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Stock-Based Compensation and Other Stock Plans - Other Stock Plans Narrative (Details) - USD ($) $ in Millions | 12 Months Ended
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Jan. 01, 2022 | Jan. 02, 2021 | Dec. 28, 2019
Directors' Fee Plan |  |  |
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items] |  |  |
Percentage of non-employee directors fee | 100.00% |  |
Number of shares issued (in shares) | 1,235 | 1,836 | 1,784
Deferred shares received (in shares) | 922 | 1,364 | 1,374
Number of shares reserved for issuance (in shares) | 189,837 |  |
Non-employee Directors | Restricted Stock |  |  |
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items] |  |  |
Shares granted (in shares) | 6,858 | 7,380 | 7,605
Vesting period | 1 year |  |
Employees Stock Purchase Plan |  |  |
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items] |  |  |
Number of shares issued (in shares) | 82,286 | 25,425 | 25,820
Number of shares reserved for issuance (in shares) | 597,275 |  |
Employee contributions for purchase of common stock | $ 3.0 |  |
Compensation expense | $ 9.6 | $ 1.1 | $ 0.1
Franchisee Stock Purchase Plan |  |  |
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items] |  |  |
Number of shares issued (in shares) | 143,388 | 55,980 | 49,921
Number of shares reserved for issuance (in shares) | 270,162 |  |
Compensation expense | $ 16.7 | $ 1.9 | $ 0.8
Franchisee contributions for purchase of common stock | $ 7.0 |  |

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