python3 - <<'EOF'
import itertools
def det(A):
 n=len(A)
 A=[row[:] for row in A]
 d=1
 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
  if p!=c: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=[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]
cnt=0
sol=[]
vars=[(i,j) for i in range(4) for j in range(i+1,4)]
for bits in itertools.product([0,1],repeat=6):
 C=[[0]*4 for _ in range(4)]
 C[0][0]=C[1][1]=1
 for (i,j),b in zip(vars,bits):C[i][j]=C[j][i]=b
 if det(C) and inv(C) and all(inv(C)[i][i]==1 for i in range(4)) and det([[C[i][j]^(i==j) for j in range(4)] for i in range(4)]):
  cnt+=1
  sol.append(C)
print(cnt)
for C in sol:print(C)
EOF