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Share-Based Compensation (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
3 Months Ended
Dec. 31, 2020
Dec. 31, 2019
Share-Based Compensation (Textual) [Abstract]    
Pre-tax share-based compensation expense $ 11.5 $ 11.5
Stock options    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 195 953
Wtd. Avg. Share Fair Value (usd per share) $ 55.47 $ 35.86
Performance shares    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 44 37
Wtd. Avg. Share Fair Value (usd per share) $ 298.10 $ 265.04
Restricted stock and restricted stock units    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 126 45
Wtd. Avg. Share Fair Value (usd per share) $ 245.07 $ 193.70
Unrestricted stock    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 4 5
Wtd. Avg. Share Fair Value (usd per share) $ 221.90 $ 162.29