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Share-Based Compensation - Restricted Stock Plan (Details)
$ in Millions
12 Months Ended
Sep. 30, 2022
USD ($)
shares
Share-Based Payment Arrangement [Abstract]  
Share-based compensation arrangement by share-based payment award, shares issued in period (in shares) 1,500,000
Share-based compensation arrangement by share-based payment award, non-option equity instruments, granted (in shares) 300,000
Employee service share-based compensation, nonvested awards, total compensation cost not yet recognized | $ $ 25.2
Employee service share-based compensation, nonvested awards, total compensation cost not yet recognized, period for recognition - restricted stock 1 year 2 months 19 days