Problem:
Score : 300 points

Problem Statement

You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:

N

Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:

h n w

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

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




my $N = <STDIN>;
my $h,$n,$w;



foreach $h(1..3500){
foreach $n(1..3500){
	my $tmp;
	$tmp=4*$h*$n-$N*$h-$N*$n;
	next if ($tmp==0);
	next if($tmp<0);

	$w=($N*$h*$n)/$tmp;
#	if($w>0)
	{	
		next if($w != int ($w));

		print "$h $n $w\n";
		exit;
	}
}
}