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.*;

class Main {
    public static void main (String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] values = br.readLine().split(" ");
        int a = Integer.parseInt(values[0]);
        int b = Integer.parseInt(values[1]);
        double C = Integer.parseInt(values[2]) * Math.PI / 180;

        double S = 0.5 * a * b * Math.sin(C);
        double L = a + b + Math.sqrt(a*a + b*b - 2*a*b*Math.cos(C));
        double h = 2 * S / a;

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