Employee and Retiree Benefits - Deferred Compensation Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 27, 2022	Aug. 28, 2021	Aug. 29, 2020
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Matching contribution amount	$ 12.0	$ 5.6	$ 3.4
Employer discretionary contribution amount	$ 12.1	6.1	0.0
Key Employees | Non-Qualified Deferred Compensation Program (1981)
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Vesting age	55 years
Requisite service period	5 years
Requisite service period prior to December 1992	20 years
Deferred compensation expense	$ 0.6	0.8	$ 0.9
Officers and Managers | Supplemental Employee Retirement Plan (SERP)
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Contractual amount of years after retirement	15 years
Officers and Key Employees | Executive Deferred Compensation Plan 2007
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Maximum salary deferral	50.00%
Maximum cash incentive award deferral	100.00%
Deferred compensation assets	$ 1.4	$ 1.0