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.

Input

The first line of input is the number of test cases T. The next T lines each have an integer N.

Output

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

Constraints

T <= 10⁴
2 <= N <= 10⁶

Example

SAMPLE INPUT
2
6
8

SAMPLE OUTPUT
1
3