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 scn = new Scanner(System.in);
        double a = scn.nextDouble();
        double b = scn.nextDouble();
        double C = scn.nextDouble();
        double S, c, L, h;
        h = b*Math.sin(Math.toRadians(C));
        S = a*h/2;
        c = Math.sqrt(Math.pow(a,2)+Math.pow(b,2)-2*a*b*Math.cos(Math.toRadians(C)));
        L = a+b+c;
        System.out.printf("%.8f%n",S);
        System.out.printf("%.8f%n",L);
        System.out.printf("%.8f%n",h);

        scn.close();

    }

}