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.Scanner;
import java.lang.Math;

class Main{
	public static void main(String[] arg){
	
		
		
		
		Scanner sc = new Scanner(System.in);
		double a,b,c,co,radian,radians;
		a=sc.nextDouble();
		b=sc.nextDouble();
		co=sc.nextDouble();
		radian=Math.toRadians(co);
		radians=Math.cos(radian);
		
		c= b*b+a*a-2*b*a*radians;
		c=Math.sqrt(c);
		double p =(a+b+c)/2;
		
		double S=Math.sqrt(p*(p-a)*(p-b)*(p-c));
		double H=2*S/a;
		double L=a+b+c;
		System.out.printf("%.8f\n",S);
		System.out.printf("%.8f\n",L);
		System.out.printf("%.8f\n",H);
		
		}
}