Matchstick Rectangles

And again I propose to have a good time on Habré, solving an interesting puzzle :)



From the matches lined field size of 10 to 15 cells. What is the minimum number of matches you need to remove so that there is not a single rectangle left?



PS In the original version of the task there was a field of 2000 for 3000 cells, but I decided to slightly simplify your life :)

')

Discussions in the comments are welcome.

Good luck!