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) {
        Scanner scan = new Scanner(System.in);
        double a = scan.nextDouble(), b = scan.nextDouble(), C = scan.nextDouble();
        double rad,s, l, h;

        rad = C * Math.PI / 180 ;

        s = a * b * Math.sin(rad) / 2 ;
        l = a + b + Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(rad));
        h = 2 * s / a ;

        System.out.printf("%8f\n%8f\n%8f",s, l, h);
    }
}