Once upon a time there was only one router in the well-known company Bmail. Years went by and over time new routers were purchased. Every time they bought a new router, they connected it to one of the routers bought before it. You are given the values p_i — the index of the router to which the i-th router was connected after being purchased (p_i < i).

There are n routers in Boogle in total now. Print the sequence of routers on the path from the first to the n-th router.

Input

The first line contains integer number n (2 ≤ n ≤ 200000) — the number of the routers. The following line contains n-1 integers p_2, p_3, ..., p_n (1 ≤ p_i < i), where p_i is equal to index of the router to which the i-th was connected after purchase.

Output

Print the path from the 1-st to the n-th router. It starts with 1 and ends with n. All the elements in the path should be distinct.

Examples

Input

8
1 1 2 2 3 2 5


Output

1 2 5 8 

Input

6
1 2 3 4 5


Output

1 2 3 4 5 6 

Input

7
1 1 2 3 4 3


Output

1 3 7 

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;

public class Bmail_2 {
	static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    
    public static void main(String[] args) throws IOException {
    	int nodes = Integer.parseInt(br.readLine());
    	String data_edge[] = br.readLine().split(" ");
    	int posiciones[] = new int[nodes-1];
    	for (int I = 0; I < data_edge.length; I++) {
			posiciones[I] = Integer.parseInt(data_edge[I]);
		}
    	
    	StringBuilder out = new StringBuilder();
    	out.append(String.valueOf(nodes)+" ");
    	int pos = nodes;
    	while(pos > 1) {
    		pos = posiciones[pos-2];
    		out.append(String.valueOf(pos)+" ");
    		if(pos == 1) {
    			break;
    		}
    	}
    	String salida[] = out.toString().split(" ");
    	out = new StringBuilder();
    	
    	for (int i = salida.length-1 ; i >= 0; i--) {
			out.append(salida[i]+" ");
		}
     	
    	bw.write(out.toString());
    	bw.close();
    	br.close();
    }
}