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: Wrong Answer)

N = int(input())
x=[]
for i in range(N):
    x.append([i,0])
y = list(map(int, input().split()))

for i in range(N):
    x[i][1]=y[i]



x.sort(key=lambda a:a[1])
tmp1=x[int(N/2)-1]
tmp2=x[int(N/2)]


for i in range(N):
    if i <N/2-1 and i !=tmp2[0]:
        print(tmp2[1])
    if i <N/2-1 and i ==tmp2[0]:
        print(tmp1[1])
    if i >=N/2-1 and i !=tmp1[0]:
        print(tmp1[1])
    if i >=N/2-1 and i ==tmp1[0]:
        print(tmp2[1])