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Goodwill and Other Intangible Assets - Other Intangible Assets (Details) - USD ($)
$ in Thousands
Oct. 02, 2021
Jan. 02, 2021
Finite-Lived Intangible Assets [Line Items]    
Gross $ 298,175 $ 283,093
Accumulated Amortization 165,412 143,230
Net 132,763 139,863
Software    
Finite-Lived Intangible Assets [Line Items]    
Gross 193,634 182,127
Accumulated Amortization 96,041 78,619
Net 97,593 103,508
Trademarks and trade names    
Finite-Lived Intangible Assets [Line Items]    
Gross 11,764 9,964
Accumulated Amortization 4,337 3,546
Net 7,427 6,418
Customer lists and other    
Finite-Lived Intangible Assets [Line Items]    
Gross 92,777 91,002
Accumulated Amortization 65,034 61,065
Net $ 27,743 $ 29,937