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() {
  int a, b, C;
  double S, L, h, rad;
  cin >> a >> b >> C;
  
  rad = acos(-1)*C / 180;
  S = a*b*sin(rad)/2;
  double c = sqrt(a*a + b*b - 2*a*b*cos(rad));
  L = a+b+c;
  h = b*sin(rad);
  
  printf("%lf\n%lf\n%lf\n", S, L, h);
  
      
}