Consider the questions of $B+$ trees below.

$($a$)$ Observe the above $B+$ tree index. What is the degree of this $B+$ tree? What is the smallest and largest number of search keys a non$-$leaf node of this B$+$ tree may have?

$($b$)$ A B$+$ tree in practice may have a much larger degree. Assume a data block can hold $4$KB data. A B$+$ tree is built on an attribute as $4-$byte integers. Each pointer is a $6-$byte file offset. What is the largest number of children a non$-$leaf B$+$ tree node can have if we allocate a data block to hold one non$-$leaf node?