For the set $\{x \mid a \leqslant x \leqslant b\}$, we call $b-a$ its length. Let the set $A=\{x \mid a \leqslant x \leqslant a+1981\}, B=\{x \mid b-1014 \leqslant x \leqslant b\}$, and both $A, B$ are subsets of the set $U=\{x \mid 0 \leqslant x \leqslant 2012\}$, then the minimum length of the set $A \cap B$ is $\qquad$ .
To ensure that the length of the set $A \cap B$ is minimized, $b-a$ needs to be as large as possible. Take $A=[0,1981], B=[998,2012]$, at this point $A \bigcap B=[998,1981]$ satisfies the condition. Therefore, the minimum length of the set $A \cap B$ is $1981-998=983$.