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 IOException{
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    String str1 = br.readLine();
    String[] str2 = str1.split(" ");
    double a, b, C, c;
    double S, L, h;

    a = Double.parseDouble(str2[0]);
    b = Double.parseDouble(str2[1]);
    C = Double.parseDouble(str2[2]);
    c = Math.toRadians(C);

    S = a * b * Math.sin(c) * 1/2;
    L = Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(c));
    h = b * Math.sin (c);

    System.out.println(S);
    System.out.println(L + a + b);
    System.out.println(h);
  }
}