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Pension Plans and Postretirement Benefits - Changes in Plan Assets (Details) - Pension Plan - USD ($)
$ in Millions
 12 Months Ended
Jan. 01, 2023
Jan. 02, 2022
Domestic    
Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]    
Fair value of net plan assets - beginning of year $ 864.3 $ 854.5
Actual return on plan assets (79.2) 74.1
Employer contribution - other benefit plan 2.2 2.3
Foreign currency changes 0.0 0.0
Benefits paid (67.6) (66.6)
Other 0.0 0.0
Fair value of net plan assets - end of year 719.7 864.3
Foreign    
Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]    
Fair value of net plan assets - beginning of year 52.9 54.4
Actual return on plan assets (12.6) 0.3
Employer contribution - other benefit plan 1.5 1.9
Foreign currency changes (4.6) (1.6)
Benefits paid (1.7) (2.2)
Other (0.5) 0.1
Fair value of net plan assets - end of year $ 35.0 $ 52.9