Accumulated Other Comprehensive Income (Loss) (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2023	Jan. 01, 2023	Jan. 02, 2022
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ (67.4)	$ (141.3)	$ (1,223.6)
OCI before reclassifications	(23.0)	57.1	8.9
Amounts reclassified from AOCI	7.2	16.8	0.2
Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent	(15.8)	73.9	1,082.3
Ending balance	(83.2)	(67.4)	(141.3)
Increase (Decrease) in Stockholders' Equity Attributable to Noncontrolling Interest [Roll Forward]
Beginning balance	7.7	26.0	21.2
OCI before reclassifications	(0.4)	(18.3)	4.8
Amounts reclassified from AOCI	0.0	0.0	0.0
Net current-period OCI	(0.4)	(18.3)	4.8
Ending balance	7.3	7.7	26.0
Tax expense for the recognition of a stranded deferred tax balance arising from deferred tax valuation allowances that was associated with certain postretirement medical benefits due to plan termination			6.4
State and local income taxes, net of federal tax benefit	1.2	2.9	0.4
Cumulative effect of adoption of new accounting standard
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance			1,073.2
Post- retirement benefit plans [Member]
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(34.7)	(86.6)	(1,119.9)
OCI before reclassifications	(2.9)	41.3	6.6
Amounts reclassified from AOCI	5.1	10.6	(3.6)
Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent	2.2	51.9	1,033.3
Ending balance	(32.5)	(34.7)	(86.6)
Increase (Decrease) in Stockholders' Equity Attributable to Noncontrolling Interest [Roll Forward]
Beginning balance	0.0	0.0	0.0
OCI before reclassifications	0.0	0.0	0.0
Amounts reclassified from AOCI	0.0	0.0	0.0
Net current-period OCI	0.0	0.0	0.0
Ending balance	0.0	0.0	0.0
Post- retirement benefit plans [Member] | Cumulative effect of adoption of new accounting standard
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance			1,030.3
Currency translation adjustment [Member]
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(70.1)	(64.9)	(55.5)
OCI before reclassifications	1.7	(25.2)	(9.4)
Amounts reclassified from AOCI	0.0	20.0	0.0
Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent	1.7	(5.2)	(9.4)
Ending balance	(68.4)	(70.1)	(64.9)
Increase (Decrease) in Stockholders' Equity Attributable to Noncontrolling Interest [Roll Forward]
Beginning balance	7.7	26.0	21.2
OCI before reclassifications	(0.4)	(18.3)	4.8
Amounts reclassified from AOCI	0.0	0.0	0.0
Net current-period OCI	(0.4)	(18.3)	4.8
Ending balance	7.3	7.7	26.0
Currency translation adjustment [Member] | Cumulative effect of adoption of new accounting standard
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance			0.0
Derivatives [Member]
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	13.5	5.1	2.1
OCI before reclassifications	(21.8)	41.0	11.7
Amounts reclassified from AOCI	1.9	(32.6)	(8.7)
Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent	(19.9)	8.4	3.0
Ending balance	(6.4)	13.5	5.1
Increase (Decrease) in Stockholders' Equity Attributable to Noncontrolling Interest [Roll Forward]
Beginning balance	0.0	0.0	0.0
OCI before reclassifications	0.0	0.0	0.0
Amounts reclassified from AOCI	0.0	0.0	0.0
Net current-period OCI	0.0	0.0	0.0
Ending balance	0.0	0.0	0.0
Derivatives [Member] | Cumulative effect of adoption of new accounting standard
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance			0.0
Accumulated Deferred Tax Asset Valuation Allowance
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	23.9	5.1	(50.3)
OCI before reclassifications	0.0	0.0	0.0
Amounts reclassified from AOCI	0.2	18.8	12.5
Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent	0.2	18.8	55.4
Ending balance	24.1	23.9	5.1
Increase (Decrease) in Stockholders' Equity Attributable to Noncontrolling Interest [Roll Forward]
Beginning balance	0.0	0.0	0.0
OCI before reclassifications	0.0	0.0	0.0
Amounts reclassified from AOCI	0.0	0.0	0.0
Net current-period OCI	0.0	0.0	0.0
Ending balance	$ 0.0	$ 0.0	0.0
Accumulated Deferred Tax Asset Valuation Allowance | Cumulative effect of adoption of new accounting standard
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance			$ 42.9