Consider the following procedure Foo$($n$),$ where the operations Make$-$Set$($x$),$ Find$-$Set$($x$),$ and Union $($x$,$ y$)$ are implemented using disjoint$-$set forest with union by rank as discussed in class.

Foo$($n$)$

$1$ for i $=1$ to n

$2$ Make$-$Set$($i$)$

$3$ for i $=1$ to n$/2$

$4$ Union$($i$,$ i $+$ n$/2)$

$5$ for j $=$ n downto n$/2+1$

$6$ if Find$-$Set$($j$)!=$ Find$-$Set$($j $-1)$

$7$ Union$($j$,$ j $-1)$

Perform Foo$(8).$

$(1)$ How many trees will be generated after executing the second for loop $($lines $3$ & $4)?$