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.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * @author pttrung
 */
public class E_8VC_2016_Round1 {

    public static long MOD = 1000000007;

    public static void main(String[] args) throws FileNotFoundException {
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File(
        // "output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        int n = in.nextInt();
        long[] data = new long[n];
        for (int i = 0; i < n; i++) {
            data[i] = in.nextInt();
        }
        Arrays.sort(data);
        long[] total = new long[n];
        total[0] = data[0];
        for (int i = 1; i < n; i++) {
            total[i] = data[i] + total[i - 1];
        }
        long[] result = {0, 1};
        int index = 0;
        int l = 0;
        boolean two = false;
        for (int i = 0; i < n; i++) {
            //System.out.println(result);
            int left = i;
            int right = n - i - 1;
            int start = 0;
            int end = left > right ? right : left;

            while (start < end) {
                int mid = (start + end) / 2;
                // System.out.println(mid + " " +i + " " + end);
                long[] a = cal(false, mid, i, n, new long[]{data[i], 1}, total);
                long[] b = cal(false, mid + 1, i, n, new long[]{data[i], 1}, total);
                if (compare(a, b) > 0) {
                    end = mid - 1;
                    if (compare(result, a) < 0) {
                        result = a;
                        index = i;
                        l = mid;
                        two = false;
                    }
                } else {
                    start = mid + 1;
                    if (compare(result, b) < 0) {
                        result = b;
                        index = i;
                        l = mid + 1;
                        two = false;
                    }
                }
            }
            // System.out.println("After " + result);
            if (i > 0) {
                left = i - 1;
                right = n - i - 1;
                start = 0;
                end = left > right ? right : left;
                //System.out.println(left + " " + right + " " + i);
                long[] mean = {data[i] + data[i - 1], 2};
                while (start < end) {
                    int mid = (start + end) / 2;
                    // System.out.println(mid + " " +i + " " + end);
                    long[] a = cal(true, mid, i, n, mean, total);
                    long[] b = cal(true, mid + 1, i, n, mean, total);
                    if (compare(a, b) > 0) {
                        end = mid - 1;
                        if (compare(result, a) < 0) {
                            result = a;
                            index = i;
                            l = mid;
                            two = true;
                        }
                    } else {
                        start = mid + 1;
                        if (compare(result, b) < 0) {
                            result = b;
                            index = i;
                            l = mid + 1;
                            two = true;
                        }
                    }
                }
            }
        }
        //out.println(result);
        if (two) {
            out.println(l * 2 + 2);
            for (int i = 0; i < n; i++) {
                if (i <= index && i >= index - l - 1) {
                    out.print(data[i] + " ");
                }
            }
            for (int i = n - 1; i >= 0; i--) {
                if (i >= n - l) {
                    out.print(data[i] + " ");
                }
            }
        } else {
            out.println(l * 2 + 1);
            for (int i = 0; i < n; i++) {
                if (i <= index && i >= index - l) {
                    out.print(data[i] + " ");
                }
            }
            for (int i = n - 1; i >= 0; i--) {
                if (i >= n - l) {
                    out.print(data[i] + " ");
                }
            }
        }
        out.close();
    }

    static long[] cal(boolean two, int need, int index, int n, long[] mean,
            long[] total) {

        long a = total[n - 1] - total[n - need - 1];

        long b = total[index]
                - (index >= need + 1 ? total[index - need - 1] : 0);
        if (two) {
            b = total[index]
                    - (index >= need + 2 ? total[index - need - 2] : 0);
        }
        //System.out.println(a + " " + b + " " + index + " " + need + " " + mean);
        long[] x = {(a + b), (need * 2 + 1 + (two ? 1 : 0))};

        minus(x, mean);
        return x;
    }

    static void minus(long[] x, long[] y) {
        long v = gcd(abs(x[1]), abs(y[1]));
        long a = x[0] * y[1] / v;
        long b = y[0] * x[1] / v;
        a -= b;
        b = (x[1] * y[1]) / v;
        x[0] = a;
        x[1] = b;
    }

    static long abs(long v) {
        return v > 0 ? v : -v;
    }

    static int compare(long[] a, long[] b) {
        long v = gcd(abs(a[1]), abs(b[1]));
        long x = a[0] * b[1] / v;
        long y = b[0] * a[1] / v;
        return Long.compare(x, y);
    }

    public static int[] KMP(String val) {
        int i = 0;
        int j = -1;
        int[] result = new int[val.length() + 1];
        result[0] = -1;
        while (i < val.length()) {
            while (j >= 0 && val.charAt(j) != val.charAt(i)) {
                j = result[j];
            }
            j++;
            i++;
            result[i] = j;
        }
        return result;

    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static int digit(long n) {
        int result = 0;
        while (n > 0) {
            n /= 10;
            result++;
        }
        return result;
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;

    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int start, int end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = 47 * hash + this.x;
            hash = 47 * hash + this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return x - o.x;
        }
    }

    public static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        public void update(int index, long value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public long get(int index) {
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, long b, long MOD) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2, MOD);
        if (b % 2 == 0) {
            return val * val % MOD;
        } else {
            return val * (val * a % MOD) % MOD;

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}