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Goodwill and Other Intangible Assets - Goodwill (Details) - USD ($)
$ in Millions
 12 Months Ended
Dec. 31, 2022
Jan. 01, 2022
Goodwill [Roll Forward]    
Goodwill, gross beginning balance $ 376.1 $ 365.5
Accumulated impairment losses (78.8) (73.0)
Goodwill, net beginning balance 297.3 292.4
Goodwill acquired (disposed) / measurement period adjustments (5.0) 10.7
Accumulated impairment losses disposed   (5.8)
Accumulated impairment losses disposed 13.6  
Goodwill, gross ending balance 371.1 376.1
Accumulated impairment losses (65.2) (78.8)
Goodwill, net ending balance 305.9 297.3
Workplace Furnishings    
Goodwill [Roll Forward]    
Goodwill, gross beginning balance 162.3 168.5
Accumulated impairment losses (78.6) (72.9)
Goodwill, net beginning balance 83.6 95.6
Goodwill acquired (disposed) / measurement period adjustments (13.6) (6.2)
Accumulated impairment losses disposed   (5.8)
Accumulated impairment losses disposed 13.6  
Goodwill, gross ending balance 148.7 162.3
Accumulated impairment losses (65.0) (78.6)
Goodwill, net ending balance 83.6 83.6
Residential Building Products    
Goodwill [Roll Forward]    
Goodwill, gross beginning balance 213.8 197.0
Accumulated impairment losses (0.1) (0.1)
Goodwill, net beginning balance 213.7 196.8
Goodwill acquired (disposed) / measurement period adjustments 8.6 16.9
Accumulated impairment losses disposed   0.0
Accumulated impairment losses disposed 0.0  
Goodwill, gross ending balance 222.4 213.8
Accumulated impairment losses (0.1) (0.1)
Goodwill, net ending balance $ 222.3 $ 213.7