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: Time Limit Exceeded)

import copy

N = int(input())
X = list(map(int, input().split()))
S_X = copy.copy(X)

for i in range(N // 2 + 1):
    for j in range(N - 1 - i):
        if(S_X[j] > S_X[j + 1]):
            tmp = S_X[j + 1]
            S_X[j + 1] = S_X[j]
            S_X[j] = tmp
# s_X = sorted(X)
miX = S_X[N // 2 - 1]
mi1X = S_X[N // 2]
# print(S_X, X)
# print(miX, mi1X)

# print(miX, mi1X)
# print(X)
for a in X:
    if(a <= miX):
        print(mi1X)
    else:
        print(miX)