#!/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;t=4
E=[(i,j) for i in range(t) for j in range(i+1,t)]
Ws=[]
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 dt(W,t):Ws.append(W)
Ls=[]
for bits in range(1<<t):
 if bits in (0,(1<<t)-1):continue
 L=[[(bits>>j)&1,1-((bits>>j)&1)] for j in range(t)]
 Ls.append(L)
print(len(Ws),len(Ls))
cnt=0;per={}
for W in Ws:
 F=iv(W,t)
 for L in Ls:
  B=[[0]*n for _ in range(n)]
  for i in range(2):
   B[i][i]=1
   for j in range(t):
    B[i][2+j]=B[2+j][i]=L[j][i]
  for i in range(t):
   for j in range(t):
    v=F[i][j]
    for a in range(2):
     for b in range(2):
      v^=L[i][a]*L[j][b]
    B[2+i][2+j]=v
  if dt(B,n):
   A=[r[:] for r in B]
   for i in range(n):A[i][i]^=1
   if dt(A,n):
    C=iv(B,n)
    if all(C[i][i]==(i<2) for i in range(n)):
     cnt+=1;per[str(W)]=per.get(str(W),0)+1
print('cnt',cnt,'numW',len(per),sorted(per.values()))