Description:
Let's call a string $$$s$$$ perfectly balanced if for all possible triplets $$$(t,u,v)$$$ such that $$$t$$$ is a non-empty substring of $$$s$$$ and $$$u$$$ and $$$v$$$ are characters present in $$$s$$$, the difference between the frequencies of $$$u$$$ and $$$v$$$ in $$$t$$$ is not more than $$$1$$$.
For example, the strings "aba" and "abc" are perfectly balanced but "abb" is not because for the triplet ("bb",'a','b'), the condition is not satisfied.
You are given a string $$$s$$$ consisting of lowercase English letters only. Your task is to determine whether $$$s$$$ is perfectly balanced or not.
A string $$$b$$$ is called a substring of another string $$$a$$$ if $$$b$$$ can be obtained by deleting some characters (possibly $$$0$$$) from the start and some characters (possibly $$$0$$$) from the end of $$$a$$$.
Input Format:
The first line of input contains a single integer $$$t$$$ ($$$1\leq t\leq 2\cdot 10^4$$$) denoting the number of testcases.
Each of the next $$$t$$$ lines contain a single string $$$s$$$ ($$$1\leq |s|\leq 2\cdot 10^5$$$), consisting of lowercase English letters.
It is guaranteed that the sum of $$$|s|$$$ over all testcases does not exceed $$$2\cdot 10^5$$$.
Output Format:
For each test case, print "YES" if $$$s$$$ is a perfectly balanced string, and "NO" otherwise.
You may print each letter in any case (for example, "YES", "Yes", "yes", "yEs" will all be recognized as positive answer).
Note:
Let $$$f_t(c)$$$ represent the frequency of character $$$c$$$ in string $$$t$$$.
For the first testcase we have $$$t$$$$$$f_t(a)$$$$$$f_t(b)$$$$$$a$$$$$$1$$$$$$0$$$$$$ab$$$$$$1$$$$$$1$$$$$$aba$$$$$$2$$$$$$1$$$$$$b$$$$$$0$$$$$$1$$$$$$ba$$$$$$1$$$$$$1$$$ It can be seen that for any substring $$$t$$$ of $$$s$$$, the difference between $$$f_t(a)$$$ and $$$f_t(b)$$$ is not more than $$$1$$$. Hence the string $$$s$$$ is perfectly balanced.
For the second testcase we have $$$t$$$$$$f_t(a)$$$$$$f_t(b)$$$$$$a$$$$$$1$$$$$$0$$$$$$ab$$$$$$1$$$$$$1$$$$$$abb$$$$$$1$$$$$$2$$$$$$b$$$$$$0$$$$$$1$$$$$$bb$$$$$$0$$$$$$2$$$ It can be seen that for the substring $$$t=bb$$$, the difference between $$$f_t(a)$$$ and $$$f_t(b)$$$ is $$$2$$$ which is greater than $$$1$$$. Hence the string $$$s$$$ is not perfectly balanced.
For the third testcase we have $$$t$$$$$$f_t(a)$$$$$$f_t(b)$$$$$$f_t(c)$$$$$$a$$$$$$1$$$$$$0$$$$$$0$$$$$$ab$$$$$$1$$$$$$1$$$$$$0$$$$$$abc$$$$$$1$$$$$$1$$$$$$1$$$$$$b$$$$$$0$$$$$$1$$$$$$0$$$$$$bc$$$$$$0$$$$$$1$$$$$$1$$$$$$c$$$$$$0$$$$$$0$$$$$$1$$$
It can be seen that for any substring $$$t$$$ of $$$s$$$ and any two characters $$$u,v\in\{a,b,c\}$$$, the difference between $$$f_t(u)$$$ and $$$f_t(v)$$$ is not more than $$$1$$$. Hence the string $$$s$$$ is perfectly balanced.