One thousand students participate in the $2011$ Canadian Closed Mathematics Challenge. Each student is assigned a unique three-digit identification number $abc$, where each of $a$, $b$, and $c$ is a digit between $0$ and $9$, inclusive. Later, when the contests are marked, a number of markers will be hired. Each of the markers will be given a unique two-digit identification number $xy$, with each of $x$ and $y$ a digit between $0$ and $9$, inclusive. Marker $xy$ will be able to mark any contest with an identification number of the form $xyA$, $xAy$, or $Axy$, for any digit $A$. What is the minimum possible number of markers to be hired to ensure that all contests will be marked?

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