Business Combinations (Details) - USD ($) $ in Millions		3 Months Ended			6 Months Ended
	Aug. 31, 2021	Feb. 25, 2023	Feb. 26, 2022	Nov. 27, 2021	Feb. 25, 2023	Feb. 26, 2022	Aug. 27, 2022	Aug. 28, 2021
Business Acquisition [Line Items]
Goodwill		$ 484.2	$ 484.2		$ 484.2	$ 484.2	$ 484.2	$ 348.1
Acquisition-related costs expensed		1.1	$ 0.4		1.7	$ 3.8
Barletta
Business Acquisition [Line Items]
Percent of voting interest acquired	100.00%
Purchase price	$ 286.3
Cash payments	240.1
Purchase price, common stock issued	$ 25.0
Discount percentage on purchase price	12.00%
Lockup restriction period	1 year
Purchase price, common stock issued after discount	$ 22.0
Earnout liability	24.2	41.8			41.8		39.8
Goodwill	136.1
Other intangible assets	$ 111.4
Transaction costs				$ 3.1
Acquisition-related costs expensed				$ 2.4
Barletta | Dealer networks
Business Acquisition [Line Items]
Weighted-average useful life	12 years
Barletta | Backlog
Business Acquisition [Line Items]
Weighted-average useful life	10 months
Barletta | Other Current Liabilities
Business Acquisition [Line Items]
Earnout liability		21.9			21.9		21.3
Barletta | Other Noncurrent Liabilities
Business Acquisition [Line Items]
Earnout liability		$ 19.9			$ 19.9		$ 18.5
Barletta | Earnout Paid In Stock
Business Acquisition [Line Items]
Earnout amount	$ 50.0
Barletta | Earnout Paid In Cash
Business Acquisition [Line Items]
Earnout amount	$ 15.0