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>
int main(){
  double a,b,c,C,S,L,h,rad;
  scanf("%lf %lf %lf",&a,&b,&C);
  rad=M_PI*C/180.0;
  S=(1.0/2.0)*a*b*sin(rad);
  c=sqrt(a*a+b*b-2*a*b*cos(rad));
  L=a+b+c;
  h=2.0*S/a;
  printf("%f\n",S);
  printf("%f\n",L);
  printf("%f\n",h);
  return 0;
}