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) {
        // write your code here
        Scanner scanner=new Scanner(System.in);
        double a=scanner.nextLong();
        double b=scanner.nextLong();
        double c=scanner.nextInt()*Math.PI/180.0;
        System.out.println(a*b*Math.sin(c)/2);
        System.out.println(Math.sqrt(Math.pow(a,2)+Math.pow(b,2)-2*a*b*Math.cos(c))+a+b);
        System.out.println(b*Math.sin(c));
    }

}