First Round

On a $4\times 4$ board, there are $16$ grass hoppers, each on its own square. At a certain time, each grass hopper jumps to an adjacent square: to the square above, below, left, or right of its current square, but not diagonally and not leaving the board. What is the maximum number of squares that can be empty after the grass hoppers have jumped? A) $8$ B) $9$ C) $10$ D) $11$ E) $12$