Consider the following algorithm which receives as input an array $$ of size $$:

$1$

while $<=$ do

$0$

$1$

for $=1$ to $$ do

$+$

for $=1$ to $$ do

$+$

$+1$

$$ State how many times each loop is executed and justify your answer.

$$ Give the running time of the algorithm in $\backslash$Theta notation. Explain how you reached the

answer.