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.math.*;
import java.util.*;

/*
   author : Multi-Thread
*/
public class A {

	// static int INF = 998244353;
	static int INF = (int) 1e9 + 7;
	static int MAX = Integer.MAX_VALUE;
	static int MIN = Integer.MIN_VALUE;

	public static void main(String[] args) {

		// int test = fs.nextInt();
		int test = 1;

		for (int cases = 0; cases < test; cases++) {

			solve();
//			System.out.println(solve());

		}
	}

	static void solve() {
		int n = fs.nextInt();
		ArrayList<Integer> al = new ArrayList<Integer>();
		HashSet<Integer> set = new HashSet<Integer>();
		for (int i = 0; i < n; i++) {
			int x = fs.nextInt();
			set.add(x);
			al.add(x);
		}
		int powers[] = new int[32];
		for (int i = 0; i < 32; i++) {
			powers[i] = (int) Math.pow(2, i);
		}
		int nn = -1, ee = -1;
		for (int i = 0; i < al.size(); i++) {
			int element = al.get(i);
			for (int a = 0; a < 31; a++) {
				int aa = powers[a];
				int nnn = element + aa;
				if (set.contains(nnn)) {
					ee = element;
					nn = nnn;
				}
				for (int b = 0; b < 31; b++) {
					int bb = powers[b];
					int prev = element - aa;
					int next = element + bb;
					int diff = Math.abs(next - prev);
					if (Integer.bitCount(diff) == 1) {
						if (set.contains(prev) && set.contains(next)) {
							System.out.println(3);
							System.out.println(prev + " " + element + " " + next);
							return;
						}
						prev = element - bb;
						next = element + aa;
						if (set.contains(prev) && set.contains(next)) {
							System.out.println(3);
							System.out.println(prev + " " + element + " " + next);
							return;
						}
					}
				}
			}
		}

		if (ee != -1) {
			System.out.println(2);
			System.out.println(ee + " " + nn);
			return;
		}
		System.out.println(1);
		System.out.println(al.get(0));

	}

	static int _min(int... ar) {
		intSort(ar, true);
		return ar[ar.length - 1];
	}

	static int _max(int... ar) {
		intSort(ar, true);
		return ar[ar.length - 1];
	}

	static void intSort(int[] a, boolean reverse) {
		ArrayList<Integer> al = new ArrayList<Integer>();
		for (int i : a)
			al.add(i);
		Collections.sort(al);
		if (reverse) {
			for (int i = 0; i < a.length; i++)
				a[i] = al.get(a.length - i - 1);
		} else {
			for (int i = 0; i < a.length; i++)
				a[i] = al.get(i);
		}
	}

	static void longSort(long[] a, boolean reverse) {
		ArrayList<Long> al = new ArrayList<>();
		for (long i : a)
			al.add(i);
		Collections.sort(al);
		if (reverse) {
			for (int i = 0; i < a.length; i++)
				a[i] = al.get(a.length - i - 1);
		} else {
			for (int i = 0; i < a.length; i++)
				a[i] = al.get(i);
		}
	}

	public static int[] radixSort(int[] f) {
		return radixSort(f, f.length);
	}

	public static int[] radixSort(int[] f, int n) {
		int[] to = new int[n];
		{
			int[] b = new int[65537];
			for (int i = 0; i < n; i++)
				b[1 + (f[i] & 0xffff)]++;
			for (int i = 1; i <= 65536; i++)
				b[i] += b[i - 1];
			for (int i = 0; i < n; i++)
				to[b[f[i] & 0xffff]++] = f[i];
			int[] d = f;
			f = to;
			to = d;
		}
		{
			int[] b = new int[65537];
			for (int i = 0; i < n; i++)
				b[1 + (f[i] >>> 16)]++;
			for (int i = 1; i <= 65536; i++)
				b[i] += b[i - 1];
			for (int i = 0; i < n; i++)
				to[b[f[i] >>> 16]++] = f[i];
			int[] d = f;
			f = to;
			to = d;
		}
		return f;
	}

	static class Pair {
		int first, second;

		public Pair(int first, int second) {
			this.first = first;
			this.second = second;
		}

		public String toString() {
			return "[" + first + "," + second + "]";
		}
	}

	static class LongPair {
		long first;
		long second;

		LongPair(long a, long b) {
			this.first = a;
			this.second = b;
		}

		public String toString() {
			return "[" + first + "," + second + "]";
		}
	}

	static boolean isPrime(long n) {
		// Corner cases
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;
		if (n % 2 == 0 || n % 3 == 0)
			return false;

		long sq = (long) Math.sqrt(n);
		for (int i = 5; i <= sq; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;

		return true;
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

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

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	static class OutputWriter {
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}

		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}

		public void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		public void println() {
			writer.print("\n");
		}

		public void printLine(Object... objects) {
			print(objects);
			writer.println();
		}

		public void close() {
			writer.close();
		}

		public void flush() {
			writer.flush();
		}

	}

	private static final FastReader fs = new FastReader();
	private static final OutputWriter out = new OutputWriter(System.out);
}