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.to_i
x_list = gets.split.map(&:to_i)

def selection_sort_ruby(ary)
  ary_with_index = ary.zip(0...ary.length)
  (0...ary.length).each{|ix|
    # 最小値を探す
    min = ary_with_index[ix..-1].min_by{|num, ix| num}

    # 最小値と ix を交換する
    ary_with_index[ix][0], ary_with_index[min[1]][0] = min[0], ary_with_index[ix][0]
  }
  ary_with_index.map{|num, ix| num}
end


for i in 0..N-1 do
    tmp_list = Marshal.load(Marshal.dump(x_list))
    tmp_list.slice!(i)
    sorted_list = selection_sort_ruby(tmp_list)
    puts(sorted_list[(sorted_list.size)/2])
end