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.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        double a = sc.nextDouble();
        double b = sc.nextDouble();
        double c = sc.nextDouble();
        double S, L, h;
        S = 0.5 * a * b * Math.sin(Math.PI * c / 180);
        double d = Math.sqrt( a * a + b * b - 2 * a * b * Math.cos(Math.PI * c / 180));
        System.out.printf("%.10f\n", S);
        System.out.printf("%.10f\n", a + b + d);
        System.out.printf("%.10f\n", 2 * S / a);
        sc.close();
    }
}