G. Eligible Segments
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$R$$$.

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 $$$(i, j)$$$.

Examples
Input
4 2
0 1
0 -1
3 0
-3 0
Output
1
Input
3 3
1 -1
-1 -1
0 1
Output
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.