<?xml version='1.0' encoding='utf-8'?>
<FilingSummary>
  <Version>3.23.2</Version>
  <ProcessingTime/>
  <ReportFormat>html</ReportFormat>
  <ContextCount>514</ContextCount>
  <ElementCount>368</ElementCount>
  <EntityCount>1</EntityCount>
  <FootnotesReported>false</FootnotesReported>
  <SegmentCount>124</SegmentCount>
  <ScenarioCount>0</ScenarioCount>
  <TuplesReported>false</TuplesReported>
  <UnitCount>12</UnitCount>
  <MyReports>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R1.htm</HtmlFileName>
      <LongName>0000001 - Document - Cover page</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/Coverpage</Role>
      <ShortName>Cover page</ShortName>
      <MenuCategory>Cover</MenuCategory>
      <Position>1</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R2.htm</HtmlFileName>
      <LongName>0000002 - Statement - CONSOLIDATED BALANCE SHEETS</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/CONSOLIDATEDBALANCESHEETS</Role>
      <ShortName>CONSOLIDATED BALANCE SHEETS</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>2</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R3.htm</HtmlFileName>
      <LongName>0000003 - Statement - CONSOLIDATED BALANCE SHEETS (Parenthetical)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/CONSOLIDATEDBALANCESHEETSParenthetical</Role>
      <ShortName>CONSOLIDATED BALANCE SHEETS (Parenthetical)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>3</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R4.htm</HtmlFileName>
      <LongName>0000004 - Statement - CONSOLIDATED AND COMBINED CONSOLIDATED STATEMENTS OF OPERATIONS (unaudited)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/CONSOLIDATEDANDCOMBINEDCONSOLIDATEDSTATEMENTSOFOPERATIONSunaudited</Role>
      <ShortName>CONSOLIDATED AND COMBINED CONSOLIDATED STATEMENTS OF OPERATIONS (unaudited)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>4</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R5.htm</HtmlFileName>
      <LongName>0000005 - Statement - CONSOLIDATED AND COMBINED CONSOLIDATED STATEMENTS OF COMPREHENSIVE LOSS (unaudited)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/CONSOLIDATEDANDCOMBINEDCONSOLIDATEDSTATEMENTSOFCOMPREHENSIVELOSSunaudited</Role>
      <ShortName>CONSOLIDATED AND COMBINED CONSOLIDATED STATEMENTS OF COMPREHENSIVE LOSS (unaudited)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>5</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R6.htm</HtmlFileName>
      <LongName>0000006 - Statement - CONSOLIDATED AND COMBINED CONSOLIDATED STATEMENT OF CHANGES IN EQUITY (unaudited)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/CONSOLIDATEDANDCOMBINEDCONSOLIDATEDSTATEMENTOFCHANGESINEQUITYunaudited</Role>
      <ShortName>CONSOLIDATED AND COMBINED CONSOLIDATED STATEMENT OF CHANGES IN EQUITY (unaudited)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>6</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R7.htm</HtmlFileName>
      <LongName>0000007 - Statement - CONSOLIDATED AND CONSOLIDATED STATEMENTS OF CASH FLOWS (unaudited)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/CONSOLIDATEDANDCONSOLIDATEDSTATEMENTSOFCASHFLOWSunaudited</Role>
      <ShortName>CONSOLIDATED AND CONSOLIDATED STATEMENTS OF CASH FLOWS (unaudited)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>7</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R8.htm</HtmlFileName>
      <LongName>0000008 - Disclosure - ORGANIZATION</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/ORGANIZATION</Role>
      <ShortName>ORGANIZATION</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>8</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R9.htm</HtmlFileName>
      <LongName>0000009 - Disclosure - BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/BASISOFPRESENTATIONANDSUMMARYOFSIGNIFICANTACCOUNTINGPOLICIES</Role>
      <ShortName>BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>9</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R10.htm</HtmlFileName>
      <LongName>0000010 - Disclosure - LEASING EQUIPMENT, NET</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/LEASINGEQUIPMENTNET</Role>
      <ShortName>LEASING EQUIPMENT, NET</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>10</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R11.htm</HtmlFileName>
      <LongName>0000011 - Disclosure - PROPERTY, PLANT AND EQUIPMENT, NET</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/PROPERTYPLANTANDEQUIPMENTNET</Role>
      <ShortName>PROPERTY, PLANT AND EQUIPMENT, NET</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>11</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R12.htm</HtmlFileName>
      <LongName>0000012 - Disclosure - INVESTMENTS</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INVESTMENTS</Role>
      <ShortName>INVESTMENTS</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>12</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R13.htm</HtmlFileName>
      <LongName>0000013 - Disclosure - INTANGIBLE ASSETS, NET</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INTANGIBLEASSETSNET</Role>
      <ShortName>INTANGIBLE ASSETS, NET</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>13</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R14.htm</HtmlFileName>
      <LongName>0000014 - Disclosure - DEBT, NET</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/DEBTNET</Role>
      <ShortName>DEBT, NET</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>14</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R15.htm</HtmlFileName>
      <LongName>0000015 - Disclosure - FAIR VALUE MEASUREMENTS</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/FAIRVALUEMEASUREMENTS</Role>
      <ShortName>FAIR VALUE MEASUREMENTS</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>15</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R16.htm</HtmlFileName>
      <LongName>0000016 - Disclosure - REVENUES</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/REVENUES</Role>
      <ShortName>REVENUES</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>16</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R17.htm</HtmlFileName>
      <LongName>0000017 - Disclosure - EQUITY-BASED COMPENSATION</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/EQUITYBASEDCOMPENSATION</Role>
      <ShortName>EQUITY-BASED COMPENSATION</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>17</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R18.htm</HtmlFileName>
      <LongName>0000018 - Disclosure - RETIREMENT BENEFIT PLANS</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/RETIREMENTBENEFITPLANS</Role>
      <ShortName>RETIREMENT BENEFIT PLANS</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>18</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R19.htm</HtmlFileName>
      <LongName>0000019 - Disclosure - INCOME TAXES</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INCOMETAXES</Role>
      <ShortName>INCOME TAXES</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>19</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R20.htm</HtmlFileName>
      <LongName>0000020 - Disclosure - MANAGEMENT AGREEMENT AND AFFILIATE TRANSACTIONS</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/MANAGEMENTAGREEMENTANDAFFILIATETRANSACTIONS</Role>
      <ShortName>MANAGEMENT AGREEMENT AND AFFILIATE TRANSACTIONS</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>20</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R21.htm</HtmlFileName>
      <LongName>0000021 - Disclosure - SEGMENT INFORMATION</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/SEGMENTINFORMATION</Role>
      <ShortName>SEGMENT INFORMATION</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>21</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R22.htm</HtmlFileName>
      <LongName>0000022 - Disclosure - REDEEMABLE PREFERRED STOCK</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/REDEEMABLEPREFERREDSTOCK</Role>
      <ShortName>REDEEMABLE PREFERRED STOCK</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>22</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R23.htm</HtmlFileName>
      <LongName>0000023 - Disclosure - EARNINGS PER SHARE AND EQUITY</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/EARNINGSPERSHAREANDEQUITY</Role>
      <ShortName>EARNINGS PER SHARE AND EQUITY</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>23</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R24.htm</HtmlFileName>
      <LongName>0000024 - Disclosure - COMMITMENTS AND CONTINGENCIES</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/COMMITMENTSANDCONTINGENCIES</Role>
      <ShortName>COMMITMENTS AND CONTINGENCIES</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>24</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R25.htm</HtmlFileName>
      <LongName>0000025 - Disclosure - SUBSEQUENT EVENTS</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/SUBSEQUENTEVENTS</Role>
      <ShortName>SUBSEQUENT EVENTS</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>25</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R26.htm</HtmlFileName>
      <LongName>9954701 - Disclosure - BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES (Policies)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/BASISOFPRESENTATIONANDSUMMARYOFSIGNIFICANTACCOUNTINGPOLICIESPolicies</Role>
      <ShortName>BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES (Policies)</ShortName>
      <MenuCategory>Policies</MenuCategory>
      <Position>26</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R27.htm</HtmlFileName>
      <LongName>9954702 - Disclosure - BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/BASISOFPRESENTATIONANDSUMMARYOFSIGNIFICANTACCOUNTINGPOLICIESTables</Role>
      <ShortName>BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/BASISOFPRESENTATIONANDSUMMARYOFSIGNIFICANTACCOUNTINGPOLICIES</ParentRole>
      <Position>27</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R28.htm</HtmlFileName>
      <LongName>9954703 - Disclosure - LEASING EQUIPMENT, NET (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/LEASINGEQUIPMENTNETTables</Role>
      <ShortName>LEASING EQUIPMENT, NET (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/LEASINGEQUIPMENTNET</ParentRole>
      <Position>28</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R29.htm</HtmlFileName>
      <LongName>9954704 - Disclosure - PROPERTY, PLANT AND EQUIPMENT, NET (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/PROPERTYPLANTANDEQUIPMENTNETTables</Role>
      <ShortName>PROPERTY, PLANT AND EQUIPMENT, NET (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/PROPERTYPLANTANDEQUIPMENTNET</ParentRole>
      <Position>29</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R30.htm</HtmlFileName>
      <LongName>9954705 - Disclosure - INVESTMENTS (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INVESTMENTSTables</Role>
      <ShortName>INVESTMENTS (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/INVESTMENTS</ParentRole>
      <Position>30</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R31.htm</HtmlFileName>
      <LongName>9954706 - Disclosure - INTANGIBLE ASSETS, NET (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INTANGIBLEASSETSNETTables</Role>
      <ShortName>INTANGIBLE ASSETS, NET (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/INTANGIBLEASSETSNET</ParentRole>
      <Position>31</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R32.htm</HtmlFileName>
      <LongName>9954707 - Disclosure - DEBT, NET (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/DEBTNETTables</Role>
      <ShortName>DEBT, NET (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/DEBTNET</ParentRole>
      <Position>32</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R33.htm</HtmlFileName>
      <LongName>9954708 - Disclosure - FAIR VALUE MEASUREMENTS (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/FAIRVALUEMEASUREMENTSTables</Role>
      <ShortName>FAIR VALUE MEASUREMENTS (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/FAIRVALUEMEASUREMENTS</ParentRole>
      <Position>33</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R34.htm</HtmlFileName>
      <LongName>9954709 - Disclosure - REVENUES (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/REVENUESTables</Role>
      <ShortName>REVENUES (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/REVENUES</ParentRole>
      <Position>34</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R35.htm</HtmlFileName>
      <LongName>9954710 - Disclosure - EQUITY-BASED COMPENSATION (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/EQUITYBASEDCOMPENSATIONTables</Role>
      <ShortName>EQUITY-BASED COMPENSATION (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/EQUITYBASEDCOMPENSATION</ParentRole>
      <Position>35</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R36.htm</HtmlFileName>
      <LongName>9954711 - Disclosure - RETIREMENT BENEFIT PLANS (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/RETIREMENTBENEFITPLANSTables</Role>
      <ShortName>RETIREMENT BENEFIT PLANS (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/RETIREMENTBENEFITPLANS</ParentRole>
      <Position>36</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R37.htm</HtmlFileName>
      <LongName>9954712 - Disclosure - INCOME TAXES (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INCOMETAXESTables</Role>
      <ShortName>INCOME TAXES (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/INCOMETAXES</ParentRole>
      <Position>37</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R38.htm</HtmlFileName>
      <LongName>9954713 - Disclosure - MANAGEMENT AGREEMENT AND AFFILIATE TRANSACTIONS (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/MANAGEMENTAGREEMENTANDAFFILIATETRANSACTIONSTables</Role>
      <ShortName>MANAGEMENT AGREEMENT AND AFFILIATE TRANSACTIONS (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/MANAGEMENTAGREEMENTANDAFFILIATETRANSACTIONS</ParentRole>
      <Position>38</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R39.htm</HtmlFileName>
      <LongName>9954714 - Disclosure - SEGMENT INFORMATION (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/SEGMENTINFORMATIONTables</Role>
      <ShortName>SEGMENT INFORMATION (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/SEGMENTINFORMATION</ParentRole>
      <Position>39</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R40.htm</HtmlFileName>
      <LongName>9954715 - Disclosure - EARNINGS PER SHARE AND EQUITY (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/EARNINGSPERSHAREANDEQUITYTables</Role>
      <ShortName>EARNINGS PER SHARE AND EQUITY (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/EARNINGSPERSHAREANDEQUITY</ParentRole>
      <Position>40</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R41.htm</HtmlFileName>
      <LongName>9954716 - Disclosure - ORGANIZATION (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/ORGANIZATIONDetails</Role>
      <ShortName>ORGANIZATION (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/ORGANIZATION</ParentRole>
      <Position>41</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R42.htm</HtmlFileName>
      <LongName>9954717 - Disclosure - BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES - Narrative (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/BASISOFPRESENTATIONANDSUMMARYOFSIGNIFICANTACCOUNTINGPOLICIESNarrativeDetails</Role>
      <ShortName>BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES - Narrative (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/BASISOFPRESENTATIONANDSUMMARYOFSIGNIFICANTACCOUNTINGPOLICIESTables</ParentRole>
      <Position>42</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R43.htm</HtmlFileName>
      <LongName>9954718 - Disclosure - BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES - Useful Life (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/BASISOFPRESENTATIONANDSUMMARYOFSIGNIFICANTACCOUNTINGPOLICIESUsefulLifeDetails</Role>
      <ShortName>BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES - Useful Life (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/BASISOFPRESENTATIONANDSUMMARYOFSIGNIFICANTACCOUNTINGPOLICIESTables</ParentRole>
      <Position>43</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R44.htm</HtmlFileName>
      <LongName>9954719 - Disclosure - LEASING EQUIPMENT, NET (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/LEASINGEQUIPMENTNETDetails</Role>
      <ShortName>LEASING EQUIPMENT, NET (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/LEASINGEQUIPMENTNETTables</ParentRole>
      <Position>44</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R45.htm</HtmlFileName>
      <LongName>9954720 - Disclosure - PROPERTY, PLANT AND EQUIPMENT, NET (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/PROPERTYPLANTANDEQUIPMENTNETDetails</Role>
      <ShortName>PROPERTY, PLANT AND EQUIPMENT, NET (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/PROPERTYPLANTANDEQUIPMENTNETTables</ParentRole>
      <Position>45</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R46.htm</HtmlFileName>
      <LongName>9954721 - Disclosure - PROPERTY, PLANT AND EQUIPMENT, NET - Depreciation (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/PROPERTYPLANTANDEQUIPMENTNETDepreciationDetails</Role>
      <ShortName>PROPERTY, PLANT AND EQUIPMENT, NET - Depreciation (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>46</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R47.htm</HtmlFileName>
      <LongName>9954722 - Disclosure - INVESTMENTS - Ownership Carrying Values (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INVESTMENTSOwnershipCarryingValuesDetails</Role>
      <ShortName>INVESTMENTS - Ownership Carrying Values (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>47</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R48.htm</HtmlFileName>
      <LongName>9954723 - Disclosure - INVESTMENTS - Share of Equity of Income (Loss) (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INVESTMENTSShareofEquityofIncomeLossDetails</Role>
      <ShortName>INVESTMENTS - Share of Equity of Income (Loss) (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>48</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R49.htm</HtmlFileName>
      <LongName>9954724 - Disclosure - INVESTMENTS - Narrative (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INVESTMENTSNarrativeDetails</Role>
      <ShortName>INVESTMENTS - Narrative (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>49</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R50.htm</HtmlFileName>
      <LongName>9954725 - Disclosure - INVESTMENTS - Equity Method Investment (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INVESTMENTSEquityMethodInvestmentDetails</Role>
      <ShortName>INVESTMENTS - Equity Method Investment (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>50</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R51.htm</HtmlFileName>
      <LongName>9954726 - Disclosure - INTANGIBLE ASSETS, NET - Summarized Intangible Assets and Liabilities (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INTANGIBLEASSETSNETSummarizedIntangibleAssetsandLiabilitiesDetails</Role>
      <ShortName>INTANGIBLE ASSETS, NET - Summarized Intangible Assets and Liabilities (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>51</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R52.htm</HtmlFileName>
      <LongName>9954727 - Disclosure - INTANGIBLE ASSETS, NET - Intangible Liabilities Amortization (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INTANGIBLEASSETSNETIntangibleLiabilitiesAmortizationDetails</Role>
      <ShortName>INTANGIBLE ASSETS, NET - Intangible Liabilities Amortization (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>52</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R53.htm</HtmlFileName>
      <LongName>9954728 - Disclosure - INTANGIBLE ASSETS, NET - Schedule of Future Amortization Expense (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INTANGIBLEASSETSNETScheduleofFutureAmortizationExpenseDetails</Role>
      <ShortName>INTANGIBLE ASSETS, NET - Schedule of Future Amortization Expense (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>53</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R54.htm</HtmlFileName>
      <LongName>9954729 - Disclosure - DEBT, NET - Schedule of Debt (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/DEBTNETScheduleofDebtDetails</Role>
      <ShortName>DEBT, NET - Schedule of Debt (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>54</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R55.htm</HtmlFileName>
      <LongName>9954730 - Disclosure - DEBT, NET - Narrative (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/DEBTNETNarrativeDetails</Role>
      <ShortName>DEBT, NET - Narrative (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>55</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R56.htm</HtmlFileName>
      <LongName>9954731 - Disclosure - FAIR VALUE MEASUREMENTS - Financial Assets Measured at Fair Value on a Recurring Basis (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/FAIRVALUEMEASUREMENTSFinancialAssetsMeasuredatFairValueonaRecurringBasisDetails</Role>
      <ShortName>FAIR VALUE MEASUREMENTS - Financial Assets Measured at Fair Value on a Recurring Basis (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>56</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R57.htm</HtmlFileName>
      <LongName>9954732 - Disclosure - FAIR VALUE MEASUREMENTS (Fair Value by Balance Sheet Grouping) (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/FAIRVALUEMEASUREMENTSFairValuebyBalanceSheetGroupingDetails</Role>
      <ShortName>FAIR VALUE MEASUREMENTS (Fair Value by Balance Sheet Grouping) (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/FAIRVALUEMEASUREMENTSTables</ParentRole>
      <Position>57</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R58.htm</HtmlFileName>
      <LongName>9954733 - Disclosure - REVENUES - Components of Revenue (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/REVENUESComponentsofRevenueDetails</Role>
      <ShortName>REVENUES - Components of Revenue (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>58</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R59.htm</HtmlFileName>
      <LongName>9954734 - Disclosure - REVENUES - Minimum Future Annual Revenues (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/REVENUESMinimumFutureAnnualRevenuesDetails</Role>
      <ShortName>REVENUES - Minimum Future Annual Revenues (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>59</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R60.htm</HtmlFileName>
      <LongName>9954735 - Disclosure - EQUITY-BASED COMPENSATION - Expenses Related to Stock-Based Compensation Expense (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/EQUITYBASEDCOMPENSATIONExpensesRelatedtoStockBasedCompensationExpenseDetails</Role>
      <ShortName>EQUITY-BASED COMPENSATION - Expenses Related to Stock-Based Compensation Expense (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>60</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R61.htm</HtmlFileName>
      <LongName>9954736 - Disclosure - EQUITY-BASED COMPENSATION (Narrative) (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/EQUITYBASEDCOMPENSATIONNarrativeDetails</Role>
      <ShortName>EQUITY-BASED COMPENSATION (Narrative) (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/EQUITYBASEDCOMPENSATIONTables</ParentRole>
      <Position>61</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R62.htm</HtmlFileName>
      <LongName>9954737 - Disclosure - RETIREMENT BENEFIT PLANS - Schedule of Costs of Retirement Plans (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/RETIREMENTBENEFITPLANSScheduleofCostsofRetirementPlansDetails</Role>
      <ShortName>RETIREMENT BENEFIT PLANS - Schedule of Costs of Retirement Plans (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>62</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R63.htm</HtmlFileName>
      <LongName>9954738 - Disclosure - RETIREMENT BENEFIT PLANS - Narrative (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/RETIREMENTBENEFITPLANSNarrativeDetails</Role>
      <ShortName>RETIREMENT BENEFIT PLANS - Narrative (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>63</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R64.htm</HtmlFileName>
      <LongName>9954739 - Disclosure - INCOME TAXES - Components of Income Tax Expense (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/INCOMETAXESComponentsofIncomeTaxExpenseDetails</Role>
      <ShortName>INCOME TAXES - Components of Income Tax Expense (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>64</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R65.htm</HtmlFileName>
      <LongName>9954740 - Disclosure - MANAGEMENT AGREEMENT AND AFFILIATE TRANSACTIONS - Narrative (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/MANAGEMENTAGREEMENTANDAFFILIATETRANSACTIONSNarrativeDetails</Role>
      <ShortName>MANAGEMENT AGREEMENT AND AFFILIATE TRANSACTIONS - Narrative (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>65</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R66.htm</HtmlFileName>
      <LongName>9954741 - Disclosure - MANAGEMENT AGREEMENT AND AFFILIATE TRANSACTIONS - Schedule of Related Party Transactions (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/MANAGEMENTAGREEMENTANDAFFILIATETRANSACTIONSScheduleofRelatedPartyTransactionsDetails</Role>
      <ShortName>MANAGEMENT AGREEMENT AND AFFILIATE TRANSACTIONS - Schedule of Related Party Transactions (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>66</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R67.htm</HtmlFileName>
      <LongName>9954742 - Disclosure - SEGMENT INFORMATION - Narrative (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/SEGMENTINFORMATIONNarrativeDetails</Role>
      <ShortName>SEGMENT INFORMATION - Narrative (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>67</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R68.htm</HtmlFileName>
      <LongName>9954743 - Disclosure - SEGMENT INFORMATION - Statement of Income by Segment (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/SEGMENTINFORMATIONStatementofIncomebySegmentDetails</Role>
      <ShortName>SEGMENT INFORMATION - Statement of Income by Segment (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>68</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R69.htm</HtmlFileName>
      <LongName>9954744 - Disclosure - SEGMENT INFORMATION - Reconciliation of Adjusted EBITDA to Net Loss (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/SEGMENTINFORMATIONReconciliationofAdjustedEBITDAtoNetLossDetails</Role>
      <ShortName>SEGMENT INFORMATION - Reconciliation of Adjusted EBITDA to Net Loss (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>69</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R70.htm</HtmlFileName>
      <LongName>9954745 - Disclosure - SEGMENT INFORMATION - Balance Sheet (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/SEGMENTINFORMATIONBalanceSheetDetails</Role>
      <ShortName>SEGMENT INFORMATION - Balance Sheet (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>70</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R71.htm</HtmlFileName>
      <LongName>9954746 - Disclosure - REDEEMABLE PREFERRED STOCK (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/REDEEMABLEPREFERREDSTOCKDetails</Role>
      <ShortName>REDEEMABLE PREFERRED STOCK (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/REDEEMABLEPREFERREDSTOCK</ParentRole>
      <Position>71</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R72.htm</HtmlFileName>
      <LongName>9954747 - Disclosure - EARNINGS PER SHARE AND EQUITY - Schedule of Earnings Per Share (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/EARNINGSPERSHAREANDEQUITYScheduleofEarningsPerShareDetails</Role>
      <ShortName>EARNINGS PER SHARE AND EQUITY - Schedule of Earnings Per Share (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>72</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R73.htm</HtmlFileName>
      <LongName>9954748 - Disclosure - EARNINGS PER SHARE AND EQUITY - Narrative (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/EARNINGSPERSHAREANDEQUITYNarrativeDetails</Role>
      <ShortName>EARNINGS PER SHARE AND EQUITY - Narrative (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>73</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R74.htm</HtmlFileName>
      <LongName>9954749 - Disclosure - EARNINGS PER SHARE AND EQUITY - Schedule of Outstanding Stock Warrants and Changes (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/EARNINGSPERSHAREANDEQUITYScheduleofOutstandingStockWarrantsandChangesDetails</Role>
      <ShortName>EARNINGS PER SHARE AND EQUITY - Schedule of Outstanding Stock Warrants and Changes (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>74</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R75.htm</HtmlFileName>
      <LongName>9954750 - Disclosure - COMMITMENTS AND CONTINGENCIES - Additional Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/COMMITMENTSANDCONTINGENCIESAdditionalInformationDetails</Role>
      <ShortName>COMMITMENTS AND CONTINGENCIES - Additional Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>75</Position>
    </Report>
    <Report instance="fip-20230630.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R76.htm</HtmlFileName>
      <LongName>9954751 - Disclosure - SUBSEQUENT EVENTS (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ftandi.com/role/SUBSEQUENTEVENTSDetails</Role>
      <ShortName>SUBSEQUENT EVENTS (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ftandi.com/role/SUBSEQUENTEVENTS</ParentRole>
      <Position>76</Position>
    </Report>
    <Report>
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <LongName>All Reports</LongName>
      <ReportType>Book</ReportType>
      <ShortName>All Reports</ShortName>
    </Report>
  </MyReports>
  <InputFiles>
    <File doctype="10-Q" original="fip-20230630.htm">fip-20230630.htm</File>
    <File>fip-20230630.xsd</File>
    <File>fip-20230630_cal.xml</File>
    <File>fip-20230630_def.xml</File>
    <File>fip-20230630_lab.xml</File>
    <File>fip-20230630_pre.xml</File>
    <File>fip6302023exhibit311.htm</File>
    <File>fip6302023exhibit312.htm</File>
    <File>fip6302023exhibit321.htm</File>
    <File>fip6302023exhibit322.htm</File>
  </InputFiles>
  <SupplementalFiles>
    <File>fip-20230630_g1.jpg</File>
  </SupplementalFiles>
  <BaseTaxonomies>
    <BaseTaxonomy items="1806">http://fasb.org/us-gaap/2023</BaseTaxonomy>
    <BaseTaxonomy items="29">http://xbrl.sec.gov/dei/2023</BaseTaxonomy>
  </BaseTaxonomies>
  <HasPresentationLinkbase>true</HasPresentationLinkbase>
  <HasCalculationLinkbase>true</HasCalculationLinkbase>
</FilingSummary>
