Problem: For given two sides of a triangle a and b and the angle C between them, calculate the following properties:

* S: Area of the triangle
* L: The length of the circumference of the triangle
* h: The height of the triangle with side a as a bottom edge



Input

The length of a, the length of b and the angle C are given in integers.

Output

Print S, L and h in a line respectively. The output should not contain an absolute error greater than 10-4.

Example

Input

4 3 90


Output

6.00000000
12.00000000
3.00000000

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc=new Scanner(System.in);
        double a=sc.nextDouble();
        double b=sc.nextDouble();
        double C=sc.nextDouble();
        double S=a*b/2*Math.sin(C*Math.PI/180);
        double d=Math.sqrt(a*a+b*b-2*a*b*Math.cos(C*Math.PI/180));
        double L=a+b+d;
        double h=S*2/a;
        System.out.println(S);
        System.out.println(L);
        System.out.println(h);
    }
}