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Revenue from Contracts with Customers - Capitalized Contract Acquisition Costs (Details) - USD ($)
$ in Thousands
 12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Capitalized Contract Acquisition Costs [Abstract]      
Balance, beginning of year $ 77,836 $ 70,396 $ 59,446
Additional capitalized contract acquisition costs 37,897 41,719 43,557
Amortization of capitalized contract acquisition costs (38,513) (34,279) (32,607)
Balance, end of year $ 77,220 $ 77,836 $ 70,396