The fundamental theorem of arithmetic states the every integer greater than 1 can be uniquely represented as a product of one or more primes. While unique, several agrragnement of the prime factors may be possible.

CSDP-222 Factors Program Introduction The fundamental theorem of arithmetic states that every integer greater than 1 can be uniquely represented as a product of one or more primes. While unique, several arrangements of the prime factors may be possible. For example: 10-2 5 -5* 2 20 = 2 * 2 * 5 -2 52 -5*2 *2 Let f/k) be the number of different arrangements of the prime factors of k. So f(10)-2 and f(20) 3. Given a positive number n, there always exist at least one number k such that flk) -n. We want to know the smallest such k. Input The input consists of at most 1,000 test cases, each on a separate line. Each test case is a positive integer n263. Output For each test case, display the number k > I and its smallest number n such that fk)- n. The numbers in the input are chosen such that k I and its smallest number n such that fk)- n. The numbers in the input are chosen such that k