python3 - <<'EOF'
import random
def det(A):
 n=len(A)
 A=[list(r) for r in A]
 for c in range(n):
  p=next((r for r in range(c,n) if A[r][c]),None)
  if p is None:return 0
  A[c],A[p]=A[p],A[c]
  for r in range(c+1,n):
   if A[r][c]:A[r]=[x^y for x,y in zip(A[r],A[c])]
 return 1
def inv(A):
 n=len(A)
 M=[list(row)+[1 if i==j else 0 for j in range(n)] for i,row in enumerate(A)]
 for c in range(n):
  p=next((r for r in range(c,n) if M[r][c]),None)
  if p is None:return None
  M[c],M[p]=M[p],M[c]
  for r in range(n):
   if r!=c and M[r][c]:M[r]=[x^y for x,y in zip(M[r],M[c])]
 return [row[n:] for row in M]
def build(R2):
 m=len(R2)
 v=[sum(row)%2 for row in R2]
 u=[sum(R2[i][j] for i in range(m))%2 for j in range(m)]
 p=sum(sum(row) for row in R2)%2
 x=1^p
 R=[[x]+u] [[v[i]]+R2[i] for i in range(m)]
 return R,u,v,p,x
for trial in range(20):
 R2=[[random.randrange(2) for _ in range(6)] for _ in range(6)]
 R,u,v,p,x=build(R2)
 if not det(R2):continue