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> g[210000];
int n, x, f[210000], size[210000];
void dfs(int x, int fa) {
  f[x] = fa;
  size[x] = 1;
  for (int i = 0; i < g[x].size(); i++) {
    int t = g[x][i];
    if (t != fa) {
      dfs(t, x);
      size[x] += size[t];
    }
  }
}
void find(int x) {
  for (int i = 0; i < g[x].size(); i++) {
    int t = g[x][i];
    if (t != f[x])
      if (size[t] % 2 == 0) find(t);
  }
  cout << x << endl;
  for (int i = 0; i < g[x].size(); i++) {
    int t = g[x][i];
    if (t != f[x])
      if (size[t] % 2 == 1) find(t);
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &x);
    if (x) {
      g[x].push_back(i);
      g[i].push_back(x);
    }
  }
  if (n % 2 == 1) {
    cout << "YES" << endl;
    dfs(1, 0);
    find(1);
  } else
    cout << "NO";
  return 0;
}