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Balance Type:	debit
Period Type:	instant

Amount of rent expense for master lease contingent on vacancies.

No definition available.

Name:	gyro_LeaseAndRentalExpenseContingentOnVacancies
Namespace Prefix:	gyro_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

The amount of cash paid for lease and rental contingency on vacancies.

No definition available.

Name:	gyro_PaymentsForLeaseAndRentalContingencyOnVacancies
Namespace Prefix:	gyro_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

Area of land held.

No definition available.

Name:	us-gaap_AreaOfLand
Namespace Prefix:	us-gaap_
Data Type:	num:areaItemType
Balance Type:	na
Period Type:	instant

Area of a real estate property.

No definition available.

Name:	us-gaap_AreaOfRealEstateProperty
Namespace Prefix:	us-gaap_
Data Type:	num:areaItemType
Balance Type:	na
Period Type:	instant

Amount classified as property, plant and equipment attributable to disposal group held for sale or disposed of.

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 205
-SubTopic 20
-Section 50
-Paragraph 5B
-Subparagraph (e)
-URI http://asc.fasb.org/extlink&oid=64827811&loc=SL51721673-107760

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 205
-SubTopic 20
-Section 45
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=65878427&loc=d3e1107-107759

Reference 3: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 50
-Paragraph 3
-Subparagraph (e)
-URI http://asc.fasb.org/extlink&oid=64862545&loc=d3e2941-110230

Reference 4: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 205
-SubTopic 20
-Section 45
-Paragraph 11
-URI http://asc.fasb.org/extlink&oid=65878427&loc=SL51721533-107759

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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

A deposit made by a purchaser of real estate to evidence good faith. It is customary for a buyer to give the seller earnest money at the time a sales contract is signed. The earnest money generally is credited to the down payment at closing, which is applied at closing as a component of payment against the purchase price.

No definition available.

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

Term of the lessee's leasing arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

No definition available.

Name:	us-gaap_LesseeLeasingArrangementsOperatingLeasesTermOfContract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

The number of units in a real estate property owned as of the balance sheet date.

No definition available.

Name:	us-gaap_NumberOfUnitsInRealEstateProperty
Namespace Prefix:	us-gaap_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

Name:	us-gaap_LongLivedAssetsHeldForSaleByAssetTypeAxis=gyro_PortJeffersonProfessionalParkMember
Namespace Prefix:
Data Type:	na
Balance Type:
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Name:	us-gaap_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis=gyro_MedicalOfficeParkMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	dei_LegalEntityAxis=gyro_ControlledByParentCompanyMember
Namespace Prefix:
Data Type:	na
Balance Type:
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Name:	us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis=gyro_FairfaxMedicalCenterMember
Namespace Prefix:
Data Type:	na
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Name:	us-gaap_CounterpartyNameAxis=gyro_JAGMember
Namespace Prefix:
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