The amount of capital contribution.

No definition available.

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Namespace Prefix:	fact_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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- Definition

Represent the amount of working capital loans.

+ References

No definition available.

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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- Definition

Represent the working capital loans convertible price per share.

+ References

No definition available.

+ Details

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Data Type:	dtr:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
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+ Details

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Balance Type:	na
Period Type:	duration

- Definition

The number of shares under options that were cancelled during the reporting period as a result of occurrence of a terminating event specified in contractual agreements pertaining to the stock option plan.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
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-SubTopic 10
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-Subparagraph (c)(1)(iv)(03)
-Publisher FASB
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+ Details

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Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Maximum number of shares that may be issued in accordance with the plan as a proportion of outstanding capital stock.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
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-Publisher FASB
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- Definition

Number of new stock issued during the period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
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-Subparagraph (SX 210.3-04)
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+ Details

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Balance Type:	na
Period Type:	duration

- Definition

Number of shares of stock issued attributable to transactions classified as other.

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Details

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- Details

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- Details

Name:	srt_TitleOfIndividualAxis=srt_BoardOfDirectorsChairmanMember
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- Details

Name:	us-gaap_StatementClassOfStockAxis=us-gaap_CommonClassBMember
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Balance Type:
Period Type:

- Details

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Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_OverAllotmentOptionMember
Namespace Prefix:
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Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_IPOMember
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Balance Type:
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- Details

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Related Party Transactions (Details) - USD ($)				6 Months Ended
Related Party Transactions (Details) - USD ($)	Jan. 10, 2025	Aug. 06, 2024	Jul. 12, 2024	Jun. 30, 2025
Related Party Transactions [Line Items]
Working capital loans (in Dollars)				$ 2,000,000
Sponsor HoldCo [Member]
Related Party Transactions [Line Items]
Capital contribution (in Dollars)			$ 25,000
Director [Member] \| Sponsor HoldCo [Member]
Related Party Transactions [Line Items]
Shares transferred		30,000
Executive Chairman [Member]
Related Party Transactions [Line Items]
Shares transferred		130,000
Class B Ordinary Shares [Member] \| Sponsor HoldCo [Member]
Related Party Transactions [Line Items]
Number of shares issued			6,708,333
Class A Ordinary Shares [Member]
Related Party Transactions [Line Items]
Working capital loans convertible price per share (in Dollars per share)				$ 10
Over-Allotment Option [Member]
Related Party Transactions [Line Items]
Shares forfeiture	875,000
IPO [Member]
Related Party Transactions [Line Items]
Percentage of issued and outstanding shares	25.00%
Founder Shares [Member]
Related Party Transactions [Line Items]
Shares transferred		220,000