Pension Plans and Postretirement Benefits (Changes in Plan Assets) (Details) - Pension Plan - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021
Domestic
Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]
Fair value of net plan assets - beginning of year	$ 854.5	$ 835.7
Actual return on plan assets	74.1	83.5
Employer contribution - other benefit plan	2.3	2.5
Foreign currency changes	0.0	0.0
Benefits paid	(66.6)	(67.2)
Other	0.0	0.0
Fair value of net plan assets - end of year	864.3	854.5
Foreign
Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]
Fair value of net plan assets - beginning of year	54.4	48.0
Actual return on plan assets	0.3	4.0
Employer contribution - other benefit plan	1.9	1.1
Foreign currency changes	(1.6)	3.4
Benefits paid	(2.2)	(1.7)
Other	0.1	(0.4)
Fair value of net plan assets - end of year	$ 52.9	$ 54.4