#!/usr/bin/env python3
from functools import lru_cache
V=[0,11,10,9,32,30,28,14,17,22,41,45,48]
O=[0]*13;O[8]=7
E=[(1,4),(1,8),(2,5),(2,8),(3,6),(3,7),(7,8),(8,9),(8,10),(8,11),(8,12)]
D=[[]for _ in range(13)]
for a,b in E:D[a].append(b)
def t(S):
 if S==0:return O[:]
 G=[[]for _ in range(13)]
 for x in(1,2,3):
  if(S>>(x-1))%2:G[0].append(x)
 for a,b in E:
  if(S>>(a-1))%2 and(S>>(b-1))%2:G[a].append(b)
 m=max((V[i],-i)for i in range(1,13)if(S>>(i-1))%2);w=-m[1]
 def R(ban):
  x={0};q=[0]
  while q:
   u=q.pop()
   for v in G[u]:
    if v!=ban and v not in x:x.add(v);q.append(v)
  return x
 sec=max([0,*[V[i]for i in range(1,13)if i!=w and(S>>(i-1))%2]])
 z=[O[i]for i in range(13)]
 for j in range(1,13):
  if(S>>(j-1))%2:
   z[j]=V[j]-sec if j==w else(7 if w not in R(j)else 0)
 return z
@lru_cache(None)
def f(i,S):
 if i>12:
  z=t(S);return(1<<S,z,z)
 inv=i<4
 if not inv:
  for a,b in E:
   if b==i and a<i and(S>>(a-1))%2:inv=1;break
 if not inv:return f(-~i,S)
 ps=f(-~i,S|(1<<(i-1)))
 pe=f(-~i,S)
 th=max(ps[1][i],pe[1][i])
 r=0
 for c in(ps,pe):
  if c[2][i]>=th:
   for j in range(4096):
    if(c[0]>>j)%2 and t(j)[i]>=th:r|=1<<j
 mn=[999]*13;mx=[-999]*13
 for j in range(4096):
  if(r>>j)%2:
   z=t(j)
   for k in range(1,13):
    if z[k]<mn[k]:mn[k]=z[k]
    if z[k]>mx[k]:mx[k]=z[k]
 return r,tuple(mn),tuple(mx)
r=f(1,0)
print(bin(r[0]).count('1'))
print([i for i in range(4096)if(r[0]>>i)%2])
print(f.cache_info())