Analyze the running time of the following algorithm fooC in terms of n$.$

$1$ fooC$($C$,$ n$,$ x$)$

$2//$ Input: An array C of n numbers and a character x

$3$ total $=0$

$4$ if x $==\text{'}$a$\text{'}$

$5$ for i $=0$ to n $-1$

$6$ total $=$ total $+$ C$[$i$]$

$7$ else if x $==\text{'}$b$\text{'}$

$8$ for i $=0$ to n $-1$

$9$ for j $=1$ to i

$10$ total $=$ total $+$ j $*$ C$[$i$]$

$11$ print total

$(1)(2\mathrm{.}5$ pts$)$ What is the worst$-$case running time of fooC? You may use either Big$-$O or Big$-$ notation. Explain what kind of input would lead to this worst$-$case running time.

$(2)(2\mathrm{.}5$ pts$)$ What is the best$-$case running time of fooC? You may use either Big$-\backslash$Omega or Big$-$ notation. Explain what kind of input would lead to this best$-$case running time.