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Share-Based Compensation (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
3 Months Ended 6 Months Ended
Mar. 31, 2020
Mar. 31, 2019
Mar. 31, 2020
Mar. 31, 2019
Share-Based Compensation (Textual) [Abstract]        
Pre-tax share-based compensation expense $ 10.9 $ 10.8 $ 22.4 $ 21.8
Stock options        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     970 946
Wtd. Avg. Share Fair Value (usd per share)     $ 35.78 $ 32.48
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)     49 41
Wtd. Avg. Share Fair Value (usd per share)     $ 192.60 $ 171.03
Unrestricted stock        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     7 6
Wtd. Avg. Share Fair Value (usd per share)     $ 171.51 $ 183.02