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Share-Based Compensation Share-Based Compensation (Details) - USD ($)
$ / shares in Units, $ in Thousands
6 Months Ended
Sep. 30, 2020
Sep. 30, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Item]    
Remaining shares available for grant 3,568,985  
Weighted-average assumptions used for options granted:    
Risk-free interest rate 0.46% 2.26%
Expected life of options 6 years 6 years 2 months 12 days
Exptected dividend yield of stock 0.96% 1.22%
Expected volatility of stock 23.04% 20.27%
Estimated forfeiture rate 2.78% 2.77%
Summary of share option activity:    
Outstanding at March 31, 2017 1,796,126  
Granted 288,936  
Exercised (292,199)  
Forfeited (32,002)  
Outstanding at June 30, 2017 1,760,861  
Exercisable at June 30, 2017 988,477  
Weighted average exercise price:    
Outstanding at March 31, 2017 $ 91.29  
Granted 181.33  
Exercised 71.96  
Forfeited 121.80  
Outstanding at June 30, 2017 108.72  
Exercisable at June 30, 2017 $ 80.98  
Average Remaining Contractual Term, Outstanding at June 30, 2017 7 years  
Aggregate Intrinsic Value, Outstanding at June 30, 2017 $ 120,484  
Average Remaining Contractual Term, Exercisable at June 30, 2017 5 years 8 months 12 days  
Aggregate Intrinsic Value, Exercisable at June 30, 2017 $ 94,113  
Non-vested stock options outstanding expected to vest 749,747  
Ordinary shares, closing price $ 176.19  
Total intrinsic value of stock options exercised $ 25,244 $ 35,886
Net cash proceeds from the exercise of stock options $ 20,600 $ 22,371
Weighted average grant date fair value of stock option grants, per share $ 27.66 $ 23.52
Summary of non-vested restricted share activity:    
Unrecognized compensation cost related to nonvested share-based compensation granted $ 57,787  
Weighted Average Period For Total Compensation Expense Not Yet Recognized 2 years 3 months 18 days  
Stock Appreciation Rights (SARs) [Member]    
Weighted average exercise price:    
FairValueOfOutstandingStockAppreciationRights $ 448 $ 587
Restricted Stock    
Summary of non-vested restricted share activity:    
Number of Restricted Shares, Non-vested at Beginning of Period 575,830  
Weighted-Average Grant Date Fair Value, Non-vested at Beginning of Period $ 98.07  
Number of Restricted Shares, Granted 137,385  
Weighted-Average Grant Date Fair Value, Granted $ 164.45  
Number of Restricted Shares, Vested (156,390)  
Weighted-Average Grant Date Fair Value, Vested $ 84.64  
Number of Restricted Shares, Canceled (15,430)  
Weighted-Average Grant Date Fair Value, Canceled $ 102.07  
Number of Restricted Shares, Non-vested at End of Period 541,395  
Weighted-Average Grant Date Fair Value, Non-vested at End of Period $ 119.72  
Fair Value, Share-based Payment Awards, Other than Options $ 14,604  
Restricted Stock Units (RSUs)    
Summary of non-vested restricted share activity:    
Number of Restricted Shares, Non-vested at Beginning of Period 30,894  
Number of Restricted Shares, Granted 14,124  
Number of Restricted Shares, Vested (16,150)  
Number of Restricted Shares, Canceled 0  
Number of Restricted Shares, Non-vested at End of Period 28,868