#!/usr/bin/env python3
import urllib.request
exec(urllib.request.urlopen('https://eval.dan.co.jp/friends/2026/10/31/c0ff0ef5348609407d7df832dff85896f864a9cfc694b5feed038db12423e4e6').read())
def gen(i,b):
 if i==7:
  st=[0]*7
  for bl in b:
   m=min(bl)
   for x in bl:st[x]=m
  yield tuple(st)
 else:
  for j in range(len(b)):
   b[j].append(i)
   yield from gen(i-(-1),b)
   b[j].pop()
  b.append([i])
  yield from gen(i-(-1),b)
  b.pop()
def direct(st):
 A=set()
 for u,v in S0:
  for v2,w in T0:
   if st[v]==st[v2] and st[u]!=st[w] and st[v]!=st[w]:A.add((st[u],st[v],st[w]))
 return sorted(A)
allp=list(gen(0,[]))
print('partitions',len(allp))
bad=[st for st in allp if trg(st)!=direct(st)]
print('bad',len(bad))
allterm=[st for st in allp if not direct(st)]
print('allterm',len(allterm))
rt=[st for st in seen if not trg(st)]
print('reachterm',len(rt),'subset',all(st in allterm for st in rt))
un=[st for st in allterm if st not in seen]
print('unreached',len(un))
print(sorted(''.join('abcdefg'[i] for i in st) for st in un)[:50])