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] 
import java.io.*;
import java.util.*;

public class new1{
	public static int func(int[][] dp, int[] arr, int x, int y) {
		
		int n = arr.length;
		if(x == n) {
			//System.out.println(x + " " + y );
			if(y == 0) return 501;
			else return -1;
		}
		if(dp[x][y] != -2) return dp[x][y];
		int a1 = -1;
		int aa1 = func(dp, arr, x + 1, y ^ arr[x]);
		if(aa1 != -1 && aa1 > arr[x]) a1 = arr[x];
		int a2 = func(dp, arr, x + 1, y);
		int ans = -1;
		if(a1 == -1 && a2 != -1) ans = a2;
		else if(a2 == -1 && a1 != -1) ans = a1;
		else if(a1 != - 1&& a2 != -1) ans = Math.max(a1, a2);
		dp[x][y] = ans;
		//System.out.println(x + " " + y + " " + ans);
		return ans;
		
	}
     

	public static void main(String[] args)  throws IOException{
    	FastReader s = new FastReader();
    	BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out));
    	int t =  1;//s.nextInt();
    	int bit = 512;
    	//long l1 = System.currentTimeMillis();
    	for(int z = 0; z < t; z++) {
    		int n = s.nextInt();
    		int[] arr = new int[n];
    		for(int i = 0; i < n; i++) {
    			arr[i] = s.nextInt();
    		}
    		int[][] dp = new int[n][bit];
    		for(int i = 0; i < n; i++) {
    			Arrays.fill(dp[i], -2);
    		}
    		int count = 0;
    		int[] ans = new int[bit]; 
    		for(int i = n; i >= 0; i--) {
	    		for(int j = 0; j < bit; j++) {
	    			if(func(dp, arr, i, j) != -1) {
	    				if(ans[j] != 1) count++;
	    				ans[j] = 1;
	    			}
	    		}
    		}
//    		for(int i = 0; i < n; i++) {
//    			System.out.println(Arrays.toString(dp[i]));
//    		}
    		System.out.println(count + " ");
    		for(int i = 0; i < bit; i++) {
    			if(ans[i] == 1) System.out.print(i + " "); 
    		}
    		System.out.println();
    	}
    	//System.out.println(System.currentTimeMillis() - l1);
    			//output.flush();	
    }
}

class FastReader {
    BufferedReader br;
    StringTokenizer st;
    public FastReader() {
        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();
    }
 
    public 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;
}}