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Share-Based Compensation (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
3 Months Ended
Dec. 31, 2021
Dec. 31, 2020
Share-Based Compensation (Textual) [Abstract]    
Pre-tax share-based compensation expense $ 15.5 $ 11.5
Stock options    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 164 195
Wtd. Avg. Share Fair Value (usd per share) $ 87.68 $ 55.47
Performance shares    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 37 44
Wtd. Avg. Share Fair Value (usd per share) $ 481.28 $ 298.10
Restricted stock and restricted stock units    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 139 126
Wtd. Avg. Share Fair Value (usd per share) $ 348.32 $ 245.07
Unrestricted stock    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 3 4
Wtd. Avg. Share Fair Value (usd per share) $ 350.76 $ 221.90