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.*;

// Driver program to read from file/System.in and increase stack size
public class Main implements Runnable {
  private final InputReader in;
  private final OutputWriter out;

  private Main(InputReader ir, OutputWriter or) {
    in = ir;
    out = or;
  }

  public static void main(String[] args) throws Exception {
    InputStream is = args.length > 0 ? new FileInputStream(args[0]) : System.in;
    InputReader in = new InputReader(is);
    OutputWriter out = new OutputWriter(System.out);
    Main r = new Main(in, out);
    new Thread(null, r, "Main", 1 << 26).start(); // 64 mb stack size
  }

  @Override
  public void run() {
    try {
      Solution.main(in, out);
    } finally {
      out.close();
    }
  }
}

class Solution {
  static void main(InputReader in, OutputWriter out) {
    int n = in.nextInt();
    long[] xs = new long[n];
    Set<Long> set = new HashSet<>(n);
    for (int i = 0; i < n; i++) {
      xs[i] = in.nextLong();
      set.add(xs[i]);
    }

    int m = 1;
    long[] res = new long[] { xs[0], Integer.MAX_VALUE, Integer.MAX_VALUE };

    outer:
    for (int i = 0; i < n; i++) {
      long elem = xs[i];
      for (int j = 0; j < 32; j++) {
        long dst = 1L << j;
        if (set.contains(elem + dst) && set.contains(elem - dst)) {
          m = 3;
          res[0] = elem;
          res[1] = elem + dst;
          res[2] = elem - dst;
          break outer;
        }
        if (m < 2 && set.contains(elem + dst)) {
          m = 2;
          res[0] = elem;
          res[1] = elem + dst;
        }
        if (m < 2 && set.contains(elem - dst)) {
          m = 2;
          res[0] = elem;
          res[1] = elem - dst;
        }
      }
    }

    out.println(m);
    out.print(res[0]);
    for (int i = 1; i < m; i++) {
      out.print(' ');
      out.print(res[i]);
    }
  }
}


// Fast I/O
// Taken and modified from here:
// https://www.quora.com/What-is-the-best-way-in-Java-to-take-input-and-write-output-for-an-Online-Judge
class InputReader {
  private InputStream is;
  private byte[] buff = new byte[8 * 1024];
  private int curChar;
  private int numChars;

  InputReader(InputStream is) {
    this.is = is;
  }

  int read() {
    if (numChars == -1) throw new InputMismatchException();
    if (curChar >= numChars) {
      curChar = 0;
      try {
        numChars = is.read(buff);
      } catch (IOException e) {
        throw new InputMismatchException();
      }
      if (numChars <= 0) return -1;
    }
    return buff[curChar++];
  }

  int nextInt() {
    int c = read();
    while (isSpaceChar(c)) c = read();
    int sgn = 1;
    if (c == '-') {
      sgn = -1;
      c = read();
    }
    int res = 0;
    do {
      if (c < '0' || c > '9')
        throw new InputMismatchException();
      res *= 10;
      res += c - '0';
      c = read();
    } while (!isSpaceChar(c));
    return res * sgn;
  }

  String nextString() {
    int c = read();
    while (isSpaceChar(c)) c = read();
    StringBuilder res = new StringBuilder();
    do {
      res.appendCodePoint(c);
      c = read();
    } while (!isSpaceChar(c));
    return res.toString();
  }

  double nextDouble() {
    int c = read();
    while (isSpaceChar(c)) c = read();
    int sgn = 1;
    if (c == '-') {
      sgn = -1;
      c = read();
    }
    double res = 0;
    while (!isSpaceChar(c) && c != '.') {
      if (c == 'e' || c == 'E')
        return res * Math.pow(10, nextInt());
      if (c < '0' || c > '9')
        throw new InputMismatchException();
      res *= 10;
      res += c - '0';
      c = read();
    }
    if (c == '.') {
      c = read();
      double m = 1;
      while (!isSpaceChar(c)) {
        if (c == 'e' || c == 'E') return res * Math.pow(10, nextInt());
        if (c < '0' || c > '9') throw new InputMismatchException();
        m /= 10;
        res += (c - '0') * m;
        c = read();
      }
    }
    return res * sgn;
  }

  long nextLong() {
    int c = read();
    while (isSpaceChar(c)) c = read();
    int sgn = 1;
    if (c == '-') {
      sgn = -1;
      c = read();
    }
    long res = 0;
    do {
      if (c < '0' || c > '9') throw new InputMismatchException();
      res *= 10;
      res += c - '0';
      c = read();
    } while (!isSpaceChar(c));
    return res * sgn;
  }

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

  String next() {
    return nextString();
  }

  int[] nextIntArray(int size) {
    int[] arr = new int[size];
    for (int i = 0; i < size; i++) arr[i] = nextInt();
    return arr;
  }
}
class OutputWriter {
  private final PrintWriter writer;

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

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

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

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

  void printf(String format, Object... objects) {
    writer.printf(format, objects);
  }

  void printfln(String format, Object... objects) {
    writer.printf(format + "\n", objects);
  }

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

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