Income Taxes (Details) - USD ($) $ in Millions	3 Months Ended	6 Months Ended
Mar. 31, 2023	Mar. 31, 2022	Mar. 31, 2023	Mar. 31, 2022	Sep. 30, 2022
Income Tax Disclosure [Abstract]
Effective income tax rate reconciliation (in percent)	22.80%	23.20%	22.80%	21.20%
Tax receivable agreement liability	$ 46.4		$ 46.4		$ 46.4
Percentage of net cash savings			85.00%

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations applicable to state and local income tax expense (benefit), net of federal tax expense (benefit).

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 6.I.Fact.4)
-URI https://asc.fasb.org/extlink&oid=122134291&loc=d3e330036-122817

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32687-109319

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Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration