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Intangible Assets, Net | 9 Months Ended | 12 Months Ended
--- | --- | ---
Sep. 30, 2022 | Dec. 31, 2021
Intangible Assets, Net |  |
Intangible Assets, Net | Note 9. Intangible Assets, Net The following table summarizes intangible assets, net as of September 30, 2022 and December 31, 2021: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | September 30, 2022
​ | ​ | ​ | ​ | Accumulated | ​ | ​
(Thousands) |  | Cost |  | Amortization |  | Net
Customer relationships | ​ | $ | 137,500 | ​ | $ | (17,036) | ​ | $ | 120,464
Favorable lease asset | ​ | ​ | 220 | ​ | ​ | (112) | ​ | ​ | 108
Software | ​ | ​ | 890 | ​ | ​ | (513) | ​ | ​ | 377
Intangible assets, net | ​ | $ | 138,610 | ​ | $ | (17,661) | ​ | $ | 120,949
​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | December 31, 2021
​ | ​ | ​ | ​ | Accumulated | ​ | ​
(Thousands) |  | Cost |  | Amortization |  | Net
Customer relationships | ​ | $ | 137,500 | ​ | $ | (12,091) | ​ | $ | 125,409
Favorable lease asset | ​ | ​ | 220 | ​ | ​ | (79) | ​ | ​ | 141
Software | ​ | ​ | 758 | ​ | ​ | (394) | ​ | ​ | 364
Intangible assets, net | ​ | $ | 138,478 | ​ | $ | (12,564) | ​ | $ | 125,914
​ Amortization expense of intangible assets was $1.7 million and $5.0 million for the three and nine months ended September 30, 2022, respectively, and amortization expense of intangible assets was $1.7 million and $5.0 million for the three and nine months ended September 30, 2021, respectively. As of September 30, 2022, the weighted average useful life for definite-lived intangibles is approximately 20 years. | Note 11. Intangible Assets, Net The following table summarizes intangible assets, net as of December 31, 2021 and 2020: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | December 31, 2021
​ | ​ | ​ | ​ | Accumulated | ​ | ​
(Thousands) |  | Cost |  | Amortization |  | Net
Customer relationships | ​ | $ | 137,500 | ​ | $ | (12,091) | ​ | $ | 125,409
Favorable lease asset | ​ | ​ | 220 | ​ | ​ | (79) | ​ | ​ | 141
Software | ​ | ​ | 758 | ​ | ​ | (394) | ​ | ​ | 364
Intangible assets, net | ​ | $ | 138,478 | ​ | $ | (12,564) | ​ | $ | 125,914
​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | December 31, 2020
​ | ​ | ​ | ​ | Accumulated | ​ | ​
(Thousands) |  | Cost |  | Amortization |  | Net
Customer relationships | ​ | $ | 137,500 | ​ | $ | (5,496) | ​ | $ | 132,004
Favorable lease asset | ​ | ​ | 220 | ​ | ​ | (36) | ​ | ​ | 184
Software | ​ | ​ | 436 | ​ | ​ | (285) | ​ | ​ | 151
Intangible assets, net | ​ | $ | 138,156 | ​ | $ | (5,817) | ​ | $ | 132,339
​ Amortization expense of intangible assets was $6.7 million and $5.6 million for the years ended December 31, 2021 and 2020, respectively. As of December 31, 2021, the weighted average useful life for definite-lived intangibles is approximately 20 years. The estimated amortization expense for intangible assets subject to amortization over the next five years is: ​
​ | ​ | ​ | ​
(Thousands) |  | ​ | ​
2022 | ​ | $ | 6,808
2023 | ​ | ​ | 6,712
2024 | ​ | ​ | 6,681
2025 | ​ | ​ | 6,616
2026 | ​ | ​ | 6,606
Thereafter | ​ | ​ | 92,491
Total | ​ | $ | 125,914
​

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