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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;

public class A {
	
	static List<List<Integer>> adj = new ArrayList<>();
	
	static int[] par;
	
	public static void main(String[] args) throws IOException {
		
        PrintWriter out = new PrintWriter(System.out);
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        
        int n = Integer.parseInt(in.readLine());
        par = new int[n];
        
        for(int i=0; i<n; i++) {
        	adj.add(new ArrayList<>());
        	par[i] = -1;
        }
        
        String[] line = in.readLine().split("\\s+");
        for(int i=0; i<n-1; i++) { 
        	int to = Integer.parseInt(line[i]) - 1;
        	adj.get(i+1).add(to);
        	adj.get(to).add(i+1);
        }
        
        
        par[0] = -100;
        dfs(0);
        
        List<Integer> ans = new ArrayList<>();
        
        int i = n-1;
        while(i != -100) {
        	ans.add((i+1));
        	i = par[i];
        }
        
        for(int j=ans.size()-1; j>=0; j--) {
        	System.out.print(ans.get(j) + " ");
        }
        
        
        out.close();
	
	}

	private static void dfs(int i) {
		
		for(int j : adj.get(i)) {
			if(par[j] == -1) {
				par[j] = i;
				dfs(j);
			}
		}
		
	}



}
