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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>

int main(void)
{
	int i, j;
	int N;
	scanf("%d", &N);
	long X[N], Y[N], tmp;
	for(i=0;i<N;i++)
	{
		scanf("%ld", &X[i]);
		Y[i] = X[i];
	}
	for(i = 1; i < N; i++)
    {
        for(j = 0; j < N - i; j++)
        {
            if(X[j] > X[j + 1])
            {
                tmp = X[j];
                X[j] = X[j + 1];
                X[j + 1] = tmp;
            }
        }
    }
            for(i=0;i<N;i++)
            {
            	if(Y[i]<=X[(N-1)/2])
            	printf("%ld\n", X[(N+1)/2]);
            	else
            	printf("%ld\n", X[(N-1)/2]);
            }
	return 0;
}