DWITE Online Computer Programming Contest, February 2008, Problem 2

Integer numbers are made up of factors, smallest numbers that when multiplied together form the original number. Factors are always prime. ~1~ and the original number itself don't count as factors. If a number has no factors, then that number is itself prime. For example, ~12~ is made up of three factors: ~2 \times 2 \times 3~ (even though ~4 \times 3~ is ~12~, ~4~ itself has two factors: ~2 \times 2~).

We care about this because factors are often involved in cryptography:

When the numbers are very large, no efficient integer factorization algorithm is publicly known; a recent effort which factored a ~200~-digit number (RSA-200) took eighteen months and used over half a century of computer time.

Though we'll be dealing with much smaller numbers for now.

The input will contain 5 lines, integers ~2 \le N \le 32~.

The output will contain 5 lines – a total number of factors in a number.

Sample Input

3
4
5
12
32

Sample Output

0
2
0
3
5

Problem Resource: DWITE