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
    return O(1,0,0)
U0=solve(0.0)
UM=solve(0.1)
U1=solve(1.0)
K1=len([s for s in U1 if bit(s,7)])
P1=[s for s in U1 if not bit(s,7)]
U=set(UM)|set(U0)|set(P1)
K0=len(U)
print('K0',K0,'K1',K1,'ans',2*K0-(-3*K1))
print('sizes',len(U0),len(UM),len(U1),len(P1))
print('UMnotU1',sorted(set(UM)-set(U1)))
print('P1notUM',sorted(set(P1)-set(UM)))