SP22269 PERIOD1 - Periodic function, trip 1

[xkcd/26](http://xkcd.com/26/)

The first line contains an integer _T_, the number of test cases. On the next _T_ lines, you will be given an integer _N_. Consider the family of all _n_-periodic functions for _n_ in \[1.._N_\]. There are some links between some functions. For example: \[2, 0\] = \[2, 0, 1, 0\] + \[0, 0, 1, 0\], with simplified notations.

Print the rank of this family ; ie the size of the largest collection of **R**-linearly independent elements of this family.