Consider the following pseudocode.$($a$)(10$ points$)$ What is the running time of Alg$2($n$)$ as a function n assuming each line of the code costs exactly $1$ time$-$step. $($You may write the answer as a summation without simplifying it into a closed form. $)($b$)(10$ points$)$ Prove that the running time of Alg$2($n$)$ is Theta$($n log n$).$