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Summary of Significant Accounting Policies (Details)
$ in Millions
12 Months Ended
Jan. 02, 2024
USD ($)
restaurant
Jan. 03, 2023
USD ($)
Dec. 28, 2021
Description of Business      
Number of company-owned upscale, casual, full-service dining restaurants 334    
Number of International locations operating under licensing agreements 33    
Number of bakery production facilities 2    
Basis of Presentation      
Length of fiscal year 364 days 371 days 364 days
Cash and Cash Equivalents      
Amounts receivable from credit card processors | $ $ 21.0 $ 19.1  
Conversion period, credit card sales 3 days