2))% 2)) for j in range(t)] for i in range(t)]
 A=[[0]*n for _ in range(n)]
 for i in range(2):
  for j in range(t):A[i][2+j]=A[2+j][i]=L[j][i]
 for i in range(t):
  for j in range(t):A[2+i][2+j]=K[i][j]
 if dt(A,n) and q==1:
  print('FOUND',m,'q',q,'rankK',rk(K,t))
  print('W',W)
  print('F',F)
  print('K',K)
  print('A',A)
  break
else:
 continue
break