Question 49
A $999\times999$ board has some cells colored white and the rest red. Consider sequences of three cells $(C_1,C_2,C_3)$ such that $C_1,C_2$ are in the same row, $C_2,C_3$ are in the same column, $C_1,C_3$ are white, and $C_2$ is red. Let $T$ be the number of such sequences. Find the largest possible $T$.