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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class B475 {
	static int[] in, par, deg;
	static boolean[] dead;
	static ArrayDeque<Integer> sol;
	static ArrayList<Integer>[] adj;
	public static void main(String[] args) {
		FS scan = new FS(System.in);
		int N = scan.nextInt();
		in = new int[N];
		par = new int[N];
		deg = new int[N];
		dead = new boolean[N];
		
		adj = new ArrayList[N];
		for(int i=0;i<N;i++)adj[i] = new ArrayList<>();
		
		for(int i=0;i<N;i++) {
			par[i] = scan.nextInt()-1;
			if(par[i]!=-1) {
				adj[par[i]].add(i);
				in[par[i]]++;
				deg[par[i]]++;
				deg[i]++;
			}
		}
		
		ArrayDeque<Integer> q = new ArrayDeque<>();
		sol = new ArrayDeque<>();
		for(int i=0;i<N;i++)if(in[i]==0)q.add(i);
		while(!q.isEmpty()) {
			int node = q.poll();
			
			if(par[node]!=-1) {
				in[par[node]]--;
				if(in[par[node]]==0)
					q.add(par[node]);
			}
			
			if(deg[node]%2==1)continue;
			
			sol.add(node);
			dead[node] = true;
			deg[node] = 0;
			for(int i : adj[node])
				deg[i]--;
			if(par[node]!=-1)deg[par[node]]--;
			
			dfs(node);
			
		}
		
		if(sol.size()!=N) {
			System.out.println("NO");
		}else {
			PrintWriter out = new PrintWriter(System.out);
			out.println("YES");
			for(int i : sol) {
				out.println(i+1);
			}
			out.close();
		}
	}
	
	private static void dfs(int node) {
		
		for(int i : adj[node]) {
			if(dead[i])continue;
			if(deg[i]%2 == 0) {
				sol.add(i);
				dead[i] = true;
				deg[i] = 0;
				for(int j : adj[i])deg[j]--;
				dfs(i);
			}
		}
	}

	private static class FS {
		BufferedReader br;
		StringTokenizer st;
		public FS(InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}
		String next(){
			while(st==null||!st.hasMoreElements()){
				try{st = new StringTokenizer(br.readLine());}
				catch(IOException e){e.printStackTrace();}
			}
			return st.nextToken();
		}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong() {return Long.parseLong(next());}
		double nextDouble() { return Double.parseDouble(next());}
	}
}