Consider the following snippet of pseudocode that takes as input an array of n integers.

$1$: function algorithm$($A$)$

$2$: n $$ length of A

$3$: num$\_$matches $0$

$4$: for i in $[0$ : n$]$ do $//$ i ranges from $0$ to n $1$

$5$: for j in $[$i $+1$ : n$]$ do $//$ j ranges from i $+1$ to n $1$

$6$: if A$[$i$]==$ A$[$j$]$ then

$7$: num$\_$matches $$ num$\_$matches $+1$

$8$: return num$\_$matches

Your task is to:

$1)$ upperbound the running time of the algorithm in terms of n using O$-$notation. $2)$ lowerbound the running time of the algorithm in terms of n Using $-$notation.