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Shareholders' Deficit - Additional Information (Details) - USD ($) shares in Millions | 12 Months Ended
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Jan. 01, 2022 | Jan. 02, 2021 | Dec. 28, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Proceeds from stock options exercised | $ 4,400,000 |  |
Tax benefit from exercise of stock options | 3,900,000 |  |
Approved share repurchase program | 600,000,000 |  |
Remaining authorized stock purchase plan | $ 403,000,000 |  |
Stock options |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Antidilutive securities excluded from computation of earnings per share, amount | 0.1 | 0.2 | 0.2
Stock options |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Stock-based compensation expense related to non-vested awards | $ 4,200,000 |  |
Weighted average period to recognize remaining expense over | 1 year 10 months 24 days |  |
Time- Based Stock Awards |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Stock-based compensation expense related to non-vested awards | $ 8,300,000 |  |
Weighted average period to recognize remaining expense over | 1 year 10 months 24 days |  |
Performance- Based Stock Awards |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Stock-based compensation expense related to non-vested awards | $ 19,400,000 |  |
Weighted average period to recognize remaining expense over | 1 year 10 months 24 days |  |

X
- Definition Securities (including those issuable pursuant to contingent stock agreements) that could potentially dilute basic earnings per share (EPS) or earnings per unit (EPU) in the future that were not included in the computation of diluted EPS or EPU because to do so would increase EPS or EPU amounts or decrease loss per share or unit amounts for the period presented. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 260 -SubTopic 10 -Section 50 -Paragraph 1 -Subparagraph (c) -URI http://asc.fasb.org/extlink&oid=124432515&loc=d3e3550-109257 + 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://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (i) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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