2008 AIME II Problem 4

There exist r unique nonnegative integers n_1 > n_2 > \cdots > n_r and r 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.