Consider the following algorithm segment. Assume that $n$ is a positive integer.

for $i$:$=1ton$

for $j$:$={|}_{{?}_{?}}\frac{i+1}{2_{{?}_{?}}}|ton$

$,x$:$=i*j$

next $j$

next $i$

$($a$)$ What is the actual number of elementary operations $($additions$,$ subtractions, multiplications, divisions, and comparisons$)$ that are performed when the algorithm ignore those implied by for$-$next loops. Express your answer in terms of $n.($Hint: See Example $11\mathrm{.}3\mathrm{.}4$ and Exercise $11\mathrm{.}3\mathrm{.}17$a in the "Read It$"$ link.$)$

For odd $n$ the number of operations is $\frac{n}{2}+\frac{1}{2}$

For even $n$ the number of operations is