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;

class Main{
	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		sc.useDelimiter("\\s");
		int a = sc.nextInt();
		int b = sc.nextInt();
		int C = sc.nextInt();

		double L = a + b + Math.sqrt(a*a + b*b - 2.0*a*b*Math.cos(Math.toRadians(C)));
		double h = b*Math.sin(Math.toRadians(C));
		double S = a*h/2.0;

		System.out.printf("%.8f\n",S);
		System.out.printf("%.8f\n",L);
		System.out.printf("%.8f\n",h);
	}
}