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 B {

	static StringTokenizer st;
	static BufferedReader br;
	static PrintWriter pw;
	static ArrayList<Integer> []ages;
	static int[]size;
	static ArrayList<Integer> ans;
	public static void main(String[] args) throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		int n = nextInt();
		ages = new ArrayList[n+1];
		for (int i = 1; i <= n; i++) {
			ages[i] = new ArrayList<>();
		}
		size = new int[n+1];
		for (int i = 1; i <= n; i++) {
			int pi = nextInt();
			if (pi != 0) {
				ages[pi].add(i);
				ages[i].add(pi);
				size[pi]++;
				size[i]++;
			}
		}
		ans = new ArrayList<>();
		int root = 1;
		for (int i = 2; i <= n; i++) {
			if (size[i] % 2==0)
				root = i;
		}
		dfs(root, 0);
		for (int i = 1; i <= n; i++) {
			if (size[i] > 0) {
				System.out.println("NO");
				return;
			}
		}
		boolean[]used = new boolean[n+1];
		for (int i : ans) {
			used[i] = true;
		}
		for (int i = 1; i <= n; i++) {
			if (!used[i])
				ans.add(i);
		}
		pw.println("YES");
		for (int i : ans) {
			pw.println(i);
		}
		
		pw.close();
	}
	private static void dfs(int v, int p) {
		for (int to : ages[v]) {
			if (to==p)
				continue;
			dfs(to, v);
		}
		if (size[v] % 2==0) {
			dfs2(v, p);
		}
	}
	private static void dfs2(int v, int p) {
		size[v] = 0;
		ans.add(v);
		for (int to : ages[v]) {
			if (size[to]==0)
				continue;
			size[to]--;
		}
		for (int to : ages[v]) {
			if (to==p || size[to]==0)
				continue;
			if (size[to]%2==0) {
				dfs2(to, v);
			}
		}
	}
	private static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}
	private static long nextLong() throws IOException {
		return Long.parseLong(next());
	}
	private static double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}
	private static String next() throws IOException {
		while (st==null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}
}