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.HashMap;
import java.util.Map;

public class DfsType_1057A {

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	    int n = Integer.parseInt(br.readLine());
	    String[] vert = br.readLine().split(" ");
	    Map<Integer, Integer> map = new HashMap<>();
	    map.put(1, null);
	    for(int i=1;i<n;i++){
	        int key = Integer.parseInt(vert[i-1]);
	        map.put(i+1, key);
	    }
//	    for(Integer key=n;key!=null;key =map.get(key))
//	    	System.out.print(key+" ");
	    recursive(map, n);

	}
	private static void recursive(Map<Integer, Integer> map, Integer key) {
		if(key==null)
			return;
		recursive(map, map.get(key));
		System.out.print(key+" ");
	}

}