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Other Assets - Schedule of Other Assets (Details) - USD ($)
$ in Millions
Jan. 01, 2023
Jan. 02, 2022
Jan. 03, 2021
Other Assets [Line Items]      
Life insurance cash surrender value $ 194.3 $ 232.9  
Intangibles, net of accumulated amortization 158.7 122.0  
Noncurrent restricted cash 8.6 6.6 $ 5.1
Workers' compensation receivable 12.1 5.5  
Other 15.8 11.4  
Other assets 403.2 389.1  
Intangible assets, accumulated amortization 44.9 28.6  
Other Assets      
Other Assets [Line Items]      
Intangible assets, accumulated amortization 55.5 39.1  
Long Term Hosted Software, net of accumulated amortization      
Other Assets [Line Items]      
Intangibles, net of accumulated amortization 13.7 10.7  
Long Term Hosted Software, net of accumulated amortization | Other Assets      
Other Assets [Line Items]      
Intangible assets, accumulated amortization $ 7.3 $ 3.2