We consider a square board of $1000\times 1000$ with $1000000$ squares $1\times 1$ . A piece placed on a square threatens all squares on the board that are inside a $19\times 19$ square. with a center in the square where the piece is placed, and with sides parallel to those of the board, except for the squares in the same row and those in the same column. Determine the maximum number of pieces that can be placed on the board so that no two pieces threaten each other.