Note 3 - Business Combination - Restructuring Activity (Details) - USD ($) $ in Thousands	3 Months Ended
Jan. 02, 2021	Dec. 28, 2019
Liability balance	$ 171
Restructuring charges	657	$ 0
Cash payments	(777)
Non-cash charges	(4)
Liability balance	47
Employee Severance [Member]
Liability balance	0
Restructuring charges	13
Cash payments	(13)
Non-cash charges	0
Liability balance	0
Equipment Relocation [Member]
Liability balance	20
Restructuring charges	88
Cash payments	(95)
Non-cash charges	0
Liability balance	13
Facility Closing [Member]
Liability balance	151
Restructuring charges	552
Cash payments	(669)
Non-cash charges	0
Liability balance	34
Asset Impairments [Member]
Liability balance	0
Restructuring charges	4
Cash payments	0
Non-cash charges	(4)
Liability balance	$ 0

Amount of cash payments made as the result of exit or disposal activities. Excludes payments associated with a discontinued operation or an asset retirement obligation.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-URI http://asc.fasb.org/extlink&oid=6394359&loc=d3e17939-110869

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 17
-Subparagraph (f)
-URI http://asc.fasb.org/extlink&oid=121586364&loc=d3e3367-108585

+ Details

Name:	us-gaap_PaymentsForRestructuring
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of expenses associated with exit or disposal activities pursuant to an authorized plan. Excludes expenses related to a discontinued operation or an asset retirement obligation.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 5.P.3)
-URI http://asc.fasb.org/extlink&oid=115931487&loc=d3e140864-122747

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=6394359&loc=d3e17939-110869

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121586364&loc=d3e3602-108585

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.P.4(b))
-URI http://asc.fasb.org/extlink&oid=115931487&loc=d3e140904-122747

+ Details

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

- Definition

Carrying amount (including both current and noncurrent portions of the accrual) as of the balance sheet date pertaining to a specified type of cost associated with exit from or disposal of business activities or restructuring pursuant to a duly authorized plan.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-URI http://asc.fasb.org/extlink&oid=6394359&loc=d3e17939-110869

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SAB TOPIC 5.P.4(b))
-URI http://asc.fasb.org/extlink&oid=115931487&loc=d3e140904-122747

+ Details

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

- Definition

Amount of decrease in the reserve for full or partial settlement through consideration other than cash.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SAB TOPIC 5.P.4(b)(2))
-URI http://asc.fasb.org/extlink&oid=115931487&loc=d3e140904-122747

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=6394359&loc=d3e17939-110869

+ Details

Name:	us-gaap_RestructuringReserveSettledWithoutCash2
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Details

Name:	us-gaap_RestructuringCostAndReserveAxis=us-gaap_EmployeeSeveranceMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RestructuringCostAndReserveAxis=iiin_EquipmentRelocationMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RestructuringCostAndReserveAxis=us-gaap_FacilityClosingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RestructuringCostAndReserveAxis=iiin_AssetImpairmentsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: