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;
const int N = 1e6;
vector<vector<int>> g(N);
bool isDeleted[N];
vector<int> res;
void del(int s, int p) {
  res.push_back(s);
  isDeleted[s] = true;
  for (auto I : g[s]) {
    if (!isDeleted[I] && I != p) {
      del(I, s);
    }
  }
}
bool dfs(int s, int p) {
  int siz = g[s].size();
  for (auto I : g[s]) {
    if (I != p) {
      bool isDeleted = dfs(I, s);
      if (isDeleted) {
        --siz;
      }
    }
  }
  if (siz % 2 == 0) {
    del(s, p);
    return true;
  } else
    return false;
}
int main() {
  int n, x;
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d", &x);
    if (x) {
      g[i].push_back(x - 1);
      g[x - 1].push_back(i);
    }
  }
  bool ans = dfs(0, -1);
  if (ans) {
    printf("YES\n");
    for (auto I : res) {
      printf("%d\n", I + 1);
    }
  } else
    printf("NO\n");
  return 0;
}