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De Boer has resigned two days after his side were beaten 2-0 by the Czech Republic and eliminated in the last 16 of the European Championship.
Switzerland scored twice in the final 10 minutes in a thrilling 3-3 draw and, following a goalless extra time, prevailed in the shootout after goalkeeper Yann Sommer saved from Mbappe.
Peru take on Paraguay in the first quarterfinal.
The result means that Argentina will face Ecuador in the last eight on Saturday while Uruguay, who beat Paraguay 1-0, will play Colombia the same day.
Kylian Mbappe's penalty was saved by Yann Sommer to send the Swiss through after a pulsating encounter.
Croatia exited from Euro 2020 in a 5-3 extra time defeat by Spain after a riveting fightback in their last 16 clash.
Alvaro Morata and Mikel Oyarzabal's strikes in extra time made the difference.
England have lost to Germany in their last three knockout meetings at major tournaments, in 1990, 1996 and 2010, with the first two coming after penalty shoot-outs in the semifinals being particularly painful.
The winger scored a stunner against Portugal in Seville, ensuring Belgium a place in the European Championship quarterfinals.
The draw at an empty stadium in central Brazil marked the first time Brazil have not picked up a win since they lost 1-0 to Argentina in a friendly in November 2019.
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