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Goodwill and Purchased Intangible Assets - Schedule of Purchased Intangible Assets (Details) - USD ($) $ in Millions	3 Months Ended	12 Months Ended
	Dec. 31, 2021	Sep. 30, 2021	Sep. 30, 2020
Acquired Finite Lived Intangible Assets [Line Items]
Weighted- Average Life (in years)	14 years 4 months 24 days	14 years 4 months 24 days
Gross	$ 756.3	$ 756.3
Accumulated Amortization	(709.4)	(706.6)
Net	46.9	49.7
Non-amortizable trade names	417.1	417.1
Intangible assets excluding goodwill, gross	1,173.4	1,173.4
Purchased intangible assets, net	$ 464.0	$ 466.8	$ 466.8
Distribution network
Acquired Finite Lived Intangible Assets [Line Items]
Weighted- Average Life (in years)	39 years 2 months 12 days	39 years 1 month 6 days
Gross	$ 55.4	$ 55.4
Accumulated Amortization	(35.6)	(35.1)
Net	$ 19.8	$ 20.3
Technology-related
Acquired Finite Lived Intangible Assets [Line Items]
Weighted- Average Life (in years)	11 years 10 months 24 days	11 years 10 months 24 days
Gross	$ 104.7	$ 104.7
Accumulated Amortization	(104.0)	(103.9)
Net	$ 0.7	$ 0.8
Customer relationships
Acquired Finite Lived Intangible Assets [Line Items]
Weighted- Average Life (in years)	12 years 7 months 6 days	12 years 7 months 6 days
Gross	$ 572.6	$ 572.6
Accumulated Amortization	(551.3)	(550.0)
Net	$ 21.3	$ 22.6
Other
Acquired Finite Lived Intangible Assets [Line Items]
Weighted- Average Life (in years)	12 years 1 month 6 days	12 years 1 month 6 days
Gross	$ 23.6	$ 23.6
Accumulated Amortization	(18.5)	(17.6)
Net	$ 5.1	$ 6.0

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