Problem C
Treehouse

Pusheen wants to build a treehouse in the Treehouse forest in Brunnshög in the north of Lund. The treehouse should to be built on a square platform in the treetops, with a tree in each of the four corners. When Pusheen has picked a spot to built the treehouse, trees that are located between the corners will be cut down. Pusheen has a 2D map with all the (x, y)-coordinates of the trees in the forest. In how many places can they build a square treehouse?

Input

The first line has an integer $4 \leq N \leq 2\, 000 $, the number of trees in the forest. Each of the following $N$ lines has two integers $-10,000\leq x_ i, y_ i \leq 10,000$, the x- and y-coordinates of tree $i$. All points are distinct.

Output

An integer, the number of suitable spots for a tree house.

Scoring

Group	Points	Limits
$1$	$20$	$N \leq 50$
$2$	$80$	No further restrictions

Sample Explanation

Sample Input 1	Sample Output 1
9 1 5 1 7 3 1 3 5 3 7 5 7 6 2 7 3 7 6	2