<?xml version="1.0" encoding="utf-8"?>
<xbrl
  xmlns="http://www.xbrl.org/2003/instance"
  xmlns:dei="http://xbrl.sec.gov/dei/2023"
  xmlns:iso4217="http://www.xbrl.org/2003/iso4217"
  xmlns:link="http://www.xbrl.org/2003/linkbase"
  xmlns:quantitative="http://www.vanguard.com/20250203"
  xmlns:rr="http://xbrl.sec.gov/rr/2023"
  xmlns:xbrldi="http://xbrl.org/2006/xbrldi"
  xmlns:xhtml="http://www.w3.org/1999/xhtml"
  xmlns:xlink="http://www.w3.org/1999/xlink">
    <link:schemaRef xlink:href="quantitative-20250203.xsd" xlink:type="simple"/>
    <context id="RetailMember_S000002913">
        <entity>
            <identifier scheme="http://www.sec.gov/CIK">0000799127</identifier>
            <segment>
                <xbrldi:explicitMember dimension="dei:DocumentInformationDocumentAxis">quantitative:RetailMember</xbrldi:explicitMember>
                <xbrldi:explicitMember dimension="dei:LegalEntityAxis">quantitative:S000002913Member</xbrldi:explicitMember>
            </segment>
        </entity>
        <period>
            <startDate>2025-01-31</startDate>
            <endDate>2025-01-31</endDate>
        </period>
    </context>
    <context id="D_31Jan2025_31Jan2025">
        <entity>
            <identifier scheme="http://www.sec.gov/CIK">0000799127</identifier>
        </entity>
        <period>
            <startDate>2025-01-31</startDate>
            <endDate>2025-01-31</endDate>
        </period>
    </context>
    <context id="RetailMember_S000002913_C000007979">
        <entity>
            <identifier scheme="http://www.sec.gov/CIK">0000799127</identifier>
            <segment>
                <xbrldi:explicitMember dimension="dei:DocumentInformationDocumentAxis">quantitative:RetailMember</xbrldi:explicitMember>
                <xbrldi:explicitMember dimension="dei:LegalEntityAxis">quantitative:S000002913Member</xbrldi:explicitMember>
                <xbrldi:explicitMember dimension="rr:ProspectusShareClassAxis">quantitative:C000007979Member</xbrldi:explicitMember>
            </segment>
        </entity>
        <period>
            <startDate>2025-01-31</startDate>
            <endDate>2025-01-31</endDate>
        </period>
    </context>
    <context id="RetailMember_S000002913_C000007980">
        <entity>
            <identifier scheme="http://www.sec.gov/CIK">0000799127</identifier>
            <segment>
                <xbrldi:explicitMember dimension="dei:DocumentInformationDocumentAxis">quantitative:RetailMember</xbrldi:explicitMember>
                <xbrldi:explicitMember dimension="dei:LegalEntityAxis">quantitative:S000002913Member</xbrldi:explicitMember>
                <xbrldi:explicitMember dimension="rr:ProspectusShareClassAxis">quantitative:C000007980Member</xbrldi:explicitMember>
            </segment>
        </entity>
        <period>
            <startDate>2025-01-31</startDate>
            <endDate>2025-01-31</endDate>
        </period>
    </context>
    <unit id="pure">
        <measure>pure</measure>
    </unit>
    <unit id="USD">
        <measure>iso4217:USD</measure>
    </unit>
    <dei:DocumentPeriodEndDate contextRef="D_31Jan2025_31Jan2025" id="apid_1">2024-09-30</dei:DocumentPeriodEndDate>
    <dei:EntityRegistrantName contextRef="D_31Jan2025_31Jan2025" id="apid_2">VANGUARD QUANTITATIVE FUNDS</dei:EntityRegistrantName>
    <dei:EntityCentralIndexKey contextRef="D_31Jan2025_31Jan2025" id="apid_3">0000799127</dei:EntityCentralIndexKey>
    <dei:AmendmentFlag contextRef="D_31Jan2025_31Jan2025" id="apid_4">false</dei:AmendmentFlag>
    <dei:DocumentCreationDate contextRef="D_31Jan2025_31Jan2025" id="apid_5">2025-02-03</dei:DocumentCreationDate>
    <dei:DocumentEffectiveDate contextRef="D_31Jan2025_31Jan2025" id="apid_6">2025-02-03</dei:DocumentEffectiveDate>
    <rr:ProspectusDate contextRef="D_31Jan2025_31Jan2025" id="apid_7">2025-01-31</rr:ProspectusDate>
    <dei:EntityInvCompanyType contextRef="D_31Jan2025_31Jan2025" id="apid_8">N-1A</dei:EntityInvCompanyType>
    <dei:DocumentType contextRef="D_31Jan2025_31Jan2025" id="apid_9">497</dei:DocumentType>
    <rr:SupplementToProspectusTextBlock
      contextRef="D_31Jan2025_31Jan2025"
      id="IXG_cf712610-7f38-40b0-a0b5-5e629b2bdd2b">&lt;span style="color:#000000;font-family:Arial;font-size:14pt;"&gt;Vanguard Growth and Income Fund&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:11pt;font-weight:bold;"&gt;Supplement to the Prospectus and Summary Prospectus&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:9.5pt;"&gt;As approved by the Fund&#x2019;s Board of Trustees, Vanguard Growth and Income Fund (the Fund) has reduced its expense ratio for Admiral Shares. Effective February 3, 2025, the Annual Fund Operating Expenses table and the hypothetical expenses examples for the Fund are hereby deleted and replaced with the following:&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:10pt;font-weight:bold;"&gt;Prospectus and Summary Prospectus Text Changes for Vanguard Growth and Income Fund&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8.5pt;font-weight:bold;"&gt;Annual Fund Operating Expenses&lt;/span&gt;
&lt;br/&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8.5pt;"&gt;(Expenses that you pay each year as a percentage of the value of your investment)&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Investor Shares&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Admiral Shares&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Management Fees&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;width:17.56pt;"&gt;0.35&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;0.23%&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;12b-1 Distribution Fee&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;None&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;None&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Other Expenses&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;width:17.56pt;"&gt;0.01&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;0.01%&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Total Annual Fund Operating Expenses&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;width:17.56pt;"&gt;0.36&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;0.24%&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;"&gt;1&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;"&gt;The expense information shown in the table has been restated for Admiral Shares to reflect current fees.&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:9.5pt;"&gt;Examples&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:9.5pt;"&gt;The following examples are intended to help you compare the cost of investing in the Fund&#x2019;s Investor Shares or Admiral Shares with the cost of investing in other mutual funds. They illustrate the hypothetical expenses that you would incur over various periods if you were to invest $10,000 in the Fund&#x2019;s shares. These examples assume that the shares provide a return of 5% each year and that total annual fund operating expenses remain as stated in the preceding table. You would incur these hypothetical expenses whether or not you were to redeem your investment at the end of the given period. Although your actual costs may be higher or lower, based on these assumptions your costs would be:&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;1 Year&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;3 Years&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;5 Years&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;10 Years&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Investor Shares&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$37&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$116&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$202&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$456&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Admiral Shares&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$25&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$77&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$135&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$306&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:7pt;line-height:7pt;"&gt;&#xa9; 2025 The Vanguard Group, Inc. All rights reserved.&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:7pt;"&gt;Vanguard Marketing Corporation, Distributor.&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8.5pt;margin-left:138.93pt;"&gt;PS 093A 022025&lt;/span&gt;</rr:SupplementToProspectusTextBlock>
    <rr:SupplementToProspectusTextBlock
      contextRef="RetailMember_S000002913"
      id="cf712610-7f38-40b0-a0b5-5e629b2bdd2b">&lt;span style="color:#000000;font-family:Arial;font-size:14pt;"&gt;Vanguard Growth and Income Fund&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:11pt;font-weight:bold;"&gt;Supplement to the Prospectus and Summary Prospectus&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:9.5pt;"&gt;As approved by the Fund&#x2019;s Board of Trustees, Vanguard Growth and Income Fund (the Fund) has reduced its expense ratio for Admiral Shares. Effective February 3, 2025, the Annual Fund Operating Expenses table and the hypothetical expenses examples for the Fund are hereby deleted and replaced with the following:&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:10pt;font-weight:bold;"&gt;Prospectus and Summary Prospectus Text Changes for Vanguard Growth and Income Fund&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8.5pt;font-weight:bold;"&gt;Annual Fund Operating Expenses&lt;/span&gt;
&lt;br/&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8.5pt;"&gt;(Expenses that you pay each year as a percentage of the value of your investment)&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Investor Shares&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Admiral Shares&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Management Fees&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;width:17.56pt;"&gt;0.35&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;0.23%&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;12b-1 Distribution Fee&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;None&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;None&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Other Expenses&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;width:17.56pt;"&gt;0.01&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;0.01%&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Total Annual Fund Operating Expenses&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;width:17.56pt;"&gt;0.36&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;0.24%&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;"&gt;1&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;"&gt;The expense information shown in the table has been restated for Admiral Shares to reflect current fees.&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:9.5pt;"&gt;Examples&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:9.5pt;"&gt;The following examples are intended to help you compare the cost of investing in the Fund&#x2019;s Investor Shares or Admiral Shares with the cost of investing in other mutual funds. They illustrate the hypothetical expenses that you would incur over various periods if you were to invest $10,000 in the Fund&#x2019;s shares. These examples assume that the shares provide a return of 5% each year and that total annual fund operating expenses remain as stated in the preceding table. You would incur these hypothetical expenses whether or not you were to redeem your investment at the end of the given period. Although your actual costs may be higher or lower, based on these assumptions your costs would be:&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;1 Year&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;3 Years&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;5 Years&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;10 Years&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Investor Shares&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$37&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$116&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$202&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$456&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;Admiral Shares&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$25&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$77&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$135&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8pt;margin-left:0.0pt;"&gt;$306&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:7pt;line-height:7pt;"&gt;&#xa9; 2025 The Vanguard Group, Inc. All rights reserved.&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:7pt;"&gt;Vanguard Marketing Corporation, Distributor.&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8.5pt;margin-left:138.93pt;"&gt;PS 093A 022025&lt;/span&gt;</rr:SupplementToProspectusTextBlock>
    <rr:OperatingExpensesCaption
      contextRef="RetailMember_S000002913"
      id="x_92046964-bb85-42ec-9d80-dce7ed78c201">&lt;span style="color:#000000;font-family:Arial;font-size:10pt;font-weight:bold;"&gt;Prospectus and Summary Prospectus Text Changes for Vanguard Growth and Income Fund&lt;/span&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8.5pt;font-weight:bold;"&gt;Annual Fund Operating Expenses&lt;/span&gt;
&lt;br/&gt;&lt;span style="color:#000000;font-family:Arial;font-size:8.5pt;"&gt;(Expenses that you pay each year as a percentage of the value of your investment)&lt;/span&gt;</rr:OperatingExpensesCaption>
    <rr:ManagementFeesOverAssets
      contextRef="RetailMember_S000002913_C000007979"
      decimals="4"
      id="x_74380240-d90e-4f03-b034-054591ceb8bd"
      unitRef="pure">0.0035</rr:ManagementFeesOverAssets>
    <rr:ManagementFeesOverAssets
      contextRef="RetailMember_S000002913_C000007980"
      decimals="4"
      id="d45b183c-9055-4200-9a4a-703ca430b515"
      unitRef="pure">0.0023</rr:ManagementFeesOverAssets>
    <rr:DistributionAndService12b1FeesOverAssets
      contextRef="RetailMember_S000002913_C000007979"
      decimals="4"
      id="x_9f5f5ba0-eeef-4031-88a1-6f808d40a3ae"
      unitRef="pure">0</rr:DistributionAndService12b1FeesOverAssets>
    <rr:DistributionAndService12b1FeesOverAssets
      contextRef="RetailMember_S000002913_C000007980"
      decimals="4"
      id="c47fb64f-f2b6-4939-9d61-841db4faa121"
      unitRef="pure">0</rr:DistributionAndService12b1FeesOverAssets>
    <rr:OtherExpensesOverAssets
      contextRef="RetailMember_S000002913_C000007979"
      decimals="4"
      id="x_9d17ee32-81c9-4404-9a73-b24856aa76ea"
      unitRef="pure">0.0001</rr:OtherExpensesOverAssets>
    <rr:OtherExpensesOverAssets
      contextRef="RetailMember_S000002913_C000007980"
      decimals="4"
      id="x_09c8a009-3d68-462b-b5e3-af1d5bb0eff1"
      unitRef="pure">0.0001</rr:OtherExpensesOverAssets>
    <rr:ExpensesOverAssets
      contextRef="RetailMember_S000002913_C000007979"
      decimals="4"
      id="f5e4216b-bf15-4008-93c1-0fdf99f1233a"
      unitRef="pure">0.0036</rr:ExpensesOverAssets>
    <rr:ExpensesOverAssets
      contextRef="RetailMember_S000002913_C000007980"
      decimals="4"
      id="ecd29747-dc6c-4b03-9441-fdeee03face6"
      unitRef="pure">0.0024</rr:ExpensesOverAssets>
    <rr:ExpenseExampleHeading
      contextRef="RetailMember_S000002913"
      id="x_0437596e-a8a5-4b68-b6ad-2c120f8c27f4">&lt;span style="color:#000000;font-family:Arial;font-size:9.5pt;"&gt;Examples&lt;/span&gt;</rr:ExpenseExampleHeading>
    <rr:ExpenseExampleNarrativeTextBlock
      contextRef="RetailMember_S000002913"
      id="d157579d-a8b0-4ca1-b521-5a9e5f4feb08">&lt;span style="color:#000000;font-family:Arial;font-size:9.5pt;"&gt;The following examples are intended to help you compare the cost of investing in the Fund&#x2019;s Investor Shares or Admiral Shares with the cost of investing in other mutual funds. They illustrate the hypothetical expenses that you would incur over various periods if you were to invest $10,000 in the Fund&#x2019;s shares. These examples assume that the shares provide a return of 5% each year and that total annual fund operating expenses remain as stated in the preceding table. You would incur these hypothetical expenses whether or not you were to redeem your investment at the end of the given period. Although your actual costs may be higher or lower, based on these assumptions your costs would be:&lt;/span&gt;</rr:ExpenseExampleNarrativeTextBlock>
    <rr:ExpenseExampleYear01
      contextRef="RetailMember_S000002913_C000007979"
      decimals="INF"
      id="b7f9f91d-c7f4-44b2-951b-ed084d73f79f"
      unitRef="USD">37</rr:ExpenseExampleYear01>
    <rr:ExpenseExampleYear03
      contextRef="RetailMember_S000002913_C000007979"
      decimals="INF"
      id="x_7249e010-a74f-4d39-ba31-5ad5cec85ee4"
      unitRef="USD">116</rr:ExpenseExampleYear03>
    <rr:ExpenseExampleYear05
      contextRef="RetailMember_S000002913_C000007979"
      decimals="INF"
      id="x_3d38d3d6-3fac-4cd4-931f-6ec0c1707ad1"
      unitRef="USD">202</rr:ExpenseExampleYear05>
    <rr:ExpenseExampleYear10
      contextRef="RetailMember_S000002913_C000007979"
      decimals="INF"
      id="c152be46-0cbb-4b30-9d61-e1a057f078df"
      unitRef="USD">456</rr:ExpenseExampleYear10>
    <rr:ExpenseExampleYear01
      contextRef="RetailMember_S000002913_C000007980"
      decimals="INF"
      id="x_88d6c6bb-5740-4669-9751-3b3894a87b0c"
      unitRef="USD">25</rr:ExpenseExampleYear01>
    <rr:ExpenseExampleYear03
      contextRef="RetailMember_S000002913_C000007980"
      decimals="INF"
      id="x_78dcbf96-2ed7-404b-98b4-8d4dca9946be"
      unitRef="USD">77</rr:ExpenseExampleYear03>
    <rr:ExpenseExampleYear05
      contextRef="RetailMember_S000002913_C000007980"
      decimals="INF"
      id="d763a2c4-fa7a-44c7-a554-f841b531e657"
      unitRef="USD">135</rr:ExpenseExampleYear05>
    <rr:ExpenseExampleYear10
      contextRef="RetailMember_S000002913_C000007980"
      decimals="INF"
      id="b807c154-fdac-4774-9a70-4dcf3d00cbc4"
      unitRef="USD">306</rr:ExpenseExampleYear10>
    <link:footnoteLink
      xlink:role="http://www.xbrl.org/2003/role/link"
      xlink:type="extended">
        <link:loc
          xlink:href="#f5e4216b-bf15-4008-93c1-0fdf99f1233a"
          xlink:label="f5e4216b-bf15-4008-93c1-0fdf99f1233a"
          xlink:type="locator"/>
        <link:footnote id="x_0001uu_cf712610-7f38-40b0-a0b5-5e629b2bdd2b" xlink:label="x_0001uu_cf712610-7f38-40b0-a0b5-5e629b2bdd2b" xlink:role="http://www.xbrl.org/2003/role/footnote" xlink:type="resource" xml:lang="en-US"><xhtml:span style="color:#000000;font-family:Arial;font-size:8pt;">The expense information shown in the table has been restated for Admiral Shares to reflect current fees.</xhtml:span></link:footnote>
        <link:footnoteArc
          xlink:arcrole="http://www.xbrl.org/2003/arcrole/fact-footnote"
          xlink:from="f5e4216b-bf15-4008-93c1-0fdf99f1233a"
          xlink:to="x_0001uu_cf712610-7f38-40b0-a0b5-5e629b2bdd2b"
          xlink:type="arc"/>
        <link:loc
          xlink:href="#ecd29747-dc6c-4b03-9441-fdeee03face6"
          xlink:label="ecd29747-dc6c-4b03-9441-fdeee03face6"
          xlink:type="locator"/>
        <link:footnoteArc
          xlink:arcrole="http://www.xbrl.org/2003/arcrole/fact-footnote"
          xlink:from="ecd29747-dc6c-4b03-9441-fdeee03face6"
          xlink:to="x_0001uu_cf712610-7f38-40b0-a0b5-5e629b2bdd2b"
          xlink:type="arc"/>
    </link:footnoteLink>
</xbrl>
