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Goodwill and Intangible Assets - Intangible Assets (Details) - USD ($) $ in Thousands	3 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Sep. 30, 2021
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible assets, cost	$ 282,945
Finite-lived intangible assets, accumulated amortization	(75,248)
Finite-lived intangible assets, carrying value	207,697
Total identifiable intangible assets, cost	282,987
Total identifiable intangible assets, carrying value	207,739		$ 171,706
Amortization expense of intangible assets	4,178	$ 3,360
Trademarks
Finite-Lived Intangible Assets [Line Items]
Indefinite-lived intangible assets	42
Merchant relationships
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible assets, cost	265,911
Finite-lived intangible assets, accumulated amortization	(69,212)
Finite-lived intangible assets, carrying value	$ 196,699
Merchant relationships | Minimum
Finite-Lived Intangible Assets [Line Items]
Amortization life	9 years
Merchant relationships | Maximum
Finite-Lived Intangible Assets [Line Items]
Amortization life	25 years
Non-compete agreements
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible assets, cost	$ 1,478
Finite-lived intangible assets, accumulated amortization	(624)
Finite-lived intangible assets, carrying value	$ 854
Non-compete agreements | Minimum
Finite-Lived Intangible Assets [Line Items]
Amortization life	3 years
Non-compete agreements | Maximum
Finite-Lived Intangible Assets [Line Items]
Amortization life	6 years
Website and brand development costs
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible assets, cost	$ 218
Finite-lived intangible assets, accumulated amortization	(116)
Finite-lived intangible assets, carrying value	$ 102
Website and brand development costs | Minimum
Finite-Lived Intangible Assets [Line Items]
Amortization life	3 years
Website and brand development costs | Maximum
Finite-Lived Intangible Assets [Line Items]
Amortization life	4 years
Trade names
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible assets, cost	$ 7,820
Finite-lived intangible assets, accumulated amortization	(3,066)
Finite-lived intangible assets, carrying value	$ 4,754
Trade names | Minimum
Finite-Lived Intangible Assets [Line Items]
Amortization life	3 years
Trade names | Maximum
Finite-Lived Intangible Assets [Line Items]
Amortization life	7 years
Residual buyouts
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible assets, cost	$ 6,718
Finite-lived intangible assets, accumulated amortization	(1,617)
Finite-lived intangible assets, carrying value	$ 5,101
Amortization life	8 years
Referral and exclusivity agreements
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible assets, cost	$ 800
Finite-lived intangible assets, accumulated amortization	(613)
Finite-lived intangible assets, carrying value	$ 187
Amortization life	5 years

X

- Definition

The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

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Useful life of finite-lived intangible assets, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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Amount before accumulated amortization of intangible assets, excluding goodwill.

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Sum of the carrying amounts of all intangible assets, excluding goodwill, as of the balance sheet date, net of accumulated amortization and impairment charges.

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