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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class E {
	static long[] acums;
	static int n;
	
	static long num(int idx, int cant) {
		return acums[idx + 1] - acums[idx - cant] + acums[n] - acums[n - cant];
	}
	
	static boolean grows(long n1, long d1, long n2, long d2) {
		return n2 * d1 > n1 * d2;
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		List<Long> valsTmp = new ArrayList<Long>(n);
		for (int i = 0; i < n; i++) {
			valsTmp.add(sc.nextLong());
		}
		Collections.sort(valsTmp);
		long[] vals = new long[n];
		for (int i = 0; i < vals.length; i++) {
			vals[i] = valsTmp.get(i);
		}
		acums = new long[n+1];
		acums[0] = 0;
		for (int i = 1; i < acums.length; i++) {
			acums[i] = acums[i-1] + vals[i-1];
		}
		long bestNum = -1, bestDen = 1;
		int bestIdx = -1, bestQty = 0;
		for (int i = 0; i < vals.length; i++) {
			int left = 0, right = Math.min(i, n - i - 1);
			while (left < right) {
				int med = (left + right) / 2;
				long num = num(i, med);
				long numN = num(i, med + 1);
				if (grows(num, 2*med+1, numN, 2*med + 3)) left = med + 1;
				else right = med;
			}
			long num = num(i, left) - vals[i] * (2*left + 1);
			if (grows(bestNum, bestDen, num, 2*left+1)) {
				bestIdx = i;
				bestQty = left;
				bestNum = num;
				bestDen = 2*left+1;
			}
		}
		StringBuilder sb = new StringBuilder();
		System.out.println(2*bestQty+1);
		for (int i = bestIdx - bestQty ;i <= bestIdx; i++) {
			sb.append(vals[i] + " ");
		}
		for (int i = n - bestQty ;i < n; i++) {
			sb.append(vals[i] + " ");
		}
		System.out.println(sb.toString());
	}
}