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 number;
  int id;
} set;

int cmpnum( const void *p, const void *q ) {
    return ((set*)p)->number - ((set*)q)->number;
}

int cmpid( const void *p, const void *q ) {
    return ((set*)p)->id - ((set*)q)->id;
}

int main(){
  int i,j,k;
  int N;
  scanf("%d",&N);
  set A[N];
  for(i=0;i<N;i++){
    scanf("%d ",&A[i].number);
    A[i].id = i;
  }
  qsort(A,sizeof(A) / sizeof(set),sizeof(set),cmpnum);
  int half = (N/2);
  int a,b;
  a = A[half-1].number;
  b = A[half].number;
  qsort(A,sizeof(A) / sizeof(set),sizeof(set),cmpid);
  for(i=0;i<N;i++){
    if(A[i].number < b){
      printf("%d\n",b);
    }
    else
      printf("%d\n",a);
  }
  return 0;
}