Problem K
Trials and Triangulations

More math? You got it. That’s what computers do, they compute.

Heron’s formula gives the area, $A$, of a triangle with sides $a$, $b$, and $c$ as $A=\sqrt{s(s-a)(s-b)(s-c)}$ where $s=(a+b+c)/2$.

Write a program that prompts for three integers, $a$, $b$, and $c$, denoting the lengths of the sides of a triangle. Calculate the area, and print the result.

Hint: You can use the sqrt function in the math module.

Input

Input consists of three lines. The first line consists of one integer $a$. The second line consists of one integer $b$. The third line consists of one integer $c$. It is guaranteed that $1\le a,b,c\le 100$ and that the values can form a triangle.

Output

Output one line with one floating point number $A$, the area of the triangle. The output number should have an absolute or relative error of at most ${10}^{-9}$.

1
1
1

0.433012701892219

1
2
3

0.000000000000000

2
2
3

1.984313483298443

12
9
19

41.952353926806062

5
4
3

6.000000000000000

5
12
13

30.000000000000000