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Summary of Significant Accounting Policies - Changes in accumulated other comprehensive income (loss) (Details) - USD ($) $ in Thousands | 12 Months Ended
--- | ---
Dec. 31, 2022 | Jan. 01, 2022 | Jan. 02, 2021
Accumulated Other Comprehensive Income (Loss) [Line Items] |  |  |
Accumulated other comprehensive loss | $ (278,472) | $ (359,084) | $ (488,428)
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax | (66,954) | (96,839) |
Gain/(loss) reclassified from accumulated other comprehensive income (effective portion) | 13,658 | 32,505 |
Other Comprehensive Income (Loss), Net of Tax | 80,612 | 129,344 | (137,495)
Unrecognized pension benefit costs, Tax | 1,995 | 39,470 |
Unrealized loss on interest rate swap, tax | 16,836 | (4,501) |
Other Comprehensive Income (Loss), Defined Benefit Plan, Gain (Loss), Reclassification Adjustment from AOCI, Tax | 37,500 |  |
Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), Tax | 21,337 | 8,619 | (7,147)
Other Comprehensive Income (Loss), Unrealized Gain (loss) Certain Investments, Tax | (400) |  |
Accumulated Foreign Currency Adjustment Attributable to Parent |  |  |
Accumulated Other Comprehensive Income (Loss) [Line Items] |  |  |
Accumulated other comprehensive loss | (205,345) | (97,654) | (49,961)
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax | 107,691 | 47,693 |
Gain/(loss) reclassified from accumulated other comprehensive income (effective portion) | 0 | 0 |
Other Comprehensive Income (Loss), Net of Tax | (107,691) | (47,693) |
Accumulated Defined Benefit Plans Adjustment Attributable to Parent |  |  |
Accumulated Other Comprehensive Income (Loss) [Line Items] |  |  |
Accumulated other comprehensive loss | (121,701) | (249,696) | (400,919)
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax | 117,840 | 137,187 |
Gain/(loss) reclassified from accumulated other comprehensive income (effective portion) | 10,155 | 14,036 |
Other Comprehensive Income (Loss), Net of Tax | 127,995 | 151,223 |
Accumulated Net Gain (Loss) from Cash Flow Hedges Attributable to Parent | Interest Rate Swap |  |  |
Accumulated Other Comprehensive Income (Loss) [Line Items] |  |  |
Accumulated other comprehensive loss | 48,574 | (13,064) | (37,548)
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax | (58,135) | (6,015) |
Gain/(loss) reclassified from accumulated other comprehensive income (effective portion) | 3,503 | 18,469 |
Other Comprehensive Income (Loss), Net of Tax | 61,638 | 24,484 |
AOCI, Accumulated Gain (Loss), Debt Securities, Available-for-sale, Parent |  |  |
Accumulated Other Comprehensive Income (Loss) [Line Items] |  |  |
Accumulated other comprehensive loss | 0 | 1,330 | $ 0
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax | 1,330 | (1,330) |
Gain/(loss) reclassified from accumulated other comprehensive income (effective portion) | 0 | 0 |
Other Comprehensive Income (Loss), Net of Tax | $ (1,330) | $ 1,330 |

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- Definition Accumulated change in equity from transactions and other events and circumstances from non-owner sources, net of tax effect, at period end. Excludes Net Income (Loss), and accumulated changes in equity from transactions resulting from investments by owners and distributions to owners. Includes foreign currency translation items, certain pension adjustments, unrealized gains and losses on certain investments in debt and equity securities, other than temporary impairment (OTTI) losses related to factors other than credit losses on available-for-sale and held-to-maturity debt securities that an entity does not intend to sell and it is not more likely than not that the entity will be required to sell before recovery of the amortized cost basis, as well as changes in the fair value of derivatives related to the effective portion of a designated cash flow hedge. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 210 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SX 210.5-02(30)(a)(4)) -URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 220 -SubTopic 10 -Section 45 -Paragraph 11 -URI https://asc.fasb.org/extlink&oid=126968391&loc=d3e637-108580 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 944 -SubTopic 210 -Section S99 -Paragraph 1 -Subparagraph (SX 210.7-03(a)(23)(a)(3)) -URI https://asc.fasb.org/extlink&oid=126734703&loc=d3e572229-122910 Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 220 -SubTopic 10 -Section 45 -Paragraph 14A -URI https://asc.fasb.org/extlink&oid=126968391&loc=SL7669686-108580 Reference 5: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 944 -SubTopic 40 -Section 65 -Paragraph 2 -Subparagraph (h)(2) -URI https://asc.fasb.org/extlink&oid=124501264&loc=SL117420844-207641 Reference 6: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 944 -SubTopic 40 -Section 65 -Paragraph 2 -Subparagraph (g)(2)(ii) -URI https://asc.fasb.org/extlink&oid=124501264&loc=SL117420844-207641 Reference 7: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 220 -SubTopic 10 -Section 45 -Paragraph 14 -URI https://asc.fasb.org/extlink&oid=126968391&loc=d3e681-108580 + Details
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