Question 9
In a $999 \times 999$ square table some cells are white and the remaining ones are red. Let $T$ be the number of triples $(C_{1}, C_{2}, C_{3})$ of cells, the first two in the same row and the last two in the same column, with $C_{1}$ and $C_{3}$ white and $C_{2}$ red. Find the maximum value $T$ can attain.