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 <stdio.h>
#include <math.h>
using namespace std;
int main() {
  double a,b,c,PI = 3.14159265359;
  cin >> a >> b >> c;
  printf("%f\n",a*b*sin(PI/180.0*c)/2.0);
  printf("%f\n",a+b+sqrt(a*a+b*b-2*a*b*cos(PI/180.0*c)));
  printf("%f\n",b*sin(PI/180.0*c));
  return 0;
}