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 CodeForces{
    /*-------------------------------------------EDITING CODE STARTS HERE-------------------------------------------*/
    public static void main(String[] args) throws IOException{
        openIO();
        int testCase = 1;
//        testCase = sc.nextInt();
        preCompute();
        for (int i = 1; i <= testCase; i++) solve(i);
        closeIO();
    }

    public static void solve(int tCase)throws IOException {
        int n = sc.nextInt();
        int[] arr = new int[n];
        for(int i=0;i<n;i++)arr[i] = sc.nextInt();
        boolean[] xorPossible = new boolean[513];
        xorPossible[0] = true;
        int[] min = new int[513];
        Arrays.fill(min,1000);
        min[0] = -10;
        for(int i=0;i<n;i++){
            for(int j=xorPossible.length-1;j>=0;j--){
                if((j^arr[i]) >= j  && xorPossible[j] && min[j] < arr[i]) {
                    xorPossible[j ^ arr[i]] = true;
                    min[j^arr[i]] = arr[i];
                }
            }
            for(int j=0;j<xorPossible.length;j++){
                if((j^arr[i]) <=j && xorPossible[j] && min[j] < arr[i]) {
                    xorPossible[j ^ arr[i]] = true;
                    min[j ^ arr[i]] = arr[i];
                }
            }
        }
        List<Integer> ans = new ArrayList<>();
        for(int j=0;j<xorPossible.length;j++)
            if(xorPossible[j])ans.add(j);
        out.println(ans.size());
        for(int ele : ans)out.print(ele+" ");

    }

    private static void  preCompute(){

    }
    /*-------------------------------------------EDITING CODE ENDS HERE-------------------------------------------*/
    static FastestReader sc;
    static PrintWriter out;
    private static void openIO() throws IOException{
        sc = new FastestReader();
        out = new PrintWriter(System.out);
    }

    /*------------------------------------------HELPER FUNCTION STARTS HERE------------------------------------------*/

    public static final int mod = (int) 1e9 +7;
    private static final int mod2 =  998244353;
    public static final int inf_int = (int) 2e9;
    public static  final long inf_long = (long) 2e18;

    // euclidean algorithm time O(max (loga ,logb))
    public static long _gcd(long a, long b) {
        long x = Math.min(a, b);
        long y = Math.max(a, b);
        if (y % x == 0) return x;
        return _gcd(y % x, x);
    }

    public static long _lcm(long a, long b) {
        // lcm(a,b) * gcd(a,b) = a * b
        return (a / _gcd(a, b)) * b;
    }
    // binary exponentiation time O(logn)
    public static long _power(long x, long n) {
        long ans = 1;
        while (n > 0) {
            if ((n & 1) == 1) {
                ans *= x;
                ans %= mod;
                n--;
            } else {
                x *= x;
                x %= mod;
                n >>= 1;
            }
        }
        return ans;
    }
    //sieve/first divisor time : O(mx * log ( log (mx) ) )
    public static int[]  _seive(int mx){
        int[] firstDivisor = new int[mx+1];
        for(int i=0;i<=mx;i++)firstDivisor[i] = i;
        for(int i=2;i*i<=mx;i++)
            if(firstDivisor[i] == i)
                for(int j = i*i;j<=mx;j+=i)
                    firstDivisor[j] = i;
        return firstDivisor;
    }

    private static boolean isPrime(long x){
        for(long i=2;i*i<=x;i++)
            if(x%i==0)return false;
        return true;
    }


    /*------------------------------------------HELPER FUNCTION ENDS HERE-------------------------------------------*/

    /*-------------------------------------------FAST INPUT STARTS HERE---------------------------------------------*/

    public static void closeIO() throws IOException{
        out.flush();
        out.close();
        sc.close();
    }
    private static final class FastestReader {
        private static final int BUFFER_SIZE = 1 << 16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;

        public FastestReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public FastestReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }

        private int skip() throws IOException {
            int b;
            //noinspection StatementWithEmptyBody
            while ((b = read()) != -1 && isSpaceChar(b)) {}
            return b;
        }

        public String next() throws IOException {
            int b = skip();
            final StringBuilder sb = new StringBuilder();
            while (!isSpaceChar(b)) { // when nextLine, (isSpaceChar(b) && b != ' ')
                sb.appendCodePoint(b);
                b = read();
            }
            return sb.toString();
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            final boolean neg = c == '-';
            if (neg) { c = read(); }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg) { return -ret; }
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') { c = read(); }
            final boolean neg = c == '-';
            if (neg) { c = read(); }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) { return -ret; }
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') { c = read(); }
            final boolean neg = c == '-';
            if (neg) { c = read(); }

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg) { return -ret; }
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) { buffer[0] = -1; }
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) { fillBuffer(); }
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            din.close();
        }
    }
    /*---------------------------------------------FAST INPUT ENDS HERE ---------------------------------------------*/
}