Let $ABCD$ be a quadrilateral whose diagonals are perpendicular, and let $S$ be the intersection of those diagonals. Let $K, L, M$ and $N$ be the reflections of $S$ on the sides $AB$, $BC$, $CD$ and $DA$ respectively. $BN$ cuts the circumcircle of $\vartriangle SKN$ at $E$ and $BM$ cuts the circumcircle of $\vartriangle SLM$ at $F$. Prove that the quadrilateral $EFLK$ is cyclic.