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Stock-Based Compensation - Narrative (Details) $ / shares in Units, $ in Millions |  | 1 Months Ended | 12 Months Ended
--- | --- | --- | ---
Feb. 15, 2022 shares | Dec. 31, 2021 shares | Feb. 28, 2021 shares | Jan. 01, 2023 USD ($) $ / shares shares | Jan. 02, 2022 USD ($) $ / shares shares | Jan. 03, 2021 USD ($) $ / shares shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Number of shares available for grant (in shares) - Fixed provision |  |  |  | 2,700,000 |  |
Tax benefit | $ |  |  |  | $ 1.1 | $ 0.8 | $ 0.4
Restricted Stock |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Award vesting period |  |  |  | 4 years |  |
Unrecognized compensation cost, unvested | $ |  |  |  | $ 8.9 |  |
Compensation cost not yet recognized, period for recognition |  |  |  | 1 year 10 months 24 days |  |
Grants in period (in dollars per share) | $ / shares |  |  |  | $ 20.16 | $ 20.91 | $ 15.97
Vested in period, fair value | $ |  |  |  | $ 2.3 | $ 2.0 | $ 2.4
Granted (in shares) |  |  |  | 417,000 |  |
Weighted average grant date fair value (in dollars per share) | $ / shares |  |  |  | $ 20.27 | $ 21.24 |
Total nonvested shares (in shares) |  |  |  | 607,000 | 403,000 |
Performance Shares, Single Financial Goal |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Award vesting period |  |  |  | 4 years | 4 years | 4 years
Performance Shares, Financial Measure |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Unrecognized compensation cost, unvested | $ |  |  |  | $ 8.4 |  |
Compensation cost not yet recognized, period for recognition |  |  |  | 2 years 4 months 24 days |  |
Grants in period (in dollars per share) | $ / shares |  |  |  | $ 21.19 |  |
Vested in period, fair value | $ |  |  |  | $ 0.9 | $ 0.3 | $ 1.8
Granted (in shares) |  |  |  | 186,000 |  |
Weighted average grant date fair value (in dollars per share) | $ / shares |  |  |  | $ 19.41 | $ 20.03 |
Total nonvested shares (in shares) |  |  |  | 692,000 | 708,000 |
Stock-based compensation cost |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Stock-based compensation cost | $ |  |  |  | $ 7.8 | $ 5.1 | $ 3.9
Class A common stock |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Maximum number of shares available for grants - Fixed provision |  |  |  | 4,700,000 |  |
2020 grant | Performance Shares, Single Financial Goal |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Granted (in shares) |  |  |  |  |  | 115,000
Weighted average grant date fair value (in dollars per share) | $ / shares |  |  |  | $ 22.59 |  |
Total nonvested shares (in shares) |  |  |  | 78,000 |  |
2021 grant | Performance Shares, Financial Measure |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Granted (in shares) |  | 308,000 | 180,000 |  |  |
Percentage of target achieved |  |  |  | 0.72 |  |
Weighted average grant date fair value (in dollars per share) | $ / shares |  |  |  | $ 18.21 |  |
Total nonvested shares (in shares) |  |  |  | 423,000 |  |
2021 grant | Maximum shares eligible to earn | Performance Shares, Financial Measure |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Maximum target percentage allowed under grant |  |  | 200.00% |  |  |
2022 grant | Performance Shares, Financial Measure |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Granted (in shares) | 186,000 |  |  |  |  |
Percentage of target achieved |  |  |  | 0.72 |  |
Weighted average grant date fair value (in dollars per share) | $ / shares |  |  |  | $ 21.19 |  |
Total nonvested shares (in shares) |  |  |  | 186,000 |  |
2022 grant | Maximum shares eligible to earn | Performance Shares, Financial Measure |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Maximum target percentage allowed under grant | 200.00% |  |  |  |  |

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