Effective income tax rate reconciliation cost of debt percentage.

No definition available.

Name:	fath_EffectiveIncomeTaxRateReconciliationCostOfDebtPercentage
Namespace Prefix:	fath_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Income tax reconciliation taxable income forecast.

+ References

No definition available.

+ Details

Name:	fath_IncomeTaxReconciliationTaxableIncomeForecast
Namespace Prefix:	fath_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Sale of stock price percentage.

+ References

No definition available.

+ Details

Name:	fath_SaleOfStockPricePercentage
Namespace Prefix:	fath_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Value of input used to measure contingent consideration liability from business combination.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)
-URI http://asc.fasb.org/extlink&oid=123874694&loc=d3e19207-110258

+ Details

Name:	us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput
Namespace Prefix:	us-gaap_
Data Type:	xbrli:decimalItemType
Balance Type:	na
Period Type:	instant

- Definition

Percentage of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32687-109319

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateContinuingOperations
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to noncontrolling interest income (loss) exempt from income taxes.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 6.I.Fact.4)
-URI http://asc.fasb.org/extlink&oid=122134291&loc=d3e330036-122817

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32687-109319

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationMinorityInterestIncomeExpense
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- 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

No definition available.

+ Details

Name:	us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to nondeductible amortization.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32687-109319

+ Details

Name:	us-gaap_IncomeTaxReconciliationNondeductibleExpenseAmortization
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Per share amount received by subsidiary or equity investee for each share of common stock issued or sold in the stock transaction.

+ References

No definition available.

+ Details

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

- Definition

The estimated measure of the percentage by which a share price is expected to fluctuate during a period. Volatility also may be defined as a probability-weighted measure of the dispersion of returns about the mean. The volatility of a share price is the standard deviation of the continuously compounded rates of return on the share over a specified period. That is the same as the standard deviation of the differences in the natural logarithms of the stock prices plus dividends, if any, over the period.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

The risk-free interest rate assumption that is used in valuing an option on its own shares.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Expected term of award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (f)(2)(i)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 14.D.2)
-URI http://asc.fasb.org/extlink&oid=122041274&loc=d3e301413-122809

+ Details

Name:	us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Value of input used to measure outstanding warrant and right embodying unconditional obligation requiring redemption by transferring asset at specified or determinable date or upon event certain to occur.

+ References

+ Details

Name:	us-gaap_WarrantsAndRightsOutstandingMeasurementInput
Namespace Prefix:	us-gaap_
Data Type:	xbrli:decimalItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_FairValueByLiabilityClassAxis=fath_TaxReceivableAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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

- Details

Name:	us-gaap_FairValueByLiabilityClassAxis=fath_EarnoutSharesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_MeasurementInputTypeAxis=us-gaap_MeasurementInputExercisePriceMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=fath_PrivatePlacementWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_MeasurementInputTypeAxis=us-gaap_MeasurementInputExpectedTermMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_MeasurementInputTypeAxis=us-gaap_MeasurementInputPriceVolatilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_MeasurementInputTypeAxis=fath_OperatingAssetVolatilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_MeasurementInputTypeAxis=fath_EquityVolatilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Fair Value Measurement - Additional Information (Details) $ / shares in Units, $ in Thousands	3 Months Ended
	Mar. 31, 2022 USD ($) yr $ / shares	Mar. 31, 2021	Dec. 31, 2021
Fair Value Balance Sheet Grouping Financial Statement Captions [Line Items]
Corporate tax rate	2.48%	1.91%
Tax Receivable Agreement [Member]
Fair Value Balance Sheet Grouping Financial Statement Captions [Line Items]
Corporate tax rate	26.90%
Non-controlling interest percentage	37.60%
Initial amortization deductions	$ 52,400
Taxable income forecast	$ 126,000
Tax Receivable Agreement [Member] \| Class A Common Stock [Member]
Fair Value Balance Sheet Grouping Financial Statement Captions [Line Items]
Business combination contingent consideration liability measurement input	85.9
Stock price, per share \| $ / shares	$ 6.18
Sale of stock price percentage	25.00%
Earnout Shares [Member]
Fair Value Balance Sheet Grouping Financial Statement Captions [Line Items]
Expected term	5 years
Risk-free interest rate	1.25%
Strike Price [Member] \| Private Placement Warrants [Member]
Fair Value Balance Sheet Grouping Financial Statement Captions [Line Items]
Fair value measurements	11.50
Expected Term [Member] \| Private Placement Warrants [Member]
Fair Value Balance Sheet Grouping Financial Statement Captions [Line Items]
Fair value measurements \| yr	5.0
Volatility [Member] \| Private Placement Warrants [Member]
Fair Value Balance Sheet Grouping Financial Statement Captions [Line Items]
Fair value measurements			25
Operating Asset Volatility [Member] \| Earnout Shares [Member]
Fair Value Balance Sheet Grouping Financial Statement Captions [Line Items]
Volatility	87.60%
Equity Volatility [Member] \| Earnout Shares [Member]
Fair Value Balance Sheet Grouping Financial Statement Captions [Line Items]
Volatility	91.70%
Minimum [Member] \| Tax Receivable Agreement [Member] \| Class A Common Stock [Member]
Fair Value Balance Sheet Grouping Financial Statement Captions [Line Items]
Cost of debt percentage	5.60%
Maximum [Member] \| Tax Receivable Agreement [Member] \| Class A Common Stock [Member]
Fair Value Balance Sheet Grouping Financial Statement Captions [Line Items]
Cost of debt percentage	9.40%