Given a rectangle $ABCD$. Points $E$ and $F$ lie on sides $BC$ and $CD$ respectively so that the area of triangles $ABE$, $ECF$, $FDA$ is equal to $1$. Determine the area of triangle $AEF$.
Problem
Source: 2023 Czech-Polish-Slovak Match Junior, Team p6 CPSJ
Tags: geometry, areas, rectangle