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.BigInteger;
import java.sql.Struct;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.StringTokenizer;

public class Main {
    static class TEST_CASES {

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt ();
            long[] a = in.nextLongArray (n);
            HashMap<Long, Boolean> mp = new HashMap<> ();
            for (int i = 0; i < n; i++) {
                mp.put (a[i], true);
            }

            for (int i = 0; i < n; i++) {
                long now = a[i];
                for (long j = 0; j < 32; j++) {
                    long jog = ((long)1 << j);
                    if (mp.containsKey (now + jog) && mp.containsKey (now + jog + jog)) {
                        out.println ("3\n" + now + " " + (now + jog) + " " + (now + jog + jog));
                        return;
                    }
                }
            }
            for (int i = 0; i < n; i++) {
                long now = a[i];
                for (long j = 0; j < 32; j++) {
                    long jog = ((long)1 << j);
                    if (mp.containsKey (now + jog) ) {
                        out.println ("2\n" + now + " " + (now + jog));
                        return;
                    }
                }
            }
            out.println ("1\n" + a[0]);

        }

    }

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader (inputStream);
        PrintWriter out = new PrintWriter (outputStream);
        int t = 1;
        //t = in.nextInt ();
        for (int i = 0; i < t; i++) {
            TEST_CASES solver = new TEST_CASES ();
            solver.solve (1, in, out);
        }
        out.close ();
    }

    static class InputReader {
        private boolean finished = false;

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

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

        public int peek() {
            if (numChars == -1) {
                return -1;
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read (buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar];
        }

        public 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;
        }

        public 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;
        }

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

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar (c);
            }
            return isWhitespace (c);
        }

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

        private String readLine0() {
            StringBuilder buf = new StringBuilder ();
            int c = read ();
            while (c != '\n' && c != -1) {
                if (c != '\r') {
                    buf.appendCodePoint (c);
                }
                c = read ();
            }
            return buf.toString ();
        }

        public String readLine() {
            String s = readLine0 ();
            while (s.trim ().length () == 0) {
                s = readLine0 ();
            }
            return s;
        }

        public String readLine(boolean ignoreEmptyLines) {
            if (ignoreEmptyLines) {
                return readLine ();
            }
            else {
                return readLine0 ();
            }
        }

        public BigInteger readBigInteger() {
            try {
                return new BigInteger (nextString ());
            } catch (NumberFormatException e) {
                throw new InputMismatchException ();
            }
        }

        public char nextCharacter() {
            int c = read ();
            while (isSpaceChar (c)) {
                c = read ();
            }
            return (char) c;
        }

        public 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;
        }

        public boolean isExhausted() {
            int value;
            while (isSpaceChar (value = peek ()) && value != -1) {
                read ();
            }
            return value == -1;
        }

        public String next() {
            return nextString ();
        }

        public SpaceCharFilter getFilter() {
            return filter;
        }

        public void setFilter(SpaceCharFilter filter) {
            this.filter = filter;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }

        public int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) array[i] = nextInt ();
            return array;
        }

        public int[] nextSortedIntArray(int n) {
            int array[] = nextIntArray (n);
            Arrays.sort (array);
            return array;
        }

        public int[] nextSumIntArray(int n) {
            int[] array = new int[n];
            array[0] = nextInt ();
            for (int i = 1; i < n; ++i) array[i] = array[i - 1] + nextInt ();
            return array;
        }

        public long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; ++i) array[i] = nextLong ();
            return array;
        }

        public long[] nextSumLongArray(int n) {
            long[] array = new long[n];
            array[0] = nextInt ();
            for (int i = 1; i < n; ++i) array[i] = array[i - 1] + nextInt ();
            return array;
        }

        public long[] nextSortedLongArray(int n) {
            long array[] = nextLongArray (n);
            Arrays.sort (array);
            return array;
        }
    }

}