#include <bits/stdc++.h>
using namespace std;
long long n, a, b, k;
const int ms = 2e5 + 17;
const int mod = 1e9 + 9;
vector<int> v[ms];
vector<int> answer;
bool killed[ms];
void kill(int x) {
  killed[x] = true;
  answer.push_back(x);
  for (int i = 0; i < v[x].size(); ++i) {
    int to = v[x][i];
    if (!killed[to]) kill(to);
  }
}
void dfs(int x, bool isRoot) {
  int deg = isRoot ? 0 : 1;
  for (int i = 0; i < v[x].size(); ++i) {
    int to = v[x][i];
    dfs(to, false);
    if (!killed[to]) ++deg;
  }
  if (deg % 2 == 0) kill(x);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, root;
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    int x;
    cin >> x;
    if (!x)
      root = i;
    else
      v[x].push_back(i);
  }
  dfs(root, 1);
  if (answer.size() < n)
    cout << "NO\n";
  else {
    cout << "YES\n";
    for (int i = 0; i < n; ++i) cout << answer[i] << '\n';
  }
}

### Prompt

Your challenge is to write a cpp solution to the following 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>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long n, a, b, k;
const int ms = 2e5 + 17;
const int mod = 1e9 + 9;
vector<int> v[ms];
vector<int> answer;
bool killed[ms];
void kill(int x) {
  killed[x] = true;
  answer.push_back(x);
  for (int i = 0; i < v[x].size(); ++i) {
    int to = v[x][i];
    if (!killed[to]) kill(to);
  }
}
void dfs(int x, bool isRoot) {
  int deg = isRoot ? 0 : 1;
  for (int i = 0; i < v[x].size(); ++i) {
    int to = v[x][i];
    dfs(to, false);
    if (!killed[to]) ++deg;
  }
  if (deg % 2 == 0) kill(x);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, root;
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    int x;
    cin >> x;
    if (!x)
      root = i;
    else
      v[x].push_back(i);
  }
  dfs(root, 1);
  if (answer.size() < n)
    cout << "NO\n";
  else {
    cout << "YES\n";
    for (int i = 0; i < n; ++i) cout << answer[i] << '\n';
  }
}

```