TH-TMO 2023 Problem 2

Let $\triangle ABC$ which $\angle ABC$ are right angle, Let $D$ be point on $AB$ ( $D \neq A , B$ ), Let $E$ be point on line $AB$ which $B$ is the midpoint of $DE$ , Let $I$ be incenter of $\triangle ACE$ and $J$ be $A$ -excenter of $\triangle ACD$ . Prove that perpendicular bisector of $BC$ bisects $IJ$