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Goodwill and Intangible Assets - Schedule of intangible assets subject to amortization (Details) - USD ($) $ in Thousands | 3 Months Ended | 6 Months Ended |
--- | --- | --- | ---
Jul. 02, 2022 | Jul. 03, 2021 | Jul. 02, 2022 | Jul. 03, 2021 | Dec. 31, 2021
Finite-lived Intangible Assets [Roll Forward] |  |  |  |  |
Intangible assets subject to amortization, beginning balance |  |  | $ 943,299 |  |
Adjustments related to acquisitions |  |  | (36) |  |
Currency translation during the period |  |  | (59,255) |  |
Intangible assets subject to amortization, ending balance | $ 884,008 |  | 884,008 |  |
Accumulated amortization, beginning balance |  |  | 738,224 |  |
Amortization during the period | 6,826 | $ 7,336 | 13,999 | $ 14,834 |
Currency translation during the period |  |  | (45,989) |  |
Accumulated amortization, ending balance | 706,234 |  | 706,234 |  |
Intangible assets subject to amortization, net as of July 2, 2022 | 177,774 |  | 177,774 |  | $ 205,075
Customer relationships |  |  |  |  |
Finite-lived Intangible Assets [Roll Forward] |  |  |  |  |
Intangible assets subject to amortization, beginning balance |  |  | 680,177 |  |
Adjustments related to acquisitions |  |  | (36) |  |
Currency translation during the period |  |  | (38,263) |  |
Intangible assets subject to amortization, ending balance | 641,878 |  | 641,878 |  |
Accumulated amortization, beginning balance |  |  | 483,748 |  |
Amortization during the period |  |  | 13,585 |  |
Currency translation during the period |  |  | (25,753) |  |
Accumulated amortization, ending balance | 471,580 |  | 471,580 |  |
Intangible assets subject to amortization, net as of July 2, 2022 | 170,298 |  | 170,298 |  |
Patents |  |  |  |  |
Finite-lived Intangible Assets [Roll Forward] |  |  |  |  |
Intangible assets subject to amortization, beginning balance |  |  | 256,336 |  |
Adjustments related to acquisitions |  |  | 0 |  |
Currency translation during the period |  |  | (20,469) |  |
Intangible assets subject to amortization, ending balance | 235,867 |  | 235,867 |  |
Accumulated amortization, beginning balance |  |  | 252,414 |  |
Amortization during the period |  |  | 320 |  |
Currency translation during the period |  |  | (20,172) |  |
Accumulated amortization, ending balance | 232,562 |  | 232,562 |  |
Intangible assets subject to amortization, net as of July 2, 2022 | 3,305 |  | 3,305 |  |
Other |  |  |  |  |
Finite-lived Intangible Assets [Roll Forward] |  |  |  |  |
Intangible assets subject to amortization, beginning balance |  |  | 6,786 |  |
Adjustments related to acquisitions |  |  | 0 |  |
Currency translation during the period |  |  | (523) |  |
Intangible assets subject to amortization, ending balance | 6,263 |  | 6,263 |  |
Accumulated amortization, beginning balance |  |  | 2,062 |  |
Amortization during the period |  |  | 94 |  |
Currency translation during the period |  |  | (64) |  |
Accumulated amortization, ending balance | 2,092 |  | 2,092 |  |
Intangible assets subject to amortization, net as of July 2, 2022 | $ 4,171 |  | $ 4,171 |  |

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- Definition The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 230 -SubTopic 10 -Section 45 -Paragraph 28 -Subparagraph (b) -URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3602-108585 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 50 -Paragraph 2 -Subparagraph (a)(2) -URI https://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 45 -Paragraph 2 -URI https://asc.fasb.org/extlink&oid=6388964&loc=d3e16225-109274 + Details
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