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.IOException;
import java.io.InputStreamReader;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.*;
import java.text.NumberFormat;
//import java.util.Arrays;
import java.util.regex.Matcher;
import java.util.regex.Pattern;
import java.util.regex.PatternSyntaxException;

public class Main {

    public static void main(String[] args) throws IOException {
        Scanner input = new Scanner(System.in);
        int n=input.nextInt();
        int[]a=new int[n+1];
        int[]res=new int[n+1];
        for (int i = 2; i < n+1; i++) {
            a[i]=input.nextInt();
        }
        int temp=n;
       
      
        int i=0;
        while(temp!=0){
            
            res[i]=temp;
            temp=a[temp];
            i++;
        }
       
        for (int j = i; j >=0; j--) {
            if(res[j]!=0){
                System.out.print(res[j]);
                System.out.print(" ");
            }
        }
    }
}
