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.*;
import java.lang.Math;

class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		String[] line = sc.nextLine().split(" ");
		double a= Double.parseDouble(line[0]);
		double b= Double.parseDouble(line[1]);
		double c= Double.parseDouble(line[2]);
		double s=Math.sin(c/180*Math.PI)*a*b/2;
		double l=a+b+Math.sqrt(a*a+b*b-2*a*b*Math.cos(c/180*Math.PI));
		double h=Math.sin(c/180*Math.PI)*b;
		System.out.printf("%.5f",s);
		System.out.println();
		System.out.printf("%.5f",l);
		System.out.println();
		System.out.printf("%.5f",h);
		System.out.println();
		
	}
}