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Intangible Assets - Gross and Net Intangible Assets by Major Class (Details) - USD ($) $ in Millions | Sep. 30, 2023 | Sep. 30, 2022
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Acquired Finite-Lived Intangible Assets [Line Items] |  |
Finite-lived intangible assets, gross amount | $ 70.9 | $ 61.5
Finite-lived intangible assets, accumulated amortization | (53.4) | (39.0)
Finite-lived intangible assets, net amount | 17.5 | 22.5
Indefinite-lived intangible assets | 5.6 | 5.5
Intangible assets, gross amount | 76.5 | 67.0
Total intangible assets, net amount | 23.1 | 28.0
Website domains |  |
Acquired Finite-Lived Intangible Assets [Line Items] |  |
Indefinite-lived intangible assets | 1.9 | 1.8
Business licenses |  |
Acquired Finite-Lived Intangible Assets [Line Items] |  |
Indefinite-lived intangible assets | 3.7 | 3.7
Trade/domain names |  |
Acquired Finite-Lived Intangible Assets [Line Items] |  |
Finite-lived trade/domain names, gross amount | 4.1 | 3.7
Finite-lived intangible assets, accumulated amortization | (2.4) | (1.6)
Finite-lived intangible assets, net amount | 1.7 | 2.1
Software programs/platforms |  |
Acquired Finite-Lived Intangible Assets [Line Items] |  |
Finite-lived software programs/platforms, gross amount | 28.5 | 28.3
Finite-lived intangible assets, accumulated amortization | (26.9) | (19.4)
Finite-lived intangible assets, net amount | 1.6 | 8.9
Client base |  |
Acquired Finite-Lived Intangible Assets [Line Items] |  |
Finite-lived customer base, gross amount | 38.3 | 29.5
Finite-lived intangible assets, accumulated amortization | (24.1) | (18.0)
Finite-lived intangible assets, net amount | $ 14.2 | $ 11.5

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