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Fair Value Measurements - Additional Information (Details) $ in Millions, $ in Millions	Feb. 12, 2025 USD ($)	Oct. 04, 2024 USD ($)	Apr. 03, 2023 USD ($)	Apr. 03, 2023 CAD ($)	Jan. 03, 2023 USD ($)
Deist
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Contingent consideration maximum	$ 7.5
Blasters [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Contingent consideration maximum					$ 6.2
Trackless
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Contingent consideration maximum			$ 4.2	$ 6.0
Standard
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Contingent consideration maximum		$ 4.8
Hog
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Contingent consideration maximum	15.0
Initial cash consideration paid for acquisition	$ 82.1

X

- Definition

For contingent consideration arrangements recognized in connection with a business combination, this element represents an estimate of the high-end of the potential range (undiscounted) of the consideration which may be paid.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 50
-Paragraph 1
-Subparagraph (c)(3)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479581/805-30-50-1

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-3

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

The cash outflow associated with the acquisition of business during the period. The cash portion only of the acquisition price.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479581/805-30-50-1

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 13
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482740/230-10-45-13

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Details

Name:	us-gaap_BusinessAcquisitionAxis=fss_DeistMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_BusinessAcquisitionAxis=fss_BlastersMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_BusinessAcquisitionAxis=fss_TracklessMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_BusinessAcquisitionAxis=fss_StandardMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_BusinessAcquisitionAxis=fss_HogMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: