Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	Feb. 26, 2022	Aug. 28, 2021
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 361,724	$ 348,725
Accumulated Amortization	271,503	264,087
Net Carrying Amount	90,221	84,638
Customer contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	246,844	237,384
Accumulated Amortization	193,249	188,255
Net Carrying Amount	53,595	49,129
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	77,295	74,475
Accumulated Amortization	42,942	40,763
Net Carrying Amount	34,353	33,712
Other intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	37,585	36,866
Accumulated Amortization	35,312	35,069
Net Carrying Amount	$ 2,273	$ 1,797