Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	Feb. 25, 2023	Aug. 27, 2022
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 365,516	$ 360,769
Accumulated Amortization	282,549	275,796
Net Carrying Amount	82,967	84,973
Customer contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	249,749	247,721
Accumulated Amortization	203,391	198,668
Net Carrying Amount	46,358	49,053
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	78,339	75,528
Accumulated Amortization	43,510	41,637
Net Carrying Amount	34,829	33,891
Other intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	37,428	37,520
Accumulated Amortization	35,648	35,491
Net Carrying Amount	$ 1,780	$ 2,029