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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.Scanner;
class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}
public class Main {
    static FastScanner scan=new FastScanner();
    static Scanner scanner=new Scanner(System.in);
    static long gcd (long a, long b) {return b>0?gcd(b,a%b):a;}
    static long lcm (long a, long b) {return a*b/gcd(a,b);}
    static int max(int a,int b) {return a>b?a:b;}
    static int min(int a,int b) {return a<b?a:b;}
    static long factorial(int i) {return i==1?1:i*factorial(i-1);}
    static int lower_bound(int a[],int key) {
        int low=0,high=a.length;
        while(low<high) {
            int mid=((high-low)/2)+low;
            if(a[mid]<=key)low=mid+1;
            else high=mid;
        }
        return high;
        }
    static int upper_bound(int a[],int key) {
        int low=0,high=a.length;
        while(low<high) {
            int mid=((high-low)/2)+low;
            if(a[mid]<key)low=mid+1;
            else high=mid;
        }
        return high;
        }
    static boolean isPrime (long n) {
        if (n==2) return true;
        if (n<2 || n%2==0) return false;
        double d = Math.sqrt(n);
        for (int i=3; i<=d; i+=2)if(n%i==0){return false;}
        return true;
    }
    static int upper_division(int a,int b) {//切り上げ(int)
        if(a%b==0) {
            return a/b;
        }
        else {
            return a/b+1;
        }
    }
    static long lupper_division(long a,long b) {//切り上げ(long)
        if(a%b==0) {
            return a/b;
        }
        else {
            return a/b+1;
        }
    }
    static long lmax(long a,long b) {return Math.max(a, b);}
    static long lmin(long a,long b) {return Math.min(a, b);}
    static int[] setArray(int a) {//配列を作る
        int b[]=new int[a];
        for(int i=0;i<a;i++) {
            b[i]=scan.nextInt();
        }
        return b;
    }
    static String reverce(String str) {//文字列を逆にする
        String strr="";
        for(int i=str.length()-1;i>=0;i--) {
            strr+=str.charAt(i);
        }
        return strr;
    }
    public static void printArray(int[] a) {//配列の空白付き出力
        for(int i=0;i<a.length-1;i++) {
        System.out.print(a[i]+" ");
        }
        System.out.println(a[a.length-1]);
    }
    public static int[][] doublesort(int[][]a) {//二次元配列のソート
        Arrays.sort(a,(x,y)->Integer.compare(x[0],y[0]));
        return a;
    }
    static long modpow(long x,long n,long mo) {//x^n%mo
        long sum=1;
        while(n>0) {
            if((n&1)==1) {
                sum=sum*x%mo;
            }
            x=x*x%mo;
            n>>=1;
        }
        return sum;
    }
    public char[] revch(char ch[]) {//char[]を逆にする
		char ret[]=new char[ch.length];
		for(int i=ch.length-1,j=0;i>=0;i--,j++) {
			ret[j]=ch[i];
		}
		return ret;
	}
	public int[] revint(int ch[]) {//int[]を逆にする
		int ret[]=new int[ch.length];
		for(int i=ch.length-1,j=0;i>=0;i--,j++) {
			ret[j]=ch[i];
		}
		return ret;
	}
    public static void main(String[] args) {
    	//2津の因数に分解したときの和が最小。
    	double a=scan.nextInt();
    	double b=scan.nextInt();
    	double c=scan.nextInt();
    	double tan=c/(b*b*a);
    	double suii=c/a*a;
    	suii=2*(b-suii);
    	if(a*a*b/2>=c) {//いれる水が水槽の半分以下
    		tan=1/tan;
    		tan/=2;
    	}
    	else {
    		double sya=2*(b-(c/(a*a)));
    		tan=sya/a;
    	}
    	if(!(a*a*b/2>=c)) {
    		System.out.println(Math.toDegrees(Math.atan(tan)));
    		return;
    	}
    	System.out.println(Math.toDegrees(Math.atan(tan)));
    }
}