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 strict;
use warnings;
use 5.010;

use Data::Dumper;

chomp(my $n = <STDIN>);
chomp(my $line = <STDIN>);
my @x = split / /, $line;
my @idx = sort { $x[$b] <=> $x[$a] } 0..$#x;
# say "@idx";
my @y = sort { $a <=> $b } @x;

my @ans;
for (0..$#y) {
    if ($_ >= $n / 2) {
        $ans[$idx[$_]] = @y[$n / 2];
    }
    else {
        $ans[$idx[$_]] = @y[$n / 2 - 1];
    }
}

say(join("\n", @ans));