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.util.*;
import java.lang.*;
import java.math.*;
import java.io.*;
 
/* spar5h */

public class cf4 implements Runnable{    
	
	public void run() {
		
		InputReader s = new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);
		
		long[] pow2 = new long[35]; pow2[0] = 1;
		
		for(int i = 1; i <= 34; i++)
			pow2[i] = pow2[i - 1] * 2;
		
		int t = 1;
		
		while(t-- > 0) {
			
			int n = s.nextInt();
			
			ArrayList<Long> list = new ArrayList<Long>();
				
			for(int i = 0; i < n; i++) 
				list.add(s.nextLong());
			
			int res = 1;
			long r1 = list.get(0), r2 = 0, r3 = 0;
			
			Collections.sort(list);
			
			int[][] dp = new int[n][35];
			
			for(int i = 0; i < n; i++) {
				
				for(int j = 0; j < 35; j++) {
					
					dp[i][j] = -1;
					
					long x = list.get(i) - pow2[j];
					
					int l = 0, r = i - 1;
					
					while(l <= r) {
						
						int mid = (l + r) / 2;
						
						if(list.get(mid) == x) {
							//w.println(list.get(i) + " " + list.get(mid) + " " + pow2[j]);
							dp[i][j] = mid; res = 2; r1 = list.get(i); r2 = list.get(mid); break;
						}
						else if(list.get(mid) < x)
							l = mid + 1;
						else 
							r = mid - 1;
					}
				}
			}
			
			if(res == 1) {
				w.println(res);
				w.println(r1); continue;
			}
			
			outerloop:
			for(int i = 0; i < n; i++) {
				
				for(int j = 0; j < 35; j++) {
					
					long x = list.get(i) - pow2[j];
					
					int l = 0, r = i - 1;
					
					while(l <= r) {
						
						int mid = (l + r) / 2;
						
						if(list.get(mid) == x) {
							
							if(dp[mid][j] != -1) {
								res = 3; r1 = list.get(dp[mid][j]); r2 = list.get(mid); r3 = list.get(i); break outerloop;
							}
							else
								break;
						}
						else if(list.get(mid) < x)
							l = mid + 1;
						else 
							r = mid - 1;
					}
				}
			}
			
			w.println(res);
			
			if(res == 2) 
				w.println(r1 + " " + r2);
			else 
				w.println(r1 + " " + r2 + " " + r3);
		}
		
		w.close();
	}
	
	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 String nextLine()
		{
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
        try
        {
            str = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
	}
	public int nextInt()
	{
		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 long nextLong() 
	{
		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 double nextDouble() 
	{
		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, nextInt());
			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, nextInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				m /= 10;
				res += (c - '0') * m;
				c = read();
			}
		}
		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 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);
	}
}

public static void main(String args[]) throws Exception
{
	new Thread(null, new cf4(),"cf4",1<<26).start();
	}
}