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=sc.nextDouble();

		double c=Math.sqrt(Math.pow(a, 2)+Math.pow(b,2)-2*a*b*Math.cos(Math.toRadians(C)));

		double s=a*b*Math.sin(Math.toRadians(C))/2;
		double L=a+b+c;
		double h=b*Math.sin(Math.toRadians(C));

		System.out.printf("%.8f\n",s);
		System.out.printf("%.8f\n",L);
		System.out.printf("%.8f\n",h);

		sc.close();
	}

}