Zakopane, Poland to Eger, Hungary--fastest way?

Hoping to travel from Zakopane to Eger in early June. Would prefer to do this in a day (leave Zakopane in the morning, Eger by afternoon/evening). Read that it could be driven in a few hours (but rental car prohibitively expensive). Have heard a combination of bus/train--perhaps through Poprad/Lysa Polana?--can accomplish this but have not seen any details regarding routes or purchasing tickets. Any suggestions?

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