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Description of the business and summary of significant accounting policies: - Revenue recognition (Details) - USD ($) $ in Millions | 12 Months Ended
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Dec. 31, 2024 | Dec. 31, 2023 | Dec. 31, 2022
Description of the business and summary of significant accounting policies: |  |  |
Contract costs | $ 31.9 | $ 24.3 |
Maximum contract lengths for billing due upon receipts (in months) | 60 months |  |
Service revenue recognized from deferred revenue balance at beginning of period | $ 6.5 | 4.9 | $ 5.0
Amortization expense for contract costs | $ 20.6 | $ 19.3 | $ 19.4

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- Definition Amount of amortization expense for asset recognized from cost incurred to obtain or fulfill contract with customer. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 340 -SubTopic 40 -Name Accounting Standards Codification -Section 50 -Paragraph 3 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479483/340-40-50-3 + Details
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- Definition Amount, after accumulated amortization and accumulated impairment loss, of asset recognized from cost incurred to obtain or fulfill contract with customer. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 340 -SubTopic 40 -Name Accounting Standards Codification -Section 50 -Paragraph 3 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479483/340-40-50-3 + Details
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- Definition Amount of revenue recognized that was previously included in balance of obligation to transfer good or service to customer for which consideration from customer has been received or is due. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 606 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 8 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479806/606-10-50-8 + Details
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