Employee Benefit Plans - Narrative (Details) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 27, 2021 USD ($) Retirement-Plan	Feb. 29, 2020 USD ($)	Feb. 27, 2021 USD ($) Retirement-Plan	Feb. 29, 2020 USD ($)
Postemployment Benefits [Abstract]
Contributions charged to expense under the plan	$ 4.3	$ 5.0	$ 10.1	$ 10.5
Number of frozen non-contributory defined benefit pension plans | Retirement-Plan	2		2
Amounts charged to expense related to the plans	$ 0.8	$ 0.3	$ 1.5	$ 0.4