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.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class Main {

	@SuppressWarnings("rawtypes")
	public static void main(String[] args) {
		@SuppressWarnings("resource")
		Scanner sc = new Scanner(System.in);

		int n = Integer.parseInt(sc.next());
		ArrayList<Integer> x = new ArrayList<Integer>();
		ArrayList<Integer> x_sort = new ArrayList<Integer>();

		for(int i = 0; i < n; i++) {
			int xi = Integer.parseInt(sc.next());
			x.add(xi);
			x_sort.add(xi);
		}
		Collections.sort(x_sort);

		int median_minor = x_sort.get((n / 2) - 1);
		int median_major = x_sort.get(n / 2);

		for(int i = 0; i < n; i++) {
			if(x.get(i) <= median_minor) {
				System.out.println(median_major);
			}else {
				System.out.println(median_minor);
			}
		}

	}

}