IR-MO 2002 Problem 10

$H,I,O,N$ are orthogonal center, incenter, circumcenter, and Nagelian point of triangle $ABC$ . $I_{a},I_{b},I_{c}$ are excenters of $ABC$ corresponding vertices $A,B,C$ . $S$ is point that $O$ is midpoint of $HS$ . Prove that centroid of triangles $I_{a}I_{b}I_{c}$ and $SIN$ concide.