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Note 13 - Leases (Details Textual) - USD ($) $ in Millions | 12 Months Ended
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Sep. 30, 2023 | Oct. 01, 2022 | Oct. 02, 2021
Operating Lease, Term Required to be Recorded on the Balance Sheet, Threshold (Month) | 12 months |  |
Operating Lease, Expense | $ 1.3 | $ 1.4 | $ 1.4

X
- Definition Represents minimum lease term required for operating lease to be recorded on the balance sheet. + References No definition available. + Details
Name: | iiin_OperatingLeaseTermRequiredToBeRecordedOnTheBalanceSheetThreshold
Namespace Prefix: | iiin_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

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- Definition Amount of operating lease expense. Excludes sublease income. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 842 -SubTopic 20 -Name Accounting Standards Codification -Section 45 -Paragraph 4 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org//1943274/2147479041/842-20-45-4 + Details
Name: | us-gaap_OperatingLeaseExpense
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration