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Impairment of Long-Lived Assets and Other Lease Charges - Narrative (Details)
$ in Millions
12 Months Ended
Jan. 02, 2022
USD ($)
restaurant
Jan. 03, 2021
USD ($)
restaurant
Sep. 27, 2020
restaurant
Lease Termination Charges | Continuing Operations      
Impairment and Other Lease Charges [Line Items]      
Gain (Loss) on Termination of Lease | $   $ 0.9  
Gain from Lease Termination | Continuing Operations      
Impairment and Other Lease Charges [Line Items]      
Gain (Loss) on Termination of Lease | $ $ (0.6) (0.2)  
Level 3      
Impairment and Other Lease Charges [Line Items]      
Level 3 assets measured at fair value | $ $ 0.4 $ 2.2  
Pollo Tropical      
Impairment and Other Lease Charges [Line Items]      
Number of closed restaurants | restaurant   1 2
Number of impaired restaurants the company continues to operate | restaurant 5 3  
Pollo Tropical | Disposal Group, Held-for-sale or Disposed of by Sale, Not Discontinued Operations      
Impairment and Other Lease Charges [Line Items]      
Number of closed restaurants | restaurant   1