VN-TST 1993 Problem 1

We call a rectangle of size $2 \times 3$ (or $3 \times 2$ ) without one cell in corner a $P$ -rectangle. We call a rectangle of size $2 \times 3$ (or $3 \times 2$ ) without two cells in opposite (under center of rectangle) corners a $S$ -rectangle. Using some squares of size $2 \times 2$ , some $P$ -rectangles and some $S$ -rectangles, one form one rectangle of size $1993 \times 2000$ (figures don't overlap each other). Let $s$ denote the sum of numbers of squares and $S$ -rectangles used in such tiling. Find the maximal value of $s$ .