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Pension Plans and Postretirement Benefits - Narrative (Details)
$ in Millions
 12 Months Ended
Jan. 01, 2023
USD ($)
plan
Jan. 02, 2022
USD ($)
Jan. 03, 2021
USD ($)
Defined Benefit Plan Disclosure [Line Items]      
Domestic qualified defined benefit pension plans | plan 2    
Non-cash reduction to stockholders' equity $ (255.5) $ (297.6)  
Deferred tax on non-cash reductions to stockholders' equity 77.6 100.9  
Total cost of plan   1.0 $ 1.0
Employer contributions to 401(k) plans $ 29.7 15.2 13.8
Deferred compensation employee contribution vesting percentage 1    
Deferred compensation liabilities $ 92.2 115.5  
Cash surrender value of life insurance 94.7 113.4  
Pension Plan      
Defined Benefit Plan Disclosure [Line Items]      
Minimum liability adjustment to be recognized for the pension plans, net gain (loss) 10.1    
Minimum liability adjustment to be recognized for the pension plans, net prior service credit $ 1.7    
Pension Plan | Domestic      
Defined Benefit Plan Disclosure [Line Items]      
Expected long-term rate of return 6.85%    
Total cost of plan $ (11.2) (11.5) (13.0)
Pension Plan | Domestic | Equity securities      
Defined Benefit Plan Disclosure [Line Items]      
Target allocation of plan assets 35.00%    
Pension Plan | Domestic | Fixed income instruments      
Defined Benefit Plan Disclosure [Line Items]      
Target allocation of plan assets 54.00%    
Pension Plan | Domestic | Alternatives      
Defined Benefit Plan Disclosure [Line Items]      
Target allocation of plan assets 11.00%    
Pension Plan | Foreign      
Defined Benefit Plan Disclosure [Line Items]      
Expected long-term rate of return 4.48%    
Total cost of plan $ (0.4) 0.2 0.2
Postretirement Plans      
Defined Benefit Plan Disclosure [Line Items]      
Total cost of plan 1.0    
Qualified plan | Pension Plan      
Defined Benefit Plan Disclosure [Line Items]      
Settlements $ 24.8 $ 24.5 $ 24.9