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();
	int c = scan.nextInt();
	double h = b * Math.sin(Math.toRadians(c));
	double x = Math.sqrt(h * h +
			     (a - b * Math.cos(Math.toRadians(c)))*(a - b * Math.cos(Math.toRadians(c))));
	double S = a * h / 2;
	System.out.println(S);
	System.out.println(a+b+x);
	System.out.println(h);
    }
}