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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Stack;
import java.util.StringTokenizer;

public class Bmail {
    public static void main(String[] args) {
//        FastScanner s = new FastScanner("input.txt");
        FastScanner s = new FastScanner();
        int N = s.nextInt();
        int arr[] = new int[N + 1];
        for (int i = 0; i < N - 1; i++) {
            arr[i + 2] = s.nextInt();
        }

        int cur = N;

        Stack<Integer> stack = new Stack<>();
        while(arr[cur] != 0){
            stack.push(cur);
            cur = arr[cur];
        }

        stack.push(cur);

        while(!stack.empty()){
            System.out.print(stack.pop());
            System.out.print(" ");
        }
        System.out.println();

    }

    public static void _(Object...objs){
        System.out.println(Arrays.deepToString(objs));
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(){
            init();
        }

        public FastScanner(String name) {
            init(name);
        }

        public FastScanner(boolean isOnlineJudge){
            if(!isOnlineJudge || System.getProperty("ONLINE_JUDGE") != null){
                init();
            }else{
                init("input.txt");
            }
        }

        private void init(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        private void init(String name){
            try {
                br = new BufferedReader(new FileReader(name));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

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

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

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

        public double nextDouble(){
            return Double.parseDouble(nextToken());
        }

    }
}
