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Goodwill and Acquired Intangibles (Tables)
 12 Months Ended
Jan. 02, 2021
Goodwill and Intangible Assets Disclosure [Abstract]  
Changes in the carrying amount of goodwill
The changes in the carrying amount of goodwill during fiscal 2020 and 2019 were as follows:
 Gross Carrying
Amount
 (In thousands)
Balance as of December 29, 2018$662,272 
Effect of foreign currency translation(416)
Balance as of December 28, 2019661,856 
Goodwill resulting from acquisitions120,564 
Effect of foreign currency translation(333)
Balance as of January 2, 2021$782,087 
Acquired intangibles with finite lives (excluding goodwill), excluding intangibles fully amortized at end of prior fiscal year
Acquired intangibles as of January 2, 2021 were as follows, excluding intangibles that were fully amortized as of December 28, 2019:
Gross Carrying
Amount		Accumulated
Amortization		Acquired
Intangibles, Net
 (In thousands)
Existing technology$370,838 $(230,654)$140,184 
Agreements and relationships180,023 (113,629)66,394 
Tradenames, trademarks and patents10,590 (6,578)4,012 
Total acquired intangibles with definite lives561,451 (350,861)210,590 
Acquired intangibles as of December 28, 2019 were as follows, excluding intangibles that were fully amortized as of December 29, 2018:
Gross Carrying
Amount		Accumulated
Amortization		Acquired
Intangibles, Net
 (In thousands)
Existing technology$363,142 $(245,902)$117,240 
Agreements and relationships146,395 (112,565)33,830 
Tradenames, trademarks and patents7,600 (5,795)1,805 
Total acquired intangibles with definite lives517,137 (364,262)152,875 
In-process technology19,500 — 19,500 
Total acquired intangibles$536,637 $(364,262)$172,375 
Amortization of acquired intangibles Amortization expense for fiscal 2020, 2019 and 2018, by consolidated income statement caption, was as follows:
202020192018
 (In thousands)
Cost of product and maintenance$46,184 $40,951 $39,247 
Amortization of acquired intangibles18,009 12,128 14,086 
Total amortization of acquired intangibles$64,193 $53,079 $53,333 
Estimated amortization expense
As of January 2, 2021, the estimated amortization expense for intangible assets with definite lives was as follows for the following five fiscal years and thereafter:
 (In thousands)
2021$61,706 
202243,401 
202327,870 
202426,408 
202515,767 
Thereafter35,438 
Total estimated amortization expense$210,590