Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	Aug. 28, 2021	Aug. 29, 2020
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 348,725	$ 335,820
Accumulated Amortization	264,087	250,284
Net Carrying Amount	84,638	85,536
Customer contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	237,384	234,065
Accumulated Amortization	188,255	177,119
Net Carrying Amount	49,129	56,946
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	74,475	66,014
Accumulated Amortization	40,763	39,020
Net Carrying Amount	33,712	26,994
Other intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	36,866	35,741
Accumulated Amortization	35,069	34,145
Net Carrying Amount	$ 1,797	$ 1,596