String

The Research Institute of the Given Strings (RIGS) is investigating a new method of infinite string construction.

Initially there is an empty string $S_{0}^{(k)} = \varepsilon$. Each next version of the string is created in the following way. The current version of the string is repeated $k$ times, and an arbitrary symbol is inserted between every two consecutive occurences. The same number $k$ is used for the construction of all versions, however, the inserted symbols may differ. This construction ultimately results in the infinite string $S_{\infty}^{(k)}$.

To illustrate, let's consider the series of strings ($k = 3$): $$\begin{align*} S_{0}^{(3)} &= \varepsilon (\text{empty})\\ S_{1}^{(3)} &= \mathbf{r}\mathbf{t} \hspace{5cm} ( S_{1}^{(3)} = \boxed{\varepsilon}\mathbf{r}\boxed{\varepsilon}\mathbf{t}\boxed{\varepsilon} ) \\ S_{2}^{(3)} &= \boxed{rt} \mathbf{x} \boxed{rt} \mathbf{r} \boxed{rt} \\ S_{3}^{(3)} &= \boxed{rtxrtrrt} \mathbf{a} \boxed{rtxrtrrt} \mathbf{r} \boxed{rtxrtrrt} \\ \phantom{S_{i}^{(3)}} & \ldots \\ S_{\infty}^{(3)} &= rtxrtrrtartxrtrrtrrtxrtrrtzrtxrtrrtartxrt\ldots \end{align*}$$

Given a string $A$ of length $n$, which is the prefix of $S_{\infty}^{(k)}$, find the minimal $k$, for which this is possible.

In other words, your task is to find the minimal $k$, for which it is possible to construct a string $S_{\infty}^{(k)}$ in a way described above, so that it will have $A$ as a prefix.

Each input file contains several tests. The first line of the file contains a single integer $T$ --- the number of tests. Then $T$ lines follow; each line describes a single test. The tests are nonempty and contain only lowercase Latin letters.

The number of tests does not exceed $10^5$. The sum of lengths of all the tests in the file does not exceed $10^6$.

The output file must contain exactly $T$ lines. Each line must contain the minimal value of $k$ for the corresponding test.