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>
#define PI 3.14159265
int main() {
	double a,b,t;
	scanf("%lf%lf%lf",&a,&b,&t);
	
	double s=0.5*a*b*sin(t/180.0*PI);
	double c=sqrt(a*a+b*b-2*a*b*cos(t/180.0*PI));
	double l=a+b+c;
	double h=s*2/a;
	
	printf("%lf %lf %lf\n",s,l,h);
	return 0;
}