CONO-SUR 2021 Problem 2

Let $ABC$ be a triangle and $I$ its incenter. The lines $BI$ and $CI$ intersect the circumcircle of $ABC$ again at $M$ and $N$ , respectively. Let $C_1$ and $C_2$ be the circumferences of diameters $NI$ and $MI$ , respectively. The circle $C_1$ intersects $AB$ at $P$ and $Q$ , and the circle $C_2$ intersects $AC$ at $R$ and $S$ . Show that $P$ , $Q$ , $R$ and $S$ are concyclic.