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>
#define _USE_MATH_DEFINES
#include <cmath>
using namespace std;
 
int main(){
  double a,b,c,s,l,h;
  cin >> a >> b >> c;
  s = (a*b*sin(M_PI*c/180.0))/2.0;
  l = a + b + sqrt(a*a+b*b-2.0*a*b*cos(M_PI*c/180.0));
  h = b*sin(M_PI*c/180.0);
  printf("%.8lf\n%.8lf\n%.8lf\n",s,l,h);
}