Employee Benefit Plans (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Mar. 02, 2024	Mar. 04, 2023	Mar. 02, 2024	Mar. 04, 2023
Defined Benefit Plan Disclosure
Weighted average expected long-term rate of return on plan assets (percent)	6.00%	6.00%	6.00%	6.00%
Domestic
Defined Benefit Plan Disclosure
Service cost	$ 0.0	$ 0.0	$ 0.0	$ 0.0
Interest cost	1.5	1.5	4.5	4.5
Expected return on plan assets	(2.3)	(2.0)	(6.9)	(6.0)
Expected administrative expenses	0.2	0.1	0.6	0.3
Net amortization loss	0.0	0.0	0.0	0.0
Settlement charge	0.0	(0.5)	0.0	(0.5)
Net periodic benefit (income) cost	(0.6)	(0.9)	(1.8)	(1.7)
International
Defined Benefit Plan Disclosure
Service cost	0.0	0.0	0.0	0.0
Interest cost	1.0	0.8	3.0	2.4
Expected return on plan assets	(1.2)	(1.2)	(3.7)	(3.5)
Net amortization loss	0.0	0.6	0.0	1.8
Settlement charge	0.0	0.0	0.0	0.0
Net periodic benefit (income) cost	$ (0.2)	$ 0.2	$ (0.7)	$ 0.7