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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.TreeMap;
import java.util.Vector;





public class con12 {
	

		
	
	public static void main(String[] args) throws IOException 
	{
	int n=i();
	int a[]=new int[n];
	HashMap<Long,Integer> tr=new HashMap<Long,Integer>();
	for(int p=0;p<n;p++)
	{
		
		long ph=l();
		a[p]=(int) ph;
		if(tr.containsKey(ph))
		{
			tr.put(ph, tr.get(ph)+1);
		}
		else
		{
			tr.put(ph,1);
		}
	}
	Iterator<Long> de=tr.keySet().iterator();
	
	TreeMap<Integer,Vector<Long>> gf=new TreeMap<Integer,Vector<Long>>();
	while(de.hasNext())
	{
		long fd=de.next();
		
		long s=fd;
		s=s+1;
		int k=1;
		while(s<=1000000000)
		{
			
			if(tr.containsKey(s))
			{
				Vector<Long> ne=new Vector<Long>();
				if(tr.containsKey((long)(fd+Math.pow(2, k))))
				{
					ne.addElement(fd);
					ne.addElement(s);
					ne.addElement((long) (fd+Math.pow(2, k)));
					int su=tr.get(fd)+tr.get(s)+tr.get((long) (fd+Math.pow(2, k)));
					gf.put(su, ne);
				}
				else
				{
					ne.addElement(fd);
					ne.addElement(s);
					int su=tr.get(fd)+tr.get(s);
					gf.put(su, ne);
				}
				
			}
			else
			{
				
				
			}
			s=(long) (fd+Math.pow(2, k));
			k++;
		}
		
	}
	if(gf.isEmpty())
	{
		out.println(1);
		out.println(a[0]);
	}
	else
	{
	Vector<Long> ds=gf.get(gf.lastKey());
	out.println(gf.lastKey());
	for(int bv=0;bv<ds.size();bv++)
	{
		long el=ds.elementAt(bv);
		int nr=tr.get(el);
		for(int f=0;f<nr;f++)
		{
			out.print(el+" ");
		}
		
	}
	}
	
	
	out.close();
	}
	 
	
	 
	  
	  
	 static InputReader in = new InputReader(System.in);
	    static OutputWriter out = new OutputWriter(System.out);
	    
	    static int i()
	    {
	    	return in.readInt();
	    }
	    
	    static long l()
	    {
	    	return in.readLong();
	    }
	    
	    static double d()
	    {
	    	return in.readDouble();
	    }
	    
	    static String s()
	    {
	    	return in.readString();
	    }
	    
	    static void Iarr( int[] array, int no )
	    {
	    	for( int i=0 ; i<no ; i++ )
	    	{
	    		array[i] = i(); 
	    	}
	    }
	    
	    static void Larr( long[] array, int no )
	    {
	    	for( int i=0 ; i<no ; i++ )
	    	{
	    		array[i] = l(); 
	    	}
	    }
	    
	    static void Darr( double[] array, int no )
	    {
	    	for( int i=0 ; i<no ; i++ )
	    	{
	    		array[i] = d(); 
	    	}
	    }
	    
	    static void Sarr( String[] array, int no )
	    {
	    	for( int i=0 ; i<no ; i++ )
	    	{
	    		array[i] = s(); 
	    	}
	    }
	    
	    private static class InputReader
	    {
	        private InputStream stream;
	        private byte[] buf = new byte[1024];
	        private int curChar;
	        private int numChars;
	        private SpaceCharFilter filter;
	 
	        public InputReader(InputStream stream)
	        {
	            this.stream = stream;
	        }
	 
	        
	        
	        
	        
	        
	        
	        public int read()
	        {
	            if (numChars == -1)
	                throw new InputMismatchException();
	            if (curChar >= numChars)
	            {
	                curChar = 0;
	                try
	                {
	                    numChars = stream.read(buf);
	                } catch (IOException e)
	                {
	                    throw new InputMismatchException();
	                }
	                if (numChars <= 0)
	                    return -1;
	            }
	            return buf[curChar++];
	        }
	 
	        public int readInt()
	        {
	            int c = read();
	            while (isSpaceChar(c))
	                c = read();
	            int sgn = 1;
	            if (c == '-')
	            {
	                sgn = -1;
	                c = read();
	            }
	            int res = 0;
	            do
	            {
	                if (c < '0' || c > '9')
	                    throw new InputMismatchException();
	                res *= 10;
	                res += c - '0';
	                c = read();
	            } while (!isSpaceChar(c));
	            return res * sgn;
	        }
	 
	        public String readString()
	        {
	            int c = read();
	            while (isSpaceChar(c))
	                c = read();
	            StringBuilder res = new StringBuilder();
	            do
	            {
	                res.appendCodePoint(c);
	                c = read();
	            } while (!isSpaceChar(c));
	            return res.toString();
	        }
	        public double readDouble() {
	            int c = read();
	            while (isSpaceChar(c))
	                c = read();
	            int sgn = 1;
	            if (c == '-') {
	                sgn = -1;
	                c = read();
	            }
	            double res = 0;
	            while (!isSpaceChar(c) && c != '.') {
	                if (c == 'e' || c == 'E')
	                    return res * Math.pow(10, readInt());
	                if (c < '0' || c > '9')
	                    throw new InputMismatchException();
	                res *= 10;
	                res += c - '0';
	                c = read();
	            }
	            if (c == '.') {
	                c = read();
	                double m = 1;
	                while (!isSpaceChar(c)) {
	                    if (c == 'e' || c == 'E')
	                        return res * Math.pow(10, readInt());
	                    if (c < '0' || c > '9')
	                        throw new InputMismatchException();
	                    m /= 10;
	                    res += (c - '0') * m;
	                    c = read();
	                }
	            }
	            return res * sgn;
	        }
	        public long readLong() {
	            int c = read();
	            while (isSpaceChar(c))
	                c = read();
	            int sgn = 1;
	            if (c == '-') {
	                sgn = -1;
	                c = read();
	            }
	            long res = 0;
	            do {
	                if (c < '0' || c > '9')
	                    throw new InputMismatchException();
	                res *= 10;
	                res += c - '0';
	                c = read();
	            } while (!isSpaceChar(c));
	            return res * sgn;
	        }
	        public boolean isSpaceChar(int c)
	        {
	            if (filter != null)
	                return filter.isSpaceChar(c);
	            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	        }
	 
	        public String next()
	        {
	            return readString();
	        }
	 
	        public interface SpaceCharFilter
	        {
	            public boolean isSpaceChar(int ch);
	        }
	    }
	 
	    private static class OutputWriter
	    {
	        private final PrintWriter writer;
	 
	        public OutputWriter(OutputStream outputStream)
	        {
	            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	        }
	 
	        public OutputWriter(Writer writer)
	        {
	            this.writer = new PrintWriter(writer);
	        }
	 
	        public void print(Object... objects)
	        {
	            for (int i = 0; i < objects.length; i++)
	            {
	                if (i != 0)
	                    writer.print(' ');
	                writer.print(objects[i]);
	            }
	        }
	 
	        public void println(Object... objects)
	        {
	            print(objects);
	            writer.println();
	        }
	 
	        public void close()
	        {
	            writer.close();
	        }
	 
	        public void flush()
	        {
	            writer.flush();
	        }
	     }
	
	 
}