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 <bits/stdc++.h>
using namespace std;

int main() {
  double a,b,c;
  cin >> a >> b >> c;
  double S = a * b * sin(c * 3.14159265 / 180) / 2;
  double L = a + b + sqrt(a*a + b*b - 2*a*b*cos(c* 3.14159265 / 180));
  double h = 2 * S / a;
 
  printf("%.8lf\n%.8lf\n%.8lf\n",S,L,h);
}