CF350B.Resort

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 _v_1, _v_2, ..., v__k (k ≥ 1) and meet the following conditions:

1. Objects with numbers _v_1, _v_2, ..., v__k - 1 are mountains and the object with number v__k is the hotel.
2. 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.
3. The path contains as many objects as possible (k is maximal).

Help Valera. Find such path that meets all the criteria of our hero!

瓦莱拉终于决定去度假了！他收拾好行装，前往一座滑雪场。

瓦莱拉本想来一次滑雪之旅，但他很快意识到自己可能会在这个新地方迷路。有人给了他一个有用的提示：该滑雪场共有 $n$ 个地点（我们将这些地点按某种方式用 $1$ 到 $n$ 的整数编号），每个地点要么是酒店，要么是山峰。

瓦莱拉还了解到，滑雪场内修建了多条滑雪道。具体来说，对每个地点 $v$，滑雪场至多存在一个地点 $u$，使得有一条从 $u$ 到 $v$ 的滑雪道。此外，我们还知道：没有任何酒店作为滑雪道的起点（即不存在从某家酒店出发指向其他地点的滑雪道）。

瓦莱拉担心自己在滑雪场中迷路，因此希望你为他规划一条行走路径。该路径需由一系列地点 $v_1,\,v_2,\,\dots,\,v_k$（其中 $k\geq 1$）构成，并满足以下条件：

1. 编号为 $v_1,\,v_2,\,\dots,\,v_{k-1}$ 的地点均为山峰，而编号为 $v_k$ 的地点为酒店；
2. 对任意整数 $i$（$1\leq i < k$），地点 $v_i$ 恰好有一条向外延伸的滑雪道，且该滑雪道通向地点 $v_{i+1}$；
3. 路径所含地点数量尽可能多（即 $k$ 取最大值）。

请帮助瓦莱拉！找出一条满足上述所有条件的路径！

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

The second line contains n space-separated integers _type_1, _type_2, ..., 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 _a_1, _a_2, ..., 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.

第一行包含一个整数 $ n $（$ 1 \leq n \leq 10^5 $）—— 表示物体的数量。

第二行包含 $ n $ 个用空格分隔的整数 $ \text{type}_1,\ \text{type}_2,\ \dots,\ \text{type}_n $ —— 表示各物体的类型。若 $ \text{type}_i = 0 $，则第 $ i $ 个物体是山；若 $ \text{type}_i = 1 $，则第 $ i $ 个物体是酒店。保证至少有一个物体是酒店。

输入的第三行包含 $ n $ 个用空格分隔的整数 $ a_1,\ a_2,\ \dots,\ a_n $（$ 0 \leq a_i \leq n $）—— 描述滑雪轨道。若 $ a_i = 0 $，则不存在物体 $ v $，使得从 $ v $ 到 $ i $ 建有一条滑雪轨道；若 $ a_i \neq 0 $，则表示从物体 $ a_i $ 到物体 $ i $ 建有一条滑雪轨道。

In the first line print k — the maximum possible path length for Valera. In the second line print k integers _v_1, _v_2, ..., v__k — the path. If there are multiple solutions, you can print any of them.

第一行输出 k —— Valera 能够达到的最大路径长度。
第二行输出 k 个整数 _v_₁, _v_₂, ..., v__k —— 该路径。若存在多种解，输出任意一种即可。