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 stdIn = new Scanner(System.in);
		int a = stdIn.nextInt();
		int b = stdIn.nextInt();
		int C = stdIn.nextInt();
		
		double Cc = C * Math.PI /180;
		
		double L = Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(Cc));
		double h = b * Math.sin(Cc);
		double S = b * Math.sin(Cc) * a /2;
		
		System.out.println(S);
		System.out.println(L + a + b);
		System.out.println(h);
	}
}