A board of size $2015 \times 2015$ is covered with sub-boards of size $2 \times 2$, each of which is painted like chessboard. Each sub-board covers exactly $4$ squares of the board and each square of the board is covered with at least one square of a sub-board (the painted of the sub-boards can be of any shape). Prove that there is a way to cover the board in such a way that there are exactly $2015$ black squares visible. What is the maximum number of visible black squares?