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 9.2.1) (judge verdict: Wrong Answer)

#include<stdio.h>
int a[200000],b[200000],k,n;
void quicksort(int a[],int s,int t){
  if(s<t){
    int i=s,j=t,p=b[a[(s+t)/2]];
    while(1){
      while(b[a[i]]<p)i++;
      while(p<b[a[j]])j--;
      if(i>=j)break;
      a[i]^=a[j]^=a[i]^=a[j];
      i++;j--;
    }
    quicksort(a,s,i-1);quicksort(a,j+1,t);
  }
}
int main(){
  scanf("%d",&n);
  for(k=0;k<n;k++){scanf("%d",&b[k]);a[k]=k;}
  quicksort(a,0,n-1);
  for(k=0;k<n;k++)printf("%d\n",a[k]<n/2?b[a[n/2]]:b[a[n/2-1]]);
}