Valera's finally decided to go on holiday! He packed up and headed for a ski resort.

Valera's fancied a ski trip but he soon realized that he could get lost in this new place. Somebody gave him a useful hint: the resort has n objects (we will consider the objects indexed in some way by integers from 1 to n), each object is either a hotel or a mountain.

Valera has also found out that the ski resort had multiple ski tracks. Specifically, for each object v, the resort has at most one object u, such that there is a ski track built from object u to object v. We also know that no hotel has got a ski track leading from the hotel to some object.

Valera is afraid of getting lost on the resort. So he wants you to come up with a path he would walk along. The path must consist of objects v1,v2,...,vk (k \ge 1) and meet the following conditions:
Objects with numbers v1,v2,...,vk-1 are mountains and the object with number vk is the hotel. For any integer i (1 \le i \lt k), there is exactly one ski track leading from object vi. This track goes to object vi+1. The path contains as many objects as possible (k is maximal).
Help Valera. Find such path that meets all the criteria of our hero!

The first line contains integer n (1 \le n \le 105) - the number of objects.

The second line contains n space-separated integers type1,type2,...,typen - the types of the objects. If typei equals zero, then the i-th object is the mountain. If typei equals one, then the i-th object is the hotel. It is guaranteed that at least one object is a hotel.

The third line of the input contains n space-separated integers a1,a2,...,an (0 \le ai \le n) - the description of the ski tracks. If number ai equals zero, then there is no such object v, that has a ski track built from v to i. If number ai doesn't equal zero, that means that there is a track built from object ai to object i.

In the first line print k - the maximum possible path length for Valera. In the second line print k integers v1,v2,...,vk - the path. If there are multiple solutions, you can print any of them.