Share-based compensation - Changes Conditional Shares (Details)	12 Months Ended
Dec. 31, 2022 € / shares shares	Dec. 31, 2022 $ / shares shares
EUR-denominated Conditional Awards
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number of Shares [Roll Forward]
Conditional shares outstanding, beginning (in shares)	452,205	452,205
Granted (in shares)	88,432	88,432
Vested (in shares)	(239,685)	(239,685)
Forfeited (in shares)	(8,187)	(8,187)
Conditional shares outstanding, ending (in shares)	292,765	292,765
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value [Abstract]
Conditional shares outstanding, beginning (in usd/eur per share) \| € / shares	€ 303.32
Granted (in usd/eur per share) \| € / shares	578.65
Vested (in usd/eur per share) \| € / shares	247.17
Forfeited (in usd/eur per share) \| € / shares	239.82
Conditional shares outstanding, ending (in usd/eur per share) \| € / shares	€ 434.10
US-denominated Conditional Awards
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number of Shares [Roll Forward]
Conditional shares outstanding, beginning (in shares)	297,001	297,001
Granted (in shares)	230,568	230,568
Vested (in shares)	(273,861)	(273,861)
Forfeited (in shares)	(15,314)	(15,314)
Conditional shares outstanding, ending (in shares)	238,394	238,394
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value [Abstract]
Conditional shares outstanding, beginning (in usd/eur per share) \| $ / shares		$ 416.07
Granted (in usd/eur per share) \| $ / shares		553.61
Vested (in usd/eur per share) \| $ / shares		418.03
Forfeited (in usd/eur per share) \| $ / shares		487.93
Conditional shares outstanding, ending (in usd/eur per share) \| $ / shares		$ 542.22

The number of equity-based payment instruments, excluding stock (or unit) options, that were forfeited during the reporting period.

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- Definition

Weighted average fair value as of the grant date of equity-based award plans other than stock (unit) option plans that were not exercised or put into effect as a result of the occurrence of a terminating event.

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The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

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The weighted average fair value at grant date for nonvested equity-based awards issued during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

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- Definition

The number of non-vested equity-based payment instruments, excluding stock (or unit) options, that validly exist and are outstanding as of the balance sheet date.

+ 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 (c)(2)(ii)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(i)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

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- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

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- Definition

Per share or unit weighted-average fair value of nonvested award under share-based payment arrangement. Excludes share and unit options.

+ 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 (c)(2)(i)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(ii)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

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- References

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- Definition

The number of equity-based payment instruments, excluding stock (or unit) options, that vested during the reporting period.

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+ Details

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- Definition

The weighted average fair value as of grant date pertaining to an equity-based award plan other than a stock (or unit) option plan for which the grantee gained the right during the reporting period, by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash in accordance with the terms of the arrangement.

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