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: Wrong Answer)

using System;

public class Problem_C
{
  public static void Main(string[] args)
  {
    var n = int.Parse(Console.ReadLine());
    var x = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
    var copy = new int[n - 1];

    Array.Sort(x);
    for (var i = 0; i < n; i++)
    {
      var front = new int[i];
      var back = new int[n - front.Length - 1];
      Array.Copy(x, front, i);
      Array.Copy(x, i + 1, back, 0, back.Length);
      Array.Copy(front, copy, front.Length);
      Array.Copy(back, 0, copy, front.Length, back.Length);
      Console.WriteLine($"{copy[copy.Length / 2]}");
    }
  }
}