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 h = b * Math.sin(c);
		double s = a * h / 2;
		double l = Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(c));
		
		System.out.println(String.format("%.4f %.4f %.4f", s, a + b + l, h));
		
		sc.close();
	}
}