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:
public class Main {
    public static void main(String[] args) {
 
        java.util.Scanner sc = new java.util.Scanner(System.in);
        double a = sc.nextDouble();
        double b = sc.nextDouble();
        double C = sc.nextDouble();

         double h = b * Math.sin(Math.toRadians(C));
        double S = 0.5 * h * a;
        double L = a + b + Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(Math.toRadians(C)));
        System.out.println(String.format("%10.8f", S));
        System.out.println(String.format("%10.8f", L));
        System.out.println(String.format("%10.8f", h));
    }
}