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Goodwill and Intangible Assets - Schedule of Intangible Assets (Details) - USD ($)
$ in Millions
Nov. 25, 2023
Aug. 26, 2023
Schedule of Intangible Assets [Line Items]    
Total amortization expense remaining $ 144.1  
Intangible Assets, Net (Excluding Goodwill) [Abstract]    
Gross Carrying Amount 628.5 $ 628.5
Accumulated Amortization 132.1 126.5
Net Carrying Value 496.4 502.0
Indefinite-lived trade names    
Schedule of Intangible Assets [Line Items]    
Gross Carrying Amount 4.1 4.1
Total amortization expense remaining 3.8 3.9
Intangible Assets, Net (Excluding Goodwill) [Abstract]    
Accumulated Amortization 0.3 0.2
Dealer networks/customer relationships    
Schedule of Intangible Assets [Line Items]    
Gross Carrying Amount 183.6 183.6
Total amortization expense remaining 104.1 108.0
Intangible Assets, Net (Excluding Goodwill) [Abstract]    
Accumulated Amortization 79.5 75.6
Backlog    
Schedule of Intangible Assets [Line Items]    
Gross Carrying Amount 43.6 43.6
Total amortization expense remaining 0.9 1.1
Intangible Assets, Net (Excluding Goodwill) [Abstract]    
Accumulated Amortization 42.7 42.5
Developed technology    
Schedule of Intangible Assets [Line Items]    
Gross Carrying Amount 38.3 38.3
Total amortization expense remaining 35.1 36.5
Intangible Assets, Net (Excluding Goodwill) [Abstract]    
Accumulated Amortization 3.2 1.8
Non-compete agreements    
Schedule of Intangible Assets [Line Items]    
Gross Carrying Amount 6.6 6.6
Total amortization expense remaining 0.2 0.2
Intangible Assets, Net (Excluding Goodwill) [Abstract]    
Accumulated Amortization 6.4 6.4
Indefinite-lived trade names    
Schedule of Intangible Assets [Line Items]    
Indefinite-lived trade names $ 352.3 $ 352.3