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.

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 2;
vector<int> t[N];
int fa[N], sz[N];
void dfs1(int u) {
  sz[u] = 1;
  for (auto v : t[u]) {
    dfs1(v);
    sz[u] += sz[v];
  }
}
void dfs(int u) {
  for (auto v : t[u])
    if (sz[v] % 2 == 0) dfs(v);
  printf("%d\n", u);
  for (auto v : t[u])
    if (sz[v] & 1) dfs(v);
}
int main() {
  int n, root = -1;
  scanf("%d", &n);
  if (n % 2 == 0) return puts("NO"), 0;
  puts("YES");
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &fa[i]);
    if (fa[i])
      t[fa[i]].push_back(i);
    else
      root = i;
  }
  dfs1(root);
  dfs(root);
  return 0;
}