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Fair Value - Schedule of Gain/(Loss) Recorded, Net of Income Taxes, in Other Comprehensive Loss (Details) - USD ($) $ in Millions | 12 Months Ended
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Jun. 01, 2024 | Jun. 03, 2023 | May 28, 2022
Interest Rate Swap Agreement |  |  |
Derivative Instruments, Gain (Loss) [Line Items] |  |  |
Interest rate swap | $ (27.1) | $ 4.7 | $ 41.4

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