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Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands | Feb. 25, 2023 | Aug. 27, 2022
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Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | $ 365,516 | $ 360,769
Accumulated Amortization | 282,549 | 275,796
Net Carrying Amount | 82,967 | 84,973
Customer contracts |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 249,749 | 247,721
Accumulated Amortization | 203,391 | 198,668
Net Carrying Amount | 46,358 | 49,053
Software |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 78,339 | 75,528
Accumulated Amortization | 43,510 | 41,637
Net Carrying Amount | 34,829 | 33,891
Other intangible assets |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 37,428 | 37,520
Accumulated Amortization | 35,648 | 35,491
Net Carrying Amount | $ 1,780 | $ 2,029

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