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Lease Obligations, Other Commitments, and Contingencies - Additional Information (Details) - USD ($)
$ in Millions
12 Months Ended
Jun. 01, 2019
Jun. 02, 2018
May 27, 2017
Commitments And Contingencies Disclosure [Abstract]      
Rent expense under operating leases $ 1.7 $ 1.8 $ 1.9