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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            int n, m, x;
            int cost = 0;
            int cost2 = 0;

            n = int.Parse(Console.ReadLine());
            //a = int.Parse(Console.ReadLine()); //標準入力
            string[] str = Console.ReadLine().Split(' ');//2つ以上のスペース区切り入力の取得

            var s = str.ToList();

            for(int i = 0;i <s.Count;i++)
            {
                s.RemoveAt(i);
                s.Sort();
                Console.WriteLine(s[s.Count/ 2]);
                s = str.ToList();
            }
            //Console.Write("改行なし a = {0} b = {1} c = {2}", a, b, c)//改行なし出力
            //Console.WriteLine("改行あり a = {0} b = {1} c = {2}", a, b, c);//改行付き出力
        }
    }
}