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.