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++14 (Clang 3.8.0) (judge verdict: Accepted)

#include <algorithm>
#include <climits>
#include <cstdio>
#include <cstdlib>
#include <cstring>

using namespace std;

#define ARRAY_SIZE 300000

int data[ARRAY_SIZE];
int sorted_data[ARRAY_SIZE];
int smaller;
int larger;

int is_smaller(const void* a, const void* b)
{
  return *(int*)a < *(int*)b;
}

void print_array(int* data, int size)
{
  for(int i = 0; i < size; i++) {
    printf("%d\n", data[i]);
  }
}

void find_median(int* data, int size)
{
  larger  = data[size/2-1];
  smaller = data[size/2];
}

int main()
{
  int n;
  scanf("%d", &n);
  for(int i = 0; i < n; i++) {
    scanf("%d", &data[i]);
  }
  memcpy(sorted_data, data, sizeof(int) * n);
  qsort(sorted_data, n, sizeof(int), is_smaller);
  //print_array(data, n);

  find_median(sorted_data, n);
  for(int i = 0; i < n; i++) {
    if(data[i] <= smaller) {
      printf("%d\n", larger);
    } else {
      printf("%d\n", smaller);
    }
  }
  return 0;
}