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 JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;
import java.util.Collections;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author WLZ
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        public int n;
        public ArrayList<Integer>[] AdjList;
        public ArrayList<Integer> ans;
        public int[] degree;

        void dfs(int u) {
            for (int v : AdjList[u]) {
                dfs(v);
            }
            ans.add(u);
            return;
        }

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            n = in.nextInt();
            AdjList = new ArrayList[n + 1];
            for (int i = 0; i <= n; i++) AdjList[i] = new ArrayList<>();
            int root = 0;
            degree = new int[n + 1];
            int[] p = new int[n + 1];
            for (int i = 0; i <= n; i++) degree[i] = 0;
            for (int i = 1; i <= n; i++) {
                int pi = in.nextInt();
                p[i] = pi;
                degree[pi]++;
                if (pi != 0) {
                    degree[i]++;
                } else {
                    root = i;
                }
                AdjList[pi].add(i);
            }


            ans = new ArrayList<>();
            dfs(root);
            ArrayList<Integer> e = new ArrayList<>();
            ArrayList<Integer> res = new ArrayList<>();
            for (int i : ans) {
                if (degree[i] % 2 == 1) {
                    if (i == root) {
                        out.println("NO");
                        return;
                    }
                    e.add(i);
                } else {
                    res.add(i);
                    degree[p[i]]--;
                }
            }
            Collections.reverse(e);
            for (int i : e) {
                res.add(i);
            }
            out.println("YES");
            for (int u : res) {
                out.println(u);
            }
        }

    }
}