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;
  scanf("%lf %lf %lf", &a, &b, &c);
  c = c / 180.0 * M_PI;
  printf("%f\n%f\n%f\n", 
    a * b * sin(c) / 2.0,
    a + b + sqrt(pow(a * sin(c), 2) + pow(b - a * cos(c), 2)),
    b * sin(c)
  );
  return 0;
}