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 
//package Codeforces;

import java.util.Scanner;

/**
 * Bmail Computer Network
 * https://codeforces.com/problemset/problem/1057/A
 *
 * @author codedsun
 */
public class Problem1057A {
    static class Node {
        int element;
        Node parent;

        public Node(int element) {
            this.element = element;
            this.parent = null;
        }

        public int getElement() {
            return element;
        }

        public void setElement(int element) {
            this.element = element;
        }

        public Node getParent() {
            return parent;
        }

        public void setParent(Node parent) {
            this.parent = parent;
        }
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] routersPosition = new int[n];
        Node[] nodes = new Node[n];
        Node root = new Node(1);
        nodes[0] = root;
        String path = ""+root.element;
        Node temp;
        for (int i = 1; i < n; i++) {
            routersPosition[i] = sc.nextInt();
            nodes[i] = new Node(i+1);
            (nodes[i]).parent = nodes[routersPosition[i]-1];
        }

        temp = nodes[n-1];
        int a[] = new int[n];
        int i=0;
        while(temp!= null){
            a[i] = temp.element;
            temp= temp.parent;
            i++;
        }
        for(int k=i-1; k>=0;k--){
            if(k==0){
                System.out.print(a[k]);
            }else {
                System.out.print(a[k] + " ");
            }
        }
    }
}
