Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	Feb. 24, 2024	Aug. 26, 2023
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 436,166	$ 439,584
Accumulated Amortization	303,688	293,966
Net Carrying Amount	132,478	145,618
Customer Contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	314,566	315,448
Accumulated Amortization	220,231	211,996
Net Carrying Amount	94,335	103,452
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	81,768	80,538
Accumulated Amortization	48,217	45,117
Net Carrying Amount	33,551	35,421
Other Intangible Assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	39,832	43,598
Accumulated Amortization	35,240	36,853
Net Carrying Amount	$ 4,592	$ 6,745