Take a square, $135 \times 135$. A bunch of smaller squares, each $1 \times 1$, are placed in some fashion inside the larger square. However,they must be placed with specific criteria: there must be an empty $1 \times 1$ gap on the north and south sides, as well as a $4 \times 1$ gap on their east side, with the $x_1$ of each measurement adjacent to the respective sides of the square. These gaps may overlap. Note that this does mean that the eastern wall has a $4$-unit gap before the first smaller squares, and the northern and southern walls have a $1$-unit gap before the first smaller squares from that direction.
What is the maximum number of small squares that may be placed in the large square given these criteria? If there is a formula that can be used, that would be amazing.