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.io.*;
public class PointsandPowersofTwo {
    
    
    
    /************************ SOLUTION STARTS HERE ************************/

	static final long MAX_LIMIT = (long) 2.5e9;
	
	static void shuffleArray(long[] array) {
		Random random = new Random();
		for (int i = array.length - 1; i > 0; i--) {
			int index = random.nextInt(i + 1);
			long temp = array[index];
			array[index] = array[i];
			array[i] = temp;
		}
	}
	
	private static void solve() {
		
		int n = nextInt();
		long arr[] = nextLongArray(n);
		shuffleArray(arr);
		Arrays.sort(arr);
		
		int atPowOf2DistToRight[][] = new int[n][40];
		HashMap<Long, Integer> posMap = new HashMap<Long, Integer>();
		posMap.put(arr[n - 1], n -1);
		Arrays.fill(atPowOf2DistToRight[n - 1], -1);
		
//		System.out.println(Arrays.toString(arr));
		
		for(int i = n - 2; i >= 0; i--) {
			long pow = 1;
			Arrays.fill(atPowOf2DistToRight[i], -1);
			for(int j = 0; pow <= MAX_LIMIT; pow *= 2L, j++)
				if(posMap.containsKey(arr[i] + pow))
					atPowOf2DistToRight[i][j] = posMap.get(arr[i] + pow);
			
			posMap.put(arr[i], i);
			
		}
		
//		for(int i = 0; i < n; i++)
//			System.out.println(arr[i] + " => " + Arrays.toString(atPowOf2DistToRight[i]));
		
		for(int i = n - 2; i >= 0; i--) {
			long pow = 1;
			for(int j = 0; pow <= MAX_LIMIT; pow *= 2L, j++) 
				if(atPowOf2DistToRight[i][j] >= 0 && atPowOf2DistToRight[atPowOf2DistToRight[i][j]][j] >= 0) {
					println(3);
					long f = arr[i];
					long s = arr[atPowOf2DistToRight[i][j]];
					long t = arr[atPowOf2DistToRight[atPowOf2DistToRight[i][j]][j]];
					println(String.format("%d %d %d", f , s , t));
					return;
				}
		}
		
		for(int i = n - 2; i >= 0; i--) {
			long pow = 1;
			for(int j = 0; pow <= MAX_LIMIT; pow *= 2L, j++) 
				if(atPowOf2DistToRight[i][j] >= 0) {
					println(2);
					println(arr[i] + " " + arr[atPowOf2DistToRight[i][j]]);
					return;
				}
		}
		
		println(1);
		println(arr[0]);
		
		
		
	}
	
    
    /************************ SOLUTION ENDS HERE ************************/
    
    
    
    
    
    /************************ TEMPLATE STARTS HERE **********************/
    
    public static void main(String[] args) throws IOException {
        reader = new BufferedReader(new InputStreamReader(System.in));
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)), false);
        st     = null;
        solve();
        reader.close();
        writer.close();
    }
    
    static BufferedReader reader;
    static PrintWriter    writer;
    static StringTokenizer st;
    
    static String next()
    {while(st == null || !st.hasMoreTokens()){try{String line = reader.readLine();if(line == null){return null;}            
    st = new StringTokenizer(line);}catch (Exception e){throw new RuntimeException();}}return st.nextToken();}
    static String nextLine()  {String s=null;try{s=reader.readLine();}catch(IOException e){e.printStackTrace();}return s;}             
    static int    nextInt()   {return Integer.parseInt(next());}
    static long   nextLong()  {return Long.parseLong(next());}     
    static double nextDouble(){return Double.parseDouble(next());}
    static char   nextChar()  {return next().charAt(0);}
    static int[]  nextIntArray(int n)         {int[] a= new int[n];   int i=0;while(i<n){a[i++]=nextInt();}  return a;}
    static long[] nextLongArray(int n)        {long[]a= new long[n];  int i=0;while(i<n){a[i++]=nextLong();} return a;}    
    static int[]  nextIntArrayOneBased(int n) {int[] a= new int[n+1]; int i=1;while(i<=n){a[i++]=nextInt();} return a;}            
    static long[] nextLongArrayOneBased(int n){long[]a= new long[n+1];int i=1;while(i<=n){a[i++]=nextLong();}return a;}            
    static void   print(Object o)  { writer.print(o);  }
    static void   println(Object o){ writer.println(o);}
    
    /************************ TEMPLATE ENDS HERE ************************/
    
}