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: Runtime Error)

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

class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        if (scanner.hasNextLine()) {
            String[] array = scanner.nextLine().split(" ");
            int N = Integer.parseInt(array[0]);

            String[] Xs = scanner.nextLine().split(" ");
            int[] intArray = new int[N];
            int[] intArray2 = new int[N];
            for (int i = 0; i < N; ++i) {
                int w = Integer.parseInt(Xs[i]);
                intArray[i] = w;
                intArray2[i] = w;
            }
            Xs = null;
            Arrays.sort(intArray2);
            int half = intArray2[N / 2];
            int halfNext =  intArray2[N / 2 + 1];
            for (int i = 0; i < N; ++i) {
                if (intArray[i] <= half) {
                    System.out.println(halfNext);
                } else {
                    System.out.println(half);
                }
            }
        }
    }
}