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Accrued Payroll and Benefits - Schedule of Accrued Payroll and Benefits (Details) - USD ($) $ in Thousands	Sep. 30, 2025	Dec. 31, 2024
Statement of Financial Position [Abstract]
Accrued bonuses	$ 23,502	$ 14,433
Accrued paid time off	4,595	4,214
Accrued payroll	12,145	11,969
Accrued other	6,057	3,632
Total accrued payroll and benefits	$ 46,299	$ 34,248

X

- Definition

Accrued paid time off.

+ References

No definition available.

+ Details

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

X

- 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
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(20))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

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

X

- 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

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(20))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

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

X

- 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

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-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_AccruedPayrollTaxesCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

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

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(20))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

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

X

- References

No definition available.

+ Details

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