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>
#pragma comment(linker, "/STACK:1000000000")
using namespace std;
const int maxn = (int)2e5 + 10;
int dp[maxn][2];
vector<int> ed[maxn];
void del(int v, int p) {
  for (int i = 0; i < (int)ed[v].size(); i++) {
    int u = ed[v][i];
    if (u == p) {
      swap(ed[v][i], ed[v].back());
      ed[v].pop_back();
      i--;
      continue;
    } else {
      del(u, v);
    }
  }
}
int st[maxn];
int go(int v, int x) {
  if (dp[v][x] != -1) {
    return dp[v][x];
  }
  int a = 0, b = 0, c = 0;
  for (int i = 0; i < (int)ed[v].size(); i++) {
    int u = ed[v][i];
    if (go(u, 0) && go(u, 1)) {
      b++;
    } else if (go(u, 0) && !go(u, 1)) {
      a++;
    } else if (!go(u, 0) && go(u, 1)) {
      c++;
    } else {
      return dp[v][x] = 0;
    }
  }
  int cnt = st[v] - x;
  cnt -= a;
  if (b == 0 && (cnt & 1)) {
    return dp[v][x] = 0;
  }
  return dp[v][x] = 1;
}
void write(int v, int x) {
  vector<int> a, b, c;
  for (int i = 0; i < (int)ed[v].size(); i++) {
    int u = ed[v][i];
    if (go(u, 0) && go(u, 1)) {
      b.push_back(u);
    } else if (go(u, 0) && !go(u, 1)) {
      a.push_back(u);
    } else if (!go(u, 0) && go(u, 1)) {
      c.push_back(u);
    } else {
      throw 1;
    }
  }
  for (int i = 0; i < (int)a.size(); i++) {
    write(a[i], 0);
  }
  int cnt = st[v] - x;
  cnt -= (int)a.size();
  if (cnt & 1) {
    if (b.empty()) {
      throw 1;
    }
    write(b.back(), 0);
    b.pop_back();
  }
  printf("%d\n", v);
  for (int i = 0; i < (int)c.size(); i++) {
    write(c[i], 1);
  }
  for (int i = 0; i < (int)b.size(); i++) {
    write(b[i], 1);
  }
}
int main() {
  memset(dp, -1, sizeof dp);
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    int x;
    scanf("%d", &x);
    if (x != 0) {
      ed[x].push_back(i);
      ed[i].push_back(x);
      st[i]++;
      st[x]++;
    }
  }
  del(1, -1);
  if (go(1, 0) == 0) {
    cout << "NO" << endl;
  } else {
    cout << "YES" << endl;
    write(1, 0);
  }
}