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Investments in Nonconsolidated Affiliates Investments in Nonconsolidated Affiliates - Schedule of Sales/Purchases to/from Nonconsolidated Affiliates (Details) - Equity Method Investee [Member] - USD ($)
$ in Millions
12 Months Ended
Jun. 02, 2018
Jun. 03, 2017
May 28, 2016
Schedule of Equity Method Investments      
Revenue from Related Parties $ 4.3 $ 4.0 $ 2.5
Related Party Transaction, Purchases from Related Party $ 6.8 $ 4.2 $ 0.9