Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	May 27, 2023	Aug. 27, 2022
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 438,676	$ 360,769
Accumulated Amortization	287,347	275,796
Net Carrying Amount	151,329	84,973
Customer contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	315,746	247,721
Accumulated Amortization	207,615	198,668
Net Carrying Amount	108,131	49,053
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	79,342	75,528
Accumulated Amortization	43,515	41,637
Net Carrying Amount	35,827	33,891
Other intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	43,588	37,520
Accumulated Amortization	36,217	35,491
Net Carrying Amount	$ 7,371	$ 2,029