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 PyPy3 (2.4.0) (judge verdict: Accepted)

def binary_search_loop(data, target):
    imin = 0
    imax = len(data) - 1
    while imin <= imax:
        imid = imin + (imax - imin) // 2
        if target == data[imid]:
            return imid
        elif target < data[imid]:
            imax = imid - 1
        else:
            imin = imid + 1
    return False
n = int(input())
lista = list(map(int, input().split()))
listb = sorted(lista)
for i in range(n):
    if binary_search_loop(listb, lista[i]) + 1 <= (n // 2):
        print(listb[(n // 2)])
    else:
        print(listb[(n // 2) - 1])