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;

public class Main {

  public static void main(String[] args) {
    Scanner stdin = new Scanner(System.in);
    double a = stdin.nextDouble();
    double b = stdin.nextDouble();
    double rad = Math.toRadians(stdin.nextInt());
    double c = Math.sqrt(Math.pow(a, 2) + Math.pow(b, 2) - 2 * a * b * Math.cos(rad));
    double S = a * b / 2 * Math.sin(rad);
    double L = a + b + c;
    double h = 2 * S / a;
    System.out.printf("%f%n%f%n%f%n", S, L, h);
  }

}