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.*;

public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();

		ArrayList<Integer> X = new ArrayList<Integer>();
		int i;
		for (i = 0; i < N; i++) {
			X.add(sc.nextInt());
		}

		for (i = 0; i < N; i++) {
			int n;
			// 全てをたよっちゃう。
			ArrayList<Integer> Y = new ArrayList<Integer>();
			for (n = 0; n < X.size(); n++) {
				Y.add(X.get(n));
			}
			Y.remove(i);
			Collections.sort(Y);
			System.out.println(Y.get((N - 1) / 2));
		}
	}
}