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Fair Value Measurements - Interest Rate Swap (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Mar. 04, 2023	Feb. 26, 2022	Mar. 04, 2023	Feb. 26, 2022
Derivative [Line Items]
Gain recognized in Other comprehensive loss (effective portion)	$ 10.3	$ 10.2	$ 31.8	$ 13.2
Gain (Loss) reclassified from Accumulated other comprehensive loss into earnings	4.9	$ (1.1)	6.9	$ (3.1)
September 2016 Interest Rate Swap
Derivative [Line Items]
Notional Amount	150.0		$ 150.0
Effective Fixed Interest Rate			1.91%
June 2017 Interest Rate Swap
Derivative [Line Items]
Notional Amount	75.0		$ 75.0
Effective Fixed Interest Rate			2.348%
January 2022 Interest Rate Swap
Derivative [Line Items]
Notional Amount	575.0		$ 575.0
Effective Fixed Interest Rate			1.65%
March 2023 Interest Rate Swap
Derivative [Line Items]
Notional Amount	$ 150.0		$ 150.0
Effective Fixed Interest Rate			3.95%