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;
using System.Collections;
using System.Collections.Generic;
using System.Text;


public class Pair
{
	public int I { get; private set; }
	public int X { get; private set; }
	public int M { get; set; }

	public Pair(int i, int x)
	{
		I = i;
		X = x;
	}
}


public class C
{
	public static void Main()
	{
		int N = Int32.Parse(Console.ReadLine());

		string[] args = Console.ReadLine().Split(' ');
		List<Pair> list = new List<Pair>(N);
		for(int i = 0; i < N; i++)
			list.Add(new Pair(i, Int32.Parse(args[i])));
		list.Sort((a,b) => a.X - b.X);

		int m1 = list[N/2].X;
		int m2 = list[N/2 - 1].X;
		for(int i = 0; i < N; i++)
			list[i].M = (i < N/2) ? m1 : m2;
		list.Sort((a,b) => a.I - b.I);

		for(int i = 0; i < N; i++)
			Console.WriteLine(list[i].M);	
	}
}