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 JAVA):

Solution:

import java.util.Arrays;

public class Main {

	private static void solve() {
		int n = ni();
		int[] p = Arrays.stream(na(n)).map(v -> v- 1).toArray();
		
		if (n % 2 == 0) {
			System.out.println("NO");
			return;
		}
		g = parentToG(p);
		dfs(0, -1);
		
		int[][] h = packD(n, from, to, ptr);
		int[] ret = sortTopologically(h);
		
		if (ret == null) {
			out.println("NO");
		} else {
			out.println("YES");
			for (int v : ret) {
				out.println(v + 1);
			}
		}
	}

	public static int[][] packD(int n, int[] from, int[] to, int sup)
	{
		int[][] g = new int[n][];
		int[] p = new int[n];
		for(int i = 0;i < sup;i++)p[from[i]]++;
		for(int i = 0;i < n;i++)g[i] = new int[p[i]];
		for(int i = 0;i < sup;i++){
			g[from[i]][--p[from[i]]] = to[i];
		}
		return g;
	}
	
	
	static int[] from = new int[300000];
	static int[] to = new int[300000];
	static int ptr = 0;
	static int[][] g;
	private static int dfs(int now, int pre) {
		int num = 1;
		for (int v : g[now]) {
			if (pre != v) {
				num += dfs(v, now);
			}
		}
		
		if (pre >= 0) {
			if (num % 2 == 1) {
				from[ptr] = pre;
				to[ptr] = now;
				ptr ++;
			} else {
				from[ptr] = now;
				to[ptr] = pre;
				ptr ++;
			}
		}
		return num;
	}

	public static int[] sortTopologically(int[][] g)
	{
		int n = g.length;
		int[] ec = new int[n];
		for(int i = 0;i < n;i++){
			for(int to : g[i])ec[to]++;
		}
		int[] ret = new int[n];
		int q = 0;
		
		// sources
		for(int i = 0;i < n;i++){
			if(ec[i] == 0)ret[q++] = i;
		}
		
		for(int p = 0;p < q;p++){
			for(int to : g[ret[p]]){
				if(--ec[to] == 0)ret[q++] = to;
			}
		}
		// loop
		for(int i = 0;i < n;i++){
			if(ec[i] > 0)return null;
		}
		return ret;
	}
	
	public static int[][] parentToG(int[] par)
	{
		int n = par.length;
		int[] ct = new int[n];
		for(int i = 0;i < n;i++){
			if(par[i] >= 0){
				ct[i]++;
				ct[par[i]]++;
			}
		}
		int[][] g = new int[n][];
		for(int i = 0;i < n;i++){
			g[i] = new int[ct[i]];
		}
		for(int i = 0;i < n;i++){
			if(par[i] >= 0){
				g[par[i]][--ct[par[i]]] = i;
				g[i][--ct[i]] = par[i];
			}
		}
		return g;
	}
	
	public static void main(String[] args) {
		new Thread(null, new Runnable() {
			@Override
			public void run() {
				long start = System.currentTimeMillis();
				String debug = args.length > 0 ? args[0] : null;
				if (debug != null) {
					try {
						is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
					} catch (Exception e) {
						throw new RuntimeException(e);
					}
				}
				reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
				solve();
				out.flush();
				tr((System.currentTimeMillis() - start) + "ms");
			}
		}, "", 64000000).start();
	}

	private static java.io.InputStream is = System.in;
	private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
	private static java.util.StringTokenizer tokenizer = null;
	private static java.io.BufferedReader reader;

	public static String next() {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new java.util.StringTokenizer(reader.readLine());
			} catch (Exception e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}

	private static double nd() {
		return Double.parseDouble(next());
	}

	private static long nl() {
		return Long.parseLong(next());
	}

	private static int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private static char[] ns() {
		return next().toCharArray();
	}

	private static long[] nal(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nl();
		return a;
	}

	private static int[][] ntable(int n, int m) {
		int[][] table = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				table[i][j] = ni();
			}
		}
		return table;
	}

	private static int[][] nlist(int n, int m) {
		int[][] table = new int[m][n];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				table[j][i] = ni();
			}
		}
		return table;
	}

	private static int ni() {
		return Integer.parseInt(next());
	}

	private static void tr(Object... o) {
		if (is != System.in)
			System.out.println(java.util.Arrays.deepToString(o));
	}
}