In the tribe of Zimmer, a boy is not considered a man until he completes a rite of passage involving a series of hikes. The first hike is a $5$ kilometer hike down the main road. The second hike is a $5\frac{1}{4}$ kilometer hike down a secondary road. Each subsequent hike is along a different road and is $\frac{1}{4}$ kilometer longer than the previous hike. The rite of passage is completed when the cumulative distance walked exceeds $1000$ kilometers. How many roads must a man walk down before he is considered a man in the tribe of Zimmer?

Let's think step by step and output the final answer within \boxed{}.
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