Employee Benefit Plans - Narrative (Details) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 26, 2022 USD ($) Retirement-Plan	Feb. 27, 2021 USD ($)	Feb. 26, 2022 USD ($) Retirement-Plan	Feb. 27, 2021 USD ($)
Postemployment Benefits [Abstract]
Contributions charged to expense under the plan	$ 3.9	$ 4.3	$ 9.5	$ 10.1
Number of frozen non-contributory defined benefit pension plans | Retirement-Plan	1		1
Amounts charged to expense related to the plans	$ 0.6	$ 0.8	$ 1.3	$ 1.5
Deferred compensation plan, employee or employer contribution charged to expense	$ 0.0		$ 0.0