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.util.*;
import java.io.*;
import java.lang.*;

public class Solution {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter out = new PrintWriter(System.out);
    StringTokenizer st = new StringTokenizer("");

    String next() {
        if (!st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {

            }
        }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    public static void main(String[] args) {
        new Solution().solve();
    }

    void solve() {
        int t = 1;
        // t = nextInt();
        for (int tt = 0; tt < t; tt++) {
            int n = nextInt();
            int arr[] = new int[n + 1];
            arr[1] = 1;
            for (int i = 2; i < n + 1; i++)
                arr[i] = nextInt();
            int curr = n;
            List<Integer> res = new ArrayList<>();
            // out.println(Arrays.toString(arr));
            while (curr != 1) {
                res.add(curr);
                curr = arr[curr];
                // out.println(curr);
                // break;
            }
            res.add(1);
            for (int i = res.size() - 1; i >= 0; i--) {
                out.print(res.get(i) + " ");
            }

        }
        out.close();
    }
}
