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Stock-Based Compensation (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Dec. 02, 2023
Dec. 03, 2022
Dec. 02, 2023
Dec. 03, 2022
Stock-Based Compensation [Abstract]        
Stock-based compensation expense $ 5.3 $ 5.5 $ 11.7 $ 10.9
Related income tax effect $ 1.2 $ 1.3 $ 2.8 $ 2.6