IMO 1984 - Shortlisted Problems Question 11

(CAN 1) Let $n$ be a natural number and $a_1,a_2,\ldots,a_{2n}$ mutually distinct integers. Find all integers $x$ satisfying
$$(x-a_1)\cdot(x-a_2)\cdots(x-a_{2n})=(-1)^n(n!)^2.$$