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Longford manager Denis Connerton says the victory over Monaghan is "one of our greatest victories".
The O'Farrell County shocked the reigning Ulster champions with a 2-13 to 1-13 victory-13 to 1-13 victory in Clones on Saturday, and Connerton, who was in charge when Longford beat the Farney County in 2004, hailed his team's "brilliant, brilliant performance".
"It's a fantastic evening," he said.
"We knew we'd be up against it and that we'd have to play out of our skins to stay in the game.
"Then to win it we really had to play way above ourselves. So we played very well this evening, it was a brilliant, brilliant performance.
"All of those guys put in such a marvellous effort, it was really gigantic what they put into that game.
"We're after taking out a top-five team. To win here in the qualifiers ranks as one of our greatest victories.
"It's tremendous for us and possibly is the greatest victory we have ever had in the qualifiers, because we are after beating the Ulster champions."
Longford will face Cork, Mayo or Kildare in the third round next weekend, and Connerton is confident his players will take the week-long turnaround in their stride.
"We'll be on a level playing field, same as the other teams in our side of the draw," he told RTÉ Sport.
"All we can do is try and recover as quickly as possible. There's euphoric scenes here but we'll just have to get everybody back to earth as quickly as we possibly can.
"You'd love to be able to enjoy the moment but really it is only a moment, because you have to start looking ahead."