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: Time Limit Exceeded)

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

int main(void){
  
  int N,x[200005],y[200005],b[200002],i,j,k,l,buff;
  char str[2500000],*p;
  
  fgets(str,sizeof(str),stdin);
  N=atoi(str);
  fgets(str,sizeof(str),stdin);
  p=strtok(str," \n");
  x[1]=atoi(p);
  for(i=2;i<N+1;i++){
   p=strtok(NULL," \n"); 
    x[i]=atoi(p);
  }
  
  for(i=1;i<N+1;i++){
    for(j=1;j<i;j++){
     y[j]=x[j] ;
    }
    for(j=i+1;j<N+1;j++){
     y[j-1]=x[j];
    }
    
    for(k=1;k<N;k++){
     for(l=N;l>k;l--){
       if(y[l-1]<y[l]){
         buff=y[l-1],y[l-1]=y[l],y[l]=buff;
       }
     }
    }
    
    b[i]=y[N/2];
    printf("%d\n",b[i]);
  }
  
 return 0; 
}