2) A class has 47 students, and the classroom has 6 rows, each with 8 seats, denoted by $(i, j)$ for the seat in the $i$-th row and $j$-th column. For the new semester, the seats are to be rearranged. If a student's original seat is $(i, j)$ and the new seat is $(m, n)$, then the student's movement is denoted as $[a, b] = [i-m, j-n]$, and the sum $a+b$ is called the student's position number. The total sum of all students' position numbers is denoted as $S$. Find the difference between the maximum and minimum possible values of $S$. (Provided by Chen Yonggao)
Add a virtual student: $A$, at this point the sum of seat numbers is denoted as $S^{\prime}$, note that swapping the positions of two adjacent students does not change the value of $S^{\prime}$, by performing a finite number of swaps of adjacent students, the previous semester's seating arrangement can be restored. Therefore, $S^{\prime}=0$. Meanwhile, the seat number of $A$ is 0, when $A$ is at position 1, the seat number of $A$ is maximum; when $A$ is at position $\mathrm{J} \AA_{1}$, the seat number of $A$ is minimum, so, the difference between the maximum and minimum values of $S$ is $5+7=12$.