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: Accepted)

import java.util.*;
import java.math.*;
     
class Main{
    public static void main(String[] args) {
        
        try(Scanner sc = new Scanner(System.in)){
 
            int n = Integer.parseInt(sc.next());
            ArrayList<Integer> list = new ArrayList<>();
            ArrayList<Integer> copyList = new ArrayList<>();
            for(int i = 0; i < n; i++){
                int add = Integer.parseInt(sc.next());
                list.add(add);
                copyList.add(add);
            }
            
            Collections.sort(copyList);
            int centerL = copyList.get(n/2 - 1);
            int centerR = copyList.get(n/2);

            for(int j = 0; j < list.size(); j++){
                if(centerL >= list.get(j)) System.out.println(centerR);
                else System.out.println(centerL);
            }

 
        }catch(Exception e){
            e.printStackTrace();
        }        
    }
}