GAIC Math 2024 Problem 113

A rook piece moves through each square of a $2023\times 2023$ grid paper once, each time moving only one square (i.e., from the current square to an adjacent square). If the squares are numbered from 1 to $n^2$ according to the order in which the rook piece reaches them, let M denote the maximum difference in numbers between adjacent squares. Then the minimum possible value of $M$ is?