OLYMPIC-REVENGE 2018 Problem 2

Let $\triangle ABC$ a scalene triangle with incenter $I$ , circumcenter $O$ and circumcircle $\Gamma$ . The incircle of $\triangle ABC$ is tangent to $BC, CA$ and $AB$ at points $D, E$ and $F$ , respectively. The line $AI$ meet $EF$ and $\Gamma$ at $N$ and $M\neq A$ , respectively. $MD$ meet $\Gamma$ at $L\neq M$ and $IL$ meet $EF$ at $K$ . The circumference of diameter $MN$ meet $\Gamma$ at $P\neq M$ . Prove that $AK, PN$ and $OI$ are concurrent.