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