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Long-Term Debt, Net - Schedule of Long-term Debt (Details) - USD ($) $ in Thousands	Sep. 30, 2023	Sep. 30, 2022	Feb. 18, 2020
Debt Instrument [Line Items]
Debt issuance costs, net	$ (4,424)	$ (2,554)
Total long-term debt, net of issuance costs	385,081	287,020
Line of Credit \| Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility
Debt Instrument [Line Items]
Long-term debt	272,505	0
Line of Credit \| Revolving lines of credit to banks under the Prior Senior Secured Credit Facility
Debt Instrument [Line Items]
Long-term debt	0	185,017
Exchangeable Notes \| 1.0% Exchangeable Senior Notes due 2025
Debt Instrument [Line Items]
Long-term debt	117,000	$ 104,557
Stated interest rate			1.00%
Debt issuance costs, net	$ (1,501)