Tony Blair's office has said: "Mr Blair's father, Leo, sadly passed away today. It was peaceful and Mr Blair was with him."
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Mladic, now 75, was the military commander of Bosnian Serb forces in the 1990s, who fought against the Bosnian Croat and Bosniak armies.
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His representatives said Cassidy, who was hospitalised last week, died "surrounded by those he loved."