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)

#![allow(unused_macros, deprecated)]

#[allow(dead_code)]
mod utils {
    use std::io::{
        self, BufRead, BufReader, BufWriter, Seek, SeekFrom, Stdin, StdinLock, Stdout, StdoutLock,
        Write,
    };
    use std::mem;
    use std::ops::{Deref, DerefMut};
    use std::ptr;
    use std::slice;
    use std::str::{self, FromStr};

    #[inline]
    fn is_space_or_line_break(b: &u8) -> bool {
        *b == b' ' || *b == b'\n'
    }

    pub struct Scanner<R: BufRead> {
        reader: R,
        buf: Vec<u8>,
    }

    impl<R: BufRead> Scanner<R> {
        #[inline]
        pub fn new(reader: R) -> Scanner<R> {
            Scanner {
                reader: reader,
                buf: Vec::with_capacity(100),
            }
        }

        pub fn read<T: FromStr>(&mut self) -> T {
            self.read_until(is_space_or_line_break);
            self.parse()
        }

        pub fn read2<T1: FromStr, T2: FromStr>(&mut self) -> (T1, T2) {
            (self.read(), self.read())
        }

        pub fn read3<T1: FromStr, T2: FromStr, T3: FromStr>(&mut self) -> (T1, T2, T3) {
            (self.read(), self.read(), self.read())
        }

        pub fn read4<T1: FromStr, T2: FromStr, T3: FromStr, T4: FromStr>(
            &mut self,
        ) -> (T1, T2, T3, T4) {
            (self.read(), self.read(), self.read(), self.read())
        }

        pub fn reads(&mut self) -> &str {
            self.read_until(is_space_or_line_break);
            unsafe { str::from_utf8_unchecked(&self.buf) }
        }

        pub fn readl(&mut self) -> &str {
            self.buf.clear();
            self.reader.read_until(b'\n', &mut self.buf).unwrap();
            let bytes = if self.buf.last() == Some(&b'\n') {
                &self.buf[..self.buf.len() - 1]
            } else {
                &self.buf
            };
            unsafe { str::from_utf8_unchecked(&bytes) }
        }

        pub fn read_vec<T: FromStr>(&mut self, count: usize) -> Vec<T> {
            (0..count).map(|_| self.read()).collect()
        }

        fn read_until<P: FnMut(&u8) -> bool>(&mut self, mut predicate: P) {
            self.buf.clear();
            let mut first = true;

            // https://doc.rust-lang.org/src/std/io/mod.rs.html#1623-1649
            loop {
                let (done, used) = {
                    let available = self.reader.fill_buf().unwrap();
                    if first && available.len() == 0 {
                        panic!("Scan Error (EOF reached)");
                    }

                    match available.iter().position(&mut predicate) {
                        Some(0) if first => (false, 1),
                        Some(i) => {
                            self.buf.extend_from_slice(&available[..i]);
                            (true, i + 1)
                        }
                        None => {
                            self.buf.extend_from_slice(available);
                            (false, available.len())
                        }
                    }
                };

                self.reader.consume(used);
                if done || used == 0 {
                    return;
                }

                first = false;
            }
        }

        #[inline]
        fn parse<T: FromStr>(&mut self) -> T {
            // 文字列をT型へパースする
            let elem = unsafe { str::from_utf8_unchecked(&self.buf) };
            elem.parse()
                .unwrap_or_else(|_| panic!(format!("failed parsing: {}", elem)))
        }
    }

    impl<R: BufRead + Seek> Seek for Scanner<R> {
        #[inline]
        fn seek(&mut self, pos: SeekFrom) -> io::Result<u64> {
            self.reader.seek(pos)
        }
    }

    pub struct StdinScanner {
        stdin: Stdin,
        scanner: Scanner<BufReader<StdinLock<'static>>>,
    }

    impl StdinScanner {
        #[inline]
        pub fn new() -> StdinScanner {
            let stdin = io::stdin();
            let stdinlock = unsafe { mem::transmute(stdin.lock()) };
            let reader = BufReader::with_capacity(4096, stdinlock);
            let scanner = Scanner::new(reader);
            StdinScanner {
                stdin: stdin,
                scanner: scanner,
            }
        }
    }

    impl Deref for StdinScanner {
        type Target = Scanner<BufReader<StdinLock<'static>>>;

        #[inline]
        fn deref(&self) -> &Self::Target {
            &self.scanner
        }
    }

    impl DerefMut for StdinScanner {
        #[inline]
        fn deref_mut(&mut self) -> &mut Self::Target {
            &mut self.scanner
        }
    }

    pub struct StdoutWriter {
        stdout: Stdout,
        writer: BufWriter<StdoutLock<'static>>,
    }

    impl StdoutWriter {
        #[inline]
        pub fn new() -> StdoutWriter {
            let stdout = io::stdout();
            let stdoutlock = unsafe { mem::transmute(stdout.lock()) };
            let writer = BufWriter::with_capacity(4096, stdoutlock);
            StdoutWriter {
                stdout: stdout,
                writer: writer,
            }
        }

        pub fn write<T: Writable>(&mut self, v: T) {
            v.display(&mut self.writer);
        }

        pub fn writeln<T: Writable>(&mut self, v: T) {
            v.display(&mut self.writer);
            self.writer.write_all(b"\n").unwrap();
        }

        pub fn write_horizontal<I>(&mut self, iter: I)
        where
            I: IntoIterator,
            I::Item: Writable,
        {
            let mut it = iter.into_iter();
            if let Some(elem) = it.next() {
                elem.display(&mut self.writer);
            } else {
                return;
            }

            for elem in it {
                elem.display(&mut self.writer);
                self.writer.write_all(b" ").unwrap();
            }
        }

        pub fn write_vertical<I>(&mut self, iter: I)
        where
            I: IntoIterator,
            I::Item: Writable,
        {
            let mut it = iter.into_iter();
            if let Some(elem) = it.next() {
                elem.display(&mut self.writer);
            } else {
                return;
            }

            for elem in it {
                elem.display(&mut self.writer);
                self.writer.write_all(b"\n").unwrap();
            }
        }
    }

    impl Write for StdoutWriter {
        #[inline]
        fn flush(&mut self) -> io::Result<()> {
            self.writer.flush()
        }

        #[inline]
        fn write(&mut self, buf: &[u8]) -> io::Result<usize> {
            self.writer.write(buf)
        }
    }

    static DEC_DIGITS_LUT: &'static [u8; 200] = b"0001020304050607080910111213141516171819\
            2021222324252627282930313233343536373839\
            4041424344454647484950515253545556575859\
            6061626364656667686970717273747576777879\
            8081828384858687888990919293949596979899";

    fn write_int<W: Write>(mut writer: W, mut n: u64, is_negative: bool) {
        unsafe {
            let mut buf: [u8; 39] = mem::uninitialized();
            let buf_ptr_start = buf.as_mut_ptr().offset(39);
            let mut buf_ptr = buf_ptr_start;
            let lut_ptr = DEC_DIGITS_LUT.as_ptr();

            while n >= 10000 {
                let rem = (n % 10000) as isize;
                n /= 10000;

                let d1 = (rem / 100) << 1;
                let d2 = (rem % 100) << 1;
                buf_ptr = buf_ptr.offset(-4);
                ptr::copy_nonoverlapping(lut_ptr.offset(d1), buf_ptr, 2);
                ptr::copy_nonoverlapping(lut_ptr.offset(d2), buf_ptr.offset(2), 2);
            }

            let mut n = n as isize; // possibly reduce 64bit math

            // decode 2 more chars, if > 2 chars
            if n >= 100 {
                let d1 = (n % 100) << 1;
                n /= 100;
                buf_ptr = buf_ptr.offset(-2);
                ptr::copy_nonoverlapping(lut_ptr.offset(d1), buf_ptr, 2);
            }

            // decode last 1 or 2 chars
            if n < 10 {
                buf_ptr = buf_ptr.offset(-1);
                *buf_ptr = (n as u8) + b'0';
            } else {
                let d1 = n << 1;
                buf_ptr = buf_ptr.offset(-2);
                ptr::copy_nonoverlapping(lut_ptr.offset(d1), buf_ptr, 2);
            }

            if is_negative {
                buf_ptr = buf_ptr.offset(-1);
                *buf_ptr = b'-';
            }

            let buf_slice =
                slice::from_raw_parts(buf_ptr, buf_ptr_start as usize - buf_ptr as usize);

            writer.write_all(buf_slice).unwrap();
        }
    }

    pub trait Writable {
        fn display<W: Write>(&self, writer: &mut W);
    }

    impl Writable for str {
        #[inline]
        fn display<W: Write>(&self, writer: &mut W) {
            writer.write_all(self.as_bytes()).unwrap()
        }
    }

    impl<'a> Writable for &'a str {
        #[inline]
        fn display<W: Write>(&self, writer: &mut W) {
            writer.write_all(self.as_bytes()).unwrap()
        }
    }

    impl Writable for String {
        #[inline]
        fn display<W: Write>(&self, writer: &mut W) {
            writer.write_all(self.as_bytes()).unwrap()
        }
    }

    impl Writable for bool {
        #[inline]
        fn display<W: Write>(&self, writer: &mut W) {
            let s = if *self { "Yes" } else { "No" };
            writer.write_all(s.as_bytes()).unwrap();
        }
    }

    macro_rules! impl_writable_int {
        ($($int:ty)*) => {
            $(
                impl Writable for $int {
                    #[allow(unused_comparisons)]
                    fn display<W: Write>(&self, writer: &mut W) {
                        let is_negative = !(*self >= 0);
                        let abs = if is_negative {
                            (!*self as u64).wrapping_add(1)
                        } else {
                            *self as u64
                        };
                        write_int(writer, abs, is_negative);
                    }
                }
            )*
        };
    }

    macro_rules! impl_writable_float {
        ($($float:ty)*) => {
            $(
                impl Writable for $float {
                    #[inline]
                    fn display<W: Write>(&self, writer: &mut W) {
                        write!(writer, "{}", *self).unwrap();
                    }
                }
            )*
        }
    }

    impl_writable_int!(u8 u16 u32 u64 usize i8 i16 i32 i64 isize);
    impl_writable_float!(f32 f64);

    pub static mut SCANNER: *mut StdinScanner = 0 as *mut StdinScanner;
    pub static mut WRITER: *mut StdoutWriter = 0 as *mut StdoutWriter;

    #[inline]
    pub fn atcoder_initialize() {
        unsafe {
            SCANNER = mem::transmute(Box::new(StdinScanner::new()));
            WRITER = mem::transmute(Box::new(StdoutWriter::new()));
        }
    }

    #[inline]
    pub fn atcoder_finish() {
        unsafe {
            (*WRITER).flush().unwrap();
        }
    }
}

macro_rules! input {
    () => {};
    (@scanner $scanner:ident, @pred [ $($pred:tt)* ], ($var1:tt, $var2:tt) : [($t1:tt, $t2:tt) ; $len:expr]) => {
        let mut $var1 = Vec::with_capacity($len as usize);
        let mut $var2 = Vec::with_capacity($len as usize);

        for _ in 0..$len {
            $var1.push(scan!($scanner, $t1));
            $var2.push(scan!($scanner, $t2));
        }
    };
    (@scanner $scanner:ident, @pred [ $($pred:tt)* ], $var:tt : $t:tt) => {
        let $($pred)* $var = scan!($scanner, $t);
    };
    (@scanner $scanner:ident,) => {};
    (@scanner $scanner:ident, $var:tt : $t:tt) => {
        input!(@scanner $scanner, @pred [], $var : $t);
    };
    (@scanner $scanner:ident, mut $var:tt : $t:tt) => {
        input!(@scanner $scanner, @pred [mut], $var : $t);
    };
    (@scanner $scanner:ident, $var:tt : $t:tt, $($r:tt)*) => {
        input!(@scanner $scanner, $var : $t);
        input!(@scanner $scanner, $($r)*);
    };
    (@scanner $scanner:ident, mut $var:tt : $t:tt, $($r:tt)*) => {
        input!(@scanner $scanner, mut $var : $t);
        input!(@scanner $scanner, $($r)*);
    };
    ($($r:tt)*) => {
        let scanner_ref = unsafe { &mut *$crate::utils::SCANNER };
        input!(@scanner scanner_ref, $($r)*);
    }
}

macro_rules! scan {
    ($scanner:ident, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| scan!($scanner, $t)).collect::<Vec<_>>()
    };
    ($scanner:ident, usize1) => {
        scan!($scanner, usize) - 1
    };
    ($scanner:ident, line) => {
        $scanner.readl().to_string()
    };
    ($scanner:ident, $t:ty) => {
        $scanner.read::<$t>()
    };
}

macro_rules! pprint {
    ($value:expr) => {
        unsafe {
            (*$crate::utils::WRITER).write($value);
        }
    };
    ($value:expr, $($r:tt)*) => {
        let writer = unsafe { &mut *$crate::utils::WRITER };
        writer.write($value);
        writer.write(" ");
        pprint!($($r)*);
    };
}

macro_rules! pprintln {
    ($value:expr) => {
        unsafe {
            (*$crate::utils::WRITER).writeln($value);
        }
    };
    ($value:expr, $($r:tt)*) => {
        let writer = unsafe { &mut *$crate::utils::WRITER };
        writer.write($value);
        writer.write(" ");
        pprintln!($($r)*);
    };
}

macro_rules! atcoder_main {
    ($func:ident) => {
        fn main() {
            $crate::utils::atcoder_initialize();
            $func();
            $crate::utils::atcoder_finish();
        }
    };
}

use std::f64::consts::PI;

fn run() {
    input! {
        a: f64,
        b: f64,
        x: f64,
    }

    let ans = if x >= a * a * b * 0.5 {
        let remain_height = b - x / (a * a);
        (remain_height / a * 2.0).atan() * 180.0 / PI
    } else {
        let dx = x * 2.0 / (a * b);
        (b / dx).atan() * 180.0 / PI
    };

    pprintln!(ans);
}

atcoder_main!(run);