KöMaL 2016 B4797

In triangle $ABC$ , $D$ , $E$ and $F$ are arbitrary interior points of sides $AB, BC$ and $CA$ , respectively. Let $G$ , $H$ and $I$ denote the centroids of triangles $ADF$ , $BED$ and $CFE$ , respectively. Furthermore, let $S$ , $K$ , $L$ be the centroids of triangles $ABC$ , $DEF$ and $GHI$ , respectively. Prove that the points $K$ , $L$ and $S$ are collinear.