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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
Jan. 01, 2022
Jan. 02, 2021
Dec. 28, 2019
Dec. 29, 2018
Revenue Recognition        
Cumulative effect of a change in accounting principle $ 205,834 $ 209,019 $ 197,751 $ 196,472
Retained Earnings        
Revenue Recognition        
Cumulative effect of a change in accounting principle $ 215,784 $ 216,999 200,249 $ 186,229
Cumulative Effect Period of Adoption, Adjustment        
Revenue Recognition        
Cumulative effect of a change in accounting principle     (203)  
Cumulative Effect Period of Adoption, Adjustment | Retained Earnings        
Revenue Recognition        
Cumulative effect of a change in accounting principle     (203)  
Cumulative Effect Period of Adoption, Adjustment | ASC 326 | Retained Earnings        
Revenue Recognition        
Cumulative effect of a change in accounting principle     $ (200)  
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