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

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

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