It is necessary to design a link-layer protocol between two hosts that are directly connected over a lossless link of length 3000 kilometers. Assume that the link bandwidth is \(10^8\) bits per second and that the propagation delay in the link is 5 nanoseconds per meter. Every transmitted data byte is assigned a unique sequence number.
Let \(N\) be the minimum number of bits needed for the sequence number field in the protocol header such that
i. the sequence numbers do not wrap around before 60 seconds, and
ii. the maximum utilization of the link is achieved.
The value of \(N\) is ____________.