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Income Taxes - Reconciliation of Income Tax Expense, Net of Federal Income Tax Rate (Detail) - USD ($) $ in Millions | 12 Months Ended
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Dec. 31, 2022 | Jan. 01, 2022 | Jan. 02, 2021
Income Taxes [Line Items] |  |  |
Income taxes at U.S. statutory rate of 21% | $ (53.1) | $ 16.9 | $ (38.7)
State income taxes, net of federal income tax | (2.3) | (1.1) | (8.1)
Adjustments for uncertain tax positions | (0.9) | (1.3) | (1.4)
Change in valuation allowance | 2.1 | 2.2 | 4.7
Tax impact of impairment in foreign jurisdiction | 3.0 | 0.0 | 0.0
Global Intangible Low Tax Income Tax | 3.8 | 3.2 | 2.5
Foreign Derived Intangible Income Tax Credit | (8.2) | (3.7) | (1.6)
Deferred Tax Assets, Tax Deferred Expense, Compensation and Benefits, Share-based Compensation Cost | 3.3 | 5.2 | 1.6
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Share-based Payment Arrangement, Amount | 1.6 | (3.7) | (4.6)
Effective Income Tax Rate Reconciliation Deferred ax on Future Dividends Due To TCJA | (0.2) | (0.9) | 1.0
Tax Adjustments, Settlements, and Unusual Provisions | 0.0 | 2.5 | 0.0
Deferred Income Taxes and Tax Credits | 0.0 | (1.2) | 0.0
Other Permanent adjustments and non-deductible expenses | (1.4) | (0.3) | 1.0
Other | 0.6 | (0.4) | 0.2
Income tax expense (benefit) | (63.8) | 13.3 | (45.5)
HONG KONG |  |  |
Income Taxes [Line Items] |  |  |
Foreign earnings taxed at rates different from the U.S. statutory rate: | (14.2) | (7.2) | (3.3)
OTHER JURISDICTIONS |  |  |
Income Taxes [Line Items] |  |  |
Foreign earnings taxed at rates different from the U.S. statutory rate: | $ 2.1 | $ 3.1 | $ 1.2

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- Definition Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from compensation and benefits costs. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 8 -URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32632-109319 Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 6 -URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32621-109319 + Details
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