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, ..., v_k (k ≥ 1) and meet the following conditions:

Objects with numbers v₁, v₂, ..., v_k - 1 are mountains and the object with number v_k is the hotel.
For any integer i (1 ≤ i < k), there is exactly one ski track leading from object v_i. This track goes to object v_i + 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!

Input

The first line contains integer n (1 ≤ n ≤ 10⁵) — the number of objects.

The second line contains n space-separated integers type₁, type₂, ..., type_n — the types of the objects. If type_i equals zero, then the i-th object is the mountain. If type_i 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, ..., a_n (0 ≤ a_i ≤ n) — the description of the ski tracks. If number a_i equals zero, then there is no such object v, that has a ski track built from v to i. If number a_i doesn't equal zero, that means that there is a track built from object a_i to object i.

Output

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

Idx	Name	Rating
A	TL	1200
B	Resort	1500
C	Bombs	1600
D	Looking for Owls	2400
E	Wrong Floyd	2200

Codeforces Round 203 (Div. 2)