2020 AMC 10A Problem 22

For how many positive integers n \le 1000 is\left\lfloor \dfrac{998}{n} \right\rfloor+\left\lfloor \dfrac{999}{n} \right\rfloor+\left\lfloor \dfrac{1000}{n}\right \rfloornot divisible by 3? (Recall that \lfloor x \rfloor is the greatest integer less than or equal to x.)

\textbf{(A) } 22 \qquad\textbf{(B) } 23 \qquad\textbf{(C) } 24 \qquad\textbf{(D) } 25 \qquad\textbf{(E) } 26

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.