This is an easier version of the problem with smaller constraints.

Korney Korneevich dag up an array a of length n. Korney Korneevich has recently read about the operation [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR), so he wished to experiment with it. For this purpose, he decided to find all integers x ≥ 0 such that there exists an increasing subsequence of the array a, in which the bitwise XOR of numbers is equal to x.

It didn't take a long time for Korney Korneevich to find all such x, and he wants to check his result. That's why he asked you to solve this problem!

A sequence s is a subsequence of a sequence b if s can be obtained from b by deletion of several (possibly, zero or all) elements.

A sequence s_1, s_2, … , s_m is called increasing if s_1 < s_2 < … < s_m.

Input

The first line contains a single integer n (1 ≤ n ≤ 10^5).

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 500) — the elements of the array a.

Output

In the first line print a single integer k — the number of found x values.

In the second line print k integers in increasing order x_1, x_2, … x_k (0 ≤ x_1 < … < x_k) — found x values.

Examples

Input


4
4 2 2 4


Output


4
0 2 4 6 


Input


8
1 0 1 7 12 5 3 2


Output


12
0 1 2 3 4 5 6 7 10 11 12 13 

Note

In the first test case:

  * To get value x = 0 it is possible to choose and empty subsequence 
  * To get value x = 2 it is possible to choose a subsequence [2] 
  * To get value x = 4 it is possible to choose a subsequence [4] 
  * To get value x = 6 it is possible to choose a subsequence [2, 4] 
/*
        "Everything in the universe is balanced. Every disappointment
                you face in life will be balanced by something good for you!
                        Keep going, never give up."

*/


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

public class Solution {
    public static void main(String[] args) throws java.lang.Exception {
        out = new PrintWriter(new BufferedOutputStream(System.out));
        sc = new FastReader();

        int test = 1;
        for (int t = 0; t < test; t++) {
            solve();
        }
        out.close();
    }

    private static void solve() {
        int n = sc.nextInt();
        int[] arr = new int[n + 1];
        for (int i = 1; i <= n; i++) {
            arr[i] = sc.nextInt();
        }

        int[] minEnding = new int[520];
        Arrays.fill(minEnding, Integer.MAX_VALUE);
        minEnding[0] = 0;

        List<Integer> list = new ArrayList<>();

        for (int i = 1; i <= n; i++) {
            for (int j = 0; j <= 512; j++) {
                if (minEnding[j] < arr[i]) {
                    minEnding[j ^ arr[i]] = Math.min(minEnding[j ^ arr[i]], arr[i]);
                }
            }
        }

        for (int i = 0; i < minEnding.length; i++) {
            if (minEnding[i] != Integer.MAX_VALUE) {
                list.add(i);
            }
        }

        out.println(list.size());
        for (int val : list) {
            out.print(val + " ");
        }
        out.println();
    }


    public static FastReader sc;
    public static PrintWriter out;
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer str;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (str == null || !str.hasMoreElements())
            {
                try
                {
                    str = new StringTokenizer(br.readLine());
                }
                catch (IOException  end)
                {
                    end.printStackTrace();
                }
            }
            return str.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 end)
            {
                end.printStackTrace();
            }
            return str;
        }
    }
}