Contest Duration: ~ (local time) (100 minutes) Back to Home
D - Water Bottle /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

この水筒の中に体積 x~\mathrm{cm}^3 の水を入れ、底面の正方形の 1 辺を軸として、この水筒を徐々に傾けます。

### 制約

• 入力は全て整数
• 1 ≤ a \leq 100
• 1 ≤ b \leq 100
• 1 ≤ x ≤ a^2b

### 入力

a b x


### 入力例 1

2 2 4


### 出力例 1

45.0000000000


### 入力例 2

12 21 10


### 出力例 2

89.7834636934


### 入力例 3

3 1 8


### 出力例 3

4.2363947991


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}.

### Sample Input 1

2 2 4


### Sample Output 1

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.

### Sample Input 2

12 21 10


### Sample Output 2

89.7834636934


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

### Sample Input 3

3 1 8


### Sample Output 3

4.2363947991


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