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Stock-Based Compensation (Additional Information) (Details)
$ / shares in Units, $ in Thousands
3 Months Ended 12 Months Ended
Sep. 30, 2022
USD ($)
item
$ / shares
shares
Sep. 30, 2021
USD ($)
$ / shares
Jun. 30, 2022
USD ($)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Total intrinsic value of options exercised $ 600 $ 6,600  
Total pre-tax unrecognized compensation costs related to non-vested awards $ 22,600    
Total pre-tax unrecognized compensation costs related to non-vested awards expected to be recognized, years 2 years 6 months    
Total fair value of options and Restricted Stock Units vested $ 12,000 12,000  
Share-based Payment Arrangement, Amount Capitalized $ 0 $ 0 $ 0
Stock Option      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Number of options granted | shares 0    
Stock Incentive Plans      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based compensation arrangements plans | item 2    
Term of options (in years) 10 years    
Vesting Period (in years) 4 years    
Weighted average estimated grant date fair values, for options granted at market price, per share | $ / shares   $ 14.72  
Common Stock, Capital Shares Reserved for Future Issuance | shares 2,892,138    
Restricted Stock Units      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value | $ / shares $ 39.53 $ 36.87  
Restricted Stock Units Outstanding, Shares Granted | shares 281,550    
Performance Based Shares      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Term of options (in years) 3 years    
Non-Performance Based Shares      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting Period (in years) 3 years   4 years
Non-Performance Based Shares | Director      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting Period (in years) 1 year