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 scan = new Scanner(System.in);

    int a = scan.nextInt();
    int b = scan.nextInt();
    int C = scan.nextInt();

    double S = a * b * Math.sin(Math.toRadians(C)) / 2;
    System.out.println(S);
    double c = Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(Math.toRadians(C)));
    System.out.println(a + b + c);
    System.out.println(2 * S / a);

  }

}