Section $8\mathrm{.}3$ Example $3$ discusses $2-$way merge sort where an unsorted list of size n is:

$1)$ split into two equal parts of size n$/2$ each

$2)$ sort the two lists of size n$/2$ using merge sort recursively

$3)$ merge the two sorted lists of size n$/2$ into a sorted list of size n by scanning down the sorted lists of size n$/2.$

An alternative to $2-$way merge sort is $4-$way merge sort where the unsorted list of size n is:

$1)$ split into four equal parts of size n$/4$ each

$2)$ sort the four lists of size n$/4$ using merge sort recursively

$3)$ merge all four sorted lists of size n$/4$ into a sorted list of size n$.$

To apply the Master Theorem $($Theorem $2$ on page $532)$ to determine the big$-$oh notation for the $4-$way merge sort we need to write the divide$-$and$-$conquer recurrence relation for the number of comparisons, f$($n$),$ in the form

f$($n$)=$ af$($n$/$b$)+$ cnd$.$

What is the big$-$oh notation of the $4-$way merge sort algorithm?