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 is Hard 
 * Before Easy 
 * Jai Mata Dii 
 */ 
 
import java.util.*;
import java.io.*; 
  
public class Main {
	static 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();}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; }} 
	static long mod = (long)(1e9+7); 
//	 static long mod = 998244353; 
//	 static Scanner sc = new Scanner(System.in); 
	static FastReader sc = new FastReader(); 
	static PrintWriter out = new PrintWriter(System.out);
	public static void main (String[] args) { 
		int ttt = 1;
//		ttt = sc.nextInt();
		z :for(int tc=1;tc<=ttt;tc++){
			int n = sc.nextInt();
			int a[] = new int[n];
			for(int i=0;i<n;i++) {
				a[i] = sc.nextInt();
			}
			int cur[] = new int[512];
			Arrays.fill(cur, Integer.MAX_VALUE);
			cur[0] = Integer.MIN_VALUE;
			for(int i=0;i<n;i++) {
				for(int j=1;j<=511;j++) {
					if(cur[j^a[i]]<=a[i]) {
						cur[j] = Math.min(cur[j], a[i]);
					}
				}
			}
			ArrayList<Integer> ans = new ArrayList<>();
			for(int i=0;i<512;i++) {
				if(cur[i]!=Integer.MAX_VALUE) {
					ans.add(i);
				}
			}
			System.out.println(ans.size());
			for(int val : ans) {
				out.write(val+" ");
			}
			out.write("\n");
		}
		out.close();
	}
	private static boolean check(StringBuilder cur) {
		int n = cur.length();
		int i = 0, j = n-1;
		while(i<j) {
			if(cur.charAt(i) != cur.charAt(j)) return false;
			i++;
			j--;
		}
		return true;
	}
	static long pow(long a, long b){long ret = 1;while(b>0){if(b%2 == 0){a = (a*a)%mod;b /= 2;}else{ret = (ret*a)%mod;b--;}}return ret%mod;}
	static long gcd(long a,long b){if(b==0) return  a; return gcd(b,a%b); } 
	private static void sort(int[] a) {List<Integer> k = new ArrayList<>();for(int val : a) k.add(val);Collections.sort(k);for(int i=0;i<a.length;i++) a[i] = k.get(i);} 
	private static void ini(List<Integer>[] tre2){for(int i=0;i<tre2.length;i++){tre2[i] = new ArrayList<>();}} 
	private static void init(List<int[]>[] tre2){for(int i=0;i<tre2.length;i++){tre2[i] = new ArrayList<>();}} 
	private static void sort(long[] a) {List<Long> k = new ArrayList<>();for(long val : a) k.add(val);Collections.sort(k);for(int i=0;i<a.length;i++) a[i] = k.get(i);} 
}