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<stdio.h>
#include<math.h>
#include<float.h>

int main(){
  double a,b,C,S,L,h,c,x,y;
  scanf("%lf %lf %lf",&a,&b,&C);
  x = sin(C*M_PI/180);
  y = cos(C*M_PI/180);
  S = a * b * x / 2;
  L = a + b + sqrt(a*a+b*b-2*a*b*y);
  h = 2*S/a;
  printf("%lf\n%lf\n%lf\n",S,L,h);
  return 0;
}