#!/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())
can=sorted(min(c)	for	c	in	L)
def	d(w):return	sum(w[i]>w[i+1]	for	i	in	range(6))
def	t(c):return	5*d(c)+sum((i+1)*(int(c[i])+2)	for	i	in	range(7))
big=[c	for	c	in	can	if	len(G[S(c)])>=3]
best=min(t(c)	for	c	in	big)
print('best',best,'ties',[''.join(c)	for	c	in	big	if	t(c)==best])
print('first15',[(t(c),''.join(c),len(G[S(c)]),sum(d(w)==2	for	w	in	G[S(c)]))	for	c	in	sorted(big,key=lambda	c:(t(c),c))[:15]])
cs=min((t(c),c)	for	c	in	big)[1]
print('rank',can.index(cs)+1,'before',[''.join(c)	for	c	in	can[:can.index(cs)]])
print('sigstar',S(cs),'bstar',sum(d(w)==2	for	w	in	G[S(cs)]),'sstar',len(G[S(cs)]))
print('allbig',[(t(c),''.join(c),len(G[S(c)]),sum(d(w)==2	for	w	in	G[S(c)]))	for	c	in	big])