Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	Feb. 27, 2021	Aug. 29, 2020
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 343,297	$ 335,820
Accumulated Amortization	258,155	250,284
Net Carrying Amount	85,142	85,536
Customer contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	236,236	234,065
Accumulated Amortization	182,798	177,119
Net Carrying Amount	53,438	56,946
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	71,061	66,014
Accumulated Amortization	40,712	39,020
Net Carrying Amount	30,349	26,994
Other intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	36,000	35,741
Accumulated Amortization	34,645	34,145
Net Carrying Amount	$ 1,355	$ 1,596