Employee Benefit Plans (Details) $ in Thousands		1 Months Ended	12 Months Ended
		Jul. 31, 2005	Jan. 01, 2022 USD ($) plan	Jan. 02, 2021 USD ($)	Dec. 28, 2019 USD ($)
Fair Value Measurement [Domain]
Change in plan assets:
Fair value of plan assets at beginning of period			$ 178,978
Fair value of plan assets at end of period			188,718	$ 178,978
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			114,143
Fair value of plan assets at end of period			110,463	114,143
Fair Value Measurement [Domain] | Significant Other Observable Inputs (Level 2) [Member]
Change in plan assets:
Fair value of plan assets at beginning of period			11,088
Fair value of plan assets at end of period			14,937	11,088
Fair Value Measurement [Domain] | Fair Value, Inputs, Level 3 [Member]
Change in plan assets:
Fair value of plan assets at beginning of period			3,249
Fair value of plan assets at end of period			2,982	3,249
Projected benefit obligation at beginning of period			235,977	212,265
Service cost			3,127	3,060	$ 2,696
Interest cost			4,816	5,721	6,828
Employee contributions			335	360
Plan combinations			5,783	5,362
Defined Benefit Plan, Benefit Obligation, Increase (Decrease) for Plan Amendment			40	0
Employee contributions			335	360
Actuarial (gain) loss			(9,031)	16,427
Benefits paid			(9,801)	(8,274)
Effect of curtailment			0	(747)
Effect of settlement			(1,572)	(2,208)
Other			(3,866)	4,011
Projected benefit obligation at end of period			225,808	235,977	212,265
Fair value of plan assets at beginning of period			178,978	155,702
Actual return on plan assets			13,139	16,029
Employer contributions			3,878	11,460
Plan combinations			5,510	4,537
Benefits paid			(9,801)	(8,274)
Effect of settlement			(1,572)	(2,208)
Other			(1,749)	1,372
Fair value of plan assets at end of period			188,718	178,978	155,702
Funded status			(37,090)	(56,999)
Amounts recognized in the consolidated balance    sheets consist of:
Current liability			(936)	(1,242)
Noncurrent liability			(36,268)	(55,757)
Net amount recognized			(37,090)	(56,999)
Assets for Plan Benefits, Defined Benefit Plan			114	0
Amounts recognized in accumulated other    comprehensive loss consist of:
Net actuarial loss			34,304	51,145
Prior service cost			176	194
Net amount recognized	[1]		34,480	51,339
Other Comprehensive Income (Loss), Pension and Other Postretirement Benefit Plans, Tax			8,800	13,000
Net pension cost includes the following components:
Service cost			3,127	3,060	2,696
Interest cost			4,816	5,721	6,828
Expected return on plan assets			(9,287)	(8,161)	(7,270)
Net amortization and deferral			4,253	3,438	4,605
Curtailment			0	(678)	(33)
Settlement			210	(22)	66
Net pension cost			$ 3,119	$ 3,358	$ 6,892
Weighted average assumptions used to determine benefit obligations:
Discount rate			2.40%	2.10%	2.77%
Rate of compensation increase			0.50%	0.45%	0.40%
Weighted average assumptions used to determine net periodic benefit cost for the employee benefit pension plans:
Discount rate			1.32%	2.13%	3.33%
Rate of increase in future compensation levels			0.52%	0.41%	0.42%
Expected long-term rate of return on assets			5.40%	5.92%	6.13%
Defined Benefit Plan, Expected Future Benefit Payment [Abstract]
2022			$ 11,219
2023			10,715
2024			11,797
2025			12,948
2026			12,634
Years 2027 – 2031			66,930
Multiemployer Plans [Abstract]
Contributions			$ 3,212	$ 3,229	$ 3,626
Number Of Multiemployer Plans, Withdrawal Obligation | plan			4
Multiemployer Plans, Withdrawal Obligation			$ 3,800
Investment Horizon of Greater Than			10 years
Defined Benefit Plan, Pension Plan with Accumulated Benefit Obligation in Excess of Plan Assets, Projected Benefit Obligation			$ 182,644	235,977
Defined Benefit Plan, Plan with Accumulated Benefit Obligation in Excess of Plan Assets, Accumulated Benefit Obligation			180,303	221,238
Defined Benefit Plan, Plan with Accumulated Benefit Obligation in Excess of Plan Assets, Plan Assets			$ 147,663	178,978
Foreign Plan [Member]
Weighted average assumptions used to determine net periodic benefit cost for the employee benefit pension plans:
Expected long-term rate of return on assets			1.90%
Fair Value, Inputs, Level 3 [Member]
Change in plan assets:
Fair value of plan assets at beginning of period			$ 3,249	4,474
Fair value of plan assets at end of period			2,982	3,249	4,474
Western Conference Of Teamsters Pension Plan [Member]
Multiemployer Plans [Abstract]
Contributions	[2]		1,294	1,429	1,514
Central States, Southeast and Southwest Areas Pension Plan [Member]
Multiemployer Plans [Abstract]
Contributions	[3],[4]		811	886	916
Multiemployer Plans, IRS Extended Amortization Period		10 years
Other Multiemployer Plans [Member]
Multiemployer Plans [Abstract]
Contributions			$ 1,107	914	$ 1,196
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] | UNITED STATES
Multiemployer Plans [Abstract]
Defined Benefit Plan, Target Plan Asset Allocations Range Minimum (Deprecated 2017-01-31)			65
Maximum [Member] | Fixed Income Securities [Member] | UNITED STATES
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] | UNITED STATES
Multiemployer Plans [Abstract]
Defined Benefit Plan, Target Plan Asset Allocations Range Minimum (Deprecated 2017-01-31)			20
Minimum [Member] | Fixed Income Securities [Member] | UNITED STATES
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			$ 128,480
Fair value of plan assets at end of period			128,382	128,480
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			114,143
Fair value of plan assets at end of period			110,463	114,143
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			11,088
Fair value of plan assets at end of period			14,937	11,088
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			3,249
Fair value of plan assets at end of period			2,982	3,249
Estimate of Fair Value Measurement [Member] | Fixed Income, Long Term [Member]
Change in plan assets:
Fair value of plan assets at beginning of period			20,082
Fair value of plan assets at end of period			29,180	20,082
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			20,082
Fair value of plan assets at end of period			29,180	20,082
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			3,585
Fair value of plan assets at end of period			3,951	3,585
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			3,585
Fair value of plan assets at end of period			3,951	3,585
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			55,454
Fair value of plan assets at end of period			45,783	55,454
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			55,454
Fair value of plan assets at end of period			45,783	55,454
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			35,022
Fair value of plan assets at end of period			31,549	35,022
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			35,022
Fair value of plan assets at end of period			31,549	35,022
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			14,337
Fair value of plan assets at end of period			17,919	14,337
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			11,088
Fair value of plan assets at end of period			14,937	11,088
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			3,249
Fair value of plan assets at end of period			2,982	3,249
Portion at Other than Fair Value Measurement [Member]
Change in plan assets:
Fair value of plan assets at beginning of period			50,498
Fair value of plan assets at end of period			$ 60,336	$ 50,498

[1] Amounts do not include deferred taxes of $8.8 million and $13.0 million at January 1, 2022 and January 2, 2021, 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. The agreements have expiration dates through April 1, 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. Certain of these agreements have expired and are being renegotiated with others having expiration dates through May 1, 2023.