Without reciprocity

For the given sequence of $n$ integers A_1, \ldots, A_n, determine the maximum length of a subsequence in which there is no pair of mutually close numbers. Two numbers are considered mutually close if each can be obtained from the other by a cyclic shift of all digits of their decimal representation. For example, numbers $7353$ and $3537$ are mutually close, while $730$ and $73$ are not, since you cannot obtain one from the other by a cyclic shift of all digits.