**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.