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.math.BigInteger;
import java.util.*;
import static java.lang.Math.*;

public class SolutionA {
    private static FastScanner in = new FastScanner();
    private static PrintWriter out =
        new PrintWriter(new BufferedOutputStream(System.out));

    public static void main(String[] args) {
    
        // tests();
        solve();
        
        out.close();
    }

    static void solve() {
        int n = in.nextInt();

        int[] id = new int[n + 2];
        for (int i = 2; i <= n; i++) {
            id[i] = in.nextInt();
        }

        Deque<Integer> stack = new LinkedList<>();
        int cur = n;
        while (cur != 0) {
            stack.push(cur);
            cur = id[cur];
        }
        for (int r : stack) {
            out.printf("%d ", r);
        }
        out.println();
    }
    
    static void tests() {
        int t = in.nextInt();
        while (t-- > 0) {
            solve();
        }
    }

    private static class FastScanner {
        private BufferedReader br;
        private StringTokenizer st;
    
        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
    
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) { e.printStackTrace(); }
            }
            return st.nextToken();
        }
    
        int nextInt() { return Integer.parseInt(next()); }
    
        long nextLong() { return Long.parseLong(next()); }
    
        double nextDouble() { return Double.parseDouble(next()); }
    
        String nextLine() {
            String str = "";
            try { str = br.readLine(); } 
            catch (IOException e) { e.printStackTrace(); }
            return str;
        }
    }
}
