Question 43
Let $n \ (\ge 4)$ be a positive integer, and $a_1, a_2, \dots, a_n$ be distinct positive integers less than or equal to $n$. Determine the maximum value of
$$
\sum_{i=1}^{n} |a_i - a_{i+1} + a_{i+2} - a_{i+3}|.
$$
($a_{n+i} = a_i$ for $i = 1, 2, 3$)
$$
\sum_{i=1}^{n} |a_i - a_{i+1} + a_{i+2} - a_{i+3}|.
$$
($a_{n+i} = a_i$ for $i = 1, 2, 3$)