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.*;

class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        double a = sc.nextDouble();
        double b = sc.nextDouble();
        double c = sc.nextDouble();

        double side = Math.sqrt(((a * a) + (b * b)) - (2 * a * b * Math.cos(Math.toRadians(c))));
        double area = a * b * Math.sin(Math.toRadians(c)) / (double)2;

        System.out.printf("%.8f\n",area);
        System.out.printf("%.8f\n",a + b + side);
        System.out.printf("%.8f\n",area * 2 / a);

    }
}