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.

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