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Segment and Geographic Information - Summary of Revenue and Profit Attributable to Our Operating Segments (Parenthetical) (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2020
Segment Reporting Revenue Reconciling Item [Line Items] |  |  |
Depreciation and amortization | $ 87,694 | $ 85,239 | $ 80,817
Unallocated |  |  |
Segment Reporting Revenue Reconciling Item [Line Items] |  |  |
Depreciation and amortization | 21,400 | 21,000 | 19,400
Software Products | Operating Segments |  |  |
Segment Reporting Revenue Reconciling Item [Line Items] |  |  |
Depreciation and amortization | 4,900 | 4,000 | 4,200
Professional Services | Operating Segments |  |  |
Segment Reporting Revenue Reconciling Item [Line Items] |  |  |
Depreciation and amortization | $ 900 | $ 1,100 | $ 1,100

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