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Mr Abdallahi became Mauritania's first democratically elected leader in 2007 after a coup two years earlier, partly instigated by General Mohamed Ould Abdelaziz.
BBC: Mauritania frees deposed leader
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He gained most votes in the capital, Nouakchott and his home Trarza region in the south-east, officials say, while Mr Abdallahi won Mauritania's other 11 regions.
BBC: Sidi Ould Cheikh Abdallahi
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Mr Daddah, 65, an economist and brother of Mauritania's first post-independence leader, unsuccessfully ran against Mr Taya in 1992 and 2003.
BBC: Sidi Ould Cheikh Abdallahi