Square-Free Numbers

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.

For each testcase, output the smallest number of square-free factors.

• T ≤ 104
• 2 ≤ N ≤ 106

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.