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 in = new Scanner(System.in);
    double a = in.nextDouble();
    double b = in.nextDouble();
    int C    = in.nextInt();

    double S = 0.5 * a * b * Math.sin(Math.toRadians(C));
    double L = a + b + Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(Math.toRadians(C)));
    double h = b * Math.sin(Math.toRadians(C));
    
    System.out.printf("%5.8f", S);
    System.out.println();
    System.out.printf("%5.8f", L);
    System.out.println();
    System.out.printf("%5.8f", h);
  }
}