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Income taxes - Changes in Uncertain Tax Positions (Detail) - USD ($) $ in Millions | 12 Months Ended
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Dec. 31, 2023 | Dec. 31, 2022 | Dec. 31, 2021
Unrecognized tax benefits: |  |  |
Amount at beginning of year | $ 3.5 | $ 6.4 | $ 9.6
Net increase (decrease): |  |  |
Tax positions taken in current period | 0.5 | 0.7 | 0.6
Lapse due to applicable statute of limitations | (1.2) | (3.4) | (3.6)
Changes in currency exchange rates |  | (0.2) | (0.2)
Amount at end of year | $ 2.8 | $ 3.5 | $ 6.4

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- Definition Amount of unrecognized tax benefits. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 15A -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org//1943274/2147482685/740-10-50-15A Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 45 -Paragraph 10B -Publisher FASB -URI https://asc.fasb.org//1943274/2147482525/740-10-45-10B + Details
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- Definition Amount of increase in unrecognized tax benefits resulting from tax positions that have been or will be taken in current period tax return. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 15A -Subparagraph (a)(2) -Publisher FASB -URI https://asc.fasb.org//1943274/2147482685/740-10-50-15A + Details
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- Definition Amount of decrease in unrecognized tax benefits resulting from lapses of applicable statutes of limitations. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 15A -Subparagraph (a)(4) -Publisher FASB -URI https://asc.fasb.org//1943274/2147482685/740-10-50-15A + Details
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