Given the code below, answer the following the questions:

$1$ for $i$ in $1..N$ loop

$2$ for $j$ in $1..$i loop

$3$ for $k$ in i$..$j loop

$4,$ Sum :$=$ Sum $+1$ ;

$5$ end loop;

$6$ end loop;

$7$ end loop;

$8$ for $p$ in $1..$N$*$N loop

$9$ for $q$ in $1..$p loop

$10$ Sum :$=$ Sum $-1$;

$11$ end loop;

$12$ end loop;

$($a$)$ How many times is statement $4$ executed? $($use big Theta notation$)$

$($b$)$ How many times is statement $10$ executed? $($use big theta notation$)$

$($c$)$ what is the run time of this piece of code?