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Stock-Based Compensation (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Nov. 27, 2021
Nov. 28, 2020
Nov. 27, 2021
Nov. 28, 2020
Stock-Based Compensation [Abstract]        
Stock-based compensation expense $ 7.0 $ 2.4 $ 22.1 $ 3.9
Related income tax effect $ 1.6 $ 0.6 $ 5.3 $ 0.9