G. Eligible Segmentstime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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}.OutputPrint the number of suitable pairs (i, j).ExamplesInput
4 2
0 1
0 -1
3 0
-3 0
Output
1Input
3 3
1 -1
-1 -1
0 1
Output
3NoteIn 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.
4 2
0 1
0 -1
3 0
-3 0

1
['geometry', '*3200']