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?

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.

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

Illustration of the two possible treehouse locations in sample 1.