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Repurchases of Common Shares (Details)
$ / shares in Units, $ in Thousands
 12 Months Ended
Mar. 31, 2023
USD ($)
shares
Mar. 31, 2022
USD ($)
shares
Mar. 31, 2021
USD ($)
shares
May 03, 2023
USD ($)
Mar. 31, 2023
EUR (€)
shares
Mar. 31, 2023
USD ($)
$ / shares
shares
Jun. 02, 2021
$ / shares
Jul. 30, 2019
USD ($)
May 07, 2019
USD ($)
Equity, Class of Treasury Stock [Line Items]                  
Preferred Stock, Shares Authorized         50,000,000 50,000,000      
Preferred Stock, Par or Stated Value Per Share | $ / shares           $ 0.001      
Stock Repurchase Program, Authorized Amount | $       $ 500,000   $ 13,932   $ 300,000 $ 78,979
Stock Repurchased During Period, Shares 1,563,983 108,368 35,000            
Stock Repurchased and Retired During Period, Value | $ $ 295,000 $ 25,000 $ 5,047            
Common Stock, Par or Stated Value Per Share | $ / shares           $ 0.001 $ 0.001    
Deferred Ordinary Shares         25,000 25,000      
Share-based Payment Arrangement, Shares Withheld for Tax Withholding Obligation 79,169 244,395 91,567            
Payment, Tax Withholding, Share-based Payment Arrangement | $ $ 13,534 $ 30,775 $ 9,599            
Euro Member Countries, Euro                  
Equity, Class of Treasury Stock [Line Items]                  
Par Value (Euros) of Deferred Ordinary Shares | €         € 1.00