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Share-based compensation - Changes Conditional Shares (Details)
12 Months Ended
Dec. 31, 2023
€ / shares
shares
Dec. 31, 2023
$ / shares
shares
EUR-denominated    
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) 292,765 292,765
Granted (in shares) 244,069 244,069
Vested (in shares) (257,451) (257,451)
Forfeited (in shares) (3,812) (3,812)
Conditional shares outstanding, ending (in shares) 275,571 275,571
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 € 434.10  
Granted (in usd/eur per share) | € / shares 587.42  
Vested (in usd/eur per share) | € / shares 425.34  
Forfeited (in usd/eur per share) | € / shares 557.77  
Conditional shares outstanding, ending (in usd/eur per share) | € / shares € 576.37  
USD-denominated    
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) 238,394 238,394
Granted (in shares) 295,235 295,235
Vested (in shares) (167,746) (167,746)
Forfeited (in shares) (2,764) (2,764)
Conditional shares outstanding, ending (in shares) 363,119 363,119
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   $ 542.22
Granted (in usd/eur per share) | $ / shares   624.10
Vested (in usd/eur per share) | $ / shares   515.96
Forfeited (in usd/eur per share) | $ / shares   622.98
Conditional shares outstanding, ending (in usd/eur per share) | $ / shares   $ 620.31