BALKAN-SL 2011 G2

Let $ABC$ be a triangle and let $O$ be its circumcentre. The internal and external bisectrices of the angle $BAC$ meet the line $BC$ at points $D$ and $E$ , respectively. Let further $M$ and $L$ respectively denote the midpoints of the segments $BC$ and $DE$ . The circles $ABC$ and $ALO$ meet again at point $N$ . Show that the angles $BAN$ and $CAM$ are equal.