Consider the following function:

int loop$($int N$)\{$

$//$Precondition: $\{$N $>=0\}$

Random rand $=$ new Random$()$;

for$($int i $=1$; i $<$ N $+1$; i$++)\{$

if$($i $\%2==0)\{$

System.out.println$("$Begin iteration"$)$;

$\}$

for$($int j $=1$; j $<$ Math.pow$(8,$ Math.pow$(3,$ i$))$; j$*=2)\{$

System.out.print$("$Type: $")$; $//$S$1$

int cond $=$ rand.nextInt$()$;

if$($cond $\%3==0)\{$

System.out.println$("$Thing$")$;

$\}$

else if$($cond $\%2==0)\{$

System.out.println$("$Something$")$;

$\}$

else$\{$

System.out.println$("$Nothing$")$;

$\}$

$\}$

$\}$

$\}$

Q $2\mathrm{.}1$

How many times will the line commented as S$1$ be run? Write your answer as a closed$-$form expression in terms of N$.$ Show your work.

Q$2\mathrm{.}2$

How many feasible paths do you have in this program? Again the answer should be expressed as a closed$-$form expression in terms of N$.$