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.io.PrintWriter;
import java.sql.Array;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {
    static BufferedReader br;
    static StringTokenizer st;

    public static String nextToken() {
        try {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
            }
        } catch (IOException e) {
            e.printStackTrace();
        }
        return st.nextToken();
    }

    static int nextInt() {
        return Integer.parseInt(nextToken());
    }

    static long nextLong() {
        return Long.parseLong(nextToken());
    }

    static Double nextDouble() {
        return Double.parseDouble(nextToken());
    }

    static char nextChar() throws IOException {
        return (char) br.read();
    }

    static String nextString() throws IOException {
        return br.readLine();
    }

    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        int n = nextInt();
        int a[] = new int[n];
        for (int i = 1; i < n; i++) {
            a[i] = nextInt();
        }
        int i = n;
        ArrayList<Integer> ans = new ArrayList<>();
        while (i != 1) {
            ans.add(i);
            i = a[i - 1];
        }
        ans.add(1);
        for (int j = ans.size() - 1; j >= 0; j--) {
            pw.print(ans.get(j));
            pw.print(' ');
        }
        pw.close();

    }

    static int binSearch(int[] a, int l, int r) {
        while (l + 1 < r) {
            int mid = (l + r) / 2;
            if (1 == 1) {

            } else {

            }
        }
        return l;
    }
}

class Pair {
    public int x1;
    public int x2;

    Pair(int x1, int x2) {
        this.x1 = x1;
        this.x2 = x2;
    }
}