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Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands | Aug. 28, 2021 | Aug. 29, 2020
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Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | $ 348,725 | $ 335,820
Accumulated Amortization | 264,087 | 250,284
Net Carrying Amount | 84,638 | 85,536
Customer contracts |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 237,384 | 234,065
Accumulated Amortization | 188,255 | 177,119
Net Carrying Amount | 49,129 | 56,946
Software |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 74,475 | 66,014
Accumulated Amortization | 40,763 | 39,020
Net Carrying Amount | 33,712 | 26,994
Other intangible assets |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 36,866 | 35,741
Accumulated Amortization | 35,069 | 34,145
Net Carrying Amount | $ 1,797 | $ 1,596

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