DWITE '07 R5 #2 - Number of factors

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Points: 5
Time limit: 2.0s
Memory limit: 64M

Problem type
Allowed languages
Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, CommonLisp, D, Dart, F#, Forth, Fortran, Go, Groovy, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, Nim, ObjC, OCaml, Octave, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig
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, is made up of three factors: (even though is , itself has two factors: ).

When the numbers are very large, no efficient integer factorization algorithm is publicly known; a recent effort which factored a -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

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