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 Java7 (OpenJDK 1.7.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

class Main{
	static void swap(int[] a, int id1, int  id2){
		int t = a[id1];
		a[id1] = a[id2];
		a[id2] = t;
	}
	public static void main(String[] args){
		Scanner stdIn = new Scanner(System.in);

		int n = stdIn.nextInt();
		int[] x = new int[n];
		for(int i = 0; i < n; i++)
			x[i] = stdIn.nextInt();
		int[] y = x.clone();
		for(int i = 0; i < n-1; i++)
			for(int j = n-1; j > i; j--)
				if(x[j-1] > x[j])
					swap(x, j-1, j);
					
		for(int i = 0; i < n; i++){
			if(y[i] <= x[(n+1)/2 - 1])
				System.out.println(x[(n+1)/2]);
			else
				System.out.println(x[(n+1)/2-1]);
		}
	}
}