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 sc = new Scanner(System.in);
        double a = sc.nextDouble();
        double b = sc.nextDouble();
        double c = Math.toRadians(sc.nextDouble());


        double S,L,h;
        S  = a*b*Math.sin(c)/2;
        L = a+b+Math.sqrt(Math.pow(a, 2)+Math.pow(b, 2)-(2*a*b*Math.cos(c)));
        h = 2*S/a;


        System.out.printf("%f\n%f\n%f\n",S,L,h);

        sc.close();
	}


}