Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	Aug. 26, 2023	Aug. 27, 2022
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 439,584	$ 360,769
Accumulated Amortization	293,966	275,796
Net Carrying Amount	145,618	84,973
Customer Contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	315,448	247,721
Accumulated Amortization	211,996	198,668
Net Carrying Amount	103,452	49,053
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	80,538	75,528
Accumulated Amortization	45,117	41,637
Net Carrying Amount	35,421	33,891
Other Intangible Assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	43,598	37,520
Accumulated Amortization	36,853	35,491
Net Carrying Amount	$ 6,745	$ 2,029