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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Div1_475B {

	static ArrayList<Integer>[] chldn;

	static boolean[] marked;
	static boolean[] rmvd;

	static ArrayList<Integer> sol = new ArrayList<>();

	public static void main(String[] args) throws IOException {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter printer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		int nV = Integer.parseInt(reader.readLine());
		chldn = new ArrayList[nV];
		for (int i = 0; i < nV; i++) {
			chldn[i] = new ArrayList<>();
		}

		int root = -1;

		StringTokenizer inputData = new StringTokenizer(reader.readLine());
		for (int i = 0; i < nV; i++) {
			int par = Integer.parseInt(inputData.nextToken()) - 1;
			if (par == -1) {
				root = i;
			} else {
				chldn[par].add(i);
			}
		}
		marked = new boolean[nV];
		for (int i = 0; i < nV; i++) {
			if (i == root) {
				marked[i] = (chldn[i].size() & 1) == 0;
			} else {
				marked[i] = (chldn[i].size() & 1) == 1;
			}
		}

		rmvd = new boolean[nV];
		dfs(root);

		if (rmvd[root]) {
			printer.println("YES");
			for (int i : sol) {
				printer.println(i + 1);
			}
		} else {
			printer.println("NO");
		}
		printer.close();
	}

	static void dfs(int cV) {
		for (int chld : chldn[cV]) {
			if (!rmvd[chld]) {
				dfs(chld);
				if (rmvd[chld]) {
					marked[cV] = !marked[cV];
				}
			}
		}
		if (marked[cV]) {
			rmvAll(cV);
		}
	}

	static void rmvAll(int cV) {
		sol.add(cV);
		rmvd[cV] = true;
		for (int chld : chldn[cV]) {
			if (!rmvd[chld]) {
				rmvAll(chld);
			}
		}
	}
}