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 MAXN = 200005;
const int MOD = 1e9 + 7;
const int INF = 1e9 + 7;
vector<int> mapp[MAXN];
set<pair<int, int> > st;
int N, degree[MAXN], height[MAXN], mk[MAXN];
void getHeight(int node, int father) {
  for (int child : mapp[node]) {
    if (child == father) continue;
    height[child] = height[node] + 1;
    getHeight(child, node);
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  ;
  while (cin >> N) {
    for (int i = 1; i <= N; ++i) mapp[i].clear();
    int tmpn;
    int rt;
    for (int i = 1; i <= N; ++i) {
      cin >> tmpn;
      if (tmpn == 0) {
        rt = i;
        continue;
      }
      mapp[i].push_back(tmpn);
      mapp[tmpn].push_back(i);
      degree[tmpn]++;
      degree[i]++;
    }
    height[rt] = 0;
    getHeight(rt, 0);
    st.clear();
    for (int i = 1; i <= N; ++i)
      if (degree[i] % 2 == 0) st.emplace(height[i], i);
    vector<int> ans;
    ans.clear();
    memset(mk, 0, sizeof(mk));
    while (!st.empty()) {
      pair<int, int> tmp = *(prev(st.end()));
      st.erase(prev(st.end()));
      mk[tmp.second] = 1;
      ans.push_back(tmp.second);
      for (int node : mapp[tmp.second]) {
        if (mk[node]) continue;
        degree[node]--;
        if (degree[node] % 2 == 0)
          st.insert(make_pair(height[node], node));
        else
          st.erase(st.find(make_pair(height[node], node)));
      }
    }
    if (ans.size() == (unsigned)N) {
      cout << "YES" << endl;
      for (int tmp : ans) cout << tmp << endl;
    } else
      cout << "NO" << endl;
  }
  return 0;
}