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.Scanner;
public class Main{
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        double a = scan.nextDouble();
        double b = scan.nextDouble();
        double C = scan.nextDouble();
        double c = Math.sqrt((a *a) + (b * b) - (2 * a * b * Math.cos(C * Math.PI / 180)));
        double l = a + b + c;
        double s = l/2;
        double area = Math.sqrt(s* (s-a) *(s-b) *(s-c));
        double h = area * (2 / a);
        System.out.printf("%.8f\n", area);
        System.out.printf("%.8f\n", l);
        System.out.printf("%.8f\n", h);

    }
}