Accrued Payroll and Benefits - Schedule of Accrued Payroll and Benefits (Details) - USD ($) $ in Thousands	Dec. 31, 2023	Dec. 31, 2022
Statement of Financial Position [Abstract]
Accrued bonuses	$ 18,453	$ 8,624
Accrued paid time off	1,316	1,088
Accrued payroll	11,814	8,410
Accrued other	3,077	2,406
Total accrued payroll and benefits	$ 34,660	$ 20,528

Accrued paid time off.

No definition available.

Name:	meg_AccruedPaidTimeOff
Namespace Prefix:	meg_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Carrying value as of the balance sheet date of obligations incurred and payable for incentive compensation awarded to employees and directors or earned by them based on the terms of one or more relevant arrangements. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.20)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

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

- Definition

Carrying value as of the balance sheet date of obligations, excluding pension and other postretirement benefits, incurred through that date and payable for perquisites provided to employees pertaining to services received from them. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ References

+ Details

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

- Definition

Carrying value as of the balance sheet date of obligations incurred and payable for statutory payroll taxes incurred through that date and withheld from employees pertaining to services received from them, including entity's matching share of the employees FICA taxes and contributions to the state and federal unemployment insurance programs. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ References

+ Details

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

- Definition

Amount of expenses incurred but not yet paid classified as other, due within one year or the normal operating cycle, if longer.

+ References

+ Details

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

- References

No definition available.

+ Details

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