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);
        double[] a = new double[]{sc.nextDouble(), sc.nextDouble(), sc.nextDouble()};
        System.out.println(a[0] * a[1] * Math.sin((Math.PI / 180) * a[2]) / 2.0);
        System.out.println(
            a[0] + a[1] + Math.sqrt(a[0] * a[0] + a[1] * a[1] - 2 * a[0] * a[1] * Math.cos(Math.PI / 180 * a[2])));
        System.out.println(a[1] * Math.sin(Math.PI / 180 * a[2]));
    }
}