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);
	C = C*3.14159265 / 180;
	printf("%f\n%f\n%f\n", 0.5*a*b*std::sin(C), a+b+std::sqrt(a*a + b*b - 2 * a*b*std::cos(C)), b*std::sin(C));
	return 0;
}