Below is a sorting algorithm. Give a big$-$O estimate for the number of operations, where an operation is a comparison, other than those used to test loop conditions. In the algorithm below, a is a list of length at least $2.$ Show how this big$-$O estimate is derived by computing the number of operations.

def bubblesort$($a$)$:

for $i$ in range$(1,n$ :

for $j$ in range $(1,n-i+1)$ :

if $a[j]>a[j+1]$ :

tmp $=a[j]$

$a[j]=a[j+1]$

$a[j+1]=tmp$