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Nature of Business and Summary of Significant Accounting Policies - Additional Information (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Property, Plant and Equipment [Line Items]
Depreciation and amortization, property and equipment	$ 20.3	$ 23.5	$ 24.2
Foreign exchange gains (losses)	0.0	1.0	0.0
Advertising and promotion costs	$ 6.9	$ 8.7	$ 3.6
Minimum
Property, Plant and Equipment [Line Items]
Stock option awards vesting period	3 years
Maximum
Property, Plant and Equipment [Line Items]
Stock option awards vesting period	4 years
Software Development \| Minimum
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	2 years
Software Development \| Maximum
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	3 years