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

////***************************************************************************
 /* public class E_Gardener_and_Tree implements Runnable{

       public static void main(String[] args) throws Exception {
        new Thread(null, new E_Gardener_and_Tree(), "E_Gardener_and_Tree", 1<<28).start();
       }
    public void run(){
         WRITE YOUR CODE HERE!!!!
         JUST WRITE EVERYTHING HERE WHICH YOU WRITE IN MAIN!!!
       }

  }
*/
/////**************************************************************************


public class F1_Korney_Korneevich_and_XOR_easy_version_{
    public static void main(String[] args) {
        FastScanner s= new FastScanner();
      //  PrintWriter out=new PrintWriter(System.out);
        //end of program
        //out.println(answer);
        //out.close();
        StringBuilder res = new StringBuilder();
        int n=s.nextInt();
        int array[]= new int[n];
        ArrayList<Integer> unique = new  ArrayList<Integer>(1005);
        HashMap<Integer,Integer> map = new HashMap<Integer,Integer>();
        for(int i=0;i<n;i++){
            array[i]=s.nextInt();
            if(!map.containsKey(array[i])){
                map.put(array[i],1);
               // unique.add(array[i]);
            }
            else{
                int a=map.get(array[i]);
                a++;
                map.remove(array[i]);
                map.put(array[i],a);
            }
        }
        HashMap<Integer,Integer> map5 = new HashMap<Integer,Integer>();
        for(int i=0;i<n;i++){
            if(!map5.containsKey(array[i])){
                map5.put(array[i],1);
                unique.add(array[i]);
            }
            else{
                int a=map5.get(array[i]);
                a++;
                map5.remove(array[i]);
                map5.put(array[i],a);
                if(a==map.get(array[i])){
                    unique.add(array[i]);
                }
            }
        }
        int size=unique.size();
        ArrayList<ArrayList<Integer>> store = new  ArrayList<ArrayList<Integer>>(size+2);
        for(int i=0;i<size;i++){
            ArrayList<Integer> obj = new  ArrayList<Integer>();
            store.add(obj);
        }
        for(int i=size-1;i>=0;i--){
            int num=unique.get(i);
            ArrayList<Integer> nice = store.get(i);
            HashMap<Integer,Integer> map2 = new  HashMap<Integer,Integer>();
            for(int j=i+1;j<size;j++){
                if(unique.get(j)>num){
                    ArrayList<Integer> yo =store.get(j);
                      for(int k=0;k<yo.size();k++){
                          int number=num^yo.get(k);
                          if(!map2.containsKey(number)){
                              map2.put(number,1);
                              nice.add(number);
                          }
                      }
                }
            }
            if(!map2.containsKey(num)){
                map2.put(num,1);
                nice.add(num);
            }
            
        }
        ArrayList<Integer> ans = new  ArrayList<Integer>(520);
        HashMap<Integer,Integer> map3 = new  HashMap<Integer,Integer>();
        ans.add(0);
        map3.put(0,1);
        for(int i=0;i<size;i++){
            ArrayList<Integer> yo = store.get(i);
             for(int j=0;j<yo.size();j++){
                 int num=yo.get(j);
                 if(!map3.containsKey(num)){
                     map3.put(num,1);
                     ans.add(num);
                 }
             }
        }
        Collections.sort(ans);
        res.append(ans.size()+"\n");
        for(int i=0;i<ans.size();i++){
            res.append(ans.get(i)+" ");
        }
        res.append("\n");
        System.out.println(res);
    }
    static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
 
		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}
 
		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String nextToken() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(nextToken());
		}
 
		long nextLong() {
			return Long.parseLong(nextToken());
		}
 
		double nextDouble() {
			return Double.parseDouble(nextToken());
		}
	}




}