Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	Nov. 27, 2021	Aug. 28, 2021
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 350,247	$ 348,725
Accumulated Amortization	267,580	264,087
Net Carrying Amount	82,667	84,638
Customer contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	237,807	237,384
Accumulated Amortization	190,604	188,255
Net Carrying Amount	47,203	49,129
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	75,614	74,475
Accumulated Amortization	41,836	40,763
Net Carrying Amount	33,778	33,712
Other intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	36,826	36,866
Accumulated Amortization	35,140	35,069
Net Carrying Amount	$ 1,686	$ 1,797