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Accumulated Other Comprehensive Income (Loss) and Shareholders' Equity - Reclassifications from Accumulated Other Comprehensive Income (Loss) (Details) - USD ($) $ in Millions | 12 Months Ended
--- | ---
Dec. 31, 2022 | Jan. 01, 2022 | Jan. 02, 2021
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items] |  |  |
Income tax expense | $ (22.5) | $ (18.5) | $ (12.5)
Gain on sale of subsidiary | 50.4 | 0.0 | 0.0
Selling and administrative expenses | (723.4) | (665.6) | (620.9)
Net income | 123.9 | 59.8 | 41.9
Reclassifications from accumulated other comprehensive income (loss) |  |  |
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items] |  |  |
Net income | 3.1 | (1.1) | (0.8)
Reclassifications from accumulated other comprehensive income (loss) | Derivative financial instruments | Interest rate swap |  |  |
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items] |  |  |
Interest expense, net | 0.1 | (1.0) | (0.3)
Income tax expense | (0.0) | 0.2 | 0.1
Reclassifications from accumulated other comprehensive income (loss) | Unrealized Gains (Losses) on Debt Securities |  |  |
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items] |  |  |
Income tax expense | (0.0) | (0.0) | (0.0)
Selling and administrative expenses | (0.0) | (0.0) | (0.0)
Reclassifications from accumulated other comprehensive income (loss) | Pension and Post-retirement Liabilities |  |  |
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items] |  |  |
Income tax expense | 0.1 | 0.1 | 0.1
Selling and administrative expenses | (0.3) | (0.5) | (0.3)
Reclassifications from accumulated other comprehensive income (loss) | Foreign Currency Translation Adjustment |  |  |
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items] |  |  |
Gain on sale of subsidiary | 3.3 | 0.0 | 0.0
Selling and administrative expenses | $ 0.0 | $ 0.0 | $ (0.4)

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- Definition Amount of gain (loss) on sale or disposal of assets, including but not limited to property plant and equipment, intangible assets and equity in securities of subsidiaries or equity method investee. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Publisher FASB -Name Accounting Standards Codification -Topic 230 -SubTopic 10 -Section 45 -Paragraph 28 -Subparagraph (b) -URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3602-108585 + Details
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