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.*;
import java.util.Arrays;
import java.util.Stack;

public class Main {


    public static void main(String[] args)throws IOException {
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));


        int[] arr = new int[Integer.parseInt(br.readLine())];

        arr= Arrays.stream(br.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();

        Stack<Integer> S1 =new Stack<>();
        Stack<Integer> S2 = new Stack<>();
        S1.push(arr.length-1);
        while (!S1.isEmpty()){

            //INV: S2() contains path from nth element to some k  where  1=<k<n
            int p =S1.pop();
            S2.push(p+2);
            if(arr[p]!=1)
                S1.push(arr[p]-2);
        }
        // Implies S1 is empty
        S2.push(1);
        while (!S2.isEmpty()){

            bw.write(S2.pop()+" ");
        }
        bw.write("\n");


        br.close();
        bw.close();
    }

}
