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Stock-Based Compensation - Employee Stock Purchase Plan (Details) - shares | 9 Months Ended
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Jun. 30, 2022 | Jun. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |
Shares issued under employee stock purchase plan (in shares) | 51,133 | 58,124
Employee Stock |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |
Purchase price of common stock (as a percent) | 85.00% |

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