#!/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	fd(w,u):
	a=[0]*(len(u)+1)
	a[0]=1
	for	ch	in	w:
		for	j	in	range(len(u)-1,-1,-1):
			if	ch==u[j]:a[j+1]+=a[j]
	return	a[-1]
def	S(w):return	tuple(fd(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())
can=sorted(min(c)	for	c	in	L)
def	d(w):return	sum(w[i]>w[i+1]	for	i	in	range(6))
print('words',len(W),'size',sum(map(len,L)),'d2direct',sum(d(w)==2	for	w	in	W),'d2class',sum(sum(d(w)==2	for	w	in	x)	for	x	in	L))
print('distinctSigs',len({S(w)	for	w	in	W}),'classes',len(L))
print('sizes_sorted',sorted(len(x)	for	x	in	L))
print('allcanon',[''.join(c)	for	c	in	can])