You are given a string $$$s$$$ of length $$$n$$$ consisting of lowercase Latin characters. Find the length of the shortest string $$$k$$$ such that several (possibly one) copies of $$$k$$$ can be concatenated together to form a string with the same length as $$$s$$$ and, at most, one different character.

More formally, find the length of the shortest string $$$k$$$ such that $$$c = \underbrace{k + \cdots + k}_{x\rm\ \text{times}}$$$ for some positive integer $$$x$$$, strings $$$s$$$ and $$$c$$$ has the same length and $$$c_i \neq s_i$$$ for at most one $$$i$$$ (i.e. there exist $$$0$$$ or $$$1$$$ such positions).

Input

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^3$$$) — the number of test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 2\cdot10^5$$$) — the length of string $$$s$$$.

The second line of each test case contains the string $$$s$$$, consisting of lowercase Latin characters.

The sum of $$$n$$$ over all test cases does not exceed $$$2\cdot10^5$$$.

Output

For each test case, print the length of the shortest string $$$k$$$ satisfying the constraints in the statement.

Note

In the first test case, you can select $$$k = \texttt{a}$$$ and $$$k+k+k+k = \texttt{aaaa}$$$, which only differs from $$$s$$$ in the second position.

In the second test case, you cannot select $$$k$$$ of length one or two. We can have $$$k = \texttt{abba}$$$, which is equal to $$$s$$$.

Nearly Shortest Repeating Substring

Examples