# Problem C

Treehouse

*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

Illustration of the two possible treehouse locations in
sample 1.

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 |