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.*;
import java.util.*;


public class Main {
	public static String taskName = "";

	public class Task {
		public void solve(int testNumber, InputReader in, PrintWriter out) {
			int[] power = {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824};
			int n = in.nextInt();
			Set<Integer> xs = new HashSet<>();
			int[] x = new int[n];
			for(int i = 0; i < n; i++) {
				x[i] = in.nextInt();
				xs.add(x[i]);
			}

			int m = 1;
			int c = x[0];
			int pow = 0;
			boolean flag = false;
			for(int i = 0; i < n; i++) {
				for(int k = 0; k < 31; k++) {
					if(xs.contains(x[i] - power[k]) && xs.contains(x[i] + power[k])) {
						m = 3;
						c = x[i];
						pow = power[k];
						flag = true;
						break;
					}
					if(xs.contains(x[i] - power[k]) || xs.contains(x[i] + power[k])) {
						m = 2;
						c = x[i];
						pow = power[k];
					}
				}
				if(flag)
					break;
			}

			out.println(m);
			if(m == 1)
				out.println(c);
			else if(m == 2)
				out.println(c + " " + (xs.contains(c + pow) ? c + pow : c - pow));
			else
				out.println((c - pow) + " " + c + " " + (c + pow));
		}
	}

	public static void main(String[] args) throws FileNotFoundException {
		if(!taskName.isEmpty()) {
			System.setIn(new BufferedInputStream(new FileInputStream(taskName + ".in")));
			System.setOut(new PrintStream(new BufferedOutputStream(new FileOutputStream(taskName + ".out"))));
		}
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Main main = new Main();
		main.run(in, out);
		out.close();
	}

	public void run(InputReader in, PrintWriter out) {
		Task solver = new Task();
		solver.solve(1, in, out);
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while(tokenizer == null || !tokenizer.hasMoreTokens())
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch(IOException e) {
					throw new RuntimeException(e);
				}
			return tokenizer.nextToken();
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public double nextShort() {
			return Short.parseShort(next());
		}

		public double nextByte() {
			return Byte.parseByte(next());
		}

		public double nextFloat() {
			return Float.parseFloat(next());
		}
	}
}