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Goodwill and Intangible Assets (Tables) | 12 Months Ended
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Dec. 31, 2020
Goodwill and Intangible Assets |
Schedule of changes in goodwill | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | Gross carrying |  | Accumulated |  | ​
​ | ​ | amount | ​ | impairment | ​ | Net amount
​ |  | (in thousands)
Balance at December 31, 2018 | ​ | $ | 430,331 | ​ | $ | 246,029 | ​ | $ | 184,302
Allocated to Assets held for sale | ​ | ​ | — | ​ | ​ | 2,359 | ​ | ​ | (2,359)
Balance at December 31, 2019 and 2020 | ​ | ​ | 430,331 | ​ | ​ | 248,388 | ​ | ​ | 181,943
Schedule of intangible assets excluding goodwill | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | ​ | ​ | December 31, 2020 | ​ | December 31, 2019
​ | ​ | Average | ​ | ​ | ​ | ​ | Accumulated | ​ | ​ | ​ | ​ | ​ | ​ | ​ | Accumulated | ​ | ​ | ​
​ |  | Remaining |  | Gross |  | Amortization |  | ​ |  | Gross |  | Amortization |  | ​
​ | ​ | Amortization | ​ | Carrying | ​ | and | ​ | Net | ​ | Carrying | ​ | and | ​ | Net
​ | ​ | Period | ​ | Amount | ​ | Impairment | ​ | Amount | ​ | Amount | ​ | Impairment | ​ | Amount
​ | ​ | (in years) | ​ | (in thousands)
Technology | ​ | 4.6 | ​ | $ | 327,908 | ​ | $ | 302,358 | ​ | $ | 25,550 | ​ | $ | 327,908 | ​ | $ | 291,766 | ​ | $ | 36,142
Customer relationships | ​ | 8.2 | ​ | ​ | 146,465 | ​ | ​ | 130,131 | ​ | ​ | 16,334 | ​ | ​ | 146,465 | ​ | ​ | 126,764 | ​ | ​ | 19,701
Trademarks and tradenames | ​ | 3.5 | ​ | ​ | 30,910 | ​ | ​ | 26,614 | ​ | ​ | 4,296 | ​ | ​ | 30,910 | ​ | ​ | 25,256 | ​ | ​ | 5,654
Other | ​ | 0.8 | ​ |  | 3,686 | ​ |  | 3,681 | ​ |  | 5 | ​ |  | 3,686 | ​ |  | 3,665 | ​ |  | 21
Total | ​ | 5.8 | ​ | $ | 508,969 | ​ | $ | 462,784 | ​ | $ | 46,185 | ​ | $ | 508,969 | ​ | $ | 447,451 | ​ | $ | 61,518
Schedule of estimated annual amortization expense, excluding in-process R&D for intangible assets with definite useful lives | ​
​ | ​ | ​ | ​
​ | ​ | Amortization
​ |  | (in thousands)
2021 | ​ | $ | 12,280
2022 | ​ |  | 10,018
2023 | ​ |  | 8,347
2024 | ​ |  | 6,708
2025 | ​ |  | 3,136
Thereafter | ​ | ​ | 5,696
Total | ​ | $ | 46,185

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