CN-TST 2022 Problem 1

In a cyclic convex hexagon $ABCDEF$ , $AB$ and $DC$ intersect at $G$ , $AF$ and $DE$ intersect at $H$ . Let $M, N$ be the circumcenters of $BCG$ and $EFH$ , respectively. Prove that the $BE$ , $CF$ and $MN$ are concurrent.