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Goodwill and Intangible Assets - Schedule of Intangible Assets (Details) - USD ($) $ in Millions | Mar. 01, 2025 | Aug. 31, 2024
--- | --- | ---
Schedule of Intangible Assets [Line Items] |  |
Total amortization expense remaining | $ 115.6 |
Intangible Assets, Net (Excluding Goodwill) [Abstract] |  |
Gross Carrying Amount | 628.5 | $ 628.5
Accumulated Amortization | 160.6 | 149.5
Net Carrying Value | 467.9 | 479.0
Indefinite-lived trade names |  |
Schedule of Intangible Assets [Line Items] |  |
Gross Carrying Amount | 4.1 | 4.1
Total amortization expense remaining | 3.0 | 3.3
Intangible Assets, Net (Excluding Goodwill) [Abstract] |  |
Accumulated Amortization | 1.1 | 0.8
Dealer networks/customer relationships |  |
Schedule of Intangible Assets [Line Items] |  |
Gross Carrying Amount | 183.6 | 183.6
Total amortization expense remaining | 84.3 | 92.1
Intangible Assets, Net (Excluding Goodwill) [Abstract] |  |
Accumulated Amortization | 99.3 | 91.5
Backlog |  |
Schedule of Intangible Assets [Line Items] |  |
Gross Carrying Amount | 43.6 | 43.6
Total amortization expense remaining | 0.1 | 0.4
Intangible Assets, Net (Excluding Goodwill) [Abstract] |  |
Accumulated Amortization | 43.5 | 43.2
Developed technology |  |
Schedule of Intangible Assets [Line Items] |  |
Gross Carrying Amount | 38.3 | 38.3
Total amortization expense remaining | 28.2 | 30.9
Intangible Assets, Net (Excluding Goodwill) [Abstract] |  |
Accumulated Amortization | 10.1 | 7.4
Non-compete agreements |  |
Schedule of Intangible Assets [Line Items] |  |
Gross Carrying Amount | 6.6 | 6.6
Total amortization expense remaining | 0.0 | 0.0
Intangible Assets, Net (Excluding Goodwill) [Abstract] |  |
Accumulated Amortization | 6.6 | 6.6
Indefinite-lived trade names |  |
Schedule of Intangible Assets [Line Items] |  |
Indefinite-lived trade names | $ 352.3 | $ 352.3

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