Piet (Mondrian)'s Puzzle

For more information, watch this video, and go to A276523 for a related sequence.

The Mondrian Puzzle (for an integer n) is the following:

Fit non-congruent rectangles into a n*n square grid. What is the smallest difference possible between the largest and the smallest rectangle?

For 6, the optimal difference for M(6) is 5, and can be demonstrated like so:

 ___________| |S|_______|| | |   L   || |_|_______|| |     |   || |_____|___||_|_________| (fig. I)

The largest rectangle (L) has an area of 2 * 4 = 8, and the smallest rectangle (S) has an area of 1 * 3 = 3. Therefore, the difference is 8 - 3 = 5.

Keep in mind that currently, no optimal solutions for n > 44 have been found.

Your task is to create a program that generates a Mondrian grid that contains a (non-optimal) solution, given an integer n.

You will be tested on the numbers from 100 to 150. Your score for each test will be the difference between the largest and smallest rectangle. Your total score is the sum of your scores for all the tests from 100 to 150.

You must present your output like so:

{number}{grid}

Where number is the score (the difference between largest and smallest), and grid is either:

• A multi-lined string, or
• A two-dimensional list.

The grid MUST clearly show where a rectangle starts and ends.

Rules:

• Your program must fit within your answer.
• Your program must output a value for any number between 100 and 150 within 1 hour on a modern laptop.
• Your program must generate the same solution for an integer n every time the program is run.
• You must provide a link to the outputs of all 51 solutions (using Pastebin, Github Gist... anything, really).
• You must have at least two rectangles on the square grid for your solution.