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Employee Benefit Plans (Tables)
 12 Months Ended
Dec. 31, 2022
Employee Benefit Plans [Abstract]  
Schedule of Net Funded Status The following table sets forth the plans’ funded status for the Company's domestic and foreign defined benefit plans and amounts recognized in the Company's Consolidated Balance Sheets based on the measurement date (December 31, 2022 and December 31, 2021) (in thousands):
    
 December 31,
2022		January 1,
2022
Change in projected benefit obligation:  
Projected benefit obligation at beginning of period$225,808 $235,977 
Service cost3,149 3,127 
Interest cost5,231 4,816 
Employee contributions353 335 
Plan combinations— 5,783 
Plan amendments— 40 
Actuarial gain(52,490)(9,031)
Benefits paid(9,919)(9,801)
Effect of settlement(476)(1,572)
Special termination benefit recognized38 — 
Other(4,148)(3,866)
Projected benefit obligation at end of period167,546 225,808 
Change in plan assets:  
Fair value of plan assets at beginning of period188,718 178,978 
Actual return on plan assets(33,841)13,139 
Employer contributions5,570 3,878 
Employee contributions353 335 
Plan combinations— 5,510 
Benefits paid(9,919)(9,801)
Effect of settlement(476)(1,572)
Other(2,639)(1,749)
Fair value of plan assets at end of period147,766 188,718 
Funded status(19,780)(37,090)
Net amount recognized$(19,780)$(37,090)
Amounts recognized in the consolidated balance
   sheets consist of:		  
Noncurrent assets$3,910 $114 
Current liability(1,152)(936)
Noncurrent liability(22,538)(36,268)
Net amount recognized$(19,780)$(37,090)
Amounts recognized in accumulated other
   comprehensive loss consist of:		  
Net actuarial loss$22,176 $34,304 
Prior service cost101 176 
Net amount recognized  (a)$22,277 $34,480 

(a)    Amounts do not include deferred taxes of $5.6 million and $8.8 million at December 31, 2022 and January 1, 2022, respectively.
Schedule of Accumulated and Projected Benefit Obligations
Information for pension plans with accumulated benefit obligations in excess of plan assets is as follows (in thousands):
    
 December 31,
2022		January 1,
2022
Projected benefit obligation$110,039 $182,644 
Accumulated benefit obligation107,807 180,303 
Fair value of plan assets86,441 147,663 
Schedule of Defined Benefit Plans Disclosures
Net pension cost includes the following components (in thousands):
    
 December 31,
2022		January 1,
2022		January 2,
2021
Service cost$3,149 $3,127 $3,060 
Interest cost5,231 4,816 5,721 
Expected return on plan assets(8,604)(9,287)(8,161)
Net amortization and deferral2,257 4,253 3,438 
Curtailment— — (678)
Settlement(22)210 (22)
Special termination benefit recognized38 — — 
Net pension cost$2,049 $3,119 $3,358 
Schedule of Amounts in Accumulated Other Comprehensive Income (Loss) to be Recognized over Next Fiscal Year
Schedule of Assumptions Used
Weighted average assumptions used to determine benefit obligations were:
    
 December 31,
2022		January 1,
2022		January 2,
2021
Discount rate4.82%2.40%2.10%
Rate of compensation increase0.55%0.50%0.45%

Weighted average assumptions used to determine net periodic benefit cost for the employee benefit pension plans were:
        
 December 31,
2022		January 1,
2022		January 2,
2021
Discount rate0.68%1.32%2.13%
Rate of increase in future compensation levels0.51%0.52%0.41%
Expected long-term rate of return on assets4.75%5.40%5.92%
Schedule of Target Allocation of Plan Assets
Fixed Income
35% - 80%
Equities
20% - 65%
Schedule of Accumulated Benefit Obligations in Excess of Fair Value of Plan Assets
The following table presents fair value measurements for the Company's defined benefit plans’ assets as categorized using the fair value hierarchy under FASB authoritative guidance (in thousands):
TotalQuoted Prices in
Active Markets for
Identical Assets		Significant Other
Observable
Inputs		Significant
Unobservable
Inputs
(In thousands of dollars)Fair Value(Level 1)(Level 2)(Level 3)
Balances as of January 1, 2022    
Fixed Income:    
Long Term$29,180 $29,180 $— $— 
Short Term3,951 3,951 — — 
Equity Securities:    
Domestic equities45,783 45,783 — — 
International equities31,549 31,549 — — 
Insurance contracts17,919 — 14,937 2,982 
Total categorized in fair value hierarchy128,382 110,463 14,937 2,982 
Other investments measured at NAV60,336 
Totals$188,718 $110,463 $14,937 $2,982 
Balances as of December 31, 2022    
Fixed Income:    
Long Term$23,028 $23,028 $— $— 
Short Term4,539 4,539 — — 
Equity Securities:    
Domestic equities33,369 33,369 — — 
International equities23,465 23,465 — — 
Insurance contracts16,713 — 14,970 1,743 
Total categorized in fair value hierarchy
101,114 84,401 14,970 1,743 
Other investments measured at NAV46,652 
Totals$147,766 $84,401 $14,970 $1,743 
Schedule of Expected Benefit Payments
The following benefit payments, which reflect expected future service, as appropriate, are expected to be paid (in thousands): 

Year EndingPension Benefits
2023$11,017 
202411,489 
202511,904 
202612,162 
202712,995 
Years 2028 – 203264,486 
Multiemployer plans The following table provides more detail on these significant multiemployer plans (contributions in thousands):
Expiration
PensionEIN PensionPension Protection Act Zone StatusFIP/RP Status Pending/ContributionsDate of Collective Bargaining
FundPlan Number20222021Implemented202220212020Agreement
Western Conference of Teamsters Pension Plan91-6145047 / 001GreenGreenNo$1,516 $1,294 $1,429 May 2025 (b)
Central States, Southeast and Southwest Areas Pension Plan (a)36-6044243 / 001RedRedYes899 811 886 April 2026 (c)
All other multiemployer plans1,035 1,107 914 
Total Company Contributions$3,450 $3,212 $3,229 

(a)     In July 2005 this plan received a 10 year extension from the IRS for amortizing unfunded liabilities. In April 2016 the IRS approved a modification of the amortization extension.

(b)     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.

(c)     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.
Schedule of Effect of Significant Unobservable Inputs, Changes in Plan Assets
The fair value measurement of plan assets using significant unobservable inputs (level 3) changed due to the following:
Insurance
(in thousands of dollars)Contracts
Balance as of January 2, 2021$3,249 
Unrealized gains (losses) relating to instruments still held in the reporting period.(16)
Purchases, sales, and settlements— 
Exchange rate changes(251)
Balance as of January 1, 20222,982 
Unrealized gains (losses) relating to instruments still held in the reporting period.(1,055)
Purchases, sales, and settlements— 
Exchange rate changes(184)
Balance as of December 31, 2022$1,743