# Count Squares

This problem is adapted from Count the Number of Squares at Wolfram Challenges, so you might want to first check out that page for illustrative visualizations of this problem.

Given a sequence of points (coordinates **x, y** as nonnegative integers), your function should count how many squares exist so that all four corners are members of points. Note that these squares are not required to be axis-aligned so that their sides would have to be either horizontal and vertical. For example, the points **(0, 3), (3, 0), (6, 3), (3, 6)** define a square, even if it may happen to look like a lozenge from our axis-aligned vantage point.

By the way, if your want to try another approach and count squares, having lines between points, The Square Chest awaits you!

**Input:** List of tuples (tuple) of two integers (int).

**Output:** Integer (int).

**Examples:**

assert count_squares([(0, 0), (1, 0), (0, 1), (1, 1)]) == 1 assert ( count_squares( [(0, 0), (1, 0), (2, 0), (0, 1), (1, 1), (2, 1), (0, 2), (1, 2), (2, 2)] ) == 6 ) assert ( count_squares( [ (4, 3), (1, 1), (5, 3), (2, 3), (3, 2), (3, 1), (4, 2), (2, 1), (3, 3), (1, 2), (5, 2), ] ) == 3 )

*If you feel yourself in need of additional chapter of explanation (tip), press this line.*

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To identify four points that constitute a square, note how every square has bottom left corner point x, y and direction vector dx, dy towards its upper left corner point that satisfies dx >= 0 & dy > 0, so that the points (x+dx,y+dy), (x+dy,y-dx), (x+dx+dy,y-dx+dy) for the top left, bottom right and top right corners of that square, respectively, are also included in points. You can therefore (effectively) iterate through all possibilities for the bottom left point and the direction vector and be guaranteed to find all squares in the grid.
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*The mission was taken from Python CCPS 109. It is taught for Ryerson Chang School of Continuing Education by Ilkka Kokkarinen*

CheckiO Extensions allow you to use local files to solve missions. More info in a blog post.

In order to install CheckiO client you'll need installed Python (version at least 3.8)

Install CheckiO Client first:

pip3 install checkio_client

Configure your tool

checkio --domain=py config --key=

Sync solutions into your local folder

checkio sync

(in beta testing) Launch local server so your browser can use it and sync solution between local file end extension on the fly. (doesn't work for safari)

checkio serv -d

Alternatevly, you can install Chrome extension or FF addon

checkio install-plugin

checkio install-plugin --ff

checkio install-plugin --chromium

Read more here about other functionality that the checkio client provides. Feel free to submit an issue in case of any difficulties.