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Commitments and contingencies (Tables) | 12 Months Ended
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Dec. 31, 2024
Commitments and contingencies: |
Schedule of future minimum annual payments under operating leases, network equipment sites and data center facilities | The Company enters into service agreements related to network equipment sites and for data center facilities. Future minimum annual payments under these arrangements are as follows (in thousands): ​
​ | ​ | ​ | ​
For the year ending December 31, |  | ​ | ​
2025 | ​ | $ | 41,100
2026 | ​ |  | 19,296
2027 | ​ |  | 11,206
2028 | ​ | ​ | 4,407
2029 | ​ |  | 1,100
Thereafter | ​ |  | 477
​ | ​ | $ | 77,586

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- Definition Tabular disclosure of undiscounted cash flows of lessee's operating lease liability. Includes, but is not limited to, reconciliation of undiscounted cash flows to operating lease liability recognized in statement of financial position. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 842 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 6 -Publisher FASB -URI https://asc.fasb.org/1943274/2147478964/842-20-50-6 + Details
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