Triangle Area by Heron Formula

Version: Phuoc Hung OJ Extended

Problem Statement

Given side lengths $a$, $b$, $c$ of a valid triangle, let its semiperimeter be $s=\dfrac{a+b+c}{2}$. Heron’s formula gives the area $S=\sqrt{s(s-a)(s-b)(s-c)}$. Print $S$ with exactly 4 decimal places.

Input

The only line contains real side lengths $a$, $b$, $c$ of the triangle.

Output

Print the triangle area $S$ with exactly 4 decimal places.

Subtasks

• Subtask 1 (100 points): $a,b,c>0$ and the three sides form a valid triangle (each pair of sides sums to more than the remaining side).

Examples

Example 1

Input

3 4 5

Output

6.0000

Explanation. Substituting 3, 4, 5 into sqrt(s(s-a)(s-b)(s-c)) gives approximately 6. The required output formatting produces 6.0000.

Example 2

Input

5 5 6

Output

12.0000

Explanation. Substituting 5, 5, 6 into sqrt(s(s-a)(s-b)(s-c)) gives approximately 12. The required output formatting produces 12.0000.

Example 3

Input

2.5 3.5 4

Output

4.3301

Explanation. Substituting 2.5, 3.5, 4 into sqrt(s(s-a)(s-b)(s-c)) gives approximately 4.33012701892. The required output formatting produces 4.3301.