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.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.StringTokenizer;

public class BMail {

    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(reader.readLine());
        StringTokenizer stringTokenizer = new StringTokenizer(reader.readLine());
        List<Integer> prev = new ArrayList<>();
        for (int i = 0; i < n - 1; i++) {
            prev.add(Integer.parseInt(stringTokenizer.nextToken()));
        }
        List<Integer> res = new ArrayList<>();
        int cur = n - 2;
        res.add(n);
        while (prev.get(cur) != 1) {
            res.add(prev.get(cur));
            cur = prev.get(cur) - 2;
        }
        res.add(1);
        Collections.reverse(res);
        for (int i = 0; i < res.size(); i++) {
            System.out.print(res.get(i)+" ");
        }
    }
}
