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An n-bit Gray code is a sequence of n-bit strings constructed according to certain rules. For example,

>>> gray 1  -- 1-bit gray code
["0","1"]

>>> gray 2  -- 2-bit gray code
["00","01","11","10"]

>>> gray 3  -- 3-bit gray code
["000","001","011","010","110","111","101","100"]

Infer the construction rules and write a function returning the n-bit Gray code.