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.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int num = Integer.parseInt(in.nextLine());
		String[] tokens = in.nextLine().split(" ");
		int[] values = new int[num];
		int[] sortedValues = new int[num];
		for (int i = 0; i < num; ++i) {
			values[i] = Integer.parseInt(tokens[i]);
			sortedValues[i] = values[i];
		}
		Arrays.sort(sortedValues);
		for (int i = 0; i < num; ++i) {
			System.out.println(getMedium(i, values, sortedValues));
		}
		in.close();
	}

	public static int getMedium(int skipIndex, int[] values, int[] sortedValues) {
		int lowerMedium = sortedValues[sortedValues.length / 2 - 1];
		int largerMedium = sortedValues[sortedValues.length / 2];
		if (values[skipIndex] < lowerMedium) {
			return largerMedium;
		} else if (values[skipIndex] > largerMedium) {
			return lowerMedium;
		} else if (values[skipIndex] == lowerMedium) {
			return largerMedium;
		} else {
			return lowerMedium;
		}
	}
}