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.io.*;
import java.util.Arrays;
import java.util.Scanner;

public class Main{
	public static void main(String[] args) throws IOException{ 
		Scanner sc = new Scanner(System.in);
		Double a = sc.nextDouble();
		Double b = sc.nextDouble();
		Double c = Math.toRadians(sc.nextDouble());
		Double s = (a*b)*(Math.sin(c))/2.0;
		Double d = Math.sqrt(a*a+b*b-2*a*b*Math.cos(c));
		Double l = a+b+d;
		Double h = b*Math.sin(c);
		System.out.printf("%.5f\n",s);
		System.out.printf("%.5f\n",l);
		System.out.printf("%.5f\n",h);
	}
}