def ef(S):
    e=0
    for b in range(11):
        u=edges[b][0]
        if bit(S,u-1):
            e=e|(1<<b)
    return e
def solve1():
    @lru_cache(None)
    def O(i,S):
        if i>12:
            return frozenset([S])
        E=ef(S)
        if not invited(i,S,E):
            return O(i-(-1),S)
        res=set()
        if i==8:
            outs8=O(9,S|B[8])
            vals8=[payoffs(T,ef(T))[8] for T in outs8]
            if min(vals8)<=7.0000001:
                res.update(O(9,S))
            if max(vals8)>=6.9999999:
                for T in outs8:
                    if payoffs(T,ef(T))[8]>=6.9999999:
                        res.add(T)
        else:
            if ZStay(i,S,i):
                res.update(O(i-(-1),S))
            res.update(O(i-(-1),S|B[i]))
        return frozenset(res)
    def ZStay(i,S,t):
        return Z(i-(-1),S|B[i],t)
    @lru_cache(None)
    def Z(i,S,t):
        if i>12:
            return payoffs(S,ef(S))[t]==0
        E=ef(S)
        if not invited(i,S,E):
            return Z(i-(-1),S,t)
        if i==8:
            outs8=O(9,S|B[8])
            vals8=[payoffs(T,ef(T))[8] for T in outs8]
            if min(vals8)<=7.0000001 and Z(9,S,t):
                return True
            for T in outs8:
                pys=payoffs(T,ef(T))
                if pys[8]>=6.9999999 and pys[t]==0:
                    return True
            return False
        if ZStay(i,S,i) and Z(i-(-1),S,t):
            return True
        return Z(i-(-1),S|B[i],t)
    return O(1,0)