Hungary's FA say Varga is in a "stable" condition as he recovers following victory over Euros opponents Scotland.
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"The players were saying he looked unconscious so everyone was really worried about his condition and worried about the fact that the doctors arrived late, we can say, but they probably didn't realise it was a dangerous situation," Rossi said.
"Thankfully he is not under risk, he will be operated on here (his cheek).
"He’s healthy, and that’s the most important thing. If we go through, he is no longer part of the team."