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Acquisitions and Divestitures (Details) $ in Millions		1 Months Ended	3 Months Ended
	May 15, 2023 USD ($)	Nov. 30, 2022 USD ($)	Nov. 30, 2023 USD ($) transaction	Aug. 31, 2023 USD ($)	Oct. 30, 2022 USD ($)	Aug. 31, 2022 USD ($)
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Number of acquisitions | transaction			0
Number of divestitures | transaction			0
Goodwill		$ 1,082.0	$ 1,097.5	$ 1,097.9		$ 1,084.3
ISG
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Goodwill		68.9	83.3	$ 83.5		$ 70.1
Preliminary goodwill			$ 15.0
KE2 Therm Solutions, Inc
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Goodwill	$ 15.0
Identified intangible assets	$ 18.0
Weighted average amortization period (in years)	15 years
Sunoptics Prismatic Skylights Business | Disposal Group, Not Discontinued Operations
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Assets transferred					$ 15.1
Pre-tax loss on the sale		$ 11.2

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