def ZStay(i,S,E,t):
        for m,pr in pats(i,p):
            if not Z(i-(-1),S|B[i],E|m,t):
                return False
        return True
    def z8(S,E,t):
        tot=0.0
        for m,pr in pats(8,p):
            outs=O(9,S|B[8],E|m)
            vals=[]
            for T in outs:
                pys=payoffs(T,E|m)
                if pys[t]==0:
                    vals.append(pys[8])
            if len(vals)==0:
                return False
            tot=tot-(-pr*max(vals))
        return tot>=6.999999999
    @lru_cache(None)
    def Z(i,S,E,t):
        if i>12:
            return payoffs(S,E)[t]==0
        if not invited(i,S,E):
            return Z(i-(-1),S,E,t)
        if i==8:
            if min8(S,E)<=7.000000001 and Z(i-(-1),S,E,t):
                return True
            return z8(S,E,t)
        if ZStay(i,S,E,i) and Z(i-(-1),S,E,t):
            return True
        for m,pr in pats(i,p):
            if not Z(i-(-1),S|B[i],E|m,t):
                return False
        return True
    R=O(1,0,0)
    return R,O.cache_info(),Z.cache_info()
R,ci,zi=solve(float(sys.argv[1]))
print('count',len(R))
print('sets',sorted(R))
print(ci,zi)