$2-$ The following function determines if all the numbers in the vector are different from each other, i$.$e$.$ they are all distinct values. Show that the function runs in O$($n$2).$ Count the number of operations and determine the Big$-$O function. You must show all steps on how to determine the Big O including the values of C and n$0.(20$ points$)$

bool allDistinct$($const vector& a$)\{$ # of primitive operations

for $($int i $=0$; i $<$ a$.$size$()1$; i$++)\{$

for $($int j $=$ i$+1$; j $<$ a$.$size$()$; j$++)\{$

if $($a$[$i$]==$ a$[$j$])$

return false;

$\}$

$\}$

return true;

$\}$