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Intangible assets, net and goodwill - Narrative (Details)
3 Months Ended 12 Months Ended
Mar. 31, 2023
USD ($)
segment
Mar. 31, 2022
USD ($)
Dec. 31, 2022
USD ($)
Finite-Lived Intangible Assets [Line Items]      
Amortization of intangible assets $ 12,700,000 $ 12,400,000  
Number of operating segments | segment 1    
Goodwill impairment $ 0   $ 0
Capitalized software development costs | Minimum      
Finite-Lived Intangible Assets [Line Items]      
Intangible assets amortization period (in years) 3 years    
Capitalized software development costs | Maximum      
Finite-Lived Intangible Assets [Line Items]      
Intangible assets amortization period (in years) 6 years    
Acquired technology | Minimum      
Finite-Lived Intangible Assets [Line Items]      
Intangible assets amortization period (in years) 5 years    
Acquired technology | Maximum      
Finite-Lived Intangible Assets [Line Items]      
Intangible assets amortization period (in years) 10 years    
Customer relationships | Minimum      
Finite-Lived Intangible Assets [Line Items]      
Intangible assets amortization period (in years) 5 years    
Customer relationships | Maximum      
Finite-Lived Intangible Assets [Line Items]      
Intangible assets amortization period (in years) 10 years    
Other | Minimum      
Finite-Lived Intangible Assets [Line Items]      
Intangible assets amortization period (in years) 5 years    
Other | Maximum      
Finite-Lived Intangible Assets [Line Items]      
Intangible assets amortization period (in years) 10 years    
Patents | Minimum      
Finite-Lived Intangible Assets [Line Items]      
Intangible assets amortization period (in years) 10 years    
Patents | Maximum      
Finite-Lived Intangible Assets [Line Items]      
Intangible assets amortization period (in years) 17 years