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.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {

//        long startTime = System.currentTimeMillis();

        Scanner scanner = new Scanner(System.in);

        int N = scanner.nextInt();

        Long[] X = new Long[N];
        for (int i = 0; i < N; i++) {
            X[i] = scanner.nextLong();
        }
        scanner.close();

        Arrays.sort(X);

        Long[] ans = new Long[2];
        Long max = 0L;
        for (int i = 0; i < N; i++) {

            Long n = X[i];
            for (int j = 0; j < i; j++) {
                Long r = X[j];
                Long c = comb(n, r);
                if (c > max) {
                    ans[0] = n;
                    ans[1] = r;
                    max = c;
                }
            }
        }
        System.out.println(ans[0] + " " + ans[1]);
//        System.out.println(System.currentTimeMillis() - startTime);
    }

    private static long comb(Long n, Long r) {
        if (n < 0 || r < 0 || n < r) {
            throw new ArithmeticException("n = " + n + ", r = " + r);
        }
        r = Math.min(r, n - r); // nCr = nCn-r
        if (r == 1) {
            return n;
        }
        long sum = 1;
        for (int i = 1; i <= r; i++) {
            sum = sum * (n - i + 1) / i;
        }
        return sum;
    }
}