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Restructuring and Integration Expense - Schedule of Severance and Employee Benefit Costs (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Mar. 04, 2023	Feb. 26, 2022	Mar. 04, 2023	Feb. 26, 2022
Changes in Restructuring Liability Balance [Roll Forward]
Integration Costs	$ 4.6	$ 0.0	$ 19.8	$ 0.0
Knoll Integration
Changes in Restructuring Liability Balance [Roll Forward]
Integration Costs	4.0	$ 5.9	12.7	101.7
Total | Knoll Integration
Changes in Restructuring Liability Balance [Roll Forward]
Beginning balance			1.4
Integration Costs			6.7
Amounts Paid			(5.9)
Non-cash costs			(0.2)
Ending balance	2.0		2.0
Severance and Employee Benefit
Changes in Restructuring Liability Balance [Roll Forward]
Beginning balance			0.0
Amounts Paid			(12.8)
Ending balance	7.0		7.0
Severance and Employee Benefit | Knoll Integration
Changes in Restructuring Liability Balance [Roll Forward]
Beginning balance			1.4
Integration Costs			3.1	$ 49.9
Amounts Paid			(2.3)
Non-cash costs			(0.2)
Ending balance	2.0		2.0
Exit and Disposal Activities | Knoll Integration
Changes in Restructuring Liability Balance [Roll Forward]
Beginning balance			0.0
Integration Costs			3.6
Amounts Paid			(3.6)
Non-cash costs			0.0
Ending balance	$ 0.0		$ 0.0

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Amount of cash payments made as the result of exit or disposal activities. Excludes payments associated with a discontinued operation or an asset retirement obligation.

+ References

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