Employee Benefit Plans - Narrative (Details)	3 Months Ended		9 Months Ended
	May 27, 2023 USD ($) RetirementPlan	May 28, 2022 USD ($)	May 27, 2023 USD ($) RetirementPlan	May 28, 2022 USD ($)	Aug. 27, 2022 USD ($)
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Contributions charged to expense under the plan	$ 4,400,000	$ 4,700,000	$ 14,300,000	$ 14,200,000
Deferred compensation plan, employee or employer contribution charged to expense	$ 100,000	0	$ 200,000	0
SERP
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Number of frozen non-contributory defined benefit pension plans | RetirementPlan	1		1
Amounts charged to expense related to the plans	$ 400,000	$ 600,000	$ 1,300,000	$ 1,900,000
Nonqualified Deferred Compensation Plan Member
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
NQDC Plan assets	$ 1,900,000		$ 1,900,000		$ 1,300,000