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Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands | May 30, 2020 | Aug. 31, 2019
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Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | $ 332,500 | $ 305,207
Accumulated Amortization | 245,571 | 232,487
Net Carrying Amount | 86,929 | 72,720
Customer contracts |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 233,922 | 221,306
Accumulated Amortization | 173,861 | 164,718
Net Carrying Amount | 60,061 | 56,588
Software |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 63,011 | 48,838
Accumulated Amortization | 37,971 | 34,813
Net Carrying Amount | 25,040 | 14,025
Other intangible assets |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 35,567 | 35,063
Accumulated Amortization | 33,739 | 32,956
Net Carrying Amount | $ 1,828 | $ 2,107

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