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 <cstdio>
#include <cmath>

int main(){
	double a, b, C;
	scanf("%lf %lf %lf", &a,&b,&C);
	printf("%.8lf\n", 0.5*a*b*sin(M_PI*C/180));
	printf("%.8lf\n", sqrt(a*a+b*b-2*a*b*cos(M_PI*C/180))+a+b);
	printf("%.8lf\n", b*sin(M_PI*C/180));	
}