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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
public class Main {
	public static void main(String[] args)throws IOException {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		String[] dat=br.readLine().split(" ");
		int a,b,c;
		double S,L,h;
		a=Integer.parseInt(dat[0]);
		b=Integer.parseInt(dat[1]);
		c=Integer.parseInt(dat[2]);
		S=0.5*a*b*Math.sin(Math.toRadians(c));
		h=b*Math.sin(Math.toRadians(c));
		L=a+b+Math.sqrt(a*a+b*b-2*a*b*Math.cos(Math.toRadians(c)));
		System.out.printf("%.8f\n",S);
		System.out.printf("%.8f\n",L);
		System.out.printf("%.8f",h);
	}
}