Income Taxes (Deferred Income Tax) (Details) - USD ($) $ in Millions	Jan. 02, 2022	Jan. 03, 2021
Long-term:
Accrued liabilities	$ 52.6	$ 22.2
Inventory valuation	41.5	15.4
Accrued vacation	9.6	7.6
Deferred compensation and other benefit plans	39.1	39.0
Postretirement benefits other than pensions	1.7	1.8
Operating lease liabilities	38.7	29.9
Capitalization of research and development	34.1	37.1
Tax credit and net operating loss carryforward	47.4	44.2
Valuation allowance	(12.7)	(12.9)
Total deferred income tax assets	252.0	184.3
Long-term:
Intangible amortization	751.5	139.4
Property, plant and equipment differences	37.8	16.5
Operating lease right-of-use assets	35.0	27.7
Unremitted earnings of foreign subsidiaries	15.9	0.0
Other	7.9	3.7
Total deferred income tax liabilities	848.1	187.3
Net deferred income tax liabilities	$ 596.1	$ 3.0