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Stock-Based Compensation - Schedule of Outstanding Stock Options (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Sep. 30, 2018
Share-based Compensation Arrangement by Share-based Payment Award        
Stock Option Awards Outstanding, Number Outstanding (in shares) 471,676 1,083,402 1,328,390 1,268,984
Stock Option Awards Outstanding, Weighted-Average Remaining Contractual Life, (in years) 6 years 8 months 12 days      
Weighted-Average Exercise Price of Outstanding Options (in dollars per share) $ 77.96 $ 74.38 $ 62.62 $ 57.03
Stock Option Awards Outstanding, Aggregate Intrinsic Value $ 11.5      
Stock Option Awards Exercisable, Number Exercisable (in shares) 251,049 537,241 709,826  
Stock Option Awards Exercisable, Weighted-Average Remaining Contractual Life (in years) 5 years 8 months 12 days      
Options exercisable, end of year (in dollars per share) $ 74.73 $ 68.16 $ 55.11  
Stock Option Awards Exercisable, Aggregate Intrinsic Value $ 6.9      
Price Range, $40.00 - $60.00        
Share-based Compensation Arrangement by Share-based Payment Award        
Stock Option Awards Outstanding, Exercise Prices, Low End of Range (in dollars per share) $ 40.00      
Stock Option Awards Outstanding, Exercise Prices, High End of Range (in dollars per share) $ 60.00      
Stock Option Awards Outstanding, Number Outstanding (in shares) 14,838      
Stock Option Awards Outstanding, Weighted-Average Remaining Contractual Life, (in years) 1 year 1 month 6 days      
Weighted-Average Exercise Price of Outstanding Options (in dollars per share) $ 41.52      
Stock Option Awards Outstanding, Aggregate Intrinsic Value $ 0.9      
Stock Option Awards Exercisable, Number Exercisable (in shares) 14,838      
Stock Option Awards Exercisable, Weighted-Average Remaining Contractual Life (in years) 1 year 1 month 6 days      
Options exercisable, end of year (in dollars per share) $ 41.52      
Stock Option Awards Exercisable, Aggregate Intrinsic Value $ 0.9      
Price Range, $60.01 - $80.00        
Share-based Compensation Arrangement by Share-based Payment Award        
Stock Option Awards Outstanding, Exercise Prices, Low End of Range (in dollars per share) $ 60.01      
Stock Option Awards Outstanding, Exercise Prices, High End of Range (in dollars per share) $ 80.00      
Stock Option Awards Outstanding, Number Outstanding (in shares) 201,069      
Stock Option Awards Outstanding, Weighted-Average Remaining Contractual Life, (in years) 6 years      
Weighted-Average Exercise Price of Outstanding Options (in dollars per share) $ 66.28      
Stock Option Awards Outstanding, Aggregate Intrinsic Value $ 7.3      
Stock Option Awards Exercisable, Number Exercisable (in shares) 122,137      
Stock Option Awards Exercisable, Weighted-Average Remaining Contractual Life (in years) 5 years 2 months 12 days      
Options exercisable, end of year (in dollars per share) $ 66.40      
Stock Option Awards Exercisable, Aggregate Intrinsic Value $ 4.4      
Price Range, $80.01 - $100.00        
Share-based Compensation Arrangement by Share-based Payment Award        
Stock Option Awards Outstanding, Exercise Prices, Low End of Range (in dollars per share) $ 80.01      
Stock Option Awards Outstanding, Exercise Prices, High End of Range (in dollars per share) $ 100.00      
Stock Option Awards Outstanding, Number Outstanding (in shares) 255,769      
Stock Option Awards Outstanding, Weighted-Average Remaining Contractual Life, (in years) 7 years 7 months 6 days      
Weighted-Average Exercise Price of Outstanding Options (in dollars per share) $ 89.25      
Stock Option Awards Outstanding, Aggregate Intrinsic Value $ 3.3      
Stock Option Awards Exercisable, Number Exercisable (in shares) 114,074      
Stock Option Awards Exercisable, Weighted-Average Remaining Contractual Life (in years) 6 years 10 months 24 days      
Options exercisable, end of year (in dollars per share) $ 87.97      
Stock Option Awards Exercisable, Aggregate Intrinsic Value $ 1.6