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)

namespace AtCoder.ABC.D144
{
    using System;
    using System.Collections.Generic;
    using System.Linq;
    using System.Numerics;
    using System.IO;

    using AtCoder.ABC.IO;

    public class Quest
    {
        public object Solve(Parser parser)
        {
            int a = parser.Integer();
            int b = parser.Integer();
            int x = parser.Integer();

            double theta1 = Math.Atan(2 * (a * a * b - x) / (double)(a * a * a));
            double theta2 = Math.Atan(b * b * a / (double)(2 * x));

            var x1 = a * a * (2 * b - a * Math.Tan(theta1)) / 2;
            var x2 = a * b / Math.Tan(theta2) / 2;

            if (a * a * b / 2.0 <= x)
            {
                return theta1 * 180 / Math.PI;
            }
            else
            {
                return theta2 * 180 / Math.PI;
            }
        }
    }

    static class Program
    {
        static void Main(string[] args)
        {
            var i = new Parser(Console.OpenStandardInput());
            var o = new Printer(Console.OpenStandardOutput());
            var got = new Quest().Solve(i);
            o.WriteLine(got);
            o.Flush();
        }
    }
}
namespace AtCoder.ABC.IO
{
    #region IO

    using System;
    using System.IO;
    using System.Text;
    using System.Linq;
    using System.Collections.Generic;
    using System.Globalization;

    public class Parser
    {
        public Parser(Stream stream)
        {
            str = stream;
        }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof;

        public bool IsEndOfStream
        {
            get { return isEof; }
        }

        public IEnumerable<Parser> Take(int n)
        {
            return Enumerable.Range(1, n).Select(_ => this);
        }

        private byte read()
        {
            if (isEof) return 0;
            if (ptr < len) return buf[ptr++];
            ptr = 0;
            if ((len = str.Read(buf, 0, 1024)) > 0) return buf[ptr++];
            isEof = true;
            return 0;
        }

        public char Char()
        {
            byte b;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }

        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n'; b = (char)read())
                if (b == 0) break;
                else if (b != '\r') sb.Append(b);
            return sb.ToString();
        }

        public long Long()
        {
            if (isEof) return long.MinValue;
            long ret = 0;
            byte b;
            var ng = false;
            do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b));
            if (b == 0) return long.MinValue;
            if (b == '-')
            {
                ng = true;
                b = read();
            }
            for (; ; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                ret = ret * 10 + b - '0';
            }
        }

        public int Integer()
        {
            return (isEof) ? int.MinValue : (int)Long();
        }

        public double Double()
        {
            var s = Scan();
            return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN;
        }

        static T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public char[] Char(int n)
        {
            return enumerate(n, Char);
        }

        public string[] Scan(int n)
        {
            return enumerate(n, Scan);
        }

        public double[] Double(int n)
        {
            return enumerate(n, Double);
        }

        public int[] Integer(int n)
        {
            return enumerate(n, Integer);
        }

        public long[] Long(int n)
        {
            return enumerate(n, Long);
        }
    }

    public class Printer : StreamWriter
    {
        public override IFormatProvider FormatProvider
        {
            get { return CultureInfo.InvariantCulture; }
        }

        public Printer(Stream stream)
            : base(stream, new UTF8Encoding(false, true))
        {
        }

        public Printer(Stream stream, Encoding encoding)
            : base(stream, encoding)
        {
        }

        public void Write<T>(string format, T[] source)
        {
            base.Write(format, source.OfType<object>().ToArray());
        }

        public void WriteLine<T>(string format, T[] source)
        {
            base.WriteLine(format, source.OfType<object>().ToArray());
        }
    }

    #endregion

}