Amount of expense for award under share-based payment arrangement. Excludes amount capitalized.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 14.F)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479830/718-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (h)(1)(i)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

+ Details

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

- Definition

Weighted-average period over which cost not yet recognized is expected to be recognized for award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (i)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of cost to be recognized for nonvested award under share-based payment arrangement. Excludes share and unit options.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (i)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

+ Details

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

- Definition

Amount of cost to be recognized for option under share-based payment arrangement.

+ References

+ Details

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

- Definition

Period over which grantee's right to exercise award under share-based payment arrangement is no longer contingent on satisfaction of service or performance condition, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. Includes, but is not limited to, combination of market, performance or service condition.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of additional shares authorized for issuance under share-based payment arrangement.

+ References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

The difference between the maximum number of shares (or other type of equity) authorized for issuance under the plan (including the effects of amendments and adjustments), and the sum of: 1) the number of shares (or other type of equity) already issued upon exercise of options or other equity-based awards under the plan; and 2) shares (or other type of equity) reserved for issuance on granting of outstanding awards, net of cancellations and forfeitures, if applicable.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

The weighted average grant-date fair value of options granted during the reporting period as calculated by applying the disclosed option pricing methodology.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (d)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Period from grant date that an equity-based award expires, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

+ Details

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

- Details

Name:	us-gaap_AwardTypeAxis=us-gaap_EmployeeStockOptionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=us-gaap_RestrictedStockUnitsRSUMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_TitleOfIndividualAxis=srt_DirectorMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_TitleOfIndividualAxis=iiin_EmployeesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_PlanNameAxis=iiin_The2015EquityIncentivePlanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Note 9 - Stock-based Compensation (Details Textual) - USD ($)		12 Months Ended
	Feb. 11, 2020	Sep. 30, 2023	Oct. 01, 2022	Oct. 02, 2021
Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Weighted Average Grant Date Fair Value		$ 13.27	$ 14.67	$ 14.47
Share-Based Payment Arrangement, Option [Member]
Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period		3 years
Share-Based Compensation Arrangement by Share-Based Payment Award, Expiration Period		10 years
Share-Based Payment Arrangement, Expense		$ 1,000,000.0	$ 1,100,000	$ 860,000
Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount		$ 731,000
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition		2 years 1 month 17 days
Restricted Stock Units (RSUs) [Member]
Share-Based Payment Arrangement, Expense		$ 1,392,000	$ 1,365,000	$ 1,128,000
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition		1 year 8 months 15 days
Share-Based Payment Arrangement, Nonvested Award, Excluding Option, Cost Not yet Recognized, Amount		$ 1,100,000
Restricted Stock Units (RSUs) [Member] \| Director [Member]
Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period		1 year
Restricted Stock Units (RSUs) [Member] \| Employees [Member]
Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period		3 years
The 2015 Equity Incentive Plan [Member]
Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Additional Shares Authorized	750,000
Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant		430,000