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Stockholders' Equity and Stock-Based Compensation Stock Option Awards (Details) - USD ($) $ in Millions |  | 12 Months Ended
--- | --- | ---
Jan. 06, 2020 | Dec. 31, 2022 | Jan. 01, 2022 | Jan. 02, 2021 | Dec. 28, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Options outstanding, Weighted-average remaining contractual life (in years) |  | 4 years 3 months 18 days | 5 years 2 months 12 days | 6 years 2 months 12 days | 6 years 6 months
Granted (in shares) |  | 0 | 0 | 550,941 |
Proceeds from stock options exercised |  | $ 0.1 | $ 0.1 | $ 0.1 |
Share-based Payment Arrangement, Exercise of Option, Tax Benefit |  | 3.7 | 4.5 | 2.4 |
Exercises in period, intrinsic value |  | 21.7 | 29.5 | 19.5 |
Vested in period, fair value |  | 24.8 | $ 19.9 | $ 17.4 |
Outstanding, intrinsic value |  | 125.0 |  |  |
Exercisable, intrinsic value |  | 119.7 |  |  |
Total compensation cost not yet recognized |  | $ 10.2 |  |  |
Share-based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition |  | 1 year 3 months 18 days |  |  |
Options exercisable, Weighted-average remaining contractual life (in years) |  | 4 years 1 month 6 days |  |  |
Nonqualified Stock Options Under Long Term Incentive Program [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Granted (in shares) | 550,941 |  |  |  |
Award vesting rights, percentage |  | 33.33% |  |  |
Expiration period |  | 10 years |  |  |
Incentive Stock Options [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Shares Issued, Shares, Share-based Payment Arrangement, before Forfeiture |  |  |  | 0 |

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- Definition Amount of cost not yet recognized for nonvested award under share-based payment arrangement. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (i) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Weighted-average period over which cost not yet recognized is expected to be recognized for award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (i) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Amount of tax benefit from exercise of option under share-based payment arrangement. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2A -Subparagraph (a) -URI https://asc.fasb.org/extlink&oid=128089324&loc=SL79508275-113901 + Details
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- Definition Fair value of share-based awards for which the grantee gained the right by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (d)(2) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Gross number of share options (or share units) granted during the period. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (c)(1)(iv)(01) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Period from grant date that an equity-based award expires, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days. + References Reference 1: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (a)(2) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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