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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args) throws IOException {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] input = br.readLine().split(" ");
		double a = Double.parseDouble(input[0]);
		double b = Double.parseDouble(input[1]);
		double th = Math.PI * Double.parseDouble(input[2]) / 180.0;
		double c = Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(th));
		double s = a * b * Math.sin(th) / 2.0;
		System.out.println(s);
		System.out.println(a + b + c);
		System.out.println(2.0 * s / a);
	}
}