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: Time Limit Exceeded)

@N = gets.chomp().to_i
X = gets.chomp.split(' ').map(&:to_i)
X_cp = X.dup

def get_mid(ary)
  p = (@N + 1) / 2
  return ary[p-1]
end

X_cp.sort!
mid_r = X_cp[@N/2]
mid_l = X_cp[@N/2-1]

if mid_l == mid_r
  @N.times{ puts mid_r }
else
  X.each_with_index do |val, index|
    if index == 0
      x_cp_ = X[1..(@N-1)] if index == 0
    else
      x_cp_ = X[0..(index-1)] + X[(index+1)..(@N-1)]
    end
    x_cp_.sort!
    p get_mid(x_cp_)
  end
end