#include <bits/stdc++.h>
using namespace std;
const bool testing = false;
void program() {
  long long n;
  cin >> n;
  vector<int> type(n + 1, 0);
  vector<int> a(n + 1, 0);
  vector<int> count(n + 1, 0);
  type[0] = 999999;
  a[0] = 999999;
  count[0] = 999999;
  for (int i = (1), _end = (n + 1); i < _end; ++i) cin >> type[i];
  for (int i = (1), _end = (n + 1); i < _end; ++i) {
    cin >> a[i];
    count[a[i]]++;
  }
  int mx = 0;
  vector<int> seqnc;
  for (int i = (1), _end = (n + 1); i < _end; ++i) {
    if (type[i] == 1 && count[i] <= 1) {
      vector<int> seq;
      seq.push_back(i);
      int c = 1;
      int j = a[i];
      while (type[j] != 1 && a[j] != 0 && count[j] == 1) {
        c++;
        seq.push_back(j);
        j = a[j];
      }
      if (type[j] == 0 && count[j] == 1) {
        c++;
        seq.push_back(j);
      }
      if (c > mx) {
        mx = c;
        seqnc = seq;
      }
    }
  }
  cout << mx << "\n";
  for (int i = seqnc.size() - 1; i >= 0; i--) cout << seqnc[i] << " ";
  cout << "\n";
}
int main() {
  if (!testing) {
    program();
    return 0;
  }
  FILE* fin = NULL;
  fin = fopen("in.txt", "w+");
  fprintf(fin, "5\n0 0 0 0 1\n0 1 2 3 4\n");
  fclose(fin);
  freopen("in.txt", "r", stdin);
  printf("test case(1) => expected : \n");
  printf("5\n1 2 3 4 5\n");
  printf("test case(1) => founded  : \n");
  program();
  fin = fopen("in.txt", "w+");
  fprintf(fin, "5\n0 0 1 0 1\n0 1 2 2 4\n");
  fclose(fin);
  freopen("in.txt", "r", stdin);
  printf("test case(2) => expected : \n");
  printf("2\n4 5\n");
  printf("test case(2) => founded  : \n");
  program();
  fin = fopen("in.txt", "w+");
  fprintf(fin, "4\n1 0 0 0\n2 3 4 2\n");
  fclose(fin);
  freopen("in.txt", "r", stdin);
  printf("test case(3) => expected : \n");
  printf("1\n1\n");
  printf("test case(3) => founded  : \n");
  program();
  return 0;
}

### Prompt

Please formulate a Cpp solution to the following problem:

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;
const bool testing = false;
void program() {
  long long n;
  cin >> n;
  vector<int> type(n + 1, 0);
  vector<int> a(n + 1, 0);
  vector<int> count(n + 1, 0);
  type[0] = 999999;
  a[0] = 999999;
  count[0] = 999999;
  for (int i = (1), _end = (n + 1); i < _end; ++i) cin >> type[i];
  for (int i = (1), _end = (n + 1); i < _end; ++i) {
    cin >> a[i];
    count[a[i]]++;
  }
  int mx = 0;
  vector<int> seqnc;
  for (int i = (1), _end = (n + 1); i < _end; ++i) {
    if (type[i] == 1 && count[i] <= 1) {
      vector<int> seq;
      seq.push_back(i);
      int c = 1;
      int j = a[i];
      while (type[j] != 1 && a[j] != 0 && count[j] == 1) {
        c++;
        seq.push_back(j);
        j = a[j];
      }
      if (type[j] == 0 && count[j] == 1) {
        c++;
        seq.push_back(j);
      }
      if (c > mx) {
        mx = c;
        seqnc = seq;
      }
    }
  }
  cout << mx << "\n";
  for (int i = seqnc.size() - 1; i >= 0; i--) cout << seqnc[i] << " ";
  cout << "\n";
}
int main() {
  if (!testing) {
    program();
    return 0;
  }
  FILE* fin = NULL;
  fin = fopen("in.txt", "w+");
  fprintf(fin, "5\n0 0 0 0 1\n0 1 2 3 4\n");
  fclose(fin);
  freopen("in.txt", "r", stdin);
  printf("test case(1) => expected : \n");
  printf("5\n1 2 3 4 5\n");
  printf("test case(1) => founded  : \n");
  program();
  fin = fopen("in.txt", "w+");
  fprintf(fin, "5\n0 0 1 0 1\n0 1 2 2 4\n");
  fclose(fin);
  freopen("in.txt", "r", stdin);
  printf("test case(2) => expected : \n");
  printf("2\n4 5\n");
  printf("test case(2) => founded  : \n");
  program();
  fin = fopen("in.txt", "w+");
  fprintf(fin, "4\n1 0 0 0\n2 3 4 2\n");
  fclose(fin);
  freopen("in.txt", "r", stdin);
  printf("test case(3) => expected : \n");
  printf("1\n1\n");
  printf("test case(3) => founded  : \n");
  program();
  return 0;
}

```