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.io.*;
 
public class Main{
    public static void main(String[] args){
        Main m = new Main();
        m.input();
    }
 
    public void input(){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int half = n / 2;
        ArrayList<Integer> numList = new ArrayList<Integer>();
        for(int i = 0; i < n; i++){
            int x = sc.nextInt();
            numList.add(x);
        }
        sc.close();
        ArrayList<Integer> nowList = (ArrayList<Integer>) numList.clone();
        Collections.sort(nowList);
        int minhalf = nowList.get((n / 2) - 1);
        int maxhalf = nowList.get(n / 2);
        for(int i = 0; i < numList.size(); i++){
            int now = numList.get(i);
            if(now < maxhalf){
                System.out.println(maxhalf);
            }else{
                System.out.println(minhalf);
            }
            
        }
        
    }

}