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.*;

class Main {
	static Scanner sc = new Scanner(System.in);
	public static void main(String[] args) {
		
		double a = sc.nextDouble(); double b = sc.nextDouble(); double angle = Math.toRadians(sc.nextDouble());
		double c = Math.sqrt(a*a+b*b-(2*a*b*Math.cos(angle)));
		
		double x = (a*a+b*b-c*c)/(2*a);
		double y = Math.sqrt(b*b-x*x);
		
		System.out.println(String.format("%.5f",a*y/2));
		System.out.println(String.format("%.5f",a+b+c));
		System.out.println(String.format("%.5f",y));
	}
}