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Pension Plans and Postretirement Benefits - Net Periodic Pension Benefit (Income) Expense (Details) - USD ($)
$ in Millions
 12 Months Ended
Jan. 01, 2023
Jan. 02, 2022
Jan. 03, 2021
Pension non-service (income) expense (in millions):      
Pension non-service (income) expense   $ 1.0 $ 1.0
Pension Plan | Domestic      
Components of net period pension benefit expense      
Service cost - benefits earned during the period (in millions) $ 7.6 9.3 9.3
Pension non-service (income) expense (in millions):      
Interest cost on benefit obligation 22.8 21.6 26.5
Expected return on plan assets (54.9) (55.8) (56.0)
Amortization of prior service cost (1.8) (3.6) (6.0)
Amortization of actuarial loss 22.7 26.3 22.5
Settlements/Curtailment 0.0 0.0 0.0
Pension non-service (income) expense (11.2) (11.5) (13.0)
Pension Plan | Foreign      
Components of net period pension benefit expense      
Service cost - benefits earned during the period (in millions) 1.0 1.3 1.1
Pension non-service (income) expense (in millions):      
Interest cost on benefit obligation 0.8 0.7 0.9
Expected return on plan assets (1.1) (1.0) (1.1)
Amortization of prior service cost 0.0 0.1 0.1
Amortization of actuarial loss 0.0 0.4 0.3
Settlements/Curtailment (0.1) 0.0 0.0
Pension non-service (income) expense $ (0.4) $ 0.2 $ 0.2