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Croatia reached the World Cup final for the first time after an extra-time goal from Mario Mandzukic gave them a 2-1 win over England.
The recent success of the Russian team, widely scorned at home for their poor performances in the past, has taken the country and the soccer world by surprise.
Belgium beat Brazil 2-1 to enter the semifinals for the first time since 1986.
Piara Powar, the head of the FARE network which monitors discrimination in European soccer, said the victims had included Russian women harassed by fans and TV reporters who had been accosted while broadcasting.
Koke's third penalty for Spain was saved by Igor Akinfeev who then saved Iago Aspas's final shot.
Croatian keeper Danijel Subasic matched the World Cup record for most saves in a shoot-out, equaling the mark set by Portugal's Ricardo against England in 2006.
Packed pubs and big-screen areas erupted as Gareth Southgate's team dispatched their opponents 2-0 to reach the semifinals of the competition for the first time in 28 years.
This is Belgium's best World Cup performance after finishing fourth in the 1986 edition.
The two sides must pick themselves up and dust themselves down after suffering the crushing disappointment of semifinal defeats to play for the modest prize of third place.
Sweden scored a 1-0 win over Switzerland and setup a quarterfinal clash with either England or Colombia.
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