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);
		int a = scan.nextInt();
		int b = scan.nextInt();
		double C = Math.toRadians(scan.nextDouble());
		double S = a * b * Math.sin(C) / 2;
		double c = Math.sqrt(Math.pow(a, 2) + Math.pow(b, 2) - 2  * a * b * Math.cos(C));
		double h = b * Math.sin(C);
		double L = a + b + c;
		String line_sep = System.getProperty("line.separator");
		System.out.println(S + line_sep + L + line_sep + h);
	}
}