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Stock-Based Compensation - Narrative (Details)
$ / shares in Units, $ in Millions
1 Months Ended 12 Months Ended
Feb. 15, 2022
shares
Dec. 31, 2021
shares
Feb. 28, 2021
shares
Jan. 01, 2023
USD ($)
$ / shares
shares
Jan. 02, 2022
USD ($)
$ / shares
shares
Jan. 03, 2021
USD ($)
$ / shares
shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Number of shares available for grant (in shares) - Fixed provision       2,700,000    
Tax benefit | $       $ 1.1 $ 0.8 $ 0.4
Restricted Stock            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Award vesting period       4 years    
Unrecognized compensation cost, unvested | $       $ 8.9    
Compensation cost not yet recognized, period for recognition       1 year 10 months 24 days    
Grants in period (in dollars per share) | $ / shares       $ 20.16 $ 20.91 $ 15.97
Vested in period, fair value | $       $ 2.3 $ 2.0 $ 2.4
Granted (in shares)       417,000    
Weighted average grant date fair value (in dollars per share) | $ / shares       $ 20.27 $ 21.24  
Total nonvested shares (in shares)       607,000 403,000  
Performance Shares, Single Financial Goal            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Award vesting period       4 years 4 years 4 years
Performance Shares, Financial Measure            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Unrecognized compensation cost, unvested | $       $ 8.4    
Compensation cost not yet recognized, period for recognition       2 years 4 months 24 days    
Grants in period (in dollars per share) | $ / shares       $ 21.19    
Vested in period, fair value | $       $ 0.9 $ 0.3 $ 1.8
Granted (in shares)       186,000    
Weighted average grant date fair value (in dollars per share) | $ / shares       $ 19.41 $ 20.03  
Total nonvested shares (in shares)       692,000 708,000  
Stock-based compensation cost            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Stock-based compensation cost | $       $ 7.8 $ 5.1 $ 3.9
Class A common stock            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Maximum number of shares available for grants - Fixed provision       4,700,000    
2020 grant | Performance Shares, Single Financial Goal            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Granted (in shares)           115,000
Weighted average grant date fair value (in dollars per share) | $ / shares       $ 22.59    
Total nonvested shares (in shares)       78,000    
2021 grant | Performance Shares, Financial Measure            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Granted (in shares)   308,000 180,000      
Percentage of target achieved       0.72    
Weighted average grant date fair value (in dollars per share) | $ / shares       $ 18.21    
Total nonvested shares (in shares)       423,000    
2021 grant | Maximum shares eligible to earn | Performance Shares, Financial Measure            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Maximum target percentage allowed under grant     200.00%      
2022 grant | Performance Shares, Financial Measure            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Granted (in shares) 186,000          
Percentage of target achieved       0.72    
Weighted average grant date fair value (in dollars per share) | $ / shares       $ 21.19    
Total nonvested shares (in shares)       186,000    
2022 grant | Maximum shares eligible to earn | Performance Shares, Financial Measure            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Maximum target percentage allowed under grant 200.00%