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Share-Based Compensation (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
3 Months Ended
Dec. 31, 2019
Dec. 31, 2018
Share-Based Compensation (Textual) [Abstract]    
Pre-tax share-based compensation expense $ 11.5 $ 11.0
Stock options    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 953 919
Wtd. Avg. Share Fair Value (usd per share) $ 35.86 $ 32.51
Performance shares    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 37 57
Wtd. Avg. Share Fair Value (usd per share) $ 265.04 $ 155.04
Restricted stock and restricted stock units    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 45 39
Wtd. Avg. Share Fair Value (usd per share) $ 193.70 $ 172.14
Unrestricted stock    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Grants (in shares) 5 4
Wtd. Avg. Share Fair Value (usd per share) $ 162.29 $ 188.01