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Share-based compensation - Stock Options (Details) € / shares in Units, $ / shares in Units, € in Millions, $ in Millions	12 Months Ended
	Dec. 31, 2023 EUR (€) € / shares	Dec. 31, 2023 USD ($) $ / shares	Dec. 31, 2022 EUR (€) € / shares	Dec. 31, 2022 USD ($) $ / shares	Dec. 31, 2021 EUR (€) € / shares	Dec. 31, 2021 USD ($) $ / shares	Dec. 31, 2023 USD ($)	Dec. 31, 2022 USD ($)	Dec. 31, 2021 USD ($)
EUR-denominated
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	€ 613.03		€ 494.14		€ 583.33
Aggregate intrinsic value of stock options exercised (in millions) | €	€ 8.1		€ 4.4		€ 5.7
Weighted average remaining contractual term of currently exercisable options (in years)	1 year 5 months 23 days	1 year 5 months 23 days	2 years 29 days	2 years 29 days	2 years 9 months 21 days	2 years 9 months 21 days
Aggregate intrinsic value of exercisable stock options (in millions) | €	€ 19.7		€ 20.3		€ 36.7
Aggregate intrinsic value of outstanding stock options (in millions) | €	€ 19.7		€ 20.3		€ 36.7
USD-denominated
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		$ 678.41		$ 565.39		$ 658.16
Aggregate intrinsic value of stock options exercised (in millions) | $		$ 4.8		$ 1.6		$ 4.1
Weighted average remaining contractual term of currently exercisable options (in years)	1 year 5 months 4 days	1 year 5 months 4 days	2 years 1 month 2 days	2 years 1 month 2 days	2 years 11 months 4 days	2 years 11 months 4 days
Aggregate intrinsic value of exercisable stock options (in millions) | $							$ 15.9	$ 14.6	$ 24.9
Aggregate intrinsic value of outstanding stock options (in millions) | $							$ 15.9	$ 14.6	$ 24.9

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Share-Based Compensation Arrangements by Share-based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price at Exercise Date

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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.

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Amount by which the current fair value of the underlying stock exceeds the exercise price of options outstanding.

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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.

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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.

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