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.*;

public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] line = br.readLine().split(" ");
        int a = Integer.parseInt(line[0]);
        int b = Integer.parseInt(line[1]);
        int C = Integer.parseInt(line[2]);
        double c = Math.sqrt(Math.pow(a, 2) + Math.pow(b, 2) - 2*a*b*Math.cos(Math.toRadians(C)));
        double S = a*b*Math.sin(Math.toRadians(C))*0.5;
        double L = a + b + c;
        double h = 2*S/a;

        System.out.println(S + "\n" + L + "\n" + h);
    }
}