Employee Benefit Plans - Narrative (Details)	3 Months Ended		9 Months Ended
	May 31, 2025 USD ($) RetirementPlan	May 25, 2024 USD ($)	May 31, 2025 USD ($) RetirementPlan	May 25, 2024 USD ($)	Aug. 31, 2024 USD ($)
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Contributions charged to expense under the plan	$ 3,900,000	$ 5,100,000	$ 11,700,000	$ 15,200,000
Other (income) expense	$ (200,000)	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	400,000	$ 1,300,000	1,300,000
Non-qualified Deferred Compensation Plan
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Amounts charged to expense related to the plans	300,000	$ 200,000	700,000	$ 600,000
NQDC Plan assets	4,400,000		4,400,000		$ 3,300,000
NQDC Plan liabilities, current	$ 2,600,000		$ 2,600,000		$ 1,600,000