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Earnings Per Share (Details) - USD ($)
$ / shares in Units, shares in Millions, $ in Millions
 3 Months Ended 9 Months Ended
May 25, 2024
May 27, 2023
May 25, 2024
May 27, 2023
Earnings per share - basic        
Net income $ 29.0 $ 59.1 $ 42.1 $ 172.1
Weighted average common shares outstanding (in shares) 29.2 30.4 29.3 30.4
Basic earnings per common share (in dollars per share) $ 0.99 $ 1.95 $ 1.43 $ 5.66
Earnings per share - diluted        
Net income $ 29.0 $ 59.1 $ 42.1 $ 172.1
Interest expense on convertible notes, net of tax 0.2 1.2 0.7 3.6
Diluted net income $ 29.2 $ 60.3 $ 42.8 $ 175.7
Dilutive impact of stock compensation awards (in shares) 0.2 0.3 0.3 0.4
Dilutive impact of convertible notes (in shares) 1.0 4.7 1.0 4.7
Weighted average common shares outstanding, assuming dilution (in shares) 30.4 35.4 30.6 35.5
Anti-dilutive securities excluded from weighted average common shares outstanding, assuming dilution (in shares) 0.2 0.1 0.2 0.1
Diluted earnings per common share (in dollars per share) $ 0.96 $ 1.71 $ 1.40 $ 4.95