Employee Benefit Plans - Narrative (Details) $ in Millions	3 Months Ended		9 Months Ended
	May 26, 2018 USD ($) retirement_plan	May 27, 2017 USD ($)	May 26, 2018 USD ($) retirement_plan	May 27, 2017 USD ($)
Postemployment Benefits [Abstract]
Contributions charged to expense under the plan	$ 5.4	$ 3.7	$ 13.5	$ 11.0
Number of frozen non-contributory defined benefit pension plans | retirement_plan	2		2
Amounts charged to expense related to the plans	$ 0.6	$ 0.9	$ 1.9	$ 2.6