Let p$,$ q$,$ r$,$ and r$$ be distinct large primes. ESpecially p$,$ q are safe primes, i$.$e$,$ there exist two other primes p$,$q$$ such that p $=2$p$+1$ and q $=2$q$+1.$ Let N$1=$ pqr$,$ N$2=$ pqr$,$ N$3=$ pq$.$ Assume that there does not exist an efficient $($probabilistic polynomial time$)$ factoring algorithm that can factor these N$1,$N$2,$N$3$ in practice. Say whether each of the following statements are TRUE or FALSE, and justify your answer with one sentence. $($a$)(3$pts$)$ There is an efficient algorithm that takes N$1$ as input and outputs r$.($b$)(3$pts$)$ There is an efficient algorithm that takes N$1$ and N$2$ as input and outputs r$.($c$)(3$pts$)$ There is an efficient algorithm that