Employee Benefit Plans - Narrative (Details) $ in Millions	3 Months Ended		9 Months Ended
	May 29, 2021 USD ($) Retirement-Plan	May 30, 2020 USD ($)	May 29, 2021 USD ($) Retirement-Plan	May 30, 2020 USD ($)
Postemployment Benefits [Abstract]
Contributions charged to expense under the plan	$ 5.1	$ 1.9	$ 15.2	$ 12.4
Number of frozen non-contributory defined benefit pension plans | Retirement-Plan	1		1
Amounts charged to expense related to the plans	$ 0.8	$ 0.7	$ 2.3	$ 1.2