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*2*3 (even though 4*3 is 12, 4 itself has two factors: 2*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 file DATA2.txt will contain 5 lines, integers 2 <= N <= 32

The output file OUT2.txt will contain 5 lines -- a total number of factors in a number.

3
4
5
12
32
		        

0
2
0
3
5