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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, 2024 EUR (€) € / shares	Dec. 31, 2024 USD ($) $ / shares	Dec. 31, 2023 EUR (€) € / shares	Dec. 31, 2023 USD ($) $ / shares	Dec. 31, 2022 EUR (€) € / shares	Dec. 31, 2022 USD ($) $ / shares	Dec. 31, 2024 USD ($)	Dec. 31, 2023 USD ($)	Dec. 31, 2022 USD ($)
EUR-denominated
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Weighted average share price at stock option exercise (in usd/eur per share) | € / shares	€ 834.48		€ 613.03		€ 494.14
Aggregate intrinsic value of exercised stock options (in millions) | €	€ 10.2		€ 8.1		€ 4.4
Weighted average remaining contractual term of exercisable options (in years)	9 months 29 days	9 months 29 days	1 year 5 months 23 days	1 year 5 months 23 days	2 years 29 days	2 years 29 days
Aggregate intrinsic value of exercisable stock options (in millions) | €	€ 11.4		€ 19.7		€ 20.3
Aggregate intrinsic value of outstanding stock options (in millions) | €	€ 11.4		€ 19.7		€ 20.3
USD-denominated
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Weighted average share price at stock option exercise (in usd/eur per share) | $ / shares		$ 911.23		$ 678.41		$ 565.39
Aggregate intrinsic value of exercised stock options (in millions) | $		$ 8.2		$ 4.8		$ 1.6
Weighted average remaining contractual term of exercisable options (in years)	10 months 2 days	10 months 2 days	1 year 5 months 4 days	1 year 5 months 4 days	2 years 1 month 2 days	2 years 1 month 2 days
Aggregate intrinsic value of exercisable stock options (in millions) | $							$ 8.2	$ 15.9	$ 14.6
Aggregate intrinsic value of outstanding stock options (in millions) | $							$ 8.2	$ 15.9	$ 14.6

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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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