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 static java.lang.Math.*;

import java.util.Scanner;
public class Main{
	public static void main(String[] args){
		Scanner scan = null;
		try{
			scan = new Scanner(System.in);
			double a, b , C;
			a = scan.nextDouble();
			b = scan.nextDouble();
			C = scan.nextDouble();
			double S = a * b * sin(toRadians(C)) / 2;
			System.out.println(S);
			double c = sqrt(pow(a , 2) + pow(b , 2) - 2 * a * b * cos(toRadians(C))) ;
			System.out.println(a + b + c);
			double h = 2 * S / a ;
			System.out.println (h);
		}finally{
			if(scan!=null)scan.close();
		}
	}
}