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Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands | May 28, 2022 | Aug. 28, 2021
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Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | $ 363,000 | $ 348,725
Accumulated Amortization | 275,371 | 264,087
Net Carrying Amount | 87,629 | 84,638
Customer contracts |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 246,934 | 237,384
Accumulated Amortization | 196,015 | 188,255
Net Carrying Amount | 50,919 | 49,129
Software |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 78,502 | 74,475
Accumulated Amortization | 43,911 | 40,763
Net Carrying Amount | 34,591 | 33,712
Other intangible assets |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 37,564 | 36,866
Accumulated Amortization | 35,445 | 35,069
Net Carrying Amount | $ 2,119 | $ 1,797

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