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Goodwill and Intangible Assets - Schedule of Intangible Assets (Details) - USD ($)
$ in Millions
Aug. 26, 2023
Aug. 27, 2022
Schedule of Intangible Assets [Line Items]    
Total amortization expense remaining $ 149.7  
Intangible Assets, Net (Excluding Goodwill) [Abstract]    
Gross Carrying Amount 628.5 $ 581.2
Accumulated Amortization 126.5 108.8
Net Carrying Value 502.0 472.4
Trade names    
Schedule of Intangible Assets [Line Items]    
Gross Carrying Amount 4.1  
Total amortization expense remaining 3.9  
Intangible Assets, Net (Excluding Goodwill) [Abstract]    
Accumulated Amortization 0.2  
Dealer networks/customer relationships    
Schedule of Intangible Assets [Line Items]    
Gross Carrying Amount 183.6 180.0
Total amortization expense remaining 108.0 119.5
Intangible Assets, Net (Excluding Goodwill) [Abstract]    
Accumulated Amortization 75.6 60.5
Backlog    
Schedule of Intangible Assets [Line Items]    
Gross Carrying Amount 43.6 42.3
Total amortization expense remaining 1.1 0.0
Intangible Assets, Net (Excluding Goodwill) [Abstract]    
Accumulated Amortization 42.5 42.3
Developed technology    
Schedule of Intangible Assets [Line Items]    
Gross Carrying Amount 38.3  
Total amortization expense remaining 36.5  
Intangible Assets, Net (Excluding Goodwill) [Abstract]    
Accumulated Amortization 1.8  
Non-compete agreements    
Schedule of Intangible Assets [Line Items]    
Gross Carrying Amount 6.6 6.6
Total amortization expense remaining 0.2 0.6
Intangible Assets, Net (Excluding Goodwill) [Abstract]    
Accumulated Amortization 6.4 6.0
Trade names    
Schedule of Intangible Assets [Line Items]    
Indefinite-lived trade names $ 352.3 $ 352.3