Document:

<PAGE>

                                                                    Exhibit 10.1

          STOCK PURCHASE AGREEMENT, dated December 3, 2001 (this "Agreement"),
between Liberty UCOMA, LLC, a Delaware limited liability company ("Buyer"), and
UnitedGlobalCom, Inc., a Delaware corporation (the "Seller").

          A.  Buyer desires to purchase from Seller, and Seller desires to sell
to Buyer, 11,976,048 shares (the "Shares") of the Class A Common Stock, par
value $.01 per share, of Seller (the "Class A Common Stock") for a purchase
price of U.S. $ 20,000,000 (the "Purchase Price").

          B.  This Agreement is being entered into concurrently with the
entrance by Seller into that certain Agreement, dated the date hereof, among
Seller, UIH Funding Corp., Salomon Smith Barney Inc., TD Securities (USA), Inc.,
J.P. Morgan Securities, Inc.,  and Donaldson Lufkin & Jenrette Securities
Corporation (the "Resale Agreement").

          C.  This Agreement is being entered into concurrently with (i) the
payment by Liberty Media Corporation ("Liberty Media") to United International
Properties, Inc. ("UIPI") of $241,309,065.79 as payment in full of all amounts
owing under the promissory note dated December 8, 2000, in the principal amount
of $200,000,000, made by Liberty Media, payable to the order of the Seller, and
currently held by UIPI (the "$200,000,000 Note"), and as a partial payment of
amounts owing under the promissory note dated December 8, 2000, in the principal
amount of $42,405,760, made by Liberty Argentina, Inc., payable to the order of
Seller, and currently held by UIPI (the ("$42,405,760 Note"), (ii) the return of
the $200,000,000 Note to Liberty Media, and (iii) the acknowledgment by UIPI of
receipt of a partial payment under the $42,405,760 Note.

          D.  The net proceeds from the sale of the Shares to Buyer hereunder,
and the net proceeds from the sale of Shares to Buyer under that certain Stock
Purchase Agreement (the "Other Stock Purchase Agreement"), dated December 3,
2001, between Buyer and Seller with respect to the purchase by Buyer of 14,970
shares of Class A Common Stock of Seller, are to be used by Seller to
repurchase, pursuant to the terms of the Resale Agreement, all of its issued and
outstanding 10 7/8% Senior Discount Notes due 2009 (the "Notes") issued under
the Indenture, dated as of April 29, 1999 (the "1999 Indenture"), between Seller
and Firstar Bank, N.A. (f/k/a Firstar Bank of Minnesota, N.A.) (the "Trustee"),
as trustee.   The 1999 Indenture and the Indenture, dated as of February 5, 1998
between Seller and the Trustee collectively are referred to herein as the
"Indentures."

          NOW, THEREFORE, in consideration of the representations, warranties,
covenants and agreements contained in this Agreement, the parties hereby agree
as follows:

     Section 1.  Purchase and Sale.  Upon the terms and subject to the
                 -----------------
conditions of this Agreement, on the date hereof Seller is selling and
delivering to Buyer the Shares, in consideration for which Buyer is paying to
Seller the Purchase Price.
<PAGE>

     Section 2.  Deliveries by the Parties. On the date hereof, the parties are
                 -------------------------
making the following deliveries:

          (a)  Seller is delivering to Buyer, against receipt of the Purchase
     Price, a single stock certificate for the Shares, duly registered in the
     name of Buyer on the stock transfer books of Seller, with any requisite
     transfer stamps attached thereto. The following restrictive legend shall be
     placed on the certificate representing the Shares:

                    The shares represented by this certificate
                    are subject to the terms of the Agreement and
                    Plan of Restructuring and Merger dated as of
                    December 3, 2001 (the "Merger Agreement"),
                    among UnitedGlobalCom, Inc., New
                    UnitedGlobalCom, Inc., United/New United
                    Merger Sub, Inc., Liberty Media Corporation,
                    Liberty Media International, Inc., Liberty
                    Global, Inc. and each individual indicated
                    therein as a "Founder," including Section
                    7.23 thereof and, following the closing of
                    the transactions contemplated by the Merger
                    Agreement, the terms of the Stockholders
                    Agreement and the Standstill Agreement
                    included as exhibits thereto. Copies of the
                    Merger Agreement, the Stockholders Agreement
                    and the Standstill Agreement, as applicable,
                    are available from UnitedGlobalCom, Inc. upon
                    request, and any sale, pledge, hypothecation,
                    transfer, assignment or other disposition of
                    the shares represented by this certificate is
                    subject to the terms of the Merger Agreement,
                    and the Stockholders Agreement and the
                    Standstill Agreement included as exhibits
                    thereto.

          (b)  Buyer is paying to Seller, against receipt of the Shares, the
     Purchase Price by wire transfer of immediately available funds to an
     account previously designated by Seller to Buyer in writing.

     Section 3.  Representations and Warranties by Seller.  Seller represents
                 ----------------------------------------
and warrants to Buyer as follows:

          (a)  Organization.  Seller is a corporation duly incorporated,
               ------------
     validly existing and in good standing under the laws of the State of
     Delaware and has the requisite power and authority to carry on its business
     substantially as it is now being conducted.

          (b)  Authority.  Seller has the power and authority to execute and
               ---------
     deliver this Agreement and to consummate the transactions contemplated
     hereby. The execution and delivery of this Agreement and the consummation
     of the transactions contemplated hereby have been duly and validly
     authorized by all requisite action on the part of Seller. This Agreement
     has been validly executed and delivered by Seller and constitutes a valid
     and binding agreement of Seller, enforceable against Seller in accordance
     with its terms, except that such enforcement may be subject to any
     bankruptcy, insolvency,

                                       2
<PAGE>

     reorganization, moratorium, fraudulent transfer or other laws, now or
     hereafter in effect, relating to or limiting creditors' rights generally
     and the application of general principles of equity.

          (c)  The Shares.  The Shares are duly and validly authorized and,
               ----------
     upon receipt by Seller of the Purchase Price, will be duly and validly
     issued, fully paid and non-assessable. Delivery of the certificate for the
     Shares will pass valid title to the Shares to Buyer, free and clear of any
     claim, pre-emptive rights, lien, charge, security interest, encumbrance,
     restriction on transfer or voting or other defect in title whatsoever
     ("Liens"), other than Liens resulting from (i) any action(s) of Buyer; (ii)
     restrictions arising under Federal and State securities laws; and (iii)
     restrictions arising under any stockholder agreements or other
     understandings to which Buyer or any affiliate of Buyer is a party.

          (d)  Consents and Approvals; No Violations.  Neither the execution
               -------------------------------------
     and delivery of this Agreement by Seller, nor the consummation by Seller of
     the transactions contemplated hereby, will (i) conflict with or result in
     any breach of any provision of the certificate of incorporation or by-laws,
     as amended, of Seller, (ii) result in a violation or breach of, or
     constitute (with or without due notice or lapse of time or both) a default
     (or give rise to any right of termination, cancellation or acceleration)
     under, or require any consent under, any indenture, license, contract,
     agreement or other instrument or obligation to which Seller is a party,
     (iii) violate any order, writ, injunction, decree or award rendered by any
     governmental or regulatory authority or court, domestic or foreign (a
     "Governmental Entity") or any statute, rule or regulation (collectively,
     "Laws") applicable to Seller or (iv) require any filing with, or the
     obtaining of any permit, authorization, consent or approval of, any
     Governmental Authority. All requirements under the Indentures that are
     required to be satisfied prior to the sale of the Shares hereunder have
     been satisfied.

     Section 4.  Representations and Warranties of Buyer. Buyer represents and
                 ---------------------------------------
warrants to Seller as follows:

          (a)  Organization.  Buyer is a limited liability company validly
               ------------
     existing and in good standing under the laws of the State of Delaware and
     has the requisite power and authority to carry on its business
     substantially as it is now being conducted. Liberty Media Corporation, a
     Delaware corporation ("Liberty"), is the sole member of Buyer.

          (b)  Authority Relative to this Agreement.  Buyer has the power and
               ------------------------------------
     authority to execute and deliver this Agreement and to consummate the
     transactions contemplated hereby. The execution and delivery of this
     Agreement and the consummation of the transactions contemplated hereby have
     been duly and validly authorized by all requisite action on the part of
     Buyer. This Agreement has been duly and validly executed and delivered by
     Buyer and constitutes a valid and binding agreement of Buyer, enforceable
     against Buyer in accordance with its terms, except that such enforcement
     may be subject to any bankruptcy, insolvency, reorganization, moratorium,
     fraudulent transfer or other laws, now or hereafter in effect, relating to
     or limiting creditors' rights generally and the application of general
     principles of equity.

                                       3
<PAGE>

          (c)  Consents and Approvals; No Violations.  Neither the execution
               -------------------------------------
     and delivery of this Agreement by Buyer, nor the consummation by Buyer of
     the transactions contemplated hereby will (i) conflict with or result in
     any breach of any provision of the operating agreement or other
     organizational documents of Buyer, (ii) result in a violation or breach of,
     or constitute (with or without due notice or lapse of time or both) a
     default (or give rise to any right of termination, cancellation or
     acceleration) under, or require any consent under, any indenture, license,
     contract, agreement or other instrument or obligation to which the Buyer is
     a party, (iii) violate any order, writ, injunction, decree or award
     rendered by any Governmental Entity or any Laws applicable to Buyer, or
     (iii) require any filing with, or the obtaining of any permit,
     authorization, consent or approval of, any Governmental Entity.

          (d)  Buyer Acknowledgment.  Buyer acknowledges and understands that
               --------------------
     the offer and sale of the Shares by Seller to Buyer hereunder has not been
     registered under the Securities Act of 1933, as amended (the "Act"), and
     that Buyer may not sell or dispose of the Shares other than in a
     transaction that complies with the registration requirements of the Act,
     unless an exemption is available therefrom. Buyer is purchasing the Shares
     for investment, and not with a view to the distribution thereof in
     violation of the Act.

     Section 5.  Covenant re Use of Proceeds. Seller covenants and agrees with
                 ---------------------------
Buyer that, immediately following payment by Buyer to Seller of the Purchase
Price hereunder and the "Purchase Price" as defined in the Other Stock Purchase
Agreement, Seller will repurchase its Notes in accordance with the terms of the
Resale Agreement.

     Section 6.  Governing Law; Waiver of Jury Trial, Etc.  This Agreement
                 -----------------------------------------
shall be governed by and construed in accordance with the laws of the State of
Colorado applied to contracts made and wholly performed in such State, without
regard to principles governing conflicts of law. Each of the parties (a) will
submit itself to the non-exclusive jurisdiction of any federal court located in
the State of Colorado or any Colorado state court having subject matter
jurisdiction in the event any dispute arises out of this Agreement, (b) agrees
that venue will be proper as to any proceeding brought in any such court with
respect to such a dispute, (c) will not attempt to deny or defeat such personal
jurisdiction or venue by motion or other request for leave from any such court
and (d) WAIVES ANY RIGHT TO A TRIAL BY JURY in any proceeding brought with
respect to this Agreement or the transactions contemplated hereby.

     Section 7.  Descriptive Headings.  The descriptive headings herein are
                 --------------------
inserted for convenience of reference only and shall in no way be construed to
define, limit, describe, explain, modify, amplify, or add to the interpretation,
construction or meaning of any provision of, or scope or intent of, this
Agreement nor in any way affect this Agreement.

     Section 8.  Counterparts. This Agreement may be signed in counter-parts
                 ------------
and all signed copies of this Agreement will together constitute one original of
this Agreement. This Agreement shall become effective when each party hereto
shall have received counterparts thereof signed by all the other parties hereto.

     Section 9.  Assignment.  Neither this Agreement nor any of the rights,
                 ----------
interests or obligations hereunder shall be assigned by any of the parties
hereto without the prior written

                                       4
<PAGE>

consent of the other party, except that Buyer may transfer the Shares (or any
portion thereof) to another direct or indirect wholly owned subsidiary of
Liberty. Subject to the preceding sentence, this Agreement will be binding upon,
inure to the benefit of and be enforceable by the parties and their respective
successors and assigns.

                                       5
<PAGE>

            Each of the undersigned has caused this Agreement to be duly signed
as of the date first above written.

                                    UNITEDGLOBALCOM, INC.

                                    By:  /s/ Michael T. Fries
                                       ----------------------------------
                                    Name:    Michael T. Fries
                                    Title: President

                                    LIBERTY UCOMA, LLC

                                    By:  /s/ Dave Flowers
                                       ----------------------------------
                                     Name:   Dave Flowers
                                     Title:  Senior Vice President

                                       6<PAGE>

                                                                    Exhibit 10.2

          STOCK PURCHASE AGREEMENT, dated December 3, 2001 (this  "Agreement"),
between Liberty UCOMA, LLC, a Delaware limited liability company ("Buyer"), and
UnitedGlobalCom, Inc., a Delaware corporation (the "Seller").

          A.  Buyer desires to purchase from Seller, and Seller desires to sell
to Buyer, 14,970 shares (the "Shares") of the Class A Common Stock, par value
$.01 per share, of Seller (the "Class A Common Stock") for a purchase price of
U.S. $ 25,000 (the "Purchase Price").

          B.  This Agreement is being entered into concurrently with the
entrance by Seller into that certain Agreement, dated the date hereof, among
Seller, UIH Funding Corp., Salomon Smith Barney Inc., TD Securities (USA), Inc.,
J.P. Morgan Securities, Inc.,  and Donaldson Lufkin & Jenrette Securities
Corporation (the "Resale Agreement").

          C.  This Agreement is being entered into concurrently with (i) the
payment by Liberty Media Corporation ("Liberty Media") to United International
Properties, Inc. ("UIPI") of $241,309,065.79 as payment in full of all amounts
owing under the promissory note dated December 8, 2000, in the principal amount
of $200,000,000, made by Liberty Media, payable to the order of the Seller, and
currently held by UIPI (the "$200,000,000 Note"), and as a partial payment of
amounts owing under the promissory note dated December 8, 2000, in the principal
amount of $42,405,760, made by Liberty Argentina, Inc., payable to the order of
Seller, and currently held by UIPI (the ("$42,405,760 Note"), (ii) the return of
the $200,000,000 Note to Liberty Media, and (iii) the acknowledgment by UIPI of
receipt of a partial payment under the $42,405,760 Note.

          D.  The net proceeds from the sale of the Shares to Buyer hereunder,
and the net proceeds from the sale of Shares to Buyer under that certain Stock
Purchase Agreement (the "Other Stock Purchase Agreement"), dated December 3,
2001, between Buyer and Seller with respect to the purchase by Buyer of
11,976,048 shares of Class A Common Stock of Seller, are to be used by Seller to
repurchase, pursuant to the terms of the Resale Agreement, all of its issued and
outstanding 10 7/8% Senior Discount Notes due 2009 (the "Notes") issued under
the Indenture, dated as of April 29, 1999 (the "1999 Indenture"), between Seller
and Firstar Bank, N.A. (f/k/a Firstar Bank of Minnesota, N.A.) (the "Trustee"),
as trustee. The 1999 Indenture and the Indenture, dated as of February 5, 1998
between Seller and the Trustee collectively are referred to herein as the
"Indentures."

          NOW, THEREFORE, in consideration of the representations, warranties,
covenants and agreements contained in this Agreement, the parties hereby agree
as follows:
<PAGE>

     Section 1.  Purchase and Sale.  Upon the terms and subject to the
                 -----------------
conditions of this Agreement, on the date hereof Seller is selling and
delivering to Buyer the Shares, in consideration for which Buyer is paying to
Seller the Purchase Price.

     Section 2.  Deliveries by the Parties. On the date hereof, the parties are
                 -------------------------
making the following deliveries:

          (a)  Seller is delivering to Buyer, against receipt of the Purchase
     Price, a single stock certificate for the Shares, duly registered in the
     name of Buyer on the stock transfer books of Seller, with any requisite
     transfer stamps attached thereto. The following restrictive legend shall be
     placed on the certificate representing the Shares:

                  The shares represented by this certificate are
                  subject to the terms of the Agreement and Plan of
                  Restructuring and Merger dated as of December 3,
                  2001 (the "Merger Agreement"), among
                  UnitedGlobalCom, Inc., New UnitedGlobalCom, Inc.,
                  United/New United Merger Sub, Inc., Liberty Media
                  Corporation, Liberty Media International, Inc.,
                  Liberty Global, Inc. and each individual indicated
                  therein as a "Founder," including Section 7.23
                  thereof and, following the closing of the
                  transactions contemplated by the Merger Agreement,
                  the terms of the Stockholders Agreement and the
                  Standstill Agreement included as exhibits thereto.
                  Copies of the Merger Agreement, the Stockholders
                  Agreement and the Standstill Agreement, as
                  applicable, are available from UnitedGlobalCom, Inc.
                  upon request, and any sale, pledge, hypothecation,
                  transfer, assignment or other disposition of the
                  shares represented by this certificate is subject to
                  the terms of the Merger Agreement, and the
                  Stockholders Agreement and the Standstill Agreement
                  included as exhibits thereto.

          (b)  Buyer is paying to Seller, against receipt of the Shares, the
     Purchase Price by check payable to the order of Seller.

     Section 3.  Representations and Warranties by Seller.  Seller represents
                 ----------------------------------------
and warrants to Buyer as follows:

          (a)  Organization.  Seller is a corporation duly incorporated,
               ------------
     validly existing and in good standing under the laws of the State of
     Delaware and has the requisite power and authority to carry on its business
     substantially as it is now being conducted.

          (b)  Authority.  Seller has the power and authority to execute and
               ---------
     deliver this Agreement and to consummate the transactions contemplated
     hereby. The execution and delivery of this Agreement and the consummation
     of the transactions contemplated hereby have been duly and validly
     authorized by all requisite action on the part of Seller.

                                       2
<PAGE>

     This Agreement has been validly executed and delivered by Seller and
     constitutes a valid and binding agreement of Seller, enforceable against
     Seller in accordance with its terms, except that such enforcement may be
     subject to any bankruptcy, insolvency, reorganization, moratorium,
     fraudulent transfer or other laws, now or hereafter in effect, relating to
     or limiting creditors' rights generally and the application of general
     principles of equity.

          (c)  The Shares.  The Shares are duly and validly authorized and,
               ----------
     upon receipt by Seller of the Purchase Price, will be duly and validly
     issued, fully paid and non-assessable. Delivery of the certificate for the
     Shares will pass valid title to the Shares to Buyer, free and clear of any
     claim, pre-emptive rights, lien, charge, security interest, encumbrance,
     restriction on transfer or voting or other defect in title whatsoever
     ("Liens"), other than Liens resulting from (i) any action(s) of Buyer; (ii)
     restrictions arising under Federal and State securities laws; and (iii)
     restrictions arising under any stockholder agreements or other
     understandings to which Buyer or any affiliate of Buyer is a party.

          (d)  Consents and Approvals; No Violations.  Neither the execution
               -------------------------------------
     and delivery of this Agreement by Seller, nor the consummation by Seller of
     the transactions contemplated hereby, will (i) conflict with or result in
     any breach of any provision of the certificate of incorporation or by-laws,
     as amended, of Seller, (ii) result in a violation or breach of, or
     constitute (with or without due notice or lapse of time or both) a default
     (or give rise to any right of termination, cancellation or acceleration)
     under, or require any consent under, any indenture, license, contract,
     agreement or other instrument or obligation to which Seller is a party,
     (iii) violate any order, writ, injunction, decree or award rendered by any
     governmental or regulatory authority or court, domestic or foreign (a
     "Governmental Entity") or any statute, rule or regulation (collectively,
     "Laws") applicable to Seller or (iv) require any filing with, or the
     obtaining of any permit, authorization, consent or approval of, any
     Governmental Authority. All requirements under the Indentures that are
     required to be satisfied prior to the sale of the Shares hereunder have
     been satisfied.

     Section 4.  Representations and Warranties of Buyer. Buyer represents and
                 ---------------------------------------
warrants to Seller as follows:

          (a)  Organization.  Buyer is a limited liability company validly
               ------------
     existing and in good standing under the laws of the State of Delaware and
     has the requisite power and authority to carry on its business
     substantially as it is now being conducted. Liberty Media Corporation, a
     Delaware corporation ("Liberty"), is the sole member of Buyer.

          (b)  Authority Relative to this Agreement.  Buyer has the power and
               ------------------------------------
     authority to execute and deliver this Agreement and to consummate the
     transactions contemplated hereby. The execution and delivery of this
     Agreement and the consummation of the transactions contemplated hereby have
     been duly and validly authorized by all requisite action on the part of
     Buyer. This Agreement has been duly and validly executed and delivered by
     Buyer and constitutes a valid and binding agreement of Buyer, enforceable
     against Buyer in accordance with its terms, except that such enforcement
     may be subject

                                       3
<PAGE>

     to any bankruptcy, insolvency, reorganization, moratorium, fraudulent
     transfer or other laws, now or hereafter in effect, relating to or limiting
     creditors' rights generally and the application of general principles of
     equity.

          (c)  Consents and Approvals; No Violations.  Neither the execution
               -------------------------------------
     and delivery of this Agreement by Buyer, nor the consummation by Buyer of
     the transactions contemplated hereby will (i) conflict with or result in
     any breach of any provision of the operating agreement or other
     organizational documents of Buyer, (ii) result in a violation or breach of,
     or constitute (with or without due notice or lapse of time or both) a
     default (or give rise to any right of termination, cancellation or
     acceleration) under, or require any consent under, any indenture, license,
     contract, agreement or other instrument or obligation to which the Buyer is
     a party, (iii) violate any order, writ, injunction, decree or award
     rendered by any Governmental Entity or any Laws applicable to Buyer, or
     (iii) require any filing with, or the obtaining of any permit,
     authorization, consent or approval of, any Governmental Entity.

          (d)  Buyer Acknowledgment.  Buyer acknowledges and understands that
               --------------------
     the offer and sale of the Shares by Seller to Buyer hereunder has not been
     registered under the Securities Act of 1933, as amended (the "Act"), and
     that Buyer may not sell or dispose of the Shares other than in a
     transaction that complies with the registration requirements of the Act,
     unless an exemption is available therefrom. Buyer is purchasing the Shares
     for investment, and not with a view to the distribution thereof in
     violation of the Act.

     Section 5.  Covenant re Use of Proceeds. Seller covenants and agrees with
                 ---------------------------
Buyer that, immediately following payment by Buyer to Seller of the Purchase
Price hereunder and the "Purchase Price" as defined in the Other Stock Purchase
Agreement, Seller will repurchase its Notes in accordance with the terms of the
Resale Agreement.

     Section 6.  Governing Law; Waiver of Jury Trial, Etc.  This Agreement
                 -----------------------------------------
shall be governed by and construed in accordance with the laws of the State of
Colorado applied to contracts made and wholly performed in such State, without
regard to principles governing conflicts of law. Each of the parties (a) will
submit itself to the non-exclusive jurisdiction of any federal court located in
the State of Colorado or any Colorado state court having subject matter
jurisdiction in the event any dispute arises out of this Agreement, (b) agrees
that venue will be proper as to any proceeding brought in any such court with
respect to such a dispute, (c) will not attempt to deny or defeat such personal
jurisdiction or venue by motion or other request for leave from any such court
and (d) WAIVES ANY RIGHT TO A TRIAL BY JURY in any proceeding brought with
respect to this Agreement or the transactions contemplated hereby.

     Section 7.  Descriptive Headings.  The descriptive headings herein are
                 --------------------
inserted for convenience of reference only and shall in no way be construed to
define, limit, describe, explain, modify, amplify, or add to the interpretation,
construction or meaning of any provision of, or scope or intent of, this
Agreement nor in any way affect this Agreement.

     Section 8.  Counterparts. This Agreement may be signed in counter-parts
                 ------------
and all signed copies of this Agreement will together constitute one original of
this Agreement. This

                                       4
<PAGE>

Agreement shall become effective when each party hereto shall have received
counterparts thereof signed by all the other parties hereto.

     Section 9.  Assignment.  Neither this Agreement nor any of the rights,
                 ----------
interests or obligations hereunder shall be assigned by any of the parties
hereto without the prior written consent of the other party, except that Buyer
may transfer the Shares (or any portion thereof) to another direct or indirect
wholly owned subsidiary of Liberty. Subject to the preceding sentence, this
Agreement will be binding upon, inure to the benefit of and be enforceable by
the parties and their respective successors and assigns.

                                       5
<PAGE>

     Each of the undersigned has caused this Agreement to be duly signed as of
the date first above written.

                                        UNITED GLOBALCOM, INC.

                                        By: /s/ Michael T. Fries
                                           ----------------------------
                                           Name:  Michael T. Fries
                                           Title: President

                                        LIBERTY UCOMA, LLC

                                        By: /s/ Dave Flowers
                                           ----------------------------
                                           Name:  Dave Flowers
                                           Title: Senior Vice President

                                       6

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