Nacho must write the $26^2=676$ integers from 1 to 676 on a $26 \times 26$ board, one in each cell. Then Julián chooses two neighboring cells (sharing a side or a vertex). Julián's goal is that the sum of the numbers in those two cells is a multiple of 4. Determine whether Nacho can distribute the numbers so that Julián cannot achieve his goal.