Exercise 3. This software implements the algorithm given in Chapter 8 to express $$U(n)$$ as an external direct product of groups of the form $$Z_k$$. Assume that $$n$$ is given in prime-power factorization form. Run your program for $$3 \oplus 5 \oplus 7, 16 \oplus 9 \oplus 5, 8 \oplus 3 \oplus 25, 9 \oplus 5 \oplus 11$$, and $$2 \oplus 27 \oplus 125$$. [ NOTE: Please enter the prime-power factorization form with a `period(".")' in between the integers and without any space. Also, this program has been written to accept $$n$$ as any integer, i.e., instead of entering $$n$$ in the factored form as 3 . 5 . 7 you could enter 105 . ]

Please enter $$n$$, you may use the prime-power factorization mode.