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, S, L, h;
  cin >> a >> b >> C;
  S = 0.5 * a * b * sin(C * M_PI / 180);
  L = a + b + sqrt(a * a + b * b - 2 * a * b * cos(C * M_PI / 180));
  h = 2 * S / a;
  cout << fixed << setprecision(6) << S << endl << L << endl << h << endl;
}