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);
        Double a=sc.nextDouble();
        Double b=sc.nextDouble();
        Double c=sc.nextDouble();
        sc.close();
        //三角形の面積
        System.out.println(a*b*Math.sin(c* (Math.PI / 180))/2);
        //周の長さ
        System.out.println(a + b + Math.sqrt(a*a + b*b - 2*a*b*Math.cos(c* (Math.PI / 180))));
        //a を底辺としたときの高さ h
        System.out.println(b*Math.sin(c* (Math.PI / 180)));
    }
}