Problem D
Hornrétt

Arnar is a poor student on his last year of studies. He’s doing his exams and only has one exam left, the mathematics exam. He’s asked whether a specific triangle has a right angle, but he can’t remember the formula to solve the problem. Usually this would be fine since one is allowed to bring a formula sheet to the exam, but Arnar was lazy and overconfident and thus didn’t prepare a formula sheet. Since he’s poor, he can’t afford to fail, he can’t afford another term of school. Can you save Arnar?

Input

The input contains three integers $a$, $b$, and $c$, the side lengths of the triangle.

Output

Print the area of the triangle if it’s possible to make a right angled triangle with side lengths $a$, $b$ and $c$, otherwise print $-1$.

Scoring

Group	Points	Constraints
1	50	$1 \leq a \leq b \leq c \leq 10^4$
2	50	$1 \leq a \leq b \leq c \leq 10^9$

Sample Input 1	Sample Output 1
3 4 5	6

Sample Input 2	Sample Output 2
4 6 7	-1