MathNet 2019-part-06 — 184 problems (EN–VI) Question 90

Let $x$, $y$, $z$, $a$, $b$, $c$ be pairwise different integers from the set $\{1,2,3,4,5,6\}$. Find the smallest possible value for the expression $x y z + a b c - a x - b y - c z$.