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Earnings Per Share - Antidilutive Securities (Details) - $ / shares	12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020	Feb. 18, 2020	Feb. 13, 2020
Class A Common Stock
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per share (shares)	10,170,668
Exchangeable notes, exchange price per share (in USD per share)	$ 40.87			$ 40.87
Warrant exercise price (in USD per share)					$ 62.88
Restricted Class A Common Stock
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per share (shares)		6,706	204,969
Out-of-the-money Options \| Class A Common Stock
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per share (shares)	4,580,844	2,495,922	1,327,500
Stock options \| Class A Common Stock
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per share (shares)	679,858	1,471,027	1,179,538