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Stock-Based Compensation and Other Stock Plans - Narrative (Details) - USD ($) $ in Millions | 12 Months Ended
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Dec. 31, 2022 | Jan. 01, 2022 | Jan. 02, 2021
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items] |  |  |
Net stock-based compensation expense | $ 34.0 | $ 41.4 | $ 19.5
Cash received from stock purchase and option plan exercises | 55.0 | 162.4 | 55.8
Tax benefit realized from exercise and vesting of share-based payment arrangements | $ 10.7 | $ 18.2 | $ 8.2
2011 Incentive Stock and Awards Plan |  |  |
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items] |  |  |
Number of shares available for future grants (in shares) | 3,122,593 |  |

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- Definition The difference between the maximum number of shares (or other type of equity) authorized for issuance under the plan (including the effects of amendments and adjustments), and the sum of: 1) the number of shares (or other type of equity) already issued upon exercise of options or other equity-based awards under the plan; and 2) shares (or other type of equity) reserved for issuance on granting of outstanding awards, net of cancellations and forfeitures, if applicable. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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