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 \( AB \) 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 ________.
