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 stdIn = new Scanner(System.in);
		int a = stdIn.nextInt();
		int b = stdIn.nextInt();
		int c = stdIn.nextInt();
	
		System.out.println(Math.sin(Math.toRadians(c))*a*b/2);
		System.out.println(Math.sqrt(Math.pow(a,2)+Math.pow(b,2)-2*a*b*Math.cos(Math.toRadians(c)))+a+b);
		System.out.println(Math.sin(Math.toRadians(c))*b);
	}
}