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Income Taxes - Differences Between Income Taxes From Continuing Operations and U.S. Statutory Rate (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021
Income Tax Disclosure [Abstract]
Income tax based on statutory rate	$ (14.9)	$ 39.0	$ (22.4)
State income taxes, net of federal benefit	1.6	1.1	(5.1)
Foreign tax rate differential	1.6	12.2	2.8
General business credits	(10.7)	(9.7)	(9.9)
Life insurance cash surrender value	7.8	(5.2)	(4.6)
Foreign items	0.2	1.7	(1.8)
Sale of foreign subsidiaries	3.9	0.0	(6.6)
Foreign business taxes	1.8	2.1	3.0
Tax law change	0.0	(5.2)	(1.7)
Non-deductible goodwill impairment	2.7	0.0	11.9
Other	(1.9)	(0.9)	0.4
Total provision	$ (7.9)	$ 35.1	$ (34.0)

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Effective Income Tax Rate Reconciliation, Foreign Items, Amount

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The portion of the difference between total income tax expense or benefit as reported in the Income Statement and the expected income tax expense or benefit computed by applying the domestic federal statutory income tax rates attributable to foreign business taxes classified as income taxes which are based on revenue or receipts reduced by one or more category of expense.

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The portion of the difference between total income tax expense or benefit as reported in the Income Statement and the expected income tax expense or benefit computed by applying the domestic federal statutory income tax rates attributable to gains and losses on company owned life insurance contracts.

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The portion of the difference between total income tax expense or benefit as reported in the Income Statement and the expected income tax expense or benefit computed by applying the domestic federal statutory income tax rates to pretax income from continuing operations, that is attributable to changes in the enacted income tax laws in the period.

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Amount of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

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Amount of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to tax credits. Including, but not limited to, research credit, foreign tax credit, investment tax credit, and other tax credits.

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