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Dover have been handed a long away trip in the second round of the FA Trophy.
Andy Hessenthaler's men will travel to Blue Square North Fleetwood Town on January 9.
Fleetwood, who are based in Lancashire, are unbeaten at home in the league this season and knocked out Blue Square Premier crisis club Chester in the first round.
The county's only other representative, Maidstone, will also be on the road if they can get past Histon in their re-arranged first round tie on Tuesday night.
The winners of that match have been drawn away to Blue Square Premier Salisbury.