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.*;
import java.math.*;
public class Main{
	static int mod = (int)1e9+7;
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	public static void main(String sp[])throws IOException{
		FastReader sc = new FastReader();
		long n = sc.nextLong();
		ArrayList<Long> al = new ArrayList<>();
		for(int i=0;i<n;i++)
			al.add(sc.nextLong());
		HashMap<Long,Integer> hm = new HashMap<>();
		for(int i=0;i<n;i++)
			hm.put(al.get(i),0);
		boolean b=true;
		
		Collections.sort(al);
		int maxcount=Integer.MIN_VALUE;
		String df="";
		
		long min  = Collections.min(al);
		long max  = Collections.max(al);
		for(int i=0;i<n;i++){
			long val = al.get(i);
			int j=0;
			long calc = 1;
			while(b==true){
				StringBuilder sb = new StringBuilder();
				sb.append(val+" ");
				int count=1;
				if(count>maxcount){
					maxcount=count;
					df=sb.toString();
				}
				calc = (long)Math.pow(2,j);
				j++;
				if(hm.containsKey(val-calc)){
					count++;
					sb.append(val-calc+" ");
					if(count>maxcount){
						maxcount=count;
						df=sb.toString();
					}
					if(hm.containsKey(val+calc)){
						count++;
						sb.append(val+calc+" ");
						if(count>maxcount){
							maxcount=count;
							df=sb.toString();
						}
					}
				}else if(hm.containsKey(val+calc)){
					count++;
					sb.append(val+calc+" ");
					if(count>maxcount){
						maxcount=count;
						df=sb.toString();
					}
				}
			
				if(j==34)
					break;
			}
		}
		
		System.out.println(maxcount);
		System.out.println(df)	;
	}
	
	public static int[] swap(int[] arr, int low, int high){
		int temp = arr[low];
		arr[low]=arr[high];
		arr[high]=temp;
		return arr;
	}
	
	
	public static long gcd(long a, long b){
		if(a==0)
			return b;
		
		return gcd(b%a,a);
	}
	
	public static void print(int[] arr){
		for(int i=0;i<arr.length;i++)
			System.out.print(arr[i]+" ");
		System.out.println();
	}
	
	public static class pair{
		int ai;
		int bi;
	}
	
	public static class comp implements Comparator<pair>{
		public int compare(pair o1, pair o2){
			return o1.bi-o2.bi;
		}
	}
	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;
	
 
		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception r) {
					r.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(next());//converts string to integer
		}
 
		double nextDouble() {
			return Double.parseDouble(next());
		}
 
		long nextLong() {
			return Long.parseLong(next());
		}
 
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception r) {
				r.printStackTrace();
			}
			return str;
		}
	}
	
}