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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using AtCoderBeginnerContest144.Questions;
using AtCoderBeginnerContest144.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace AtCoderBeginnerContest144.Questions
{
    public class QuestionD : AtCoderQuestionBase
    {
        double a;
        double b;

        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var abx = inputStream.ReadDoubleArray();
            a = abx[0];
            b = abx[1];
            var x = abx[2];

            yield return ToDegree(BinarySearch(theta => Volume(theta) - x, 0, Math.PI / 2 - double.Epsilon));
        }

        private double ToDegree(double radian) => radian * 180 / Math.PI;

        private double Volume(double theta)
        {
            if (a * Math.Tan(theta) <= b)
            {
                return a * a * (b - a * Math.Tan(theta) / 2);
            }
            else
            {
                return a * b * b / (Math.Tan(theta) * 2);
            }
        }

        private double BinarySearch(Func<double, double> func, double begin, double end)
        {
            const double epsilon = 1e-9;
            var fa = func(begin);
            var fb = func(end);

            if (fa == 0)
            {
                return begin;
            }
            else if (fb == 0)
            {
                return end;
            }

            while (end - begin > epsilon)
            {
                var x = (end + begin) / 2;
                
                var fx = func(x);
                if (fx * fa == 0)
                {
                    return x;
                }
                else if (fx * fa > 0)
                {
                    begin = x;
                    fa = func(begin);
                }
                else
                {
                    end = x;
                }
            }

            return (end + begin) / 2;
        }
    }
}


namespace AtCoderBeginnerContest144
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionD();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace AtCoderBeginnerContest144.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace AtCoderBeginnerContest144.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion