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;

public class Main {
	public static void main(String[]args){
		Scanner sc=new Scanner(System.in);
		double a=sc.nextDouble(),b=sc.nextDouble(),c=sc.nextDouble(),PI=Math.acos(-1),c1=c*PI/180,S,L,h;
		S=a*b*Math.sin(c1)/2;
		L=a+b+Math.sqrt(a*a+b*b-2*a*b*Math.cos(c1));
		h=b*Math.sin(c1);
		System.out.println(S);
		System.out.println(L);
		System.out.println(h);
	}
}