DWITE Online Computer Programming Contest
February 2008
Problem 2
Number of factors

Integer numbers are made up of factors, which are the 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 -- the total number of factors in the number.

Sample Input:
3
4
5
12
32
		        
Sample Output:
0
2
0
3
5