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Share-Based Compensation - Options by Exercise Price (Details)
12 Months Ended
Sep. 30, 2020
$ / shares
shares
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Number of outstanding options (in share) | shares 1,408,036
Weighted average exercise price (in dollars per share) $ 38.79
Weighted average remaining term (in years) 4 years 1 month 28 days
$0 - $5,00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit $ 0
Exercise price range, upper range limit $ 5.00
Number of outstanding options (in share) | shares 0
$5.00 - $10.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit $ 5.00
Exercise price range, upper range limit $ 10.00
Number of outstanding options (in share) | shares 0
$10.00 - $15.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit $ 10.00
Exercise price range, upper range limit $ 15.00
Number of outstanding options (in share) | shares 0
$15.00 - $20.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit $ 15.00
Exercise price range, upper range limit $ 20.00
Number of outstanding options (in share) | shares 0
$20.00 - $25.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit $ 20.00
Exercise price range, upper range limit $ 25.00
Number of outstanding options (in share) | shares 0
$25.00 - $30.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit $ 25.00
Exercise price range, upper range limit $ 30.00
Number of outstanding options (in share) | shares 420,000
Weighted average exercise price (in dollars per share) $ 25.91
Weighted average remaining term (in years) 1 year 4 months 9 days
$30.00 - $35.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit $ 30.00
Exercise price range, upper range limit $ 35.00
Number of outstanding options (in share) | shares 0
$35.00 - $40.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit $ 35.00
Exercise price range, upper range limit $ 40.00
Number of outstanding options (in share) | shares 126,161
Weighted average exercise price (in dollars per share) $ 39.65
Weighted average remaining term (in years) 2 years 7 days
$40.00 - $45.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit $ 40.00
Exercise price range, upper range limit $ 45.00
Number of outstanding options (in share) | shares 859,875
Weighted average exercise price (in dollars per share) $ 44.92
Weighted average remaining term (in years) 5 years 10 months 2 days
$45.00 - $50.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit $ 45.00
Exercise price range, upper range limit $ 50.00
Number of outstanding options (in share) | shares 0
$50.00 - $55.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit $ 50.00
Exercise price range, upper range limit $ 55.00
Number of outstanding options (in share) | shares 0
$55.00 - $60.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise price range, lower range limit $ 55.00
Exercise price range, upper range limit $ 60.00
Number of outstanding options (in share) | shares 2,000
Weighted average exercise price (in dollars per share) $ 55.28
Weighted average remaining term (in years) 1 year 10 months 20 days