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.Collections.Generic;

public class Program
{
    public static void Main()
    {
        // Your code here!
        string input1 = Console.ReadLine();
        string[] input2 = Console.ReadLine().Split(' ');
        int[] array = Array.ConvertAll(input2, s => int.Parse(s)); //型変換
        
        for(int i = 0; i < array.Length; i++)//中央値をarray.Length回出力する．
        {
            List<int> list = new List<int>(); //1つ削除したものを入れるリスト
            list.AddRange(array);
            list.RemoveAt(i);
            list.Sort();　　　　　　//昇順に並び替え
            
            Console.WriteLine(list[list.Count-(int.Parse(input1)/2)]);
        }
    }
}