Question 165
Let $n \ge 4$ be a positive integer. Consider any set $A$ formed by $n$ distinct real numbers such that the following condition holds: for every $a \in A$, there exist distinct elements $x, y, z \in A$ such that $|x - a|, |y - a|, |z - a| \ge 1$. For each $n$, find the greatest real number $M$ such that
$$
\sum_{a \in A} |a| \ge M
$$
always holds.
$$
\sum_{a \in A} |a| \ge M
$$
always holds.