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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N X_1 X_2 ... X_N

outputFormat

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

样例

6
5 5 4 4 3 3

4
4
4
4
4
4

</p>