Mickey Harte's first championship game in charge of Louth will see the Wee County play Offaly for the right to play Kildare in the last-eight.
Meath will face either Carlow or Longford in the quarters with the other last-eight clash pitting Westmeath against Laois.
Six in-a-row All-Ireland champions Dublin will go to Wexford or Wicklow in the quarter-finals.
Holders Kilkenny await the winners of Laois and Wexford in the semi-finals of the Leinster Senior Hurling Championship.
The other last-four tie will see Galway play either Dublin or McDonagh Cup winners Antrim.
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