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    Hong,<br>
    <br>
    Everything seems to be working well so far.<br>
    I would say there is nothing to acknowledge, but I don't mind...<br>
    <br>
    Please let me know if there will be support for mpiaij_mpidense.<br>
    <br>
    Thanks for this great support.<br>
    <br>
    On 08.02.2012 18:43, Hong Zhang wrote:
    <blockquote
cite="mid:CAGCphBsuHe2wKMN1ZpjrNkv1Ev6vT3cuDSTHWNoUdmPu0Zh5yg@mail.gmail.com"
      type="cite">Alexander:
      <div>Recently, we add error flags in petsc-dev
        requiring MatXXXSetPreallocation() for many matrix creation
        routines.</div>
      <div>I've updated relevant routines for your code, and add your
        contributed testing code as a petsc example with acknowledge:</div>
      <div>petsc-dev/src/mat/examples/tests/ex165.c</div>
      <div>Let me know if you do not want your name to be acknowledge in
        the example.</div>
      <div><br>
      </div>
      <div>I tested ex165 with your A and B in sequential (np=1) and
        parallel (np=2, 6):</div>
      <div>mpiexec -n <np> ./ex165 -fA A.dat -fB B.dat -view_C</div>
      <div><br>
      </div>
      <div>Checking the size of output file C.dat, I see the sequential
        run and parallel run give identical bit size. </div>
      <div>Please get the updated petsc-dev and test it. Let me know if
        you still have problem.</div>
      <div><br>
      </div>
      <div>It is inefficient to compute C=A^T*B via MatTranspose() and
        MatMatMult().</div>
      <div>I'll see if I can write a C=A^T*B  for mpiaij_mpidense. </div>
      <div><br>
      </div>
      <div>Hong</div>
      <div>
        <div class="gmail_quote">
          <blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt
            0.8ex; border-left: 1px solid rgb(204, 204, 204);
            padding-left: 1ex;">
            <div bgcolor="#ffffff" text="#000000"><br>
              In addition, I changed my code and form A^T explicitly (to
              avoid previous error) and I got another one:
              <div class="im"><br>
                <br>
                [1]PETSC ERROR: --------------------- Error Message
                ------------------------------------<br>
              </div>
              [1]PETSC ERROR: Object is in wrong state!<br>
              [1]PETSC ERROR: Must call MatXXXSetPreallocation() or
              MatSetUp() on argument 1 "mat" before MatAssemblyBegin()!<br>
              [1]PETSC ERROR:
              ------------------------------------------------------------------------<br>
              [1]PETSC ERROR: Petsc Development HG revision:
              249597282bcb6a1051042a9fdfa5705679ed4f18  HG Date: Tue Feb
              07 09:44:23 2012 -0600<br>
              [1]PETSC ERROR: See docs/changes/index.html for recent
              updates.<br>
              [1]PETSC ERROR: See docs/faq.html for hints about trouble
              shooting.<br>
              [1]PETSC ERROR: See docs/index.html for manual pages.<br>
              [1]PETSC ERROR:
              ------------------------------------------------------------------------<br>
              [1]PETSC ERROR: solveTest on a openmpi-i named glic1 by
              agrayver Wed Feb  8 13:06:45 2012<br>
              [1]PETSC ERROR: Libraries linked from
              /home/lib/petsc-dev/openmpi-intel-complex-debug-f-mkl/lib<br>
              [1]PETSC ERROR: Configure run at Tue Feb  7 18:19:58 2012<br>
              [1]PETSC ERROR: Configure options
              --with-petsc-arch=openmpi-intel-complex-debug-f-mkl
              --with-fortran-interfaces=1 --download-superlu
              --download-superlu_dist --download-mumps
              --download-parmetis --download-ptscotch --download-metis
              --with-scalapack-lib=/opt/intel/Compiler/11.1/072/mkl/lib/em64t/libmkl_scalapack_lp64.a

              --with-scalapack-include=/opt/intel/Compiler/11.1/072/mkl/include

              --with-blacs-lib=/opt/intel/Compiler/11.1/072/mkl/lib/em64t/libmkl_blacs_openmpi_lp64.a

              --with-blacs-include=/opt/intel/Compiler/11.1/072/mkl/include

              --with-mpi-dir=/opt/mpi/intel/openmpi-1.4.2
              --with-scalar-type=complex
              --with-blas-lapack-lib="[/opt/intel/Compiler/11.1/072/mkl/lib/em64t/libmkl_intel_lp64.a,/opt/intel/Compiler/11.1/072/mkl/lib/em64t/libmkl_intel_thread.a,/opt/intel/Compiler/11.1/072/mkl/lib/em64t/libmkl_core.a,/opt/intel/Compiler/11.1/072/lib/intel64/libiomp5.a]"

              --with-precision=double --with-x=0<br>
              [1]PETSC ERROR:
              ------------------------------------------------------------------------<br>
              [1]PETSC ERROR: MatAssemblyBegin() line 4795 in
              /home/lib/petsc-dev/src/mat/interface/matrix.c<br>
              [1]PETSC ERROR: MatMatMultSymbolic_MPIAIJ_MPIDense() line
              638 in
              /home/lib/petsc-dev/src/mat/impls/aij/mpi/mpimatmatmult.c<br>
              [1]PETSC ERROR: MatMatMult_MPIAIJ_MPIDense() line 594 in
              /home/lib/petsc-dev/src/mat/impls/aij/mpi/mpimatmatmult.c<br>
              [1]PETSC ERROR: MatMatMult() line 8618 in
              /home/lib/petsc-dev/src/mat/interface/matrix.c
              <div>
                <div class="h5"><br>
                  <br>
                  On 08.02.2012 17:45, Hong Zhang wrote:
                  <blockquote type="cite">Alexander :
                    <div>I can repeat the crash, and am working on it.</div>
                    <div>I'll let you know after the bug is fixed.</div>
                    <div><br>
                    </div>
                    <div>Thanks for your patience,</div>
                    <div>Hong<br>
                      <div class="gmail_quote">
                        <blockquote class="gmail_quote" style="margin:
                          0pt 0pt 0pt 0.8ex; border-left: 1px solid
                          rgb(204, 204, 204); padding-left: 1ex;">
                          <div bgcolor="#ffffff" text="#000000"> <br>
                            It seems now I know why I used
                            MAT_REUSE_MATRIX and preallocated matrix.<br>
                            I removed MatCreateMPIAIJ() and use just
                            MatTranspose with MAT_INITIAL_MATRIX.<br>
                            As a consequence I get hundreds of errors
                            like:<br>
                            <br>
                            [30]PETSC ERROR: MatSetValues_MPIAIJ() line
                            538 in
                            /home/mt/agrayver/lib/petsc-dev/src/mat/impls/aij/mpi/mpiaij.c<br>
                            [30]PETSC ERROR: MatAssemblyEnd_MPIAIJ()
                            line 653 in
                            /home/mt/agrayver/lib/petsc-dev/src/mat/impls/aij/mpi/mpiaij.c<br>
                            [30]PETSC ERROR: MatAssemblyEnd() line 4978
                            in
                            /home/mt/agrayver/lib/petsc-dev/src/mat/interface/matrix.c<br>
                            [30]PETSC ERROR: MatTranspose_MPIAIJ() line
                            2061 in
                            /home/mt/agrayver/lib/petsc-dev/src/mat/impls/aij/mpi/mpiaij.c<br>
                            [30]PETSC ERROR: MatTranspose() line 4397 in
/home/mt/agrayver/lib/petsc-dev/src/mat/interface/matrix.c<br>
                            [31]PETSC ERROR: --------------------- Error
                            Message ------------------------------------<br>
                            [31]PETSC ERROR: Argument out of range!<br>
                            [31]PETSC ERROR: New nonzero at (1659,53337)
                            caused a malloc!<br>
                            <br>
                            Ans this is the lastest petsc-dev revision.
                            <br>
                            I know there were some changes in petsc-dev
                            concerning this issue. <br>
                            Can you give me a hint how to avoid this?<br>
                            <br>
                            As for why I need C=A^T*B. This product is
                            used further as a system matrix for LSQR
                            solver. The largest dimension is on the
                            order of 10^6<br>
                            Since I form A and B myself I can, of
                            course, form A^T explicitly, but I thought I
                            would first implement everything as it is
                            written down on paper and then optimize once
                            it works (I thought it's easier way).
                            <div>
                              <div><br>
                                <br>
                                On 07.02.2012 20:44, Hong Zhang wrote:
                                <blockquote type="cite">Alexander,
                                  <div>I'm curious about why do you need
                                    parallel C=A^T*B?</div>
                                  <div>How large your matrices are?</div>
                                  <div><br>
                                  </div>
                                  <div>In petsc-dev, we
                                    have MatTransposeMatMult() for
                                    mpiaij and mpiaij, but not mpiaij
                                    and mpidense.</div>
                                  <div>We may add support
                                    of MatTransposeMatMult_MPIAIJ_MPIDense()
                                    if there is such need.</div>
                                  <div><br>
                                  </div>
                                  <div>Hong</div>
                                  <div><br>
                                    <br>
                                    <div class="gmail_quote">On Tue, Feb
                                      7, 2012 at 1:18 PM, <a
                                        moz-do-not-send="true"
                                        href="mailto:agrayver@gfz-potsdam.de"
                                        target="_blank">agrayver@gfz-potsdam.de</a>
                                      <span dir="ltr"><<a
                                          moz-do-not-send="true"
                                          href="mailto:agrayver@gfz-potsdam.de"
                                          target="_blank">agrayver@gfz-potsdam.de</a>></span>
                                      wrote:<br>
                                      <blockquote class="gmail_quote"
                                        style="margin: 0pt 0pt 0pt
                                        0.8ex; border-left: 1px solid
                                        rgb(204, 204, 204);
                                        padding-left: 1ex;">Hong,<br>
                                        <br>
                                        Thanks for explanation. I will
                                        try this tomorrow. Good to have
                                        this stuff in the help now.<br>
                                        <br>
                                        And sorry for misleading you
                                        initially.<br>
                                        <br>
                                        Regards,<br>
                                        Alexander
                                        <div>
                                          <div><br>
                                            <br>
                                            <div>----- Reply message
                                              -----<br>
                                              From: "Hong Zhang" <<a
                                                moz-do-not-send="true"
                                                href="mailto:hzhang@mcs.anl.gov"
                                                target="_blank">hzhang@mcs.anl.gov</a>><br>
                                              To: "For users of the
                                              development version of
                                              PETSc" <<a
                                                moz-do-not-send="true"
                                                href="mailto:petsc-dev@mcs.anl.gov"
                                                target="_blank">petsc-dev@mcs.anl.gov</a>><br>
                                              Subject: [petsc-dev]
                                              MatMatMult gives different
                                              results<br>
                                              Date: Tue, Feb 7, 2012
                                              19:09<br>
                                              <br>
                                            </div>
                                            <br>
                                            Alexander :
                                            <div class="gmail_quote">
                                              <blockquote
                                                class="gmail_quote"
                                                style="margin: 0pt 0pt
                                                0pt 0.8ex; border-left:
                                                1px solid rgb(204, 204,
                                                204); padding-left:
                                                1ex;">
                                                <div bgcolor="#ffffff"
                                                  text="#000000"><br>
                                                  There is something I
                                                  didn't get yet, I hope
                                                  you could clarify it.
                                                  <br>
                                                  <br>
                                                  So, when I use flag
                                                  MAT_INITIAL_MATRIX in
                                                  test program it works
                                                  fine.<br>
                                                </div>
                                              </blockquote>
                                              <div>Good to know :-)</div>
                                              <div> </div>
                                              <blockquote
                                                class="gmail_quote"
                                                style="margin: 0pt 0pt
                                                0pt 0.8ex; border-left:
                                                1px solid rgb(204, 204,
                                                204); padding-left:
                                                1ex;">
                                                <div bgcolor="#ffffff"
                                                  text="#000000"> If I
                                                  put this flag in my
                                                  original program I get
                                                  dozens of exceptions
                                                  like:<br>
                                                  [42]PETSC ERROR:
                                                  Argument out of range!<br>
                                                  [42]PETSC ERROR: New
                                                  nonzero at
                                                  (1336,153341) caused a
                                                  malloc!<br>
                                                </div>
                                              </blockquote>
                                              <div>You cannot do </div>
                                              <div> <span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;">MatCreateMPIAIJ()</span></div>
                                              <div><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;">MatTranspose(A,MAT_INITIAL_MATRIX,&AT);</span></div>
                                              <div><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;"><br>
                                                </span></div>
                                              <div><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;">MatCreateMPIAIJ()

                                                  creates AT and
                                                  preallocates
                                                  approximate nonzeros,
                                                  which does not match
                                                  exactly the nonzeros
                                                  in </span></div>
                                              <div><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;">MatTranspose(A,MAT_INITIAL_MATRIX,&AT);</span></div>
                                              <div><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;">MatTranspose(A,MAT_INITIAL_MATRIX,&AT)


                                                  creates matrix AT and
                                                  sets correct nonzero
                                                  pattern and values in
                                                  AT. </span></div>
                                              <div><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;">MatTranspose()

                                                  only takes in "</span><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;">MAT_INITIAL_MATRIX"

                                                  - for a new AT,</span></div>
                                              <div><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;">and
                                                  "MAT_REUSE_MATRIX"
                                                  when AT is created
                                                  with </span><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;">MatTranspose(A,MAT_INITIAL_MATRIX,&AT)</span></div>
                                              <div><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;">and
                                                  reuse for updating its
                                                  values (not nonzero
                                                  patten).</span></div>
                                              <div><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;"><br>
                                                </span></div>
                                              <div><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;">I'm
                                                  updating petsc help
                                                  menu on </span><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;">MatTranspose().

                                                  Thanks for the report.</span></div>
                                              <div><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;"><br>
                                                </span></div>
                                              <div><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;">Hong</span></div>
                                              <div><span
                                                  style="border-collapse:
                                                  collapse; color:
                                                  rgb(80, 0, 80);
                                                  font-family:
                                                  arial,sans-serif;
                                                  font-size: 14px;"><br>
                                                </span></div>
                                              <blockquote
                                                class="gmail_quote"
                                                style="margin: 0pt 0pt
                                                0pt 0.8ex; border-left:
                                                1px solid rgb(204, 204,
                                                204); padding-left:
                                                1ex;">
                                                <div bgcolor="#ffffff"
                                                  text="#000000"> <br>
                                                  I changed this flag to
                                                  MAT_REUSE_MATRIX and
                                                  exceptions
                                                  disappeared, but
                                                  result is incorrect
                                                  again (same as for
                                                  MAT_IGNORE_MATRIX)  <br>
                                                  I tried test program
                                                  with MAT_REUSE_MATRIX
                                                  and it also gives
                                                  different matrix
                                                  product.<br>
                                                  <br>
                                                  Since there is no
                                                  description of
                                                  MatReuse structure for
                                                  MatTranspose it's a
                                                  bit confusing what to
                                                  expect from it. <br>
                                                  <div>
                                                    <div> <br>
                                                      <blockquote
                                                        type="cite">
                                                        <div
                                                          class="gmail_quote">
                                                          <blockquote
                                                          class="gmail_quote"
                                                          style="margin:
                                                          0pt 0pt 0pt
                                                          0.8ex;
                                                          border-left:
                                                          1px solid
                                                          rgb(204, 204,
                                                          204);
                                                          padding-left:
                                                          1ex;">
                                                          <div
                                                          bgcolor="#ffffff"
                                                          text="#000000">
                                                          <div>
                                                          <blockquote
                                                          type="cite">
                                                          <div>
                                                          <div
                                                          class="gmail_quote">
                                                          <div><br>
                                                          </div>
                                                          <div>Do you
                                                          mean 'Cm =
                                                          A'*B;'? </div>
                                                          <div>'Cm =
                                                          A.'*B;' gives
                                                          component-wise
                                                          matrix
                                                          product, not
                                                          matrix
                                                          product.</div>
                                                          </div>
                                                          </div>
                                                          </blockquote>
                                                          <br>
                                                          </div>
                                                          .' operator
                                                          means
                                                          non-Hermitian
                                                          transpose.
                                                          That is what I
                                                          get with
                                                          MatTranspose
                                                          (in contrast
                                                          with
                                                          MatHermitianTranspose)<br>
                                                          component-wise
                                                          matrix product
                                                          would be .*</div>
                                                          </blockquote>
                                                          <div>You are
                                                          correct.</div>
                                                          <div><br>
                                                          </div>
                                                          <div>Hong </div>
                                                          <blockquote
                                                          class="gmail_quote"
                                                          style="margin:
                                                          0pt 0pt 0pt
                                                          0.8ex;
                                                          border-left:
                                                          1px solid
                                                          rgb(204, 204,
                                                          204);
                                                          padding-left:
                                                          1ex;">
                                                          <div
                                                          bgcolor="#ffffff"
                                                          text="#000000">
                                                          <div>
                                                          <div><br>
                                                          <br>
                                                          <blockquote
                                                          type="cite">
                                                          <div>
                                                          <div
                                                          class="gmail_quote">
                                                          <div><br>
                                                          </div>
                                                          <div>Hong</div>
                                                          <div><br>
                                                          </div>
                                                          <div> </div>
                                                          <blockquote
                                                          class="gmail_quote"
                                                          style="margin:
                                                          0pt 0pt 0pt
                                                          0.8ex;
                                                          border-left:
                                                          1px solid
                                                          rgb(204, 204,
                                                          204);
                                                          padding-left:
                                                          1ex;">
                                                          <div
                                                          bgcolor="#ffffff"
                                                          text="#000000">
                                                          C =
                                                          PetscBinaryRead('C.dat','complex',true);<br>
                                                          <br>
                                                          Matrix C is
                                                          different
                                                          depending on
                                                          number of
                                                          cores I use. <br>
                                                          My PETSc is:<br>
                                                          Using Petsc
                                                          Development HG
                                                          revision:
                                                          876c894d95f4fa6561d0a91310ca914592527960 
                                                          HG Date: Tue
                                                          Jan 10
                                                          19:27:14 2012
                                                          +0100
                                                          <div>
                                                          <div><br>
                                                          <br>
                                                          On 06.02.2012
                                                          17:13, Hong
                                                          Zhang wrote:
                                                          <blockquote
                                                          type="cite">MatMatMult()


                                                          in petsc is
                                                          not
                                                          well-tested
                                                          for complex -
                                                          could be
                                                          buggy.
                                                          <div>Can you
                                                          send us the
                                                          matrices A and
                                                          B in petsc
                                                          binary format
                                                          for
                                                          investigation?</div>
                                                          <div><br>
                                                          </div>
                                                          <div>Hong<br>
                                                          <br>
                                                          <div
                                                          class="gmail_quote">On


                                                          Mon, Feb 6,
                                                          2012 at 5:55
                                                          AM, Alexander
                                                          Grayver <span
                                                          dir="ltr"><<a
moz-do-not-send="true" href="mailto:agrayver@gfz-potsdam.de"
                                                          target="_blank">agrayver@gfz-potsdam.de</a>></span>
                                                          wrote:<br>
                                                          <blockquote
                                                          class="gmail_quote"
                                                          style="margin:
                                                          0pt 0pt 0pt
                                                          0.8ex;
                                                          border-left:
                                                          1px solid
                                                          rgb(204, 204,
                                                          204);
                                                          padding-left:
                                                          1ex;">Dear
                                                          PETSc team,<br>
                                                          <br>
                                                          I try to use:<br>
                                                          call
MatMatMult(A,B,MAT_INITIAL_MATRIX,PETSC_DEFAULT_DOUBLE_PRECISION,C,ierr);CHKERRQ(ierr)<br>
                                                          <br>
                                                          Where both A
                                                          and B are
                                                          rectangular,
                                                          but A is
                                                          sparse and B
                                                          is dense. Both
                                                          are double
                                                          complex and
                                                          distributed.<br>
                                                          The product
                                                          PETSc gives me
                                                          contains some
                                                          errors in some
                                                          part of the
                                                          matrix.<br>
                                                          I output A, B
                                                          and C then
                                                          computed
                                                          product in
                                                          matlab.<br>
                                                          <br>
                                                          Attached you
                                                          see figure
                                                          plotted as:<br>
imagesc(log10(abs(C-Cm)))<br>
                                                          <br>
                                                          Where Cm --
                                                          product
                                                          computed in
                                                          matlab.<br>
                                                          <br>
                                                          The pattern
                                                          and amplitude
                                                          vary depending
                                                          on the number
                                                          of cores I
                                                          use. This
                                                          picture is
                                                          obtained for
                                                          48 cores (I've
                                                          tried 12, 64
                                                          cores as
                                                          well).<br>
                                                          <br>
                                                          Where should I
                                                          look for
                                                          possible
                                                          explanation?<span><font
color="#888888"><br>
                                                          <br>
                                                          -- <br>
                                                          Regards,<br>
                                                          Alexander<br>
                                                          </font></span></blockquote>
                                                          </div>
                                                          <br>
                                                          </div>
                                                          </blockquote>
                                                          <br>
                                                          <br>
                                                          </div>
                                                          </div>
                                                          <span><font
                                                          color="#888888">
                                                          <pre cols="72">-- 
Regards,
Alexander</pre>
                                                          </font></span></div>
                                                          </blockquote>
                                                          </div>
                                                          <br>
                                                          </div>
                                                          </blockquote>
                                                          <br>
                                                          <br>
                                                          </div>
                                                          </div>
                                                          <span><font
                                                          color="#888888">
                                                          <pre cols="72">-- 
Regards,
Alexander</pre>
                                                          </font></span></div>
                                                          </blockquote>
                                                        </div>
                                                        <br>
                                                      </blockquote>
                                                      <br>
                                                      <br>
                                                    </div>
                                                  </div>
                                                  <span><font
                                                      color="#888888">
                                                      <pre cols="72">-- 
Regards,
Alexander</pre>
                                                    </font></span></div>
                                              </blockquote>
                                            </div>
                                            <br>
                                          </div>
                                        </div>
                                      </blockquote>
                                    </div>
                                    <br>
                                  </div>
                                </blockquote>
                                <br>
                                <br>
                              </div>
                            </div>
                            <span><font color="#888888">
                                <pre cols="72">-- 
Regards,
Alexander</pre>
                              </font></span></div>
                        </blockquote>
                      </div>
                      <br>
                    </div>
                  </blockquote>
                  <br>
                  <br>
                </div>
              </div>
              <span class="HOEnZb"><font color="#888888">
                  <pre cols="72">-- 
Regards,
Alexander</pre>
                </font></span></div>
          </blockquote>
        </div>
        <br>
      </div>
    </blockquote>
    <br>
    <br>
    <pre class="moz-signature" cols="72">-- 
Regards,
Alexander</pre>
  </body>
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