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Pension Plans and Postretirement Benefits - Funded Status (Details) - USD ($)
$ in Millions
Jan. 01, 2023
Jan. 02, 2022
Amounts recognized in the consolidated balance sheets as a debit (credit):    
Prepaid pension assets $ 178.4 $ 123.7
Accrued pension obligations long-term (50.2) (67.2)
Pension Plan | Domestic    
Funded Status and Amounts Recognized in Balance Sheets [Abstract]    
Funded (unfunded) status 136.7 65.0
Amounts recognized in the consolidated balance sheets as a debit (credit):    
Prepaid pension assets 178.4 118.9
Accrued pension obligations short-term (3.9) (3.7)
Accrued pension obligations long-term (37.8) (50.2)
Net amount recognized 136.7 65.0
Amounts recognized in AOCI:    
Net prior service cost (credit) (1.2) (3.0)
Net loss 330.2 397.7
Net amount recognized, before tax effect 329.0 394.7
Pension Plan | Foreign    
Funded Status and Amounts Recognized in Balance Sheets [Abstract]    
Funded (unfunded) status (10.2) (7.3)
Amounts recognized in the consolidated balance sheets as a debit (credit):    
Prepaid pension assets 0.0 4.8
Accrued pension obligations short-term (0.5) (0.4)
Accrued pension obligations long-term (9.7) (11.7)
Net amount recognized (10.2) (7.3)
Amounts recognized in AOCI:    
Net prior service cost (credit) 0.5 0.6
Net loss 5.6 3.4
Net amount recognized, before tax effect $ 6.1 $ 4.0