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(),b=sc.nextDouble(),c=sc.nextDouble();

		double h=b*Math.sin(Math.toRadians(c));
		double S=a*h/2;
		double l=Math.sqrt(a*a+b*b-2*a*b*Math.cos(Math.toRadians(c)))+a+b;
		System.out.printf("%f", S);
		System.out.println();
		System.out.printf("%f", l);
		System.out.println();
		System.out.printf("%f", h);


	}
}