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Investments in Nonconsolidated Affiliates - Schedule of Sales/Purchases to/from Nonconsolidated Affiliates (Details) - Equity Method Investee - USD ($) $ in Millions	12 Months Ended
	Jun. 01, 2024	Jun. 03, 2023	May 28, 2022
Schedule of Equity Method Investments
Sales to nonconsolidated affiliates	$ 2.1	$ 2.8	$ 0.7
Purchases from nonconsolidated affiliates	$ 0.0	$ 0.0	$ 0.6

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