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Equity (Tables) | 12 Months Ended
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Dec. 31, 2022
Equity [Abstract] |
Schedule of Share Repurchase Activity Table Text Block | A summary of the stock repurchase activity under the Repurchase Program, is summarized as follows (in thousands, except share and per share amounts):
|  | Successor |
|  | Year Ended December 31, 2022 |
Shares repurchased |  |  | 4,670,975 |
Average price per share |  | $ | 12.94 |
Costs recorded to accumulated deficit |  |  |
Total repurchase costs |  | $ | 60,438 |
Additional associated costs |  |  | 92 |
Total costs recorded to accumulated deficit |  | $ | 60,530 |

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- Definition Schedule of share repurchase activity table text block. + References No definition available. + Details
Name: | fa_ScheduleOfShareRepurchaseActivityTableTextBlock
Namespace Prefix: | fa_
Data Type: | dtr-types:textBlockItemType
Balance Type: | na
Period Type: | duration

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- References No definition available. + Details
Name: | us-gaap_EquityAbstract
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration