USAMO 1985 Problem 5

$0<a_{1} \leq a_{2} \leq a_{3} \leq \ldots$ is an unbounded sequence of integers. Let $b_{n}=m$ if $a_{m}$ is the first member of the sequence to equal or exceed $n$. Given that $a_{19}=85$, what is the maximum possible value of $a_{1}+a_{2}+\ldots+$ $\mathrm{a}_{19}+\mathrm{b}_{1}+\mathrm{b}_{2}+\ldots+\mathrm{b}_{8} ?$