Question 1Let $n$ be a positive integer and $a_1,a_2,\ldots,a_{2n}$ be $2n$ distinct integers. Given that the equation $$|x-a_1||x-a_2|\cdots|x-a_{2n}|=(n!)^2$$ has an integer solution $x=m$, find $m$ in terms of $a_1,\ldots,a_{2n}$.