IRL_ABooklet

Let $AOB$ be a triangle with $\angle AOB=90^{\circ }$. Define a sequence of points $X_1,X_2,X_3,\dots ,X_{2022}$ as follows: * $X_1$ lies on the ray $\overrightarrow{OA}$ with $|O{X}_1|=1$. * $X_2$ lies on the ray $\overrightarrow{OB}$ with $|X_1{X}_2|=2$ * For $3\le n\le 2022$, the $X_n$ lie alternately on $\overrightarrow{OA}$ ($n$ odd) or $\overrightarrow{OB}$ ($n$ even), with $|X_{n-1}{X}_n|=n$. Find the distance $|X_{2020}{X}_{2022}|$.