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(void)
{
	int a,b,c;
	double s=0,l=0,h=0,ra,pi=3.141592653589;
	scanf("%d%d%d",&a,&b,&c);
	ra=c*pi/180;
	s=0.5*a*b*sin(ra);
	l=sqrt(a*a+b*b-2*a*b*cos(ra))+a+b;
	h=s*2/a;
	printf("%8lf\n%8lf\n%8lf\n",s,l,h);
    return 0;
}