Row Reduction & Rank · Superchallenge problem

Let $A$ be the $4\times 8$ matrix with entries $a_{ij} = j^{\,i-1}$ for $1 \le i \le 4$, $1 \le j \le 8$; its rows are $(1, 1, \ldots, 1)$, $(1, 2, \ldots, 8)$, $(1, 4, \ldots, 64)$ and $(1, 8, \ldots, 512)$. Find the sum of the eight entries in the first row of the reduced row echelon form of $A$.