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.*;
public class Main {
    public static Scanner sc = new Scanner(System.in);
    public static void main(String[] args) throws Exception {
    	int i, j, k;
    	
    	double a = sc.nextDouble();
    	double b = sc.nextDouble();
    	double c = sc.nextDouble();
    	
    	double S = a * b * Math.sin(Math.toRadians(c)) / 2;
    	double L = a + b + Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(Math.toRadians(c)));
    	double h = 2 * S / a;
    	
    	System.out.printf("%f\n%f\n%f", S, L, h);
    }
}