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 {
	void run() {
		Scanner scan = new Scanner(System.in);
		double a = scan.nextDouble();
		double b = scan.nextDouble();
		double c = scan.nextDouble();
		double s = 0.5 * a * b * Math.sin(Math.toRadians(c));
		double l = a + b + Math.sqrt((a*a) + (b*b) - (2*a*b*Math.cos(Math.toRadians(c))));
		double h = b * Math.sin(Math.toRadians(c));
		System.out.printf("%f %f %f", s, l, h);
	}
	public static void main(String[] args) {
		new Main().run();
	}
}