Middle European Mathematical Olympiad 2015 Problem T-3

There are $n$ students standing in line in positions $1$ to $n$. While the teacher looks away, some students change their positions. When the teacher looks back, they are standing in line again. If a student who was initially in position $i$ is now in position $j$, we say the student moved for $|i - j|$ steps. Determine the maximal sum of steps of all students that they can achieve.