Akhil and colored balls, wrong example ?

ok, so in problem link umm, it said that “BWBW” is the only solution, but I finds out that “BWWW” can be the answe too, ok, let’s break it down
“WBWB” and “BWBW”, all of them are different so hammington distance is 4, “WBBB” and “BWBW” have hammington distance of 3, pos 1, 2, and 4, total of 7, and for “BWWW”, “WBWB” and “BWWW” have hammington distance 3, and “WBBB” and “BWWW” have hamington distance of 4…which equals 7, now there has become two answers…also, there is another constraint which says lexicographically smallest arangement…hmm, does that matter and I have been stupid ? ( anyways I don’t understand what lexicographically smallest arangement means )

Lexicographically means Alphabetically(Dictionary wise),

For example:

abb < acb, aab < aac, bba < bca , BWBW<BWWW…

welp…apparently I was right that lexicographically is important in the problem, thanks