Problem: There are n distinct points on a coordinate line, the coordinate of i-th point equals to x_i. Choose a subset of the given set of points such that the distance between each pair of points in a subset is an integral power of two. It is necessary to consider each pair of points, not only adjacent. Note that any subset containing one element satisfies the condition above. Among all these subsets, choose a subset with maximum possible size.

In other words, you have to choose the maximum possible number of points x_{i_1}, x_{i_2}, ..., x_{i_m} such that for each pair x_{i_j}, x_{i_k} it is true that |x_{i_j} - x_{i_k}| = 2^d where d is some non-negative integer number (not necessarily the same for each pair of points).

Input

The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of points.

The second line contains n pairwise distinct integers x_1, x_2, ..., x_n (-10^9 ≤ x_i ≤ 10^9) — the coordinates of points.

Output

In the first line print m — the maximum possible number of points in a subset that satisfies the conditions described above.

In the second line print m integers — the coordinates of points in the subset you have chosen.

If there are multiple answers, print any of them.

Examples

Input

6
3 5 4 7 10 12


Output

3
7 3 5

Input

5
-1 2 5 8 11


Output

1
8

Note

In the first example the answer is [7, 3, 5]. Note, that |7-3|=4=2^2, |7-5|=2=2^1 and |3-5|=2=2^1. You can't find a subset having more points satisfying the required property.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class Ishu
{
    static class Reader 
        { 
            final private int BUFFER_SIZE = 1 << 16; 
            private DataInputStream din; 
            private byte[] buffer; 
            private int bufferPointer, bytesRead; 
      
            public Reader() 
            { 
                din = new DataInputStream(System.in); 
                buffer = new byte[BUFFER_SIZE]; 
                bufferPointer = bytesRead = 0; 
            } 
      
            public Reader(String file_name) throws IOException 
            { 
                din = new DataInputStream(new FileInputStream(file_name)); 
                buffer = new byte[BUFFER_SIZE]; 
                bufferPointer = bytesRead = 0; 
            } 
      
            public String readLine() throws IOException 
            { 
                byte[] buf = new byte[64]; // line length 
                int cnt = 0, c; 
                while ((c = read()) != -1) 
                { 
                    if (c == '\n') 
                        break; 
                    buf[cnt++] = (byte) c; 
                } 
                return new String(buf, 0, cnt); 
            } 
      
            public int nextInt() throws IOException 
            { 
                int ret = 0; 
                byte c = read(); 
                while (c <= ' ') 
                    c = read(); 
                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(); 
                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(); 
                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 
            { 
                if (din == null) 
                    return; 
                din.close(); 
            } 
        } 
    static Reader scan = new Reader();
    static BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out)); 
    static void tc() throws Exception
    {
    int n = scan.nextInt();
    int[] a = new int[n];
    int i,j;
    
    Map<Integer, Boolean> map = new HashMap<Integer, Boolean>();
    
    for(i=0;i<n;++i)
        {
        a[i] = scan.nextInt();
        if(!map.containsKey(a[i]))
            map.put(a[i], true);
        }
        
    Arrays.sort(a, 0, n);    
        
    for(i=1;i<n-1;++i)
        {
        int cr = a[i];
        int pow = 1;
        for(j=1;j<=32;++j, pow *= 2)
            {
            int pr = cr - pow;
            int nr = cr + pow;
            if(map.containsKey(pr) && map.containsKey(nr))
                {
                output.write("3\n");
                output.write(pr + " " + cr + " " + nr + "\n");
                output.flush();
                return;
                }
            }
        }
    for(i=1;i<n;++i)
        {
        int cr = a[i];
        int pow = 1;
        for(j=1;j<=32;++j, pow *= 2)
            {
            int pr = cr - pow;
            if(map.containsKey(pr))
                {
                output.write("2\n");
                output.write(pr + " " + cr + "\n");
                output.flush();
                return;
                }
            }
        } 
    output.write("1\n");
    output.write(a[0] + "\n");
    output.flush();
    }
    public static void main(String[] args) throws Exception
    {
    int t = 1;
    //t = scan.nextInt();
    while(t-- > 0)
        tc();
    }
}