B - Gentle Pairs

Score : $200$ points

Problem Statement

On the $xy$-plane, We have $N$ points numbered $1$ to $N$. Point $i$ is at $(x_i, y_i)$, and the $x$-coordinates of the $N$ points are pairwise different.

Find the number of pairs of integers $(i, j)\ (i < j)$ that satisfy the following condition:

• The line passing through Point $i$ and Point $j$ has a slope between $-1$ and $1$ (inclusive).

Constraints

• All values in input are integers.
• $1 \le N \le 10^3$
• $|x_i|, |y_i| \le 10^3$
• $x_i \neq x_j$ for $i \neq j$.

Input

Input is given from Standard Input in the following format:

$N$

$x_1$ $y_1$

$\vdots$

$x_N$ $y_N$

Output

Print the answer.

3
0 0
1 2
2 1

2

The slopes of the lines passing through $(0, 0)$ and $(1, 2)$, passing through $(0, 0)$ and $(2, 1)$, and passing through $(1, 2)$ and $(2, 1)$ are $2$, $\frac{1}{2}$, and $-1$, respectively.

1
-691 273

0

10
-31 -35
8 -36
22 64
5 73
-14 8
18 -58
-41 -85
1 -88
-21 -85
-11 82

11