#include <bits/stdc++.h>
using namespace std;
const int inf = ~0U >> 1, maxn = 100000 + 10;
int n, ans = 0;
int back[maxn], d[maxn], now[maxn], trace[maxn];
bool style[maxn], v[maxn];
void setIO(string name) {}
long long gI() {
  char c = getchar();
  while ((c < '0' || c > '9') && c != '-') c = getchar();
  long long p = 0, flag = 1;
  if (c == '-') flag = -1, c = getchar();
  while (c >= '0' && c <= '9') p = p * 10 + c - '0', c = getchar();
  return p * flag;
}
template <class T>
void debug(const T &a, const int &n) {
  for (int i = 0; i < n; ++i) cout << a[i] << " ";
  puts("");
}
int Find(int x, bool first) {
  if (x == -1 || d[x] > 1 || (!first && style[x])) return 0;
  int t = Find(back[x], 0);
  now[t] = x;
  return t + 1;
}
int main() {
  setIO("test");
  memset(d, 0, sizeof(d));
  n = gI();
  for (int i = 0; i < n; ++i) style[i] = gI();
  for (int i = 0; i < n; ++i) {
    back[i] = gI() - 1;
    if (back[i] != -1) ++d[back[i]];
  }
  for (int i = 0; i < n; ++i)
    if (style[i]) {
      int t = Find(i, 1);
      if (t > ans) {
        ans = t;
        for (int j = 0; j < ans; ++j) trace[j] = now[j] + 1;
      }
    }
  printf("%d\n", ans);
  for (int i = 0; i < ans; ++i) {
    printf("%d", trace[i]);
    (i == ans - 1) ? puts("") : printf(" ");
  }
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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 int inf = ~0U >> 1, maxn = 100000 + 10;
int n, ans = 0;
int back[maxn], d[maxn], now[maxn], trace[maxn];
bool style[maxn], v[maxn];
void setIO(string name) {}
long long gI() {
  char c = getchar();
  while ((c < '0' || c > '9') && c != '-') c = getchar();
  long long p = 0, flag = 1;
  if (c == '-') flag = -1, c = getchar();
  while (c >= '0' && c <= '9') p = p * 10 + c - '0', c = getchar();
  return p * flag;
}
template <class T>
void debug(const T &a, const int &n) {
  for (int i = 0; i < n; ++i) cout << a[i] << " ";
  puts("");
}
int Find(int x, bool first) {
  if (x == -1 || d[x] > 1 || (!first && style[x])) return 0;
  int t = Find(back[x], 0);
  now[t] = x;
  return t + 1;
}
int main() {
  setIO("test");
  memset(d, 0, sizeof(d));
  n = gI();
  for (int i = 0; i < n; ++i) style[i] = gI();
  for (int i = 0; i < n; ++i) {
    back[i] = gI() - 1;
    if (back[i] != -1) ++d[back[i]];
  }
  for (int i = 0; i < n; ++i)
    if (style[i]) {
      int t = Find(i, 1);
      if (t > ans) {
        ans = t;
        for (int j = 0; j < ans; ++j) trace[j] = now[j] + 1;
      }
    }
  printf("%d\n", ans);
  for (int i = 0; i < ans; ++i) {
    printf("%d", trace[i]);
    (i == ans - 1) ? puts("") : printf(" ");
  }
  return 0;
}

```