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Employee Benefit Plans (Details) $ in Thousands | 1 Months Ended | 12 Months Ended
--- | --- | ---
Jul. 31, 2005 | Dec. 31, 2022 USD ($) plan | Jan. 01, 2022 USD ($) | Jan. 02, 2021 USD ($)
Fair Value Measurement [Domain] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | $ 188,718 |  |
Fair value of plan assets at end of period |  |  | 147,766 | $ 188,718 |
Fair Value Measurement [Domain] | Quoted Prices in Active Markets for Identical Assets (Level 1) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 110,463 |  |
Fair value of plan assets at end of period |  |  | 84,401 | 110,463 |
Fair Value Measurement [Domain] | Significant Other Observable Inputs (Level 2) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 14,937 |  |
Fair value of plan assets at end of period |  |  | 14,970 | 14,937 |
Fair Value Measurement [Domain] | Fair Value, Inputs, Level 3 [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 2,982 |  |
Fair value of plan assets at end of period |  |  | 1,743 | 2,982 |
Projected benefit obligation at beginning of period |  |  | 225,808 | 235,977 |
Service cost |  |  | 3,149 | 3,127 | $ 3,060
Interest cost |  |  | $ 5,231 | $ 4,816 | $ 5,721
Defined Benefit Plan, Net Periodic Benefit Cost (Credit), Interest Cost, Statement of Income or Comprehensive Income [Extensible Enumeration] |  |  | Other expense, net | Other expense, net | Other expense, net
Employee contributions |  |  | $ 353 | $ 335 |
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) Excluding Service Cost, Statement of Income or Comprehensive Income [Extensible Enumeration] |  |  | Other expense, net | Other expense, net | Other expense, net
Plan combinations |  |  | $ 0 | $ 5,783 |
Defined Benefit Plan, Benefit Obligation, Increase (Decrease) for Plan Amendment |  |  | 0 | 40 |
Employee contributions |  |  | 353 | 335 |
Actuarial gain |  |  | (52,490) | (9,031) |
Benefits paid |  |  | (9,919) | (9,801) |
Effect of settlement |  |  | (476) | (1,572) |
Special termination benefit recognized |  |  | (38) | 0 | $ 0
Other |  |  | (4,148) | (3,866) |
Projected benefit obligation at end of period |  |  | 167,546 | 225,808 | 235,977
Fair value of plan assets at beginning of period |  |  | 188,718 | 178,978 |
Actual return on plan assets |  |  | (33,841) | 13,139 |
Employer contributions |  |  | 5,570 | 3,878 |
Plan combinations |  |  | 0 | 5,510 |
Benefits paid |  |  | (9,919) | (9,801) |
Effect of settlement |  |  | (476) | (1,572) |
Other |  |  | (2,639) | (1,749) |
Fair value of plan assets at end of period |  |  | 147,766 | 188,718 | 178,978
Funded status |  |  | (19,780) | (37,090) |
Amounts recognized in the consolidated balance sheets consist of: |  |  |  |  |
Current liability |  |  | (1,152) | (936) |
Noncurrent liability |  |  | (22,538) | (36,268) |
Net amount recognized |  |  | (19,780) | (37,090) |
Assets for Plan Benefits, Defined Benefit Plan |  |  | 3,910 | 114 |
Amounts recognized in accumulated other comprehensive loss consist of: |  |  |  |  |
Net actuarial loss |  |  | 22,176 | 34,304 |
Prior service cost |  |  | 101 | 176 |
Net amount recognized | [1] |  | 22,277 | 34,480 |
Other Comprehensive Income (Loss), Pension and Other Postretirement Benefit Plans, Tax |  |  | 5,600 | 8,800 |
Net pension cost includes the following components: |  |  |  |  |
Service cost |  |  | 3,149 | 3,127 | 3,060
Interest cost |  |  | 5,231 | 4,816 | 5,721
Expected return on plan assets |  |  | (8,604) | (9,287) | (8,161)
Net amortization and deferral |  |  | 2,257 | 4,253 | 3,438
Curtailment |  |  | 0 | 0 | (678)
Settlement |  |  | (22) | 210 | (22)
Special termination benefit recognized |  |  | (38) | 0 | 0
Net pension cost |  |  | $ 2,049 | $ 3,119 | $ 3,358
Weighted average assumptions used to determine benefit obligations: |  |  |  |  |
Discount rate |  |  | 4.82% | 2.40% | 2.10%
Rate of compensation increase |  |  | 0.55% | 0.50% | 0.45%
Weighted average assumptions used to determine net periodic benefit cost for the employee benefit pension plans: |  |  |  |  |
Discount rate |  |  | 0.68% | 1.32% | 2.13%
Rate of increase in future compensation levels |  |  | 0.51% | 0.52% | 0.41%
Expected long-term rate of return on assets |  |  | 4.75% | 5.40% | 5.92%
Defined Benefit Plan, Expected Future Benefit Payment [Abstract] |  |  |  |  |
2023 |  |  | $ 11,017 |  |
2024 |  |  | 11,489 |  |
2025 |  |  | 11,904 |  |
2026 |  |  | 12,162 |  |
2027 |  |  | 12,995 |  |
Years 2028 – 2032 |  |  | 64,486 |  |
Multiemployer Plans [Abstract] |  |  |  |  |
Contributions |  |  | $ 3,450 | $ 3,212 | $ 3,229
Number Of Multiemployer Plans, Withdrawal Obligation | plan |  |  | 3 |  |
Multiemployer Plans, Withdrawal Obligation |  |  | $ 3,900 |  |
Investment Horizon of Greater Than |  |  | 10 years |  |
Defined Benefit Plan, Pension Plan with Accumulated Benefit Obligation in Excess of Plan Assets, Projected Benefit Obligation |  |  | $ 110,039 | 182,644 |
Defined Benefit Plan, Plan with Accumulated Benefit Obligation in Excess of Plan Assets, Accumulated Benefit Obligation |  |  | 107,807 | 180,303 |
Defined Benefit Plan, Plan with Accumulated Benefit Obligation in Excess of Plan Assets, Plan Assets |  |  | $ 86,441 | $ 147,663 |
Defined Benefit Plan, Net Periodic Benefit (Cost) Credit, Settlement Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration] |  |  | Other expense, net | Other expense, net | Other expense, net
Fair Value, Inputs, Level 3 [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | $ 2,982 | $ 3,249 |
Fair value of plan assets at end of period |  |  | 1,743 | 2,982 | $ 3,249
Western Conference Of Teamsters Pension Plan [Member] |  |  |  |  |
Multiemployer Plans [Abstract] |  |  |  |  |
Contributions | [2] |  | 1,516 | 1,294 | 1,429
Central States, Southeast and Southwest Areas Pension Plan [Member] |  |  |  |  |
Multiemployer Plans [Abstract] |  |  |  |  |
Contributions | [3],[4] |  | 899 | 811 | 886
Multiemployer Plans, IRS Extended Amortization Period |  | 10 years |  |  |
Other Multiemployer Plans [Member] |  |  |  |  |
Multiemployer Plans [Abstract] |  |  |  |  |
Contributions |  |  | $ 1,035 | 1,107 | $ 914
Maximum [Member] |  |  |  |  |
Defined Benefit Plan Disclosure [Line Items] |  |  |  |  |
Multiemployer Plan, Contributions To Individual Plan, Percent |  |  | 5.00% |  |
Multiemployer Plans [Abstract] |  |  |  |  |
Investment Objectives Achievement Period |  |  | 7 years |  |
Maximum [Member] | Equity Securities [Member] |  |  |  |  |
Multiemployer Plans [Abstract] |  |  |  |  |
Defined Benefit Plan, Target Plan Asset Allocations Range Minimum (Deprecated 2017-01-31) |  |  | 65 |  |
Maximum [Member] | Fixed Income Securities [Member] |  |  |  |  |
Multiemployer Plans [Abstract] |  |  |  |  |
Defined Benefit Plan, Target Plan Asset Allocations Range Minimum (Deprecated 2017-01-31) |  |  | 80 |  |
Minimum [Member] |  |  |  |  |
Multiemployer Plans [Abstract] |  |  |  |  |
Investment Objectives Achievement Period |  |  | 5 years |  |
Minimum [Member] | Equity Securities [Member] |  |  |  |  |
Multiemployer Plans [Abstract] |  |  |  |  |
Defined Benefit Plan, Target Plan Asset Allocations Range Minimum (Deprecated 2017-01-31) |  |  | 20 |  |
Minimum [Member] | Fixed Income Securities [Member] |  |  |  |  |
Multiemployer Plans [Abstract] |  |  |  |  |
Defined Benefit Plan, Target Plan Asset Allocations Range Minimum (Deprecated 2017-01-31) |  |  | 35 |  |
Estimate of Fair Value Measurement [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | $ 128,382 |  |
Fair value of plan assets at end of period |  |  | 101,114 | 128,382 |
Estimate of Fair Value Measurement [Member] | Quoted Prices in Active Markets for Identical Assets (Level 1) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 110,463 |  |
Fair value of plan assets at end of period |  |  | 84,401 | 110,463 |
Estimate of Fair Value Measurement [Member] | Significant Other Observable Inputs (Level 2) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 14,937 |  |
Fair value of plan assets at end of period |  |  | 14,970 | 14,937 |
Estimate of Fair Value Measurement [Member] | Fair Value, Inputs, Level 3 [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 2,982 |  |
Fair value of plan assets at end of period |  |  | 1,743 | 2,982 |
Estimate of Fair Value Measurement [Member] | Fixed Income, Long Term [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 29,180 |  |
Fair value of plan assets at end of period |  |  | 23,028 | 29,180 |
Estimate of Fair Value Measurement [Member] | Fixed Income, Long Term [Member] | Quoted Prices in Active Markets for Identical Assets (Level 1) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 29,180 |  |
Fair value of plan assets at end of period |  |  | 23,028 | 29,180 |
Estimate of Fair Value Measurement [Member] | Fixed Income, Long Term [Member] | Significant Other Observable Inputs (Level 2) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 0 |  |
Fair value of plan assets at end of period |  |  | 0 | 0 |
Estimate of Fair Value Measurement [Member] | Fixed Income, Long Term [Member] | Fair Value, Inputs, Level 3 [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 0 |  |
Fair value of plan assets at end of period |  |  | 0 | 0 |
Estimate of Fair Value Measurement [Member] | Fixed Income, Short Term [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 3,951 |  |
Fair value of plan assets at end of period |  |  | 4,539 | 3,951 |
Estimate of Fair Value Measurement [Member] | Fixed Income, Short Term [Member] | Quoted Prices in Active Markets for Identical Assets (Level 1) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 3,951 |  |
Fair value of plan assets at end of period |  |  | 4,539 | 3,951 |
Estimate of Fair Value Measurement [Member] | Fixed Income, Short Term [Member] | Significant Other Observable Inputs (Level 2) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 0 |  |
Fair value of plan assets at end of period |  |  | 0 | 0 |
Estimate of Fair Value Measurement [Member] | Fixed Income, Short Term [Member] | Fair Value, Inputs, Level 3 [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 0 |  |
Fair value of plan assets at end of period |  |  | 0 | 0 |
Estimate of Fair Value Measurement [Member] | Equity Securities, Domestic [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 45,783 |  |
Fair value of plan assets at end of period |  |  | 33,369 | 45,783 |
Estimate of Fair Value Measurement [Member] | Equity Securities, Domestic [Member] | Quoted Prices in Active Markets for Identical Assets (Level 1) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 45,783 |  |
Fair value of plan assets at end of period |  |  | 33,369 | 45,783 |
Estimate of Fair Value Measurement [Member] | Equity Securities, Domestic [Member] | Significant Other Observable Inputs (Level 2) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 0 |  |
Fair value of plan assets at end of period |  |  | 0 | 0 |
Estimate of Fair Value Measurement [Member] | Equity Securities, Domestic [Member] | Fair Value, Inputs, Level 3 [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 0 |  |
Fair value of plan assets at end of period |  |  | 0 | 0 |
Estimate of Fair Value Measurement [Member] | Equity Securities, International [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 31,549 |  |
Fair value of plan assets at end of period |  |  | 23,465 | 31,549 |
Estimate of Fair Value Measurement [Member] | Equity Securities, International [Member] | Quoted Prices in Active Markets for Identical Assets (Level 1) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 31,549 |  |
Fair value of plan assets at end of period |  |  | 23,465 | 31,549 |
Estimate of Fair Value Measurement [Member] | Equity Securities, International [Member] | Significant Other Observable Inputs (Level 2) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 0 |  |
Fair value of plan assets at end of period |  |  | 0 | 0 |
Estimate of Fair Value Measurement [Member] | Equity Securities, International [Member] | Fair Value, Inputs, Level 3 [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 0 |  |
Fair value of plan assets at end of period |  |  | 0 | 0 |
Estimate of Fair Value Measurement [Member] | Insurance Contracts [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 17,919 |  |
Fair value of plan assets at end of period |  |  | 16,713 | 17,919 |
Estimate of Fair Value Measurement [Member] | Insurance Contracts [Member] | Quoted Prices in Active Markets for Identical Assets (Level 1) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 0 |  |
Fair value of plan assets at end of period |  |  | 0 | 0 |
Estimate of Fair Value Measurement [Member] | Insurance Contracts [Member] | Significant Other Observable Inputs (Level 2) [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 14,937 |  |
Fair value of plan assets at end of period |  |  | 14,970 | 14,937 |
Estimate of Fair Value Measurement [Member] | Insurance Contracts [Member] | Fair Value, Inputs, Level 3 [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 2,982 |  |
Fair value of plan assets at end of period |  |  | 1,743 | 2,982 |
Portion at Other than Fair Value Measurement [Member] |  |  |  |  |
Change in plan assets: |  |  |  |  |
Fair value of plan assets at beginning of period |  |  | 60,336 |  |
Fair value of plan assets at end of period |  |  | $ 46,652 | $ 60,336 |
[1] | Amounts do not include deferred taxes of $5.6 million and $8.8 million at December 31, 2022 and January 1, 2022, respectively.
[2] | The Company has several plants that participate in the Western Conference of Teamsters Pension Plan under collective bargaining agreements that require minimum funding contributions. Certain of these agreements have expired and are being renegotiated with others having expiration dates through May 31, 2025.
[3] | In July 2005 this plan received a 10 year extension from the IRS for amortizing unfunded liabilities.
[4] | The Company has several processing plants that participate in the Central States, Southeast and Southwest Areas Pension Plan under collective bargaining agreements that require minimum funding contributions. The agreements have expiration dates through April 2, 2026.

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