Employee Benefit Plans - Narrative (Details) $ in Millions	3 Months Ended		9 Months Ended
	May 25, 2019 USD ($) Retirement-Plan	May 26, 2018 USD ($)	May 25, 2019 USD ($) Retirement-Plan	May 26, 2018 USD ($)
Postemployment Benefits [Abstract]
Contributions charged to expense under the plan	$ 5.8	$ 5.4	$ 14.6	$ 13.5
Number of frozen non-contributory defined benefit pension plans | Retirement-Plan	2		2
Amounts charged to expense related to the plans	$ 0.5	$ 0.6	$ 1.6	$ 1.9