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) throws Exception {
		Scanner sc = new Scanner(System.in);
		
		int a = sc.nextInt();
		int b = sc.nextInt();
		int r = sc.nextInt();
		
		double h = Math.sin(Math.toRadians(r))*b;
		double S = a*h/2.0;
		
		double l1 = Math.cos(Math.toRadians(r))*b;
		double l2 = a-l1;
		double c = Math.sqrt(l2*l2+h*h);
		
		System.out.println(String.format("%.5f", S));
		System.out.println(String.format("%.5f", a+b+c));
		System.out.println(String.format("%.5f", h));
	}
}