#!/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]
ch=min((t(c),c)	for	c	in	big)
cs=ch[1]
A=B=0
for	r,c	in	enumerate(can,1):
	X=G[S(c)]
	b=sum(d(w)==2	for	w	in	X)
	A+=r*(len(X)+2)*(b+3)
	B+=r*(sum((i+1)*(int(c[i])+3)	for	i	in	range(7))+5)
Cv=sum((i+1)*(int(cs[i])+4)	for	i	in	range(7))*(f(cs,'01')+2*f(cs,'12')+3*f(cs,'23')+5)
print('N',len(L),'K',len(big),'star',''.join(cs),'theta',t(cs),'rank',can.index(cs)+1)
print('A',A-101*(A//101),'B',B-103*(B//103),'C',Cv-107*(Cv//107))
print('hist',{k:sum(len(x)==k	for	x	in	L)	for	k	in	sorted(set(len(x)	for	x	in	L))})