Problem:
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.

Solution in Rust (1.15.1) (judge verdict: Accepted)

// 解説動画視聴後に解答

// 標準入力から一行を読み取り、指定の型に変換する
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}
    
// 標準入力から一行を読み取り、空白文字で分割し、各要素を指定の型に変換する関数
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}
    
fn main() {
    let a_b_x: Vec<f64> = read_vec();
    let side_length  = a_b_x[0];
    let box_height   = a_b_x[1];
    let water_volume = a_b_x[2];
    let result_degree: f64;
    let theta: f64;

    // 垂直状態で実際に入っている水を容器の横から見たときの面積
    let water_area: f64 = water_volume / side_length;
    // 横から見たときの容器の面積
    let box_area: f64 = side_length * box_height;
    // こぼれる寸前まで傾けた時に、容器の横から見たときの水が入っていない部分の面積
    let blank_area: f64 = box_area - water_area;
    
    // 場合分け
    if water_area >= box_area / 2.0
    {
        // こぼれる寸前まで傾けた時における、直角三角形の辺の高さ
        let height: f64 = (blank_area * 2.0) / side_length;

        // こぼれる寸前の角度
        theta = (height / side_length).atan();
    }
    else
    {
        // こぼれる寸前まで傾けた時における、直角三角形の辺の幅
        let width: f64 = (water_area * 2.0) / box_height;

        // こぼれる寸前の角度
        theta = (box_height / width).atan();
    }

    // ラジアン => 度数法
    result_degree = (theta / (std::f64::consts::PI * 2.0)) * 360.0;
    println!("{}", result_degree);
}