$(5)(4$ pts$)$ Almost all routers use TCAM to speed up table lookup. Due to the need of performing maximum

sequencing matching, we organize the prefix entries in the lookup table according to their lengths $($shortest one at

the top$).$ Assume we have a TCAM which can hold $256$ prefix entries. The current occupancy looks like the one

shown in the figure below. The lengths of all prefixes in the network range from $10$ to $20.$ To simplify the

discussion, we assume there are $20$ prefixes of each length group at the moment. $($a$)$ Now suppose we want to add

one more prefix with length $11$ to the lookup table. Obviously we need to re$-$arrange the locations of some entries

in the table. What is the minimum number of entries we need to rearrange? $($b$)$ As the number of entries in the

table gets larger, rearrangement becomes a time consuming task. Can you suggest a simple way to store prefixes

in the table that can significantly reduce the number of re$-$arranged entries?