Shift Count Nine

A transfer runs over a 2.5 Gbit/s path with an 80 ms round trip and no loss.

$\text{BDP} = 2.5 \times 10^9\ \text{bit/s} \times 0.08\ \text{s} = 25\ \text{MB}$

The unscaled TCP window field tops out at 65,535 bytes. RFC 7323 multiplies the advertised window by $2^{s}$, where s is the shift count carried in the Window Scale option and is capped at 14.

What is the smallest s that lets the window cover the bandwidth-delay product?