IZhO 2022 Problem 4

In triangle $ABC$ , a point $M$ is the midpoint of $AB$ , and a point $I$ is the incentre. Point $A_1$ is the reflection of $A$ in $BI$ , and $B_1$ is the reflection of $B$ in $AI$ . Let $N$ be the midpoint of $A_1B_1$ . Prove that $IN > IM$ .