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Share-Based Compensation - Options by Exercise Price (Details)
12 Months Ended
Sep. 30, 2022
$ / shares
shares
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Number of outstanding options (in shares) | shares 1,199,345
Weighted average exercise price (in dollars per share) $ 50.46
Weighted average remaining term (in years) 4 years 6 months 14 days
$0 - $5.00  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit (in dollars per share) $ 0
Exercise price range, upper range limit (in dollars per share) $ 5.00
Number of outstanding options (in shares) | shares 0
$5.00 - $10.00  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit (in dollars per share) $ 5.00
Exercise price range, upper range limit (in dollars per share) $ 10.00
Number of outstanding options (in shares) | shares 0
$10.00 - $15.00  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit (in dollars per share) $ 10.00
Exercise price range, upper range limit (in dollars per share) $ 15.00
Number of outstanding options (in shares) | shares 0
$15.00 - $20.00  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit (in dollars per share) $ 15.00
Exercise price range, upper range limit (in dollars per share) $ 20.00
Number of outstanding options (in shares) | shares 0
$20.00 - $25.00  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit (in dollars per share) $ 20.00
Exercise price range, upper range limit (in dollars per share) $ 25.00
Number of outstanding options (in shares) | shares 0
$25.00 - $30.00  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit (in dollars per share) $ 25.00
Exercise price range, upper range limit (in dollars per share) $ 30.00
Number of outstanding options (in shares) | shares 0
$30.00 - $35.00  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit (in dollars per share) $ 30.00
Exercise price range, upper range limit (in dollars per share) $ 35.00
Number of outstanding options (in shares) | shares 0
$35.00 - $40.00  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit (in dollars per share) $ 35.00
Exercise price range, upper range limit (in dollars per share) $ 40.00
Number of outstanding options (in shares) | shares 53,627
Weighted average exercise price (in dollars per share) $ 39.79
Weighted average remaining term (in years) 4 months 13 days
$40.00 - $45.00  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit (in dollars per share) $ 40.00
Exercise price range, upper range limit (in dollars per share) $ 45.00
Number of outstanding options (in shares) | shares 700,000
Weighted average exercise price (in dollars per share) $ 45.00
Weighted average remaining term (in years) 4 years 2 months 4 days
$45.00 - $50.00  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit (in dollars per share) $ 45.00
Exercise price range, upper range limit (in dollars per share) $ 50.00
Number of outstanding options (in shares) | shares 0
$50.00 - $55.00  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit (in dollars per share) $ 50.00
Exercise price range, upper range limit (in dollars per share) $ 55.00
Number of outstanding options (in shares) | shares 0
$55.00 - $60.00  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit (in dollars per share) $ 55.00
Exercise price range, upper range limit (in dollars per share) $ 60.00
Number of outstanding options (in shares) | shares 0
$60.00 - $65.00  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit (in dollars per share) $ 60.00
Exercise price range, upper range limit (in dollars per share) $ 65.00
Number of outstanding options (in shares) | shares 445,718
Weighted average exercise price (in dollars per share) $ 60.33
Weighted average remaining term (in years) 5 years 7 months 9 days