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) throws Exception {
		Scanner scan=new Scanner(System.in);
		int a=scan.nextInt();//a
		int b=scan.nextInt();//b
		int c=scan.nextInt();//間
		double cos=Math.cos(Math.toRadians(c));//cos A
		double d=Math.sqrt(b*b+a*a-2*a*b*cos);//c
		double l=a+b+d;
		double ad=b*cos;
		double h=Math.sqrt(b*b-ad*ad);
		double S=a*h/2;
		System.out.println(S+" "+l+" "+h);
	}
}