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;
using System.Linq; 
using E = System.Linq.Enumerable; 

class Program { 
     static void Main(string[] args) {
     //入力を受け取る
     var N = int.Parse(Console.ReadLine());
     var X = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
     int[] Y = new int[N];
     Array.Copy(X, Y, X.Length);
     Array.Sort(X);
     
     for(int i = 0;i < N;i++){
         var y = Y[i];
         //Console.WriteLine(y);
         if(y <= X[N/2-1]){
             //N/2+1番目を出力
             Console.WriteLine(X[N/2]);
         }else{
              //N/2番目を出力
            Console.WriteLine(X[N/2-1]);
         }
     }
     }
     }