Problem: Define the simple skewness of a collection of numbers to be the collection's mean minus its median. You are given a list of n (not necessarily distinct) integers. Find the non-empty subset (with repetition) with the maximum simple skewness.

The mean of a collection is the average of its elements. The median of a collection is its middle element when all of its elements are sorted, or the average of its two middle elements if it has even size.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 200 000) — the number of elements in the list.

The second line contains n integers xi (0 ≤ xi ≤ 1 000 000) — the ith element of the list.

Output

In the first line, print a single integer k — the size of the subset.

In the second line, print k integers — the elements of the subset in any order.

If there are multiple optimal subsets, print any.

Examples

Input

4
1 2 3 12


Output

3
1 2 12 


Input

4
1 1 2 2


Output

3
1 1 2 


Input

2
1 2


Output

2
1 2

Note

In the first case, the optimal subset is <image>, which has mean 5, median 2, and simple skewness of 5 - 2 = 3.

In the second case, the optimal subset is <image>. Note that repetition is allowed.

In the last case, any subset has the same median and mean, so all have simple skewness of 0.

Solution (in JAVA):

Solution:
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.InputStream;
import java.util.Random;
import java.io.OutputStreamWriter;
import java.math.BigInteger;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.IOException;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author ilyakor
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskE solver = new TaskE();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskE {
    int[] a;
    long[] sum;
    int n;

    public void solve(int testNumber, InputReader in, OutputWriter out) {
        n = in.nextInt();
        a = new int[n];
        for (int i = 0; i < n; ++i) {
            a[i] = in.nextInt();
        }

        Random random = new Random();


        for (int i = 0; i < n; ++i) {
            int j = random.nextInt(n);
            if (i != j) {
                int t = a[i];
                a[i] = a[j];
                a[j] = t;
            }
        }
        Arrays.sort(a);

        sum = new long[a.length + 1];
        for (int i = 0; i < a.length; ++i)
            sum[i + 1] = sum[i] + a[i];


        BigRational ans = new BigRational(Long.MIN_VALUE);
        int ai = -1, ak = -1;
        for (int i = 0; i < 2 * n - 1; ++i) {
            int l0 = i / 2, r0 = (i + 1) / 2;
            int num0 = l0 == r0 ? a[l0] : (a[l0] + a[r0]);
            int den0 = i % 2 == 0 ? 1 : 2;

            int down = 0, up = n + 2;
            while (up - down > 1) {
                int t = (up + down) / 2;
                int l1 = l0 - t;
                int l2 = n - t;
                if (l2 <= r0 || l1 < 0) {
                    up = t;
                    continue;
                }

                long num = getSum(l1, l0 - 1) + getSum(l2, n - 1);
                long den = 2 * t;
                num += num0;
                den += den0;

                long prevNum = getSum(l1 + 1, l0 - 1) + getSum(l2 + 1, n - 1);
                long prevDen = 2 * t - 2;
                prevNum += num0;
                prevDen += den0;

                if (BigInteger.valueOf(num).multiply(BigInteger.valueOf(prevDen)).subtract(BigInteger.valueOf(den).multiply(BigInteger.valueOf(prevNum))).compareTo(BigInteger.ZERO) >= 0) {
                    down = t;
                } else {
                    up = t;
                }
            }

            int l1 = l0 - down;
            int l2 = n - down;
            long num = getSum(l1, l0 - 1) + getSum(l2, n - 1);
            long den = 2 * down;
            num += num0;
            den += den0;

            BigRational cur = new BigRational(BigInteger.valueOf(num), BigInteger.valueOf(den));
            cur = cur.subtract(new BigRational(BigInteger.valueOf(num0), BigInteger.valueOf(den0)));
            if (cur.compareTo(ans) > 0) {
                ans = cur;
                ai = i;
                ak = down;
            }
        }

        int l0 = ai / 2, r0 = (ai + 1) / 2;
        int l1 = l0 - ak;
        int l2 = n - ak;
        int den0 = ai % 2 == 0 ? 1 : 2;
        den0 += 2 * ak;
        out.printLine(den0);
        for (int i = l1; i < l0; ++i)
            out.print(a[i] + " ");
        for (int i = l0; i <= r0; ++i)
            out.print(a[i] + " ");
        for (int i = l2; i < n; ++i)
            out.print(a[i] + " ");
        out.printLine();
    }

    long getSum(int l, int r) {
        if (l > r)
            return 0;
        return sum[r + 1] - sum[l];
    }
}

class InputReader {
    private InputStream stream;
    private byte[] buffer = new byte[10000];
    private int cur;
    private int count;

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

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

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

    public int readSkipSpace() {
        int c;
        do {
            c = read();
        } while (isSpace(c));
        return c;
    }

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

}

class OutputWriter {
    private final PrintWriter writer;

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

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

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

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

}

class BigRational implements Comparable<BigRational> {
    BigInteger num, den;

    public BigRational(BigInteger num, BigInteger den) {
        this.num = num;
        this.den = den;
        if (den.compareTo(BigInteger.ZERO) < 0) {
            this.num = this.num.negate();
            this.den = this.den.negate();
        }
    }

    public BigRational(long x) {
        this.num = BigInteger.valueOf(x);
        this.den = BigInteger.ONE;
    }

    public int compareTo(BigRational other) {
        return num.multiply(other.den).subtract(den.multiply(other.num)).compareTo(BigInteger.ZERO);
    }

    public BigRational subtract(BigRational other) {
        return new BigRational(num.multiply(other.den).subtract(den.multiply(other.num)), den.multiply(other.den));
    }
}