Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	May 28, 2022	Aug. 28, 2021
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 363,000	$ 348,725
Accumulated Amortization	275,371	264,087
Net Carrying Amount	87,629	84,638
Customer contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	246,934	237,384
Accumulated Amortization	196,015	188,255
Net Carrying Amount	50,919	49,129
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	78,502	74,475
Accumulated Amortization	43,911	40,763
Net Carrying Amount	34,591	33,712
Other intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	37,564	36,866
Accumulated Amortization	35,445	35,069
Net Carrying Amount	$ 2,119	$ 1,797