Problem: You are given a tree (a graph with n vertices and n - 1 edges in which it's possible to reach any vertex from any other vertex using only its edges).

A vertex can be destroyed if this vertex has even degree. If you destroy a vertex, all edges connected to it are also deleted.

Destroy all vertices in the given tree or determine that it is impossible.

Input

The first line contains integer n (1 ≤ n ≤ 2·105) — number of vertices in a tree.

The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ n). If pi ≠ 0 there is an edge between vertices i and pi. It is guaranteed that the given graph is a tree.

Output

If it's possible to destroy all vertices, print "YES" (without quotes), otherwise print "NO" (without quotes).

If it's possible to destroy all vertices, in the next n lines print the indices of the vertices in order you destroy them. If there are multiple correct answers, print any.

Examples

Input

5
0 1 2 1 2


Output

YES
1
2
3
5
4


Input

4
0 1 2 3


Output

NO

Note

In the first example at first you have to remove the vertex with index 1 (after that, the edges (1, 2) and (1, 4) are removed), then the vertex with index 2 (and edges (2, 3) and (2, 5) are removed). After that there are no edges in the tree, so you can remove remaining vertices in any order.

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Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
vector<int> tree[200100];
bool vis[200100];
int size[200100];
int dfs_size(int u) {
  vis[u] = 1;
  size[u] = 1;
  for (auto i = tree[u].begin(); i != tree[u].end(); i++) {
    int v = *i;
    if (!vis[v]) {
      size[u] += dfs_size(v);
    }
  }
  return size[u];
}
void dfs(int u) {
  vis[u] = 1;
  for (auto i = tree[u].begin(); i != tree[u].end(); i++) {
    int v = *i;
    if (!vis[v] && (size[v] % 2) == 0) {
      dfs(v);
    }
  }
  printf("%d ", u);
  for (auto i = tree[u].begin(); i != tree[u].end(); i++) {
    int v = *i;
    if (!vis[v] && (size[v] % 2) == 1) {
      dfs(v);
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, i, j;
  int root;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> j;
    if (j != 0) {
      tree[j].push_back(i);
      tree[i].push_back(j);
    } else
      root = i;
  }
  if (n % 2 == 0) {
    cout << "NO" << endl;
  } else {
    cout << "YES" << endl;
    dfs_size(root);
    for (i = 0; i <= n + 1; i++) vis[i] = 0;
    dfs(root);
  }
  return 0;
}