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Schedule II - Valuation Reserves (Details) - Valuation Reserves - Deferred tax assets valuation allowance - USD ($) $ in Millions | 12 Months Ended
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Jan. 01, 2023 | Jan. 02, 2022 | Jan. 03, 2021
SEC Schedule, 12-09, Movement in Valuation Allowances and Reserves [Roll Forward] |  |  |
Balance at beginning of year | $ 19.0 | $ 20.2 | $ 19.0
Charged to costs and expenses | 15.8 | 0.5 | 3.7
Charged to other accounts | 0.0 | 0.0 | 0.0
Currency exchange effects | (0.7) | (0.8) | 0.5
Deductions from reserves | (0.1) | (0.9) | (3.0)
Balance at end of year | $ 34.0 | $ 19.0 | $ 20.2

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- Definition Amount of increase (decrease) in valuation and qualifying accounts and reserves from adjustment. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Publisher FASB -Name Accounting Standards Codification -Topic 235 -SubTopic 10 -Section S99 -Paragraph 4 -Subparagraph (SX 210.12-09) -URI https://asc.fasb.org/extlink&oid=120395691&loc=d3e24092-122690 + Details
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