Consolidated Balance Sheets (Parentheticals) - $ / shares	Dec. 31, 2022	Dec. 31, 2021
Preference shares, par value (in Dollars per share)	$ 0.0001	$ 0.0001
Preference shares, shares authorized	1,000,000	1,000,000
Preference shares, shares issued
Preference shares, shares outstanding
Class A Ordinary Shares
Ordinary shares subject to possible redemption	34,500,000	34,500,000
Ordinary shares, par value (in Dollars per share)	$ 0.0001	$ 0.0001
Ordinary shares, shares authorized	200,000,000	200,000,000
Ordinary shares, shares outstanding	34,500,000	34,500,000
Class B Ordinary Shares
Ordinary shares, par value (in Dollars per share)	$ 0.0001	$ 0.0001
Ordinary shares, shares authorized	20,000,000	20,000,000
Ordinary shares, shares issued	8,625,000	8,625,000
Ordinary shares, shares outstanding	8,625,000	8,625,000

Shares subject to possible redemption.

No definition available.

Name:	fact_SharesSubjectToPossibleRedemption
Namespace Prefix:	fact_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Face amount or stated value per share of common stock.

+ References

+ Details

Name:	us-gaap_CommonStockParOrStatedValuePerShare
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

The maximum number of common shares permitted to be issued by an entity's charter and bylaws.

+ References

+ Details

Name:	us-gaap_CommonStockSharesAuthorized
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Total number of common shares of an entity that have been sold or granted to shareholders (includes common shares that were issued, repurchased and remain in the treasury). These shares represent capital invested by the firm's shareholders and owners, and may be all or only a portion of the number of shares authorized. Shares issued include shares outstanding and shares held in the treasury.

+ References

+ Details

Name:	us-gaap_CommonStockSharesIssued
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of shares of common stock outstanding. Common stock represent the ownership interest in a corporation.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 50
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=126973232&loc=d3e21463-112644

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_CommonStockSharesOutstanding
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Face amount or stated value per share of preferred stock nonredeemable or redeemable solely at the option of the issuer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(28))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 50
-Paragraph 13
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=126973232&loc=SL123496158-112644

+ Details

Name:	us-gaap_PreferredStockParOrStatedValuePerShare
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

The maximum number of nonredeemable preferred shares (or preferred stock redeemable solely at the option of the issuer) permitted to be issued by an entity's charter and bylaws.

+ References

+ Details

Name:	us-gaap_PreferredStockSharesAuthorized
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Total number of nonredeemable preferred shares (or preferred stock redeemable solely at the option of the issuer) issued to shareholders (includes related preferred shares that were issued, repurchased, and remain in the treasury). May be all or portion of the number of preferred shares authorized. Excludes preferred shares that are classified as debt.

+ References

+ Details

Name:	us-gaap_PreferredStockSharesIssued
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Aggregate share number for all nonredeemable preferred stock (or preferred stock redeemable solely at the option of the issuer) held by stockholders. Does not include preferred shares that have been repurchased.

+ References

+ Details

Name:	us-gaap_PreferredStockSharesOutstanding
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_StatementClassOfStockAxis=us-gaap_CommonClassAMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementClassOfStockAxis=us-gaap_CommonClassBMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: