Consider the following Java code fragment:

$//$ Print out all ordered pairs of numbers between $1$ and $n$

for$(i=0$;$in$;$i++$

for

System.out.println $(i+,+j$;

$\}$

$\}$

$($a$)(3$ points$)$ Use the statement counting approach to determine the exact number of statements that

are executed when we run this code fragment as a function of $n.$ Show all of your calculations.

$($b$)(1$ point$)$ Express the answer you obtained in part $($a$)$ in big$-$ notation $($since the best and worst

cases are the same $-$ there is only one path of execution through this loop$).$