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Note 5 - Fair Value Measurements (Details Textual) - USD ($) $ in Thousands | Apr. 02, 2022 | Oct. 02, 2021
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Non Financial [Member] | Fair Value, Nonrecurring [Member] |  |
Assets, Fair Value Disclosure | $ 0 | $ 0

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- Definition Fair value portion of probable future economic benefits obtained or controlled by an entity as a result of past transactions or events. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 820 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (a) -URI http://asc.fasb.org/extlink&oid=123874694&loc=d3e19207-110258 + Details
Name: | us-gaap_AssetsFairValueDisclosure
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant

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- Details
Name: | us-gaap_FairValueByAssetClassAxis=iiin_NonFinancialMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | us-gaap_FairValueByMeasurementFrequencyAxis=us-gaap_FairValueMeasurementsNonrecurringMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |