Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	Nov. 26, 2022	Aug. 27, 2022
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 364,158	$ 360,769
Accumulated Amortization	279,308	275,796
Net Carrying Amount	84,850	84,973
Customer contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	249,448	247,721
Accumulated Amortization	201,080	198,668
Net Carrying Amount	48,368	49,053
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	77,230	75,528
Accumulated Amortization	42,658	41,637
Net Carrying Amount	34,572	33,891
Other intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	37,480	37,520
Accumulated Amortization	35,570	35,491
Net Carrying Amount	$ 1,910	$ 2,029