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) {
		try(Scanner sc = new Scanner(System.in)){
			int a = sc.nextInt();
			int b = sc.nextInt();
			int C = sc.nextInt();
			double rad = (double)C / 180 * Math.PI;
			double S = a*b*Math.sin(rad)/2;
			double L = a+b+Math.sqrt(a*a+b*b-2*a*b*Math.cos(rad));
			double H = S*2/a;
			System.out.println(S);
			System.out.println(L);
			System.out.println(H);
		}
	}
}