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 CPP):

Solution:
#include <stdio.h>
#include <math.h>

int main(){
  double a, b, c, s, l, h;
  scanf("%lf%lf%lf", &a, &b, &c);
  h = b * sin(c * M_PI / 180);
  s = a * h / 2;
  l = a + b + (pow((a - b * cos(c * M_PI / 180)) * (a - b * cos(c * M_PI /180)) + h * h, 0.5));
  printf("%lf\n%lf\n%lf\n", s, l, h);
}