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>
#define swap(type, x, y)  do{ type t = x;  x = y;  y = t; }while(0)

void quick(int array[], int left, int right){
  int pl = left, pr = right, x = array[(left + right) / 2];
  do{
    while(array[pl] < x)  pl++;
    while(array[pr] > x)  pr--;
    if(pl <= pr){
      swap(int, array[pl], array[pr]);
      pl++, pr--;
    }
  }while(pl <= pr);
  if(pl < right)  quick(array, pl, right);
  if(pr > left)   quick(array, left, pr);
}

int main(){
  int n;  scanf("%d", &n);
  int x[200005], xcopy[200005];
  for(int i=0; i<n; i++){
    scanf("%d", x+i);
    xcopy[i] = x[i];
  }
  quick(x, 0, n-1);
  int medianl = x[n/2-1],  medianr = x[n/2];
  
  for(int i=0; i<n; i++){
    if(xcopy[i] <= medianl)  printf("%d\n", medianr);
    else                     printf("%d\n", medianl);
  }

  //  printf("%ls\n", x);

  return 0;
}