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){
    Scanner input = new Scanner(System.in);
    int a, b, c;
    a = input.nextInt();
    b = input.nextInt();
    c = input.nextInt();

    double rad, l, s, h;
    rad = c * Math.PI / 180.0;
    s = 1 / 2.0 * Math.sin(rad) * a * b;
    l = a + b + Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(rad));
    h = 2 * s / a;

    System.out.println(s + "\n" + l + "\n" + h);
  }
}