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) {
        int a, b, c;
        double s, l, h;
        Scanner sc = new Scanner(System.in);
        a = sc.nextInt();
        b = sc.nextInt();
        c = sc.nextInt();
        h = b * Math.sin(Math.toRadians(c));
        s = a * h / 2;
        l = a + b + Math.sqrt((a - b*Math.cos(Math.toRadians(c))) * (a - b*Math.cos(Math.toRadians(c))) + h * h);
        System.out.printf("%f\n%f\n%f\n", s, l, h);
    }
}