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Smith responded by lifting Saqibul over midwicket to bring up his 17th Test century and Amla hit Mehrab over the top for his sixth.
BBC: Smith and Amla punish Bangladesh
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The departure of McKenzie, taken by Mehrab Hossain jnr at backward point, proved to be the only glimmer of light on a disappointing day for Bangladesh.
BBC: Smith and Amla punish Bangladesh
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Both centurions survived chances - Bangladesh wicketkeeper Mushfiqur Rahim could not make a stumping when Smith was on 83 and Amla was on 93 when he was dropped at slip by Mashrafe Mortaza off Mehrab.
BBC: Smith and Amla punish Bangladesh