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Stock-Based Compensation and Earnings Per Share - Awards of Equity Instruments (Details) - $ / shares
3 Months Ended
Dec. 31, 2017
Dec. 31, 2016
Stock-Based Compensation    
Maximum number of common stock shares that can be issued in respect of performance shares granted (in shares) 338,000  
Options    
Stock-Based Compensation    
Number Issued (in shares) 0 646,600
Weighted Average Fair Value (in dollars per share) $ 0.00 $ 17.18
Performance Shares    
Stock-Based Compensation    
Number Issued (in shares) 140,800 125,000
Weighted Average Fair Value (in dollars per share) $ 138.68 $ 87.95
Restricted Stock Units    
Stock-Based Compensation    
Number Issued (in shares) 252,400 2,800
Weighted Average Fair Value (in dollars per share) $ 133.36 $ 85.37