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 std = new Scanner(System.in);
		double a = Double.parseDouble(std.next());
		double b = Double.parseDouble(std.next());
		double c = Math.toRadians(Double.parseDouble(std.next()));

		double s = 0.5 * a * b * Math.sin(c);
		double l = Math.pow(a*a + b*b - 2*a*b*Math.cos(c),0.5) + a + b;
		double h = 2 * s / a;

		System.out.println(String.format("%.5f", s));
		System.out.println(String.format("%.5f", l));
		System.out.println(String.format("%.5f", h));
	}
}