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.BufferedWriter;
import java.util.Scanner;

/**
 * Created by aka_npou on 14.10.2018.
 */
public class Test {
    public static void main(String[] args) throws Exception{
        new Test().run();
    }

    private void run() {
        Scanner scanner = new Scanner(System.in);
        int n=scanner.nextInt();
        int[] m = new int [n-1];
        for (int i=0;i<n-1;i++) {
            m[i]=scanner.nextInt();
        }

        Stack stack = new Stack(n);
        int q=m[n-2];
        stack.push(q);
        while (true) {
            if (q==1)
                break;
            q=m[q-2];
            stack.push(q);
        }

        while (stack.top!=-1) {
            System.out.print(stack.pop()+" ");
        }
        System.out.println(n);


    }

    private class Stack {
        int[] m;
        int top=-1;
        Stack(int n) {
            m = new int[n];
        }

        int pop() {
            return m[top--];
        }

        void push(int s) {
            m[++top]=s;
        }
    }
}
