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Nature of Business and Summary of Significant Accounting Policies - Additional Information (Details) - USD ($) $ in Millions | 12 Months Ended
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Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2022
Accounting Policies [Abstract] |  |  |
Depreciation and amortization, property and equipment | $ 9.4 | $ 10.1 | $ 15.2
Foreign exchange gains (losses) | (0.6) | (2.6) | 1.9
Advertising and promotion costs | $ 12.3 | $ 9.8 | $ 8.1

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