In the editorial it is written like below:

With respect to a single string, the total number of bits rotated after N operations is 1+2+3+….+N which is (N*(N+1))/2.

We get back the original string only when the total number of rotated bits is a multiple of the length of the string S(LEN).This can be done in O(N) time for each string (Summation of length of all strings is <= 1e6), by finding all (N

(N+1))/2 where N starts from 1 and goes upto (2LEN-1).

I understood the (N*(N+1))/2 logic but could not understand how it relates to **2* LEN - 1**? Why are we checking no of rotation to be a multiple of LEN till 2*LEN -1?