Here is the pseudocode for Selection Sort:

for i $=0$ to n$-2$ minindex $=$ i

for j $=$ i$+1$ to n$-1$

if A$[$j$]<$ A$[$minindex$]$

minindex $=$ j end

end

swap A$[$i$]$ with A$[$minindex$]$ end

Suppose that:

$$ The mathematical function m$($i$)$ returns the minindex appearing in the code and corre$-$

sponding to the index i as the code runs.

$$ It takes $|$i$1$ i$2|$ seconds to swap the entries at indices i$1$ and i$2.$

$$ The entire conditional block takes $1$ second.

$$ Nothing else takes any time at all.

$($a$)$ Write down the nested sum expression for the total time required to run Selection Sort. Do not simplify. You should not need an absolute value in your answer!