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Revenues and Accounts Receivable - Schedule of Contract Balances (Details) - USD ($) $ in Thousands	Sep. 30, 2025	Dec. 31, 2024
Revenues And Accounts Receivable [Abstract]
Contract assets	$ 68,743	$ 52,091
Contract liabilities	$ 13,827	$ 9,297

X

- Definition

Revenues and accounts receivable abstract.

+ References

No definition available.

+ Details

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Namespace Prefix:	meg_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

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- Definition

Amount of obligation to transfer good or service to customer for which consideration has been received or is receivable, classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479806/606-10-50-11

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479837/606-10-45-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479806/606-10-50-8

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479837/606-10-45-2

+ Details

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

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- Definition

Amount received for services rendered and products shipped, but not yet billed, for non-contractual agreements due within one year or the normal operating cycle, if longer.

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant