Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	May 29, 2021	Aug. 29, 2020
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 348,601	$ 335,820
Accumulated Amortization	262,691	250,284
Net Carrying Amount	85,910	85,536
Customer contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	236,390	234,065
Accumulated Amortization	185,656	177,119
Net Carrying Amount	50,734	56,946
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	75,214	66,014
Accumulated Amortization	42,023	39,020
Net Carrying Amount	33,191	26,994
Other intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	36,997	35,741
Accumulated Amortization	35,012	34,145
Net Carrying Amount	$ 1,985	$ 1,596