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).

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.

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 $i \neq j$.

Sample Input 1

3
0 0
1 2
2 1

Sample Output 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.

Sample Input 2

1
-691 273

Sample Output 2

0

Sample Input 3

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

Sample Output 3

11

见题面 Input 部分

见题面 Output 部分