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 <iostream>
#include <cstdio>
#include <cmath>
using namespace std;
int main(){

  int a,b,c;
  double s,l,h,d,e;
  
  cin >>a>>b>>c;

  d=c*M_PI/180;
  s=((double)1/(double)2)*a*b*sin(d);
  l=a*a+b*b-2*a*b*cos(d);
  h=b*sin(d);
  e=sqrt(l)+a+b;

  printf("%0.8f\n%0.8f\n%0.8f\n",s,e,h);

  return 0;

}