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Investments in Nonconsolidated Affiliates - Schedule of Equity Method Earnings (Details) - USD ($) $ in Millions	12 Months Ended
	Jun. 01, 2024	Jun. 03, 2023	May 28, 2022
Equity Method Investments and Joint Ventures [Abstract]
Equity (loss) earnings from nonconsolidated affiliate, net of tax	$ (0.4)	$ (0.8)	$ 0.0

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Income (Loss) From Equity Method Investments, After Tax

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