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Other Intangible Assets, Net- Gross carrying amount and accumulated amortization (Details) - USD ($) $ in Thousands | 12 Months Ended |
--- | --- | ---
Dec. 31, 2022 | Jan. 01, 2022
Other Intangible Assets, Net |  |
Gross Amount | $ 212,127 | $ 277,013
Accumulated Amortization | (127,220) | (158,035)
Decrease in gross intangible assets due to the assets were fully amortized | $ 64,900 |
Weighted Average |  |
Other Intangible Assets, Net |  |
Weighted-Average Amortization Period (Years) | 8 years |
Developed technology |  |
Other Intangible Assets, Net |  |
Gross Amount | $ 211,217 | 238,092
Accumulated Amortization | $ (126,424) | (124,337)
Developed technology | Weighted Average |  |
Other Intangible Assets, Net |  |
Weighted-Average Amortization Period (Years) | 8 years |
Trademarks |  |
Other Intangible Assets, Net |  |
Gross Amount | $ 910 | 11,471
Accumulated Amortization | $ (796) | (8,740)
Trademarks | Weighted Average |  |
Other Intangible Assets, Net |  |
Weighted-Average Amortization Period (Years) | 12 years |
Customer relationships |  |
Other Intangible Assets, Net |  |
Gross Amount |  | 27,450
Accumulated Amortization |  | $ (24,958)

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- Definition Accumulated amount of amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 50 -Paragraph 2 -Subparagraph (a)(1) -URI https://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275 Reference 2: 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(16)) -URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682 + Details
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