Income Taxes - Additional Information (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019	Dec. 30, 2018
Operating Loss Carryforwards [Line Items]
U.S. Federal Net Operating Loss Carryforwards	$ 365.6
Corporate Tax Rate Decrease	21.00%	21.00%	21.00%
Comparision of statutory rate to effective tax rate	91.40%	10.30%	17.90%
U.S. Statutory rate	21.00%	21.00%	21.00%
Net deferred tax asset for tax losses and credit carryforwards	$ 571.1	$ 535.8
Deferred Tax Assets, Tax Credit Carryforwards	32.8
Deferred Tax Asset, Interest Carryforward	172.7
Unrecognized tax Benefits	27.9	27.5	$ 110.4	$ 143.4
Unrecognized tax benefits including interest and penalties	34.3
Unrecognized tax benefits that would affect effective income tax rate	22.9	23.1
Indemnification Tax That Would Impact Earnings(loss) Before Provision For Taxes On Income	10.5	11.6
Unrecognized tax benefit, accrued interest and penalties	6.4	6.1
Income taxes paid	22.2	16.8	8.4
Deferred tax assets valuation allowance in United States and Luxembourg	591.2	554.8
Net Cost Impact Due To Valuation Allowances	44.7	63.8	60.0
Net Benefit Due to Increase In Interest Expenses	23.8	23.1	32.2
Net Cost Due to Tax Rate Difference	11.8
Increase (Decrease) in Unrecognized Tax Benefits	3.0
Change in reserves pre-acquisition for uncertain tax position		37.3	43.0
Change in reserves post-acquisition for uncertain tax position		5.7	11.2
Other Assets [Member]
Operating Loss Carryforwards [Line Items]
Indemnification receivable	15.4	17.0
Current Assets [Member]
Operating Loss Carryforwards [Line Items]
Indemnification receivable	0.7
Johnson And Johnson [Member]
Operating Loss Carryforwards [Line Items]
Unrecognized tax benefit, interest expense and penalties	0.4	$ 35.2	$ 1.5
Indemnification receivable	$ 16.1
General Business Tax Credit Carryforward
Operating Loss Carryforwards [Line Items]
Tax credit carry forwards, expire period	2034
Domestic Tax Authority
Operating Loss Carryforwards [Line Items]
U.S. Federal Net Operating Loss Carryforwards	$ 887.1
Federal operating loss carryforwards net	473.0
Operating loss carryforwards net, not subject to expiry	$ 414.1
Net operating loss carry forwards, expire period	2037
State and Local Jurisdiction
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards net, not subject to expiry	$ 25.6
State operating loss carryforwards net	$ 528.5
Tax credit carry forwards, expire period	2029
State and Local Jurisdiction | Beginning Year
Operating Loss Carryforwards [Line Items]
Net operating loss carry forwards, expire period	2022
State and Local Jurisdiction | Ending Year
Operating Loss Carryforwards [Line Items]
Net operating loss carry forwards, expire period	2041
State and Local Jurisdiction | General Business Tax Credit Carryforward
Operating Loss Carryforwards [Line Items]
Federal operating loss carryforwards net	$ 12.6
Foreign Tax Authority
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards net, not subject to expiry	304.9
State operating loss carryforwards net	$ 513.8
Net operating loss carry forwards, expire period	2041
Foreign Tax Authority | 2040 expiration year [Member]
Operating Loss Carryforwards [Line Items]
Net deferred tax asset for tax losses and credit carryforwards	$ 208.9
UNITED KINGDOM
Operating Loss Carryforwards [Line Items]
Comparision of statutory rate to effective tax rate	19.00%