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;
import java.util.Arrays;

class Main{
	public static void main(String[] args){
		Scanner scanner = new Scanner(System.in);
		int a = scanner.nextInt();
		int b = scanner.nextInt();
		int c = scanner.nextInt();
		String s = String.format("%.5f", a * b * Math.sin(Math.toRadians(c)) / 2);
		String l = String.format("%.5f", a + b + Math.sqrt(a*a + b*b - 2*a*b*Math.cos(Math.toRadians(c))));
		String h = String.format("%.5f", b * Math.sin(Math.toRadians(c)));
		
		System.out.println(s + " " + l + " " + h);
	}
}