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:
/*
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 * and open the template in the editor.
 */

/**
 *
 * @author romit17
 */
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Hashtable;
import java.util.Random;
import java.util.InputMismatchException;

public class D988{
    
    void solve() throws IOException {
        PrintWriter out = new PrintWriter(System.out);
        StringBuilder sb = new StringBuilder("");        
        int n = ni();
        long[] a = na(n);randomize(a, n);
        Arrays.sort(a);
        Hashtable<Long,Integer> h = new Hashtable<>();
        Hashtable<Integer,Integer>[] hh = new Hashtable[n];
        for(int i=0;i<n;i++)
            hh[i] = new Hashtable<>();
        for(int i=0;i<n;i++)
            h.put(a[i], i);
        
        long hg = a[n-1];
        for(int i=n-2;i>=0;i--)
        {
            int count = -1;
            long val;
            while((val=(a[i]+(1L<<++count)))<=hg)
            {
                if(!h.containsKey(val))
                    continue;
                int index = h.get(val);
                if(hh[index].containsKey(count))
                {
                    System.out.println(3);
                    System.out.println(a[i]+" "+val+" "+a[hh[index].get(count)]);
                    return;
                }
                hh[i].put(count,index);
            }
        }
        for(int i=0;i<n;i++)
        {
            if(hh[i].size()>0)
            {
                int temp = -1;
                for(int tt:hh[i].values())
                {
                    temp = tt;
                    break;
                }
                System.out.println(2);
                System.out.println(a[i]+" "+a[temp]);
                return;
            }
        }
        System.out.println(1);
        System.out.println(a[0]);
    }
    
    static void randomize( long arr[], int n)
    {
        // Creating a object for Random class
        Random r = new Random();
         
        // Start from the last element and swap one by one. We don't
        // need to run for the first element that's why i > 0
        for (int i = n-1; i > 0; i--) {
             
            // Pick a random index from 0 to i
            int j = r.nextInt(i);
             
            // Swap arr[i] with the element at random index
            long temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }
    
    public static void main(String[] args) throws IOException {
        new D988().solve();
    }    
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;    
    InputStream is = System.in;

    private int readByte() {
        if (lenbuf == -1) {
            throw new InputMismatchException();
        }
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) {
                return -1;
            }
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }
    
    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b));
        return b;
    }
    
    private double nd() {
        return Double.parseDouble(ns());
    }
    
    private char nc() {
        return (char) skip();
    }
    
    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) {
            map[i] = ns(m);
        }
        return map;
    }
    
    private long[] na(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nl();
        }
        return a;
    }
    
    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
}