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 void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int a=sc.nextInt();
		int b=sc.nextInt();
		int c=sc.nextInt();
		double C=Math.toRadians(c);
		double S=0.5*a*b*Math.sin(C);
		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", S);
		System.out.printf("%.8f\n", L);
		System.out.printf("%.8f\n", h);
	}
}