Employee Benefit Plans - Narrative (Details) $ in Millions	3 Months Ended
	Nov. 27, 2021 USD ($) Retirement-Plan	Nov. 28, 2020 USD ($) Retirement-Plan
Postemployment Benefits [Abstract]
Contributions charged to expense under the plan	$ 5.5	$ 5.8
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