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.List;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

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

    static class TaskB {
        List<Integer> stage0 = new ArrayList<>();
        List<Integer> stage1 = new ArrayList<>();

        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            if (n % 2 == 0) {
                out.println("NO");
                return;
            }
            out.println("YES");

            List<Integer>[] adj = new List[n];
            for (int i = 0; i < n; i++) {
                adj[i] = new ArrayList<>();
            }

            for (int i = 0; i < n; i++) {
                int p = in.nextInt() - 1;
                if (p >= 0) {
                    adj[p].add(i);
                    adj[i].add(p);
                }
            }

            dfs(0, -1, adj);
            List<Integer> ans = new ArrayList<>();
            ans.addAll(stage0);
            Collections.reverse(stage1);
            ans.addAll(stage1);
            for (int v : ans) {
                out.println(v + 1);
            }
        }

        private int dfs(int v, int p, List<Integer>[] adj) {
            int parity = 1;
            for (int u : adj[v]) {
                if (u == p) {
                    continue;
                }
                parity ^= dfs(u, v, adj);
            }
            if (parity == 0) {
                stage0.add(v);
            } else {
                stage1.add(v);
            }
            return parity;
        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}