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();
        System.out.printf("%.8f %.8f %.8f%n",
        		a * b * Math.sin(Math.toRadians(c)) / 2,
        		a + b + Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(Math.toRadians(c))),
        		b * Math.sin(Math.toRadians(c)));
    }
}