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Note 7 - Real Estate - Real Estate Disclosure (Details) - USD ($)	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
Net Realizable Value at beginning of period	$ 48,270,000	$ 36,201,270
Increase (decrease) in net realizable value	(9,220,000)	12,068,730
Net Realizable Value on December 31,	39,050,000	48,270,000
Cortlandt Manor Medical Center [Member]
Increase (decrease) in net realizable value	(3,820,000)	2,010,000
Flowerfield Properties, Inc. [Member]
Increase (decrease) in net realizable value	$ (5,400,000)	$ 10,058,730

X

- Definition

Amount of increase (decrease) before accumulated depreciation of investments in land and buildings held for sale, excluding real estate considered to be inventory of the entity.

+ References

No definition available.

+ Details

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Namespace Prefix:	gyro_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Carrying amount as of the balance sheet date of investments in land and buildings held for sale, excluding real estate considered to be inventory of the entity.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03.1(f))
-URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910

+ Details

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

X

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_LongLivedAssetsHeldForSaleByAssetTypeAxis=gyro_FlowerfieldPropertiesIncMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: