# Programming contests

## ACM ICPC programozó csapatverseny, házi forduló, 2013. október 20.

October 20, 2013 10:10 AM – October 20, 2013 3:10 PM

# 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:

```            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 Specification

The input consists of at most 1000 test cases, each on a separate line. Each test case is a positive integer n < 263.

## Output Specification

For 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 < 263.

## Sample Input

1. `1`
2. `2`
3. `3`
4. `105`
1. `1 2`
2. `2 6`
3. `3 12`
4. `105 720`