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 scan = new Scanner(System.in);
    	
    	double a = scan.nextDouble();
    	double b = scan.nextDouble();
    	double C = scan.nextDouble();
    	
    	double c = Math.sqrt(((a*a) + (b*b))-2*a*b*Math.cos(Math.toRadians(C)));
    	
    	double L = a + b + c;
    	double h = b * Math.sin(Math.toRadians(C));
    	double S = a * h / 2.0;
    	
    	System.out.println(String.format("%.8f", S));
    	System.out.println(String.format("%.8f", L));
    	System.out.println(String.format("%.8f", h));
     }
}