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Goodwill and Other Intangible Assets - Finite-Lived Intangible Assets (Details) - USD ($)
$ in Thousands
Jun. 30, 2023
Sep. 30, 2022
Finite-Lived Intangible Assets [Line Items]    
Gross Amount $ 2,666,224 $ 2,608,324
Accumulated Amortization (584,258) (494,598)
Net Amount 2,081,966 2,113,726
Customer relationship assets    
Finite-Lived Intangible Assets [Line Items]    
Gross Amount 1,504,999 1,474,588
Accumulated Amortization (570,553) (487,877)
Net Amount 934,446 986,711
Trade names    
Finite-Lived Intangible Assets [Line Items]    
Gross Amount 1,161,225 1,133,736
Accumulated Amortization (13,705) (6,721)
Net Amount $ 1,147,520 $ 1,127,015