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.*;
import java.util.*;

public class _8VCVentureCupqE {

	static final int mod = (int) 1e9 + 7;
	static int n;
	static int a[];
	static long p[];

	public static void main(String[] args) {
		InputReader in = new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);

		n = in.nextInt();

		a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = in.nextInt();

		Arrays.sort(a);

		p = new long[n];
		for (int i = 0; i < n; i++)
			p[i] = a[i] + (i == 0 ? 0 : p[i - 1]);

		int idx = 0, length = 0;
		Fraction ans = new Fraction(0, 1);

		for (int i = 0; i < n; i++) {

			int max = Math.min(i, n - 1 - i), start = 0, end = max, bestLength = 0;
			Fraction bestAns = new Fraction(0, 1);

			while (end - start + 1 > 3) {
				int mid1 = start + (end - start) / 3;
				int mid2 = end - (end - start) / 3;

				Fraction ans1 = f(i, mid1);
				Fraction ans2 = f(i, mid2);

				if (ans1.compareTo(ans2) < 0) {
					if (ans2.compareTo(bestAns) > 0) {
						bestAns = ans2;
						bestLength = mid2;
					}
					start = mid1;
				}

				else {
					if (ans.compareTo(bestAns) > 0) {
						bestAns = ans1;
						bestLength = mid1;
					}
					end = mid2;
				}
			}

			for (int j = start; j <= end; j++) {
				Fraction ans1 = f(i, j);
				if (ans1.compareTo(bestAns) > 0) {
					bestAns = ans1;
					bestLength = j;
				}
			}

			if (bestAns.compareTo(ans) > 0) {
				ans = bestAns;
				idx = i;
				length = bestLength;
			}
		}

		w.println(2 * length + 1);

		w.print(a[idx] + " ");
		for (int i = 1; i <= length; i++) {
			w.print(a[idx - i] + " ");
			w.print(a[n - i] + " ");
		}

		w.println();
		w.close();
	}

	static Fraction f(int center, int length) {
		if (length == 0)
			return new Fraction(0L, 1L);
		long sum = a[center] + p[center - 1]
				- (center - 1 - length < 0 ? 0 : p[center - 1 - length])
				+ p[n - 1] - p[n - 1 - length];
		return new Fraction(sum - a[center] * (1L + 2 * length), 1 + 2 * length);
	}

	static Fraction brute(int[] a) {
		int n = a.length;
		Fraction max = new Fraction(0, 1);
		for (int i = 1; i < n - 1; i++) {
			long sum = a[i], cnt = 1;
			for (int x = i - 1, y = n - 1; x >= 0 && y > i; x--, y--) {
				sum += a[x] + a[y];
				cnt += 2;
				if (new Fraction(sum - cnt * a[i], cnt).compareTo(max) > 0)
					max = new Fraction(sum - cnt * a[i], cnt);
			}
		}
		return max;
	}

	static class Fraction {
		long num, den;

		Fraction(long num, long den) {
			this.num = num;
			this.den = den;
		}

		public int compareTo(Fraction b) {
			return Long.compare(num * b.den, b.num * den);
		}
	}

	static class InputReader {

		private InputStream stream;
		private byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;

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

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

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

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

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

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

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

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