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.math.BigDecimal;
import java.util.Scanner;

public class Main {
	private static Scanner sc = new Scanner(System.in);

	public static void main(String[] args) {
		double a = sc.nextDouble();
		double b = sc.nextDouble();
		int C = sc.nextInt();

		double S = (a * b * Math.sin(Math.toRadians(C))) /2 ;
		double c = Math.sqrt(Math.pow(a, 2) + Math.pow(b, 2) - 2 * a * b * Math.cos(Math.toRadians(C)));
		double L = a + b + c;
		double h = 2 * S / a;

		System.out.println(BigDecimal.valueOf(S).toPlainString() + " " + BigDecimal.valueOf(L).toPlainString() + " " + BigDecimal.valueOf(h).toPlainString());

	}

}