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 <stdlib.h>
#define MAX(x,y) x>y?x:y

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

int main(){
	long N,*arr;
	scanf("%ld",&N);
	arr=malloc(sizeof(long)*N);
	for(long i=0;i<N;i++) scanf("%ld",&arr[i]);
	for(long i=0;i<N;i++)
	{
		long *Arr;
		Arr=malloc(sizeof(long)*(N-1));
		for(long j=0;j<N;j++)
		{
			Arr[j]=arr[j<i?j:j+1];
		}
		qsort(arr,N,sizeof(long),cmpfunc);
		printf("%ld\n",Arr[N/2-1]);
		free(Arr);
	}	
	free(arr);
	return 0;
}