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Share-Based Compensation (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
3 Months Ended
Dec. 31, 2022
Dec. 31, 2021
Share-Based Compensation (Textual) [Abstract]    
Pre-tax share-based compensation expense $ 18.4 $ 15.5
Stock options    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 233 164
Wtd. Avg. Share Fair Value (usd per share) $ 77.62 $ 87.68
Performance shares    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 66 37
Wtd. Avg. Share Fair Value (usd per share) $ 340.77 $ 481.28
Restricted stock and restricted stock units    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 211 139
Wtd. Avg. Share Fair Value (usd per share) $ 259.67 $ 348.32
Unrestricted stock    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 6 3
Wtd. Avg. Share Fair Value (usd per share) $ 259.81 $ 350.76