<html><head><base href="x-msg://77/"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br><div><div>On Jan 5, 2012, at 6:12 PM, Ravi Kannan wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><span class="Apple-style-span" style="border-collapse: separate; font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><div lang="EN-US" link="blue" vlink="purple" style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div class="WordSection1" style="page: WordSection1; "><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">Hi Mark,<o:p></o:p></span></div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "><o:p> </o:p></span></div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "><o:p> </o:p></span></div><div><div style="border-right-style: none; border-bottom-style: none; border-left-style: none; border-width: initial; border-color: initial; border-top-style: solid; border-top-color: rgb(181, 196, 223); border-top-width: 1pt; padding-top: 3pt; padding-right: 0in; padding-bottom: 0in; padding-left: 0in; "><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><b><span style="font-size: 10pt; font-family: Tahoma, sans-serif; ">From:</span></b><span style="font-size: 10pt; font-family: Tahoma, sans-serif; "><span class="Apple-converted-space"> </span><a href="mailto:petsc-dev-bounces@mcs.anl.gov" style="color: blue; text-decoration: underline; ">petsc-dev-bounces@mcs.anl.gov</a><span class="Apple-converted-space"> </span>[mailto:petsc-dev-bounces@mcs.anl.gov]<span class="Apple-converted-space"> </span><b>On Behalf Of<span class="Apple-converted-space"> </span></b>Mark F. Adams<br><b>Sent:</b><span class="Apple-converted-space"> </span>Wednesday, January 04, 2012 12:09 PM<br><b>To:</b><span class="Apple-converted-space"> </span>For users of the development version of PETSc<br><b>Subject:</b><span class="Apple-converted-space"> </span>Re: [petsc-dev] boomerAmg scalability<o:p></o:p></span></div></div></div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><o:p> </o:p></div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; ">Is your problem unsymmetric? I don't think this is the problem, it was fixed recently.<o:p></o:p></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><o:p> </o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; ">If not, can you run with -pc_gamg_verbose and -info and send me the output?<o:p></o:p></div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">I have attached the verbose+info outputs for both the serial and the parallel (2 partitions). NOTE: the serial output at some location says PC=Jacobi! Is it implicitly converting the PC to a Jacobi?</span></div></div></div></div></span></blockquote><div><br></div>That is an error in the print out.</div><div>Mark<br><blockquote type="cite"><span class="Apple-style-span" style="border-collapse: separate; font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><div lang="EN-US" link="blue" vlink="purple" style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div class="WordSection1" style="page: WordSection1; "><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "><o:p></o:p></span></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><o:p> </o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; ">You don't need to set the block size if it is 1.<o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><o:p> </o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; ">I have a feeling it has to do with not setting the buffer sizes correctly. There are some heuristics in there and this needs to be improved. What kind of discretization are you using? What order, how many non-zeros per row? Maybe try the smallest case that you have with more processors. I have a feeling it is trashing around mallocing stuff in MatSetValues so it just "looks" hung.<o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><o:p> </o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; ">Mark<o:p></o:p></div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "><o:p> </o:p></span></div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">Thanks,<o:p></o:p></span></div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">Ravi.<o:p></o:p></span></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><o:p> </o:p></div></div><div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; ">On Jan 4, 2012, at 12:14 PM, Ravi Kannan wrote:<o:p></o:p></div></div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><br><br><o:p></o:p></div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">Hi Mark, Matt,</span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "> </span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">We recently downloaded the petsc development version, to test the gamg package.</span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "> </span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">This works in serial : we tried for small cases. The parallel case (even with 2 partitions) just hangs. As of now, we have not set any parameters. So I guess that the default parameters are being used.</span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "> </span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">Do we need to explicitly set the block size to MatSetBlockSize(mat,1) for a PARALLEL run? Our solver solves U,V,W and P separately.</span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "> </span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">Any input on this would be great.</span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "> </span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">Thanks,</span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">Ravi.</span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "> </span><o:p></o:p></div></div><div><div style="border-right-style: none; border-bottom-style: none; border-left-style: none; border-width: initial; border-color: initial; border-top-style: solid; padding-top: 3pt; padding-right: 0in; padding-bottom: 0in; padding-left: 0in; border-width: initial; border-color: initial; "><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><b><span style="font-size: 10pt; font-family: Tahoma, sans-serif; ">From:</span></b><span class="apple-converted-space"><span style="font-size: 10pt; font-family: Tahoma, sans-serif; "> </span></span><span style="font-size: 10pt; font-family: Tahoma, sans-serif; "><a href="mailto:petsc-dev-bounces@mcs.anl.gov" style="color: blue; text-decoration: underline; ">petsc-dev-bounces@mcs.anl.gov</a><span class="apple-converted-space"> </span>[mailto:petsc-dev-bounces@mcs.anl.gov]<span class="apple-converted-space"> </span><b>On Behalf Of<span class="apple-converted-space"> </span></b>Mark F. Adams<br><b>Sent:</b><span class="apple-converted-space"> </span>Thursday, December 15, 2011 1:18 PM<br><b>To:</b><span class="apple-converted-space"> </span>For users of the development version of PETSc<br><b>Subject:</b><span class="apple-converted-space"> </span>Re: [petsc-dev] boomerAmg scalability</span><o:p></o:p></div></div></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "> <o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "> <o:p></o:p></div></div><div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; ">On Dec 15, 2011, at 1:56 PM, Matthew Knepley wrote:<o:p></o:p></div></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><br><br><br><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; ">On Thu, Dec 15, 2011 at 10:23 AM, Ravi Kannan <<a href="mailto:rxk@cfdrc.com" style="color: blue; text-decoration: underline; ">rxk@cfdrc.com</a>> wrote:<o:p></o:p></div></div><div><blockquote style="border-top-style: none; border-right-style: none; border-bottom-style: none; border-width: initial; border-color: initial; border-left-style: solid; padding-top: 0in; padding-right: 0in; padding-bottom: 0in; padding-left: 6pt; margin-left: 4.8pt; margin-top: 5pt; margin-right: 0in; margin-bottom: 5pt; border-width: initial; border-color: initial; z-index: auto; "><div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">Dear All,</span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "> </span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">This is Ravi Kannan from CFD Research Corporation. Recently, we are experimenting with the BoomerAMG preconditioner for some “stiff” CFD problems. In that regard, all the other standard solver-preconditioner combinations failed for the current CFD problem. The boomer is the only one which is able to provide with “converged” solutions.</span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "> </span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">We noticed that the scalability of this boomer preconditioner is really poor. For instance, even with a cell size of 2 million, we cannot scale to even 16 partitions (in contrast, the other solver-preconditioner combinations like the BI-CGS/BJacobi gave good enough scalability).</span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "> </span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">Are we missing something? Do we need to use a more latest version of boomer?</span><o:p></o:p></div></div></div></div></blockquote><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "> <o:p></o:p></div></div></div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; ">Have you tried -pc_type gamg in petsc-dev?<o:p></o:p></div></div></div></div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "> <o:p></o:p></div></div></div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; ">For gamg you also want to use MPIAIJ matrices and set the block size MatSetBlockSize(mat,3), for a 3D velocity field, for instance. You can also try '-pc_gamg_type pa' or '-pc_gamg_type sa'. "pa", for plain aggregation might be better for CFD problems.<o:p></o:p></div></div></div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "> <o:p></o:p></div></div></div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; ">Mark<o:p></o:p></div></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><br><br><br><o:p></o:p></div></div><div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "> <o:p></o:p></div></div></div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "> Matt<o:p></o:p></div></div></div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "> <span class="apple-style-span"><span style="font-size: 14.5pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); "> </span></span><o:p></o:p></div></div></div><blockquote style="border-top-style: none; border-right-style: none; border-bottom-style: none; border-width: initial; border-color: initial; border-left-style: solid; padding-top: 0in; padding-right: 0in; padding-bottom: 0in; padding-left: 6pt; margin-left: 4.8pt; margin-top: 5pt; margin-right: 0in; margin-bottom: 5pt; border-width: initial; border-color: initial; "><div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">Thanks,</span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><span style="font-size: 14pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125); ">Ravi.</span><o:p></o:p></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "> <o:p></o:p></div></div></div></div></blockquote></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><br clear="all"><o:p></o:p></div></div><div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "> <o:p></o:p></div></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; ">--<span class="apple-converted-space"> </span><br>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener<o:p></o:p></div></div></div><div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "> <o:p></o:p></div></div></div></div><div style="margin-top: 0in; margin-right: 0in; margin-left: 0in; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; "><o:p> </o:p></div></div></div></div></span></blockquote></div><br></body></html>