Geometry Essentials · Superchallenge problem

Seven rays $OA_1, OA_2, \ldots, OA_7$ leave point $O$ in that order around it, splitting the full turn into the seven angles $\angle A_1OA_2, \angle A_2OA_3, \ldots, \angle A_6OA_7, \angle A_7OA_1$. The bisectors of these seven angles are drawn. The angle between the bisectors of $\angle A_1OA_2$ and $\angle A_2OA_3$ is $52^\circ$; going on around $O$, the angles between the bisectors of consecutive angles are $52^\circ, 45^\circ, 53^\circ, 65^\circ, 42^\circ, 50^\circ, 53^\circ$ (the last is between the bisectors of $\angle A_7OA_1$ and $\angle A_1OA_2$). Find $m\angle A_1OA_2$ in degrees.