USEMO 2022 Problem 1

A stick is defined as a $1 \times k$ or $k\times 1$ rectangle for any integer $k \ge 1$ . We wish to partition the cells of a $2022 \times 2022$ chessboard into $m$ non-overlapping sticks, such that any two of these $m$ sticks share at most one unit of perimeter. Determine the smallest $m$ for which this is possible.

Holden Mui