Cookie Farm

Cookie Farm is a clicker game. Players click a picture of a giant cookie to earn cookies, then spend those cookies on buildings that make cookies arrive faster.

In this problem you start with 0 cookies and earn 2 cookies per second by clicking the giant cookie. Whenever you hold at least $C$ cookies you can buy one cookie farm. Each farm costs $C$ cookies and permanently adds $F$ cookies per second to your production.

You win the moment you hold $X$ cookies that you have not spent on farms. Write a program that finds how long winning takes under the best possible strategy.

Cookies arrive continuously. $0.1$ seconds after the game starts you have $0.2$ cookies, and $\pi$ seconds after it starts you have $2\pi$ cookies.

For $C = 500.0$, $F = 4.0$ and $X = 2000.0$ the best strategy plays out like this.

1. You start with 0 cookies and a production of 2 cookies per second.
2. After $250$ seconds you hold $C = 500$ cookies, so you buy a farm that adds $F = 4$ cookies per second.
3. After the purchase you hold 0 cookies and your total production is 6 cookies per second.
4. The next farm also costs 500 cookies, which you can afford about $83.3333333$ seconds later.
5. After the second purchase you hold 0 cookies and your total production is 10 cookies per second.
6. The farm after that also costs 500 cookies, which you can afford $50$ seconds later.
7. After the third purchase you hold 0 cookies and your total production is 14 cookies per second.
8. A fourth farm would also cost 500 cookies, but skipping it is better. Waiting instead until you hold $X = 2000$ cookies takes about $142.8571429$ seconds.

The total is $250 + 83.3333333 + 50 + 142.8571429 = 526.1904762$ seconds.

The first line contains the number of test cases $T$ ($1 \le T \le 100$).

Each of the next $T$ lines contains three space-separated real numbers $C$, $F$ and $X$, with the meanings given above.

$1.0 \le C \le 500.0$, $1.0 \le F \le 4.0$, $1.0 \le X \le 2000.0$.

Each of $C$, $F$ and $X$ is written as one or more digits, then a single decimal point, then 1 to 5 digits. No value has a leading zero.

For each test case print one line of the form Case #x: y, where $x$ is the test case number starting from 1 and $y$ is the minimum number of seconds before you hold $X$ cookies.

Round $y$ to four decimal places and print exactly four digits after the decimal point.