Defined contribution plan participant's compensation percent.

No definition available.

Name:	meg_DefinedContributionPlanParticipantsCompensationPercent
Namespace Prefix:	meg_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Defined contribution plan percentage of participants elective deferrals.

+ References

No definition available.

+ Details

Name:	meg_DefinedContributionPlanPercentageOfParticipantsElectiveDeferrals
Namespace Prefix:	meg_
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

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 715
-SubTopic 70
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480794/715-70-50-1

+ Details

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

- Definition

Amount of discretionary contributions made by an employer to a defined contribution plan.

+ References

No definition available.

+ Details

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

- Definition

Percentage employer matches of the employee's percentage contribution matched.

+ References

No definition available.

+ Details

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

- Definition

Maximum percentage of employee gross pay the employee may contribute to a defined contribution plan.

+ References

No definition available.

+ Details

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

- Definition

Description of defined contribution pension and other postretirement plans.

+ References

No definition available.

+ Details

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

- Details

Name:	us-gaap_IncomeStatementLocationAxis=us-gaap_SellingGeneralAndAdministrativeExpensesMember
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:

Defined Contribution Plan - Additional Information (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended		12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2023	Sep. 30, 2022	Dec. 31, 2022
Defined Contribution Plan Disclosure [Line Items]
Defined contribution plan, description			401(k) Savings Plan
Defined contribution plan, maximum annual contributions per employee, percent			85.00%		85.00%
Defined contribution plan, employer matching contribution, percent of match			100.00%
Defined contribution plan participant's compensation percent			3.00%
Defined contribution plan percentage of participant's elective deferrals			50.00%
Selling, General and Administrative Expenses
Defined Contribution Plan Disclosure [Line Items]
Defined contribution plan, employer discretionary contribution amount	$ 2.0	$ 1.2	$ 5.9	$ 4.6
Minimum
Defined Contribution Plan Disclosure [Line Items]
Defined contribution plan participant's compensation percent			3.00%
Maximum
Defined Contribution Plan Disclosure [Line Items]
Defined contribution plan participant's compensation percent			5.00%