Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	May 25, 2024	Aug. 26, 2023
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 435,470	$ 439,584
Accumulated Amortization	309,593	293,966
Net Carrying Amount	125,877	145,618
Customer Contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	314,705	315,448
Accumulated Amortization	224,319	211,996
Net Carrying Amount	90,386	103,452
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	80,945	80,538
Accumulated Amortization	49,546	45,117
Net Carrying Amount	31,399	35,421
Other Intangible Assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	39,820	43,598
Accumulated Amortization	35,728	36,853
Net Carrying Amount	$ 4,092	$ 6,745