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) {
		
		try (Scanner sc = new Scanner(System.in);) {
			
			double a = sc.nextDouble();
			double b = sc.nextDouble();
			double C = sc.nextDouble();
			
			double S = a * b * Math.sin(C / 180 * Math.PI) / 2;
			double L = a + b + Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(C / 180 * Math.PI));
			double h = 2 * S / a;
			
			System.out.format("%.6f %.6f %.6f\n", S, L, h);
		}
	}
}