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Goodwill and Other Intangible Assets (Tables) | 12 Months Ended
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Dec. 31, 2018
Goodwill and Intangible Assets Disclosure [Abstract] |
Schedule of Goodwill | The changes in the net carrying amount of goodwill for the years ended December 31, are as follows:
| 2018 |  | 2017
Balance as of January 1, | $ | 401,954 |  |  | $ | 397,664 |
Goodwill resulting from business combinations | — |  |  | 2,209 |
Foreign currency translation | (1,514 | ) |  | 2,081 |
Balance as of December 31, | $ | 400,440 |  |  | $ | 401,954 |
Schedule of Finite-Lived and Indefinite-Lived Intangible Assets | Other intangible assets consist of the following:
| December 31, 2018 |  | December 31, 2017
| Weighted Average Amortization Period (Years) | Gross Carrying Amount |  | Accumulated Amortization |  | Gross Carrying Amount |  | Accumulated Amortization
Intangible assets with definite lives: |  |  |  |  |  |  |  |
Customer and distributor relationships | 29 | $ | 214,577 |  |  | $ | (97,131 | ) |  | $ | 214,685 |  |  | $ | (86,137 | )
Sales representation, marketing and promotional rights | 25 | 149,376 |  |  | (42,000 | ) |  | 149,376 |  |  | (36,000 | )
Patents and other intangible assets | 14 | 61,473 |  |  | (44,242 | ) |  | 69,668 |  |  | (42,127 | )
Developed technology | 16 | 91,965 |  |  | (7,369 | ) |  | 62,283 |  |  | (3,352 | )
Intangible assets with indefinite lives: |  |  |  |  |  |  |  |  |  |  |  |
Trademarks and tradenames |  | 86,544 |  |  | — |  |  | 86,544 |  |  | — |
| 24 | $ | 603,935 |  |  | $ | (190,742 | ) |  | $ | 582,556 |  |  | $ | (167,616 | )
Schedule of Estimated Amortization Expense | The estimated amortization expense related to intangible assets at December 31, 2018 and for each of the five succeeding years is as follows:
| Amortization included in expense |  | Amortization recorded as a reduction of revenue |  | Total
2019 | 17,978 |  |  | 6,000 |  |  | $ | 23,978 |
2020 | 17,995 |  |  | 6,000 |  |  | $ | 23,995 |
2021 | 17,042 |  |  | 6,000 |  |  | $ | 23,042 |
2022 | 15,583 |  |  | 6,000 |  |  | $ | 21,583 |
2023 | 14,879 |  |  | 6,000 |  |  | $ | 20,879 |

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