Basketball and tennis ball: Part II

Now consider n balls, $B_{1}, \cdots , B_{n}$ having masses $m_{1}, m_{2}, \cdots , m_{n}$ (with $m_{1} >>m_{2}>> \cdots >> m_{n}$ ) , sitting in a vertical stack. The bottom of $B_{1}$ is a height h above the ground, and the bottom of $B_{n}$ is a height $h + l$ above the ground. The balls are dropped. In terms of n, to what height does the top ball bounce?

Note: Work in the approximation where $m_{1}$ is much larger than $m_{2}$ , which is much larger than $m_{3}$ , etc., and assume that the balls bounce elastically. If $h = 1$ meter, what is the minimum number of balls needed for the top one to bounce to a height of at least 1 kilometer? To reach escape velocity? Assume that the balls still bounce elastically (which is a bit absurd here). Ignore wind resistance, etc., and assume that l is negligible.