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Goodwill and Intangible Assets - Changes in Carrying Amounts of Goodwill (Details) - USD ($)
$ in Thousands
3 Months Ended 12 Months Ended
Apr. 05, 2020
Jan. 02, 2022
Jan. 03, 2021
Dec. 29, 2019
Goodwill [Line Items]        
Goodwill   $ 147,025 $ 165,777 $ 257,439
Goodwill, impairment loss $ (116,500)   (116,495)  
Goodwill, foreign currency translation   (18,752) 24,833  
Operating Segments | AMS        
Goodwill [Line Items]        
Goodwill   108,505 122,344 116,202
Goodwill, impairment loss     0  
Goodwill, foreign currency translation   (13,839) 6,142  
Operating Segments | EAAA        
Goodwill [Line Items]        
Goodwill   38,520 43,433 $ 141,237
Goodwill, impairment loss     (116,495)  
Goodwill, foreign currency translation   $ (4,913) $ 18,691