Revenues and Accounts Receivable - Additional Information (Details) - USD ($) $ in Millions	12 Months Ended
Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2021
Accounts Notes And Loans Receivable [Line Items]
Contracts assets acquired through business acquisitions	$ 2.2	$ 1.7
Contract liabilities acquired through business acquisitions	0.0	0.0
Contract with customer liabilities, revenue recognized	14.4
Revenue remaining performance obligations	$ 81.9	$ 100.4
Customer Concentration Risk \| Revenue \| Customer One
Accounts Notes And Loans Receivable [Line Items]
Concentration risk percentage	10.00%	14.40%	10.00%
Customer Concentration Risk \| Accounts Receivable \| Significant Customer
Accounts Notes And Loans Receivable [Line Items]
Concentration risk percentage	10.00%	10.00%

Contracts with customer assets acquired through business acquisitions.

No definition available.

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

- Definition

Contracts with customer liabilities acquired through business acquisitions.

+ References

No definition available.

+ Details

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

- Definition

For an entity that discloses a concentration risk in relation to quantitative amount, which serves as the "benchmark" (or denominator) in the equation, this concept represents the concentration percentage derived from the division.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 280
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 42
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482810/280-10-50-42

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 21
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482907/825-10-50-21

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 20
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482907/825-10-50-20

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 275
-SubTopic 10
-Section 50
-Paragraph 18
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482861/275-10-50-18

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 275
-SubTopic 10
-Section 50
-Paragraph 20
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482861/275-10-50-20

+ Details

Name:	us-gaap_ConcentrationRiskPercentage1
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of revenue recognized that was previously included in balance of obligation to transfer good or service to customer for which consideration from customer has been received or is due.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479806/606-10-50-8

+ Details

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

- Definition

Amount of transaction price allocated to performance obligation that has not been recognized as revenue.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 13
-Subparagraph (a)
-SubTopic 10
-Topic 606
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479806/606-10-50-13

+ Details

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

- Details

Name:	us-gaap_ConcentrationRiskByTypeAxis=us-gaap_CustomerConcentrationRiskMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ConcentrationRiskByBenchmarkAxis=us-gaap_RevenueFromContractWithCustomerMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_MajorCustomersAxis=meg_CustomerOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ConcentrationRiskByBenchmarkAxis=us-gaap_AccountsReceivableMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_MajorCustomersAxis=meg_SignificantCustomerMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: