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Stockholders' Equity (Dividends Declared and Paid) (Details) - USD ($)
$ / shares in Units, $ in Thousands
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Equity [Abstract]      
Dividends declared and paid $ 44,978 $ 36,041 $ 37,664
Cash dividends per share $ 0.7325 $ 0.5688 $ 0.6050