Eligible Segments
Description
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 $(i, j)$.
Input
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 $10^{-2}$.
Output
Print the number of suitable pairs $(i, j)$.
Samples
4 2
0 1
0 -1
3 0
-3 0
1
3 3
1 -1
-1 -1
0 1
3
Note
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.