

FactorsThe 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 20 = 2 * 2 * 5 = 5 * 2 = 2 * 5 * 2 = 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 exists at least one number k such that f(k) = n. We want to know the smallest such k. Input SpecificationThe input consists of at most 1000 test cases, each on a separate line. Each test case is a positive integer n < 2^{63}. Output SpecificationFor each test case, display its number n and, after a space, the smallest number k > 1 such that f(k) = n. The numbers in the input are chosen such that k < 2^{63}. Sample Input
Output for Sample Input


University of Debrecen; Faculty of Informatics; v. 03/01/2019 