CF1584G.Eligible Segments

You are given $n$ distinct points $p_1, p_2, \ldots, p_n$ on the plane and a positive integer $R$ .

Find the number of pairs of indices $(i, j)$ such that $1 \le i < j \le n$ , and for every possible $k$ ( $1 \le k \le n$ ) the distance from the point $p_k$ to the segment between points $p_i$ and $p_j$ is at most $R$ .

The first line contains two integers $n$ , $R$ ( $1 \le n \le 3000$ , $1 \le R \le 10^5$ ) — the number of points and the maximum distance between a point and a segment.

Each of the next $n$ lines contains two integers $x_i$ , $y_i$ ( $-10^5 \le x_i, y_i \le 10^5$ ) that define the $i$ -th point $p_i=(x_i, y_i)$ . All points are distinct.

It is guaranteed that the answer does not change if the parameter $R$ is changed by at most $10^{-2}$ .

Print the number of suitable pairs $(i, j)$ .

In the first example, the only pair of points $(-3, 0)$ , $(3, 0)$ is suitable. The distance to the segment between these points from the points $(0, 1)$ and $(0, -1)$ is equal to $1$ , which is less than $R=2$ .

In the second example, all possible pairs of points are eligible.