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: Accepted)

#include <stdio.h>
#include <stdlib.h>

typedef struct {
	int x, idx;
} Rec;

int compare(const void *a, const void *b) {
	return ((const Rec *)a)->x - ((const Rec *)b)->x;
}

Rec rec[200000];
int order[200000];

int main(void) {
	int n;

	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
		scanf("%d", &rec[i].x);
		rec[i].idx = i;
	}

	qsort(rec, n, sizeof(Rec), &compare);

	for (int i = 0; i < n; i++)
		order[rec[i].idx] = i;

	for (int i = 0; i < n; i++)
		printf("%d\n", rec[order[i] < n / 2 ? n / 2 : n / 2 - 1].x);

	return 0;
}