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.*;
import java.io.*;

public class Main {
	
  public static void main(String[] args) {
    Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
    
    int N = in.nextInt();
    Num[] original = new Num[N];
    Num[] sorted = new Num[N];
    
    for (int i = 0; i < N; i++) {
    	int n = in.nextInt();
    	original[i] = new Num(i, n);
    	sorted[i] = new Num(i, n);
    }
    
    Arrays.sort(sorted);
    Map<Integer, Integer> order = new HashMap<Integer, Integer>(); // Keeps index in original => index in sorted
    for (int i = 0; i < N; i++) {
    	order.put(sorted[i].index, i);
    }
    
    for (int i = 0; i < N; i++) {
    	int index = order.get(original[i].index);
    	
    	if (index < N / 2) {
    		System.out.println(sorted[N / 2].n);
    	} else {
    		System.out.println(sorted[N / 2 - 1].n);
    	}
    }
  }
}

class Num implements Comparable<Num> {
	int index;
	int n;
	
	public Num(int index, int n) {
		this.index = index;
		this.n = n;
	}

	@Override
	public int compareTo(Num o) {
		return this.n - o.n;
	}
	
	
}