#!/usr/local/bin/python3
from	itertools	import	permutations	as	P,combinations	as	Q
from	collections	import	defaultdict	as	D
W=sorted(set(P('0011223')))
def	f(w,u):
	s=0
	for	I	in	Q(range(7),len(u)):
		if	all(w[I[j]]==u[j]	for	j	in	range(len(u))):s+=1
	return	s
def	S(w):return	tuple(f(w,u)	for	u	in	('01','12','23','012','123','0123'))
G=D(list)
for	w	in	W:G[S(w)].append(w)
L=list(G.values())
idx={w:k	for	k,x	in	enumerate(L)	for	w	in	x}
def	rv(w):return	tuple(reversed(w))
ex={}
br={}
for	k,x	in	enumerate(L):
	R={rv(w)	for	w	in	x}
	ks={idx[z]	for	z	in	R}
	if	len(ks)==1:
		j=list(ks)[0]
		br[k]=j
		if	len(L[j])==len(R):ex[k]=j
print('Mex',len(ex),'fix',sum(k==v	for	k,v	in	ex.items()),'Mbr',len(br),'fixbr',sum(k==v	for	k,v	in	br.items()))
print('brnotext',[(k,v,len(L[k]),len(L[v]))	for	k,v	in	br.items()	if	k	not	in	ex])
print('notbr',[(k,len(L[k]),len({idx[rv(w)]	for	w	in	x}))	for	k,x	in	enumerate(L)	if	k	not	in	br])