Fair Value of Financial Instruments - Summary of Financial Instruments Measured at Fair Value on Recurring Basis (Details) - Fair Value, Recurring - Level 3 - USD ($) $ in Thousands	9 Months Ended
Sep. 30, 2021	Sep. 30, 2020
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Beginning balance	$ 75,353	$ 32,971
Series A-2 compound embedded option		(9,361)
Issuance of warrant option		30,097
Acquisitions	7,004	45,204
Changes in fair value included in earnings	25,686	34,879
Payment of contingent consideration payable	(50,154)	(12,464)
Foreign currency translation of contingent consideration payment		(208)
Write off of the contingent put option		12,140
Exercise of warrant options		(56,287)
Ending balance	57,889	76,971
Contingent Put Option
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Beginning balance		7,100
Changes in fair value included in earnings		(19,240)
Write off of the contingent put option		12,140
Compound Embedded Option
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Series A-2 compound embedded option		(9,361)
Changes in fair value included in earnings		27,420
Ending balance		18,059
Business Acquisitions Contingent Consideration, Current
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Beginning balance	49,902	8,614
Acquisitions	1,000	34,661
Changes in fair value included in earnings	13,774	18,387
Payment of contingent consideration payable	(50,154)	(12,464)
Foreign currency translation of contingent consideration payment		(208)
Reclass of long term to short term contingent liabilities	16,630	180
Ending balance	31,152	49,170
Business Acquisitions Contingent Consideration, Long-Term
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Beginning balance	4,565	379
Acquisitions	6,004	10,543
Changes in fair value included in earnings	10,261	(1,000)
Reclass of long term to short term contingent liabilities	(16,630)	(180)
Ending balance	4,200	9,742
Conversion Option
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Beginning balance	20,886
Changes in fair value included in earnings	1,651
Ending balance	$ 22,537
Warrant Option
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Beginning balance		16,878
Issuance of warrant option		30,097
Changes in fair value included in earnings		9,312
Exercise of warrant options		$ (56,287)

Fair value measurement with unobservable inputs reconciliation recurring basis liability exercise of warrant options.

No definition available.

Name:	meg_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityExerciseOfWarrantOptions
Namespace Prefix:	meg_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Fair value measurement with unobservable inputs reconciliation recurring basis liability foreign currency translation of contingent consideration payment.

+ References

No definition available.

+ Details

Name:	meg_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityForeignCurrencyTranslationOfContingentConsiderationPayment
Namespace Prefix:	meg_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Fair value measurement with unobservable inputs reconciliation recurring basis liability reclass of long term to short term contingent liabilities.

+ References

No definition available.

+ Details

Name:	meg_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityReclassOfLongTermToShortTermContingentLiabilities
Namespace Prefix:	meg_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Fair value measurement with unobservable inputs reconciliation recurring basis liability series a 2 compound embedded option.

+ References

No definition available.

+ Details

Name:	meg_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySeriesA2CompoundEmbeddedOption
Namespace Prefix:	meg_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Fair value measurement with unobservable inputs reconciliation recurring basis liability write off of contingent put option.

+ References

No definition available.

+ Details

Name:	meg_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityWriteOffOfContingentPutOption
Namespace Prefix:	meg_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of gain (loss) recognized in income from liability measured at fair value on recurring basis using unobservable input (level 3).

+ 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 (c)(1)
-URI http://asc.fasb.org/extlink&oid=123874694&loc=d3e19207-110258

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of issuances of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)
-URI http://asc.fasb.org/extlink&oid=123874694&loc=d3e19207-110258

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of purchases of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of settlements of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

+ Details

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

- Definition

Fair value of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=123874694&loc=d3e19207-110258

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	us-gaap_FairValueByMeasurementFrequencyAxis=us-gaap_FairValueMeasurementsRecurringMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel3Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_OptionIndexedToIssuersEquityTypeAxis=us-gaap_PutOptionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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

- Details

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

- Details

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

- Details

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

- Details

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