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Pension Plans and Postretirement Benefits -Schedule of Changes in Benefit Obligation (Details) - Pension Plan - USD ($)
$ in Millions
 12 Months Ended
Jan. 01, 2023
Jan. 02, 2022
Jan. 03, 2021
United States      
Defined Benefit Plan, Change in Benefit Obligation [Roll Forward]      
Benefit obligation - beginning of year $ 799.3 $ 846.8  
Service cost - benefits earned during the year 7.6 9.3 $ 9.3
Interest cost on projected benefit obligation 22.8 21.6 26.5
Actuarial (gain) loss (179.1) (11.8)  
Benefits paid (67.6) (66.6)  
Other - including foreign currency, settlements/curtailments 0.0 0.0  
Benefit obligation - end of year 583.0 799.3 846.8
Accumulated benefit obligation - end of year 580.5 795.4  
Foreign      
Defined Benefit Plan, Change in Benefit Obligation [Roll Forward]      
Benefit obligation - beginning of year 60.2 70.4  
Service cost - benefits earned during the year 1.0 1.3 1.1
Interest cost on projected benefit obligation 0.8 0.7 0.9
Actuarial (gain) loss (12.0) (7.4)  
Benefits paid (1.6) (2.2)  
Other - including foreign currency, settlements/curtailments (3.2) (2.6)  
Benefit obligation - end of year 45.2 60.2 $ 70.4
Accumulated benefit obligation - end of year $ 42.2 $ 55.8