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.*;

class Main {
	public static void main(String[] args) {
		Scanner stdIn = new Scanner(System.in);
		int a = stdIn.nextInt();
		int b = stdIn.nextInt();
		double C = Math.PI*stdIn.nextInt()/180;
		double S = a*b*Math.sin(C)/2;
		double c = Math.pow(Math.pow(a,2)+Math.pow(b,2)-2*a*b*Math.cos(C),(double)1/2);
		double L = a + b + c;
		double h = Math.sin(C)*b;
		System.out.printf("%.5f\n",S);
		System.out.printf("%.5f\n",L);
		System.out.printf("%.5f\n",h);
	}
}