该比赛已结束，您无法在比赛模式下递交该题目。您可以点击“在题库中打开”以普通模式查看和递交本题。

D - Water Bottle

Score : $400$ points

Problem Statement

Takahashi has a water bottle with the shape of a rectangular prism whose base is a square of side $a~\mathrm{cm}$ and whose height is $b~\mathrm{cm}$. (The thickness of the bottle can be ignored.)

We will pour $x~\mathrm{cm}^3$ of water into the bottle, and gradually tilt the bottle around one of the sides of the base.

When will the water be spilled? More formally, find the maximum angle in which we can tilt the bottle without spilling any water.

Constraints

• All values in input are integers.
• $1 \leq a \leq 100$
• $1 \leq b \leq 100$
• $1 \leq x \leq a^2b$

Input

Input is given from Standard Input in the following format:

$a$ $b$ $x$

Output

Print the maximum angle in which we can tilt the bottle without spilling any water, in degrees. Your output will be judged as correct when the absolute or relative error from the judge's output is at most $10^{-6}$.

2 2 4

45.0000000000

This bottle has a cubic shape, and it is half-full. The water gets spilled when we tilt the bottle more than $45$ degrees.

12 21 10

89.7834636934

This bottle is almost empty. When the water gets spilled, the bottle is nearly horizontal.

3 1 8

4.2363947991

This bottle is almost full. When the water gets spilled, the bottle is still nearly vertical.