9684: ABC187 —— B - Gentle Pairs
[Creator : ]
Description
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).
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).
Input
Input is given from Standard Input in the following format:
```
$N$
$x_1$ $y_1$
$\vdots$
$x_N$ $y_N$
```
```
$N$
$x_1$ $y_1$
$\vdots$
$x_N$ $y_N$
```
Output
Print the answer.
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 $i \neq j$.
- $1 \le N \le 10^3$
- $|x_i|, |y_i| \le 10^3$
- $x_i \neq x_j$ for $i \neq j$.
Sample 1 Input
3
0 0
1 2
2 1
Sample 1 Output
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.
Sample 2 Input
10
-31 -35
8 -36
22 64
5 73
-14 8
18 -58
-41 -85
1 -88
-21 -85
-11 82
Sample 2 Output
11