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v3.25.1

Note 9 - Employee Benefit Plans (Details Textual) | 6 Months Ended
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Mar. 29, 2025
Supplemental Employee Retirement Plan [Member] |
Supplemental Retirement Benefit Period | 15 years
Defined Benefit Plan Percent of Highest Average Salary Base | 50.00%
Defined Benefit Plan Number of Years in Average Annual Base Salary (Year) | 5 years
Defined Benefit Plan Number of Years Preceding Retirement for Average Annual Base Salary Calculation (Year) | 10 years
Supplemental Employee Retirement Plan [Member] | Minimum [Member] |
Defined Benefit Plan, Employment Term (Year) | 30 years
Reduced SERP [Member] |
Defined Benefit Plan Retirement Age | 55
Defined Benefit Plan, Reduction for Each Month | 0.28%
Reduced SERP [Member] | Minimum [Member] |
Defined Benefit Plan, Employment Term (Year) | 10 years

X
- Definition The number of years of continuous service required to receive the maximum benefit under the SERP. + References No definition available. + Details
Name: | iiin_DefinedBenefitPlanEmploymentTerm
Namespace Prefix: | iiin_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

X
- Definition The number of consecutive years used to determine a Participant's highest average annual base salary in a supplemental employee retirement plan. + References No definition available. + Details
Name: | iiin_DefinedBenefitPlanNumberOfYearsInAverageAnnualBaseSalary
Namespace Prefix: | iiin_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

X
- Definition Defined benefit plan number of years preceding retirement for average annual base salary calculation + References No definition available. + Details
Name: | iiin_DefinedBenefitPlanNumberOfYearsPrecedingRetirementForAverageAnnualBaseSalaryCalculation
Namespace Prefix: | iiin_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

X
- Definition The percentage of a Participant's highest average base salary that will be paid out to the Participant as supplemental retirement benefits if they meet the continuous service requirement. + References No definition available. + Details
Name: | iiin_DefinedBenefitPlanPercentOfHighestAverageSalaryBase
Namespace Prefix: | iiin_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | duration

X
- Definition The benefit will be reduced by a certain percentage for each month short of 30 years that the Participant was employed by the Company assuming the minimum continuous service and age requirements. + References No definition available. + Details
Name: | iiin_DefinedBenefitPlanReductionForEachMonth
Namespace Prefix: | iiin_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | instant

X
- Definition The minimum age that an employee may retire at to receive benefits. + References No definition available. + Details
Name: | iiin_DefinedBenefitPlanRetirementAge
Namespace Prefix: | iiin_
Data Type: | xbrli:integerItemType
Balance Type: | na
Period Type: | duration

X
- Definition The maximum period of time that a Participant will be paid supplemental retirement benefits if they are eligible for full benefits. + References No definition available. + Details
Name: | iiin_SupplementalRetirementBenefitPeriod
Namespace Prefix: | iiin_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

X
- Details
Name: | us-gaap_RetirementPlanTypeAxis=us-gaap_SupplementalEmployeeRetirementPlanDefinedBenefitMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_RangeAxis=srt_MinimumMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_RetirementPlanTypeAxis=iiin_ReducedSERPMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |