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.*;

class Main {
        public static void main(String args[]) {
                try (Scanner sc = new Scanner(System.in)) {
                        double a = sc.nextDouble();
                        double b = sc.nextDouble();
                        double c = Math.toRadians(sc.nextDouble());
                        System.out.println(a * b * Math.sin(c) / 2.);
                        System.out.println((a + b + Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(c))));
                        System.out.println(b * Math.sin(c));
                }
        }
}