#include <bits/stdc++.h>
using namespace std;
int n;
vector<int> hm;
vector<int> to;
vector<int> visited;
int hotel;
int main(int argc, char **argv) {
  scanf("%d", &n);
  for (int i = 0; i < 100000; i++) {
    to.push_back(0);
    visited.push_back(0);
  }
  for (int i = 0; i < n; i++) {
    int temp;
    scanf("%d", &temp);
    if (temp == 1) hotel = i + 1;
    hm.push_back(temp);
  }
  for (int i = 0; i < n; i++) {
    int temp;
    scanf("%d", &temp);
    if (temp != 0) {
      if (to[temp - 1] == 0)
        to[temp - 1] = i + 1;
      else
        to[temp - 1] = -1;
    }
  }
  vector<int> pathF;
  for (int i = 0; i < n; i++) {
    if (hm[i] == 0 && to[i] > 0 && visited[i] == 0) {
      vector<int> path;
      path.push_back(i + 1);
      int cycle = i;
      int t1 = i;
      int d = -1;
      visited[i] = 1;
      int found = 0;
      while (1) {
        d = to[t1] - 1;
        if (d == cycle) break;
        if (to[d] > 0) {
          path.push_back(d + 1);
          t1 = d;
          visited[d] = 1;
        } else {
          if (hm[d] == 1) {
            path.push_back(d + 1);
            found = 1;
          }
          break;
        }
      }
      if (found == 1 && path.size() > pathF.size()) pathF = path;
    }
  }
  if (pathF.size() > 1) {
    printf("%d\n", pathF.size());
    for (int i = 0; i < pathF.size(); i++) printf("%d ", pathF[i]);
  } else {
    printf("1\n%d", hotel);
  }
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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 ≥ 1) and meet the following conditions:

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

Input

The first line contains integer n (1 ≤ n ≤ 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 ≤ ai ≤ 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.

Output

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.

Examples

Input

5
0 0 0 0 1
0 1 2 3 4


Output

5
1 2 3 4 5


Input

5
0 0 1 0 1
0 1 2 2 4


Output

2
4 5


Input

4
1 0 0 0
2 3 4 2


Output

1
1

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int n;
vector<int> hm;
vector<int> to;
vector<int> visited;
int hotel;
int main(int argc, char **argv) {
  scanf("%d", &n);
  for (int i = 0; i < 100000; i++) {
    to.push_back(0);
    visited.push_back(0);
  }
  for (int i = 0; i < n; i++) {
    int temp;
    scanf("%d", &temp);
    if (temp == 1) hotel = i + 1;
    hm.push_back(temp);
  }
  for (int i = 0; i < n; i++) {
    int temp;
    scanf("%d", &temp);
    if (temp != 0) {
      if (to[temp - 1] == 0)
        to[temp - 1] = i + 1;
      else
        to[temp - 1] = -1;
    }
  }
  vector<int> pathF;
  for (int i = 0; i < n; i++) {
    if (hm[i] == 0 && to[i] > 0 && visited[i] == 0) {
      vector<int> path;
      path.push_back(i + 1);
      int cycle = i;
      int t1 = i;
      int d = -1;
      visited[i] = 1;
      int found = 0;
      while (1) {
        d = to[t1] - 1;
        if (d == cycle) break;
        if (to[d] > 0) {
          path.push_back(d + 1);
          t1 = d;
          visited[d] = 1;
        } else {
          if (hm[d] == 1) {
            path.push_back(d + 1);
            found = 1;
          }
          break;
        }
      }
      if (found == 1 && path.size() > pathF.size()) pathF = path;
    }
  }
  if (pathF.size() > 1) {
    printf("%d\n", pathF.size());
    for (int i = 0; i < pathF.size(); i++) printf("%d ", pathF[i]);
  } else {
    printf("1\n%d", hotel);
  }
  return 0;
}

```