You all know about factorization of an integer. Here we want you to factor a number into as few factors as possible. That is easy, you say, just have the number itself, and that will be the smallest number of factors i.e. 1.
But wait, I haven't finished -- each of the factors that you find must be square-free. A square-free number, however you factor it, won't have any factor that is a perfect square. Of course, you can never include 1 as a factor.
The first line of input is the number of test cases T.
The next T lines each have an integer N.
T <= 1e4
2 <= N <= 1e6
For each testcase, output the smallest number of square-free factors.
2 6 8
1 3
6 can be factored as just 6 (further factorable as 2x3 only, and hence square free), a single factor. 8 has to be factored as 2x2x2 so that all factors are square-free.
Migrated from old NTUJ.
Regional Amritapuri 2010
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