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Restructuring and Integration Expense - Schedule of Severance and Employee Benefit Costs (Details) - USD ($)
$ in Millions
 3 Months Ended
Sep. 03, 2022
Aug. 28, 2021
Changes in Restructuring Liability Balance [Roll Forward]    
Integration Costs $ 0.5 $ 0.0
Knoll Integration    
Changes in Restructuring Liability Balance [Roll Forward]    
Integration Costs 4.6 $ 55.6
Total | Knoll Integration    
Changes in Restructuring Liability Balance [Roll Forward]    
Beginning balance 1.4  
Integration Costs 2.6  
Amounts Paid (2.9)  
Non-cash costs (0.2)  
Ending balance 0.9  
Severance and Employee Benefit    
Changes in Restructuring Liability Balance [Roll Forward]    
Beginning balance 0.0  
Integration Costs 0.5  
Amounts Paid 0.0  
Ending balance 0.5  
Severance and Employee Benefit | Knoll Integration    
Changes in Restructuring Liability Balance [Roll Forward]    
Beginning balance 1.4  
Integration Costs 1.2  
Amounts Paid (1.5)  
Non-cash costs (0.2)  
Ending balance 0.9  
Exit and Disposal Activities | Knoll Integration    
Changes in Restructuring Liability Balance [Roll Forward]    
Beginning balance 0.0  
Integration Costs 1.4  
Amounts Paid (1.4)  
Non-cash costs 0.0  
Ending balance $ 0.0