ENGE$602$ Mathematics for Software Engineering $1$ Week $4$ Tutorial: Counting Coprimes Via Sets of Prime Factors Aim: This week, we will explore Euler's totient function, $$($n$),$ which counts the positive integers less than integer n that are relatively prime to n$.$ That is$,$ it counts the positive integers m template class, the set$>$ template class is a container provided by the C$++$ Standard Template Library. It behaves like a set, in that elements can be inserted only once. In this example code, note the following: set set$1$; declares a set that contains elements of type unsigned $($unsigned integer$).$ set:iterator it; declares an iterator, which behaves like a pointer, a special object that is able to visit every element in a set Part A: Extend the example code to create a vector of $1001$ sets of integers; e$.$g$.$ unsigned max $=1000$; vector$<$ set $>$ prime$\_$factors $($max $+1)$; and fill each set with the prime factors of the vector index, such that prime$\_$factors$[$j$]$ is equal to the set of the prime factors of j$.$ Use a strategy similar to that used in the Sieve of Eratosthenes: start with j$=2$ and insert the number $2$ into the sets of prime factors of all multiples of $2.$ Then repeat for all prime numbers, noting that if the set prime$\_$factors$[$k$]$ is empty, then k is prime. Also note that a prime factor appears only once in the set of prime factors, even if it appears more than once in the factorization.#include $//$ cout #include $//$ set #include $//$ inserter using namespace std; int main$()\{$ set set$1$; set$1.$insert$(3)$; seti.insert$(4)$; seti.insert$(5)$; set set$2$; set$2.$insert$(4)$; set$2.$insert$(5)$; set$2.$insert$(6)$; set intersection; set$\_$intersection $($setl$.$begin$(),$ set$1.$end$(),$ set$2.$begin$(),$ set$2.$end$(),$ inserter$($intersection$,$ intersection.begin$()))$; cout $<<$ "The intersection has $<<$ intersection.size$()<<"$ elements:" $<<$ endl; set:iterator it; for $($it$-$intersection.begin$()$; it$!=$intersection.end$()$; $++$it$)$ cout $<<\text{'}\text{'}<<$ it; cout $<<$ endl; set union$12$; set$\_$union $($set$1.$begin$(),$ setl.end$(),$ set$2.$begin$(),$ set$2.$end$(),$ inserter $($union $12,$ union$12.$begin$()))$; cout $<<$ "The union has $<$ union $12.$size$()$