Chef has a string $S$ consisting of lowercase English characters. Chef defined functions left shift $L(X)$ and right shift $R(X)$ as follows.
$L(X)$ is defined as shifting all characters of string $X$ one step towards left and moving the first character to the end.
$R(X)$ is defined as shifting all characters of string $X$ one step towards the right and moving the last character to the beginning.

For example, L("abcd") = "bcda" and R("abcd") = "dabc"

Chef wants to find out whether there exists a string $V$ of the same length as $S$ such that both $L(V) = S$ and $R(V) = S$ holds.

------ Input: ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains a string $S$.

------ Output: ------
For each test case, If there exists a valid string $V$, print "YES", otherwise print "NO" (without the quotes).

------ Constraints ------
$1 ≤ T ≤ 100$
$1 ≤ |S| ≤ 10^{6}$
$S$ contains all lower case English alphabets.
It's guaranteed that the total length of the strings in one test file doesn't exceed $10^{6}$

----- Sample Input 1 ------
4
a
ab
abcd
aaaaa
----- Sample Output 1 ------
YES
YES
NO
YES
----- explanation 1 ------
- In the first test case, Chef can choose $V = S$
- In the second test case, Chef can choose $V$ = "ba" which satisfies both conditions.
- There doesn't exist any valid choice for string $V$ in the third test case.

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