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;
int addnum, vel[410000], ne[410000], head[410000];
int addedgenum, vet[410000], nex[410000], last[410000];
int siz[210000], fa[210000], q[210000], du[210000];
int n, he, ta;
void add(int u, int v) {
  addnum++;
  vel[addnum] = v;
  ne[addnum] = head[u];
  head[u] = addnum;
}
void addedge(int u, int v) {
  du[v]++;
  addedgenum++, vet[addedgenum] = v;
  nex[addedgenum] = last[u];
  last[u] = addedgenum;
}
void getsize(int x, int fa) {
  siz[x] = 1;
  for (int e = head[x]; e; e = ne[e]) {
    int v = vel[e];
    if (v == fa) continue;
    getsize(v, x);
    siz[x] += siz[v];
  }
}
int main() {
  scanf("%d", &n);
  if (n % 2) {
    printf("YES\n");
    for (int i = 1; i <= n; i++) {
      scanf("%d", &fa[i]);
      if (fa[i] != 0) add(fa[i], i), add(i, fa[i]);
    }
    for (int i = 1; i <= n; i++)
      if (!fa[i]) getsize(i, -1);
    for (int i = 1; i <= n; i++)
      if (fa[i] != 0) {
        if (siz[i] % 2)
          addedge(fa[i], i);
        else
          addedge(i, fa[i]);
      }
    for (int i = 1; i <= n; i++)
      if (!du[i]) q[++ta] = i;
    while (he < ta) {
      int u = q[++he];
      for (int e = last[u]; e; e = nex[e]) {
        int v = vet[e];
        du[v]--;
        if (!du[v]) q[++ta] = v;
      }
    }
    for (int i = 1; i <= n; i++) printf("%d\n", q[i]);
  } else
    printf("NO\n");
}