D. Disruptor's Incapacitated Capacitor
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
You were already dead from the neck up, now from the neck down.
— Thrall, the Disruptor

After winning a hard-fought battle against Ogre Magi, Thrall returned to his manufactory in upland Druud to repair his stormcrafting device. He was tinkering around with the plates of a faulty circular parallel plate capacitor that he retrieved from the heart of the device. Both of the circular plates have a uniform radius of $$$r$$$ units. Thrall wanted to control the distance $$$d$$$ between the two plates, and so he decided to join them by soldering many equally spaced strings of length $$$L$$$. One end of each string was soldered to the side of the $$$+ve$$$ plate, while the other end was soldered to the side of the $$$-ve$$$ plate.

(a) The circular plates of the capacitor.(b) Thrall's contraption.

Figure 1: Salvaging the spoils of war.

This contraption enabled him to rotate one of the circular plates (say, the $$$+ve$$$ plate) and consequently calibrate the value of $$$d$$$.

(a) $$$\theta = 60^\circ$$$(b) $$$\theta = 90^\circ$$$(c) $$$\theta = 120^\circ$$$

Figure 2: Rotating the $$$+ve$$$ plate by different angles ($$$\theta$$$).

If Thrall rotates the $$$+ve$$$ circular plate by an angle of $$$\theta$$$ degrees, what would be the corresponding value of $$$d$$$, the distance between the circular plates?

Input

The first line contains an integer $$$t$$$ $$$(1 \leq t \leq 100)$$$ — the number of test cases.

Each test case consists of a single line containing three space-separated integers $$$r$$$ $$$(0 \lt r \leq 10^9)$$$, $$$L$$$ $$$(0 \lt L \leq 10^9)$$$, and $$$\theta$$$ $$$(0^{\circ} \lt \theta^{\circ} \lt 180^{\circ})$$$ — the radius of the plates, the length of the strings, and the angle (in degrees) by which Thrall rotates the $$$+ve$$$ plate respectively.

It is guaranteed that for all test cases, the string length $$$L$$$ is sufficient to allow the rotation of the $$$+ve$$$ plate by $$$\theta$$$ degrees, resulting in a real and non-negative value of $$$d$$$.

Output

For each test case, output a single number $$$d$$$ in a line — the distance between the circular plates.

The answer will be considered correct if the absolute error does not exceed $$$10^{-6}$$$.

Examples
Input
4
1 2 60
1 2 90
1 2 120
420 911 69
Output
1.732051
1.414214
1.000000
776.886872
Input
2
17 42 1
500000000 1000000000 179
Output
41.998952
8726535.498374