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Denmark will face Norway in the semi-finals on Thursday after edging France on penalties at the end of a tight contest in Linkoping.
Few were backing the Danes to prevail, but history repeated itself in agonising fashion for Les Bleues after Louisa Necib's penalty had cancelled out Johanna Rasmussen's opener in normal time. France lost a quarter-final on spot kicks to the Netherlands at Finland 2009, and after Necib had her attempt saved by the excellent Stina Petersen, they were heading for similar heartbreak. Sarah Bouhaddi kept out Theresa Nielsen, but Sabrina Delannoy hit the woodwork and Janni Arnth did the rest.
Élise Bussaglia swerved an effort wide to announce France's presence as the teams settled, but there was no lack of energy and commitment from their opponents, who were clearly going to have their say in the contest. Switching from 4-3-3 to 4-4-2 to tighten up their midfield, Kenneth Heiner-Møller's charges looked anything but overawed, and laid down a capable passing game to back up their ambitions.
It was Petersen who had to be the most alert of the goalkeepers early on, but Bruno Bini must surely have hoped for a more incisive start – and his side's frustration turned to angst when Rasmussen raced onto Katrine Søndergaard Pedersen's long ball over the top and blasted beyond Sarah Bouhaddi.