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: Runtime Error)

class Board
  def initialize(board)
    @board = board
  end

  def point_symmetry?
    done = Array.new($w, false)
    ($w-1).times do |i|
      next if done[i]
      (i+1..$w-1).each do |j|
        next if done[j]
        done[i], done[j] = true, true if symmetry?(i, j)
      end
    end
    if $w.odd? && done.count(false) == 1
      i = done.index(false)
      return symmetry?(i, i)
    end
    done.all?
  end

  def symmetry?(i, j)
    $h.times do |k|
      return false if @board[k][i] != @board[$h-k-1][j]
    end
    true
  end
end

def permutation(pairs)
  pairs.permutation do |xs|
    a = []
    b = []
    xs.each do |x|
      a << $g[x[0]]
      b << $g[x[1]]
    end
    board = Board.new(a + b.reverse)
    if board.point_symmetry?
      puts 'YES'
      exit 0
    end
  end
end

def make_pairs(p, done, pairs)
  if p == $ps.size
    permutation(pairs)
    return
  end
  v = $ps[p]
  n = v.size
  (n-1).times do |i|
    next if done[v[i]]
    (i+1..n-1).each do |j|
      next if done[v[j]]
      done[v[i]], done[v[j]] = true, true
      pairs << [v[i], v[j]]
      make_pairs(p + 1, done, pairs)
      done[v[i]], done[v[j]] = false, false
      pairs.pop
    end
  end
end

$h, $w = gets.split.map(&:to_i)
$g = []

$h.times do
  $g << gets.chomp
end

$ps = $g.map.with_index { |s,i| [s.split('').sort.join, i] }.reduce(Hash.new { |k,v| k[v] = [] }) { |z, x| z[x[0]] << x[1]; z }.map { |k,v| v }

make_pairs(0, Array.new($h, false), [])
puts 'NO'