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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main{

    public static void main(String args[]){

        Scanner scan = new Scanner(System.in);
        Integer n = scan.nextInt();
        ArrayList<Long> x = new ArrayList<Long>();
        ArrayList<Long> x2 = new ArrayList<Long>();

        for(int i=0;i<n;i++){
            long t = scan.nextLong();
            x.add(t);
            x2.add(t);
        }
        Collections.sort(x2);

        for(int i=0;i<n;i++){
            int index = x2.indexOf(x.get(i));
            x2.remove(index);
            System.out.println(x2.get(x2.size()/2));
            x2.add(index,x.get(i));
        }
    }

    static int factorial(int n){
        if(n == 0){
          return 1;
        }
        return n * factorial(n-1);
    }


}