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 Ruby (2.3.3) (judge verdict: Accepted)

n = gets.chomp.to_i
arr = gets.chomp.split(' ').map(&:to_i)

sorted_arr = arr.dup
sorted_arr.sort!

def binary_search(arr, n, key)
  left = 0
  right = n
  while left < right
    mid = (left + right) / 2
    if arr[mid] == key
      return mid
    elsif key < arr[mid]
      right = mid
    else
      left = mid + 1
    end
  end
  return false
end

(0..n-1).each do |i|
  key = arr[i]
  index = binary_search(sorted_arr, n, key)
  if index < n/2
    puts sorted_arr[n/2]
  else
    puts sorted_arr[n/2 - 1]
  end
end