Pension Plans and Postretirement Benefits (Narrative) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Defined Benefit Plan Disclosure [Line Items]
Non-cash reduction to stockholders' equity		$ 297.6	$ 347.8
Deferred tax on non-cash reductions to stockholders' equity		100.9	110.5
Employer contributions to 401(k) plans		15.2	13.8	$ 13.4
Pension Plan
Defined Benefit Plan Disclosure [Line Items]
Minimum liability adjustment to be recognized for the pension plans, net gain (loss)		22.7
Minimum liability adjustment to be recognized for the pension plans, net prior service credit		1.7
Pension Plan | Domestic
Defined Benefit Plan Disclosure [Line Items]
Expected long-term rate of return				7.80%
Total cost of plan		$ (11.5)	(13.0)	$ (7.8)
Pension Plan | Domestic | Expected
Defined Benefit Plan Disclosure [Line Items]
Expected long-term rate of return	6.82%
Pension Plan | Domestic | Equity instruments
Defined Benefit Plan Disclosure [Line Items]
Target allocation of plan assets		34.00%
Pension Plan | Domestic | Fixed income instruments
Defined Benefit Plan Disclosure [Line Items]
Target allocation of plan assets		55.00%
Pension Plan | Domestic | Alternatives
Defined Benefit Plan Disclosure [Line Items]
Target allocation of plan assets		11.00%
Pension Plan | Foreign
Defined Benefit Plan Disclosure [Line Items]
Total cost of plan		$ 0.2	0.2	(0.3)
Pension Plan | Foreign | Expected
Defined Benefit Plan Disclosure [Line Items]
Expected long-term rate of return	2.23%
Postretirement Plans
Defined Benefit Plan Disclosure [Line Items]
Total cost of plan		1.0	1.0	1.0
Qualified plan | Pension Plan
Defined Benefit Plan Disclosure [Line Items]
Settlements		$ 24.5	$ 24.9	$ 17.2