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Tanzid Hasan Tamim became the first Bangladesh cricketer to score a Test century in Australia as the visitors continued to dominate on day two in Darwin.
The opener, playing in just his second Test match, hit 101 off 197 balls as Bangladesh closed on 351-6, a lead of 153.
"I can't describe it in words, but it was very special for me," he said. "I love to play in these conditions, the pitch is getting better and better."
Hasan began the day on 32 with Bangladesh 96-1, having bowled Australia out for 198 on day one after the hosts won the toss.
The 25-year-old put on 102 for the second wicket with Mominul Haque, who was dismissed by Josh Hazlewood for 49 before lunch.
Tanzid then put on 93 with captain Najmul Hossain Shanto as Australia toiled in stiflingly hot conditions at the Marrara Oval.
His innings finally came to an end when he drove a Nathan Lyon delivery to Mitchell Starc at long-off during the afternoon session.
Australia rallied with three quick wickets with the new ball after tea, but Mehidy Hasan Miraz and Hasan Mahmud put on an unbeaten 43 before stumps to keep Bangladesh on top.
Australia have never lost a home Test to Bangladesh, only losing once to the Tigers in six previous Tests - at Mirpur in 2017.
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