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){
        Scanner sc = new Scanner(System.in);

        int a = sc.nextInt();
        int b = sc.nextInt();
        int deg = sc.nextInt();

        double rad = Math.toRadians(deg);

        double S = a * b * Math.sin(rad) / 2.0;
        double L = a + b + Math.sqrt(Math.pow(a * Math.cos(rad) - b * 1.0, 2.0) + Math.pow(a * Math.sin(rad), 2.0));
        double h = 2.0 * S / (double)a;

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

        sc.close();
    }
}