In an $2023\times 2023$ grid we fill in numbers $1,2,\cdots,2023^2$ without duplicating. Find the largest integer $M$ such that there exists a way to fill the numbers, satisfying that any two adjacent numbers has a difference at least $M$ (two squares $(x_1,y_1),(x_2,y_2)$ are adjacent if $x_1=x_2$ and $y_1-y_2\equiv \pm1\pmod{2023}$ or $y_1=y_2$ and $x_1-x_2\equiv \pm1\pmod{2023}$). Proposed by chengbilly.