Question 5
The set $\{2, 3, 4, \ldots, 2020\}$ is partitioned into triples. In each triple $(a, b, c)$ the numbers were arranged in the ascending order, i.e. $a \lt b \lt c$, and the difference $|b - \frac{a+c}{2}|$ is called the error of this triple. Find the maximal possible sum of errors of all $673$ triples.