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

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