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[en] Let be rotations on the unit circle and define as for , , where is the shift, and and are rotational angles. It is first proved that the system exhibits maximal distributional chaos for any (no assumption of ), generalizing Theorem 1 in Wu and Chen (Topol. Appl. 162:91–99, 2014). It is also obtained that is cofinitely sensitive and -sensitive and that is densely chaotic if and only if .