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There were Senior Football Championship Qualifier triumphs for Derry, Cork and Mayo on Saturday, with Longford recording a shock win at Monaghan.
Elsewhere, Cavan and Kildare also secured progress to Round 3.
Longford produced a surprise 2-13 to 1-13 win over Monaghan in Clones.
Michael Quinn netted early on for the visitors but the home side found their feet towards the end of the first period, thanks in a part to a Colin Walshe goal, and led by three points at the interval.
Longford, though, battled back to ensure parity, before scores from Brian Kavanagh and Liam Connerton edged the Leinster side ahead.
A Robbie Smyth goal left Longford four points ahead with time running out, and the underdogs were able to cling on for a highly unanticipated win.
Derry defeated Meath 1-14 to 1-11 in a thriller at Owenbeg to book a berth in the third round.
A Donnacha Tobin goal helped Meath to a seven-point half-time lead over the hosts in Dungiven.
The Leinster side, however, succumbed to a sensational fightback from the Oak Leaf men, which included a fine Niall Loughlin goal, as the Ulster outfit recorded an excellent triumph.
Peter Kelleher hit the net for Cork in a relatively comfortable win over Limerick at Semple Stadium.
Paul Kerrigan grabbed the Rebels' second goal late on in Thurles, as Cork defeated their Munster rivals 2-12 to 0-10.
Mayo secured a place in the next round thanks to a hard-fought 2-14 to 1-12 win over Fermanagh at MacHale Park.
Alan Freeman netted during the first half for the hosts but Sean Quigley quickly responded in kind for Fermanagh, who went at the break with a six-point advantage.
Mayo, though, rallied in second period, helped by a converted Cillian O'Connor penalty following a controversial fall by Aidan O'Shea, to secure the victory.
Cavan overcame the hurdle of Carlow, winning 2-13 to 0-12 at Breffni Park.
Eugene Keating struck an early goal for the Ulster side, with the hosts going on to lead by three points at the interval.
Cian Mackey netted midway through the second half to allow Cavan breathing space on their way to an uninspiring win.
In Newbridge, Kildare had just too much for Offaly, winning a nervy encounter by 1-22 to 2-14.
Tommy Moolick netted in the first period for the home side, who held a five-point half-time advantage.
Offaly, though, helped by a goal from the impressive Nigel Dunne, kept well in touch with the favourites.
Peter Cunningham struck a successful penalty for the visitors, who levelled through Dunne inside the final 15 minutes.
However, scores from Eoghan O'Flaherty steadied the Kildare ship, before Offaly lost Eoin Carroll to a second yellow card, as the home side ultimately progressed.