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Tipperary will host last season's All-Ireland finalists Mayo in the pick of the SFC Round 2 Qualifiers.
The match is a repeat of the 2016 All-Ireland semi-final, where a late Conor O'Shea goal sealed a 2-13 to 0-14 victory for Mayo against a Tipp side making their first appearance in the last four for 81 years.
Cavan's reward for an impressive 11-point win over Wicklow at Joule Park on Saturday is a home draw against fellow Ulster side Down.
Beaten Leinster semi-finalists Carlow host Tyrone, who overcame Meath 2-14 to 0-19 after extra-time in Saturday's Round 1 qualifier at Páirc Tailteann, Navan.
Waterford, 3-14 to 1-18 winners over neighbours Wexford at Wexford Park on Saturday, will host beaten Ulster semi-finalists Monaghan in the second round.
The first team drawn enjoys home advantage unless they are a Division One or Two side and are paired with a side from Division Three or Four.
So Division Three side Longford, initially drawn second out of the pot, will host Division One side Kildare.
The games will be played over the weeskend of 23 and 24 June, with venues and dates to be confirmed later on Monday, and all games will finish on the day.
All-Ireland SFC round two qualifiers
Tipperary v Mayo
Waterford v Monaghan
Cavan v Down
Carlow v Tyrone
Offaly v Clare
Longford v Kildare
Sligo v Armagh
Leitrim v Louth
Image: Inpho/ Cathal Noonan
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