#!/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]
n=6
E=[(i,j) for i in range(n) for j in range(i+1,n)];c={}
for m in range(1<<len(E)):
 A=[[0]*n for _ in range(n)]
 for k,(i,j) in enumerate(E):
  if m>>k&1:A[i][j]=A[j][i]=1
 if dt(A,n):
  B=[r[:] for r in A]
  for i in range(n):B[i][i]^=1
  if dt(B,n):
   C=iv(B,n)
   if all(C[i][i]==(i<2) for i in range(n)):
    D=[r[:] for r in C]
    D[0][0]^=1;D[1][1]^=1;
    r=rk(D,n)
    c[r]=c.get(r,0)+1
print(c)