; and (bb) during the marriage or relationship intended by the alien to be legally a marriage, the alien or a child of the alien has been battered or has been the subject of extreme cruelty perpetrated by the alien's spouse or intended spouse. (II) For purposes of subclause (I), an alien described in this subclause is an alien— (aa) (AA) who is the spouse of a citizen of the United States or lawful permanent resident; (BB) who believed that he or she had married a citizen of the United States or lawful permanent resident and with whom a marriage ceremony was actually performed and who otherwise meets any applicable requirements under this Act to establish the existence of and bona fides of a marriage, but whose marriage is not legitimate solely because of the bigamy of such citizen of the United States or lawful permanent resident; or (CC) who was a bona fide spouse of a citizen of the United States or a lawful permanent resident within the past 2 years and whose spouse died within the past 2 years, whose spouse renounced citizenship status or renounced or lost status as a lawful permanent resident within the past 2 years related to an incident of domestic violence, or who demonstrates a connection between the legal termination of the marriage within the past 2 years and battering or extreme cruelty by a spouse who is a citizen of the United States or a lawful permanent resident spouse; (bb) who is a person of good moral character; (cc) who is eligible to be classified as an immediate relative under section 201(b)(2)(B) or who would have been so classified but for the bigamy of the citizen of the United States or lawful permanent resident that the alien intended to marry; and (dd) who has resided with the alien's spouse or intended spouse.