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Dartford and Dover Athletic have both been drawn away to Football League clubs in the FA Cup second round while Maidstone United will also be away if they win their first round replay.
A trip to Yorkshire awaits Dartford, who will face Bradford City of League 1 at Valley Parade.
Tony Burman's men, who are on their best FA Cup run for 30 years, won 4-3 at Bromley on Saturday and now they're eyeing their first appearance in round three since 1936-37.
Dover, who knocked out Morecambe in the first round, will face League 2 opposition again.
The Whites have been drawn away to Cheltenham Town and they will believe they can emulate their run of four seasons ago, when they went all the way to the third round.
Maidstone will be on the road again if they come through their replay against Stevenage next week.
The first game finished 0-0 at Broadhall Way and the winners of the rematch at the Gallagher Stadium will be away to Vanarama Conference side Wrexham in round two.
The ties will be played over the weekend of December 6.
FA CUP SECOND ROUND DRAW
Bradford City v Dartford
Cheltenham Town v Dover Athletic
Wrexham v Stevenage or Maidstone United