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 Perl (v5.18.2) (judge verdict: Accepted)

use v5.18;
use warnings;
use List::Util qw( sum min );
sub read_line { chomp( my $str = <STDIN> ); $str }
sub splited_read_line { split / /, read_line }
use Data::Dumper;

my $n         = read_line;
my @orig_nums = splited_read_line;
my @nums =
  sort { $a->{num} <=> $b->{num} } map { +{ num => $orig_nums[$_], orig_index => $_ } } 0 .. $n - 1;
my %table = map { $nums[$_]->{orig_index} => $_ } 0 .. $n - 1;

sub medium_index {
  my $remove_index = shift;
  state $medium = int $n / 2;
  $remove_index < $medium ? $medium : $medium - 1;
}

for my $remove_index (0 .. $n - 1) {
  my $sorted_remove_index = $table{$remove_index};
  my $medium_index = medium_index $sorted_remove_index;
  say $nums[$medium_index]->{num}
}