SMO 2017 Junior Round 1 Question 18

Let $ABC$ be a triangle, $D$ be a point on $AC$ such that $AD=DC$ and $E$ be a point on $BC$ such that $BE=2EC$. Let $F$ be the intersection of $BD$ and $AE$. If the area of the triangle $ABC$ is 100, find the area of triangle $ADF$.