Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	Aug. 27, 2022	Aug. 28, 2021
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 360,769	$ 348,725
Accumulated Amortization	275,796	264,087
Net Carrying Amount	84,973	84,638
Customer contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	247,721	237,384
Accumulated Amortization	198,668	188,255
Net Carrying Amount	49,053	49,129
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	75,528	74,475
Accumulated Amortization	41,637	40,763
Net Carrying Amount	33,891	33,712
Other intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	37,520	36,866
Accumulated Amortization	35,491	35,069
Net Carrying Amount	$ 2,029	$ 1,797