Question II $(15$ points$)$: Consider the following algorithm, where the input $$ is a positive power of $4.$

for$($i $=0$; i $<=$ n; i$+=4)\{$

for$($j $=1$; j $<=$ n ; j$*=2)\{$

x $=$ x $+2$; $//$Statement $1$

$\}$

$\}$

$1.(13$ points$)$ Determine the number of times Statement $1$ gets executed, showing all the steps.

$2.(2$ points$)$ Write the cost of the algorithm using Big $\backslash$Theta $()$ notation.