Triangle Cutting

Consider a right triangle. If we drop an altitude from the right angle to the hypotenuse, the triangle is split into two smaller right triangles.

split triangle1

Now, choose one of these two smaller triangles and remove the other. The remaining triangle is still right-angled, so the same operation can be performed again.

split triangle2

You are given the lengths of the two legs of the initial right triangle, $A$ and $B$ . If you perform this operation exactly $K$ times (always choosing one of the two triangles to keep), determine the maximum possible area of the remaining triangle.

Constraints

$1 \leq A, B \leq 100$
$1 \leq K \leq 10$
$A$ , $B$ , and $K$ are integers

Input Format

The first line contains an integer $T$ — the number of test cases.
Each of the following $T$ lines contains three integers $A$ , $B$ , and $K$ .

Output Format

Output $T$ lines. On the $i$ -th line, print Case #i: area, where $a re a$ is the maximum possible area of the remaining triangle after $K$ operations in the $i$ -th test.
Your answer must have an absolute or relative error of at most $1 0^{- 5}$ from the correct value.

Example

Input

2
3 4 1
6 8 3

Output

Case #1: 3.84
Case #2: 6.291456

Explanation

For $A = 6$ and $B = 8$ , see this picture for all the possible triangles left after 3 operations.
The largest one is colored yellow.

sample