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: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

class Program
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        int[] x = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        Dictionary<int, int> dic = new Dictionary<int, int>();
        int idx = (n - 1) / 2;

        for (int i = 0; i < n; i++)
        {
            dic.Add(i, x[i]);
        }

        dic = dic.OrderBy(p => p.Value).ToDictionary(p => p.Key, p => p.Value);

        for(int i = 0; i < n; i++)
        {
            int tmp = dic[i];
            dic.Remove(i);

            Console.WriteLine(dic.Values.ToArray()[idx]);

            dic.Add(i, tmp);
        }
    }
}