Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	Nov. 25, 2023	Aug. 26, 2023
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 435,683	$ 439,584
Accumulated Amortization	297,215	293,966
Net Carrying Amount	138,468	145,618
Customer Contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	314,542	315,448
Accumulated Amortization	216,104	211,996
Net Carrying Amount	98,438	103,452
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	81,336	80,538
Accumulated Amortization	46,407	45,117
Net Carrying Amount	34,929	35,421
Other Intangible Assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	39,805	43,598
Accumulated Amortization	34,704	36,853
Net Carrying Amount	$ 5,101	$ 6,745