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.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Set;

public class DestrutionOfTree {
	private static int[] subtreeSizes;
	private static ArrayList<Set<Integer>> children;

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		br.readLine();
		int[] parents = Arrays.stream(br.readLine().split(" ")).mapToInt(x -> Integer.parseInt(x) - 1).toArray();
		if (parents.length % 2 == 0) {
			System.out.println("NO");
			return;
		} else {
			System.out.println("YES");
		}

		children = new ArrayList<>();
		for (int i = 0; i < parents.length; i++) {
			children.add(new HashSet<Integer>());
		}
		int root = -1;
		for (int i = 0; i < parents.length; i++) {
			if (parents[i] != -1) {
				children.get(parents[i]).add(i);
			} else {
				root = i;
			}
		}

		subtreeSizes = new int[parents.length];
		calcSubtreeSizes(root);

		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
		search(root,out);
		out.flush();
	}

	private static void calcSubtreeSizes(int root) {
		int size = 1;
		for (int child : children.get(root)) {
			calcSubtreeSizes(child);
			size += subtreeSizes[child];
		}
		subtreeSizes[root] = size;
	}

	private static void search(int start,BufferedWriter out) throws IOException{
		Iterator<Integer> it = children.get(start).iterator();
		while (it.hasNext()) {
			int child = it.next();
			if (subtreeSizes[child] % 2 == 0) {
				search(child,out);
				it.remove();
			}
		}
		out.write((1 + start) + System.lineSeparator());
		for (int child : children.get(start)) {
			search(child,out);
		}
		children.get(start).clear();
	}
}