Below is an awkward algorithm to solve the above problem.

ComputeSumUpperTriangular$($U$,$n$)$

inputs: U is an nxn matrix. n is the dimension of the matrix

output: a real number equal to

$1$: sum $=0$

$2$: for i $=$ n to $1$

$3$: psum $=0$

$4$: for j $=$ i to n

$5$: psum $=$ psum $+$ U$[$i$,$j$]$

$6$: sum $=$ sum $+$psum

$7$: return sum

All the questions in this exercise are related to the ComputeSumUpperTriangular$($L$,$n$)$ algorithm. The objective of this exercise is to explore whether the asymptotic time complexity will change if we count different $$actions$.$

$(40$ points$)$ Comparison Action $($Lines $2$ and $4).$

In this case, we count the total number of comparisons performed by the $$for loops statements$($Lines $2$ and $4$ only$).$ Answer the following questions to determine the total number of comparisons performed by the algorithm.

$(2$ points$)$ How many comparisons in total are performed by the $$for loop$$ statement in Line $2$ during the execution of the algorithm?