python3 - <<'EOF'
import itertools
C=[[1,1,0,1],[1,1,1,0],[0,1,0,1],[1,0,1,0]]
allm=list(itertools.product([0,1],repeat=4))
def det(A):
 A=[list(r) for r in A]
 n=len(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
for Q in itertools.product(allm,repeat=4):
 if not det(Q):continue
 if tuple(tuple(sum(Q[i][k]*Q[j][k] for k in range(4))%2 for j in range(4)) for i in range(4))!=tuple(tuple(r) for r in C):continue
 if [sum(Q[i][j] for i in range(4))%2 for j in range(4)]!=[1,1,1,1]:continue
 if [Q[i][0] for i in range(4)]!=[1,0,0,0]:continue
 print('Q',Q)
 R=[row[1:] for row in Q[1:]]
 print('R',R)
 print('r',[sum(row)%2 for row in R])
 print('s',[sum(R[i][j] for i in range(3))%2 for j in range(3)])
 break
else:print('none')
EOF