Problem:
Score : 300 points

Problem Statement

When l is an odd number, the median of l numbers a_1, a_2, ..., a_l is the (\frac{l+1}{2})-th largest value among a_1, a_2, ..., a_l.

You are given N numbers X_1, X_2, ..., X_N, where N is an even number.
For each i = 1, 2, ..., N, let the median of X_1, X_2, ..., X_N excluding X_i, that is, the median of X_1, X_2, ..., X_{i-1}, X_{i+1}, ..., X_N be B_i.

Find B_i for each i = 1, 2, ..., N.

Constraints

2 \leq N \leq 200000

N is even.

1 \leq X_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
X_1 X_2 ... X_N

Output

Print N lines.
The i-th line should contain B_i.

Sample Input 1

4
2 4 4 3

Sample Output 1

4
3
3
4

Since the median of X_2, X_3, X_4 is 4, B_1 = 4.

Since the median of X_1, X_3, X_4 is 3, B_2 = 3.

Since the median of X_1, X_2, X_4 is 3, B_3 = 3.

Since the median of X_1, X_2, X_3 is 4, B_4 = 4.

Sample Input 2

2
1 2

Sample Output 2

2
1

Sample Input 3

6
5 5 4 4 3 3

Sample Output 3

4
4
4
4
4
4

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

class Program
{
	static void Main()
	{
		var n = int.Parse(Console.ReadLine());
		var baseNumbers = Array.ConvertAll(Console.ReadLine().Split(new[] { ' ' }), number => int.Parse(number));
		var sortedNumbers = baseNumbers.Clone() as int[];
		Array.Sort(sortedNumbers);

		var centerIndex = (n + 1) / 2;
		var frontCenterValue = sortedNumbers[n / 2 - 1];
		var backCenterValue = sortedNumbers[n / 2];
		for (var i = 0; i < n; ++i) {
			if (baseNumbers[i] <= frontCenterValue) {
				Console.WriteLine(backCenterValue);
			} else {
				Console.WriteLine(frontCenterValue);
			}
		}

		Console.ReadKey();
	}
}