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Share-based compensation - Outstanding Stock Options (Details) - 12 months ended Dec. 31, 2022
€ / shares
shares
$ / shares
shares
EUR-denominated Option Awards    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Number of outstanding options, Range of exercise prices (in shares) 47,607 47,607
Weighted average remaining contractual life of outstanding (years) 2 years 29 days 2 years 29 days
EUR-denominated Option Awards | Price Range Three    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Range of exercise prices, lower limit (in usd/eur per share) | € / shares € 50  
Range of exercise prices, upper limit (in usd/eur per share) | € / shares € 60  
Number of outstanding options, Range of exercise prices (in shares) 5,268 5,268
Weighted average remaining contractual life of outstanding (years) 11 months 15 days 11 months 15 days
EUR-denominated Option Awards | Price Range Four    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Range of exercise prices, lower limit (in usd/eur per share) | € / shares € 60  
Range of exercise prices, upper limit (in usd/eur per share) | € / shares € 70  
Number of outstanding options, Range of exercise prices (in shares) 10,773 10,773
Weighted average remaining contractual life of outstanding (years) 11 months 15 days 11 months 15 days
EUR-denominated Option Awards | Price Range Five    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Range of exercise prices, lower limit (in usd/eur per share) | € / shares € 70  
Range of exercise prices, upper limit (in usd/eur per share) | € / shares € 80  
Number of outstanding options, Range of exercise prices (in shares) 10,109 10,109
Weighted average remaining contractual life of outstanding (years) 2 years 4 months 6 days 2 years 4 months 6 days
EUR-denominated Option Awards | Price Range Six    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Range of exercise prices, lower limit (in usd/eur per share) | € / shares € 80  
Range of exercise prices, upper limit (in usd/eur per share) | € / shares € 90  
Number of outstanding options, Range of exercise prices (in shares) 10,791 10,791
Weighted average remaining contractual life of outstanding (years) 2 years 9 months 29 days 2 years 9 months 29 days
EUR-denominated Option Awards | Price Range Seven    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Range of exercise prices, lower limit (in usd/eur per share) | € / shares € 90  
Range of exercise prices, upper limit (in usd/eur per share) | € / shares € 100  
Number of outstanding options, Range of exercise prices (in shares) 10,666 10,666
Weighted average remaining contractual life of outstanding (years) 2 years 8 months 23 days 2 years 8 months 23 days
EUR-denominated Option Awards | Price Range Eight    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Range of exercise prices, lower limit (in usd/eur per share) | € / shares € 100  
Range of exercise prices, upper limit (in usd/eur per share) | € / shares € 110  
Number of outstanding options, Range of exercise prices (in shares) 0 0
Weighted average remaining contractual life of outstanding (years) 0 years 0 years
US-denominated Option Awards    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Number of outstanding options, Range of exercise prices (in shares) 32,138 32,138
Weighted average remaining contractual life of outstanding (years) 2 years 1 month 2 days 2 years 1 month 2 days
US-denominated Option Awards | Price Range Three    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Range of exercise prices, lower limit (in usd/eur per share) | $ / shares   $ 50
Range of exercise prices, upper limit (in usd/eur per share) | $ / shares   $ 60
Number of outstanding options, Range of exercise prices (in shares) 0 0
Weighted average remaining contractual life of outstanding (years) 0 years 0 years
US-denominated Option Awards | Price Range Four    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Range of exercise prices, lower limit (in usd/eur per share) | $ / shares   $ 60
Range of exercise prices, upper limit (in usd/eur per share) | $ / shares   $ 70
Number of outstanding options, Range of exercise prices (in shares) 278 278
Weighted average remaining contractual life of outstanding (years) 21 days 21 days
US-denominated Option Awards | Price Range Five    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Range of exercise prices, lower limit (in usd/eur per share) | $ / shares   $ 70
Range of exercise prices, upper limit (in usd/eur per share) | $ / shares   $ 80
Number of outstanding options, Range of exercise prices (in shares) 828 828
Weighted average remaining contractual life of outstanding (years) 3 months 18 days 3 months 18 days
US-denominated Option Awards | Price Range Six    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Range of exercise prices, lower limit (in usd/eur per share) | $ / shares   $ 80
Range of exercise prices, upper limit (in usd/eur per share) | $ / shares   $ 90
Number of outstanding options, Range of exercise prices (in shares) 8,855 8,855
Weighted average remaining contractual life of outstanding (years) 1 year 10 months 24 days 1 year 10 months 24 days
US-denominated Option Awards | Price Range Seven    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Range of exercise prices, lower limit (in usd/eur per share) | $ / shares   $ 90
Range of exercise prices, upper limit (in usd/eur per share) | $ / shares   $ 100
Number of outstanding options, Range of exercise prices (in shares) 15,308 15,308
Weighted average remaining contractual life of outstanding (years) 2 years 18 days 2 years 18 days
US-denominated Option Awards | Price Range Eight    
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]    
Range of exercise prices, lower limit (in usd/eur per share) | $ / shares   $ 100
Range of exercise prices, upper limit (in usd/eur per share) | $ / shares   $ 110
Number of outstanding options, Range of exercise prices (in shares) 6,869 6,869
Weighted average remaining contractual life of outstanding (years) 2 years 8 months 26 days 2 years 8 months 26 days