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 <cmath>
using namespace std;
int main(){
  double a, b, C;
  scanf("%lf %lf %lf", &a, &b, &C);
  printf("%lf\n", a*b*sin(C*M_PI/180)/2);
  printf("%lf\n", a+b+sqrt(a*a+b*b-2*a*b*cos(C*M_PI/180)));
  printf("%lf\n", b*sin(C*M_PI/180));
}