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.Text;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		// 整数の入力
		int N = int.Parse(Console.ReadLine());
		// スペース区切りの整数の入力
		string[] Xs = Console.ReadLine().Split(' ');
      	List<int> array1 = new List<int>(Xs.Length);
      	List<int> array2 = new List<int>(Xs.Length);
      	
      	// parsing
      	for(int i = 0; i < Xs.Length; i++)
        {
        	array1.Add(Int32.Parse(Xs[i]));
          	array2.Add(array1[i]);
        }
      	array2.Sort();
      	// logic
      	int Left = array2[Xs.Length / 2 - 1];
      	int Right = array2[Xs.Length / 2];
		//出力
      	for(int i = 0; i < Xs.Length; i++)
        {
          ///*
          if(Left < array1[i])
          {
			Console.WriteLine(Left);
          }
          else
          {
          	Console.WriteLine(Right);
          }
          //*/
        }
	}
}