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Stockholders' Equity and Stock-Based Compensation Stock Option Awards (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 06, 2020
Jan. 25, 2019
Jan. 01, 2022
Jan. 02, 2021
Dec. 28, 2019
Dec. 29, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Options outstanding, Weighted-average remaining contractual life (in years)     5 years 2 months 12 days 6 years 2 months 12 days 6 years 6 months 6 years 10 months 24 days
Granted (in shares)     0 550,941 610,953  
Proceeds from stock options exercised     $ 0.1 $ 0.1 $ 0.1  
Share-based Payment Arrangement, Exercise of Option, Tax Benefit     4.5 2.4 0.4  
Exercises in period, intrinsic value     29.5 19.5 4.7  
Vested in period, fair value     19.9 $ 17.4 $ 15.5  
Outstanding, intrinsic value     163.2      
Exercisable, intrinsic value     140.1      
Total compensation cost not yet recognized     $ 7.6      
Share-based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition     1 year 2 months 12 days      
Options exercisable, Weighted-average remaining contractual life (in years)     4 years 8 months 12 days      
Nonqualified Stock Options Under Long Term Incentive Program [Member]            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Granted (in shares) 550,941 610,953        
Award vesting rights, percentage     33.33%      
Expiration period     10 years      
Incentive Stock Options [Member]            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Shares Issued, Shares, Share-based Payment Arrangement, before Forfeiture       0 0