RU-TST 2014 Problem 2

In an acute-angled triangle $ABC$ , the point $H{}$ is the orthocenter, $M{}$ is the midpoint of the side $BC$ and $\omega$ is the circumcircle. The lines $AH, BH$ and $CH{}$ intersect $\omega$ a second time at points $D, E$ and $F{}$ respectively. The ray $MH$ intersects $\omega$ at point $J{}$ . The points $K{}$ and $L{}$ are the centers of the inscribed circles of the triangles $DEJ$ and $DFJ$ respectively. Prove that $KL\parallel BC$ .