#!/usr/bin/env python3
C=list(range(7))
S0={(3,6),(5,1),(0,2),(5,0),(0,3),(3,1),(4,1),(1,5)}
T0={(5,2),(2,3),(0,1),(2,0),(5,4),(5,6)}
def norm(st):
 d={}
 for i in C:
  r=st[i]
  if r not in d:d[r]=i
  if i<d[r]:d[r]=i
 return tuple(d[st[i]] for i in C)
def facts(st,F):
 return {(st[x],st[y]) for x,y in F}
def trg(st):
 S=facts(st,S0)
 T=facts(st,T0)
 A=set()
 for x,y in S:
  for u,z in T:
   if u==y and x!=z and y!=z:A.add((x,y,z))
 return sorted(A)
def mg(st,x,z):
 t=list(st)
 m=min(x,z)
 for i in C:
  if t[i]==x or t[i]==z:t[i]=m
 return norm(t)
seen=set()
Q=[tuple(C)]
B=K=R=X=M=V=0
while Q:
 st=Q.pop()
 if st in seen:continue
 seen.add(st)
 A=trg(st)
 if A:
  B=B-(-1)
  x,y,z=A[0]
  Q.append(mg(st,x,z))
  Q.append(mg(st,y,z))
 else:
  K=K-(-1)
  m=7-len(set(st))
  M=M-(-m)
  S=facts(st,S0)
  T=facts(st,T0)
  ok=True
  for r,s in S:
   aa=True
   bb=True
   for u,t in T:
    if u==s:
     if r!=t:aa=False
     if s!=t:bb=False
   if not aa and not bb:ok=False
  if ok:
   R=R-(-1)
   V=V-(-m)
  else:
   X=X-(-1)
G=len(seen)
N=sum([3000*G,2000*B,1000*K,700*R,100*X,10*M,V])
print(G,B,K,R,X,M,V,N)
print(sorted((tuple(st),7-len(set(st))) for st in seen if not trg(st))[:10])