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 maxN = 2e5 + 9;
vector<int> graph[maxN];
bool removed[maxN] = {0};
vector<int> removedNodes;
int par[maxN];
int deg[maxN];
void addEdge(int x, int y) {
  graph[x].push_back(y);
  graph[y].push_back(x);
}
void removeVertex(int node) {
  removed[node] = true;
  removedNodes.push_back(node);
  for (int v : graph[node]) {
    if (v == par[node]) continue;
    if (removed[v]) continue;
    removeVertex(v);
  }
  int parent = par[node];
  if (parent != -1) deg[parent]--;
}
void dfs(int node, int parent) {
  par[node] = parent;
  deg[node] = graph[node].size();
  for (int v : graph[node]) {
    if (v == parent) continue;
    dfs(v, node);
  }
  if (deg[node] % 2 == 0) {
    removeVertex(node);
  }
}
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int node;
    cin >> node;
    node--;
    if (node != -1) addEdge(node, i);
  }
  dfs(0, -1);
  if (removedNodes.size() != n)
    cout << "NO";
  else {
    cout << "YES\n";
    for (int v : removedNodes) cout << v + 1 << "\n";
  }
}