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Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands | Feb. 27, 2021 | Aug. 29, 2020
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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

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