Question 3
Define a domino to be a $1\times2$ rectangular block. A $2023\times2023$ square grid is filled with non-overlapping dominoes, leaving a single $1\times1$ gap. John then repeatedly slides dominoes into the gap; each domino is moved at most once. What is the maximum number of times that John could have moved a domino?
(Example: In the $3\times3$ grid shown below, John could move $2$ dominoes: $D$, followed by $A$.)
(Example: In the $3\times3$ grid shown below, John could move $2$ dominoes: $D$, followed by $A$.)