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 <cstdio>
#include <cmath>
using namespace std;

int main() {
  double a, b, C;
  scanf("%lf %lf %lf", &a, &b, &C);
  printf("%.6f\n", a * b * sin(M_PI*C/180) / 2);
  printf("%.6f\n", a + b + sqrt(pow(a,2)+pow(b,2)-2*a*b*cos(M_PI*C/180)));
  printf("%.6f\n", b * sin(M_PI*C/180));
  return 0;
}