C. Crazy? I Was Crazy Twice
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Qatada is perfectly sane. He tells himself this every morning.

However, ever since the Al-A3damiya Incident involving a very chill spooder, his friends have started bringing a straightjacket to every meeting just in case.

It is finally time for the AFPC, and as judges, Qatada and Abd Alrhman are supposed to be setting up the hall. Qatada, however, had a better plan: Escape.

He almost made it to the exit before Abu Tahun, who was smoking outside, caught him. After Qatada tried to bolt a second time, Abu Tahun and Abd Alrhman reached a consensus that Qatada must be locked in the corner.

The moment the lock turned, Qatada began screaming at the ceiling:

Crazy? I was crazy twice! They locked me in the Internet Hall! Internet Hall! And Internet Halls make me crazy!

To distract him from his second mental breakdown, Abu Tahun pointed at the security cameras.

Look, Qatada! Geometry!

Qatada immediately stopped screaming and pulled out a cigarette. He stared at camera $$$A$$$ and camera $$$B$$$. He noticed that their vision lines crossed at point $$$C$$$, creating a large triangle $$$\triangle ABC$$$ near the ceiling.

On the floor, a smaller triangle $$$\triangle CDE$$$ was formed by the same two vision lines.

Abu Tahun told him the following information:

The ceiling segment $$$AB$$$ is parallel to the floor segment $$$DE$$$.

Points $$$A$$$, $$$C$$$, and $$$D$$$ are collinear.

Points $$$B$$$, $$$C$$$, and $$$E$$$ are collinear.

The length of $$$AB$$$ is known.

The length of $$$DE$$$ is known.

The area of the smaller triangle $$$\triangle CDE$$$ is known.

Qatada muttered, his eyes twitching:

I must calculate the area of the ceiling triangle to find the exact coordinates of my sanity.

Given $$$AB$$$, $$$DE$$$, and the area of $$$\triangle CDE$$$, calculate the area of $$$\triangle ABC$$$.

It is guaranteed that $$$AB \parallel DE$$$, points $$$A$$$, $$$C$$$, and $$$D$$$ are collinear, and points $$$B$$$, $$$C$$$, and $$$E$$$ are collinear.

Since $$$AB \parallel DE$$$, triangles $$$\triangle ABC$$$ and $$$\triangle CDE$$$ are similar.

Therefore, the ratio between their corresponding side lengths is $$$\frac{AB}{DE}$$$.

Since areas scale by the square of the similarity ratio, the required area is:

$$$$$$S \cdot \left(\frac{AB}{DE}\right)^2$$$$$$

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). — The description of the test cases follows.

The first line of each test case contains three integers $$$a, b, s$$$ ($$$1 \le a,b,s \le 10^9$$$) — where $$$a$$$ is the Distance between cameras, $$$b$$$ is the Width of the floor overlap and $$$s$$$ is the Area of the bottom triangle

Output

For each test case, output the area of triangle $$$\triangle ABC$$$. Your answer is correct if its absolute or relative error does not exceed $$$10^{-6}$$$.

Example
Input
2
12 3 6
5 2 7
Output
96.0000000000
43.7500000000