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INTANGIBLE ASSETS: (Tables) | 12 Months Ended
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Dec. 31, 2019
INTANGIBLE ASSETS: |
Schedule of major classes of intangible assets and goodwill | ​
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | At December 31,
(in millions) |  | 2019 |  | 2018
Mining concessions | ​ | $ | 121.2 | ​ | $ | 121.2
Mine engineering and development studies | ​ |  | 19.8 | ​ |  | 19.8
Software | ​ |  | 55.9 | ​ |  | 49.6
​ | ​ |  | 196.9 | ​ |  | 190.6
Accumulated amortization: | ​ |  | ​ | ​ | ​ | ​
Mining concessions | ​ | ​ | (38.0) | ​ | ​ | (37.4)
Mine engineering and development studies | ​ | ​ | (16.3) | ​ | ​ | (15.3)
Software | ​ | ​ | (36.1) | ​ | ​ | (32.1)
​ | ​ | ​ | (90.4) | ​ | ​ | (84.8)
Goodwill | ​ |  | 41.9 | ​ |  | 41.9
Intangible assets, net | ​ | $ | 148.4 | ​ | $ | 147.7
Schedule of estimated amortization of intangible assets for future periods | ​
​ | ​ | ​ | ​
Estimated amortization expense (in millions): |  | ​ | ​
2020 | ​ | $ | 9.6
2021 | ​ | ​ | 5.5
2022 | ​ | ​ | 5.6
2023 | ​ | ​ | 5.5
2024 | ​ | ​ | 4.3
Total 2020 - 2024 | ​ | $ | 30.5
Average annual | ​ | $ | 6.1

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