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(Loss) Earnings Per Share (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Income per common share      
Net income $ 208.9 $ 249.9 $ (60.1)
Weighted-average shares outstanding-basic (in shares) 71,700,000 74,900,000 73,400,000
Effect of dilutive stock options and unvested time-based restricted stock (in shares) 500,000 500,000 0
Weighted average shares outstanding-diluted (in shares) 72,200,000 75,400,000 73,400,000
(Loss) earnings per share-basic (in dollars per share) $ 2.91 $ 3.34 $ (0.82)
(Loss) earnings per share-diluted (in dollars per share) $ 2.89 $ 3.31 $ (0.82)
Performance Shares      
Income per common share      
Shares with anti-dilutive effect excluded from the computation of diluted earnings per share 373,000 450,000 400,000
Stock Option Awards and Time Based Stock Awards      
Income per common share      
Shares with anti-dilutive effect excluded from the computation of diluted earnings per share 300,000 800,000 2,800,000