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Net Income (Loss) per Share - Anti-dilutive Securities (Details) - shares
12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Restricted Stock Units (RSUs)      
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]      
Anti-dilutive securities excluded from computation of diluted earnings per share (in shares) 332,029 64,122 24,012