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Share-based compensation - Stock Options (Details) € / shares in Units, $ / shares in Units, € in Millions, $ in Millions | 12 Months Ended |  |  |
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Dec. 31, 2022 EUR (€) € / shares | Dec. 31, 2022 USD ($) $ / shares | Dec. 31, 2021 EUR (€) € / shares | Dec. 31, 2021 USD ($) $ / shares | Dec. 31, 2020 EUR (€) € / shares | Dec. 31, 2020 USD ($) $ / shares | Dec. 31, 2022 USD ($) | Dec. 31, 2021 USD ($) | Dec. 31, 2020 USD ($)
EUR-denominated Option Awards |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Weighted average share price at the exercise date of stock options (in usd/eur per share) | € / shares | € 494.14 |  | € 583.33 |  | € 302.20 |  |  |  |
Aggregate intrinsic value of stock options exercised (in millions) | € | € 4.4 |  | € 5.7 |  | € 4.8 |  |  |  |
Weighted average remaining contractual term of currently exercisable options (in years) | 2 years 29 days | 2 years 29 days | 2 years 9 months 21 days | 2 years 9 months 21 days | 3 years 6 months 18 days | 3 years 6 months 18 days |  |  |
Aggregate intrinsic value of exercisable stock options (in millions) | € | € 20.3 |  | € 36.7 |  | € 22.4 |  |  |  |
Aggregate intrinsic value of outstanding stock options (in millions) | € | € 20.3 |  | € 36.7 |  | € 22.4 |  |  |  |
US-denominated Option Awards |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Weighted average share price at the exercise date of stock options (in usd/eur per share) | $ / shares |  | $ 565.39 |  | $ 658.16 |  | $ 355.44 |  |  |
Aggregate intrinsic value of stock options exercised (in millions) | $ |  | $ 1.6 |  | $ 4.1 |  | $ 3.7 |  |  |
Weighted average remaining contractual term of currently exercisable options (in years) | 2 years 1 month 2 days | 2 years 1 month 2 days | 2 years 11 months 4 days | 2 years 11 months 4 days | 3 years 7 months 28 days | 3 years 7 months 28 days |  |  |
Aggregate intrinsic value of exercisable stock options (in millions) | $ |  |  |  |  |  |  | $ 14.6 | $ 24.9 | $ 16.9
Aggregate intrinsic value of outstanding stock options (in millions) | $ |  |  |  |  |  |  | $ 14.6 | $ 24.9 | $ 16.9

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- Definition Share-based Compensation Arrangements by Share-based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price at Exercise Date + References No definition available. + Details
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- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References No definition available. + Details
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- Definition Amount of accumulated difference between fair value of underlying shares on dates of exercise and exercise price on options exercised (or share units converted) into shares. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (d)(2) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Amount by which the current fair value of the underlying stock exceeds the exercise price of options outstanding. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Amount of difference between fair value of the underlying shares reserved for issuance and exercise price of vested portions of options outstanding and currently exercisable. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Weighted average remaining contractual term for vested portions of options outstanding and currently exercisable or convertible, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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