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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include <stdint.h>
#include <string.h>

uint32_t numList[200000];
uint32_t numListSorted[200000];

int cmpfunc(const void * a, const void * b) {
	return *(uint32_t *)a - *(uint32_t *)b;
}

static void printMedians(const uint32_t * const numList, const uint32_t * const numListSorted, const uint32_t listSize) {
	const uint32_t medianLeft = numListSorted[listSize / 2 - 1];
	const uint32_t medianRight = numListSorted[listSize / 2];

	for (uint32_t idx = 0; idx < listSize; idx++) {
		if (numList[idx] <= medianLeft) {
			printf("%I32u\n", medianRight);
		}
		else {
			printf("%I32u\n", medianLeft);
		}
	}
}

int main(void) {
	uint32_t listSize;

	scanf("%I32u\n", &listSize);

	for (uint32_t idx = 0; idx < listSize - 1; idx++) {
		scanf("%I32u ", &(numList[idx]));
	}
	scanf("%I32u", &(numList[listSize - 1]));
	memcpy(numListSorted, numList, sizeof(uint32_t)*listSize);

	qsort(numListSorted, listSize, sizeof(uint32_t), cmpfunc);

	printMedians(numList, numListSorted, listSize);

	return 0;
}