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Goodwill and Acquired Intangibles (Tables)
 6 Months Ended
Jul. 03, 2021
Goodwill and Intangible Assets Disclosure [Abstract]  
Changes in the carrying amount of goodwill
The changes in the carrying amount of goodwill during the six months ended July 3, 2021 were as follows:
 Gross Carrying
Amount
 (In thousands)
Balance as of January 2, 2021$782,087 
Goodwill resulting from acquisitions150,021 
Effect of foreign currency translation(2,583)
Balance as of July 3, 2021$929,525 
Schedule of acquired intangibles with finite and indefinite lives (excluding goodwill)
Acquired intangibles as of July 3, 2021 were as follows, excluding intangibles that were fully amortized as of January 2, 2021:
Gross Carrying
Amount		Accumulated
Amortization		Acquired
Intangibles, Net
 (In thousands)
Existing technology$402,440 $(231,006)$171,434 
Agreements and relationships205,928 (120,674)85,254 
Tradenames, trademarks and patents10,830 (2,729)8,101 
Total acquired intangibles$619,198 $(354,409)$264,789 
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 lives$561,451 $(350,861)$210,590 
Amortization of acquired intangibles Amortization expense for the three and six months ended July 3, 2021 and June 27, 2020 by condensed consolidated income statement caption was as follows:
 Three Months Ended Six Months Ended
 July 3,
2021		June 27,
2020		July 3,
2021		June 27,
2020
 (In thousands)
Cost of product and maintenance$12,232 $11,484 $24,000 $22,344 
Amortization of acquired intangibles5,030 4,590 9,661 8,796 
Total amortization of acquired intangibles$17,262 $16,074 $33,661 $31,140 
Estimated amortization expense
As of July 3, 2021, the estimated amortization expense for acquired intangible assets with definite lives was as follows for the following five fiscal years and thereafter:
 (In thousands)
2021 - remaining period$33,316 
202249,716 
202334,186 
202432,723 
202522,204 
Thereafter92,644 
Total estimated amortization expense$264,789