There are 47 students in a classroom with seats arranged in 6 rows $\times$ 8 columns, and the seat in the $i$-th row and $j$-th column is denoted by $(i,j)$. Now, an adjustment is made for students’ seats in the new school term. For a student with the original seat $(i,j)$, if his/her new seat is $(m,n)$, we say that the student is moved by $[a, b] = [i - m, j - n]$ and define the position value of the student as $a + b$. Let $S$ denote the sum of the position values of all the students. Determine the difference between the greatest and smallest possible values of $S$.

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