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Summary of Significant Accounting Policies - Revenue Recognition and Allowances for Accounts Receivable and Unbilled Services (Details) - USD ($)
$ in Thousands
12 Months Ended
Dec. 31, 2022
Jan. 01, 2022
Jan. 02, 2021
Dec. 29, 2019
Dec. 28, 2019
Revenue Recognition          
Cumulative effect of a change in accounting principle $ 211,154 $ 205,834 $ 209,019   $ 197,751
Cumulative Effect Period of Adoption, Adjustment          
Revenue Recognition          
Cumulative effect of a change in accounting principle       $ (200) $ (203)
Minimum          
Revenue Recognition          
Period in which engagements are generally completed (months) 3 months        
Maximum          
Revenue Recognition          
Period in which engagements are generally completed (months) 6 months