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 Python (3.4.3) (judge verdict: Accepted)

def main():
    """
    N=2*10^5
    毎回sortは無理
    sort済みにして計算量を落とす

    元が偶数個なので中央値を考えてsortしたとき
    中央付近には2つ,sort済み値が存在する m1<=m2
    1つ除外したとき
        除外したものがm1以下: 小さい方にずれるのでm2
        除外したものがm2以上: 大きい方にずれるのでm1
    """
    N = int(input())
    *X, = map(int, input().split())

    X_sorted = sorted(X)
    mid = N // 2
    m1 = X_sorted[mid-1]
    m2 = X_sorted[mid]
    for i in range(N):
        if X[i] <= m1:
            ans = m2
        else:
            ans = m1

        print(ans)


if __name__ == '__main__':
    main()