SMO 2020 Junior Round 1 Question 17

In the following diagram, $ABCD$ is a rectangle where $E$ and $F$ are points on $BC$ and $CD$ respectively. The area of triangle $AEF$, denoted $[AEF]$, is $2037$. If
$$[AECF]=2[ABE]=3[ADF],$$
what is the area of the rectangle $ABCD$?