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.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {

	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		
		final int a = sc.nextInt();
		final int b = sc.nextInt();
		final int C = sc.nextInt();
		
		final double h = Math.sin(Math.toRadians(C)) * b;
		final double rest_a = a - Math.cos(Math.toRadians(C)) * b;
		
		final double c = Math.sqrt(h * h + rest_a * rest_a);
		
		System.out.printf("%.7f\n%.7f\n%.7f\n", a * h / 2, a + b + c, h);
		
	}
}