The letters $A$, $J$, $H$, $S$, $M$, $E$ and the digits $1$, $9$, $8$, $9$ are "cycled" separately as follows and put together in a numbered list:
$$\begin{aligned}&&&\mathrm{AJHSME}\quad1989\\&1.&&\mathrm{JHSMEA}\quad9891\\&2.&&\mathrm{HSMEAJ}\quad8919\\&3.&&\mathrm{SMEAJH}\quad9198\\&&&.........\end{aligned}$$
What is the number of the line on which $AJHSME 1989$ will appear for the first time?

Let's think step by step and output the final answer within \boxed{}.
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