Fascinated by the beauty of randomness, a Kaboobly Dooist asks the craftsmen to paint a linear wall consisting of \(2^{16}\) stones in the following way:
###### Inspired by Math with Bad Drawings.

For each stone: Flip a coin; If the toss results heads, paint the stone white; If the toss results tails, paint the stone black.

What is the expected longest contiguous streak consisting of consecutive black stones?

If the answer is \(n\), enter your answer as \( \lfloor n \rfloor \).

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