#include <bits/stdc++.h>
using namespace std;
long long MAX(long long a, long long b) { return a < b ? b : a; }
long long MIN(long long a, long long b) { return a > b ? b : a; }
int gcd(int a, int b) { return a ? gcd(b % a, a) : b; }
bool is_letter_s(char a) {
  if ((a >= 'a') && (a <= 'z'))
    return true;
  else
    return false;
}
bool is_letter_b(char a) {
  if ((a >= 'A') && (a <= 'Z'))
    return true;
  else
    return false;
}
bool is_number(char a) {
  if ((a >= '0') && (a <= '9'))
    return true;
  else
    return false;
}
vector<int> prefix(string s) {
  int n = s.length();
  vector<int> v(n);
  for (int i = 1; i <= n - 1; i++) {
    int j = v[i - 1];
    while (j > 0 && s[i] != s[j]) j = v[j - 1];
    if (s[i] == s[j]) j++;
    v[i] = j;
  }
  return v;
}
int main() {
  cin.sync_with_stdio(0);
  int n;
  cin >> n;
  int a[110000];
  int b[110000];
  int num[110000];
  memset(num, 0, sizeof num);
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) {
    cin >> b[i];
    num[b[i]]++;
  }
  a[0] = 1;
  b[0] = 0;
  stack<int> st;
  stack<int> best_stack;
  for (int i = 1; i <= n; i++)
    if (a[i] == 1) {
      int x = i;
      st.push(x);
      x = b[x];
      while (a[x] == 0 && x != 0 && num[x] == 1) {
        st.push(x);
        x = b[x];
      }
      if (st.size() > best_stack.size()) best_stack = st;
      while (!st.empty()) st.pop();
    }
  cout << best_stack.size() << "\n";
  while (!best_stack.empty()) {
    cout << best_stack.top() << " ";
    best_stack.pop();
  }
}

### Prompt

Develop a solution in CPP 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;
long long MAX(long long a, long long b) { return a < b ? b : a; }
long long MIN(long long a, long long b) { return a > b ? b : a; }
int gcd(int a, int b) { return a ? gcd(b % a, a) : b; }
bool is_letter_s(char a) {
  if ((a >= 'a') && (a <= 'z'))
    return true;
  else
    return false;
}
bool is_letter_b(char a) {
  if ((a >= 'A') && (a <= 'Z'))
    return true;
  else
    return false;
}
bool is_number(char a) {
  if ((a >= '0') && (a <= '9'))
    return true;
  else
    return false;
}
vector<int> prefix(string s) {
  int n = s.length();
  vector<int> v(n);
  for (int i = 1; i <= n - 1; i++) {
    int j = v[i - 1];
    while (j > 0 && s[i] != s[j]) j = v[j - 1];
    if (s[i] == s[j]) j++;
    v[i] = j;
  }
  return v;
}
int main() {
  cin.sync_with_stdio(0);
  int n;
  cin >> n;
  int a[110000];
  int b[110000];
  int num[110000];
  memset(num, 0, sizeof num);
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) {
    cin >> b[i];
    num[b[i]]++;
  }
  a[0] = 1;
  b[0] = 0;
  stack<int> st;
  stack<int> best_stack;
  for (int i = 1; i <= n; i++)
    if (a[i] == 1) {
      int x = i;
      st.push(x);
      x = b[x];
      while (a[x] == 0 && x != 0 && num[x] == 1) {
        st.push(x);
        x = b[x];
      }
      if (st.size() > best_stack.size()) best_stack = st;
      while (!st.empty()) st.pop();
    }
  cout << best_stack.size() << "\n";
  while (!best_stack.empty()) {
    cout << best_stack.top() << " ";
    best_stack.pop();
  }
}

```