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: Runtime Error)

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<math.h>
int main(void) {
	long n, x[20000], i, j, z, l, m = 0;
	scanf("%ld", &n);
	for (i = 0; i < n; i++ ) {
		scanf("%ld", &x[i]);
	}
	for (i = n; i > 0; i--) {
		for (j = 0; j < i - 1; j++) {
			if (x[j] > x[j + 1]) {
				z = x[j];
				x[j] = x[j + 1];
				x[j + 1] = z;
			}
		}
	}
	l = n / 2;
	for (i = 0; i < n; i++) {
		for (j = 0; j < n; j++) {
			if (j == i)continue;
			m++;
			if (m == l) {
				printf("%ld\n", x[j]);
				m = 0;
				break;
			}
		}
	}
	return 0;
}