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>

void minheap_insert(int value,int heap[],int counter) //counterは0からスタート
{
  int spot=counter;
  while(spot != 0 && heap[(spot-1)/2] > value)
    {
      heap[spot] = heap[(spot-1)/2];
      spot = (spot-1)/2;
    }
  heap[spot] = value;
}

int minheap_delete(int heap[],int counter) //counterは要素数-1からスタート
{
  int spot=0,temp,re;
  re = heap[spot];
  heap[spot] = heap[counter];
  while(1)
    {
      if(spot*2+2 < counter)
	{
	  if(heap[spot*2+2] < heap[spot*2+1])
	    {
	      if(heap[spot] > heap[spot*2+2])
		{
		  temp = heap[spot];
		  heap[spot] = heap[spot*2+2];
		  heap[spot*2+2] = temp;
		  spot = spot*2+2;
		  continue;
		}
	    }
	}
      if(spot*2+1 < counter && heap[spot] > heap[spot*2+1])
	{
	  temp = heap[spot];
	  heap[spot] = heap[spot*2+1];
	  heap[spot*2+1] = temp;
	  spot = spot*2+1;
	}
      else
	{
	  break;
	}
    }
  return re;
}


int main(void)
{
  int n,i,ans_low,ans_high,tail,lost;
  scanf("%d",&n);
  int array[n],heap[n];
  for(i=0;i<n;i++)
    {
      scanf("%d",&array[i]);
      minheap_insert(array[i],heap,i);
    }
  tail = n-1;;
  for(i=0;i<n;i++)
    {
      if(i == n/2-1)
	{
	  ans_low = minheap_delete(heap,tail);
	}
      else if(i == n/2)
	{
	  ans_high = minheap_delete(heap,tail);
	}
      else
	{
	  lost = minheap_delete(heap,tail);
	}
      tail--;
    }
  for(i=0;i<n;i++)
    {
      if(array[i] <= ans_low)
	{
	  printf("%d\n",ans_high);
	}
      else if(array[i] >= ans_high)
	{
	  printf("%d\n",ans_low);
	}
    }
  return 0;
}