Beautiful Necklace

You are given a circular necklace represented as a string s of length n. The necklace is considered beautiful if there exists an integer l with (1 \leq l \leq \frac{n}{2}) and a substring (p = s[0:l]) such that when we consider the necklace's circular property (i.e. by concatenating s+s), the number of non-overlapping occurrences of (p) is at least (2\cdot\left\lfloor \frac{n}{l} \right\rfloor). For example, for s = "abcabcabc", the necklace is beautiful, while for s = "abcdefgh" it is not. Determine for each test case whether the given necklace is beautiful.

inputFormat

The input begins with an integer T representing the number of test cases. Each of the next T lines contains a single string representing a circular necklace.

outputFormat

For each test case, output a single line containing either YES if the necklace is beautiful, or NO otherwise.## sample

3
abcabcabc
aaaaa
abcdefgh

YES
YES
NO