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Employee Benefit Plans Employee Benefit Plans - Phantom (Details) - USD ($)
12 Months Ended
Jun. 01, 2019
Jun. 03, 2017
Jun. 02, 2018
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]      
Defined Benefit Plan, Accumulated Benefit Obligation $ 106,400,000   $ 103,100,000
Domestic      
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]      
Defined Benefit Plan, Accumulated Benefit Obligation     $ 1,000,000
Deferred Profit Sharing [Member]      
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]      
Defined Contribution Plan, Employer Discretionary Contribution Amount $ 0 $ 6,000,000