#!/usr/bin/env python3
W=[(0,0,1,2,2,1),(0,1,0,2,1,2),(1,0,2,0,2,1),(2,2,1,0,0,1)]
U=set()
for w in W:
 n=len(w)
 for mask in range(1,2**n):
  U.add(tuple(w[i] for i in range(n) if (mask//(2**i))%2))
P=sorted(U,key=lambda x:(len(x),x))
n=len(P)
def sub(a,b):
 j=0
 for x in a:
  while j<len(b) and b[j]!=x: j+=1
  if j==len(b): return False
  j+=1
 return True
leq=[[sub(P[i],P[j]) for j in range(n)] for i in range(n)]
mu=[[0]*n for _ in range(n)]
for i in range(n):
 mu[i][i]=1
 for j in range(n):
  if j!=i and leq[i][j]:
   t=0
   for k in range(n):
    if k!=j and leq[i][k] and leq[k][j]: t=t+mu[i][k]
   mu[i][j]=-t
def norm(a,b):
 L=len(b)
 first=[i==0 or b[i]!=b[i-1] for i in range(L)]
 cnt=0
 for mask in range(1,2**L):
  inds=[i for i in range(L) if (mask//(2**i))%2]
  if len(inds)!=len(a): continue
  if tuple(b[i] for i in inds)!=a: continue
  ok=True
  for i in range(L):
   if i not in inds and not first[i]: ok=False
  if ok: cnt+=1
 return cnt
mism=[]
for i in range(n):
 for j in range(n):
  if i!=j and leq[i][j]:
   N=norm(P[i],P[j])
   e=((-1)**(len(P[j])-len(P[i])))*N
   if mu[i][j]!=e: mism.append((P[i],P[j],mu[i][j],N,e))
print('mismatches',len(mism))
print(mism[:20])
from collections import Counter
print('normal counts',Counter(norm(P[i],P[j]) for i in range(n) for j in range(n) if i!=j and leq[i][j]))