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] 
/**
 * check out my youtube channel sh0rkyboy
 * https://tinyurl.com/zdxe2y4z
 * I do screencasts, solutions, and other fun stuff in the future
 */

import java.util.*;
import java.io.*;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import static java.lang.Math.max;
public class EdC {
	static long[] mods = {1000000007, 998244353, 1000000009};
	static long mod = mods[0];
	public static MyScanner sc;
    public static PrintWriter out;
	public static void main(String[] largewang) throws Exception{
		// TODO Auto-generated method stub
 		sc = new MyScanner();
 		out = new PrintWriter(System.out);
 			int n = sc.nextInt();
 			int[] arr = readArrayInt(n);
 			int[] dp = new int[512];
 			Arrays.fill(dp,  Integer.MAX_VALUE); //dp[i] represents smallest ending value for xor sum of i
 			dp[0] = 0;
 			dp[arr[0]] = arr[0];
 			for(int j = 1;j<n;j++){
 				for(int k = 0;k<512;k++){
 					if (dp[k] != Integer.MAX_VALUE && arr[j] > dp[k]){
 						dp[k^arr[j]] = min(dp[k^arr[j]], arr[j]);
 					}
 				}
 			}
 			int count = 0;
 			for(int j = 0;j<512;j++){
 				if (dp[j] != Integer.MAX_VALUE)
 					count++;
 			}
 			out.println(count);
 			for(int j = 0;j<512;j++){
 				if (dp[j] != Integer.MAX_VALUE)
 					out.print(j  + " ");
 			}
 			out.println();
 			
 			
 		out.close();
 		
 	}
	static class Pair{
		int val; int index;
		public Pair(int val, int index){
			this.index = index;
		}
	}
	static class BIT {
        long[] tree;
        public BIT(int size) {
            tree = new long[size + 1];
        }
        public long sum(int i) {
            long ans = 0;
            while (i > 0) {
                ans += tree[i];
                i -= i & -i;
            }
            return ans;
        }
 
        public long query(int i, int j) {
            return sum(j) - sum(i - 1);
        }
 
        public void add(int i, long val) {
            while (i < tree.length) {
                tree[i] += val;
                i += i & -i;
            }
        }
 
        public void set(int i, long val) {
            add(i, val - query(i, i));
        }
    }
	
	public static void sort(int[] array){
		ArrayList<Integer> copy = new ArrayList<>();
		for (int i : array)
			copy.add(i);
		Collections.sort(copy);
		for(int i = 0;i<array.length;i++)
			array[i] = copy.get(i);
	}
	static String[] readArrayString(int n){
		String[] array = new String[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.next();
		return array;
	}
	static int[] readArrayInt(int n){
    	int[] array = new int[n];
    	for(int j = 0;j<n;j++)
    		array[j] = sc.nextInt();
    	return array;
    }
	static int[] readArrayInt1(int n){
		int[] array = new int[n+1];
		for(int j = 1;j<=n;j++){
			array[j] = sc.nextInt();
		}
		return array;
	}
	static long[] readArrayLong(int n){
		long[] array = new long[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.nextLong();
		return array;
	}
	static double[] readArrayDouble(int n){
		double[] array = new double[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.nextDouble();
		return array;
	}
	static int minIndex(int[] array){
		int minValue = Integer.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static int minIndex(long[] array){
		long minValue = Long.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static int minIndex(double[] array){
		double minValue = Double.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static long power(long x, long y){
		if (y == 0)
			return 1;
		if (y%2 == 1)
			return (x*power(x, y-1))%mod;
		return power((x*x)%mod, y/2)%mod;
	}
	static void verdict(boolean a){
        out.println(a ? "YES" : "NO");
    }
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
        public MyScanner() {
            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();
        }
        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;
        }
        
    }	
}

//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is