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Note 13 - Leases (Details Textual) - USD ($) $ in Millions	12 Months Ended
	Sep. 28, 2024	Sep. 30, 2023	Oct. 01, 2022
Operating Lease, Term Required to be Recorded on the Balance Sheet, Threshold (Month)	12 months
Operating Lease, Expense	$ 1.3	$ 1.3	$ 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

X

- 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