2008 AIME II Problem 4

There exist $r$ unique nonnegative integers $n_1 > n_2 > \cdots > n_r$ and $r$ unique integers $a_k$ $( 1\le k\le r)$ with each $a_k$ either $1$ or $- 1$ such that

$a_13^{n_1} + a_23^{n_2} + \cdots + a_r3^{n_r} = 2008.$Find $n_1 + n_2 + \cdots + n_r$.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.