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 sc = new Scanner(System.in);
            
        int a = sc.nextInt();
        int b = sc.nextInt();
        int C = sc.nextInt();
        
        double S = (a * b) / 2 * Math.sin(Math.toRadians(C));
        double c = Math.sqrt(a*a + b*b - 2 * a * b * Math.cos(Math.toRadians(C)));
        double h = b * Math.sin(Math.toRadians(C));
        
        System.out.println(S);
        System.out.println(a + b + c);
        System.out.println(h);
            
        sc.close();
    }
}