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.DataInputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.Set;

//题意：给定n个坐标轴上的点，选出最多的点满足任意两点之间距离为2的幂
public class D {
    Reader in;
    PrintWriter out;
    public static void main(String[] args)
    {
        new D().runIO();
    }

    private void runIO() {
        in = new Reader();
        out = new PrintWriter(System.out, false);
        solve();
        out.close();
    }

    private void solve() {
        int n = in.nextInt();
        long[] points = new long[n];
        HashSet<Long> pset = new HashSet<Long>();
        for (int i=0; i<n; i++){
            points[i] = in.nextLong();
            pset.add(points[i]);
        }

        int flag = 1;
        long ans1 = -999;
        long ansdi = -999;

        for (int i=0; i<n; i++){
            for(long di = 1; di <= 2e9; di <<= 1){
                if (pset.contains(points[i] + di) &&
                        pset.contains(points[i] + 2 * di)){
                    flag = 3;
                    ans1 = points[i];   ansdi = di;
                    break;
                }
            }
            if (flag != 1)
                break;
        }

        for (int i=0; i<n; i++){
            if (flag != 1)
                break;
            for (long di = 1; di <= 2e9; di <<= 1){
                if (pset.contains(points[i] + di)){
                    flag = 2;
                    ans1 = points[i];
                    ansdi = di;
                    break;
                }
            }
            if (flag != 1)
                break;
        }

        System.out.println(flag);
        if (flag == 1){
            System.out.println(points[0]);
        } else if (flag == 2){
            long ans2 = ans1 + ansdi;
            System.out.println(ans1 + " " + ans2);
        }else {
            long ans2 = ans1 + ansdi;
            long ans3 = ans2 + ansdi;
            System.out.println(ans1 + " " + ans2 + " " + ans3);
        }
    }


    // input/output
    static class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader()
        {
            din = new DataInputStream(System.in);

            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }



        public final String next()
        {
            int c = read();
            while (isSpaceChar(c))
            {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do
            {
                res.append((char) c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        private boolean isSpaceChar(int c)
        {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int nextInt()
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong()
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble()
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (c == '.')
                while ((c = read()) >= '0' && c <= '9')
                    ret += (c - '0') / (div *= 10);
            if (neg)
                return -ret;
            return ret;
        }

        public int[] readIntArray(int size)
        {
            int[] arr = new int[size];
            for (int i = 0; i < size; i++)
                arr[i] = nextInt();
            return arr;
        }

        public long[] readLongArray(int size)
        {
            long[] arr = new long[size];
            for (int i = 0; i < size; i++)
                arr[i] = nextInt();
            return arr;
        }

        private void fillBuffer()
        {
            try
            {
                bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            }
            catch (IOException e)
            {

            }

            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read()
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
    }
}