Problems
Factors
Factors
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:
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 data
The input consists of at most 1000 test cases, each on a separate line. Each test case is a positive integer n < 2^63.
Output data
For each test case, display its number n and the smallest number k > 1 such that f(k) = n. The numbers in the input are chosen such that k < 2^63.
Examples
Input example #1
1 2 3 105
Output example #1
1 2 2 6 3 12 105 720