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New Zealand, who were put into bat by Australia, struggled early on and they were reduced to 74-4 before McCullum and Corey Anderson put on 179 for the fifth wicket.
McCullum was given a reprieve on 39 when he was caught off a no-ball and he made the most of it, smashing 21 fours and six sixes before falling to James Pattinson for 145 off 79 balls.
Anderson went for 72 shortly after before BJ Watling's 58 helped the Black Caps post a first-innings total of 370.
In reply, Australia lost David Warner for 12 in the eighth over of their innings, but Joe Burns (27*) and Usman Khawaja (18*) held firm to guide the tourists to 57-1, 313 runs behind, by the close of play.body check tags ::