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.*;

class Main {
	public static void main(String[] arg)throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] div = br.readLine().split(" ");
		int a = Integer.parseInt(div[0]);
		int b = Integer.parseInt(div[1]);
		double c = Math.toRadians(Integer.parseInt(div[2]));

		double S = a*b*Math.sin(c)/2;
		double L = a+b+Math.sqrt(a*a+b*b-2*a*b*Math.cos(c));
		double H = b*Math.sin(c);
		System.out.printf("%.8f\n%.8f\n%.8f\n",S,L,H);
	}
}