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 sc = new Scanner(System.in);
    int a = sc.nextInt();
    int b = sc.nextInt();
    int c = sc.nextInt();
    double r = c * Math.PI / 180.0;
    double H = b * Math.sin(r);
    double S = a * H / 2;
    double L = a + b + Math.sqrt(H * H + (a - b * Math.cos(r)) * (a - b * Math.cos(r)));
    System.out.print(S + "\n" + L + "\n" + H + "\n");
  }
}