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: Wrong Answer)

import java.util.Scanner;
import java.util.Arrays;

public class Main {

	public int[] binarySearch(long[] a, long[] b, int n) {
		boolean[] check = new boolean[n];
		int[] aIndex = new int[n];

		for(int i = 0; i < n; i++) {
			long x = a[i];
			int index = binarySearch(check, b, x, 0, n - 1);
			aIndex[i] = index;
		}

		return aIndex;
	}

	public int binarySearch(boolean[] check, long[] a, long x, int low, int high) {
		int mid = (low + high) / 2;

		if(x == a[mid] && !check[mid]) {
			check[mid] = true;
			return mid;
		}

		if(low < high) {
			if(x < a[mid]) {
				high = mid - 1;
			}
			else {
				low = mid + 1;
			}
			return binarySearch(check, a, x, low, high);
		}

		return -1;
	}

	public void run() {
		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		long[] x = new long[n];
		for(int i = 0; i < n; i++) {
			x[i] = sc.nextLong();
		}

		long[] y = Arrays.copyOf(x, x.length);

		Arrays.sort(x);

		int[] xIndex = binarySearch(y, x, n);

		for(int i = 0; i < n; i++) {
			int j = xIndex[i];
			if(j < (n / 2)) {
				System.out.println(x[n / 2]);
			}
			else {
				System.out.println(x[(n / 2) - 1]);
			}
		}
	}

	public static void main(String[] args) {
		new Main().run();
	}
}