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 _988_D_PointsAndPowersOfTwo {

	public static void main(String[] args) throws IOException {
		int N=readInt();Long arr[] = new Long[N+1];for(int i = 1; i<=N; i++) arr[i] = readLong(); Arrays.sort(arr, 1, N+1);
		int ans1 = 0, ans2 = 0; for(int i = 1; i<=N; i++) for(int j = 0; j<31; j++) {
			int idx1 = Arrays.binarySearch(arr, 1, N+1, arr[i] - (1L<<j)), 
					idx2 = Arrays.binarySearch(arr, 1, N+1, arr[i] + (1L<<j));
			if(idx1 > 0 && idx2 > 0) {println(3); println(arr[idx1] + " " + arr[idx2] + " " + arr[i]); exit();}  
			if(idx1 > 0 || idx2 > 0) {ans1 = i; ans2 = idx1 > 0 ? idx1 : idx2;}
		}
		if(ans1 > 0) {println(2); println(arr[ans1] + " " + arr[ans2]);} else {println(1); println(arr[1]);}
		exit();
	}


	final private static int BUFFER_SIZE = 1 << 16;
	private static DataInputStream din = new DataInputStream(System.in);
	private static byte[] buffer = new byte[BUFFER_SIZE];
	private static int bufferPointer = 0, bytesRead = 0;
	static PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

	public static String readLine() throws IOException {
		byte[] buf = new byte[64]; // line length
		int cnt = 0, c;
		while ((c = Read()) != -1) {
			if (c == '\n')
				break;
			buf[cnt++] = (byte) c;
		}
		return new String(buf, 0, cnt);
	}

	public static String read() throws IOException {
		byte[] ret = new byte[1024];
		int idx = 0;
		byte c = Read();
		while (c <= ' ') {
			c = Read();
		}
		do {
			ret[idx++] = c;
			c = Read();
		} while (c != -1 && c != ' ' && c != '\n' && c != '\r');
		return new String(ret, 0, idx);
	}

	public static int readInt() throws IOException {
		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 static long readLong() throws IOException {
		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 static double readDouble() throws IOException {
		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;
	}

	private static void fillBuffer() throws IOException {
		bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
		if (bytesRead == -1)
			buffer[0] = -1;
	}

	private static byte Read() throws IOException {
		if (bufferPointer == bytesRead)
			fillBuffer();
		return buffer[bufferPointer++];
	}

	static void print(Object o) {
		pr.print(o);
	}

	static void println(Object o) {
		pr.println(o);
	}

	static void flush() {
		pr.flush();
	}

	static void println() {
		pr.println();
	}

	static void exit() throws IOException {
		din.close();
		pr.close();
		System.exit(0);
	}


}