Probability Experiment

Running a probability experiment as a computer simulation is a standard tool in mathematics and statistics. Draw a circle inside a large square, scatter a huge number of random points, and the fraction that lands inside the circle approximates $\pi$.

Here is a different experiment. Pick three random points on the circumference of a circle and consider the probability that the triangle they form is acute. A triangle is acute when all three of its interior angles are smaller than 90 degrees. A short calculation shows that this probability is $0.25$. To check whether a simulation lands near that value, count the acute triangles in one sample. Given $N$ points on a circle, count how many acute triangles can be formed by choosing three of them. Count the same triangle only once: after counting triangle abc, do not count bca, cab, or cba again.

The first line has the number of points $N$ and the radius $R$ of the circle. ($1 \le N \le 200000$, $1 \le R \le 100000$)

The circle is centered at the origin. When a point $P$ on the circle sits $\theta$ degrees counterclockwise from the positive $x$ axis, its position is written as $\phi = \theta \times 1000$, so the coordinates of $P$ are $(R\cos\theta,\ R\sin\theta)$.

Each of the next $N$ lines has the $\phi$ value of one point, given in increasing order of $\phi$. Every $\phi$ is an integer ($0 \le \phi < 360000$), and the $N$ values are all different.

Print the number of acute triangles.

The intermediate values and the answer can exceed the range of a 32-bit integer, so use a 64-bit integer type (long long in C++).