A9258 | 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!

The first line contains integer $n$ ( $1<=n<=10^{5}$ ) — 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 $i$ .

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.