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Goodwill and Acquired Intangibles (Details 1) - USD ($) $ in Thousands | Oct. 02, 2021 | Jan. 02, 2021
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Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year |  |
Gross carrying amount | $ 618,835 | $ 561,451
Accumulated amortization | (371,207) | (350,861)
Total estimated amortization expense | 247,628 | 210,590
Existing Technology [Member] |  |
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year |  |
Gross carrying amount | 402,640 | 370,838
Accumulated amortization | (242,829) | (230,654)
Total estimated amortization expense | 159,811 | 140,184
Agreements and Relationships [Member] |  |
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year |  |
Gross carrying amount | 205,454 | 180,023
Accumulated amortization | (125,436) | (113,629)
Total estimated amortization expense | 80,018 | 66,394
Tradenames Trademarks And Patents [Member] |  |
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year |  |
Gross carrying amount | 10,741 | 10,590
Accumulated amortization | (2,942) | (6,578)
Total estimated amortization expense | $ 7,799 | $ 4,012

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