#!/usr/bin/env python3
from functools import lru_cache
from math import isqrt
@lru_cache(None)
def search(B):
 S={a+b for a in B for b in B}
 if 113 in S:return False
 D=S-{a*b for a in B for b in B}
 if not D:return True
 def factors(s):
  return [(u,s//u) for u in range(1,isqrt(s)+1) if s%u==0 and s//u<113]
 s=min(D,key=lambda s:len(factors(s)))
 return any(search(tuple(sorted(set(B)|{u,v}))) for u,v in factors(s))
print(search((1,2,3,5,7)),search.cache_info())