p03381 AtCoder Regular Contest 095 - Many Medians
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.

Examples

Input

4
2 4 4 3


Output

4
3
3
4


Input

2
1 2


Output

2
1


Input

6
5 5 4 4 3 3


Output

4
4
4
4
4
4
```python
N=int(input())
X=list(map(int,input().split()))

X_sort=sorted(X)

med_n=X_sort[N//2-1]
med_p=X_sort[N//2]

for i in range(N):
    if X[i]<=med_n:
        print(med_p)
    else:
        print(med_n)

```