IR-MO 2004 Problem 24

In triangle $ABC$ , points $M,N$ lie on line $AC$ such that $MA=AB$ and $NB=NC$ . Also $K,L$ lie on line $BC$ such that $KA=KB$ and $LA=LC$ . It is know that $KL=\frac12{BC}$ and $MN=AC$ . Find angles of triangle $ABC$ .