$a_1, a_2, ..., a_8$ are $8$ distinct positive integers. $b_1, b_2, ..., b_8$ are another $8$ distinct positive integers $(a_i, b_j$ are not necessarily distinct for $i, j = 1, 2, ...8)$. Enter the smallest possible value of $a^2_1b_1 + a^22b_2 + ... + a^2_8b_8$.