A line passes through $A(4,-6,-2)$ and $B(16,-2,4)$. The point $P(a, b, c)$, where $a, b, c$ are non-negative integers, on the line $A B$ lies at a distance of 21 units, from the point $A$. The distance between the points $P(a, b, c)$ and $Q(4,-12,3)$ is equal to __________.