@lru_cache(None)
def payoffs(S,E):
    stay=[i for i in range(1,13) if bit(S,i-1)]
    res=[0]*13
    for i in range(1,13):
        if not bit(S,i-1):
            res[i]=outopt[i]
    if len(stay)==0:
        return tuple(res)
    win=stay[0]
    for i in stay[1:]:
        if v[i]>v[win]:
            win=i
    second=0
    for i in stay:
        if i!=win and v[i]>second:
            second=v[i]
    adj=[[] for i in range(13)]
    for i in stay:
        if i<=3:
            adj[0].append(i)
    for b in range(11):
        u=edges[b][0]
        w=edges[b][1]
        if bit(E,b) and bit(S,u-1) and bit(S,w-1):
            adj[u].append(w)
    def reach(avoid):
        seen=[False]*13
        stack=[0]
        seen[0]=True
        while len(stack)>0:
            x=stack.pop()
            for y in adj[x]:
                if y!=avoid and not seen[y]:
                    seen[y]=True
                    stack.append(y)
        return seen[win]
    res[win]=v[win]-second
    for i in stay:
        if i!=win:
            if not reach(i):
                res[i]=7
    return tuple(res)