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] 
					/*
					ID: abdelra29
LANG: JAVA
PROG: zerosum
					*/
						/*
						TO LEARN
				
						2-euler tour
					
						*/
						/*
						TO SOLVE 
						codeforces 722 kavi on pairing duty
						*/
						/*
						bit manipulation shit
						1-Computer Systems: A Programmer's Perspective
						2-hacker's delight
						*/
						/*
						TO WATCH
						
						*/
						            import java.util.*;
								    import java.math.*;
								    import java.io.*; 
								    import java.util.stream.Collectors;

								       public class A{
						            static FastScanner scan=new FastScanner();
									     public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));

			static int arr[][];
			static ArrayList<Integer>now;
			static int n,m;
			static void ty(int x)
			{
				now=new ArrayList();
				ArrayList<Pair>diffs=new ArrayList<Pair>();
				for(int i=0;i<m;i++)
				{
										
						diffs.add(new Pair(arr[i][x]-arr[i][n-1],i));
					
				}

				Collections.sort(diffs,Collections.reverseOrder());
				//if(x==1)
				//out.println(diffs);
				int sum=0;
				for(Pair i:diffs)
				{
					sum+=i.x;
					if(sum<0)
						now.add((int)i.y);
				}

			}
				public static void main(String[] args)  throws Exception 
						      {
						 /*
						 very important tips 
						 1-just fucking think backwards once in your shitty life
						 2-consider brute forcing and finding some patterns and observations
						 3-when you're in contest don't get out because you think there is no enough time
						
						 */
						
							//scan=new FastScanner("binary.in");
								///out = new PrintWriter("zerosum.out");
								 
								 							 /*
								 READING 
							
								 3-Introduction to DP with Bitmasking codefoces
								 4-Bit Manipulation hackerearth
								 5-read more about mobious and inculsion-exclusion 
								 */
								 /*
								

								 */
								
					
								    int tt=1;
								 
								    
				//tt=scan.nextInt();
						

				int T=1;

							 outer:while(tt-->0)
								    {
								    	int n=scan.nextInt();
								    	int arr[]=new int[n];
								    	for(int i=0;i<n;i++)
								    		arr[i]=scan.nextInt();
								     long [][]dp = new long[n + 1][601];
   
    
    for(int i = 0; i <= n; i++)
        for(int j = 0; j <= m; j++)
            dp[i][j] = 0;
   
   
    dp[0][0] = 1;
   
    // Fill the dp table
    for(int i = 1; i <= n; i++){
        for(int j = 0; j <= 600; j++){
    
dp[i][j] = dp[i - 1][j];
        	if(j>(j^arr[i-1])&&dp[i][j]==0){
    dp[i][j]+=dp[i - 1][j ^ arr[i - 1]];
}
    }    }
ArrayList<Integer>res=new ArrayList<Integer>();
//out.println(dp[50][0]);
for(int i=0;i<550;i++)
if(dp[n][i]>=1)
	res.add(i);
out.println(res.size());
for(int i:res)
	out.print(i+" ");






								    


	 }

								

		out.close();
					}
					
			static class Point { int x; int y; 
				public Point(int x, int y) { this.x = x; this.y = y; } } 
				static class Triangle { 

					 public static float area(Point A, Point B, Point C) {
					  float area = (A.x * (B.y - C.y) + B.x * (C.y - A.y) + C.x * (A.y - B.y)) / 2.0f; return Math.abs(area); }

}


					static class special{
					boolean is;
					char c;
					public special(boolean is,char c)
					{
						this.is=is;
						this.c=c;
					}

						 @Override
								            public int hashCode() {
								                return (int)(c+ 31 *(is?1:0));
								            }
						  @Override
								            public boolean equals(Object o){
								            //	System.out.println("FUCK");
								                if (o == this) return true;
								                if (o.getClass() != getClass()) return false;
								                special t = (special)o;
								                return t.is == is && t.c == c;
								            }
					}
		
								   
								     static long binexp(long a,long n)
								    {
								        if(n==0)
								            return 1;
								        long res=binexp(a,n/2);
								        if(n%2==1)
								            return res*res*a;
								        else 
								            return res*res;
								    }
								     
								    static long powMod(long base, long exp, long mod) {
								           if (base == 0 || base == 1) return base;
								           if (exp == 0) return 1;
								           if (exp == 1) return (base % mod+mod)%mod;
								           long R = (powMod(base, exp/2, mod) % mod+mod)%mod;
								           R *= R;
								           R %= mod;
								           if ((exp & 1) == 1) {
								               return (base * R % mod+mod)%mod;
								           }
								           else return (R %mod+mod)%mod;
								       }
								    static double dis(double x1,double y1,double x2,double y2)
								    {
								        return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
								    }
								    static long mod(long x,long y)
								        {
								            if(x<0)
								                x=x+(-x/y+1)*y;
								            return x%y;
								        }
								     public static  long pow(long b, long e) {
								                long r = 1;
								                while (e > 0) {
								                    if (e % 2 == 1) r = r * b ;
								                    b = b * b;
								                    e >>= 1;
								                }
								                return r;
								            }
								    private static void sort(long[] arr) {
								            List<Long> list = new ArrayList<>();
								            for (long object : arr) list.add(object);
								            Collections.sort(list);
								        //Collections.reverse(list);
								            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
								        }
								    private static void sort2(long[] arr) {
								            List<Long> list = new ArrayList<>();
								            for (Long object : arr) list.add(object);
								            Collections.sort(list);
								        Collections.reverse(list);
								            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
								        }
								     static class FastScanner
						{
						    private int BS = 1 << 16;
						    private char NC = (char) 0;
						    private byte[] buf = new byte[BS];
						    private int bId = 0, size = 0;
						    private char c = NC;
						    private double cnt = 1;
						    private BufferedInputStream in;
						 
						    public FastScanner() {
						        in = new BufferedInputStream(System.in, BS);
						    }
						 
						    public FastScanner(String s) {
						        try {
						            in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
						        } catch (Exception e) {
						            in = new BufferedInputStream(System.in, BS);
						        }
						    }
						 
						    private char getChar() {
						        while (bId == size) {
						            try {
						                size = in.read(buf);
						            } catch (Exception e) {
						                return NC;
						            }
						            if (size == -1) return NC;
						            bId = 0;
						        }
						        return (char) buf[bId++];
						    }
						 
						    public int nextInt() {
						        return (int) nextLong();
						    }
						 
						    public int[] nextInts(int N) {
						        int[] res = new int[N];
						        for (int i = 0; i < N; i++) {
						            res[i] = (int) nextLong();
						        }
						        return res;
						    }
						 
						    public long[] nextLongs(int N) {
						        long[] res = new long[N];
						        for (int i = 0; i < N; i++) {
						            res[i] = nextLong();
						        }
						        return res;
						    }
						 
						    public long nextLong() {
						        cnt = 1;
						        boolean neg = false;
						        if (c == NC) c = getChar();
						        for (; (c < '0' || c > '9'); c = getChar()) {
						            if (c == '-') neg = true;
						        }
						        long res = 0;
						        for (; c >= '0' && c <= '9'; c = getChar()) {
						            res = (res << 3) + (res << 1) + c - '0';
						            cnt *= 10;
						        }
						        return neg ? -res : res;
						    }
						 
						    public double nextDouble() {
						        double cur = nextLong();
						        return c != '.' ? cur : cur + nextLong() / cnt;
						    }
						 
						    public double[] nextDoubles(int N) {
						        double[] res = new double[N];
						        for (int i = 0; i < N; i++) {
						            res[i] = nextDouble();
						        }
						        return res;
						    }
						 
						    public String next() {
						        StringBuilder res = new StringBuilder();
						        while (c <= 32) c = getChar();
						        while (c > 32) {
						            res.append(c);
						            c = getChar();
						        }
						        return res.toString();
						    }
						 
						    public String nextLine() {
						        StringBuilder res = new StringBuilder();
						        while (c <= 32) c = getChar();
						        while (c != '\n') {
						            res.append(c);
						            c = getChar();
						        }
						        return res.toString();
						    }
						 
						    public boolean hasNext() {
						        if (c > 32) return true;
						        while (true) {
						            c = getChar();
						            if (c == NC) return false;
						            else if (c > 32) return true;
						        }
						    }
						}

								     static class Pair implements Comparable<Pair>{
								            public long x, y,z;
								            public Pair(long x1, long y1,long z1) {
								                x=x1;
								                y=y1;
								                z=z1;
								            }
								             public Pair(long x1, long y1) {
								                x=x1;
								                y=y1;
								    
								            }
								            
								            @Override
								            public int hashCode() {
								                return (int)(x + 31 * y);
								            }
								            public String toString() {
								                return x + " " + y+" "+z;
								            }
								            @Override
								            public boolean equals(Object o){
								                if (o == this) return true;
								                if (o.getClass() != getClass()) return false;
								                Pair t = (Pair)o;
								                return t.x == x && t.y == y&&t.z==z;
								            }
								    public int compareTo(Pair o)
								    {
								  	
								return (int)(x-o.x);
								     
								        }
								     
								    }
								}
								
								    
								   

								     
