(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 2092231, 51277] NotebookOptionsPosition[ 2054526, 50310] NotebookOutlinePosition[ 2073769, 50747] CellTagsIndexPosition[ 2073687, 50742] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Implicitization via the Gr\[ODoubleDot]bner Walk\ \>", "Title", CellChangeTimes->{{3.390223907378748*^9, 3.390223919017443*^9}, { 3.390224311241296*^9, 3.390224324840173*^9}}], Cell["\<\ Daniel Lichtblau Wolfram Research, Inc. 100 Trade Center Dr. Champaign IL USA 61820 danl@wolfram.com\ \>", "Author", CellChangeTimes->{ 3.390223946997383*^9, {3.390224085170671*^9, 3.390224087938007*^9}, 3.390860617924356*^9}, FontSlant->"Plain"], Cell["\<\ ACA 2007 Approximate Algebraic Computation Session Oakland University Rochester MI July 19\[Hyphen]22, 2007\ \>", "Author", CellChangeTimes->{{3.390317517673263*^9, 3.390317599419289*^9}, { 3.390317640333511*^9, 3.390317659126299*^9}, 3.390858909209144*^9}, FontSize->18, FontSlant->"Plain"], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell["\<\ Abstract: The Gr\[ODoubleDot]bner walk is a useful method for conversion from \ a \"simple\" Gr\[ODoubleDot]bner basis to a different one in a desired term \ order.Various issues along the way include coefficient swell (similar to that \ seen in the classical Buchberger algorithm), polynomials with many initial \ elements in the \"end-game\" phase, and the like.We take as benchmark the \ implicitization of the 32 bicubic parametric patches in the Newell (Utah) \ teapot.We will see how the Gr\[ODoubleDot]bner walk can be used to \ implicitize all of them, using in some cases approximate arithmetic and an \ early abort strategy, with a result that can be certified a posteriori.To the \ best of my knowledge the four spout patches have never before been amenable \ to a Gr\[ODoubleDot]bner basis approach. We show some other nontrivial \ examples from the implicitization literature.\ \>", "Abstract", CellChangeTimes->{ 3.390224163584063*^9, {3.390224300686546*^9, 3.390224304027503*^9}, { 3.390224334389834*^9, 3.390224371286941*^9}, {3.390414205534237*^9, 3.390414227228353*^9}, 3.390580394752952*^9, {3.390581597214943*^9, 3.390581616171803*^9}, {3.3908530174004*^9, 3.390853020093636*^9}}, FontSize->18], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Introduction", "Section", CellChangeTimes->{ 3.390224482398088*^9, {3.390224527680198*^9, 3.390224529799909*^9}}], Cell[CellGroupData[{ Cell["What is the Gr\[ODoubleDot]bner walk?", "Subsection", CellChangeTimes->{{3.390225384811269*^9, 3.390225415716788*^9}}], Cell["\<\ It is a method to convert from an \"easy\" Gr\[ODoubleDot]bner basis to a \ desired one that might be more difficult to compute directly.\ \>", "Subsubsection", CellChangeTimes->{{3.390224531897484*^9, 3.390224675876451*^9}, 3.390225420465026*^9, {3.390746893221656*^9, 3.390746894849695*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["What is it used for?", "Subsection", CellChangeTimes->{{3.390224531897484*^9, 3.390224678961919*^9}, 3.39022543094581*^9}], Cell["\<\ Many things. Among them, implicitization of parametrized curves and surfaces. \ This is the application we consider in this talk.\ \>", "Subsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, 3.390225433318186*^9}] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["How does it work?", "Section", CellChangeTimes->{{3.390224531897484*^9, 3.390224678961919*^9}, { 3.390224744271755*^9, 3.390224746693201*^9}, 3.390225438089326*^9}], Cell[CellGroupData[{ Cell["\<\ In brief, one moves between cones in the Gr\[ODoubleDot]bner fan, beginning \ with the initial order and moving along a \"line\" in weight vector space \ toward the terminal (desired) term order. Good references are (Collart et al \ 1997) and (Amrhein et al 1997).\ \>", "Subsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, 3.390225446761699*^9, { 3.390414050512434*^9, 3.39041406843247*^9}, {3.390563530461057*^9, 3.390563531668403*^9}, {3.390566488589665*^9, 3.390566489193474*^9}, { 3.390566813368777*^9, 3.390566848041723*^9}, 3.3905689589687*^9}, FontSize->16], Cell[CellGroupData[{ Cell["\<\ The term orders are regarded as weight matrices with each vector comprised of \ integers. General theory then says they must be square, have full rank, and \ have the first nonzero in each column be positive.\ \>", "Subsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, 3.390225446761699*^9, { 3.390414050512434*^9, 3.39041406843247*^9}, {3.390563530461057*^9, 3.390563531668403*^9}, {3.390566488589665*^9, 3.390566574241208*^9}, { 3.39056663159194*^9, 3.390566687151853*^9}}], Cell["One could opt for more generality. We do not.", "Subsubsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, 3.390225446761699*^9, { 3.390414050512434*^9, 3.39041406843247*^9}, {3.390563530461057*^9, 3.390563531668403*^9}, {3.390566488589665*^9, 3.390566574241208*^9}, { 3.39056663159194*^9, 3.390566687151853*^9}, {3.39085959513324*^9, 3.390859596466044*^9}}] }, Open ]] }, Open ]], Cell["\<\ One starts by computing a Gr\[ODoubleDot]bner basis with respect to the start \ order.\ \>", "Subsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, 3.390225446761699*^9, { 3.390414050512434*^9, 3.39041406843247*^9}, {3.390563530461057*^9, 3.390563531668403*^9}, {3.390566488589665*^9, 3.390566489193474*^9}, { 3.390566813368777*^9, 3.390566848041723*^9}, 3.3905689589687*^9, 3.390859349668786*^9}, FontSize->16], Cell["\<\ Polynomial \"initials\" are the sum of those monomials in a given polynomial \ that are equal with respect to the first weight vector.\ \>", "Subsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390225004503048*^9}, {3.390413790320377*^9, 3.390413797504926*^9}, {3.390414123353198*^9, 3.390414154934771*^9}, { 3.390563473801204*^9, 3.390563511977009*^9}, {3.390566604619209*^9, 3.390566612069575*^9}}], Cell[CellGroupData[{ Cell["\<\ Each move is relatively simple because it involves only ideals of initials of \ polynomials in the current basis, and these are mostly monomials.\ \>", "Subsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390225004503048*^9}, {3.390413790320377*^9, 3.390413815627271*^9}, {3.390566618928996*^9, 3.390566620013265*^9}}], Cell["Convert the initials ideal to get into the neighboring cone.", \ "Subsubsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390225004503048*^9}, {3.390413790320377*^9, 3.390413797504926*^9}, {3.390414123353198*^9, 3.390414154934771*^9}}], Cell["\<\ Use this to carry along the full polynomial set (\"lifting\" step).\ \>", "Subsubsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390225004503048*^9}, {3.390413790320377*^9, 3.39041379377628*^9}, {3.390414128338626*^9, 3.39041415629453*^9}}], Cell["(Optionally) interreduce.", "Subsubsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390225004503048*^9}, {3.390413790320377*^9, 3.390413795171573*^9}, {3.390414148574652*^9, 3.390414157714893*^9}}], Cell["\<\ If not yet in terminal cone, restart by looking for the next neighboring cone.\ \>", "Subsubsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390225004503048*^9}, {3.390413790320377*^9, 3.390413795171573*^9}, {3.390414151686788*^9, 3.390414170206087*^9}}] }, Open ]] }, Open ]] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Complexity issues", "Section", CellChangeTimes->{{3.390224531897484*^9, 3.390224678961919*^9}, { 3.390224744271755*^9, 3.390224746693201*^9}, {3.390225010273288*^9, 3.390225016368355*^9}, 3.390225450233811*^9, {3.390315304865015*^9, 3.390315318151415*^9}}], Cell[CellGroupData[{ Cell["\<\ There are many ways for this process to bog down. The point of this talk is \ to discuss some, and ways to make them less intolerable. Here are a few items.\ \>", "Item", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, {3.390225022230664*^9, 3.390225059836842*^9}, {3.390225093729702*^9, 3.390225173148207*^9}, { 3.390225224843366*^9, 3.390225345538396*^9}, 3.390225459666216*^9, { 3.390315239997359*^9, 3.390315260022744*^9}, 3.390315351819384*^9}], Cell[CellGroupData[{ Cell["The initial basis may be slow to compute.", "Subsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, {3.390225022230664*^9, 3.390225059836842*^9}, {3.390225093729702*^9, 3.390225173148207*^9}, { 3.390225224843366*^9, 3.390225345538396*^9}, 3.390225459666216*^9, { 3.390315239997359*^9, 3.390315260022744*^9}, {3.390315351819384*^9, 3.390315356227544*^9}, {3.390413495676218*^9, 3.390413508380461*^9}}], Cell["\<\ One typically uses a degree-reverse-lexicographic term order but of course \ any valid term order might be used.\ \>", "Subsubsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, {3.390225022230664*^9, 3.390225059836842*^9}, {3.390225093729702*^9, 3.390225173148207*^9}, { 3.390225224843366*^9, 3.390225345538396*^9}, 3.390225459666216*^9, { 3.390315239997359*^9, 3.390315260022744*^9}, {3.390315351819384*^9, 3.390315356227544*^9}, {3.390413495676218*^9, 3.390413497227734*^9}}] }, Open ]], Cell["Coefficient swell as we go through cones can be a problem.", \ "Subsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, {3.390225022230664*^9, 3.390225059836842*^9}, {3.390225093729702*^9, 3.390225173148207*^9}, { 3.390225224843366*^9, 3.390225345538396*^9}, 3.390225459666216*^9, { 3.390315239997359*^9, 3.390315260022744*^9}, {3.390315351819384*^9, 3.390315358285244*^9}, 3.390413523937175*^9}], Cell["\<\ We might encounter cone traversals where the initials ideal contains \ polynomials with many terms. This more or less defeats the purpose of the Gr\ \[ODoubleDot]bner walk. It is especially common once we are on the boundary \ of the final cone.\ \>", "Subsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, {3.390225022230664*^9, 3.390225059836842*^9}, {3.390225093729702*^9, 3.390225173148207*^9}, { 3.390225224843366*^9, 3.390225345538396*^9}, 3.390225459666216*^9, { 3.390315239997359*^9, 3.390315260022744*^9}, {3.390315351819384*^9, 3.390315360342521*^9}, 3.390413534512948*^9, {3.390573845925661*^9, 3.390573848637083*^9}}], Cell["\<\ For purposes of variable elimination (needed e.g. for implicitization) it \ might be unnecessary and inefficient to compute the full basis with respect \ to a given elimination ordering.\ \>", "Subsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, {3.390225022230664*^9, 3.390225059836842*^9}, {3.390225093729702*^9, 3.390225173148207*^9}, { 3.390225224843366*^9, 3.390225345538396*^9}, 3.390225459666216*^9, { 3.390315239997359*^9, 3.390315260022744*^9}, {3.390315351819384*^9, 3.390315360342521*^9}, 3.39041354635393*^9}], Cell[CellGroupData[{ Cell["\<\ Interreduction of intermediate bases is not actually necessary.\ \>", "Subsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, {3.390225022230664*^9, 3.390225059836842*^9}, {3.390225093729702*^9, 3.390225173148207*^9}, { 3.390225224843366*^9, 3.390225345538396*^9}, 3.390225459666216*^9, { 3.390315239997359*^9, 3.390315260022744*^9}, {3.390315351819384*^9, 3.390315360342521*^9}, {3.39041354635393*^9, 3.390413573143782*^9}}], Cell["\<\ If not done, then one encounters \"false cones\" problem wherein ties in new \ initials do not actually get us always to a new cone.\ \>", "Subsubsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, {3.390225022230664*^9, 3.390225059836842*^9}, {3.390225093729702*^9, 3.390225173148207*^9}, { 3.390225224843366*^9, 3.390225345538396*^9}, 3.390225459666216*^9, { 3.390315239997359*^9, 3.390315260022744*^9}, {3.390315351819384*^9, 3.390315356227544*^9}, {3.390413495676218*^9, 3.390413497227734*^9}, { 3.390413581121759*^9, 3.390413608046483*^9}}], Cell["\<\ In practice the false cones problem is MUCH worse for efficiency than the \ slowness of interreduction. We always interreduce.\ \>", "Subsubsection", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, {3.390225022230664*^9, 3.390225059836842*^9}, {3.390225093729702*^9, 3.390225173148207*^9}, { 3.390225224843366*^9, 3.390225345538396*^9}, 3.390225459666216*^9, { 3.390315239997359*^9, 3.390315260022744*^9}, {3.390315351819384*^9, 3.390315356227544*^9}, {3.390413495676218*^9, 3.390413497227734*^9}, { 3.390413581121759*^9, 3.390413652526099*^9}}] }, Open ]] }, Open ]] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Tactics we use or otherwise discuss", "Section", CellChangeTimes->{{3.390317374889652*^9, 3.390317382145568*^9}, { 3.390317484661572*^9, 3.390317494404714*^9}}], Cell[CellGroupData[{ Cell["Perturbation of initial weight vector", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, 3.390318079643587*^9}], Cell["\<\ This is important because if not done we are more likely to bog down in \ intermediate Gr\[ODoubleDot]bner basis computations involving initials. \ Reason: We may make a cone crossing that is not through the interior of a \ proper face, and in this circumstance the initials may have many more \ monomials than would otherwise be the case. The point of the \ Gr\[ODoubleDot]bner walk is to work with ideals generated by small initials.\ \>", "Text", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318030804977*^9}}, FontSize->16] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Handling of final weight vector", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}}], Cell[CellGroupData[{ Cell["\<\ This is important in those (very common) cases where the first weight vector \ for the final cone puts us at a border of many cones, by virtue of being not \ in the interior of that cone. There are many ways discussed in the literature \ for dealing with this.\ \>", "Subsubsection", CellChangeTimes->{{3.39031774747937*^9, 3.390318052949743*^9}, { 3.390318090244054*^9, 3.390318092471445*^9}, {3.390569497229889*^9, 3.390569500021346*^9}}], Cell["\<\ Do nothing and bear the consequences of a slow final conversion.\ \>", "Subsubsubsection", CellChangeTimes->{{3.39031774747937*^9, 3.390318052949743*^9}, { 3.390318090244054*^9, 3.390318092471445*^9}, {3.390569497229889*^9, 3.39056951258298*^9}, {3.390569565306541*^9, 3.390569578021871*^9}, { 3.390569879050591*^9, 3.390569896430301*^9}}], Cell["\<\ (Amrhein et al 1997) Heuristic perturbation. One adds decreasing multiples of \ later weight vectors to the first one. With probability 1 this puts us in the \ interior of SOME cone. If it turns out not to be the correct cone we make the \ multiples smaller and repeat.\ \>", "Subsubsubsection", CellChangeTimes->{{3.39031774747937*^9, 3.390318052949743*^9}, { 3.390318090244054*^9, 3.390318092471445*^9}, {3.390569497229889*^9, 3.39056951258298*^9}, {3.390569565306541*^9, 3.390569578021871*^9}, { 3.390569623095743*^9, 3.390569639092194*^9}, {3.390921057520401*^9, 3.390921059014231*^9}}], Cell["(Amrhein et al 1997) Other methods such as fractal walk.", \ "Subsubsubsection", CellChangeTimes->{{3.39031774747937*^9, 3.390318052949743*^9}, { 3.390318090244054*^9, 3.390318092471445*^9}, {3.390569497229889*^9, 3.39056951258298*^9}, {3.390569565306541*^9, 3.390569578021871*^9}, { 3.390569623095743*^9, 3.390569639092194*^9}, {3.390569859380547*^9, 3.390569869324995*^9}}], Cell["\<\ (Tran 2000) Deterministic perturbation. One computes a term order that is a \ priori in the interior of the final cone.\ \>", "Subsubsubsection", CellChangeTimes->{{3.39031774747937*^9, 3.390318052949743*^9}, { 3.390318090244054*^9, 3.390318092471445*^9}, {3.390569497229889*^9, 3.39056951258298*^9}, {3.390569565306541*^9, 3.390569578021871*^9}, { 3.390921064166013*^9, 3.390921065491602*^9}}], Cell["(Fukuda et al 2007) Use a symbolic perturbation.", "Subsubsubsection", CellChangeTimes->{{3.39031774747937*^9, 3.390318052949743*^9}, { 3.390318090244054*^9, 3.390318092471445*^9}, {3.390569497229889*^9, 3.39056951258298*^9}, {3.390569565306541*^9, 3.390569578021871*^9}, { 3.390569623095743*^9, 3.390569639092194*^9}, {3.390569859380547*^9, 3.390569869324995*^9}, {3.390569911227417*^9, 3.390569935678736*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["My synopsis", "Subsubsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390571312964945*^9, 3.390571314516541*^9}, { 3.390596485361038*^9, 3.39059648725741*^9}}], Cell["\<\ Heuristic or simulated perturbation are the methods of choice.\ \>", "Subsubsubsection", CellChangeTimes->{{3.390570077664148*^9, 3.390570205236265*^9}, { 3.390571258550148*^9, 3.390571259148622*^9}}], Cell["\<\ Deterministic perturbation can generate weight vectors with HUGE integers, \ and will hang in exponent arithmetic, if there are more than 5 or so \ variables present.\ \>", "Subsubsubsection", CellChangeTimes->{{3.390570077664148*^9, 3.390570205236265*^9}, { 3.390571258550148*^9, 3.390571270661105*^9}}], Cell["\<\ Doing nothing will hang for same reason as Buchberger algorithm.\ \>", "Subsubsubsection", CellChangeTimes->{{3.390570077664148*^9, 3.390570205236265*^9}, { 3.390571258550148*^9, 3.390571275709028*^9}}], Cell["\<\ Other methods are more trouble for less gain than heuristic and simulated \ perturbation.\ \>", "Subsubsubsection", CellChangeTimes->{{3.390570077664148*^9, 3.390570205236265*^9}, { 3.390571258550148*^9, 3.39057128069734*^9}}] }, Open ]] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Elimination order", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318162234282*^9}, { 3.390579768982225*^9, 3.390579771560705*^9}, {3.390579975417561*^9, 3.39057997671509*^9}}], Cell[CellGroupData[{ Cell["\<\ As we do elimination in the examples herein, we use a destination term order \ well suited for this.\ \>", "Subsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, {3.390579777800954*^9, 3.39057990483112*^9}}], Cell["\<\ Weight monomials with elimination variables higher than monomials without \ them.\ \>", "Subsubsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, {3.390579777800954*^9, 3.39057990483112*^9}, {3.390579941401955*^9, 3.390579946745544*^9}}], Cell["\<\ Break ties based on degree reverse lexicographic ordering of the entire \ varaible set.\ \>", "Subsubsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, {3.390579777800954*^9, 3.39057990483112*^9}, {3.390579941401955*^9, 3.390579952412337*^9}}], Cell["This term order is discussed in (Cox et al 2007).", "Subsubsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, {3.390579777800954*^9, 3.39057990483112*^9}, {3.390579941401955*^9, 3.390579952412337*^9}}] }, Open ]] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Initial order", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318162234282*^9}, { 3.390579768982225*^9, 3.390579771560705*^9}, {3.390579975417561*^9, 3.39057997671509*^9}, {3.390580228123715*^9, 3.390580229077633*^9}}], Cell["It is helpful to use a \"sensible\" initial ordering.", "Subsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, {3.390579777800954*^9, 3.39057990483112*^9}, {3.390580029335875*^9, 3.390580040569692*^9}, { 3.390921098029533*^9, 3.390921103945969*^9}}], Cell[CellGroupData[{ Cell["Could use degree reverse lexicographic.", "Subsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, {3.390579777800954*^9, 3.39057990483112*^9}, {3.390579941401955*^9, 3.390579946745544*^9}, { 3.390580047304345*^9, 3.390580059224531*^9}}], Cell["\<\ We do this, and pay a cost in the need to compute an initial basis with \ respect to this term order.\ \>", "Subsubsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, {3.390579777800954*^9, 3.39057990483112*^9}, {3.390579941401955*^9, 3.390579946745544*^9}, { 3.390580047304345*^9, 3.390580095232646*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ If we begin with a rational parametrization, could use an initial order such \ that input, with denominators cleared, is already a Gr\[ODoubleDot]bner \ basis. This would have a weight matrix with initial vector \ (0,...,0,1,1,...,1).\ \>", "Subsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, {3.390579777800954*^9, 3.39057990483112*^9}, {3.390579941401955*^9, 3.390579946745544*^9}, { 3.390580047304345*^9, 3.390580059224531*^9}, {3.390580103392308*^9, 3.390580182040798*^9}, {3.390580240034034*^9, 3.390580263620821*^9}}], Cell["\<\ In practice such orders can sometimes cause huge inefficiency in the walk \ process. We will not use them.\ \>", "Subsubsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, {3.390579777800954*^9, 3.39057990483112*^9}, {3.390579941401955*^9, 3.390579946745544*^9}, { 3.390580047304345*^9, 3.390580095232646*^9}, {3.390580281495411*^9, 3.390580304709696*^9}}] }, Open ]] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Early abort for elimination orders", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318162234282*^9}, { 3.390579768982225*^9, 3.390579771560705*^9}}], Cell[CellGroupData[{ Cell["\<\ In implicitization and other elimination tasks we can check at intermediate \ stages of the walk to see if a basis happens to be an elimination basis for \ the polynomials.\ \>", "Subsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, 3.390596516227462*^9, { 3.390685116262453*^9, 3.390685188944878*^9}, {3.390825804569383*^9, 3.39082594043288*^9}, {3.390829567894773*^9, 3.390829578570193*^9}, { 3.390829611049695*^9, 3.390829616193254*^9}, {3.390925922227228*^9, 3.390925923099363*^9}}], Cell[TextData[{ "This is defined as a basis ", Cell[BoxData[ FormBox["G", TraditionalForm]]], " for the ideal ", Cell[BoxData[ FormBox["I", TraditionalForm]]], " such that, if the noneliminated variable set is ", Cell[BoxData[ FormBox["Y", TraditionalForm]]], " and the field is ", Cell[BoxData[ FormBox["K", TraditionalForm]]], ", then ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[DoubleStruckCapitalK]", "[", "Y", "]"}], "\[Intersection]", "G"}], TraditionalForm]]], " generates the elimination ideal ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"K", "[", "Y", "]"}], "\[Intersection]", "I", " "}], TraditionalForm]]], "." }], "Text", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, 3.390596516227462*^9, { 3.390685116262453*^9, 3.390685188944878*^9}, {3.390825804569383*^9, 3.39082594043288*^9}, {3.390829567894773*^9, 3.390829578570193*^9}, { 3.390829611049695*^9, 3.390829616193254*^9}, {3.390925922227228*^9, 3.390925923099363*^9}, {3.390925973344938*^9, 3.390925977206809*^9}}], Cell["\<\ If so, we may often use it just as we would the basis we were trying for. We \ simply take those polynomials in the basis that are free of the variables we \ were eliminating (see next subsection for why this works). For many purposes, \ e.g. surface implicitization, this is a single polynomial.\ \>", "Text", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, 3.390596516227462*^9, { 3.390685116262453*^9, 3.390685212444021*^9}, {3.390685434689718*^9, 3.390685495542702*^9}, {3.390686718462512*^9, 3.390686764405172*^9}, { 3.390860963865588*^9, 3.390860989717294*^9}}], Cell["\<\ This applies even though the intermediate Gr\[ODoubleDot]bner basis is NOT a \ Gr\[ODoubleDot]bner basis with respect to the provided termination ordering. \ Hence it is a bona fide \"short cut\".\ \>", "Text", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, 3.390596516227462*^9, { 3.390685116262453*^9, 3.390685212444021*^9}, {3.390685434689718*^9, 3.390685463792651*^9}}] }, Open ]], Cell["\<\ Early version of this called \"sudden death\" (Amrhein et al 1997).\ \>", "Subsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, 3.390596516227462*^9, { 3.390685116262453*^9, 3.390685212444021*^9}, {3.390685245358849*^9, 3.390685287029715*^9}}], Cell["\<\ Recent version called \"ideal\[Hyphen]specific elimination order\" (Tran \ 2004).\ \>", "Subsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, 3.390596516227462*^9, { 3.390685116262453*^9, 3.390685212444021*^9}, {3.390685245358849*^9, 3.390685295190078*^9}, {3.390685346801985*^9, 3.390685373871562*^9}, { 3.390685536641048*^9, 3.390685540144123*^9}, {3.390828871119453*^9, 3.390828905097273*^9}, {3.390829660523947*^9, 3.390829662118259*^9}}], Cell["\<\ Me, I've always viewed it as \"opportunistic intermediate processing\".\ \>", "Subsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, 3.390596516227462*^9, { 3.390685116262453*^9, 3.390685212444021*^9}, {3.390685245358849*^9, 3.390685295190078*^9}, {3.390685346801985*^9, 3.390685417338352*^9}, { 3.39068552425286*^9, 3.39068552725939*^9}}] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Algorithmic underpinnings of this early abort strategy", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318162234282*^9}, { 3.390579768982225*^9, 3.390579771560705*^9}, {3.390860852361303*^9, 3.390860862924186*^9}, {3.390860906319713*^9, 3.390860915255425*^9}}], Cell["\<\ The condition is simple to check algorithmically due to a basic result.\ \>", "Text", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, 3.390596516227462*^9, { 3.390685116262453*^9, 3.390685188944878*^9}, {3.390685908785147*^9, 3.390686014716897*^9}, {3.390686066434921*^9, 3.39068623337789*^9}, { 3.390825286099302*^9, 3.39082529909354*^9}, 3.390827725054582*^9}], Cell[TextData[{ "Proposition (Tran 2004): A Gr\[ODoubleDot]bner basis ", Cell[BoxData[ FormBox["G", TraditionalForm]]], " for an ideal ", Cell[BoxData[ FormBox["I", TraditionalForm]]], " is an elimination basis for a set of variables ", Cell[BoxData[ FormBox["X", TraditionalForm]]], " if, for each polynomial ", Cell[BoxData[ FormBox[ RowBox[{"g", "\[Element]", "G"}], TraditionalForm]]], ", either the head term of ", Cell[BoxData[ FormBox["g", TraditionalForm]]], " contains variables in ", Cell[BoxData[ FormBox["X", TraditionalForm]]], ", or else ", Cell[BoxData[ FormBox["g", TraditionalForm]]], " is entirely free of variables in ", Cell[BoxData[ FormBox["X", TraditionalForm]]], "." }], "Subsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, 3.390596516227462*^9, { 3.390685116262453*^9, 3.390685188944878*^9}, {3.390685908785147*^9, 3.390686014716897*^9}, {3.390686066434921*^9, 3.39068623337789*^9}, { 3.390825286099302*^9, 3.39082529909354*^9}, {3.390827725054582*^9, 3.390827738581108*^9}, {3.390829427243671*^9, 3.390829430895808*^9}, 3.390829467888363*^9}], Cell[TextData[{ "Proof: As above, denote the complementary variable set as ", Cell[BoxData[ FormBox["Y", TraditionalForm]]], " and the field as ", Cell[BoxData[ FormBox["\[DoubleStruckCapitalK]", TraditionalForm]]], ". We refer to polynomials in ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[DoubleStruckCapitalK]", "[", "Y", "]"}], "\[Intersection]", "G"}], TraditionalForm]]], " as ", Cell[BoxData[ FormBox[ SubscriptBox["G", "Y"], TraditionalForm]]], ". Take ", Cell[BoxData[ FormBox[ RowBox[{"f", "\[Element]", RowBox[{ RowBox[{"\[DoubleStruckCapitalK]", "[", "Y", "]"}], "\[Intersection]", "I"}]}], TraditionalForm]]], ". Without loss of generality assume ", Cell[BoxData[ FormBox["f", TraditionalForm]]], " is reduced with respect to ", Cell[BoxData[ FormBox[ SubscriptBox["G", "Y"], TraditionalForm]]], " and the given term order. If ", Cell[BoxData[ FormBox[ RowBox[{"f", "\[NotEqual]", "0"}], TraditionalForm]]], " then, since ", Cell[BoxData[ FormBox["G", TraditionalForm]]], " is a Gr\[ODoubleDot]bner basis with respect to that term order, ", Cell[BoxData[ FormBox["f", TraditionalForm]]], " can be further reduced by some ", Cell[BoxData[ FormBox[ RowBox[{"g", "\[Element]", RowBox[{"G", "-", SubscriptBox["G", "Y"]}]}], TraditionalForm]]], ". But the head term condition shows no such ", Cell[BoxData[ FormBox["g", TraditionalForm]]], " can reduce ", Cell[BoxData[ FormBox["f", TraditionalForm]]], ", so ", Cell[BoxData[ FormBox[ RowBox[{"f", "=", "0"}], TraditionalForm]]], ". So ", Cell[BoxData[ FormBox[ RowBox[{"f", "\[Element]", SubscriptBox["G", "Y"]}], TraditionalForm]]], ". Hence ", Cell[BoxData[ FormBox[ SubscriptBox["G", "Y"], TraditionalForm]]], " generates ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[DoubleStruckCapitalK]", "[", "Y", "]"}], "\[Intersection]", "I"}], TraditionalForm]]], ".\[EmptySquare]" }], "Subsubsection", CellChangeTimes->{{3.390573635936301*^9, 3.390573643940218*^9}, { 3.390573901416668*^9, 3.39057390892636*^9}, 3.390596516227462*^9, { 3.390685116262453*^9, 3.390685188944878*^9}, {3.390685908785147*^9, 3.390686014716897*^9}, {3.390686066434921*^9, 3.39068623337789*^9}, { 3.390825157603446*^9, 3.390825192978219*^9}, {3.390825225316273*^9, 3.390825273645434*^9}, {3.390825315544863*^9, 3.39082553359635*^9}, { 3.390825620844786*^9, 3.390825751292*^9}, {3.39082594832318*^9, 3.390826012629122*^9}, {3.390826054442467*^9, 3.390826092875479*^9}, { 3.390826185612994*^9, 3.390826191264823*^9}, {3.390827767195907*^9, 3.390827789780401*^9}, 3.390829471991745*^9, {3.390829502759484*^9, 3.390829556138639*^9}, {3.390829618994884*^9, 3.390829627514453*^9}}] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Approximate arithmetic", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318162234282*^9}, { 3.390579768982225*^9, 3.390579771560705*^9}, {3.390581241452572*^9, 3.39058124515466*^9}}], Cell["\<\ In some cases we will use finite precision to \"guess\" a result. This allows \ us to avoid intermediate coefficient swell. The result can be verified after \ the fact. We show this in some examples below.\ \>", "Subsubsection", CellChangeTimes->{{3.390581251108642*^9, 3.390581300731495*^9}}] }, Open ]] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Examples", "Section", CellChangeTimes->{{3.390224531897484*^9, 3.390224678961919*^9}, { 3.390224744271755*^9, 3.390224746693201*^9}, {3.390225010273288*^9, 3.390225016368355*^9}, 3.390225450233811*^9, {3.390315304865015*^9, 3.390315318151415*^9}, {3.39031559609309*^9, 3.390315603320894*^9}, 3.390317508233939*^9, {3.390581200876782*^9, 3.390581201147973*^9}}], Cell[TextData[{ "I will take as benchmarks several examples from the literature of \ implicitization of bicubic polynomial patch surface parametrizations (Tran \ 2007). This by no means captures the full range of examples of interest to Gr\ \[ODoubleDot]bner walk enthusiasts. But it does give a means to gauge \ developments and strategies for some of the issues raised above. These will \ have Cartesian coordinates ", Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}], TraditionalForm]]], " and surface parameters ", Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{"s", ",", "t"}], "}"}], TraditionalForm]]], ". We will need to eliminate the latter. For further examples I will use an \ algebraic but nonrational parametrization from previous work of my own \ (Lichtblau 2006), and a rational nonpolynomial parametrization from (Tran \ 2004) ." }], "Text", CellChangeTimes->{{3.390224531897484*^9, 3.3902246901434*^9}, { 3.390224753732524*^9, 3.390224990648855*^9}, {3.390225022230664*^9, 3.390225059836842*^9}, {3.390225093729702*^9, 3.390225173148207*^9}, { 3.390225224843366*^9, 3.390225345538396*^9}, 3.390225459666216*^9, { 3.390315239997359*^9, 3.390315260022744*^9}, 3.390315351819384*^9, { 3.390315611626167*^9, 3.390315732079948*^9}, {3.390315827958166*^9, 3.390315895004741*^9}, {3.390315930456799*^9, 3.39031594222298*^9}, { 3.390409632298059*^9, 3.390409699065496*^9}, {3.390563644561*^9, 3.39056373851398*^9}, {3.390568979227967*^9, 3.390568988295965*^9}, { 3.390569336402458*^9, 3.390569339453521*^9}}], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["\<\ Example 1 (Bicubic parametrization attributed to C. Hoffmann)\ \>", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318162234282*^9}, { 3.390579768982225*^9, 3.390579771560705*^9}, {3.390581241452572*^9, 3.39058124515466*^9}, 3.390688082348449*^9}], Cell[BoxData[{ RowBox[{ RowBox[{"elims", "=", RowBox[{"{", RowBox[{"s", ",", "t"}], "}"}]}], ";"}], "\n", RowBox[{ RowBox[{"vars", "=", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], ";"}]}], "Input", InitializationCell->True], Cell[BoxData[ RowBox[{ RowBox[{"HoffmannPolys", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"3", " ", "t", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"t", "-", "1"}], ")"}], "2"]}], "+", SuperscriptBox[ RowBox[{"(", RowBox[{"s", "-", "1"}], ")"}], "3"], "+", RowBox[{"3", " ", "s"}], "-", "x"}], ",", RowBox[{ RowBox[{"3", " ", "s", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"s", "-", "1"}], ")"}], "2"]}], "+", 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Cell["Example 3 (Newell)", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318162234282*^9}, { 3.390579768982225*^9, 3.390579771560705*^9}, {3.390581241452572*^9, 3.39058124515466*^9}, 3.390688082348449*^9, 3.39068811511107*^9, 3.390688156910107*^9}], Cell["\<\ This is the 32 patches of Newell's notorious \"Utah teapot\". I grabbed the \ data points from a MathSource item, rationalized the coordinates, obtaining \ parametric polynomial systems. As they are long I only show two.\ \>", "Text", CellChangeTimes->{{3.390315772690309*^9, 3.390315822339053*^9}, 3.390315956690874*^9, {3.390317105743871*^9, 3.390317178676522*^9}, { 3.390317231395127*^9, 3.390317237515111*^9}, {3.390317272227173*^9, 3.390317284059299*^9}, {3.390409065185456*^9, 3.390409081611653*^9}}] }, Open ]], Cell["\<\ In past some of these have proven difficult for Gr\[ODoubleDot]bner bases and \ Dixon resultants. Robert Lewis' program Fermat now can handle them using the \ latter approach, with times ranging from split second to approximately a \ minute (Lewis 2007).\ \>", "Text", CellChangeTimes->{{3.390315772690309*^9, 3.390315822339053*^9}, 3.390315956690874*^9, {3.390317105743871*^9, 3.390317178676522*^9}, { 3.390317231395127*^9, 3.390317237515111*^9}, {3.390317272227173*^9, 3.390317284059299*^9}, {3.390409065185456*^9, 3.390409081611653*^9}, { 3.39117700775542*^9, 3.39117707785112*^9}, {3.393544681926361*^9, 3.393544692081974*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"patches3D", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "7"}], "/", "5"}], "+", RowBox[{ RowBox[{"(", RowBox[{"231", "*", RowBox[{"s", "^", "2"}]}], ")"}], "/", "125"}], "-", RowBox[{ RowBox[{"(", RowBox[{"56", "*", RowBox[{"s", "^", "3"}]}], ")"}], "/", "125"}], "+", RowBox[{ RowBox[{"(", RowBox[{"3", "*", "t"}], ")"}], "/", "16"}], "-", RowBox[{ RowBox[{"(", RowBox[{"99", "*", RowBox[{"s", 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CellChangeTimes->{{3.390415387511651*^9, 3.390415391033295*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Timing", "[", RowBox[{ RowBox[{"gbmod", "=", RowBox[{"GroebnerBasis", "[", RowBox[{"TranPolys", ",", "vars", ",", "elims", ",", RowBox[{"Sort", "->", "True"}], ",", RowBox[{"MonomialOrder", "\[Rule]", "EliminationOrder"}], ",", RowBox[{"Modulus", "\[Rule]", RowBox[{"Prime", "[", "1000001", "]"}]}], ",", RowBox[{"Method", "\[Rule]", "\"\\""}]}], "]"}]}], ";"}], "]"}]], "Input", CellChangeTimes->{{3.39041537476643*^9, 3.390415374985587*^9}, { 3.390416295227644*^9, 3.390416298658376*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"581.84", ",", "Null"}], "}"}]], "Output", CellChangeTimes->{ 3.390415383494739*^9, 3.390416472724362*^9, 3.390416518997935*^9, { 3.390417369782344*^9, 3.390417372813415*^9}}] }, Open ]], Cell["\<\ But the early elimination check helps tremendously for this example.\ \>", "Text", CellChangeTimes->{{3.390415387511651*^9, 3.390415422663784*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Timing", "[", RowBox[{ RowBox[{"gbmod", "=", RowBox[{"GroebnerBasis", "[", RowBox[{"TranPolys", ",", "vars", ",", "elims", ",", RowBox[{"Sort", "->", "True"}], ",", RowBox[{"MonomialOrder", "\[Rule]", "EliminationOrder"}], ",", RowBox[{"Modulus", "\[Rule]", RowBox[{"Prime", "[", "1000001", "]"}]}], ",", RowBox[{"Method", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"\"\\"", "\[Rule]", "True"}]}], "}"}]}]}], "]"}]}], ";"}], "]"}]], "Input", CellChangeTimes->{{3.39041537476643*^9, 3.390415374985587*^9}, { 3.390416295227644*^9, 3.390416298658376*^9}, {3.390416496000148*^9, 3.390416509455455*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"157.078", ",", "Null"}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "Of note: the input is already a Gr\[ODoubleDot]bner basis with respect to \ the monomial order given (with variable order ", Cell[BoxData[ FormBox[ RowBox[{"s", ">", "t", ">", "x", ">", "y", ">", "z"}], TraditionalForm]]], ") by the weight matrix below." }], "Text", CellChangeTimes->{{3.390415387511651*^9, 3.390415422663784*^9}, { 3.390416309837722*^9, 3.390416348816813*^9}, {3.39041638220382*^9, 3.390416422039838*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "0", ",", " ", "0", ",", " ", "1", ",", " ", "1", ",", " ", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ "1", ",", " ", "1", ",", " ", "0", ",", " ", "0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", " ", "0", ",", " ", "0", ",", " ", "0", ",", " ", RowBox[{"-", "1"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", " ", "0", ",", " ", "0", ",", " ", RowBox[{"-", "1"}], ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", "1"}], ",", " ", "0", ",", " ", "0", ",", " ", "0"}], "}"}]}], "}"}], "}"}]], "DisplayFormula", CellChangeTimes->{{3.390415387511651*^9, 3.390415422663784*^9}, { 3.390416309837722*^9, 3.390416378457836*^9}}], Cell["\<\ If we use this as initial order for the Gr\[ODoubleDot]bner walk then it \ instead takes longer than I was willing to wait. So we do not use this order.\ \ \>", "Text", CellChangeTimes->{{3.390415387511651*^9, 3.390415422663784*^9}, { 3.390416309837722*^9, 3.390416348816813*^9}, {3.39041638220382*^9, 3.390416460098584*^9}, {3.390565495113234*^9, 3.390565501430678*^9}, { 3.390571694860708*^9, 3.390571731187642*^9}}] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Example 2 in characteristic zero", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318190967937*^9}, 3.390415373003343*^9, {3.390565956343654*^9, 3.390565965790697*^9}}], Cell["How long to do this in characteristic zero?", "Text", CellChangeTimes->{{3.390415387511651*^9, 3.390415422663784*^9}, { 3.390416309837722*^9, 3.390416348816813*^9}, {3.39041638220382*^9, 3.390416460098584*^9}, {3.390416559639222*^9, 3.390416569351948*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Timing", "[", RowBox[{ RowBox[{"gb", "=", RowBox[{"GroebnerBasis", "[", RowBox[{"TranPolys", ",", "vars", ",", "elims", ",", RowBox[{"Sort", "->", "True"}], ",", RowBox[{"MonomialOrder", "\[Rule]", "EliminationOrder"}], ",", RowBox[{"Method", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"\"\\"", "\[Rule]", "True"}]}], "}"}]}]}], "]"}]}], ";"}], "]"}]], "Input", CellChangeTimes->{{3.39041537476643*^9, 3.390415374985587*^9}, { 3.390416295227644*^9, 3.390416298658376*^9}, {3.390416496000148*^9, 3.390416509455455*^9}, {3.390416599156336*^9, 3.39041660260753*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"17656.9", ",", "Null"}], "}"}]], "Output", CellChangeTimes->{3.390416633055033*^9}] }, Open ]], Cell["\<\ Ouch. The gremlin in the machinery is the coefficient swell. We will now see \ how to keep this at bay.\ \>", "Text", CellChangeTimes->{{3.390415387511651*^9, 3.390415422663784*^9}, { 3.390416309837722*^9, 3.390416348816813*^9}, {3.39041638220382*^9, 3.390416460098584*^9}, {3.390416559639222*^9, 3.390416569351948*^9}, { 3.390416639240751*^9, 3.390416682889028*^9}, {3.390563769070906*^9, 3.390563805249712*^9}, 3.390564898555758*^9, {3.390565975276225*^9, 3.390565981410418*^9}, {3.390571019782334*^9, 3.390571057269024*^9}, { 3.390571682715698*^9, 3.390571684771182*^9}}] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Example 2 approximated, then rationalized", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318190967937*^9}, 3.390415373003343*^9, {3.390565956343654*^9, 3.390565999114812*^9}}], Cell["\<\ We can obtain a result in reasonable time using approximation, then \ rationalization, then verification. For this particular example the total \ time, including verification, is around 12 minutes. We start by computing a \ numerical Gr\[ODoubleDot]bner basis to high precision.\ \>", "Text", CellChangeTimes->{{3.390415387511651*^9, 3.390415422663784*^9}, { 3.390416309837722*^9, 3.390416348816813*^9}, {3.39041638220382*^9, 3.390416460098584*^9}, {3.390416559639222*^9, 3.390416569351948*^9}, { 3.390416639240751*^9, 3.390416682889028*^9}, {3.390563769070906*^9, 3.390563805249712*^9}, 3.390564898555758*^9, {3.390565975276225*^9, 3.390566086583749*^9}, {3.390571059356917*^9, 3.390571060294673*^9}, { 3.390572797156845*^9, 3.39057280425176*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Timing", "[", RowBox[{ RowBox[{"gbapprox", "=", RowBox[{"GroebnerBasis", "[", RowBox[{"TranPolys", ",", "vars", ",", "elims", ",", RowBox[{"MonomialOrder", "\[Rule]", "EliminationOrder"}], ",", RowBox[{"CoefficientDomain", "\[Rule]", RowBox[{"InexactNumbers", "[", "600", "]"}]}], ",", RowBox[{"Method", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"\"\\"", "\[Rule]", "True"}]}], "}"}]}]}], "]"}]}], ";"}], "]"}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.39056475340897*^9, 3.390564786357652*^9}, 3.390564942725128*^9}], Cell[OutputFormData["\<\ {383.9, Null}\ \>", "\<\ {383.9, Null}\ \>"], "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{3.390565419715139*^9}, FontWeight->"Plain"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"implicit", "=", RowBox[{"Rationalize", "[", RowBox[{"gbapprox", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Precision", "[", "implicit", "]"}]}], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.39056475340897*^9, 3.390564786357652*^9}, { 3.390564823641611*^9, 3.39056483872438*^9}, 3.390565427527744*^9}], Cell[OutputFormData["\<\ Infinity\ \>", "\<\ Infinity\ \>"], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.390565409110612*^9, 3.39056542752808*^9}}, FontWeight->"Plain"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"rules", "=", RowBox[{"First", "[", RowBox[{"Solve", "[", RowBox[{ RowBox[{"Tranpolys", "\[Equal]", "0"}], ",", "vars"}], "]"}], "]"}]}], ";"}], "\n", RowBox[{"Timing", "[", RowBox[{ RowBox[{"Expand", "[", RowBox[{"implicit", "/.", "rules"}], "]"}], "\[Equal]", "0"}], "]"}]}], "Input", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.390564886960564*^9, 3.390564887877545*^9}, 3.390565466640985*^9, {3.393277817739936*^9, 3.393277818265559*^9}}], Cell[OutputFormData["\<\ {340.485, True}\ \>", "\<\ {340.485, True}\ \>"], "Input", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.390565447883956*^9, 3.390565466643236*^9}}, FontWeight->"Plain"] }, Open ]], Cell["\<\ See (Shirayanagi 1996), (Lichtblau 2000) for discussion regarding computation \ of numerical Gr\[ODoubleDot]bner bases.\ \>", "Text", CellChangeTimes->{{3.390415387511651*^9, 3.390415422663784*^9}, { 3.390416309837722*^9, 3.390416348816813*^9}, {3.39041638220382*^9, 3.390416460098584*^9}, {3.390416559639222*^9, 3.390416569351948*^9}, { 3.390416639240751*^9, 3.390416682889028*^9}, {3.390563769070906*^9, 3.390563805249712*^9}, 3.390564898555758*^9, {3.390565975276225*^9, 3.390566086583749*^9}, {3.390571059356917*^9, 3.390571060294673*^9}, { 3.390572797156845*^9, 3.390572832965438*^9}}] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Another possibility for example 2", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318190967937*^9}, 3.390415373003343*^9, {3.390565956343654*^9, 3.390565999114812*^9}, { 3.390581332704835*^9, 3.390581341363222*^9}}], Cell["\<\ Use a prime modulus, then Hensel lift or else use skeleton of result to solve \ a linear system.\ \>", "Subsubsection", CellChangeTimes->{{3.390581343812764*^9, 3.39058138352415*^9}}], Cell["\<\ I tried the latter and got a huge sparse system I was unable to solve without \ blowing up memory.\ \>", "Text", CellChangeTimes->{{3.390581387948285*^9, 3.39058146267251*^9}}], Cell["\<\ Might do better when I get some sparse linear algebra for matrices with \ arbitrary size integers.\ \>", "Text", CellChangeTimes->{{3.390581387948285*^9, 3.39058146267251*^9}}] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Example 3, modulo a reasonably large prime", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318190967937*^9}}], Cell["\<\ We will attempt the implicitization of all patches, using a modulus to keep \ coefficient swell from occurring.\ \>", "Text", CellChangeTimes->{{3.390407811500473*^9, 3.39040791158197*^9}, { 3.39056611574863*^9, 3.390566149191439*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"Timing", "[", RowBox[{ RowBox[{ RowBox[{"implicitmod", "[", "j", "]"}], "=", RowBox[{"GroebnerBasis", "[", RowBox[{ RowBox[{"patches3D", "[", RowBox[{"[", "j", "]"}], "]"}], ",", "vars", ",", "elims", ",", RowBox[{"MonomialOrder", "\[Rule]", "EliminationOrder"}], ",", RowBox[{"Modulus", "\[Rule]", RowBox[{"Prime", "[", "1000001", "]"}]}], ",", RowBox[{"Method", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"\"\\"", "\[Rule]", "True"}]}], "}"}]}]}], "]"}]}], ";"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"Length", "[", "patches3D", "]"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{ 3.390319291698336*^9, {3.390407923004789*^9, 3.390407923442176*^9}, 3.390408111251158*^9, {3.390408689299949*^9, 3.390408690920423*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.032002", ",", "0.032002", ",", "0.028002", ",", "0.032002", ",", "0.088006", ",", "0.052003", ",", "0.052003", ",", "0.048003", ",", "0.076005", ",", "0.108007", ",", "0.136008", ",", "0.144009", ",", "4.63229", ",", "6.90443", ",", "11.6047", ",", "11.5567", ",", "147.553", ",", "169.359", ",", "503.495", ",", "548.386", ",", "3.43621", ",", "3.49622", ",", "3.48822", ",", "3.49622", ",", "0.188011", ",", "0.188012", ",", "0.188012", ",", "0.192012", ",", "0.176011", ",", "0.176011", ",", "0.176011", ",", "0.176011"}], "}"}]], "Output", CellChangeTimes->{ 3.390407806086693*^9, 3.390408123338154*^9, {3.390408703512722*^9, 3.390408706786551*^9}}] }, Open ]], Cell["\<\ We do them all, many in \"real time\". We will show timings for the \ nonmodular case for all but the four spout parametrizations (patches 17-20), \ where we will resort to different methods to get the implicitizations.\ \>", "Text", CellChangeTimes->{{3.390407811500473*^9, 3.39040791158197*^9}}] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Example 3 in characteristic zero", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318190967937*^9}, { 3.390408637479827*^9, 3.390408642819006*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"Timing", "[", RowBox[{ RowBox[{ RowBox[{"implicit", "[", "j", "]"}], "=", RowBox[{"GroebnerBasis", "[", RowBox[{ RowBox[{"patches3D", "[", RowBox[{"[", "j", "]"}], "]"}], ",", "vars", ",", "elims", ",", RowBox[{"MonomialOrder", "\[Rule]", "EliminationOrder"}], ",", RowBox[{"Method", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"\"\\"", "\[Rule]", "True"}]}], "}"}]}]}], "]"}]}], ";"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "16"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.390407930802289*^9, 3.390407946211715*^9}, 3.390408105251211*^9}], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ "0.044002", ",", "0.032002", ",", "0.032002", ",", "0.032002", ",", "0.108007", ",", "0.112007", ",", "0.116007", ",", "0.116007", ",", "0.192012", ",", "0.184012", ",", "0.184011", ",", "0.196013", ",", "8.23251", ",", "9.39659", ",", "17.3571", ",", "17.7891"}], "}"}], "}"}]], "Output", CellChangeTimes->{ 3.390408054707984*^9, 3.3904081296138*^9, {3.39040854038594*^9, 3.390408547173793*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"Timing", "[", RowBox[{ RowBox[{ RowBox[{"implicit", "[", "j", "]"}], "=", RowBox[{"GroebnerBasis", "[", RowBox[{ RowBox[{"patches3D", "[", RowBox[{"[", "j", "]"}], "]"}], ",", "vars", ",", "elims", ",", RowBox[{"MonomialOrder", "\[Rule]", "EliminationOrder"}], ",", RowBox[{"Method", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"\"\\"", "\[Rule]", "True"}]}], "}"}]}]}], "]"}]}], ";"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"{", RowBox[{"j", ",", "21", ",", RowBox[{"Length", "[", "patches3D", "]"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.390407941717947*^9, 3.390407943135*^9}, 3.390408059536864*^9, 3.390408497624833*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ "5.67636", ",", "5.73236", ",", "5.78836", ",", "5.77636", ",", "0.220014", ",", "0.224014", ",", "0.224014", ",", "0.216014", ",", "0.196012", ",", "0.224014", ",", "0.216013", ",", "0.204013"}], "}"}]], "Output", CellChangeTimes->{3.390408615659201*^9}] }, Open ]], Cell["\<\ It is interesting to note that without doing a perturbation of the initial \ weight vector, several of these take substantially longer (more than a factor \ of 10). They seem to get caught in large intermediate Gr\[ODoubleDot]bner \ basis computations because ideal initials are not always small.\ \>", "Text", CellChangeTimes->{{3.390407811500473*^9, 3.39040791158197*^9}, { 3.390408733618158*^9, 3.390408798623517*^9}, {3.390408873890874*^9, 3.390408910211821*^9}, {3.390412016706452*^9, 3.390412108353817*^9}, 3.390861575482443*^9}] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], 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"PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell["\<\ One might expect from comparing the modular and characteristic zero timings \ that the remaining four cases could be handled in reasonable time (an hour \ each, say). This turns out not to be the case, at least with option settings \ I have tried. We instead resort to numerical computations followed by \ rationalization.\ \>", "Text", CellChangeTimes->{{3.390407811500473*^9, 3.39040791158197*^9}, { 3.390408733618158*^9, 3.390408798623517*^9}, {3.390408873890874*^9, 3.390408910211821*^9}, {3.390571004833093*^9, 3.390571009214375*^9}, { 3.390572848551148*^9, 3.390572863719878*^9}}], Cell[BoxData[ RowBox[{"Timing", "[", RowBox[{ RowBox[{"implicit17approx", "=", RowBox[{"GroebnerBasis", "[", RowBox[{ RowBox[{"patches3D", "[", RowBox[{"[", "17", "]"}], "]"}], ",", "vars", ",", "elims", ",", RowBox[{"MonomialOrder", "\[Rule]", "EliminationOrder"}], ",", RowBox[{"CoefficientDomain", "\[Rule]", RowBox[{"InexactNumbers", "[", "700", "]"}]}], ",", RowBox[{"Method", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"\"\\"", "\[Rule]", "True"}]}], "}"}]}]}], "]"}]}], ";"}], "]"}]], "Input", CellChangeTimes->{{3.390573521160952*^9, 3.390573526083148*^9}, 3.390574716555558*^9}], Cell[OutputFormData["\<\ {445.356, Null}\ \>", "\<\ {445.356, Null}\ \>"], "Input", FontWeight->"Plain"], Cell["\<\ We rationalize, clear denominators (not necessary, but nice to have result \ with integer coefficients), plug in original relations and check that it \ expands to zero.\ \>", "Text", CellChangeTimes->{{3.390573107459497*^9, 3.390573157047841*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"implicit17attempt", "=", RowBox[{"Rationalize", "[", "implicit17approx", "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"imp2", "=", RowBox[{"Apply", "[", RowBox[{"List", ",", RowBox[{"implicit17attempt", "[", RowBox[{"[", "1", "]"}], "]"}]}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"imp2", "=", RowBox[{"imp2", "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "1"}], ",", RowBox[{"y", "\[Rule]", "1"}], ",", RowBox[{"z", "\[Rule]", "1"}]}], "}"}]}]}], ";"}], "\n", RowBox[{ RowBox[{"den", "=", RowBox[{"Denominator", "[", "imp2", "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"den", "=", RowBox[{"Apply", "[", RowBox[{"LCM", ",", "den"}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"implicit17", "=", RowBox[{"Expand", "[", RowBox[{"den", "*", RowBox[{"implicit17attempt", "[", RowBox[{"[", "1", "]"}], "]"}]}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"rules17", "=", RowBox[{"First", "[", RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"patches3D", "[", RowBox[{"[", "17", "]"}], "]"}], "\[Equal]", "0"}], ",", "vars"}], "]"}], "]"}]}], ";"}], "\n", RowBox[{"Timing", "[", RowBox[{ RowBox[{"Expand", "[", RowBox[{"implicit17", "/.", "rules17"}], "]"}], "\[Equal]", "0"}], "]"}]}], "Input", CellChangeTimes->{{3.390573070251147*^9, 3.390573078968744*^9}, 3.390573222101093*^9}], Cell[OutputFormData["\<\ {280.038, True}\ \>", "\<\ {280.038, True}\ \>"], "Input", CellChangeTimes->{{3.390573070251147*^9, 3.390573076723519*^9}}, FontWeight->"Plain"] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell["Example 3 cont'd", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318190967937*^9}, { 3.390408637479827*^9, 3.390408653722993*^9}}], Cell["\<\ We just show timings for computing the remaining three patch implicitizations \ to 700 digits. That turns out to suffice for rationalizing and recovering the \ correct exact polynomials.\ \>", "Text", CellChangeTimes->{{3.390573107459497*^9, 3.390573157047841*^9}, { 3.39057319062844*^9, 3.390573196585126*^9}, {3.390573229104338*^9, 3.390573265328677*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Timing", "[", RowBox[{ RowBox[{"implicit18approx", "=", RowBox[{"GroebnerBasis", "[", RowBox[{ RowBox[{"patches3D", "[", RowBox[{"[", "18", "]"}], "]"}], ",", "vars", ",", "elims", ",", RowBox[{"MonomialOrder", "\[Rule]", "EliminationOrder"}], ",", RowBox[{"CoefficientDomain", "\[Rule]", RowBox[{"InexactNumbers", "[", "700", "]"}]}], ",", RowBox[{"Method", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"\"\\"", "\[Rule]", "True"}]}], "}"}]}]}], "]"}]}], ";"}], "]"}]], "Input", CellChangeTimes->{{3.390573331631485*^9, 3.390573335254446*^9}, 3.390574722565318*^9}], Cell[OutputFormData["\<\ {465.629, Null}\ \>", "\<\ {465.629, Null}\ \>"], "Input", CellChangeTimes->{3.390575796534252*^9}, FontWeight->"Plain"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Timing", "[", RowBox[{ RowBox[{"implicit19approx", "=", RowBox[{"GroebnerBasis", "[", RowBox[{ RowBox[{"patches3D", "[", RowBox[{"[", "19", "]"}], "]"}], ",", "vars", ",", "elims", ",", RowBox[{"MonomialOrder", "\[Rule]", "EliminationOrder"}], ",", RowBox[{"CoefficientDomain", "\[Rule]", RowBox[{"InexactNumbers", "[", "700", "]"}]}], ",", RowBox[{"Method", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"\"\\"", "\[Rule]", "True"}]}], "}"}]}]}], "]"}]}], ";"}], "]"}]], "Input", CellChangeTimes->{{3.390573388551053*^9, 3.390573391932532*^9}, 3.390574775018397*^9}], Cell[OutputFormData["\<\ {1216.11, Null}\ \>", "\<\ {1216.11, Null}\ \>"], "Input", CellChangeTimes->{3.390573404117725*^9}, FontWeight->"Plain"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Timing", "[", RowBox[{ RowBox[{"implicit20approx", "=", RowBox[{"GroebnerBasis", "[", RowBox[{ RowBox[{"patches3D", "[", RowBox[{"[", "20", "]"}], "]"}], ",", "vars", ",", "elims", ",", RowBox[{"MonomialOrder", "\[Rule]", "EliminationOrder"}], ",", RowBox[{"CoefficientDomain", "\[Rule]", RowBox[{"InexactNumbers", "[", "700", "]"}]}], ",", RowBox[{"Method", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"\"\\"", "\[Rule]", "True"}]}], "}"}]}]}], "]"}]}], ";"}], "]"}]], "Input", CellChangeTimes->{3.390574784318731*^9}], Cell[OutputFormData["\<\ {1291.09, Null}\ \>", "\<\ {1291.09, Null}\ \>"], "Input", CellChangeTimes->{3.390581156615398*^9}, FontWeight->"Plain"] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Example 4", "Subsection", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318190967937*^9}, { 3.390408637479827*^9, 3.390408653722993*^9}, 3.390409548832761*^9}], Cell["\<\ This next example requires use of a perturbation of the target weight vector. \ Moreover an a priori computation a la (Tran 2000) is out of the question \ because the number of variables would cause the exponent vectors to have too \ many digits to allow the arithmetic to be feasible. We use the method of \ (Amrheim et al) though the simulated perturbation of (Fukuda et al) would \ also work here.\ \>", "Text", CellChangeTimes->{{3.390407811500473*^9, 3.39040791158197*^9}, { 3.390408733618158*^9, 3.390408798623517*^9}, {3.390408873890874*^9, 3.390408910211821*^9}, {3.390409914843827*^9, 3.390410070247338*^9}, { 3.390861989911048*^9, 3.390862001774961*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Timing", "[", RowBox[{"implicitpoly", "=", RowBox[{"Factor", "[", RowBox[{"First", "[", RowBox[{"GroebnerBasis", "[", RowBox[{"polys", ",", "mainvars", ",", "elimvars", ",", RowBox[{"Sort", "\[Rule]", "True"}], ",", RowBox[{"MonomialOrder", "\[Rule]", "EliminationOrder"}], ",", RowBox[{"Method", "->", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"\"\\"", "\[Rule]", "True"}]}], "}"}]}]}], "]"}], "]"}], "]"}]}], "]"}]], "Input", CellChangeTimes->{{3.36916044649758*^9, 3.36916049389199*^9}, { 3.39040950108511*^9, 3.390409518189341*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"125.79586199999999", ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "5"}], "*", "x"}], "+", RowBox[{"5", "*", RowBox[{"x", "^", "2"}]}], "+", RowBox[{"5", "*", RowBox[{"x", "^", "3"}]}], "-", RowBox[{"5", "*", RowBox[{"x", "^", "4"}]}], "+", RowBox[{"x", "^", "5"}], "-", "y"}], ")"}], "*", RowBox[{"(", RowBox[{"5", "+", RowBox[{"5", "*", "x"}], "-", RowBox[{"20", "*", RowBox[{"x", "^", "3"}]}], "+", RowBox[{"16", "*", RowBox[{"x", "^", "5"}]}], "+", RowBox[{"4", "*", "y"}]}], ")"}], "*", RowBox[{"(", RowBox[{"5400", "+", RowBox[{"11700", "*", "x"}], "-", RowBox[{"8675", "*", RowBox[{"x", "^", "2"}]}], "-", RowBox[{"37800", "*", RowBox[{"x", "^", "3"}]}], "-", RowBox[{"20600", "*", RowBox[{"x", "^", "4"}]}], "+", RowBox[{"14880", "*", RowBox[{"x", "^", "5"}]}], "+", RowBox[{"13680", "*", RowBox[{"x", "^", "6"}]}], "-", RowBox[{"1920", "*", RowBox[{"x", "^", "7"}]}], "-", RowBox[{"3200", "*", RowBox[{"x", "^", "8"}]}], "+", RowBox[{"256", "*", RowBox[{"x", "^", "10"}]}], "-", RowBox[{"1980", "*", "y"}], "-", RowBox[{"6230", "*", "x", "*", "y"}], "-", RowBox[{"7280", "*", RowBox[{"x", "^", "2"}], "*", "y"}], "-", RowBox[{"3800", "*", RowBox[{"x", "^", "3"}], "*", "y"}], "-", RowBox[{"800", "*", RowBox[{"x", "^", "4"}], "*", "y"}], "-", RowBox[{"32", "*", RowBox[{"x", "^", "5"}], "*", "y"}], "+", RowBox[{"y", "^", "2"}]}], ")"}]}]}], "}"}]], "Output", CellChangeTimes->{3.390409894730445*^9}] }, Open ]], Cell["\<\ Note that the result factors nontrivially, that is, it is not prime. 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Mdot .57016 .27256 Mdot .14332 .10441 Mdot .22134 .25997 Mdot .80713 .26825 Mdot .03635 .30601 Mdot .60548 .40341 Mdot .41097 .11906 Mdot .371 .17043 Mdot .17673 .17489 Mdot .03601 .12739 Mdot .06445 .13521 Mdot .11763 .17169 Mdot .09958 .2774 Mdot .28025 .39585 Mdot .68241 .57711 Mdot .12365 .07911 Mdot .18931 .32291 Mdot .05773 .12852 Mdot .16997 .1954 Mdot .49347 .15913 Mdot .61029 .17745 Mdot .29384 .37324 Mdot .22076 .29266 Mdot .44798 .27598 Mdot .19603 .21198 Mdot .09311 .15875 Mdot .20748 .19469 Mdot .54847 .34096 Mdot .29921 .52569 Mdot .41075 .08778 Mdot .8342 .1099 Mdot .06264 .31664 Mdot .90216 .11531 Mdot .46208 .16261 Mdot .44259 .27209 Mdot .02778 .13924 Mdot .06055 .51037 Mdot .78601 .31049 Mdot .31295 .12801 Mdot .33559 .46869 Mdot .90605 .12444 Mdot .78899 .19798 Mdot .64366 .47226 Mdot .11781 .17303 Mdot .85642 .17807 Mdot .1081 .09815 Mdot .18438 .10008 Mdot .86143 .07573 Mdot .87906 .07392 Mdot .72272 .12619 Mdot .16535 .45199 Mdot .04371 .19121 Mdot .12712 .12303 Mdot .12669 .13707 Mdot .07475 .08494 Mdot .43488 .27737 Mdot .09804 .30013 Mdot .09045 .37418 Mdot .03679 .14814 Mdot .03167 .19767 Mdot .08843 .32012 Mdot .11354 .19145 Mdot .42338 .12961 Mdot .08382 .10819 Mdot .05326 .18849 Mdot .7392 .13953 Mdot .09617 .11579 Mdot .08254 .0921 Mdot .4385 .1464 Mdot .03809 .17757 Mdot .40254 .41232 Mdot .88961 .11589 Mdot .09922 .29557 Mdot .23852 .25641 Mdot .10795 .21761 Mdot .38215 .14078 Mdot .54506 .10151 Mdot .26454 .49009 Mdot .22408 .57042 Mdot .40502 .0784 Mdot .81328 .13224 Mdot .40475 .20843 Mdot .23578 .1911 Mdot .3607 .32319 Mdot .20057 .4692 Mdot .14201 .23797 Mdot .12797 .11085 Mdot .60458 .45819 Mdot .43184 .15266 Mdot .67793 .57726 Mdot .51738 .18369 Mdot .8721 .07348 Mdot .4017 .26169 Mdot .69092 .40985 Mdot .21306 .41508 Mdot .04818 .14115 Mdot .11173 .19332 Mdot .66992 .10813 Mdot .38973 .14449 Mdot .45147 .16 Mdot .22356 .18943 Mdot .85471 .17933 Mdot .56138 .08597 Mdot .60819 .20453 Mdot .55051 .2165 Mdot .96236 .43571 Mdot .12837 .11529 Mdot .08151 .11833 Mdot .38018 .15629 Mdot .11001 .20933 Mdot .26071 .4795 Mdot .43916 .11959 Mdot .35377 .10745 Mdot .2812 .13017 Mdot .07586 .43503 Mdot .06424 .46467 Mdot .44087 .1278 Mdot .07401 .54437 Mdot .6666 .57325 Mdot .2398 .17802 Mdot .11034 .15256 Mdot .72377 .14119 Mdot .75619 .30775 Mdot .3024 .4482 Mdot .78025 .41255 Mdot .21203 .10527 Mdot .28976 .57785 Mdot .68106 .14501 Mdot .12988 .12743 Mdot .3404 .10167 Mdot .14801 .14164 Mdot .12986 .13419 Mdot .88217 .10724 Mdot .24994 .14243 Mdot .80616 .12865 Mdot .95212 .33878 Mdot .93272 .21158 Mdot .2587 .21144 Mdot .25057 .19311 Mdot .24809 .29999 Mdot .15973 .10545 Mdot .08191 .29693 Mdot .24953 .22866 Mdot .18695 .17975 Mdot .15419 .37521 Mdot .19017 .556 Mdot .14764 .16936 Mdot .16816 .26954 Mdot .22421 .54045 Mdot .94672 .29746 Mdot .81834 .20899 Mdot .37635 .40289 Mdot .39857 .35349 Mdot .48445 .13221 Mdot .50438 .22239 Mdot .09575 .12147 Mdot .06162 .1511 Mdot .52533 .18338 Mdot .3659 .12207 Mdot .45956 .25987 Mdot .18987 .20483 Mdot .32214 .46478 Mdot .13851 .20812 Mdot .97052 .52901 Mdot .48209 .13238 Mdot .42816 .07574 Mdot .74319 .41557 Mdot .71134 .44761 Mdot .34836 .41094 Mdot .31469 .33572 Mdot .0904 .37585 Mdot .11843 .07761 Mdot .8616 .07338 Mdot .54191 .10387 Mdot .16375 .43352 Mdot .56023 .10143 Mdot .3597 .23649 Mdot .24999 .5252 Mdot .698 .49585 Mdot .23389 .55739 Mdot .10234 .21733 Mdot .36509 .34029 Mdot .96781 .49627 Mdot .03501 .14678 Mdot .81061 .10709 Mdot .14417 .27938 Mdot .3513 .16806 Mdot .04196 .34073 Mdot .67577 .10681 Mdot .1424 .25487 Mdot .53986 .15485 Mdot .09259 .34708 Mdot .14713 .09868 Mdot .21018 .37413 Mdot .14383 .13327 Mdot .63932 .39662 Mdot .0706 .44418 Mdot .34264 .21471 Mdot .75131 .13001 Mdot .46751 .16028 Mdot .71439 .22983 Mdot .05933 .22046 Mdot .13155 .12146 Mdot .30691 .26353 Mdot .02382 .07239 Mdot .21508 .40755 Mdot .76501 .33856 Mdot .07759 .43947 Mdot .333 .47995 Mdot .54331 .10887 Mdot .05166 .22009 Mdot .26424 .12752 Mdot .1705 .0807 Mdot .5883 .07498 Mdot .66567 .49016 Mdot .13822 .23632 Mdot .14552 .10389 Mdot .06565 .11171 Mdot .14083 .10076 Mdot .79312 .13632 Mdot .45486 .14542 Mdot .33498 .11655 Mdot .4633 .13325 Mdot .37536 .11816 Mdot .19167 .41617 Mdot .11058 .1405 Mdot .30044 .45738 Mdot .17068 .12895 Mdot .50943 .2178 Mdot .81275 .12346 Mdot .11909 .09817 Mdot .96589 .47421 Mdot .24321 .49115 Mdot .36325 .15214 Mdot .60617 .131 Mdot .97381 .57111 Mdot .67844 .3839 Mdot .11235 .11414 Mdot .07663 .50116 Mdot .393 .07525 Mdot .25492 .23637 Mdot .1218 .14928 Mdot .87489 .13365 Mdot .13463 .12948 Mdot .09692 .27229 Mdot .45701 .23407 Mdot .28858 .13665 Mdot .47734 .20294 Mdot .14305 .26337 Mdot .0492 .21674 Mdot .71718 .17118 Mdot .30045 .35671 Mdot .25459 .24141 Mdot .77754 .15477 Mdot .48693 .19681 Mdot .11381 .18044 Mdot .66825 .53612 Mdot .68526 .56599 Mdot .75453 .13675 Mdot .81693 .25584 Mdot .32747 .32233 Mdot .18838 .17357 Mdot .16442 .08873 Mdot .24396 .11938 Mdot .12727 .13144 Mdot .12984 .13395 Mdot .08418 .30562 Mdot .24242 .48506 Mdot .2863 .39938 Mdot .05626 .54062 Mdot .11857 .07907 Mdot .16163 .15742 Mdot .03431 .12487 Mdot .18138 .17947 Mdot .66065 .47447 Mdot .74281 .30807 Mdot .08871 .27189 Mdot .08414 .34605 Mdot .63043 .08165 Mdot .24504 .16335 Mdot .64627 .13714 Mdot .53209 .12257 Mdot .35825 .08883 Mdot .72659 .52388 Mdot .28805 .25641 Mdot .17598 .20541 Mdot .54243 .1038 Mdot .10786 .22373 Mdot .62555 .29743 Mdot .04826 .26099 Mdot .4798 .17787 Mdot .42947 .07645 Mdot .16403 .15614 Mdot .08237 .44659 Mdot .11369 .10018 Mdot .21511 .36344 Mdot .1277 .12349 Mdot .29351 .347 Mdot .34428 .1012 Mdot .13171 .13335 Mdot .10816 .16859 Mdot .10531 .24252 Mdot .06079 .31066 Mdot .15729 .3625 Mdot .84193 .15306 Mdot .25741 .1975 Mdot .22788 .12203 Mdot .88444 .10924 Mdot .08299 .32961 Mdot .21481 .15562 Mdot .26075 .34743 Mdot .08311 .46253 Mdot .04759 .14085 Mdot .06581 .45883 Mdot .78182 .22238 Mdot .73018 .53831 Mdot .96704 .48732 Mdot .66459 .13678 Mdot .1951 .10075 Mdot .68508 .53715 Mdot .4172 .2826 Mdot .17365 .26658 Mdot .51346 .13315 Mdot .42748 .19021 Mdot .14522 .10086 Mdot .2339 .15555 Mdot .0361 .13082 Mdot .13484 .13138 Mdot .03148 .15647 Mdot .12316 .1145 Mdot .25778 .2278 Mdot .43785 .08186 Mdot .74666 .28969 Mdot .14499 .12982 Mdot .90837 .12386 Mdot .1513 .18745 Mdot .20249 .5549 Mdot .12827 .12144 Mdot .40932 .11936 Mdot .20132 .12755 Mdot .2918 .39283 Mdot .28779 .13299 Mdot .03828 .14724 Mdot .67354 .2352 Mdot .1033 .21221 Mdot .03269 .20387 Mdot .06154 .43185 Mdot .18812 .07804 Mdot .63262 .4878 Mdot .46079 .11071 Mdot .46152 .15096 Mdot .34368 .13663 Mdot .06091 .24616 Mdot .04807 .32852 Mdot .85319 .07477 Mdot .07596 .52953 Mdot .16486 .17251 Mdot .19157 .3132 Mdot .22586 .3829 Mdot .32477 .2893 Mdot .21598 .53501 Mdot .74232 .18099 Mdot .13743 .12886 Mdot .23445 .37976 Mdot .042 .40297 Mdot .46126 .11036 Mdot .07486 .21909 Mdot .13694 .14361 Mdot .12803 .11144 Mdot .51063 .14574 Mdot .83496 .08524 Mdot .15237 .37331 Mdot .11079 .1268 Mdot .35117 .25087 Mdot .61798 .39246 Mdot .94649 .29561 Mdot .33754 .53428 Mdot .61423 .20378 Mdot .10669 .2417 Mdot .07904 .50506 Mdot .23675 .45154 Mdot .20175 .11762 Mdot .12591 .09181 Mdot .10572 .17396 Mdot .12783 .12238 Mdot .10796 .15093 Mdot .09259 .35279 Mdot .0618 .48616 Mdot .07474 .31387 Mdot .46298 .21227 Mdot .36964 .49597 Mdot .09545 .33245 Mdot .62777 .5312 Mdot .39701 .42825 Mdot .14845 .122 Mdot .58304 .22736 Mdot .04387 .18934 Mdot .18596 .5386 Mdot .06365 .40214 Mdot .66958 .35483 Mdot .07412 .40486 Mdot .13486 .11225 Mdot .24609 .52 Mdot .38394 .11855 Mdot .78311 .3915 Mdot .11641 .08333 Mdot .12923 .12617 Mdot .04193 .31359 Mdot .53527 .13632 Mdot .57191 .20275 Mdot .12138 .08005 Mdot .13082 .12354 Mdot .12031 .15911 Mdot .8211 .285 Mdot .7757 .30665 Mdot .14229 .16541 Mdot .68062 .56474 Mdot .36468 .162 Mdot .38323 .1428 Mdot .30829 .20651 Mdot .28937 .2107 Mdot .31182 .52437 Mdot .22912 .20501 Mdot .16632 .17811 Mdot .65831 .18771 Mdot .14573 .24456 Mdot .49127 .19679 Mdot .06992 .33114 Mdot .1335 .17334 Mdot .17027 .09186 Mdot .78202 .40033 Mdot .51186 .1289 Mdot .50503 .19703 Mdot .14333 .16465 Mdot .09124 .36358 Mdot .67159 .10441 Mdot .17182 .25838 Mdot .41099 .37949 Mdot .12282 .08408 Mdot .23407 .22798 Mdot .16223 .41313 Mdot .19388 .30187 Mdot .26581 .1739 Mdot .12562 .13949 Mdot .64656 .08507 Mdot .54316 .32218 Mdot .13317 .13173 Mdot .32065 .29423 Mdot .15443 .34723 Mdot .94988 .32014 Mdot .21454 .34244 Mdot .17665 .27446 Mdot .74351 .42414 Mdot .97266 .55615 Mdot .62323 .15012 Mdot .10822 .21768 Mdot .27677 .33873 Mdot .12544 .12111 Mdot .64223 .08721 Mdot .07209 .11566 Mdot .51764 .13782 Mdot .10026 .22008 Mdot .13554 .11017 Mdot .65487 .53178 Mdot .16623 .0853 Mdot .65642 .46077 Mdot .18091 .41852 Mdot .08626 .42604 Mdot .90742 .13235 Mdot .61643 .28831 Mdot .79554 .29024 Mdot .31073 .22449 Mdot .57526 .32776 Mdot .14284 .11789 Mdot .55837 .16719 Mdot .12095 .14848 Mdot .29289 .16411 Mdot .15009 .35196 Mdot .41858 .07723 Mdot .82996 .14798 Mdot .43026 .31854 Mdot .28967 .47647 Mdot .16015 .08727 Mdot .13825 .10418 Mdot .03047 .11543 Mdot .96977 .51979 Mdot .26167 .13687 Mdot .1277 .12808 Mdot .1084 .17014 Mdot .74817 .34031 Mdot .0996 .2949 Mdot .41799 .34289 Mdot .0997 .25413 Mdot .057 .23005 Mdot .30461 .34727 Mdot .53213 .12225 Mdot .34615 .19901 Mdot .58914 .17042 Mdot .06191 .21555 Mdot .21983 .10431 Mdot .59058 .45412 Mdot .05331 .14154 Mdot .05049 .50477 Mdot .39619 .21151 Mdot .7271 .14004 Mdot .30251 .57836 Mdot .1063 .16401 Mdot .12874 .11969 Mdot .25777 .54271 Mdot .2835 .4088 Mdot .17272 .12168 Mdot .15294 .09056 Mdot .69342 .11969 Mdot .23974 .37925 Mdot .11064 .20782 Mdot .13996 .2458 Mdot .0481 .47998 Mdot .41241 .2453 Mdot .87819 .07479 Mdot .0316 .14281 Mdot .15396 .07927 Mdot .13346 .17454 Mdot .19759 .53211 Mdot .08094 .25832 Mdot .4876 .18969 Mdot .15941 .12816 Mdot .1254 .13979 Mdot .12134 .15814 Mdot .06908 .09465 Mdot .45469 .14544 Mdot .13191 .11987 Mdot .24342 .13706 Mdot .6744 .55221 Mdot .75699 .2072 Mdot .08217 .4626 Mdot .15529 .07693 Mdot .58968 .41585 Mdot .74673 .40136 Mdot .1101 .17352 Mdot .0341 .12498 Mdot .70933 .49151 Mdot .2073 .56666 Mdot .12187 .07304 Mdot .1273 .11922 Mdot .11099 .08852 Mdot .05633 .13978 Mdot .2181 .22754 Mdot .86454 .11261 Mdot .19286 .08072 Mdot .64156 .14874 Mdot .54798 .32593 Mdot .20795 .15215 Mdot .51359 .15439 Mdot .49743 .17291 Mdot .18671 .18982 Mdot .05187 .42174 Mdot .08959 .27526 Mdot .9053 .11648 Mdot .16129 .3728 Mdot .79174 .34392 Mdot .04888 .24006 Mdot .51359 .25076 Mdot .14639 .15596 Mdot .77797 .33608 Mdot .7327 .5062 Mdot .44465 .11965 Mdot .15185 .0991 Mdot .13997 .12202 Mdot .33515 .22621 Mdot .10495 .15478 Mdot .05287 .53229 Mdot .02502 .08893 Mdot .85879 .13915 Mdot .25956 .29278 Mdot .07056 .54248 Mdot .1176 .1099 Mdot .28241 .57137 Mdot .29446 .55062 Mdot .15926 .10146 Mdot .3881 .13584 Mdot .37446 .48198 Mdot .17218 .14986 Mdot .27862 .57007 Mdot .13834 .11082 Mdot .1134 .17801 Mdot .20064 .38005 Mdot .49212 .14732 Mdot .02758 .12563 Mdot .62498 .18871 Mdot .12241 .08281 Mdot .27369 .1414 Mdot .64641 .19845 Mdot .85817 .13203 Mdot .0634 .51603 Mdot .19685 .1241 Mdot .62371 .16604 Mdot .14082 .22898 Mdot .12026 .07552 Mdot .03465 .20344 Mdot .58916 .14371 Mdot .09808 .27678 Mdot .08135 .33036 Mdot .77278 .30866 Mdot .50634 .13869 Mdot .80911 .32465 Mdot .20299 .09501 Mdot .37032 .11615 Mdot .73668 .48295 Mdot .30664 .29579 Mdot .10484 .1009 Mdot .69128 .19532 Mdot .15461 .34481 Mdot .12564 .12384 Mdot .66833 .09879 Mdot .41076 .08131 Mdot .2094 .26258 Mdot .57608 .14179 Mdot .02822 .10599 Mdot .10838 .22423 Mdot .21332 .16226 Mdot .09894 .07747 Mdot .57201 .17234 Mdot .26278 .42008 Mdot .64206 .38767 Mdot .7294 .27522 Mdot .51784 .12752 Mdot .77507 .16635 Mdot .08235 .18845 Mdot .29332 .36607 Mdot .05282 .49373 Mdot .81011 .22074 Mdot .83061 .08829 Mdot .09579 .3007 Mdot .23789 .29299 Mdot .69835 .39052 Mdot .60583 .43299 Mdot .37668 .12916 Mdot .93082 .19923 Mdot .74044 .50746 Mdot .10868 .10251 Mdot .73111 .46056 Mdot .62619 .08244 Mdot .87914 .10603 Mdot .68302 .4686 Mdot .17392 .39242 Mdot .13389 .18346 Mdot .31103 .56542 Mdot .14813 .14477 Mdot .50308 .15914 Mdot .06506 .37178 Mdot .37403 .11459 Mdot .0298 .14919 Mdot .60473 .07921 Mdot .12688 .10098 Mdot .38334 .17746 Mdot .19555 .09662 Mdot .11481 .14097 Mdot .76749 .43297 Mdot .27009 .12766 Mdot .43354 .0962 Mdot .1732 .24332 Mdot .3217 .19382 Mdot .13265 .12659 Mdot .59479 .41478 Mdot .6507 .40309 Mdot .46735 .10243 Mdot .88518 .07772 Mdot .30165 .15039 Mdot .09136 .36171 Mdot .07462 .24154 Mdot .09016 .07423 Mdot .63682 .37449 Mdot .10481 .1887 Mdot .20198 .23446 Mdot .74379 .51373 Mdot .75857 .31881 Mdot .95231 .34098 Mdot .15912 .40477 Mdot .94592 .29068 Mdot .8856 .08113 Mdot .12719 .1263 Mdot .15228 .16531 Mdot .79752 .3015 Mdot .08955 .07794 Mdot .02567 .09336 Mdot .28687 .1488 Mdot .11554 .16817 Mdot .41799 .21762 Mdot .10211 .09996 Mdot .02697 .10946 Mdot .16386 .11926 Mdot .05669 .16489 Mdot .21873 .11668 Mdot .57614 .37124 Mdot .05013 .41606 Mdot .14661 .29222 Mdot .05874 .10448 Mdot .19774 .22576 Mdot .73358 .12833 Mdot .29803 .46595 Mdot .48358 .17457 Mdot .11488 .10992 Mdot .11743 .12699 Mdot .44335 .30337 Mdot .25637 .44735 Mdot .09752 .27941 Mdot .32811 .3779 Mdot .14382 .2563 Mdot .1186 .12182 Mdot .06689 .56569 Mdot .38186 .15159 Mdot .07556 .39105 Mdot .13707 .11334 Mdot .51174 .13297 Mdot .18657 .55167 Mdot .93883 .24146 Mdot .05198 .52553 Mdot .06116 .57118 Mdot .13929 .24793 Mdot .39874 .22995 Mdot .8899 .11716 Mdot .65578 .25868 Mdot .52562 .14926 Mdot .26868 .19567 Mdot .54902 .15958 Mdot .07128 .51535 Mdot .0345 .1814 Mdot .0382 .25137 Mdot .88876 .12838 Mdot .16258 .20309 Mdot .27778 .4318 Mdot .42551 .08347 Mdot .40777 .08037 Mdot .26801 .34716 Mdot .09913 .29713 Mdot .31752 .28387 Mdot .08857 .345 Mdot .76852 .2368 Mdot .8694 .12548 Mdot .09412 .22218 Mdot .9708 .53246 Mdot .6907 .57897 Mdot .25948 .48616 Mdot .39887 .07915 Mdot .31813 .11604 Mdot .10733 .19872 Mdot .40344 .09476 Mdot .2321 .51028 Mdot .30497 .17538 Mdot .19371 .33628 Mdot .26542 .44423 Mdot .63612 .54215 Mdot .22365 .32026 Mdot .18837 .5504 Mdot .08258 .38591 Mdot .02679 .1189 Mdot .08895 .32873 Mdot .78125 .16039 Mdot .49666 .12747 Mdot .54165 .13386 Mdot .07756 .5163 Mdot .06448 .15116 Mdot .32189 .28689 Mdot .09575 .16611 Mdot .1201 .08092 Mdot .46607 .17214 Mdot .2135 .12809 Mdot .41752 .12909 Mdot .11959 .09105 Mdot .26893 .17817 Mdot .04805 .48486 Mdot .12643 .12346 Mdot .08021 .40194 Mdot .41306 .36741 Mdot .15658 .13073 Mdot .21662 .10118 Mdot .07672 .51966 Mdot .07886 .41267 Mdot .52217 .23945 Mdot .10905 .15202 Mdot .57125 .10165 Mdot .06806 .13407 Mdot .12786 .1283 Mdot .72889 .47334 Mdot .35484 .14879 Mdot .11845 .16561 Mdot .07266 .29579 Mdot .59986 .21883 Mdot .75934 .44644 Mdot .07841 .46465 Mdot .61056 .08186 Mdot .53352 .12897 Mdot .96052 .41661 Mdot .28268 .41576 Mdot .11545 .09175 Mdot .10799 .19901 Mdot .14869 .18213 Mdot .14843 .30619 Mdot .19992 .13705 Mdot .56085 .11175 Mdot .48546 .1925 Mdot .18163 .14612 Mdot .85752 .16556 Mdot .18746 .13902 Mdot .91394 .1355 Mdot .35499 .11156 Mdot .191 .36934 Mdot .07588 .52195 Mdot .43145 .25328 Mdot .16745 .25485 Mdot .8878 .11933 Mdot .06804 .4023 Mdot .24782 .51439 Mdot .62422 .08958 Mdot .11872 .16174 Mdot .07124 .40439 Mdot .06955 .5526 Mdot .21549 .18736 Mdot .37677 .47594 Mdot .15632 .2124 Mdot .13635 .17752 Mdot .05571 .46994 Mdot .14903 .19478 Mdot .71858 .30943 Mdot .89876 .12251 Mdot .53293 .13418 Mdot .13473 .13542 Mdot .11686 .0836 Mdot .26875 .12885 Mdot .13877 .10601 Mdot .53889 .19474 Mdot .37882 .19539 Mdot .37039 .44075 Mdot .1085 .21396 Mdot .75879 .14271 Mdot .051 .31427 Mdot .65223 .56469 Mdot .18849 .43194 Mdot .53113 .17391 Mdot .81127 .24062 Mdot .05094 .51183 Mdot .36903 .4469 Mdot .45921 .26376 Mdot .1443 .14583 Mdot .13777 .23116 Mdot .0698 .39881 Mdot .22685 .20528 Mdot .96662 .48241 Mdot .7282 .19626 Mdot .18579 .5455 Mdot .26024 .21343 Mdot .32049 .26707 Mdot .62494 .38374 Mdot .18942 .33898 Mdot .11385 .16242 Mdot .20038 .1544 Mdot .22896 .34605 Mdot .89539 .08876 Mdot .26331 .24152 Mdot .91811 .15277 Mdot .09819 .07759 Mdot .33311 .22206 Mdot .17226 .31334 Mdot .24546 .30437 Mdot .28886 .33615 Mdot .93948 .2456 Mdot .15296 .19501 Mdot .23681 .19328 Mdot .45445 .27527 Mdot .44903 .12597 Mdot .61386 .50592 Mdot .66445 .5737 Mdot .12627 .11991 Mdot .14315 .27415 Mdot .3416 .15346 Mdot .53963 .12216 Mdot .07363 .40763 Mdot .64026 .10034 Mdot .17375 .07275 Mdot .56643 .16766 Mdot .79402 .29812 Mdot .06324 .46116 Mdot .30161 .26966 Mdot .23368 .48833 Mdot .31319 .36455 Mdot .48103 .16263 Mdot .73034 .42923 Mdot .18721 .5453 Mdot .20454 .21313 Mdot .20248 .13225 Mdot .20788 .3713 Mdot .05416 .11171 Mdot .19298 .35098 Mdot .12356 .12333 Mdot .30951 .12924 Mdot .36791 .08306 Mdot .09767 .10373 Mdot .15302 .18399 Mdot .03879 .19373 Mdot .76901 .18157 Mdot .5803 .09518 Mdot .0921 .35182 Mdot .16826 .12416 Mdot .1788 .08476 Mdot .31433 .42349 Mdot .3018 .27873 Mdot .83972 .22289 Mdot .41387 .11629 Mdot .05983 .37876 Mdot .13431 .12782 Mdot .0424 .40943 Mdot .16391 .17236 Mdot .38326 .09575 Mdot .33648 .10241 Mdot .19823 .16555 Mdot .92265 .1616 Mdot .12211 .12823 Mdot .31981 .17465 Mdot .30348 .1502 Mdot .04241 .30024 Mdot .36685 .0845 Mdot .1327 .11765 Mdot .18309 .11357 Mdot .1108 .17682 Mdot .43459 .12477 Mdot .07083 .14591 Mdot .0855 .32658 Mdot .11054 .21434 Mdot .13325 .11694 Mdot .82984 .14485 Mdot .18196 .24672 Mdot .08027 .4111 Mdot .32796 .1945 Mdot .95307 .34707 Mdot .03714 .21835 Mdot .14418 .09198 Mdot .45392 .10289 Mdot .8927 .08895 Mdot .42048 .32148 Mdot .0469 .16346 Mdot .13072 .12354 Mdot .03872 .33816 Mdot .16722 .39757 Mdot .20451 .32361 Mdot .38112 .12611 Mdot .14248 .16667 Mdot .42051 .10055 Mdot .88564 .13031 Mdot .12502 .12262 Mdot .69002 .25653 Mdot .22263 .11065 Mdot .12594 .13883 Mdot .1794 .23308 Mdot .11094 .19128 Mdot .15875 .07483 Mdot .28116 .27631 Mdot .84013 .16175 Mdot .16867 .19517 Mdot .15246 .08444 Mdot .19475 .2593 Mdot .66724 .15926 Mdot .27674 .30404 Mdot .72598 .45464 Mdot .20216 .23598 Mdot .03669 .23166 Mdot .02464 .08114 Mdot .09944 .1992 Mdot .3025 .2003 Mdot .02975 .17151 Mdot .45253 .1 Mdot .75772 .47024 Mdot .15859 .31678 Mdot .27376 .35211 Mdot .34038 .10065 Mdot .63823 .54409 Mdot .09137 .31241 Mdot .18714 .33241 Mdot .84521 .17055 Mdot .66922 .15141 Mdot .21303 .19887 Mdot .12526 .09359 Mdot .04408 .26551 Mdot .09498 .16959 Mdot .46541 .15854 Mdot .15712 .1364 Mdot .06795 .50145 Mdot .03173 .1194 Mdot .75426 .39333 Mdot .54792 .34326 Mdot .4642 .23784 Mdot .13966 .13335 Mdot .08023 .49329 Mdot .10205 .21862 Mdot .24209 .45063 Mdot .66667 .53219 Mdot .73687 .36734 Mdot .38368 .11558 Mdot .19435 .38455 Mdot .56437 .27292 Mdot .3993 .12052 Mdot .18066 .2529 Mdot .5603 .18305 Mdot .49328 .17827 Mdot .142 .1162 Mdot .31716 .20539 Mdot .03202 .13311 Mdot .24303 .24167 Mdot .11295 .13125 Mdot .92926 .19203 Mdot .15146 .286 Mdot .462 .22268 Mdot .10924 .12202 Mdot .23656 .29669 Mdot .12241 .12684 Mdot .14181 .16439 Mdot .71557 .12969 Mdot .34303 .26781 Mdot .128 .12392 Mdot .69688 .48471 Mdot .77842 .1529 Mdot .52563 .13442 Mdot .42842 .11189 Mdot .17686 .50929 Mdot .13297 .12102 Mdot .27474 .44562 Mdot .33902 .54542 Mdot .33252 .39105 Mdot .14298 .19542 Mdot .30338 .31328 Mdot .21611 .12834 Mdot .1087 .15538 Mdot .38889 .36786 Mdot .58419 .42486 Mdot .21683 .12712 Mdot .2971 .55222 Mdot .93409 .21959 Mdot .09434 .33388 Mdot .19535 .28068 Mdot .74858 .50103 Mdot .43399 .07838 Mdot .26605 .16061 Mdot .75648 .47623 Mdot .15675 .36736 Mdot .10086 .28407 Mdot .06649 .12525 Mdot .26837 .22966 Mdot .12622 .0944 Mdot .15578 .07876 Mdot .29755 .29626 Mdot .59299 .28497 Mdot .08357 .29505 Mdot .05191 .19488 Mdot .61429 .07612 Mdot .09141 .36075 Mdot .05142 .11622 Mdot .06499 .56523 Mdot .07282 .08316 Mdot .62224 .2503 Mdot .63253 .48812 Mdot .24464 .13004 Mdot .04804 .42509 Mdot .66973 .4576 Mdot .20426 .1259 Mdot .12933 .12735 Mdot .16437 .45515 Mdot .16559 .10049 Mdot .53531 .11171 Mdot .10254 .07869 Mdot .18657 .5124 Mdot .32127 .29612 Mdot .23983 .50017 Mdot .37928 .19985 Mdot .68192 .55476 Mdot .40171 .1248 Mdot .12668 .10165 Mdot .73178 .30138 Mdot .94371 .27366 Mdot .1415 .24755 Mdot .60677 .22318 Mdot .11499 .13237 Mdot .03709 .1818 Mdot .52489 .12445 Mdot .64272 .26012 Mdot .11333 .15176 Mdot .2026 .2966 Mdot .55371 .0962 Mdot .34654 .16186 Mdot .14409 .12477 Mdot .34361 .19225 Mdot .38287 .09673 Mdot .86253 .09621 Mdot .12644 .13814 Mdot .16683 .1838 Mdot .28541 .39777 Mdot .45633 .11775 Mdot .12136 .07488 Mdot .11023 .17537 Mdot .05416 .53429 Mdot .09745 .30951 Mdot .52629 .15261 Mdot .29331 .5432 Mdot .12946 .12812 Mdot .3626 .09275 Mdot .88248 .13317 Mdot .19158 .22481 Mdot .3662 .22533 Mdot .46383 .2229 Mdot .43306 .3288 Mdot .48652 .18163 Mdot .17697 .41309 Mdot .10601 .1681 Mdot .68321 .10797 Mdot .14704 .17259 Mdot .59454 .07207 Mdot .83391 .24111 Mdot .53647 .29174 Mdot .12513 .11761 Mdot .03619 .30313 Mdot .55521 .12663 Mdot .14414 .28211 Mdot .21284 .32411 Mdot .82809 .10075 Mdot .02869 .13469 Mdot .75825 .32185 Mdot .79007 .13305 Mdot .77806 .26309 Mdot .90258 .10232 Mdot .30828 .57701 Mdot .07935 .404 Mdot .14443 .28363 Mdot .36735 .10787 Mdot .12583 .1212 Mdot .56572 .13569 Mdot .04806 .36832 Mdot .14283 .147 Mdot .19211 .15601 Mdot .09792 .24148 Mdot .11094 .16555 Mdot .04413 .12778 Mdot .38072 .14431 Mdot .1376 .14872 Mdot .82217 .27861 Mdot .1911 .56235 Mdot .12882 .12342 Mdot .4831 .18535 Mdot .76563 .12597 Mdot .49302 .12284 Mdot .12289 .08683 Mdot .16291 .38457 Mdot .77658 .29369 Mdot .40118 .09326 Mdot .14465 .10601 Mdot .55997 .23258 Mdot .40126 .22055 Mdot .73031 .27782 Mdot .3467 .51357 Mdot .18057 .08129 Mdot .15871 .108 Mdot .07809 .47248 Mdot .76985 .4139 Mdot .7792 .38444 Mdot .40306 .37684 Mdot .50502 .14672 Mdot .23085 .28092 Mdot .65416 .13714 Mdot .31953 .56062 Mdot .41418 .12844 Mdot .96754 .49314 Mdot .08596 .36722 Mdot .18041 .07391 Mdot .36447 .47689 Mdot .15598 .12539 Mdot .11097 .18903 Mdot .28938 .37886 Mdot .17195 .07332 Mdot .12199 .12305 Mdot .45947 .1191 Mdot .03151 .14253 Mdot .10054 .1711 Mdot .02571 .10408 Mdot .30801 .46869 Mdot .16087 .08221 Mdot .0491 .45884 Mdot .36044 .36977 Mdot .07682 .08197 Mdot .23938 .30401 Mdot .06727 .54059 Mdot .62395 .20299 Mdot .15415 .15615 Mdot .1047 .22594 Mdot .13538 .1141 Mdot .16889 .25912 Mdot .12453 .13478 Mdot .33872 .39308 Mdot .4127 .30132 Mdot .97388 .57211 Mdot .14999 .22595 Mdot .22717 .2441 Mdot .20789 .25025 Mdot .19152 .15656 Mdot .5341 .28723 Mdot .92307 .16357 Mdot .48262 .11421 Mdot .12145 .14153 Mdot .47691 .1597 Mdot .35879 .13448 Mdot .41937 .165 Mdot .37365 .1029 Mdot .3381 .11122 Mdot .12943 .12852 Mdot .35704 .14515 Mdot .08243 .4701 Mdot .15204 .17844 Mdot .07113 .32141 Mdot .03429 .12946 Mdot .95716 .38371 Mdot .36249 .51063 Mdot .26904 .18311 Mdot .27247 .3114 Mdot .31334 .21837 Mdot .31353 .11954 Mdot .04798 .46606 Mdot .21211 .32995 Mdot .07671 .39994 Mdot .37678 .08376 Mdot .69555 .18477 Mdot .27575 .35251 Mdot .74201 .4335 Mdot .08827 .40485 Mdot .15159 .09977 Mdot .3747 .13946 Mdot .89894 .12666 Mdot .03377 .15086 Mdot .03443 .20485 Mdot .10207 .2239 Mdot .93194 .20681 Mdot .72415 .42094 Mdot .53222 .18328 Mdot .12663 .1364 Mdot .15506 .13129 Mdot .40214 .12439 Mdot .2676 .28171 Mdot .87313 .09761 Mdot .21101 .36466 Mdot .08069 .33487 Mdot .3783 .11333 Mdot .42782 .08752 Mdot .2469 .12618 Mdot .5027 .17501 Mdot .0434 .41198 Mdot .34426 .19473 Mdot .81068 .31643 Mdot .10757 .21422 Mdot .09498 .32212 Mdot .23679 .42298 Mdot .66117 .5296 Mdot .49181 .15295 Mdot .13306 .17346 Mdot .24944 .52379 Mdot .79523 .20101 Mdot .28075 .28583 Mdot .13097 .13437 Mdot .33712 .11277 Mdot .05774 .46318 Mdot .6493 .33378 Mdot .07906 .41352 Mdot .69216 .12393 Mdot .26044 .4032 Mdot .41618 .37852 Mdot .55621 .13573 Mdot .08394 .31905 Mdot .48943 .12051 Mdot .53128 .11697 Mdot .69552 .57762 Mdot .10438 .25393 Mdot .32031 .49029 Mdot .42919 .12365 Mdot .79028 .33714 Mdot .27256 .56234 Mdot .55719 .16715 Mdot .31612 .34689 Mdot .33991 .54422 Mdot .14347 .12698 Mdot .05573 .19039 Mdot .08995 .20438 Mdot .14338 .16628 Mdot .79029 .37996 Mdot .27464 .35641 Mdot .19675 .21423 Mdot .08778 .37905 Mdot .35436 .15182 Mdot .11067 .13391 Mdot .13591 .16811 Mdot .38381 .08658 Mdot .25463 .47194 Mdot .17283 .17682 Mdot .65125 .3166 Mdot .47559 .16654 Mdot .78175 .12216 Mdot .68306 .31841 Mdot .34733 .11926 Mdot .21151 .55965 Mdot .62837 .5006 Mdot .82629 .09503 Mdot .17607 .22532 Mdot .34253 .14385 Mdot .08046 .4191 Mdot .59409 .17339 Mdot .18769 .30706 Mdot .55963 .08687 Mdot .57441 .08782 Mdot .18567 .23341 Mdot .14088 .11154 Mdot .14792 .28896 Mdot .11891 .1656 Mdot .11706 .16183 Mdot .83656 .15079 Mdot .42012 .18205 Mdot .0442 .27211 Mdot .72054 .43033 Mdot .06491 .56619 Mdot .14767 .12571 Mdot .10195 .07817 Mdot .18003 .27673 Mdot .36194 .38505 Mdot .11512 .18938 Mdot .47701 .17001 Mdot .36208 .23951 Mdot .68739 .17021 Mdot .66366 .13608 Mdot .36228 .49396 Mdot .22224 .33793 Mdot .60936 .44812 Mdot .19366 .2486 Mdot .13095 .14649 Mdot .85121 .08369 Mdot .38878 .42681 Mdot .23876 .50191 Mdot .17874 .24778 Mdot .91779 .14842 Mdot .0457 .12858 Mdot .8508 .0761 Mdot .1652 .24894 Mdot .05122 .25575 Mdot .08018 .48699 Mdot .13734 .11858 Mdot .84904 .077 Mdot .09568 .31396 Mdot .21038 .15591 Mdot .20571 .49812 Mdot .19065 .26398 Mdot .32097 .23899 Mdot .86585 .11771 Mdot .14846 .28782 Mdot .13817 .21445 Mdot .49127 .14793 Mdot .84408 .20345 Mdot .19741 .18556 Mdot .55629 .15369 Mdot .11956 .08149 Mdot .14925 .12903 Mdot .12408 .12003 Mdot .20188 .09678 Mdot .20211 .28187 Mdot .09033 .3752 Mdot .04493 .13894 Mdot .89136 .11943 Mdot .18994 .08759 Mdot .60487 .42996 Mdot .74335 .12944 Mdot .11197 .17717 Mdot .24524 .4157 Mdot .1251 .14341 Mdot .02381 .07229 Mdot .95089 .32821 Mdot .11912 .15022 Mdot .12104 .1435 Mdot .09848 .11872 Mdot .05399 .52985 Mdot .37038 .14783 Mdot .09547 .2794 Mdot .78723 .39683 Mdot .61951 .51115 Mdot .07459 .54033 Mdot .2661 .21327 Mdot .84196 .08374 Mdot .33605 .49797 Mdot .10627 .20768 Mdot .54549 .23631 Mdot .53959 .11972 Mdot .46061 .25879 Mdot .06933 .40011 Mdot .12264 .15322 Mdot .28254 .56532 Mdot .03691 .31086 Mdot .69877 .48175 Mdot .44155 .09621 Mdot .56728 .14552 Mdot .87393 .0744 Mdot .0968 .32012 Mdot .78925 .36785 Mdot .23473 .32948 Mdot .72315 .54963 Mdot .13397 .18654 Mdot .12652 .13375 Mdot .0422 .15012 Mdot .07261 .19353 Mdot .11834 .1093 Mdot .22803 .462 Mdot .67661 .14918 Mdot .13455 .11274 Mdot .16352 .238 Mdot .44005 .18933 Mdot .1367 .13585 Mdot .26773 .22126 Mdot .91028 .13676 Mdot .56147 .10687 Mdot .02689 .10482 Mdot .25255 .23977 Mdot .0983 .30332 Mdot .09129 .35168 Mdot .0308 .12734 Mdot .46959 .20822 Mdot .72768 .34327 Mdot .30131 .57913 Mdot .08032 .10992 Mdot .16237 .20066 Mdot .08357 .44724 Mdot .11666 .17955 Mdot .75949 .15303 Mdot .12522 .11734 Mdot .12721 .10772 Mdot .92621 .17593 Mdot .4496 .24214 Mdot .54419 .13088 Mdot .15253 .07963 Mdot .12959 .13068 Mdot .0518 .47274 Mdot .09296 .10546 Mdot .95054 .32551 Mdot .75383 .16074 Mdot .62489 .11096 Mdot .04635 .14102 Mdot .02664 .11903 Mdot .08112 .39015 Mdot .13217 .16 Mdot .19715 .16521 Mdot .1389 .11084 Mdot .08599 .24361 Mdot .0871 .07444 Mdot .91558 .15079 Mdot .11509 .14452 Mdot .85815 .17167 Mdot .15763 .28814 Mdot .07438 .53528 Mdot .37661 .21328 Mdot .10214 .2481 Mdot .05251 .26677 Mdot .88192 .10568 Mdot .79221 .11975 Mdot .02945 .13587 Mdot .17542 .19479 Mdot .04215 .37826 Mdot .41736 .10129 Mdot .04874 .46187 Mdot .3516 .37461 Mdot .26457 .48593 Mdot .60623 .07161 Mdot .33445 .1798 Mdot .09742 .3146 Mdot .52198 .21339 Mdot .09003 .08796 Mdot .23185 .1378 Mdot .25449 .49864 Mdot .34328 .18231 Mdot .3513 .13909 Mdot .34688 .09557 Mdot .19437 .08316 Mdot .10884 .20204 Mdot .08437 .09128 Mdot .52833 .12051 Mdot .21616 .18629 Mdot .23295 .24917 Mdot .39256 .14251 Mdot .97038 .5273 Mdot .02743 .10625 Mdot .29425 .2801 Mdot .24478 .51139 Mdot .25395 .15097 Mdot .90768 .11434 Mdot .13049 .13392 Mdot .05801 .43822 Mdot .053 .47027 Mdot .40699 .0719 Mdot .14309 .23158 Mdot .21553 .28354 Mdot .16479 .36918 Mdot .21159 .13195 Mdot .92391 .17673 Mdot .07444 .08068 Mdot .36086 .18842 Mdot .02483 .08777 Mdot .07355 .54165 Mdot .88084 .13174 Mdot .74266 .49926 Mdot .18496 .21777 Mdot .10273 .24994 Mdot .84244 .1009 Mdot .91181 .1439 Mdot .08577 .4335 Mdot .91371 .14737 Mdot .83025 .19669 Mdot .58183 .41795 Mdot .07387 .50148 Mdot .23846 .38317 Mdot .02868 .12245 Mdot .26383 .50941 Mdot .49215 .17022 Mdot .23048 .41257 Mdot .79659 .34103 Mdot .1638 .37164 Mdot .21939 .29872 Mdot .12747 .11016 Mdot .14779 .23732 Mdot .45805 .09528 Mdot .3526 .38464 Mdot .04117 .26847 Mdot .50107 .1311 Mdot .61188 .43026 Mdot .11628 .1701 Mdot .03397 .16488 Mdot .0246 .08327 Mdot .59326 .42094 Mdot .71209 .25855 Mdot .10535 .17731 Mdot .38889 .08829 Mdot .36398 .30987 Mdot .10635 .17874 Mdot .15395 .12235 Mdot .1352 .11266 Mdot .66442 .29027 Mdot .45312 .27044 Mdot .17081 .33385 Mdot .12936 .12767 Mdot .15946 .12459 Mdot .34541 .09769 Mdot .1294 .12809 Mdot .07628 .0785 Mdot .36813 .28436 Mdot .43085 .32745 Mdot .84534 .16854 Mdot .3255 .28333 Mdot .35796 .14399 Mdot .77567 .42759 Mdot .22468 .1744 Mdot .33211 .25632 Mdot .23789 .53613 Mdot .92664 .1791 Mdot .14214 .11653 Mdot .14141 .12167 Mdot .31783 .3839 Mdot .82306 .23418 Mdot .09482 .07296 Mdot .37028 .37379 Mdot .30567 .47981 Mdot .24696 .52033 Mdot .48211 .13909 Mdot .27688 .272 Mdot .77368 .20415 Mdot .15344 .17536 Mdot .19057 .24035 Mdot .29764 .13004 Mdot .69505 .37468 Mdot .11256 .09125 Mdot .14311 .24191 Mdot .28001 .13047 Mdot .02571 .10176 Mdot .14971 .15483 Mdot .14464 .30364 Mdot .57079 .07954 Mdot .21673 .33946 Mdot .42876 .15869 Mdot .1304 .12919 Mdot .24248 .53602 Mdot .15257 .37524 Mdot .65064 .09012 Mdot .88367 .08913 Mdot .06169 .43848 Mdot .08542 .15892 Mdot .37238 .13676 Mdot .60689 .48936 Mdot .22149 .39031 Mdot .0308 .18979 Mdot .84918 .14731 Mdot .07046 .3791 Mdot .14865 .08574 Mdot .20277 .12899 Mdot .0548 .52626 Mdot .19821 .53802 Mdot .70228 .53848 Mdot .15292 .13742 Mdot .12463 .08634 Mdot .12674 .09969 Mdot .56886 .19879 Mdot .46613 .23076 Mdot .36711 .14822 Mdot .13579 .12018 Mdot .12614 .0959 Mdot .17233 .32853 Mdot .59912 .09852 Mdot .0993 .27181 Mdot .86517 .07188 Mdot .82332 .13945 Mdot .11676 .08882 Mdot .2485 .50557 Mdot .1592 .17544 Mdot .07633 .16054 Mdot .13646 .12156 Mdot .25974 .38113 Mdot .92861 .19102 Mdot .39111 .2807 Mdot .73474 .21524 Mdot .42327 .07511 Mdot .56745 .25169 Mdot .70415 .43028 Mdot .13777 .13419 Mdot .09271 .27441 Mdot .18629 .49506 Mdot .12843 .12545 Mdot .15632 .1417 Mdot .42392 .08315 Mdot .12946 .12807 Mdot .098 .17315 Mdot .07309 .47081 Mdot .10765 .23482 Mdot .41379 .12507 Mdot .36129 .17839 Mdot .12855 .12812 Mdot .19804 .08506 Mdot .69192 .12874 Mdot .0393 .34703 Mdot .60484 .30347 Mdot .25693 .12864 Mdot .05695 .26624 Mdot .35642 .09813 Mdot .10779 .22998 Mdot .13647 .12474 Mdot .12249 .09827 Mdot .12433 .10396 Mdot .5556 .22613 Mdot .89805 .09464 Mdot .1297 .127 Mdot .02904 .13071 Mdot .51756 .23329 Mdot .22097 .43998 Mdot .12649 .10304 Mdot .52491 .20569 Mdot .23455 .1163 Mdot .18329 .07528 Mdot .87732 .10874 Mdot .45398 .09854 Mdot .47954 .12132 Mdot .23968 .11901 Mdot .36324 .13898 Mdot .69093 .52463 Mdot .92425 .17619 Mdot .04744 .32849 Mdot .1122 .20007 Mdot .27246 .42714 Mdot .04604 .1283 Mdot .5254 .12471 Mdot .06896 .53347 Mdot .61751 .41926 Mdot .14636 .11681 Mdot .03643 .29801 Mdot .04027 .36856 Mdot .26525 .45744 Mdot .02604 .1057 Mdot .08063 .491 Mdot .16301 .1079 Mdot .71734 .29019 Mdot .07188 .54287 Mdot .12286 .11155 Mdot .96351 .44788 Mdot .12729 .10936 Mdot .12052 .12408 Mdot .24255 .22254 Mdot .82256 .15745 Mdot .96462 .46001 Mdot .12442 .12977 Mdot .09278 .35769 Mdot .84873 .15835 Mdot .076 .14116 Mdot .21685 .20387 Mdot .06846 .11652 Mdot .29298 .34368 Mdot .31347 .57718 Mdot .54058 .31382 Mdot .93213 .20439 Mdot .83312 .09661 Mdot .88406 .09268 Mdot .0509 .40615 Mdot .23319 .11366 Mdot .0436 .42728 Mdot .25723 .45689 Mdot .12124 .07234 Mdot .14755 .31514 Mdot .08911 .18663 Mdot .05295 .32141 Mdot .12166 .08572 Mdot .03383 .16041 Mdot .25571 .48074 Mdot .07734 .34188 Mdot .23598 .54576 Mdot .13458 .18933 Mdot .59331 .46046 Mdot .57739 .09223 Mdot .48505 .12194 Mdot .28916 .28151 Mdot .14044 .2567 Mdot .08876 .39985 Mdot .92712 .18406 Mdot .80068 .17189 Mdot .20942 .29674 Mdot .31045 .12303 Mdot .15249 .36043 Mdot .04198 .375 Mdot .65015 .52824 Mdot .14891 .10731 Mdot .11702 .1006 Mdot .13872 .11009 Mdot .13864 .11967 Mdot .94735 .30025 Mdot .0794 .4994 Mdot .82881 .25655 Mdot .2371 .40779 Mdot .48745 .15452 Mdot .91583 .13944 Mdot .19204 .44617 Mdot .45399 .09985 Mdot .17998 .07347 Mdot .45777 .26382 Mdot .63263 .17914 Mdot .07018 .41156 Mdot .72291 .1353 Mdot .05457 .54477 Mdot .39468 .09439 Mdot .42257 .28575 Mdot .51162 .12871 Mdot .5232 .22379 Mdot .10803 .08863 Mdot .16849 .19536 Mdot .37188 .08714 Mdot .83372 .21476 Mdot .78334 .13395 Mdot .09931 .10904 Mdot .79428 .15796 Mdot .62556 .12149 Mdot .19884 .29261 Mdot .13394 .12708 Mdot .1251 .09556 Mdot .06648 .32839 Mdot .67194 .50824 Mdot .74162 .43896 Mdot .14135 .12154 Mdot .95984 .40992 Mdot .11254 .17649 Mdot .06838 .3222 Mdot .03653 .29772 Mdot .47453 .10806 Mdot .17135 .22402 Mdot .22539 .18117 Mdot .29861 .21467 Mdot .10599 .18149 Mdot .12068 .15909 Mdot .14633 .10065 Mdot .26079 .39429 Mdot .21627 .19727 Mdot .10441 .16925 Mdot .31759 .13426 Mdot .82984 .13627 Mdot .09895 .27617 Mdot .29039 .52383 Mdot .12928 .12676 Mdot .08454 .33469 Mdot .78491 .37313 Mdot .1254 .09446 Mdot .02844 .12466 Mdot .13556 .11223 Mdot .13801 .164 Mdot .13614 .20915 Mdot .50463 .15065 Mdot .15698 .17183 Mdot .41569 .08992 Mdot .30494 .22025 Mdot .06362 .40659 Mdot .68753 .27716 Mdot .24749 .44981 Mdot .16755 .22369 Mdot .72295 .30417 Mdot .86584 .13972 Mdot .03225 .22506 Mdot .28861 .31283 Mdot .1287 .12166 Mdot .91854 .14433 Mdot .12537 .13703 Mdot .34904 .18073 Mdot .79674 .14382 Mdot .33741 .55444 Mdot .13485 .11191 Mdot .91813 .15408 Mdot .5268 .15675 Mdot .79076 .15151 Mdot .17394 .50168 Mdot .64519 .48756 Mdot .1198 .08751 Mdot .78503 .13124 Mdot .60318 .30595 Mdot .10975 .20867 Mdot .91478 .14896 Mdot .52183 .17973 Mdot .12383 .11851 Mdot .39524 .13583 Mdot .1179 .13025 Mdot .33101 .56066 Mdot .57875 .23188 Mdot .18028 .52737 Mdot .38555 .36408 Mdot .12591 .1328 Mdot .19564 .54875 Mdot .65636 .09783 Mdot .14312 .18058 Mdot .43747 .30977 Mdot .51108 .12812 Mdot .08928 .3056 Mdot .28395 .14272 Mdot .27438 .35131 Mdot .02623 .10491 Mdot .17472 .20112 Mdot .12799 .11578 Mdot .44654 .09543 Mdot .11333 .11499 Mdot .75105 .46628 Mdot .1209 .15292 Mdot .13145 .12216 Mdot .27767 .54687 Mdot .39564 .37356 Mdot .2575 .12635 Mdot .19795 .28564 Mdot .60138 .32062 Mdot .1687 .10486 Mdot .21394 .1552 Mdot .05464 .49912 Mdot .17577 .07977 Mdot .18907 .42776 Mdot .41381 .34346 Mdot .50823 .15232 Mdot .14833 .31952 Mdot .71141 .15812 Mdot .61658 .07396 Mdot .09922 .28372 Mdot .29596 .18289 Mdot .93534 .22178 Mdot .71948 .16211 Mdot .02668 .11649 Mdot .41954 .15531 Mdot .37943 .07902 Mdot .50849 .13463 Mdot .95399 .35528 Mdot .03276 .21463 Mdot .70764 .47211 Mdot .36707 .37361 Mdot .19844 .49288 Mdot .70633 .37938 Mdot .32158 .29577 Mdot .25201 .4188 Mdot .35841 .14103 Mdot .15757 .09694 Mdot .30138 .14844 Mdot .29049 .38852 Mdot .2474 .45892 Mdot .47115 .15481 Mdot .45822 .23647 Mdot .23334 .24877 Mdot .25069 .39797 Mdot .05028 .49627 Mdot .79399 .11593 Mdot .14193 .22721 Mdot .11257 .19535 Mdot .22889 .4183 Mdot .28389 .4893 Mdot .30166 .19882 Mdot .09752 .31209 Mdot .89898 .11442 Mdot .14921 .08359 Mdot .45326 .1063 Mdot .29037 .14982 Mdot .38082 .07678 Mdot .53685 .11061 Mdot .58759 .42495 Mdot .09056 .37839 Mdot .02978 .16632 Mdot .35706 .18422 Mdot .43106 .11135 Mdot .10997 .20137 Mdot .66591 .37847 Mdot .59463 .18076 Mdot .13091 .14789 Mdot .04227 .32467 Mdot .26522 .27144 Mdot .1474 .24451 Mdot .23784 .51224 Mdot .84806 .15024 Mdot .50998 .24524 Mdot .21437 .20769 Mdot .07998 .14015 Mdot .06944 .18845 Mdot .17322 .1885 Mdot .1473 .25729 Mdot .70677 .53147 Mdot .26598 .17931 Mdot .08635 .41723 Mdot .11094 .11693 Mdot .14 .25529 Mdot .2353 .29378 Mdot .1963 .31508 Mdot .39562 .10995 Mdot .62155 .41202 Mdot .25941 .12627 Mdot .10611 .10875 Mdot .08403 .20613 Mdot .04378 .15114 Mdot .81357 .30991 Mdot .15486 .07956 Mdot .26128 .13388 Mdot .34593 .21218 Mdot .42645 .33907 Mdot .11901 .0973 Mdot .12762 .11783 Mdot .1586 .16666 Mdot .30763 .40999 Mdot .15006 .19139 Mdot .43383 .1234 Mdot .71887 .40116 Mdot .55034 .09887 Mdot .46891 .16096 Mdot .16995 .19503 Mdot .03031 .15099 Mdot .86743 .11276 Mdot .54904 .09609 Mdot .17098 .10879 Mdot .33368 .25855 Mdot .83869 .08289 Mdot .26349 .44862 Mdot .17803 .1506 Mdot .06913 .52607 Mdot .26301 .4018 Mdot .11847 .13541 Mdot .64488 .18865 Mdot .7686 .15562 Mdot .42597 .21759 Mdot .67262 .43266 Mdot .12947 .12802 Mdot .52975 .1216 Mdot .05639 .29476 Mdot .23372 .11555 Mdot .38063 .13366 Mdot .331 .19602 Mdot .0267 .0996 Mdot .15947 .11131 Mdot .116 .16289 Mdot .31228 .53084 Mdot .0548 .54662 Mdot .78923 .28363 Mdot .15984 .17567 Mdot .24033 .20169 Mdot .57307 .07859 Mdot .15499 .36914 Mdot .11168 .15423 Mdot .54721 .13929 Mdot .23068 .28936 Mdot .31167 .12298 Mdot .86948 .08876 Mdot .15048 .18937 Mdot .10196 .07818 Mdot .17897 .33653 Mdot .48963 .19666 Mdot .27706 .53252 Mdot .10045 .25768 Mdot .38849 .41165 Mdot .1103 .19744 Mdot .02847 .15441 Mdot .1838 .43002 Mdot .20059 .19529 Mdot .30935 .2214 Mdot .50778 .15312 Mdot .11435 .17408 Mdot .54533 .1645 Mdot .63339 .08508 Mdot .86189 .14557 Mdot .43143 .12878 Mdot .58201 .3878 Mdot .07609 .52899 Mdot .14395 .11937 Mdot .67277 .50038 Mdot .15342 .35442 Mdot .22455 .22014 Mdot .25095 .47725 Mdot .16334 .31793 Mdot .46673 .11753 Mdot .47417 .22193 Mdot .60558 .41827 Mdot .20433 .09189 Mdot .13953 .25065 Mdot .85965 .09651 Mdot .27048 .4418 Mdot .42441 .07717 Mdot .07159 .55746 Mdot .04493 .41579 Mdot .18654 .54427 Mdot .19241 .15738 Mdot .13602 .14496 Mdot .06483 .55808 Mdot .12395 .08009 Mdot .11239 .09514 Mdot .15463 .27944 Mdot .16616 .11117 Mdot .66661 .26717 Mdot .26649 .54921 Mdot .05459 .34839 Mdot .15723 .29751 Mdot .44769 .29225 Mdot .83856 .16796 Mdot .22999 .12789 Mdot .19731 .16329 Mdot .10763 .23455 Mdot .55152 .09453 Mdot .27982 .20962 Mdot .4212 .07493 Mdot .07531 .11946 Mdot .12673 .09993 Mdot .04248 .14352 Mdot .1046 .20523 Mdot .12102 .08672 Mdot .17151 .09401 Mdot .80941 .2768 Mdot .22014 .39787 Mdot .02632 .11467 Mdot .15477 .26669 Mdot .24725 .17199 Mdot .09842 .30539 Mdot .33197 .10937 Mdot .89367 .11073 Mdot .14147 .20611 Mdot .14787 .29542 Mdot .16329 .42411 Mdot .60543 .27732 Mdot .11249 .14869 Mdot .12945 .12882 Mdot .66713 .09698 Mdot .91277 .13042 Mdot .07977 .36774 Mdot .12832 .11885 Mdot .10619 .23535 Mdot .10189 .27288 Mdot .6229 .52243 Mdot .2691 .12925 Mdot .21828 .40118 Mdot .05066 .39751 Mdot .69863 .18395 Mdot .2658 .27239 Mdot .28755 .31747 Mdot .15262 .10481 Mdot .13368 .17883 Mdot .28711 .17278 Mdot .2555 .50147 Mdot .53361 .11394 Mdot .79837 .34902 Mdot .08209 .13409 Mdot .21399 .17701 Mdot .04277 .13054 Mdot .40891 .21686 Mdot .10125 .2311 Mdot .05715 .55063 Mdot .25488 .25929 Mdot .33392 .27664 Mdot .09544 .0804 Mdot .8563 .17992 Mdot .07619 .52811 Mdot .60054 .10042 Mdot .15509 .07707 Mdot .16351 .25219 Mdot .22095 .36771 Mdot .58939 .09162 Mdot .40896 .12763 Mdot .11251 .09342 Mdot .9238 .16567 Mdot .34416 .31206 Mdot .22669 .42986 Mdot .26717 .45924 Mdot .04243 .27791 Mdot .15888 .13924 Mdot .08917 .20227 Mdot .05038 .45624 Mdot .18694 .51426 Mdot .13905 .22234 Mdot .47166 .1649 Mdot .10242 .15576 Mdot .30409 .16191 Mdot .46257 .09846 Mdot .87219 .07275 Mdot .88363 .07638 Mdot .0459 .20188 Mdot .27695 .37561 Mdot .75646 .13513 Mdot .68688 .5579 Mdot .10993 .12339 Mdot .31479 .18856 Mdot .5861 .43707 Mdot .23029 .12192 Mdot .32846 .12326 Mdot .2978 .32683 Mdot .50909 .1482 Mdot .15306 .33177 Mdot .15449 .37908 Mdot .67692 .55695 Mdot .36715 .23402 Mdot .68163 .56725 Mdot .76735 .41816 Mdot .51884 .1345 Mdot .30993 .56224 Mdot .08518 .43964 Mdot .11988 .15093 Mdot .23829 .49011 Mdot .1143 .16116 Mdot .04949 .47089 Mdot .16103 .09754 Mdot .07658 .38095 Mdot .30313 .35431 Mdot .37736 .36612 Mdot .10886 .22689 Mdot .48647 .11778 Mdot .18989 .15761 Mdot .14018 .09896 Mdot .16006 .07548 Mdot .2103 .22766 Mdot .95171 .33537 Mdot .35332 .19612 Mdot .22813 .13155 Mdot .15156 .11013 Mdot .11026 .1183 Mdot .11016 .08741 Mdot .21001 .12447 Mdot .10315 .23932 Mdot .97105 .53568 Mdot .80213 .28251 Mdot .17473 .07982 Mdot .06715 .22052 Mdot .22144 .18724 Mdot .4919 .12176 Mdot .10548 .24806 Mdot .25858 .23862 Mdot .31019 .23286 Mdot .2303 .20953 Mdot .77302 .19754 Mdot .21015 .57521 Mdot .8173 .14705 Mdot .10491 .25416 Mdot .12626 .09442 Mdot .27996 .13825 Mdot .78259 .2285 Mdot .38702 .1482 Mdot .13829 .13261 Mdot .355 .09167 Mdot .23139 .39255 Mdot .03373 .2279 Mdot .31996 .14076 Mdot .28225 .24151 Mdot .25526 .13378 Mdot .24218 .48894 Mdot .06499 .50465 Mdot .55231 .10085 Mdot .29563 .37632 Mdot .11484 .16497 Mdot .4559 .10738 Mdot .62348 .39279 Mdot .17907 .3436 Mdot .19142 .4768 Mdot .55961 .37086 Mdot .37915 .10593 Mdot .82798 .09542 Mdot .77538 .12275 Mdot .16241 .07271 Mdot .66872 .54044 Mdot .51532 .1642 Mdot .08625 .26156 Mdot .14905 .18898 Mdot .27472 .36689 Mdot .32467 .12498 Mdot .61243 .50324 Mdot .035 .15114 Mdot .53446 .12055 Mdot .09426 .33837 Mdot .24777 .50745 Mdot .31269 .23569 Mdot .31844 .57255 Mdot .8505 .14564 Mdot .15552 .2351 Mdot .40922 .29652 Mdot .34472 .10245 Mdot .22389 .23207 Mdot .31742 .19255 Mdot .53921 .25365 Mdot .72917 .22104 Mdot .48727 .13129 Mdot .12589 .13188 Mdot .79852 .34844 Mdot .13307 .12509 Mdot .48504 .14611 Mdot .79861 .11908 Mdot .81111 .1751 Mdot .59036 .11823 Mdot .35439 .20579 Mdot .11099 .21337 Mdot .51317 .18497 Mdot .4127 .11805 Mdot .83407 .08613 Mdot .11552 .17033 Mdot .49138 .13335 Mdot .33013 .15982 Mdot .14163 .26743 Mdot .69134 .56354 Mdot .10677 .21175 Mdot .43312 .11663 Mdot .44299 .28495 Mdot .11565 .08369 Mdot .24958 .19098 Mdot .11128 .21084 Mdot .41243 .25121 Mdot .97105 .53569 Mdot .19821 .20298 Mdot .31439 .11682 Mdot .48652 .1877 Mdot .11518 .13821 Mdot .16592 .18025 Mdot .13066 .12609 Mdot .29866 .12714 Mdot .3504 .14452 Mdot .13359 .18164 Mdot .80218 .12836 Mdot .62154 .07749 Mdot .79028 .22285 Mdot .74253 .34931 Mdot .09412 .33513 Mdot .27296 .48309 Mdot .64458 .09543 Mdot .12783 .13322 Mdot .24681 .48291 Mdot .29524 .3431 Mdot .19592 .33212 Mdot .58091 .08655 Mdot .44045 .23875 Mdot .96798 .4983 Mdot .68343 .51963 Mdot .71973 .19303 Mdot .10078 .20205 Mdot .09415 .34473 Mdot .22129 .17769 Mdot .96274 .43959 Mdot .102 .16437 Mdot .21503 .2188 Mdot .84239 .09777 Mdot .37492 .1652 Mdot .54569 .32669 Mdot .31929 .29546 Mdot .19178 .17728 Mdot .24429 .50785 Mdot .13518 .14359 Mdot .03688 .23077 Mdot .80289 .12935 Mdot .03891 .33157 Mdot .04759 .13961 Mdot .79275 .12406 Mdot .06499 .43565 Mdot .70225 .24206 Mdot .1115 .11618 Mdot .11948 .10158 Mdot .56507 .1678 Mdot .39426 .14011 Mdot .6809 .4181 Mdot .38004 .08113 Mdot .36972 .09883 Mdot .14378 .26666 Mdot .14754 .28626 Mdot .11394 .19532 Mdot .7409 .52006 Mdot .19614 .5709 Mdot .19105 .22558 Mdot .15053 .0913 Mdot .0718 .08625 Mdot .77479 .41285 Mdot .13201 .13299 Mdot .11875 .12092 Mdot .553 .2042 Mdot .12473 .08629 Mdot .36193 .15549 Mdot .20561 .39569 Mdot .20541 .27647 Mdot .26803 .45228 Mdot .1414 .13472 Mdot .4855 .1915 Mdot .15806 .20962 Mdot .3876 .12602 Mdot .97199 .5475 Mdot .19451 .32078 Mdot .53416 .22022 Mdot .37587 .13941 Mdot .80159 .31135 Mdot .03586 .25073 Mdot .13189 .13174 Mdot .5029 .21436 Mdot .30211 .12642 Mdot .22584 .19207 Mdot .50871 .14016 Mdot .04634 .41974 Mdot .5171 .13707 Mdot .79163 .37496 Mdot .92367 .16977 Mdot .14205 .11337 Mdot .93216 .21065 Mdot .7924 .26524 Mdot .0839 .45428 Mdot .71785 .12261 Mdot .18658 .07771 Mdot .09355 .12055 Mdot .36675 .16793 Mdot .87407 .07696 Mdot .16422 .16986 Mdot .52079 .17074 Mdot .25547 .12597 Mdot .0542 .52901 Mdot .15184 .11266 Mdot .05841 .4044 Mdot .38791 .0874 Mdot .08429 .28665 Mdot .88434 .09467 Mdot .69654 .15599 Mdot .17142 .32571 Mdot .4005 .3438 Mdot .37962 .2843 Mdot .06694 .45304 Mdot .08721 .0787 Mdot .07792 .51625 Mdot .65724 .20218 Mdot .94266 .26908 Mdot .22228 .37364 Mdot .05661 .55943 Mdot .28655 .23232 Mdot .3136 .22111 Mdot .02448 .08235 Mdot .95453 .35958 Mdot .14758 .28087 Mdot .05034 .49073 Mdot .52025 .12613 Mdot .70406 .53278 Mdot .19711 .41374 Mdot .61131 .17344 Mdot .11832 .16598 Mdot .3544 .13388 Mdot .87159 .1474 Mdot .80526 .10656 Mdot .0782 .18905 Mdot .82675 .21854 Mdot .56625 .18862 Mdot .14187 .15951 Mdot .89058 .11299 Mdot .13395 .12939 Mdot .10062 .26998 Mdot .27785 .25267 Mdot .09943 .29662 Mdot .11209 .11653 Mdot .12659 .09923 Mdot .19866 .39243 Mdot .27205 .34145 Mdot .13079 .12828 Mdot .18853 .08261 Mdot .97257 .55492 Mdot .11199 .11201 Mdot .12243 .14105 Mdot .37744 .15466 Mdot .16031 .17772 Mdot .52815 .12127 Mdot .23045 .53258 Mdot .35305 .52888 Mdot .05002 .35063 Mdot .21041 .4162 Mdot .21563 .36038 Mdot .20221 .1259 Mdot .18789 .25764 Mdot .16219 .44376 Mdot .24825 .51325 Mdot .86067 .16552 Mdot .44803 .1017 Mdot .26299 .1966 Mdot .06809 .18541 Mdot .46635 .11951 Mdot .07289 .35825 Mdot .46691 .11197 Mdot .08867 .14538 Mdot .1635 .07692 Mdot .43944 .10356 Mdot .11667 .10321 Mdot .09828 .07412 Mdot .09136 .20187 Mdot .24297 .51062 Mdot .13482 .13449 Mdot .57364 .35389 Mdot .2719 .15047 Mdot .40616 .12933 Mdot .91557 .15184 Mdot .30847 .39997 Mdot .15027 .30739 Mdot .21291 .27433 Mdot .25627 .27847 Mdot .75971 .1278 Mdot .27436 .17959 Mdot .11355 .15402 Mdot .26246 .48659 Mdot .58391 .21211 Mdot .46317 .10108 Mdot .07701 .4972 Mdot .68159 .24335 Mdot .65771 .34585 Mdot .08329 .07499 Mdot .71327 .55347 Mdot .11228 .19804 Mdot .5684 .14526 Mdot .61243 .08869 Mdot .29273 .57922 Mdot .148 .1088 Mdot .54399 .20021 Mdot .31063 .57323 Mdot .29968 .30444 Mdot .53867 .29903 Mdot .76283 .12961 Mdot .15425 .15435 Mdot .31868 .11686 Mdot .55801 .09031 Mdot .03915 .29888 Mdot .52265 .1267 Mdot .09588 .31627 Mdot .63594 .32858 Mdot .14712 .08901 Mdot .815 .27164 Mdot .09965 .29483 Mdot .2166 .5788 Mdot .14197 .23745 Mdot .53808 .14934 Mdot .0945 .32549 Mdot .13627 .18711 Mdot .6252 .28187 Mdot .39285 .08295 Mdot .15141 .09433 Mdot .21323 .20333 Mdot .39816 .10607 Mdot .18613 .54766 Mdot .62758 .31866 Mdot .07 .54979 Mdot .17761 .07915 Mdot .42335 .12522 Mdot .57187 .14287 Mdot .13349 .11522 Mdot .21512 .18165 Mdot .59513 .08934 Mdot .27519 .25446 Mdot .0978 .27566 Mdot .89973 .11828 Mdot .1528 .35772 Mdot .69319 .21601 Mdot .24804 .38062 Mdot .46416 .1235 Mdot .35959 .13938 Mdot .53629 .21939 Mdot .31305 .32315 Mdot .0379 .13639 Mdot .84583 .20077 Mdot .49774 .201 Mdot .23402 .11543 Mdot .73141 .37021 Mdot .04457 .28109 Mdot .66043 .36874 Mdot .66423 .55855 Mdot .17778 .22611 Mdot .15495 .13771 Mdot .06378 .57979 Mdot .66466 .20086 Mdot .90598 .13515 Mdot .50341 .19143 Mdot .33979 .1946 Mdot .59697 .07318 Mdot .08228 .4724 Mdot .14132 .26831 Mdot .2699 .45497 Mdot .08155 .3221 Mdot .90857 .13867 Mdot .4399 .08441 Mdot .12005 .14334 Mdot .29783 .4279 Mdot .12864 .11848 Mdot .04374 .16593 Mdot .68089 .1371 Mdot .14259 .28171 Mdot .22163 .3277 Mdot .97449 .58021 Mdot .6216 .27884 Mdot .08339 .30907 Mdot .82304 .10373 Mdot .10904 .18663 Mdot .04005 .22067 Mdot .27452 .44002 Mdot .53985 .11395 Mdot .3078 .2614 Mdot .49501 .1432 Mdot .06399 .43559 Mdot .87263 .07187 Mdot .06257 .4417 Mdot .47828 .16106 Mdot .81967 .235 Mdot .16219 .20733 Mdot .06508 .09847 Mdot .61351 .28961 Mdot .32235 .1269 Mdot .89723 .10007 Mdot .33763 .154 Mdot .2585 .4921 Mdot .25149 .14657 Mdot .54431 .10603 Mdot .20802 .33372 Mdot .65175 .15833 Mdot .03902 .14868 Mdot .08726 .39016 Mdot .81796 .25146 Mdot .33474 .16399 Mdot .13427 .13796 Mdot .27144 .54104 Mdot .4337 .12779 Mdot .29271 .3886 Mdot .38139 .15113 Mdot .77125 .1898 Mdot .13075 .13098 Mdot .3051 .31148 Mdot .08088 .43147 Mdot .75135 .38957 Mdot .29011 .40038 Mdot .40336 .07628 Mdot .23751 .38963 Mdot .10715 .08612 Mdot .15012 .0865 Mdot .28741 .19343 Mdot .38701 .43235 Mdot .70428 .34221 Mdot .0922 .35039 Mdot .73562 .17267 Mdot .95424 .35748 Mdot .92438 .17499 Mdot .31881 .57113 Mdot .22858 .14449 Mdot .20253 .33225 Mdot .37736 .4745 Mdot .15837 .35645 Mdot .20982 .30838 Mdot .04327 .32956 Mdot .65946 .56704 Mdot .61453 .22543 Mdot .24303 .22152 Mdot .52881 .11985 Mdot .17658 .51671 Mdot .12836 .12054 Mdot .15562 .08784 Mdot .84452 .21133 Mdot .84986 .17915 Mdot .11261 .10288 Mdot .14693 .20348 Mdot .50269 .13089 Mdot .29417 .19747 Mdot .07966 .45383 Mdot .86009 .10278 Mdot .18444 .08845 Mdot .11285 .20071 Mdot .37666 .12355 Mdot .67284 .46203 Mdot .15225 .19359 Mdot .45874 .09571 Mdot .25144 .50701 Mdot .08714 .40757 Mdot .05548 .13469 Mdot .21281 .41639 Mdot .14895 .1467 Mdot .05178 .23171 Mdot .41667 .31805 Mdot .57655 .08923 Mdot .12985 .13155 Mdot .17957 .08335 Mdot .36724 .16794 Mdot .25958 .51666 Mdot .10334 .19966 Mdot .2707 .3526 Mdot .73404 .51453 Mdot .2313 .52373 Mdot .08616 .24257 Mdot .51077 .13461 Mdot .10692 .22604 Mdot .66073 .15882 Mdot .11349 .1367 Mdot .16154 .39859 Mdot .63904 .18878 Mdot .47136 .23299 Mdot .33298 .17733 Mdot .11783 .11034 Mdot .09695 .11974 Mdot .75626 .15289 Mdot .90553 .13104 Mdot .5832 .20942 Mdot .05757 .52058 Mdot .43782 .31789 Mdot .49798 .12817 Mdot .03867 .3452 Mdot .57005 .32453 Mdot .50559 .12795 Mdot .05374 .14444 Mdot .16946 .14702 Mdot .11038 .13899 Mdot .04581 .26654 Mdot .20164 .16673 Mdot .16623 .23395 Mdot .47673 .18517 Mdot .24372 .12916 Mdot .03149 .16448 Mdot .14497 .0987 Mdot .20049 .15443 Mdot .31113 .16669 Mdot .09168 .35918 Mdot .14241 .27467 Mdot .11086 .20149 Mdot .3224 .57023 Mdot .32609 .50851 Mdot .26346 .26204 Mdot .02825 .14797 Mdot .1269 .1 Mdot .02497 .08539 Mdot .28507 .41544 Mdot .71489 .50741 Mdot .41638 .12439 Mdot .15781 .29379 Mdot .06732 .24652 Mdot .19622 .09002 Mdot .19759 .31087 Mdot .07535 .07963 Mdot .02999 .13832 Mdot .90017 .11808 Mdot .60971 .10458 Mdot .05379 .14603 Mdot .63636 .13329 Mdot .1208 .08251 Mdot .11444 .09065 Mdot .92068 .16237 Mdot .09957 .15267 Mdot .24108 .43787 Mdot .56698 .08893 Mdot .51899 .13825 Mdot .12855 .12057 Mdot .30289 .18176 Mdot .29832 .13528 Mdot .34937 .14925 Mdot .04051 .35615 Mdot .7473 .41185 Mdot .17 .17215 Mdot .90547 .12824 Mdot .12947 .12912 Mdot .19207 .11303 Mdot .36098 .41311 Mdot .81205 .28891 Mdot .29861 .22479 Mdot .66988 .45004 Mdot .15204 .09541 Mdot .24758 .18653 Mdot .8262 .10944 Mdot .36011 .15725 Mdot .09351 .27351 Mdot .33947 .52032 Mdot .17026 .11019 Mdot .2024 .22647 Mdot .10224 .16964 Mdot .40245 .12409 Mdot .52801 .1531 Mdot .133 .13767 Mdot .1825 .39439 Mdot .0873 .41501 Mdot .09729 .30665 Mdot .14737 .21105 Mdot .94912 .31525 Mdot .05037 .17283 Mdot .15881 .21428 Mdot .56559 .08251 Mdot .65053 .54555 Mdot .81401 .23714 Mdot .13319 .1508 Mdot .1085 .18608 Mdot .15072 .12312 Mdot .44576 .09288 Mdot .26697 .41898 Mdot .10555 .24906 Mdot .2132 .17918 Mdot .56627 .23125 Mdot .50009 .16059 Mdot .13877 .16152 Mdot .27151 .20899 Mdot .20055 .33385 Mdot .22386 .32842 Mdot .8232 .09379 Mdot .02777 .12567 Mdot .19668 .51481 Mdot .28412 .15161 Mdot .12917 .12748 Mdot .12755 .10687 Mdot .19088 .14616 Mdot .47129 .13435 Mdot .6367 .41386 Mdot .89557 .10269 Mdot .07084 .41841 Mdot .15564 .12665 Mdot .13883 .20571 Mdot .69349 .57087 Mdot .16673 .17041 Mdot .12804 .13112 Mdot .3355 .19129 Mdot .10419 .25448 Mdot .10248 .21124 Mdot .21151 .25849 Mdot .55228 .09311 Mdot .31025 .37188 Mdot .12602 .13989 Mdot .87169 .08477 Mdot .25347 .23703 Mdot .64083 .09936 Mdot .1962 .50869 Mdot .04572 .44099 Mdot .03801 .31073 Mdot .90607 .12758 Mdot .67742 .53807 Mdot .39032 .10406 Mdot .88804 .09015 Mdot .12644 .1206 Mdot .2914 .16162 Mdot .03 .16562 Mdot .07705 .08881 Mdot .18716 .33211 Mdot .44186 .08424 Mdot .15688 .15253 Mdot .24546 .13871 Mdot .10707 .17152 Mdot .02759 .10305 Mdot .47613 .15027 Mdot .0762 .40466 Mdot .08224 .42751 Mdot .21777 .42568 Mdot .07416 .08862 Mdot .29901 .27986 Mdot .54599 .24113 Mdot .24997 .1294 Mdot .23602 .40061 Mdot .18296 .25359 Mdot .78568 .15323 Mdot .11456 .19288 Mdot .83171 .24962 Mdot .5382 .16806 Mdot .206 .43302 Mdot .07075 .13221 Mdot .25991 .1396 Mdot .23192 .22194 Mdot .21839 .4577 Mdot .0826 .4557 Mdot .05074 .50614 Mdot .36061 .23913 Mdot .21303 .1977 Mdot .1428 .15593 Mdot .05089 .11695 Mdot .18204 .52968 Mdot .17115 .07166 Mdot .40306 .10675 Mdot .63331 .33127 Mdot .34487 .15753 Mdot .23714 .48291 Mdot .12838 .12259 Mdot .16156 .30787 Mdot .30156 .16681 Mdot .12672 .13426 Mdot .83055 .17694 Mdot .80926 .10933 Mdot .14521 .24439 Mdot .32081 .49112 Mdot .13797 .15215 Mdot .16726 .39218 Mdot .11613 .17608 Mdot .31098 .19091 Mdot .89726 .09221 Mdot .55801 .22384 Mdot .52956 .28699 Mdot .21031 .17167 Mdot .54787 .09828 Mdot .11826 .1016 Mdot .03087 .17114 Mdot .88108 .10895 Mdot .85863 .12684 Mdot .36179 .18672 Mdot .1563 .21124 Mdot .54883 .20135 Mdot .23323 .1619 Mdot .81506 .30377 Mdot .17346 .4121 Mdot .05902 .38809 Mdot .0685 .1579 Mdot .1401 .14861 Mdot .07135 .56146 Mdot .06596 .50507 Mdot .02812 .10691 Mdot .32756 .22415 Mdot .84143 .08408 Mdot .02402 .07503 Mdot .54702 .19366 Mdot .10594 .20826 Mdot .09746 .08237 Mdot .95268 .34405 Mdot .96674 .48383 Mdot .10375 .25808 Mdot .05853 .52445 Mdot .39675 .15927 Mdot .08745 .07872 Mdot .36838 .34171 Mdot .06548 .57694 Mdot .49145 .13714 Mdot .10524 .22454 Mdot .10425 .22379 Mdot .24423 .29555 Mdot .10251 .25797 Mdot .28051 .36996 Mdot .50669 .13085 Mdot .61444 .28721 Mdot .46563 .20778 Mdot .14065 .14796 Mdot .39121 .44451 Mdot .2455 .17006 Mdot .32482 .29124 Mdot .76765 .32509 Mdot .40262 .07762 Mdot .11836 .08429 Mdot .15887 .40618 Mdot .78008 .2623 Mdot .36562 .28767 Mdot .24172 .4697 Mdot .91243 .12648 Mdot .94968 .31889 Mdot .62225 .08524 Mdot .23094 .19325 Mdot .13063 .14354 Mdot .63817 .11337 Mdot .20812 .22682 Mdot .38214 .07665 Mdot .53492 .12334 Mdot .78492 .38077 Mdot .25526 .33163 Mdot .56589 .29953 Mdot .10485 .13211 Mdot .70595 .51263 Mdot .60417 .1205 Mdot .15986 .29741 Mdot .36522 .22369 Mdot .25594 .34124 Mdot .06909 .56899 Mdot .03128 .14474 Mdot .27331 .13195 Mdot .08395 .1682 Mdot .95684 .38075 Mdot .16976 .19897 Mdot .08517 .07239 Mdot .42338 .12631 Mdot .06972 .50214 Mdot .8124 .13386 Mdot .12659 .11026 Mdot .58639 .43257 Mdot .62677 .10658 Mdot .20798 .10382 Mdot .15015 .355 Mdot .36831 .28751 Mdot .15218 .27875 Mdot .24332 .42971 Mdot .37164 .17096 Mdot .911 .12152 Mdot .5055 .13265 Mdot .59718 .10348 Mdot .37592 .477 Mdot .87862 .09797 Mdot .12246 .10767 Mdot .1406 .21761 Mdot .9277 .1867 Mdot .06535 .56494 Mdot .17876 .45903 Mdot .69843 .37352 Mdot .26555 .14819 Mdot .86983 .15042 Mdot .62525 .51385 Mdot .78233 .40777 Mdot .07645 .52551 Mdot .76153 .168 Mdot .61089 .15966 Mdot .18896 .07874 Mdot .42318 .33718 Mdot .08665 .08534 Mdot .04189 .40151 Mdot .12792 .12597 Mdot .39999 .088 Mdot .20576 .53092 Mdot .86845 .12645 Mdot .15667 .36175 Mdot .17513 .23145 Mdot .38276 .08576 Mdot .08338 .27913 Mdot .05545 .49912 Mdot .39096 .13118 Mdot .03036 .11539 Mdot .17273 .34535 Mdot .54532 .13192 Mdot .40568 .30614 Mdot .11553 .14182 Mdot .44636 .09601 Mdot .39669 .09252 Mdot .17911 .1238 Mdot .10466 .07973 Mdot .79988 .11306 Mdot .14544 .10785 Mdot .69578 .25537 Mdot .25439 .39308 Mdot .45018 .11645 Mdot .54625 .291 Mdot .96246 .4366 Mdot .06652 .37327 Mdot .37004 .08391 Mdot .49591 .16408 Mdot .17569 .38731 Mdot .25993 .31945 Mdot .43035 .08945 Mdot .10249 .22639 Mdot .10667 .19126 Mdot .79319 .23828 Mdot .11224 .141 Mdot .47763 .14239 Mdot .16982 .15739 Mdot .11195 .11006 Mdot .39448 .42738 Mdot .51738 .2187 Mdot .5846 .35339 Mdot .07396 .49599 Mdot .10333 .25428 Mdot .4746 .1078 Mdot .90672 .10999 Mdot .23786 .38598 Mdot .18834 .29402 Mdot .2738 .23775 Mdot .12585 .10896 Mdot .30414 .45143 Mdot .59264 .08466 Mdot .04268 .19533 Mdot .75179 .28536 Mdot .04219 .12728 Mdot .19056 .09269 Mdot .26489 .46556 Mdot .08685 .41663 Mdot .29987 .26502 Mdot .21996 .27622 Mdot .26036 .36874 Mdot .81913 .29152 Mdot .71061 .56268 Mdot .85368 .18126 Mdot .09006 .18664 Mdot .69726 .54689 Mdot .73394 .50685 Mdot .44786 .08695 Mdot .39079 .44503 Mdot .53136 .13529 Mdot .20122 .09219 Mdot .11543 .18743 Mdot .14472 .18 Mdot .27104 .44698 Mdot .2513 .23803 Mdot .12925 .12627 Mdot .17816 .31659 Mdot .08284 .18864 Mdot .05207 .47323 Mdot .59192 .43546 Mdot .15759 .3255 Mdot .11264 .18319 Mdot .31473 .26117 Mdot .82376 .24198 Mdot .22311 .19857 Mdot .6092 .49022 Mdot .68108 .49752 Mdot .46363 .15234 Mdot .59853 .14982 Mdot .27973 .43882 Mdot .22644 .12352 Mdot .68407 .3534 Mdot .03823 .32019 Mdot .07889 .50096 Mdot .40909 .11836 Mdot .16254 .41905 Mdot .09045 .07202 Mdot .06234 .21693 Mdot .10213 .09753 Mdot .20091 .50934 Mdot .19613 .10615 Mdot .082 .44289 Mdot .20776 .2844 Mdot .12934 .12751 Mdot .75666 .15469 Mdot .18664 .25989 Mdot .12056 .15996 Mdot .15119 .08207 Mdot .86232 .14346 Mdot .50991 .12802 Mdot .30182 .25073 Mdot .26671 .19272 Mdot .56597 .16167 Mdot .64013 .12195 Mdot .3754 .11382 Mdot .39691 .34653 Mdot .641 .31217 Mdot .08255 .46994 Mdot .10726 .15332 Mdot .12555 .09644 Mdot .05794 .34984 Mdot .31806 .35443 Mdot .16238 .09361 Mdot .10144 .07706 Mdot .13547 .14508 Mdot .13491 .1168 Mdot .29399 .38307 Mdot .09636 .12195 Mdot .75008 .45716 Mdot .17175 .12121 Mdot .20622 .38098 Mdot .74934 .43594 Mdot .65097 .38832 Mdot .17831 .51696 Mdot .54312 .30903 Mdot .40998 .08196 Mdot .61279 .49865 Mdot .07535 .52527 Mdot .75269 .47589 Mdot .15449 .07846 Mdot .43261 .27846 Mdot .49581 .14069 Mdot .08019 .47914 Mdot .14519 .14819 Mdot .44183 .20265 Mdot .1345 .13498 Mdot .07372 .52132 Mdot .4739 .20811 Mdot .08727 .41635 Mdot .19934 .25027 Mdot .29724 .48669 Mdot .69011 .34318 Mdot .3502 .15553 Mdot .10998 .11692 Mdot .13101 .12715 Mdot .38694 .14873 Mdot .33856 .10706 Mdot .78571 .11905 Mdot .47468 .13816 Mdot .59719 .46997 Mdot .09563 .13498 Mdot .38193 .42189 Mdot .09754 .29115 Mdot .66001 .5498 Mdot .16997 .48471 Mdot .13211 .16064 Mdot .7384 .20744 Mdot .09725 .23485 Mdot .14076 .15159 Mdot .22273 .20566 Mdot .40728 .09017 Mdot .72193 .37033 Mdot .12845 .1162 Mdot .11831 .14283 Mdot .14196 .09825 Mdot .0357 .16922 Mdot .81528 .12691 Mdot .50578 .15608 Mdot .36603 .32315 Mdot .31785 .25726 Mdot .34948 .09448 Mdot .48344 .14188 Mdot .20283 .57798 Mdot .32273 .18486 Mdot .12382 .11076 Mdot .0896 .08111 Mdot .83054 .09046 Mdot .78221 .15488 Mdot .56018 .35921 Mdot .87245 .10895 Mdot .11705 .1593 Mdot .50439 .15235 Mdot .6178 .42787 Mdot .23114 .38702 Mdot .36617 .45773 Mdot .11543 .17924 Mdot .53951 .16002 Mdot .81701 .27904 Mdot .21472 .18041 Mdot .71299 .43457 Mdot .03483 .12567 Mdot .89519 .09934 Mdot .71985 .55133 Mdot .55675 .26728 Mdot .32586 .40107 Mdot .04017 .1289 Mdot .14357 .18642 Mdot .57476 .175 Mdot .39451 .13804 Mdot .25707 .53846 Mdot .79876 .30643 Mdot .15352 .31822 Mdot .2066 .22245 Mdot .13976 .25357 Mdot .14165 .26981 Mdot .0489 .18989 Mdot .05501 .53915 Mdot .89118 .10711 Mdot .81335 .30322 Mdot .39413 .40405 Mdot .19424 .14475 Mdot .05755 .4769 Mdot .15277 .0937 Mdot .28743 .43881 Mdot .45119 .20735 Mdot .05552 .49971 Mdot .05116 .18127 Mdot .85172 .11166 Mdot .74845 .15683 Mdot .76723 .44655 Mdot .94051 .25349 Mdot .30217 .35009 Mdot .15351 .10963 Mdot .39303 .22841 Mdot .14609 .26639 Mdot .04611 .41815 Mdot .51852 .13539 Mdot .79359 .33026 Mdot .5674 .11473 Mdot .48083 .11421 Mdot .91556 .15084 Mdot .16462 .24371 Mdot .96888 .50896 Mdot .12051 .12767 Mdot .14113 .09692 Mdot .38593 .30114 Mdot .10202 .21934 Mdot .21117 .47113 Mdot .3003 .24447 Mdot .54719 .21347 Mdot .12896 .12729 Mdot .86215 .10265 Mdot .13012 .13768 Mdot .07126 .46093 Mdot .1301 .13707 Mdot .91141 .12205 Mdot .32835 .27358 Mdot .49829 .14667 Mdot .22361 .45795 Mdot .06015 .11598 Mdot .9211 .15372 Mdot .24656 .5175 Mdot .18809 .0848 Mdot .29373 .15693 Mdot .74882 .30202 Mdot .25617 .14925 Mdot .19206 .08063 Mdot .46023 .09584 Mdot .14825 .33035 Mdot .10288 .20957 Mdot .45482 .17177 Mdot .48706 .18268 Mdot .31465 .13619 Mdot .14769 .3036 Mdot .13193 .1602 Mdot .82747 .14294 Mdot .10058 .25446 Mdot .17808 .20439 Mdot .68796 .2258 Mdot .06463 .38774 Mdot .36269 .28941 Mdot .62859 .51035 Mdot .40298 .10092 Mdot .08542 .32902 Mdot .09462 .30246 Mdot .8146 .10131 Mdot .28571 .37532 Mdot .86091 .07559 Mdot .35922 .51697 Mdot .04503 .37509 Mdot .04446 .27563 Mdot .03203 .13385 Mdot .16172 .1091 Mdot .24422 .25416 Mdot .08509 .36157 Mdot .12268 .07623 Mdot .116 .08301 Mdot .20679 .12936 Mdot .76512 .13694 Mdot .10368 .09548 Mdot .15105 .11777 Mdot .8608 .16447 Mdot .19001 .24922 Mdot .0525 .16309 Mdot .11634 .10223 Mdot .14081 .0974 Mdot .56938 .10776 Mdot .7025 .55935 Mdot .36747 .49561 Mdot .17921 .08862 Mdot .06608 .11973 Mdot .27442 .41657 Mdot .6828 .28836 Mdot .14272 .09397 Mdot .22556 .19437 Mdot .06597 .37984 Mdot .5409 .14061 Mdot .33403 .13948 Mdot .604 .19318 Mdot .12391 .09851 Mdot .89132 .12204 Mdot .15624 .13256 Mdot .02567 .0956 Mdot .13077 .14489 Mdot .1393 .14524 Mdot .31983 .22386 Mdot .67184 .32156 Mdot .6931 .5227 Mdot .57294 .35832 Mdot .08133 .07667 Mdot .11663 .15695 Mdot .42458 .12903 Mdot .21293 .53908 Mdot .8241 .27488 Mdot .41274 .07442 Mdot .10183 .27416 Mdot .80392 .3293 Mdot .2341 .26771 Mdot .93995 .24975 Mdot .11174 .20034 Mdot .5618 .11598 Mdot .27298 .341 Mdot .25244 .52332 Mdot .61514 .21916 Mdot .6104 .41332 Mdot .44376 .08599 Mdot .92608 .1752 Mdot .10237 .15087 Mdot .92244 .16596 Mdot .32962 .20445 Mdot .93629 .23125 Mdot .5 g .01 w [ .15 .07 ] 0 setdash .97619 .60332 m .97615 .60273 L .97611 .60214 L .97609 .60195 L .97606 .60155 L .97602 .60096 L .97598 .60037 L .97593 .59978 L .97589 .59919 L .97585 .59861 L .97581 .59802 L .97576 .59743 L .97572 .59684 L .97568 .59625 L .97563 .59566 L .97559 .59507 L .97555 .59448 L .9755 .59389 L .97546 .5933 L .97542 .59271 L .97537 .59212 L .97533 .59154 L .97529 .59095 L .97524 .59036 L .9752 .58977 L .97516 .58918 L .97511 .58859 L .97507 .588 L .97503 .58741 L .97499 .58694 L .97498 .58682 L .97494 .58623 L .9749 .58564 L .97485 .58505 L .97481 .58446 L .97476 .58388 L .97472 .58329 L .97468 .5827 L .97463 .58211 L .97459 .58152 L .97455 .58093 L .9745 .58034 L .97446 .57975 L .97441 .57916 L .97437 .57857 L .97432 .57798 L .97428 .57739 L .97424 .57681 L .97419 .57622 L .97415 .57563 L Mistroke .9741 .57504 L .97406 .57445 L .97401 .57386 L .97397 .57327 L .97393 .57268 L .97389 .57223 L .97388 .57209 L .97384 .5715 L .97379 .57091 L .97375 .57032 L .9737 .56973 L .97366 .56915 L .97361 .56856 L .97357 .56797 L .97352 .56738 L .97348 .56679 L .97343 .5662 L .97339 .56561 L .97334 .56502 L .9733 .56443 L .97325 .56384 L .97321 .56325 L .97316 .56266 L .97312 .56208 L .97307 .56149 L .97303 .5609 L .97298 .56031 L .97294 .55972 L .97289 .55913 L .97285 .55854 L .9728 .55795 L .97279 .55783 L .97276 .55736 L .97271 .55677 L .97266 .55618 L .97262 .55559 L .97257 .55501 L .97253 .55442 L .97248 .55383 L .97244 .55324 L .97239 .55265 L .97234 .55206 L .9723 .55147 L .97225 .55088 L .97221 .55029 L .97216 .5497 L .97212 .54911 L .97207 .54852 L .97202 .54793 L .97198 .54735 L Mistroke .97193 .54676 L .97188 .54617 L .97184 .54558 L .97179 .54499 L .97175 .5444 L .9717 .54381 L .97169 .54373 L .97165 .54322 L .97161 .54263 L .97156 .54204 L .97151 .54145 L .97147 .54086 L .97142 .54028 L .97137 .53969 L .97133 .5391 L .97128 .53851 L .97123 .53792 L .97119 .53733 L .97114 .53674 L .97109 .53615 L .97104 .53556 L .971 .53497 L .97095 .53438 L .9709 .53379 L .97086 .5332 L .97081 .53262 L .97076 .53203 L .97071 .53144 L .97067 .53085 L .97062 .53026 L .97059 .52993 L .97057 .52967 L .97052 .52908 L .97048 .52849 L .97043 .5279 L .97038 .52731 L .97033 .52672 L .97029 .52613 L .97024 .52555 L .97019 .52496 L .97014 .52437 L .97009 .52378 L .97005 .52319 L .97 .5226 L .96995 .52201 L .9699 .52142 L .96985 .52083 L .96981 .52024 L .96976 .51965 L .96971 .51906 L Mistroke .96966 .51848 L .96961 .51789 L .96956 .5173 L .96952 .51671 L .96949 .51642 L .96947 .51612 L .96942 .51553 L .96937 .51494 L .96932 .51435 L .96927 .51376 L .96922 .51317 L .96918 .51258 L .96913 .51199 L .96908 .5114 L .96903 .51082 L .96898 .51023 L .96893 .50964 L .96888 .50905 L .96883 .50846 L .96878 .50787 L .96873 .50728 L .96869 .50669 L .96864 .5061 L .96859 .50551 L .96854 .50492 L .96849 .50433 L .96844 .50375 L .96839 .50321 L .96839 .50316 L .96834 .50257 L .96829 .50198 L .96824 .50139 L .96819 .5008 L .96814 .50021 L .96809 .49962 L .96804 .49903 L .96799 .49844 L .96794 .49785 L .96789 .49726 L .96784 .49667 L .96779 .49609 L .96774 .4955 L .96769 .49491 L .96764 .49432 L .96759 .49373 L .96754 .49314 L .96749 .49255 L .96744 .49196 L .96739 .49137 L .96734 .49078 L Mistroke .96729 .49028 L .96729 .49019 L .96724 .4896 L .96718 .48902 L .96713 .48843 L .96708 .48784 L .96703 .48725 L .96698 .48666 L .96693 .48607 L .96688 .48548 L .96683 .48489 L .96678 .4843 L .96673 .48371 L .96667 .48312 L .96662 .48253 L .96657 .48195 L .96652 .48136 L .96647 .48077 L .96642 .48018 L .96636 .47959 L .96631 .479 L .96626 .47841 L .96621 .47782 L .96619 .47764 L .96616 .47723 L .96611 .47664 L .96605 .47605 L .966 .47546 L .96595 .47487 L .9659 .47429 L .96585 .4737 L .96579 .47311 L .96574 .47252 L .96569 .47193 L .96564 .47134 L .96558 .47075 L .96553 .47016 L .96548 .46957 L .96543 .46898 L .96537 .46839 L .96532 .4678 L .96527 .46722 L .96522 .46663 L .96516 .46604 L .96511 .46545 L .96509 .46528 L .96506 .46486 L .965 .46427 L .96495 .46368 L .9649 .46309 L Mistroke .96484 .4625 L .96479 .46191 L .96474 .46132 L .96468 .46073 L .96463 .46014 L .96458 .45956 L .96452 .45897 L .96447 .45838 L .96442 .45779 L .96436 .4572 L .96431 .45661 L .96425 .45602 L .9642 .45543 L .96415 .45484 L .96409 .45425 L .96404 .45366 L .96399 .45319 L .96398 .45307 L .96393 .45249 L .96387 .4519 L .96382 .45131 L .96377 .45072 L .96371 .45013 L .96366 .44954 L .9636 .44895 L .96355 .44836 L .96349 .44777 L .96344 .44718 L .96338 .44659 L .96333 .446 L .96327 .44542 L .96322 .44483 L .96316 .44424 L .96311 .44365 L .96305 .44306 L .963 .44247 L .96294 .44188 L .96289 .44139 L .96289 .44129 L .96283 .4407 L .96277 .44011 L .96272 .43952 L .96266 .43893 L .96261 .43834 L .96255 .43776 L .96249 .43717 L .96244 .43658 L .96238 .43599 L .96233 .4354 L .96227 .43481 L Mistroke .96221 .43422 L .96216 .43363 L .9621 .43304 L .96204 .43245 L .96199 .43186 L .96193 .43127 L .96187 .43069 L .96182 .4301 L .96179 .42985 L .96176 .42951 L .9617 .42892 L .96165 .42833 L .96159 .42774 L .96153 .42715 L .96148 .42656 L .96142 .42597 L .96136 .42538 L .9613 .42479 L .96125 .4242 L .96119 .42362 L .96113 .42303 L .96107 .42244 L .96102 .42185 L .96096 .42126 L .9609 .42067 L .96084 .42008 L .96078 .41949 L .96073 .4189 L .96069 .41859 L .96067 .41831 L .96061 .41772 L .96055 .41713 L .96049 .41654 L .96043 .41596 L .96038 .41537 L .96032 .41478 L .96026 .41419 L .9602 .4136 L .96014 .41301 L .96008 .41242 L .96002 .41183 L .95996 .41124 L .9599 .41065 L 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.446 L .58692 .44542 L .58677 .44503 L .58669 .44483 L .58645 .44424 L .58621 .44365 L .58597 .44306 L .58573 .44247 L .58567 .44231 L .58549 .44188 L .58526 .44129 L .58502 .4407 L .58478 .44011 L .58457 .43958 L .58454 .43952 L .58431 .43893 L .58407 .43834 L .58384 .43776 L .5836 .43717 L .58347 .43684 L .58336 .43658 L .58313 .43599 L .58289 .4354 L .58266 .43481 L .58242 .43422 L .58237 .43408 L .58219 .43363 L .58196 .43304 L .58172 .43245 L .58149 .43186 L .58127 .43131 L .58125 .43127 L .58102 .43069 L .58079 .4301 L .58056 .42951 L .58032 .42892 L .58017 .42853 L .58009 .42833 L .57986 .42774 L .57963 .42715 L .57939 .42656 L .57916 .42597 L .57907 .42573 L Mistroke .57893 .42538 L .5787 .42479 L .57847 .4242 L .57824 .42362 L .57801 .42303 L .57797 .42292 L .57778 .42244 L .57755 .42185 L .57732 .42126 L .57709 .42067 L .57687 .42011 L .57686 .42008 L .57663 .41949 L .5764 .4189 L .57617 .41831 L .57594 .41772 L .57577 .41728 L .57571 .41713 L .57549 .41654 L .57526 .41596 L .57503 .41537 L .5748 .41478 L .57467 .41444 L .57457 .41419 L .57435 .4136 L .57412 .41301 L .57389 .41242 L .57366 .41183 L .57357 .41159 L .57344 .41124 L .57321 .41065 L .57298 .41006 L .57276 .40947 L .57253 .40889 L .57247 .40873 L .5723 .4083 L .57208 .40771 L .57185 .40712 L .57162 .40653 L .5714 .40594 L .57137 .40586 L .57117 .40535 L .57095 .40476 L .57072 .40417 L .5705 .40358 L .57027 .40299 L .57027 .40299 L .57005 .4024 L .56982 .40181 L .5696 .40123 L Mistroke .56937 .40064 L .56917 .4001 L .56915 .40005 L .56892 .39946 L .5687 .39887 L .56848 .39828 L .56825 .39769 L .56807 .39721 L .56803 .3971 L .5678 .39651 L .56758 .39592 L .56736 .39533 L .56713 .39474 L .56697 .39431 L .56691 .39416 L .56669 .39357 L .56646 .39298 L .56624 .39239 L .56602 .3918 L .56587 .39141 L .5658 .39121 L .56557 .39062 L .56535 .39003 L .56513 .38944 L .5649 .38885 L .56477 .3885 L .56468 .38826 L .56446 .38767 L .56424 .38709 L .56402 .3865 L .56379 .38591 L .56367 .38558 L .56357 .38532 L .56335 .38473 L .56313 .38414 L .56291 .38355 L .56268 .38296 L .56257 .38266 L .56246 .38237 L .56224 .38178 L .56202 .38119 L .5618 .3806 L .56158 .38001 L .56147 .37974 L .56136 .37943 L .56113 .37884 L .56091 .37825 L .56069 .37766 L .56047 .37707 L .56037 .37681 L Mistroke .56025 .37648 L .56003 .37589 L .55981 .3753 L .55959 .37471 L .55937 .37412 L .55927 .37387 L .55915 .37353 L .55892 .37294 L .5587 .37236 L .55848 .37177 L .55826 .37118 L .55817 .37094 L .55804 .37059 L .55782 .37 L .5576 .36941 L .55738 .36882 L .55716 .36823 L .55707 .368 L .55694 .36764 L .55672 .36705 L .5565 .36646 L .55628 .36587 L .55606 .36528 L .55597 .36505 L .55584 .3647 L .55562 .36411 L .5554 .36352 L .55518 .36293 L .55496 .36234 L .55487 .36211 L .55474 .36175 L .55452 .36116 L .5543 .36057 L .55408 .35998 L .55386 .35939 L .55377 .35917 L .55364 .3588 L .55342 .35821 L .5532 .35763 L .55298 .35704 L .55276 .35645 L .55267 .35622 L .55254 .35586 L .55232 .35527 L .5521 .35468 L .55188 .35409 L .55166 .3535 L .55157 .35327 L .55144 .35291 L .55122 .35232 L Mistroke .551 .35173 L .55078 .35114 L .55056 .35056 L .55047 .35033 L .55034 .34997 L .55012 .34938 L .5499 .34879 L .54968 .3482 L .54946 .34761 L .54937 .34738 L .54924 .34702 L .54902 .34643 L .5488 .34584 L .54858 .34525 L .54836 .34466 L .54827 .34444 L .54814 .34407 L .54792 .34348 L .5477 .3429 L .54748 .34231 L .54726 .34172 L .54717 .3415 L .54704 .34113 L .54682 .34054 L .5466 .33995 L .54638 .33936 L .54616 .33877 L .54608 .33856 L .54593 .33818 L .54571 .33759 L .54549 .337 L .54527 .33641 L .54505 .33583 L .54498 .33562 L .54483 .33524 L .54461 .33465 L .54439 .33406 L .54417 .33347 L .54395 .33288 L .54388 .33268 L .54373 .33229 L .54351 .3317 L .54329 .33111 L .54306 .33052 L .54284 .32993 L .54278 .32975 L .54262 .32934 L .5424 .32875 L .54218 .32817 L .54196 .32758 L Mistroke .54174 .32699 L .54168 .32683 L .54152 .3264 L .54129 .32581 L .54107 .32522 L .54085 .32463 L .54063 .32404 L .54058 .3239 L .54041 .32345 L .54018 .32286 L .53996 .32227 L .53974 .32168 L .53952 .3211 L .53948 .32099 L .5393 .32051 L .53907 .31992 L .53885 .31933 L .53863 .31874 L .53841 .31815 L .53838 .31807 L .53818 .31756 L .53796 .31697 L .53774 .31638 L .53751 .31579 L .53729 .3152 L .53728 .31517 L .53707 .31461 L .53684 .31403 L .53662 .31344 L .5364 .31285 L .53618 .31227 L .53617 .31226 L .53595 .31167 L .53573 .31108 L .5355 .31049 L .53528 .3099 L .53508 .30937 L .53505 .30931 L .53483 .30872 L .53461 .30813 L .53438 .30754 L .53416 .30695 L .53398 .30649 L .53393 .30637 L .53371 .30578 L .53348 .30519 L .53326 .3046 L .53303 .30401 L .53288 .30361 L .53281 .30342 L Mistroke .53258 .30283 L .53235 .30224 L .53213 .30165 L .5319 .30106 L .53178 .30074 L .53168 .30047 L .53145 .29988 L .53122 .2993 L .531 .29871 L .53077 .29812 L .53068 .29788 L .53054 .29753 L .53032 .29694 L .53009 .29635 L .52986 .29576 L .52963 .29517 L .52958 .29503 L .52941 .29458 L .52918 .29399 L .52895 .2934 L .52872 .29281 L .52849 .29222 L .52848 .29218 L .52827 .29164 L .52804 .29105 L .52781 .29046 L .52758 .28987 L .52738 .28935 L .52735 .28928 L .52712 .28869 L .52689 .2881 L .52666 .28751 L .52643 .28692 L .52628 .28653 L .5262 .28633 L .52597 .28574 L .52574 .28515 L .52551 .28457 L .52528 .28398 L .52518 .28372 L .52505 .28339 L .52482 .2828 L .52459 .28221 L .52435 .28162 L .52412 .28103 L .52408 .28092 L .52389 .28044 L .52366 .27985 L .52343 .27926 L .52319 .27867 L Mistroke .52298 .27813 L .52296 .27808 L .52273 .2775 L .52249 .27691 L .52226 .27632 L .52203 .27573 L .52188 .27536 L .52179 .27514 L .52156 .27455 L .52132 .27396 L .52109 .27337 L .52085 .27278 L .52078 .2726 L .52062 .27219 L .52038 .2716 L .52015 .27101 L .51991 .27042 L .51968 .26985 L .51967 .26984 L .51944 .26925 L .5192 .26866 L .51896 .26807 L .51873 .26748 L .51858 .26711 L .51849 .26689 L .51825 .2663 L .51801 .26571 L .51778 .26512 L .51754 .26453 L .51748 .26439 L .5173 .26394 L .51706 .26335 L .51682 .26277 L .51658 .26218 L .51638 .26169 L .51634 .26159 L .5161 .261 L .51586 .26041 L .51562 .25982 L .51538 .25923 L .51528 .259 L .51513 .25864 L .51489 .25805 L .51465 .25746 L .51441 .25687 L .51418 .25632 L .51416 .25628 L .51392 .2557 L .51368 .25511 L .51343 .25452 L Mistroke .51319 .25393 L .51308 .25367 L .51295 .25334 L .5127 .25275 L .51246 .25216 L .51221 .25157 L .51198 .25102 L .51196 .25098 L .51172 .25039 L .51147 .2498 L .51122 .24921 L .51098 .24862 L .51088 .2484 L .51073 .24804 L .51048 .24745 L .51023 .24686 L .50998 .24627 L .50978 .24579 L .50973 .24568 L .50948 .24509 L .50923 .2445 L .50898 .24391 L .50873 .24332 L .50868 .2432 L .50848 .24273 L .50823 .24214 L .50798 .24155 L .50773 .24097 L .50758 .24063 L .50747 .24038 L .50722 .23979 L .50697 .2392 L .50671 .23861 L .50648 .23808 L .50646 .23802 L .5062 .23743 L .50595 .23684 L .50569 .23625 L .50543 .23566 L .50538 .23555 L .50518 .23507 L .50492 .23448 L .50466 .23389 L .5044 .23331 L .50428 .23303 L .50414 .23272 L .50389 .23213 L .50363 .23154 L .50336 .23095 L .50318 .23054 L Mistroke .5031 .23036 L .50284 .22977 L .50258 .22918 L .50232 .22859 L .50208 .22807 L .50206 .228 L .50179 .22741 L .50153 .22682 L .50126 .22624 L .501 .22565 L .50098 .22561 L .50073 .22506 L .50047 .22447 L .5002 .22388 L .49993 .22329 L .49988 .22318 L .49966 .2227 L .4994 .22211 L .49913 .22152 L .49886 .22093 L .49878 .22077 L .49859 .22034 L .49832 .21975 L .49804 .21917 L .49777 .21858 L .49768 .21839 L .4975 .21799 L .49723 .2174 L .49695 .21681 L .49668 .21622 L .49658 .21602 L .4964 .21563 L .49612 .21504 L .49585 .21445 L .49557 .21386 L .49548 .21368 L .49529 .21327 L .49501 .21268 L .49473 .21209 L .49445 .21151 L .49439 .21136 L .49417 .21092 L .49389 .21033 L .49361 .20974 L .49332 .20915 L .49329 .20907 L .49304 .20856 L .49275 .20797 L .49247 .20738 L .49219 .2068 L Mistroke .49218 .20679 L .49189 .2062 L .49161 .20561 L .49132 .20502 L .49109 .20455 L .49103 .20444 L .49074 .20385 L .49044 .20326 L .49015 .20267 L .48999 .20233 L .48986 .20208 L .48956 .20149 L .48927 .2009 L .48897 .20031 L .48889 .20014 L .48868 .19972 L .48838 .19913 L .48808 .19854 L .48779 .19797 L .48778 .19795 L .48748 .19736 L .48718 .19678 L .48687 .19619 L .48669 .19583 L .48657 .1956 L .48626 .19501 L .48596 .19442 L .48565 .19383 L .48559 .19371 L .48534 .19324 L .48503 .19265 L .48472 .19206 L .48449 .19162 L .48441 .19147 L .48409 .19088 L .48378 .19029 L .48346 .18971 L .48339 .18956 L .48315 .18912 L .48283 .18853 L .48251 .18794 L .48229 .18753 L .48219 .18735 L .48187 .18676 L .48155 .18617 L .48122 .18558 L .48119 .18552 L .48089 .18499 L .48057 .1844 L .48024 .18381 L Mistroke .48009 .18354 L .47991 .18322 L .47958 .18264 L .47924 .18205 L .47899 .1816 L .47891 .18146 L .47857 .18087 L .47824 .18028 L .4779 .17969 L .47789 .17968 L .47755 .1791 L .47721 .17851 L .47687 .17792 L .47679 .17779 L .47652 .17733 L .47617 .17674 L .47582 .17615 L .47569 .17593 L .47547 .17556 L .47512 .17498 L .47476 .17439 L .47459 .1741 L .47441 .1738 L .47405 .17321 L .47369 .17262 L .47349 .1723 L .47332 .17203 L .47296 .17144 L .47259 .17085 L .47239 .17053 L .47222 .17026 L .47185 .16967 L .47147 .16908 L .47129 .1688 L .4711 .16849 L .47072 .16791 L .47034 .16732 L .47019 .16709 L .46995 .16673 L .46957 .16614 L .46918 .16555 L .46909 .16542 L .46878 .16496 L .46839 .16437 L .46799 .16378 L .46799 .16378 L .46759 .16319 L .46719 .1626 L .46689 .16217 L .46678 .16201 L Mistroke .46637 .16142 L .46596 .16083 L .46579 .1606 L .46554 .16025 L .46512 .15966 L .4647 .15907 L .46469 .15906 L .46427 .15848 L .46384 .15789 L .46359 .15755 L .46341 .1573 L .46297 .15671 L .46253 .15612 L .46249 .15608 L .46208 .15553 L .46163 .15494 L .46139 .15464 L .46117 .15435 L .46071 .15376 L .46029 .15323 L .46025 .15318 L .45978 .15259 L .4593 .152 L .45919 .15186 L .45882 .15141 L .45833 .15082 L .45809 .15053 L .45784 .15023 L .45734 .14964 L .45699 .14923 L .45684 .14905 L .45633 .14846 L .45589 .14797 L .45581 .14787 L .45528 .14728 L .45479 .14674 L .45475 .14669 L .45421 .14611 L .45369 .14555 L .45366 .14552 L .4531 .14493 L .45259 .1444 L .45254 .14434 L .45196 .14375 L .45149 .14328 L .45137 .14316 L .45078 .14257 L .45039 .1422 L .45017 .14198 L .44955 .14139 L Mistroke .44929 .14116 L .44891 .1408 L .44826 .14021 L .44819 .14015 L .4476 .13962 L .44709 .13918 L .44692 .13903 L .44622 .13845 L .44599 .13826 L .44551 .13786 L .44489 .13737 L .44477 .13727 L .44401 .13668 L .44379 .13651 L .44323 .13609 L .4427 .1357 L .44241 .1355 L .4416 .13493 L .44157 .13491 L .44069 .13432 L .4405 .13419 L .43977 .13373 L .4394 .1335 L .43881 .13314 L .4383 .13284 L .43779 .13255 L .4372 .13223 L .4367 .13196 L .4361 .13165 L .43554 .13138 L .435 .13112 L .43427 .13079 L .4339 .13062 L .43286 .1302 L .4328 .13017 L .4317 .12976 L .43127 .12961 L .4306 .12939 L .4295 .12906 L .42936 .12902 L .4284 .12877 L .4273 .12852 L .42684 .12843 L .4262 .12831 L .4251 .12815 L .424 .12803 L .4229 .12795 L .4218 .12791 L .4207 .12792 L .4196 .12796 L Mistroke .4185 .12805 L .4174 .12819 L .4163 .12836 L .41593 .12843 L .4152 .12858 L .4141 .12884 L .41343 .12902 L .413 .12914 L .4119 .12949 L .41156 .12961 L .4108 .12988 L .40999 .1302 L .4097 .13031 L .40861 .13079 L .4086 .13079 L .4075 .13131 L .40737 .13138 L .4064 .13187 L .40623 .13196 L .4053 .13248 L .40517 .13255 L .4042 .13313 L .40418 .13314 L .40324 .13373 L .4031 .13382 L .40235 .13432 L .402 .13456 L .4015 .13491 L .4009 .13534 L .40068 .1355 L .3999 .13609 L .3998 .13616 L .39914 .13668 L .3987 .13703 L .39841 .13727 L .3977 .13786 L .3976 .13794 L .39701 .13845 L .3965 .13889 L .39634 .13903 L .39569 .13962 L .3954 .13989 L .39506 .14021 L .39444 .1408 L .3943 .14093 L .39383 .14139 L .39323 .14198 L .3932 .14201 L .39265 .14257 L .3921 .14314 L Mistroke .39208 .14316 L .39152 .14375 L .39101 .14431 L .39098 .14434 L .39044 .14493 L .38991 .14552 L .38991 .14552 L .38939 .14611 L .38887 .14669 L .38881 .14677 L .38837 .14728 L .38787 .14787 L .38771 .14807 L .38738 .14846 L .3869 .14905 L .38661 .14941 L .38642 .14964 L .38595 .15023 L .38551 .15079 L .38549 .15082 L .38503 .15141 L .38458 .152 L .38441 .15222 L .38413 .15259 L .38369 .15318 L .38331 .15369 L .38325 .15376 L .38282 .15435 L .38239 .15494 L .38221 .1552 L .38197 .15553 L .38155 .15612 L .38113 .15671 L .38111 .15675 L .38072 .1573 L .38032 .15789 L .38001 .15834 L .37992 .15848 L .37952 .15907 L .37912 .15966 L .37891 .15998 L .37873 .16025 L .37834 .16083 L .37796 .16142 L .37781 .16166 L .37758 .16201 L .3772 .1626 L .37682 .16319 L .37671 .16338 L .37645 .16378 L Mistroke .37608 .16437 L .37572 .16496 L .37561 .16514 L .37535 .16555 L .37499 .16614 L .37464 .16673 L .37451 .16694 L .37428 .16732 L .37393 .16791 L .37358 .16849 L .37341 .16878 L .37323 .16908 L .37288 .16967 L .37254 .17026 L .37231 .17066 L .3722 .17085 L .37186 .17144 L .37153 .17203 L .37121 .17259 L .37119 .17262 L .37086 .17321 L .37053 .1738 L .3702 .17439 L .37011 .17455 L .36988 .17498 L .36955 .17556 L .36923 .17615 L .36901 .17656 L .36891 .17674 L .36859 .17733 L .36827 .17792 L .36796 .17851 L .36791 .1786 L .36764 .1791 L .36733 .17969 L .36702 .18028 L .36681 .18068 L .36671 .18087 L .36641 .18146 L .3661 .18205 L .3658 .18264 L .36571 .18281 L .3655 .18322 L .3652 .18381 L .3649 .1844 L .36461 .18497 L .3646 .18499 L .3643 .18558 L .36401 .18617 L .36371 .18676 L Mistroke .36351 .18717 L .36342 .18735 L .36313 .18794 L .36284 .18853 L .36255 .18912 L .36241 .18941 L .36227 .18971 L .36198 .19029 L .3617 .19088 L .36141 .19147 L .36131 .19169 L .36113 .19206 L .36085 .19265 L .36057 .19324 L .36029 .19383 L .36021 .194 L .36002 .19442 L .35974 .19501 L .35946 .1956 L .35919 .19619 L .35911 .19636 L .35892 .19678 L .35865 .19736 L .35837 .19795 L .3581 .19854 L .35801 .19875 L .35784 .19913 L .35757 .19972 L .3573 .20031 L .35704 .2009 L .35691 .20117 L .35677 .20149 L .35651 .20208 L .35624 .20267 L .35598 .20326 L .35581 .20364 L .35572 .20385 L .35546 .20444 L .3552 .20502 L .35494 .20561 L .35471 .20614 L .35468 .2062 L .35443 .20679 L .35417 .20738 L .35392 .20797 L .35366 .20856 L .35361 .20868 L .35341 .20915 L .35316 .20974 L .3529 .21033 L Mistroke .35265 .21092 L .35251 .21125 L .3524 .21151 L .35215 .21209 L .35191 .21268 L .35166 .21327 L .35141 .21386 L .35141 .21386 L .35116 .21445 L .35092 .21504 L .35067 .21563 L .35043 .21622 L .35031 .2165 L .35018 .21681 L .34994 .2174 L .3497 .21799 L .34946 .21858 L .34922 .21917 L .34921 .21917 L .34898 .21975 L .34874 .22034 L .3485 .22093 L .34826 .22152 L .34811 .22189 L .34802 .22211 L .34779 .2227 L .34755 .22329 L .34731 .22388 L .34708 .22447 L .34701 .22463 L .34684 .22506 L .34661 .22565 L .34638 .22624 L .34614 .22682 L .34591 .22741 L .34591 .22741 L .34568 .228 L .34545 .22859 L .34522 .22918 L .34499 .22977 L .34481 .23022 L .34476 .23036 L .34453 .23095 L .3443 .23154 L .34407 .23213 L .34385 .23272 L .34371 .23306 L .34362 .23331 L .34339 .23389 L .34317 .23448 L Mistroke .34294 .23507 L .34272 .23566 L .34261 .23594 L .3425 .23625 L .34227 .23684 L .34205 .23743 L .34183 .23802 L .3416 .23861 L .34151 .23884 L .34138 .2392 L .34116 .23979 L .34094 .24038 L .34072 .24097 L .3405 .24155 L .34041 .24178 L .34028 .24214 L .34006 .24273 L .33984 .24332 L .33962 .24391 L .33941 .2445 L .33932 .24475 L .33919 .24509 L .33897 .24568 L .33876 .24627 L .33854 .24686 L .33833 .24745 L .33822 .24775 L .33811 .24804 L .3379 .24862 L .33768 .24921 L .33747 .2498 L .33725 .25039 L .33712 .25078 L .33704 .25098 L .33683 .25157 L .33662 .25216 L .3364 .25275 L .33619 .25334 L .33602 .25383 L .33598 .25393 L .33577 .25452 L .33556 .25511 L .33535 .2557 L .33514 .25628 L .33493 .25687 L .33492 .25692 L .33472 .25746 L .33451 .25805 L .33431 .25864 L .3341 .25923 L Mistroke .33389 .25982 L .33382 .26003 L .33368 .26041 L .33348 .261 L .33327 .26159 L .33306 .26218 L .33286 .26277 L .33272 .26317 L .33265 .26335 L .33245 .26394 L .33224 .26453 L .33204 .26512 L .33183 .26571 L .33163 .2663 L .33162 .26634 L .33143 .26689 L .33122 .26748 L .33102 .26807 L .33082 .26866 L .33062 .26925 L .33052 .26954 L .33041 .26984 L .33021 .27042 L .33001 .27101 L .32981 .2716 L .32961 .27219 L .32942 .27276 L .32941 .27278 L .32921 .27337 L .32901 .27396 L .32881 .27455 L .32861 .27514 L .32841 .27573 L .32832 .276 L .32821 .27632 L .32801 .27691 L .32781 .2775 L .32762 .27808 L .32742 .27867 L .32722 .27926 L .32722 .27927 L .32702 .27985 L .32683 .28044 L .32663 .28103 L .32643 .28162 L .32624 .28221 L .32612 .28257 L .32604 .2828 L .32584 .28339 L .32565 .28398 L Mistroke .32545 .28457 L .32526 .28515 L .32506 .28574 L .32502 .28588 L .32487 .28633 L .32467 .28692 L .32448 .28751 L .32429 .2881 L .32409 .28869 L .32392 .28922 L .3239 .28928 L .32371 .28987 L .32351 .29046 L .32332 .29105 L .32313 .29164 L .32294 .29222 L .32282 .29259 L .32274 .29281 L .32255 .2934 L .32236 .29399 L .32217 .29458 L .32198 .29517 L .32179 .29576 L .32172 .29597 L .3216 .29635 L .3214 .29694 L .32121 .29753 L .32102 .29812 L .32083 .29871 L .32064 .2993 L .32062 .29937 L .32045 .29988 L .32027 .30047 L .32008 .30106 L .31989 .30165 L .3197 .30224 L .31952 .3028 L .31951 .30283 L .31932 .30342 L .31913 .30401 L .31894 .3046 L .31876 .30519 L .31857 .30578 L .31842 .30624 L .31838 .30637 L .31819 .30695 L .31801 .30754 L .31782 .30813 L .31763 .30872 L .31745 .30931 L Mistroke .31732 .30971 L .31726 .3099 L .31707 .31049 L .31689 .31108 L .3167 .31167 L .31651 .31226 L .31633 .31285 L .31622 .31319 L .31614 .31344 L .31596 .31403 L .31577 .31461 L .31559 .3152 L .3154 .31579 L .31522 .31638 L .31512 .31669 L .31503 .31697 L .31485 .31756 L .31466 .31815 L .31448 .31874 L .31429 .31933 L .31411 .31992 L .31402 .32021 L .31393 .32051 L .31374 .3211 L .31356 .32168 L .31338 .32227 L .31319 .32286 L .31301 .32345 L .31292 .32374 L .31283 .32404 L .31264 .32463 L .31246 .32522 L .31228 .32581 L .31209 .3264 L .31191 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.30221 .3588 L .30204 .35939 L .30192 .35977 L Mistroke .30186 .35998 L .30168 .36057 L .3015 .36116 L .30133 .36175 L .30115 .36234 L .30097 .36293 L .30082 .36343 L .3008 .36352 L .30062 .36411 L .30044 .3647 L .30026 .36528 L .30009 .36587 L .29991 .36646 L .29973 .36705 L .29972 .36709 L .29956 .36764 L .29938 .36823 L .2992 .36882 L .29903 .36941 L .29885 .37 L .29867 .37059 L .29862 .37076 L .2985 .37118 L .29832 .37177 L .29814 .37236 L .29797 .37294 L .29779 .37353 L .29762 .37412 L .29752 .37443 L .29744 .37471 L .29726 .3753 L .29709 .37589 L .29691 .37648 L .29673 .37707 L .29656 .37766 L .29642 .37811 L .29638 .37825 L .29621 .37884 L .29603 .37943 L .29585 .38001 L .29568 .3806 L .2955 .38119 L .29533 .38178 L .29532 .38179 L .29515 .38237 L .29497 .38296 L .2948 .38355 L .29462 .38414 L .29444 .38473 L .29427 .38532 L Mistroke .29422 .38547 L .29409 .38591 L .29392 .3865 L .29374 .38709 L .29357 .38767 L .29339 .38826 L .29321 .38885 L .29312 .38915 L .29304 .38944 L .29286 .39003 L .29269 .39062 L .29251 .39121 L .29233 .3918 L .29216 .39239 L .29202 .39283 L .29198 .39298 L .29181 .39357 L .29163 .39416 L .29145 .39474 L .29128 .39533 L .2911 .39592 L .29093 .39651 L .29092 .39651 L .29075 .3971 L .29057 .39769 L .2904 .39828 L .29022 .39887 L .29004 .39946 L .28987 .40005 L .28982 .40019 L .28969 .40064 L .28952 .40123 L .28934 .40181 L .28916 .4024 L .28899 .40299 L .28881 .40358 L .28873 .40387 L .28863 .40417 L .28846 .40476 L .28828 .40535 L .28811 .40594 L .28793 .40653 L .28775 .40712 L .28763 .40754 L .28758 .40771 L .2874 .4083 L .28722 .40889 L .28705 .40947 L .28687 .41006 L .28669 .41065 L Mistroke .28653 .41121 L .28652 .41124 L .28634 .41183 L .28616 .41242 L .28598 .41301 L .28581 .4136 L .28563 .41419 L .28545 .41478 L .28543 .41487 L .28528 .41537 L .2851 .41596 L .28492 .41654 L .28474 .41713 L .28457 .41772 L .28439 .41831 L .28433 .41852 L .28421 .4189 L .28403 .41949 L .28386 .42008 L .28368 .42067 L .2835 .42126 L .28332 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.27357 .45366 L .27339 .45425 L .27333 .45444 L .2732 .45484 L .27302 .45543 L .27283 .45602 L .27265 .45661 L .27246 .4572 L .27228 .45779 L .27223 .45794 L .27209 .45838 L .27191 .45897 L .27172 .45956 L .27153 .46014 L .27135 .46073 L .27116 .46132 L Mistroke .27113 .46143 L .27098 .46191 L .27079 .4625 L .2706 .46309 L .27041 .46368 L .27023 .46427 L .27004 .46486 L .27003 .46489 L .26985 .46545 L .26966 .46604 L .26947 .46663 L .26929 .46722 L .2691 .4678 L .26893 .46833 L .26891 .46839 L .26872 .46898 L .26853 .46957 L .26834 .47016 L .26815 .47075 L .26796 .47134 L .26783 .47174 L .26777 .47193 L .26758 .47252 L .26739 .47311 L .2672 .4737 L .26701 .47429 L .26681 .47487 L .26673 .47513 L .26662 .47546 L .26643 .47605 L .26624 .47664 L .26604 .47723 L .26585 .47782 L .26566 .47841 L .26563 .4785 L .26546 .479 L .26527 .47959 L .26508 .48018 L .26488 .48077 L .26469 .48136 L .26453 .48183 L .26449 .48195 L .2643 .48253 L .2641 .48312 L .26391 .48371 L .26371 .4843 L .26351 .48489 L .26343 .48514 L .26332 .48548 L .26312 .48607 L Mistroke .26292 .48666 L .26272 .48725 L .26252 .48784 L .26233 .48841 L .26233 .48843 L .26213 .48902 L .26193 .4896 L .26173 .49019 L .26153 .49078 L .26133 .49137 L .26123 .49166 L .26113 .49196 L .26092 .49255 L .26072 .49314 L .26052 .49373 L .26032 .49432 L .26013 .49487 L .26012 .49491 L .25991 .4955 L .25971 .49609 L .25951 .49667 L .2593 .49726 L .2591 .49785 L .25903 .49804 L .25889 .49844 L .25868 .49903 L .25848 .49962 L .25827 .50021 L .25807 .5008 L .25793 .50118 L .25786 .50139 L .25765 .50198 L .25744 .50257 L .25723 .50316 L .25702 .50375 L .25683 .50428 L .25681 .50433 L .2566 .50492 L .25639 .50551 L .25618 .5061 L .25597 .50669 L .25576 .50728 L .25573 .50735 L .25554 .50787 L .25533 .50846 L .25511 .50905 L .2549 .50964 L .25468 .51023 L .25463 .51037 L .25447 .51082 L Mistroke .25425 .5114 L .25403 .51199 L .25382 .51258 L .2536 .51317 L .25353 .51335 L .25338 .51376 L .25316 .51435 L .25294 .51494 L .25272 .51553 L .2525 .51612 L .25243 .51629 L .25227 .51671 L .25205 .5173 L .25183 .51789 L .2516 .51848 L .25138 .51906 L .25133 .51919 L .25115 .51965 L .25093 .52024 L .2507 .52083 L .25047 .52142 L .25024 .52201 L .25023 .52203 L .25001 .5226 L .24978 .52319 L .24955 .52378 L .24932 .52437 L .24913 .52484 L .24909 .52496 L .24885 .52555 L .24862 .52613 L .24838 .52672 L .24814 .52731 L .24803 .52759 L .24791 .5279 L .24767 .52849 L .24743 .52908 L .24719 .52967 L .24695 .53026 L .24693 .53029 L .2467 .53085 L .24646 .53144 L .24622 .53203 L .24597 .53262 L .24583 .53294 L .24572 .5332 L .24548 .53379 L .24523 .53438 L .24498 .53497 L .24473 .53554 L Mistroke .24473 .53556 L .24447 .53615 L .24422 .53674 L .24396 .53733 L .24371 .53792 L .24363 .53809 L .24345 .53851 L .24319 .5391 L .24293 .53969 L .24267 .54028 L .24253 .54057 L .2424 .54086 L .24214 .54145 L .24187 .54204 L .2416 .54263 L .24143 .543 L .24133 .54322 L .24106 .54381 L .24079 .5444 L .24051 .54499 L .24033 .54537 L .24024 .54558 L .23996 .54617 L .23968 .54676 L .2394 .54735 L .23923 .54768 L .23911 .54793 L .23882 .54852 L .23854 .54911 L .23824 .5497 L .23813 .54992 L .23795 .55029 L .23766 .55088 L .23736 .55147 L .23706 .55206 L .23704 .55211 L .23676 .55265 L .23645 .55324 L .23614 .55383 L .23594 .55422 L .23583 .55442 L .23552 .55501 L .2352 .55559 L .23488 .55618 L .23484 .55627 L .23456 .55677 L .23423 .55736 L .2339 .55795 L .23374 .55825 L .23357 .55854 L Mistroke .23323 .55913 L .23289 .55972 L .23264 .56015 L .23255 .56031 L .2322 .5609 L .23184 .56149 L .23154 .56199 L .23148 .56208 L .23112 .56266 L .23075 .56325 L .23044 .56375 L .23038 .56384 L .23 .56443 L .22961 .56502 L .22934 .56543 L .22922 .56561 L .22882 .5662 L .22841 .56679 L .22824 .56704 L .228 .56738 L .22758 .56797 L .22714 .56856 L .22714 .56857 L .2267 .56915 L .22625 .56973 L .22604 .57001 L .22579 .57032 L .22532 .57091 L .22494 .57137 L .22483 .5715 L .22433 .57209 L .22384 .57265 L .22381 .57268 L .22328 .57327 L .22274 .57384 L .22272 .57386 L .22214 .57445 L .22164 .57494 L .22154 .57504 L .22091 .57563 L .22054 .57595 L .22024 .57622 L .21952 .57681 L .21944 .57687 L .21876 .57739 L .21834 .5777 L .21793 .57798 L .21724 .57843 L .217 .57857 L .21614 .57906 L Mistroke .21594 .57916 L .21504 .57959 L .21465 .57975 L .21394 .58001 L .21284 .58034 L .21283 .58034 L .21174 .58056 L .21064 .58067 L .20954 .58067 L .20844 .58055 L .20737 .58034 L .20734 .58033 L .20624 .57999 L .20563 .57975 L .20514 .57953 L .20442 .57916 L .20404 .57895 L .20343 .57857 L .20294 .57824 L .20258 .57798 L .20184 .57742 L .20181 .57739 L .20112 .57681 L .20074 .57646 L .20048 .57622 L .19988 .57563 L .19964 .57538 L .19932 .57504 L .19879 .57445 L .19854 .57417 L .19828 .57386 L .1978 .57327 L .19744 .57282 L .19733 .57268 L .19689 .57209 L .19646 .5715 L .19634 .57134 L .19604 .57091 L .19564 .57032 L .19525 .56973 L .19524 .56972 L .19487 .56915 L .19451 .56856 L .19415 .56797 L .19414 .56796 L .1938 .56738 L .19346 .56679 L .19312 .5662 L .19304 .56606 L .1928 .56561 L Mistroke .19248 .56502 L .19216 .56443 L .19194 .56401 L .19186 .56384 L .19155 .56325 L .19126 .56266 L .19097 .56208 L .19084 .56182 L .19068 .56149 L .1904 .5609 L .19013 .56031 L .18985 .55972 L .18974 .55948 L .18959 .55913 L .18932 .55854 L .18906 .55795 L .18881 .55736 L .18864 .55699 L .18855 .55677 L .1883 .55618 L .18806 .55559 L .18782 .55501 L .18758 .55442 L .18754 .55434 L .18734 .55383 L .1871 .55324 L .18687 .55265 L .18664 .55206 L .18644 .55154 L .18642 .55147 L .1862 .55088 L .18597 .55029 L .18576 .5497 L .18554 .54911 L .18535 .54858 L .18533 .54852 L .18511 .54793 L .1849 .54735 L .1847 .54676 L .18449 .54617 L .18429 .54558 L .18425 .54546 L .18409 .54499 L .18389 .5444 L .18369 .54381 L .18349 .54322 L .1833 .54263 L .18315 .54217 L .1831 .54204 L .18291 .54145 L Mistroke .18272 .54086 L .18253 .54028 L .18235 .53969 L .18216 .5391 L .18205 .53872 L .18198 .53851 L .1818 .53792 L .18162 .53733 L .18144 .53674 L .18126 .53615 L .18108 .53556 L .18095 .5351 L .18091 .53497 L .18073 .53438 L .18056 .53379 L .18039 .5332 L .18022 .53262 L .18005 .53203 L .17988 .53144 L .17985 .53131 L .17971 .53085 L .17955 .53026 L .17938 .52967 L .17922 .52908 L .17906 .52849 L .1789 .5279 L .17875 .52735 L .17874 .52731 L .17858 .52672 L .17842 .52613 L .17826 .52555 L .1781 .52496 L .17795 .52437 L .17779 .52378 L .17765 .52321 L .17764 .52319 L .17749 .5226 L .17734 .52201 L .17718 .52142 L .17703 .52083 L .17688 .52024 L .17674 .51965 L .17659 .51906 L .17655 .5189 L .17644 .51848 L .1763 .51789 L .17615 .5173 L .17601 .51671 L .17586 .51612 L .17572 .51553 L Mistroke .17558 .51494 L .17545 .5144 L .17544 .51435 L .17529 .51376 L .17515 .51317 L .17501 .51258 L .17488 .51199 L .17474 .5114 L .1746 .51082 L .17446 .51023 L .17435 .50972 L .17433 .50964 L .17419 .50905 L .17406 .50846 L .17392 .50787 L .17379 .50728 L .17366 .50669 L .17353 .5061 L .17339 .50551 L .17326 .50492 L .17325 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.16097 .43717 L .16088 .43658 L .16079 .43599 L .1607 .4354 L Mistroke .16062 .43481 L .16053 .43422 L .16044 .43363 L .16035 .43304 L .16026 .43245 L .16017 .43186 L .16009 .43127 L .16005 .43103 L .16 .43069 L .15991 .4301 L .15982 .42951 L .15974 .42892 L .15965 .42833 L .15956 .42774 L .15948 .42715 L .15939 .42656 L .15931 .42597 L .15922 .42538 L .15914 .42479 L .15905 .4242 L .15897 .42362 L .15895 .42351 L .15888 .42303 L .1588 .42244 L .15871 .42185 L .15863 .42126 L .15854 .42067 L .15846 .42008 L .15838 .41949 L .15829 .4189 L .15821 .41831 L .15813 .41772 L .15804 .41713 L .15796 .41654 L .15788 .41596 L .15785 .41576 L .15779 .41537 L .15771 .41478 L .15763 .41419 L .15755 .4136 L .15747 .41301 L .15739 .41242 L .1573 .41183 L .15722 .41124 L .15714 .41065 L .15706 .41006 L .15698 .40947 L .1569 .40889 L .15682 .4083 L .15675 .40779 L Mistroke .15674 .40771 L .15666 .40712 L .15658 .40653 L .1565 .40594 L .15642 .40535 L .15634 .40476 L .15626 .40417 L .15618 .40358 L .1561 .40299 L .15602 .4024 L .15595 .40181 L .15587 .40123 L .15579 .40064 L .15571 .40005 L .15565 .39959 L .15563 .39946 L .15556 .39887 L .15548 .39828 L .1554 .39769 L .15532 .3971 L .15525 .39651 L .15517 .39592 L .15509 .39533 L .15501 .39474 L .15494 .39416 L .15486 .39357 L .15479 .39298 L .15471 .39239 L .15463 .3918 L .15456 .39121 L .15455 .39116 L .15448 .39062 L .15441 .39003 L .15433 .38944 L .15426 .38885 L .15418 .38826 L .15411 .38767 L .15403 .38709 L .15396 .3865 L .15388 .38591 L .15381 .38532 L .15373 .38473 L .15366 .38414 L .15358 .38355 L .15351 .38296 L .15345 .38249 L .15344 .38237 L .15336 .38178 L .15329 .38119 L .15322 .3806 L Mistroke .15314 .38001 L .15307 .37943 L .153 .37884 L .15292 .37825 L .15285 .37766 L .15278 .37707 L .15271 .37648 L .15263 .37589 L .15256 .3753 L .15249 .37471 L .15242 .37412 L .15235 .37358 L .15235 .37353 L .15227 .37294 L .1522 .37236 L .15213 .37177 L .15206 .37118 L .15199 .37059 L .15192 .37 L .15185 .36941 L .15177 .36882 L .1517 .36823 L .15163 .36764 L .15156 .36705 L .15149 .36646 L .15142 .36587 L .15135 .36528 L .15128 .3647 L .15125 .36444 L .15121 .36411 L .15114 .36352 L .15107 .36293 L .151 .36234 L .15093 .36175 L .15086 .36116 L .1508 .36057 L .15073 .35998 L .15066 .35939 L .15059 .3588 L .15052 .35821 L .15045 .35763 L .15038 .35704 L .15031 .35645 L .15025 .35586 L .15018 .35527 L .15015 .35505 L .15011 .35468 L .15004 .35409 L .14997 .3535 L .14991 .35291 L Mistroke .14984 .35232 L .14977 .35173 L .1497 .35114 L .14964 .35056 L .14957 .34997 L .1495 .34938 L .14943 .34879 L .14937 .3482 L .1493 .34761 L .14923 .34702 L .14917 .34643 L .1491 .34584 L .14905 .34541 L .14903 .34525 L .14897 .34466 L .1489 .34407 L .14884 .34348 L .14877 .3429 L .1487 .34231 L .14864 .34172 L .14857 .34113 L .14851 .34054 L .14844 .33995 L .14838 .33936 L .14831 .33877 L .14825 .33818 L .14818 .33759 L .14812 .337 L .14805 .33641 L .14799 .33583 L .14795 .33552 L .14792 .33524 L .14786 .33465 L .14779 .33406 L .14773 .33347 L .14766 .33288 L .1476 .33229 L .14753 .3317 L .14747 .33111 L .14741 .33052 L .14734 .32993 L .14728 .32934 L .14722 .32875 L .14715 .32817 L .14709 .32758 L .14702 .32699 L .14696 .3264 L .1469 .32581 L .14685 .32538 L .14684 .32522 L Mistroke .14677 .32463 L .14671 .32404 L .14665 .32345 L .14658 .32286 L .14652 .32227 L .14646 .32168 L .1464 .3211 L .14633 .32051 L .14627 .31992 L .14621 .31933 L .14615 .31874 L .14608 .31815 L .14602 .31756 L .14596 .31697 L .1459 .31638 L .14584 .31579 L .14578 .3152 L .14575 .31498 L .14571 .31461 L .14565 .31403 L .14559 .31344 L .14553 .31285 L .14547 .31226 L .14541 .31167 L .14535 .31108 L .14529 .31049 L .14522 .3099 L .14516 .30931 L .1451 .30872 L .14504 .30813 L .14498 .30754 L .14492 .30695 L .14486 .30637 L .1448 .30578 L .14474 .30519 L .14468 .3046 L .14465 .30433 L .14462 .30401 L .14456 .30342 L .1445 .30283 L .14444 .30224 L .14438 .30165 L .14432 .30106 L .14426 .30047 L .1442 .29988 L .14414 .2993 L .14408 .29871 L .14402 .29812 L .14396 .29753 L .14391 .29694 L Mistroke .14385 .29635 L .14379 .29576 L .14373 .29517 L .14367 .29458 L .14361 .29399 L .14355 .29341 L .14355 .2934 L .14349 .29281 L .14344 .29222 L .14338 .29164 L .14332 .29105 L .14326 .29046 L .1432 .28987 L .14314 .28928 L .14309 .28869 L .14303 .2881 L .14297 .28751 L .14291 .28692 L .14285 .28633 L .1428 .28574 L .14274 .28515 L .14268 .28457 L .14262 .28398 L .14257 .28339 L .14251 .2828 L .14245 .28223 L .14245 .28221 L .14239 .28162 L .14234 .28103 L .14228 .28044 L .14222 .27985 L .14217 .27926 L .14211 .27867 L .14205 .27808 L .142 .2775 L .14194 .27691 L .14188 .27632 L .14183 .27573 L .14177 .27514 L .14171 .27455 L .14166 .27396 L .1416 .27337 L .14154 .27278 L .14149 .27219 L .14143 .2716 L .14138 .27101 L .14135 .27078 L .14132 .27042 L .14126 .26984 L .14121 .26925 L Mistroke .14115 .26866 L .1411 .26807 L .14104 .26748 L .14099 .26689 L .14093 .2663 L .14088 .26571 L .14082 .26512 L .14076 .26453 L .14071 .26394 L .14065 .26335 L .1406 .26277 L .14054 .26218 L .14049 .26159 L .14043 .261 L .14038 .26041 L .14032 .25982 L .14027 .25923 L .14025 .25906 L .14022 .25864 L .14016 .25805 L .14011 .25746 L .14005 .25687 L .14 .25628 L .13994 .2557 L .13989 .25511 L .13983 .25452 L .13978 .25393 L .13973 .25334 L .13967 .25275 L .13962 .25216 L .13956 .25157 L .13951 .25098 L .13946 .25039 L .1394 .2498 L .13935 .24921 L .1393 .24862 L .13924 .24804 L .13919 .24745 L .13915 .24706 L .13914 .24686 L .13908 .24627 L .13903 .24568 L .13898 .24509 L .13892 .2445 L .13887 .24391 L .13882 .24332 L .13876 .24273 L .13871 .24214 L .13866 .24155 L .1386 .24097 L Mistroke .13855 .24038 L .1385 .23979 L .13845 .2392 L .13839 .23861 L .13834 .23802 L .13829 .23743 L .13824 .23684 L .13818 .23625 L .13813 .23566 L .13808 .23507 L .13805 .23478 L .13803 .23448 L .13798 .23389 L .13792 .23331 L .13787 .23272 L .13782 .23213 L .13777 .23154 L .13772 .23095 L .13766 .23036 L .13761 .22977 L .13756 .22918 L 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.1345 .19324 L .13446 .19265 L .13441 .19206 L .13436 .19147 L .13431 .19088 L .13426 .19029 L .13421 .18971 L .13417 .18912 L .13412 .18853 L .13407 .18794 L .13402 .18735 L .13397 .18676 L .13393 .18617 L .13388 .18558 L .13383 .18499 L .13378 .1844 L Mistroke .13373 .18381 L .13369 .18322 L .13366 .18285 L .13364 .18264 L .13359 .18205 L .13354 .18146 L .13349 .18087 L .13345 .18028 L .1334 .17969 L .13335 .1791 L .1333 .17851 L .13326 .17792 L .13321 .17733 L .13316 .17674 L .13312 .17615 L .13307 .17556 L .13302 .17498 L .13297 .17439 L .13293 .1738 L .13288 .17321 L .13283 .17262 L .13279 .17203 L .13274 .17144 L .13269 .17085 L .13264 .17026 L .1326 .16967 L .13256 .16914 L .13255 .16908 L .1325 .16849 L .13246 .16791 L .13241 .16732 L .13236 .16673 L .13232 .16614 L .13227 .16555 L .13222 .16496 L .13218 .16437 L .13213 .16378 L .13209 .16319 L .13204 .1626 L .13199 .16201 L .13195 .16142 L .1319 .16083 L .13185 .16025 L .13181 .15966 L .13176 .15907 L .13172 .15848 L .13167 .15789 L .13162 .1573 L .13158 .15671 L .13153 .15612 L Mistroke .13149 .15553 L .13146 .15513 L .13144 .15494 L .1314 .15435 L .13135 .15376 L .1313 .15318 L .13126 .15259 L .13121 .152 L .13117 .15141 L .13112 .15082 L .13108 .15023 L .13103 .14964 L .13099 .14905 L .13094 .14846 L .1309 .14787 L .13085 .14728 L .1308 .14669 L .13076 .14611 L .13071 .14552 L .13067 .14493 L .13062 .14434 L .13058 .14375 L .13053 .14316 L .13049 .14257 L .13044 .14198 L .1304 .14139 L .13036 .14082 L .13035 .1408 L .13031 .14021 L .13026 .13962 L .13022 .13903 L .13018 .13845 L .13013 .13786 L .13009 .13727 L .13004 .13668 L .13 .13609 L .12995 .1355 L .12991 .13491 L .12986 .13432 L .12982 .13373 L .12978 .13314 L .12973 .13255 L .12969 .13196 L .12964 .13138 L .1296 .13079 L .12955 .1302 L .12951 .12961 L .12947 .12902 L .12942 .12843 L .12938 .12784 L Mistroke .12933 .12725 L .12929 .12666 L .12926 .12621 L .12925 .12607 L .1292 .12548 L .12916 .12489 L .12911 .1243 L .12907 .12372 L .12903 .12313 L .12898 .12254 L .12894 .12195 L .1289 .12136 L .12885 .12077 L .12881 .12018 L .12877 .11959 L .12872 .119 L .12868 .11841 L .12864 .11782 L .12859 .11723 L .12855 .11665 L .12851 .11606 L .12846 .11547 L .12842 .11488 L .12838 .11429 L .12833 .1137 L .12829 .11311 L .12825 .11252 L .1282 .11193 L .12816 .11134 L .12816 .11129 L .12812 .11075 L .12807 .11016 L .12803 .10958 L .12799 .10899 L .12795 .1084 L .1279 .10781 L .12786 .10722 L .12782 .10663 L .12777 .10604 L .12773 .10545 L .12769 .10486 L .12765 .10427 L .1276 .10368 L .12756 .10309 L .12752 .1025 L .12748 .10192 L .12743 .10133 L .12739 .10074 L .12735 .10015 L .12731 .09956 L Mistroke .12726 .09897 L .12722 .09838 L .12718 .09779 L .12714 .0972 L .1271 .09661 L .12706 .09606 L .12705 .09602 L .12701 .09543 L .12697 .09485 L .12693 .09426 L .12689 .09367 L .12684 .09308 L .1268 .09249 L .12676 .0919 L .12672 .09131 L .12668 .09072 L .12663 .09013 L .12659 .08954 L .12655 .08895 L .12651 .08836 L .12647 .08778 L .12643 .08719 L .12638 .0866 L .12634 .08601 L .1263 .08542 L .12626 .08483 L .12622 .08424 L .12618 .08365 L .12614 .08306 L .12609 .08247 L .12605 .08188 L .12601 .08129 L .12597 .0807 L .12596 .08051 L .12593 .08012 L .12589 .07953 L .12585 .07894 L .12581 .07835 L .12576 .07776 L .12572 .07717 L .12568 .07658 L .12564 .07599 L .1256 .0754 L .12556 .07481 L .12552 .07422 L .12548 .07363 L .12544 .07305 L .1254 .07246 L .12535 .07187 L .12531 .07128 L Mistroke .12527 .07069 L .12523 .0701 L .12519 .06951 L .12515 .06892 L .12511 .06833 L .12507 .06774 L .12503 .06715 L .12499 .06656 L .12495 .06597 L .12491 .06539 L .12487 .0648 L .12486 .06465 L .12483 .06421 L .12479 .06362 L .12475 .06303 L .12471 .06244 L .12466 .06185 L .12462 .06126 L .12458 .06067 L .12454 .06008 L .1245 .05949 L .12446 .0589 L .12442 .05832 L .12438 .05773 L .12434 .05714 L .1243 .05655 L .12426 .05596 L .12422 .05537 L .12418 .05478 L .12414 .05419 L .1241 .0536 L .12406 .05301 L .12402 .05242 L .12398 .05183 L .12394 .05125 L .1239 .05066 L .12386 .05007 L .12382 .04948 L .12379 .04889 L .12376 .04847 L .12375 .0483 L .12371 .04771 L .12367 .04712 L .12363 .04653 L .12359 .04594 L .12355 .04535 L .12351 .04476 L .12347 .04417 L .12343 .04359 L .12339 .043 L Mistroke .12335 .04241 L .12331 .04182 L .12327 .04123 L .12323 .04064 L .12319 .04005 L .12315 .03946 L .12311 .03887 L .12308 .03828 L .12304 .03769 L .123 .0371 L .12296 .03652 L .12292 .03593 L .12288 .03534 L .12284 .03475 L .1228 .03416 L .12276 .03357 L .12272 .03298 L .12269 .03239 L .12266 .03197 L .12265 .0318 L .12261 .03121 L .12257 .03062 L .12253 .03003 L .12249 .02944 L .12245 .02886 L .12241 .02827 L .12237 .02768 L .12234 .02709 L .1223 .0265 L .12226 .02591 L .12222 .02532 L .12218 .02473 L .12214 .02414 L .1221 .02355 L .12207 .02296 L .12203 .02237 L .12199 .02179 L .12195 .0212 L .12191 .02061 L .12187 .02002 L .12184 .01943 L .1218 .01884 L .12176 .01825 L .12172 .01766 L .12168 .01707 L .12164 .01648 L .12161 .01589 L .12157 .0153 L .12156 .01513 L .12153 .01472 L Mistroke Mfstroke .35 g .012 w [ .12 .08 ] 0 setdash .12926 .12622 m .12929 .12666 L .12934 .12725 L .12926 .12757 L .12913 .12725 L .12891 .12666 L .12926 .12622 L s .02478 .08236 m .02479 .08247 L .02485 .08306 L .02492 .08365 L .02499 .08424 L .02505 .08483 L .02512 .08542 L .02519 .08601 L .02526 .0866 L .02533 .08719 L .02478 .08775 L .02474 .08719 L .02471 .0866 L .02467 .08601 L .02464 .08542 L .0246 .08483 L .02457 .08424 L .02453 .08365 L .02449 .08306 L .02446 .08247 L .02478 .08236 L s .08636 .07177 m .08746 .07153 L .08856 .07137 L .08966 .07131 L .09076 .07135 L .09186 .07147 L .09296 .07169 L .09363 .07187 L .09406 .072 L .09516 .07241 L .09528 .07246 L .09626 .0729 L .09654 .07305 L .09736 .0735 L .0976 .07363 L .09846 .07418 L .09853 .07422 L .09937 .07481 L .09956 .07495 L .10014 .0754 L .10066 .07582 L .10087 .07599 L .10154 .07658 L .10176 .07678 L .10218 .07717 L .10279 .07776 L .10286 .07782 L .10338 .07835 L .10394 .07894 L .10396 .07896 L .10447 .07953 L .105 .08012 L .10506 .08019 L .1055 .0807 L .10599 .08129 L .10616 .0815 L .10646 .08188 L .10692 .08247 L .10726 .0829 L .10737 .08306 L .10781 .08365 L .10825 .08424 L .10836 .08439 L .10865 .08483 L .10907 .08542 L .10946 .08596 L .10948 .08601 L .10983 .0866 L .11024 .08719 L .11056 .08762 L Mistroke .11066 .08778 L .11104 .08836 L .11132 .08895 L .11166 .08936 L .11177 .08954 L .11213 .09013 L .11249 .09072 L .11276 .09118 L .11283 .09131 L .11318 .0919 L .11352 .09249 L .11385 .09308 L .11386 .09309 L .11399 .09308 L .11409 .09249 L .11418 .0919 L .11428 .09131 L .11437 .09072 L .11447 .09013 L .11457 .08954 L .11467 .08895 L .11477 .08836 L .11491 .08778 L .11496 .08727 L .11497 .08719 L .11508 .0866 L .11519 .08601 L .1153 .08542 L .11541 .08483 L .11553 .08424 L .11564 .08365 L .11576 .08306 L .11588 .08247 L .116 .08188 L .11606 .08162 L .11613 .08129 L .11626 .0807 L .11639 .08012 L .11653 .07953 L .11668 .07894 L .11683 .07835 L .11698 .07776 L .11714 .07717 L .11716 .07712 L .11731 .07658 L .11748 .07599 L .11767 .0754 L .11788 .07481 L .1181 .07422 L .11826 .07385 L Mistroke .1183 .07363 L .11847 .07305 L .11878 .07246 L .11936 .07189 L .11938 .07187 L .12046 .07132 L .1213 .07187 L .12156 .07221 L .12171 .07246 L .12203 .07305 L .12229 .07363 L .12251 .07422 L .12266 .07463 L .12273 .07481 L .12294 .0754 L .12313 .07599 L .1233 .07658 L .12346 .07717 L .12359 .07776 L .1237 .07835 L .12376 .07869 L .12382 .07894 L .12395 .07953 L .12408 .08012 L .12421 .0807 L .12433 .08129 L .12444 .08188 L .12455 .08247 L .12465 .08306 L .12474 .08365 L .12483 .08424 L .12486 .08444 L .12492 .08483 L .12502 .08542 L .12512 .08601 L .12521 .0866 L .12531 .08719 L .1254 .08778 L .12548 .08836 L .12557 .08895 L .12565 .08954 L .12573 .09013 L .12581 .09072 L .12588 .09131 L .12595 .0919 L .12596 .09199 L .12602 .09249 L .1261 .09308 L .12618 .09367 L .12626 .09426 L Mistroke .12633 .09485 L .1264 .09543 L .12648 .09602 L .12655 .09661 L .12662 .0972 L .12669 .09779 L .12675 .09838 L .12682 .09897 L .12688 .09956 L .12694 .10015 L .127 .10074 L .12705 .10133 L .12706 .10141 L .12711 .10192 L .12718 .1025 L .12724 .10309 L .12731 .10368 L .12737 .10427 L .12744 .10486 L .1275 .10545 L .12757 .10604 L .12763 .10663 L .12769 .10722 L .12776 .10781 L .12782 .1084 L .12788 .10899 L .12794 .10958 L .128 .11016 L .12806 .11075 L .12811 .11134 L .12808 .11193 L .12813 .11252 L .12816 .11279 L .12819 .11311 L .12825 .1137 L .12831 .11429 L .12838 .11488 L .12845 .11547 L .12853 .11606 L .12849 .11665 L .12854 .11723 L .12859 .11782 L .12864 .11841 L .12869 .119 L .12873 .11959 L .12878 .12018 L .12883 .12077 L .12888 .12136 L .12892 .12195 L .12897 .12254 L Mistroke .12902 .12313 L .12906 .12372 L .12911 .1243 L .12816 .12466 L .12802 .1243 L .12779 .12372 L .12757 .12313 L .12734 .12254 L .12711 .12195 L .12706 .12182 L .12688 .12136 L .12665 .12077 L .12641 .12018 L .12618 .11959 L .12596 .11904 L .12594 .119 L .12565 .11841 L .12535 .11782 L .12506 .11723 L .12499 .11665 L .12486 .11632 L .12474 .11606 L .12448 .11547 L .12422 .11488 L .12398 .11429 L .12377 .1137 L .12376 .11367 L .12351 .11311 L .12326 .11252 L .123 .11193 L .12276 .11134 L .12266 .11109 L .12251 .11075 L .12225 .11016 L .12199 .10958 L .12173 .10899 L .12156 .10858 L .12147 .1084 L .12121 .10781 L .12094 .10722 L .12068 .10663 L .12046 .10615 L .12041 .10604 L .12014 .10545 L .11987 .10486 L .11959 .10427 L .11936 .10378 L .11931 .10368 L .11904 .10309 L .11876 .1025 L Mistroke .11847 .10192 L .11826 .10149 L .11819 .10133 L .11791 .10074 L .11762 .10015 L .11731 .09956 L .11716 .09927 L .1171 .09897 L .11685 .09838 L .11649 .09779 L .1161 .0972 L .11606 .09713 L .11578 .09661 L .11547 .09602 L .11516 .09543 L .11496 .09507 L .11484 .09485 L .11451 .09426 L .11386 .09401 L .11382 .09426 L .11373 .09485 L .11365 .09543 L .11356 .09602 L .11347 .09661 L .11339 .0972 L .11331 .09779 L .11322 .09838 L .11314 .09897 L .1129 .09956 L .11287 .10015 L .11283 .10074 L .11279 .10133 L .11276 .10176 L .11274 .10192 L .11265 .1025 L .11257 .10309 L .11249 .10368 L .11241 .10427 L .11234 .10486 L .11226 .10545 L .11219 .10604 L .11211 .10663 L .11204 .10722 L .11197 .10781 L .1119 .1084 L .11183 .10899 L .11176 .10958 L .11169 .11016 L .11166 .11044 L .11162 .11075 L Mistroke .11155 .11134 L .11148 .11193 L .11141 .11252 L .11134 .11311 L .11127 .1137 L .1112 .11429 L .11113 .11488 L .11107 .11547 L .111 .11606 L .11093 .11665 L .11087 .11723 L .1108 .11782 L .11073 .11841 L .11067 .119 L .1106 .11959 L .11056 .12 L .11054 .12018 L .11047 .12077 L .11041 .12136 L .11035 .12195 L .11028 .12254 L .11022 .12313 L .11015 .12372 L .11009 .1243 L .11003 .12489 L .10997 .12548 L .1099 .12607 L .10984 .12666 L .10978 .12725 L .10972 .12784 L .10966 .12843 L .1096 .12902 L .10954 .12961 L .10948 .1302 L .10946 .13036 L .10942 .13079 L .10936 .13138 L .1093 .13196 L .10924 .13255 L .10918 .13314 L .10912 .13373 L .10906 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.50669 L .04986 .5061 L .0498 .50551 L .04975 .50492 L .04969 .50433 L .04964 .50375 L .04958 .50316 L .04953 .50257 L .04947 .50198 L .04942 .50139 L .04936 .5008 L .04931 .50021 L .04925 .49962 L .0492 .49903 L .04914 .49844 L .04909 .49785 L .04904 .49726 L .04898 .49667 L .04897 .49654 L .04893 .49609 L .04888 .4955 L .04882 .49491 L Mistroke .04877 .49432 L .04872 .49373 L .04867 .49314 L .04862 .49255 L .04856 .49196 L .04851 .49137 L .04846 .49078 L .04841 .49019 L .04836 .4896 L .04831 .48902 L .04825 .48843 L .0482 .48784 L .04815 .48725 L .0481 .48666 L .04805 .48607 L .048 .48548 L .04795 .48489 L .0479 .4843 L .04787 .48394 L .04785 .48371 L .0478 .48312 L .04775 .48253 L .0477 .48195 L .04765 .48136 L .04761 .48077 L .04756 .48018 L .04751 .47959 L .04746 .479 L .04741 .47841 L .04736 .47782 L .04731 .47723 L .04727 .47664 L .04722 .47605 L .04717 .47546 L .04712 .47487 L .04707 .47429 L .04703 .4737 L .04698 .47311 L .04693 .47252 L .04688 .47193 L .04684 .47134 L .04679 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.04416 .4354 L .04411 .43481 L .04407 .43422 L .04403 .43363 L .04399 .43304 L .04395 .43245 L .04391 .43186 L .04387 .43127 L .04383 .43069 L .04379 .4301 L .04375 .42951 L .0437 .42892 L .04366 .42833 L .04362 .42774 L .04358 .42715 L .04354 .42656 L .0435 .42597 L .04347 .42553 L .04346 .42538 L .04342 .42479 L .04338 .4242 L .04334 .42362 L .0433 .42303 L .04326 .42244 L .04322 .42185 L .04318 .42126 L .04314 .42067 L .0431 .42008 L .04306 .41949 L .04303 .4189 L .04299 .41831 L .04295 .41772 L .04291 .41713 L .04287 .41654 L .04283 .41596 L .04279 .41537 L .04275 .41478 L .04271 .41419 L .04267 .4136 L .04263 .41301 L .0426 .41242 L .04256 .41183 L .04252 .41124 L .04248 .41065 L .04244 .41006 L .0424 .40947 L Mistroke .04237 .40903 L .04236 .40889 L .04232 .4083 L .04229 .40771 L .04225 .40712 L .04221 .40653 L .04217 .40594 L .04213 .40535 L .0421 .40476 L .04206 .40417 L .04202 .40358 L .04198 .40299 L .04194 .4024 L .04191 .40181 L .04187 .40123 L .04183 .40064 L .04179 .40005 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.32817 L .03747 .32758 L .03744 .32699 L .03741 .3264 L .03738 .32581 L .03734 .32522 L .03731 .32463 L .03728 .32404 L Mistroke .03724 .32345 L .03721 .32286 L .03718 .32227 L .03714 .32168 L .03711 .3211 L .03708 .32051 L .03705 .31992 L .03701 .31933 L .03698 .31874 L .03695 .31815 L .03692 .31756 L .03688 .31697 L .03687 .3168 L .03685 .31638 L .03682 .31579 L .03679 .3152 L .03675 .31461 L .03672 .31403 L .03669 .31344 L .03666 .31285 L .03662 .31226 L .03659 .31167 L .03656 .31108 L .03653 .31049 L .03649 .3099 L .03646 .30931 L .03643 .30872 L .0364 .30813 L .03636 .30754 L .03633 .30695 L .0363 .30637 L .03627 .30578 L .03624 .30519 L .0362 .3046 L .03617 .30401 L .03614 .30342 L .03611 .30283 L .03607 .30224 L .03604 .30165 L .03601 .30106 L .03598 .30047 L .03595 .29988 L .03591 .2993 L .03588 .29871 L .03585 .29812 L .03582 .29753 L .03579 .29694 L .03577 .29671 L .03575 .29635 L .03572 .29576 L Mistroke .03569 .29517 L .03566 .29458 L .03563 .29399 L .0356 .2934 L .03556 .29281 L .03553 .29222 L .0355 .29164 L .03547 .29105 L .03544 .29046 L .03541 .28987 L .03537 .28928 L .03534 .28869 L .03531 .2881 L .03528 .28751 L .03525 .28692 L .03522 .28633 L .03518 .28574 L .03515 .28515 L .03512 .28457 L .03509 .28398 L .03506 .28339 L .03503 .2828 L .03499 .28221 L .03496 .28162 L .03493 .28103 L .0349 .28044 L .03487 .27985 L .03484 .27926 L .03481 .27867 L .03478 .27808 L .03474 .2775 L .03471 .27691 L .03468 .27632 L .03467 .27619 L .03465 .27573 L .03462 .27514 L .03459 .27455 L .03456 .27396 L .03453 .27337 L .03449 .27278 L .03446 .27219 L .03443 .2716 L .0344 .27101 L .03437 .27042 L .03434 .26984 L .03431 .26925 L .03428 .26866 L .03424 .26807 L .03421 .26748 L .03418 .26689 L Mistroke .03415 .2663 L .03412 .26571 L .03409 .26512 L .03406 .26453 L .03403 .26394 L .034 .26335 L .03397 .26277 L .03393 .26218 L .0339 .26159 L .03387 .261 L .03384 .26041 L .03381 .25982 L .03378 .25923 L .03375 .25864 L .03372 .25805 L .03369 .25746 L .03366 .25687 L .03363 .25628 L .0336 .2557 L .03357 .2553 L .03356 .25511 L .03353 .25452 L .0335 .25393 L .03347 .25334 L .03344 .25275 L .03341 .25216 L .03338 .25157 L .03335 .25098 L .03332 .25039 L .03329 .2498 L .03326 .24921 L .03323 .24862 L .0332 .24804 L .03316 .24745 L .03313 .24686 L .0331 .24627 L .03307 .24568 L .03304 .24509 L .03301 .2445 L .03298 .24391 L .03295 .24332 L .03292 .24273 L .03289 .24214 L .03286 .24155 L .03283 .24097 L .0328 .24038 L .03277 .23979 L .03274 .2392 L .03271 .23861 L .03268 .23802 L Mistroke .03265 .23743 L .03261 .23684 L .03258 .23625 L .03255 .23566 L .03252 .23507 L .03249 .23448 L .03247 .23413 L .03246 .23389 L .03243 .23331 L .0324 .23272 L .03237 .23213 L .03234 .23154 L .03231 .23095 L .03228 .23036 L .03225 .22977 L .03222 .22918 L .03219 .22859 L .03216 .228 L .03213 .22741 L .0321 .22682 L .03207 .22624 L .03204 .22565 L .03201 .22506 L .03198 .22447 L .03195 .22388 L .03192 .22329 L .03189 .2227 L .03186 .22211 L .03183 .22152 L .03179 .22093 L .03176 .22034 L .03173 .21975 L .0317 .21917 L .03167 .21858 L .03164 .21799 L .03161 .2174 L .03158 .21681 L .03155 .21622 L .03152 .21563 L .03149 .21504 L .03146 .21445 L .03143 .21386 L .0314 .21327 L .03137 .21275 L .03137 .21268 L .03134 .21209 L .03131 .21151 L .03128 .21092 L .03125 .21033 L .03122 .20974 L Mistroke .03119 .20915 L .03116 .20856 L .03113 .20797 L .0311 .20738 L .03107 .20679 L .03104 .2062 L .03101 .20561 L .03098 .20502 L .03095 .20444 L .03092 .20385 L .03089 .20326 L .03086 .20267 L .03083 .20208 L .0308 .20149 L .03077 .2009 L .03074 .20031 L .03071 .19972 L .03068 .19913 L .03065 .19854 L .03062 .19795 L .03059 .19736 L .03056 .19678 L .03053 .19619 L .0305 .1956 L .03047 .19501 L .03044 .19442 L .03041 .19383 L .03038 .19324 L .03035 .19265 L .03032 .19206 L .03029 .19147 L .03028 .19128 L .03026 .19088 L .03023 .19029 L .03019 .18971 L .03016 .18912 L .03013 .18853 L .0301 .18794 L .03007 .18735 L .03004 .18676 L .03001 .18617 L .02998 .18558 L .02995 .18499 L .02992 .1844 L .02989 .18381 L .02986 .18322 L .02983 .18264 L .0298 .18205 L .02977 .18146 L .02974 .18087 L Mistroke .02971 .18028 L .02968 .17969 L .02965 .1791 L .02962 .17851 L .02959 .17792 L .02956 .17733 L .02953 .17674 L .0295 .17615 L .02947 .17556 L .02944 .17498 L .02941 .17439 L .02938 .1738 L .02935 .17321 L .02932 .17262 L .02929 .17203 L .02926 .17144 L .02923 .17085 L .0292 .17026 L .02918 .16981 L .02917 .16967 L .02914 .16908 L .02911 .16849 L .02908 .16791 L .02905 .16732 L .02902 .16673 L .02899 .16614 L .02896 .16555 L .02893 .16496 L .0289 .16437 L .02887 .16378 L .02883 .16319 L .0288 .1626 L .02877 .16201 L .02874 .16142 L .02871 .16083 L .02868 .16025 L .02865 .15966 L .02862 .15907 L .02859 .15848 L .02856 .15789 L .02853 .1573 L .0285 .15671 L .02847 .15612 L .02844 .15553 L .02841 .15494 L .02838 .15435 L .02835 .15376 L .02832 .15318 L .02829 .15259 L .02826 .152 L Mistroke .02823 .15141 L .0282 .15082 L .02817 .15023 L .02813 .14964 L .0281 .14905 L .02808 .1485 L .02807 .14846 L .02804 .14787 L .02801 .14728 L .02798 .14669 L .02795 .14611 L .02792 .14552 L .02789 .14493 L .02786 .14434 L .02783 .14375 L .0278 .14316 L .02776 .14257 L .02773 .14198 L .0277 .14139 L .02767 .1408 L .02764 .14021 L .02761 .13962 L .02758 .13903 L .02754 .13845 L .02751 .13786 L .02748 .13727 L .02745 .13668 L .02742 .13609 L .02739 .1355 L .02736 .13491 L .02732 .13432 L .02729 .13373 L .02726 .13314 L .02723 .13255 L .0272 .13196 L .02717 .13138 L .02714 .13079 L .02711 .1302 L .02708 .12961 L .02705 .12902 L .02702 .12843 L .02699 .12784 L .02698 .12752 L .02696 .12725 L .02693 .12666 L .02689 .12607 L .02686 .12548 L .02683 .12489 L .02679 .1243 L .02676 .12372 L Mistroke .02672 .12313 L .02669 .12254 L .02665 .12195 L .02661 .12136 L .02657 .12077 L .02653 .12018 L .02649 .11959 L .02645 .119 L .02641 .11841 L .02636 .11782 L .02631 .11723 L .02626 .11665 L .0262 .11606 L .02633 .11547 L .0263 .11488 L .02627 .11429 L .02623 .1137 L .0262 .11311 L .02617 .11252 L .02614 .11193 L .02611 .11134 L .02607 .11075 L .02604 .11016 L .02601 .10958 L .02598 .10899 L .02595 .1084 L .02591 .10781 L .02588 .10722 L .02588 .10714 L .02585 .10663 L .02582 .10604 L .02578 .10545 L .02575 .10486 L .02572 .10427 L .02568 .10368 L .02565 .10309 L .02562 .1025 L .02559 .10192 L .02555 .10133 L .02552 .10074 L .02549 .10015 L .02545 .09956 L .02542 .09897 L .02539 .09838 L .02535 .09779 L .02532 .0972 L .02529 .09661 L .02525 .09602 L .02522 .09543 L .02519 .09485 L Mistroke .02515 .09426 L .02512 .09367 L .02509 .09308 L .02505 .09249 L .02502 .0919 L .02588 .09152 L .02593 .0919 L .02601 .09249 L .02609 .09308 L .02617 .09367 L .02625 .09426 L .02634 .09485 L .02643 .09543 L .02651 .09602 L .0266 .09661 L .02669 .0972 L .02678 .09779 L .02687 .09838 L .02697 .09897 L .02698 .09902 L .02706 .09956 L .02716 .10015 L .02726 .10074 L .02736 .10133 L .02746 .10192 L .02757 .1025 L .02767 .10309 L .02778 .10368 L .02789 .10427 L .028 .10486 L .02808 .10524 L .02813 .10545 L .02831 .10604 L .0285 .10663 L .02847 .10722 L .0286 .10781 L .02872 .1084 L .02885 .10899 L .02898 .10958 L .02912 .11016 L .02918 .11041 L .02927 .11075 L .02943 .11134 L .0296 .11193 L .02977 .11252 L .02994 .11311 L .0301 .1137 L .03022 .11429 L .03028 .1147 L .03033 .11488 L Mistroke .03051 .11547 L .0307 .11606 L .03088 .11665 L .03107 .11723 L .03126 .11782 L .03137 .11822 L .03144 .11841 L .03166 .119 L .03188 .11959 L .03212 .12018 L .03235 .12077 L .03247 .12107 L .0326 .12136 L .03287 .12195 L .03316 .12254 L .03346 .12313 L .03357 .12334 L .03379 .12372 L .03415 .1243 L .03454 .12489 L .03467 .12508 L .03498 .12548 L .03549 .12607 L .03577 .12636 L .03609 .12666 L .03687 .12723 L .03689 .12725 L .03797 .12773 L .03841 .12784 L .03907 .12791 L .03991 .12784 L .04017 .12779 L .04127 .12741 L .04163 .12725 L .04237 .12679 L .04258 .12666 L .04336 .12607 L .04347 .12597 L .04404 .12548 L .04457 .12497 L .04465 .12489 L .04522 .1243 L .04567 .1238 L .04575 .12372 L .04626 .12313 L .04674 .12254 L .04677 .1225 L .04721 .12195 L .04766 .12136 L .04787 .12107 L Mistroke .04809 .12077 L .04852 .12018 L .04893 .11959 L .04897 .11954 L .04934 .119 L .04974 .11841 L .05007 .11791 L .05013 .11782 L .05052 .11723 L .0509 .11665 L .05117 .11622 L .05127 .11606 L .05164 .11547 L .05201 .11488 L .05227 .11445 L .05237 .11429 L .05273 .1137 L .05309 .11311 L .05337 .11264 L .05344 .11252 L .0538 .11193 L .05415 .11134 L .05447 .1108 L .0545 .11075 L .05484 .11016 L .05519 .10958 L .05553 .10899 L .05557 .10892 L .05588 .1084 L .05622 .10781 L .05656 .10722 L .05667 .10703 L .0569 .10663 L .05724 .10604 L .05758 .10545 L .05777 .10513 L .05792 .10486 L .05827 .10427 L .05861 .10368 L .05887 .10323 L .05895 .10309 L .05929 .1025 L .05963 .10192 L .05997 .10134 L .05998 .10133 L .06032 .10074 L .06067 .10015 L .06101 .09956 L .06107 .09946 L .06136 .09897 L Mistroke .06171 .09838 L .06206 .09779 L .06217 .09761 L .06241 .0972 L .06277 .09661 L .06312 .09602 L .06327 .09579 L .06348 .09543 L .06384 .09485 L .06421 .09426 L .06437 .094 L .06458 .09367 L .06494 .09308 L .06532 .09249 L .06547 .09225 L .06569 .0919 L .06607 .09131 L .06646 .09072 L .06657 .09055 L .06684 .09013 L .06724 .08954 L .06763 .08895 L .06767 .0889 L .06803 .08836 L .06844 .08778 L .06877 .0873 L .06885 .08719 L .06927 .0866 L .06969 .08601 L .06987 .08577 L .07012 .08542 L .07056 .08483 L .07097 .0843 L .07101 .08424 L .07146 .08365 L .07193 .08306 L .07207 .08289 L .0724 .08247 L .07289 .08188 L .07317 .08155 L .07339 .08129 L .0739 .0807 L .07427 .08029 L .07442 .08012 L .07496 .07953 L .07537 .0791 L .07552 .07894 L .0761 .07835 L .07647 .07798 L .0767 .07776 L Mistroke .07733 .07717 L .07757 .07695 L .07798 .07658 L .07867 .076 L .07868 .07599 L .07942 .0754 L .07977 .07514 L .0802 .07481 L .08087 .07435 L .08106 .07422 L .08197 .07366 L .08201 .07363 L .08306 .07305 L .08308 .07305 L .08416 .07254 L .08435 .07246 L .08526 .07211 L .08601 .07187 L .08636 .07177 L Mfstroke .97619 .60332 m .97615 .60273 L .97611 .60214 L .97609 .60195 L .97606 .60155 L .97602 .60096 L .97598 .60037 L .97593 .59978 L .97589 .59919 L .97585 .59861 L .97581 .59802 L .97576 .59743 L .97572 .59684 L .97568 .59625 L .97563 .59566 L .97559 .59507 L .97555 .59448 L .9755 .59389 L .97546 .5933 L .97542 .59271 L .97537 .59212 L .97533 .59154 L .97529 .59095 L .97524 .59036 L .9752 .58977 L .97516 .58918 L .97511 .58859 L .97507 .588 L .97503 .58741 L .97499 .58694 L .97498 .58682 L .97494 .58623 L .9749 .58564 L .97485 .58505 L .97481 .58446 L .97476 .58388 L .97472 .58329 L .97468 .5827 L .97463 .58211 L .97459 .58152 L .97455 .58093 L .9745 .58034 L .97446 .57975 L .97441 .57916 L .97437 .57857 L .97432 .57798 L .97428 .57739 L .97424 .57681 L .97419 .57622 L .97415 .57563 L Mistroke .9741 .57504 L .97406 .57445 L .97401 .57386 L .97397 .57327 L .97393 .57268 L .97389 .57223 L .97388 .57209 L .97384 .5715 L .97379 .57091 L .97375 .57032 L 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.60106 .07131 L .59996 .07133 L .59886 .07136 L .59777 .07141 L .59667 .07149 L .59557 .07158 L .59447 .07169 L .59337 .07183 L .59306 .07187 L .59227 .07198 L .59117 .07215 L .59007 .07235 L .58952 .07246 L .58897 .07257 L Mistroke .58787 .07281 L .58685 .07305 L .58677 .07307 L .58567 .07335 L .58463 .07363 L .58457 .07365 L .58347 .07398 L .58268 .07422 L .58237 .07432 L .58127 .07469 L .58093 .07481 L .58017 .07509 L .57933 .0754 L .57907 .0755 L .57797 .07594 L .57785 .07599 L .57687 .0764 L .57646 .07658 L .57577 .07689 L .57515 .07717 L .57467 .07739 L .57391 .07776 L .57357 .07793 L .57273 .07835 L .57247 .07848 L .5716 .07894 L .57137 .07906 L .57051 .07953 L .57027 .07966 L .56947 .08012 L .56917 .08029 L .56846 .0807 L .56807 .08094 L .56748 .08129 L .56697 .08161 L .56654 .08188 L .56587 .08231 L .56562 .08247 L .56477 .08303 L .56473 .08306 L .56386 .08365 L .56367 .08378 L .56301 .08424 L .56257 .08455 L .56219 .08483 L .56147 .08535 L .56138 .08542 L .56059 .08601 L .56037 .08617 L .55981 .0866 L Mistroke .55927 .08702 L .55906 .08719 L .55831 .08778 L .55817 .08789 L .55758 .08836 L .55707 .08878 L .55687 .08895 L .55616 .08954 L .55597 .0897 L .55547 .09013 L .55487 .09065 L .55479 .09072 L .55412 .09131 L .55377 .09162 L .55346 .0919 L .55281 .09249 L .55267 .09262 L .55217 .09308 L .55157 .09364 L .55154 .09367 L .55092 .09426 L .55047 .09469 L .55031 .09485 L .5497 .09543 L .54937 .09576 L .54911 .09602 L .54852 .09661 L .54827 .09686 L .54793 .0972 L .54736 .09779 L .54717 .09798 L .54679 .09838 L .54622 .09897 L .54608 .09913 L .54567 .09956 L .54512 .10015 L .54498 .1003 L .54457 .10074 L .54403 .10133 L .54388 .1015 L .5435 .10192 L .54297 .1025 L .54278 .10272 L .54245 .10309 L .54193 .10368 L .54168 .10397 L .54142 .10427 L .54091 .10486 L .54058 .10525 L .5404 .10545 L Mistroke .53991 .10604 L .53948 .10655 L .53941 .10663 L .53892 .10722 L .53843 .10781 L .53838 .10788 L .53795 .1084 L .53747 .10899 L .53728 .10923 L .537 .10958 L .53653 .11016 L .53618 .11061 L .53606 .11075 L .5356 .11134 L .53514 .11193 L .53508 .11201 L .53468 .11252 L .53423 .11311 L .53398 .11344 L .53378 .1137 L .53333 .11429 L .53289 .11488 L .53288 .11489 L .53245 .11547 L .53201 .11606 L .53178 .11637 L .53157 .11665 L .53114 .11723 L .53071 .11782 L .53068 .11787 L .53029 .11841 L .52986 .119 L .52958 .1194 L .52944 .11959 L .52902 .12018 L .52861 .12077 L .52848 .12096 L .5282 .12136 L .52778 .12195 L .52738 .12253 L .52738 .12254 L .52697 .12313 L .52657 .12372 L .52628 .12414 L .52617 .1243 L .52577 .12489 L .52537 .12548 L .52518 .12577 L .52498 .12607 L .52458 .12666 L Mistroke .52419 .12725 L .52408 .12742 L .5238 .12784 L .52342 .12843 L .52303 .12902 L .52298 .1291 L .52265 .12961 L .52227 .1302 L .52189 .13079 L .52188 .1308 L .52152 .13138 L .52114 .13196 L .52078 .13253 L .52077 .13255 L .5204 .13314 L .52003 .13373 L .51968 .13429 L .51966 .13432 L .51929 .13491 L .51893 .1355 L .51858 .13606 L .51856 .13609 L .5182 .13668 L .51784 .13727 L .51749 .13786 L .51748 .13787 L .51713 .13845 L .51677 .13903 L .51642 .13962 L .51638 .13969 L .51607 .14021 L .51572 .1408 L .51537 .14139 L .51528 .14154 L .51502 .14198 L .51468 .14257 L .51433 .14316 L .51418 .14342 L .51399 .14375 L .51365 .14434 L .5133 .14493 L .51308 .14531 L .51296 .14552 L .51263 .14611 L .51229 .14669 L .51198 .14724 L .51195 .14728 L .51162 .14787 L .51129 .14846 L .51095 .14905 L Mistroke .51088 .14918 L .51062 .14964 L .51029 .15023 L .50997 .15082 L .50978 .15115 L .50964 .15141 L .50931 .152 L .50899 .15259 L .50868 .15314 L .50866 .15318 L .50834 .15376 L .50802 .15435 L .5077 .15494 L .50758 .15516 L .50738 .15553 L .50706 .15612 L .50674 .15671 L .50648 .1572 L .50643 .1573 L .50611 .15789 L .5058 .15848 L .50548 .15907 L .50538 .15926 L .50517 .15966 L .50486 .16025 L .50455 .16083 L .50428 .16134 L .50424 .16142 L .50393 .16201 L .50362 .1626 L .50332 .16319 L .50318 .16345 L .50301 .16378 L .50271 .16437 L .5024 .16496 L .5021 .16555 L .50208 .16558 L .5018 .16614 L .5015 .16673 L .5012 .16732 L .50098 .16773 L .5009 .16791 L .5006 .16849 L .5003 .16908 L .5 .16967 L .49988 .1699 L .4997 .17026 L .49941 .17085 L .49911 .17144 L .49882 .17203 L Mistroke .49878 .1721 L .49853 .17262 L .49823 .17321 L .49794 .1738 L .49768 .17432 L .49765 .17439 L .49736 .17498 L .49707 .17556 L .49678 .17615 L .49658 .17656 L .49649 .17674 L .49621 .17733 L .49592 .17792 L .49563 .17851 L .49548 .17882 L .49535 .1791 L .49506 .17969 L .49478 .18028 L .4945 .18087 L .49439 .1811 L .49421 .18146 L .49393 .18205 L .49365 .18264 L .49337 .18322 L .49329 .1834 L .49309 .18381 L .49281 .1844 L .49253 .18499 L .49225 .18558 L .49219 .18572 L .49198 .18617 L .4917 .18676 L .49142 .18735 L .49115 .18794 L .49109 .18807 L .49087 .18853 L .4906 .18912 L .49032 .18971 L .49005 .19029 L .48999 .19043 L .48978 .19088 L .4895 .19147 L .48923 .19206 L .48896 .19265 L .48889 .19282 L .48869 .19324 L .48842 .19383 L .48815 .19442 L .48788 .19501 L .48779 .19522 L Mistroke .48761 .1956 L .48735 .19619 L .48708 .19678 L .48681 .19736 L .48669 .19764 L .48655 .19795 L .48628 .19854 L .48602 .19913 L .48575 .19972 L .48559 .20009 L .48549 .20031 L .48522 .2009 L .48496 .20149 L .4847 .20208 L .48449 .20255 L .48443 .20267 L .48417 .20326 L .48391 .20385 L .48365 .20444 L .48339 .20502 L .48339 .20503 L .48313 .20561 L .48287 .2062 L .48261 .20679 L .48235 .20738 L .48229 .20753 L .48209 .20797 L .48184 .20856 L .48158 .20915 L .48132 .20974 L .48119 .21005 L .48107 .21033 L .48081 .21092 L .48055 .21151 L .4803 .21209 L .48009 .21258 L .48004 .21268 L .47979 .21327 L .47954 .21386 L .47928 .21445 L .47903 .21504 L .47899 .21514 L .47878 .21563 L .47852 .21622 L .47827 .21681 L .47802 .2174 L .47789 .21771 L .47777 .21799 L .47752 .21858 L .47727 .21917 L Mistroke .47702 .21975 L .47679 .2203 L .47677 .22034 L .47652 .22093 L .47627 .22152 L .47602 .22211 L .47577 .2227 L .47569 .2229 L .47553 .22329 L .47528 .22388 L .47503 .22447 L .47478 .22506 L .47459 .22552 L .47454 .22565 L .47429 .22624 L .47405 .22682 L .4738 .22741 L .47356 .228 L .47349 .22816 L .47331 .22859 L .47307 .22918 L .47282 .22977 L .47258 .23036 L .47239 .23082 L .47233 .23095 L .47209 .23154 L .47185 .23213 L .47161 .23272 L .47136 .23331 L .47129 .23349 L .47112 .23389 L .47088 .23448 L .47064 .23507 L .4704 .23566 L .47019 .23617 L .47016 .23625 L .46992 .23684 L .46968 .23743 L .46944 .23802 L .4692 .23861 L .46909 .23888 L .46896 .2392 L .46872 .23979 L .46848 .24038 L .46824 .24097 L .46801 .24155 L .46799 .24159 L .46777 .24214 L .46753 .24273 L .46729 .24332 L Mistroke .46706 .24391 L .46689 .24432 L .46682 .2445 L .46658 .24509 L .46635 .24568 L .46611 .24627 L .46588 .24686 L .46579 .24707 L .46564 .24745 L .4654 .24804 L .46517 .24862 L .46494 .24921 L .4647 .2498 L .46469 .24983 L .46447 .25039 L .46423 .25098 L .464 .25157 L .46377 .25216 L .46359 .2526 L .46353 .25275 L .4633 .25334 L .46307 .25393 L .46283 .25452 L .4626 .25511 L .46249 .25539 L .46237 .2557 L .46214 .25628 L .46191 .25687 L .46168 .25746 L .46144 .25805 L .46139 .25819 L .46121 .25864 L .46098 .25923 L .46075 .25982 L .46052 .26041 L .46029 .261 L .46029 .261 L .46006 .26159 L .45983 .26218 L .4596 .26277 L .45937 .26335 L .45919 .26382 L .45915 .26394 L .45892 .26453 L .45869 .26512 L .45846 .26571 L .45823 .2663 L .45809 .26666 L .458 .26689 L .45778 .26748 L Mistroke .45755 .26807 L .45732 .26866 L .45709 .26925 L .45699 .26951 L .45687 .26984 L .45664 .27042 L .45641 .27101 L .45619 .2716 L .45596 .27219 L .45589 .27237 L .45573 .27278 L .45551 .27337 L .45528 .27396 L .45506 .27455 L .45483 .27514 L .45479 .27524 L .45461 .27573 L .45438 .27632 L .45416 .27691 L .45393 .2775 L .45371 .27808 L .45369 .27812 L .45348 .27867 L .45326 .27926 L .45303 .27985 L .45281 .28044 L .45259 .28101 L .45258 .28103 L .45236 .28162 L .45214 .28221 L .45191 .2828 L .45169 .28339 L .45149 .28391 L .45147 .28398 L .45125 .28457 L .45102 .28515 L .4508 .28574 L .45058 .28633 L .45039 .28682 L .45035 .28692 L .45013 .28751 L .44991 .2881 L .44969 .28869 L .44947 .28928 L .44929 .28974 L .44925 .28987 L .44902 .29046 L .4488 .29105 L .44858 .29164 L .44836 .29222 L Mistroke .44819 .29267 L .44814 .29281 L .44792 .2934 L .4477 .29399 L .44748 .29458 L .44726 .29517 L .44709 .2956 L .44704 .29576 L .44682 .29635 L .4466 .29694 L .44638 .29753 L .44616 .29812 L .44599 .29855 L .44594 .29871 L .44572 .2993 L .4455 .29988 L .44528 .30047 L .44506 .30106 L .44489 .3015 L .44484 .30165 L .44462 .30224 L .4444 .30283 L .44418 .30342 L .44396 .30401 L .44379 .30446 L .44374 .3046 L .44352 .30519 L .44331 .30578 L .44309 .30637 L .44287 .30695 L .4427 .30742 L .44265 .30754 L .44243 .30813 L .44221 .30872 L .442 .30931 L .44178 .3099 L .4416 .3104 L .44156 .31049 L .44134 .31108 L .44113 .31167 L .44091 .31226 L .44069 .31285 L .4405 .31337 L .44047 .31344 L .44026 .31403 L .44004 .31461 L .43982 .3152 L .4396 .31579 L .4394 .31636 L .43939 .31638 L Mistroke .43917 .31697 L .43895 .31756 L .43874 .31815 L .43852 .31874 L .4383 .31933 L .4383 .31935 L .43809 .31992 L .43787 .32051 L .43765 .3211 L .43744 .32168 L .43722 .32227 L .4372 .32234 L .437 .32286 L .43679 .32345 L .43657 .32404 L .43636 .32463 L .43614 .32522 L .4361 .32534 L .43592 .32581 L .43571 .3264 L .43549 .32699 L .43528 .32758 L .43506 .32817 L .435 .32834 L .43484 .32875 L .43463 .32934 L .43441 .32993 L .4342 .33052 L .43398 .33111 L .4339 .33135 L .43377 .3317 L .43355 .33229 L .43334 .33288 L .43312 .33347 L .43291 .33406 L .4328 .33435 L .43269 .33465 L .43247 .33524 L .43226 .33583 L .43204 .33641 L .43183 .337 L .4317 .33737 L .43161 .33759 L .4314 .33818 L .43118 .33877 L .43097 .33936 L .43075 .33995 L .4306 .34038 L .43054 .34054 L .43032 .34113 L Mistroke .43011 .34172 L .42989 .34231 L .42968 .3429 L .4295 .34339 L .42946 .34348 L .42925 .34407 L .42903 .34466 L .42882 .34525 L .42861 .34584 L .4284 .34641 L .42839 .34643 L .42818 .34702 L .42796 .34761 L .42775 .3482 L .42753 .34879 L .42732 .34938 L .4273 .34943 L .4271 .34997 L .42689 .35056 L .42667 .35114 L .42646 .35173 L .42624 .35232 L .4262 .35245 L .42603 .35291 L .42581 .3535 L .4256 .35409 L .42538 .35468 L .42517 .35527 L .4251 .35546 L .42495 .35586 L .42474 .35645 L .42453 .35704 L .42431 .35763 L .4241 .35821 L .424 .35848 L .42388 .3588 L .42367 .35939 L .42345 .35998 L .42324 .36057 L .42302 .36116 L .4229 .3615 L .42281 .36175 L .42259 .36234 L .42238 .36293 L .42216 .36352 L .42195 .36411 L .4218 .36451 L .42173 .3647 L .42152 .36528 L .4213 .36587 L Mistroke .42109 .36646 L .42087 .36705 L .4207 .36753 L .42066 .36764 L .42044 .36823 L .42023 .36882 L .42001 .36941 L .4198 .37 L .4196 .37054 L .41958 .37059 L .41937 .37118 L .41915 .37177 L .41894 .37236 L .41872 .37294 L .4185 .37353 L .4185 .37355 L .41829 .37412 L .41807 .37471 L .41786 .3753 L .41764 .37589 L .41743 .37648 L .4174 .37655 L .41721 .37707 L .41699 .37766 L .41678 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.33589 .55677 L .33543 .55736 L .33497 .55795 L .33492 .55802 L .3345 .55854 L .33403 .55913 L .33382 .55939 L .33355 .55972 L .33306 .56031 L .33272 .56072 L .33257 .5609 L .33207 .56149 L .33162 .56201 L .33156 .56208 L .33105 .56266 L .33052 .56325 L .33052 .56326 L .32999 .56384 L .32945 .56443 L .32942 .56447 L .3289 .56502 L .32835 .56561 L .32832 .56564 L .32778 .5662 L .32722 .56677 L .3272 .56679 L .32661 .56738 L .32612 .56786 L .326 .56797 L .32539 .56856 L .32502 .5689 L .32476 .56915 L .32411 .56973 L .32392 .56991 L .32345 .57032 L .32282 .57087 L .32276 .57091 L .32206 .5715 L .32172 .57179 L .32134 .57209 L .32062 .57266 L .32059 .57268 L .31982 .57327 L .31952 .57349 L .31901 .57386 L .31842 .57428 L .31818 .57445 L .31732 .57502 L .3173 .57504 L Mistroke .31637 .57563 L .31622 .57572 L .3154 .57622 L .31512 .57638 L .31435 .57681 L .31402 .57699 L .31323 .57739 L .31292 .57755 L .312 .57798 L .31182 .57807 L .31072 .57854 L .31064 .57857 L .30962 .57897 L .30907 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.27225 .56443 L .27223 .56441 L .27175 .56384 L .27126 .56325 L .27113 .56309 L .27078 .56266 L .2703 .56208 L .27003 .56173 L .26983 .56149 L .26937 .5609 L .26893 .56032 L .26892 .56031 L .26847 .55972 L .26803 .55913 L .26783 .55886 L .2676 .55854 L .26717 .55795 L .26674 .55736 L .26673 .55734 L .26633 .55677 L .26591 .55618 L .26563 .55578 L .2655 .55559 L .2651 .55501 L Mistroke .2647 .55442 L .26453 .55416 L .26431 .55383 L .26392 .55324 L .26353 .55265 L .26343 .55249 L .26315 .55206 L .26277 .55147 L .2624 .55088 L .26233 .55077 L .26203 .55029 L .26166 .5497 L .2613 .54911 L .26123 .54901 L .26094 .54852 L .26058 .54793 L .26022 .54735 L .26013 .54719 L .25987 .54676 L .25953 .54617 L .25918 .54558 L .25903 .54532 L .25884 .54499 L .2585 .5444 L .25816 .54381 L .25793 .5434 L .25783 .54322 L .2575 .54263 L .25717 .54204 L .25684 .54145 L .25683 .54143 L .25652 .54086 L .2562 .54028 L .25588 .53969 L .25573 .53942 L .25556 .5391 L .25525 .53851 L .25493 .53792 L .25463 .53735 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.24106 .50787 L .24082 .50728 L .24058 .50669 L .24034 .5061 L .24033 .50608 L .2401 .50551 L .23987 .50492 L .23963 .50433 L .23939 .50375 L .23923 .50335 L .23916 .50316 L .23892 .50257 L .23869 .50198 L .23846 .50139 L .23822 .5008 L .23813 .50057 L .23799 .50021 L .23776 .49962 L .23753 .49903 L .2373 .49844 L .23708 .49785 L .23704 .49775 L .23685 .49726 L .23662 .49667 L .2364 .49609 L .23617 .4955 L .23595 .49491 L .23594 .49488 L .23572 .49432 L .2355 .49373 L .23528 .49314 L .23505 .49255 L .23484 .49197 L .23483 .49196 L .23461 .49137 L .23439 .49078 L .23417 .49019 L .23395 .4896 L .23374 .48902 L .23374 .48902 L .23352 .48843 L .2333 .48784 L .23308 .48725 L .23287 .48666 L .23265 .48607 L .23264 .48602 L .23244 .48548 L .23223 .48489 L .23201 .4843 L Mistroke .2318 .48371 L .23159 .48312 L .23154 .48298 L .23138 .48253 L .23116 .48195 L .23095 .48136 L .23074 .48077 L .23054 .48018 L .23044 .4799 L .23033 .47959 L .23012 .479 L .22991 .47841 L .2297 .47782 L .2295 .47723 L .22934 .47678 L .22929 .47664 L .22908 .47605 L .22888 .47546 L .22867 .47487 L .22847 .47429 L .22827 .4737 L .22824 .47361 L .22806 .47311 L .22786 .47252 L .22766 .47193 L .22746 .47134 L .22725 .47075 L .22714 .47041 L .22705 .47016 L .22685 .46957 L .22665 .46898 L .22645 .46839 L .22625 .4678 L .22605 .46722 L .22604 .46716 L .22586 .46663 L .22566 .46604 L .22546 .46545 L .22526 .46486 L .22507 .46427 L .22494 .46388 L .22487 .46368 L .22468 .46309 L .22448 .4625 L .22429 .46191 L .22409 .46132 L .2239 .46073 L .22384 .46056 L .2237 .46014 L .22351 .45956 L Mistroke .22332 .45897 L .22312 .45838 L .22293 .45779 L .22274 .4572 L .22274 .4572 L .22255 .45661 L .22236 .45602 L .22217 .45543 L .22198 .45484 L .22179 .45425 L .22164 .4538 L .2216 .45366 L .22141 .45307 L .22122 .45249 L .22103 .4519 L .22084 .45131 L .22065 .45072 L .22054 .45036 L .22046 .45013 L .22028 .44954 L .22009 .44895 L .2199 .44836 L .21972 .44777 L .21953 .44718 L .21944 .44689 L .21935 .44659 L .21916 .446 L .21898 .44542 L .21879 .44483 L .21861 .44424 L .21842 .44365 L .21834 .44338 L .21824 .44306 L .21805 .44247 L .21787 .44188 L .21769 .44129 L .21751 .4407 L .21732 .44011 L .21724 .43984 L .21714 .43952 L .21696 .43893 L .21678 .43834 L .2166 .43776 L .21642 .43717 L .21624 .43658 L .21614 .43626 L .21606 .43599 L .21588 .4354 L .2157 .43481 L .21552 .43422 L Mistroke .21534 .43363 L .21516 .43304 L .21504 .43265 L .21498 .43245 L .2148 .43186 L .21462 .43127 L .21445 .43069 L .21427 .4301 L .21409 .42951 L .21394 .42901 L .21391 .42892 L .21374 .42833 L .21356 .42774 L .21338 .42715 L .21321 .42656 L .21303 .42597 L .21286 .42538 L .21284 .42533 L .21268 .42479 L .21251 .4242 L .21233 .42362 L .21216 .42303 L .21198 .42244 L .21181 .42185 L .21174 .42162 L .21163 .42126 L .21146 .42067 L .21129 .42008 L .21111 .41949 L .21094 .4189 L .21077 .41831 L .21064 .41788 L .21059 .41772 L .21042 .41713 L .21025 .41654 L .21008 .41596 L .20991 .41537 L .20973 .41478 L .20956 .41419 L .20954 .41411 L .20939 .4136 L .20922 .41301 L .20905 .41242 L .20888 .41183 L .20871 .41124 L .20854 .41065 L .20844 .41031 L .20837 .41006 L .2082 .40947 L .20803 .40889 L Mistroke .20786 .4083 L .20769 .40771 L .20752 .40712 L .20735 .40653 L .20734 .40649 L .20718 .40594 L .20702 .40535 L .20685 .40476 L .20668 .40417 L .20651 .40358 L .20634 .40299 L .20624 .40263 L .20618 .4024 L .20601 .40181 L .20584 .40123 L .20567 .40064 L .20551 .40005 L .20534 .39946 L .20517 .39887 L .20514 .39875 L .20501 .39828 L .20484 .39769 L .20468 .3971 L .20451 .39651 L .20434 .39592 L .20418 .39533 L .20404 .39484 L .20401 .39474 L .20385 .39416 L .20368 .39357 L .20352 .39298 L .20335 .39239 L .20319 .3918 L .20303 .39121 L .20294 .39091 L .20286 .39062 L .2027 .39003 L .20253 .38944 L .20237 .38885 L .20221 .38826 L .20204 .38767 L .20188 .38709 L .20184 .38695 L .20172 .3865 L .20155 .38591 L .20139 .38532 L .20123 .38473 L .20106 .38414 L .2009 .38355 L .20074 .38297 L Mistroke .20074 .38296 L .20058 .38237 L .20041 .38178 L .20025 .38119 L .20009 .3806 L .19993 .38001 L .19977 .37943 L .19964 .37897 L .19961 .37884 L .19944 .37825 L .19928 .37766 L .19912 .37707 L .19896 .37648 L .1988 .37589 L .19864 .3753 L .19854 .37494 L .19848 .37471 L .19832 .37412 L .19816 .37353 L .198 .37294 L .19784 .37236 L .19768 .37177 L .19752 .37118 L .19744 .3709 L .19736 .37059 L .1972 .37 L .19704 .36941 L .19688 .36882 L .19672 .36823 L .19656 .36764 L .1964 .36705 L .19634 .36683 L .19624 .36646 L .19608 .36587 L .19593 .36528 L .19577 .3647 L .19561 .36411 L .19545 .36352 L .19529 .36293 L .19524 .36275 L .19513 .36234 L .19498 .36175 L .19482 .36116 L .19466 .36057 L .1945 .35998 L .19434 .35939 L .19419 .3588 L .19414 .35865 L .19403 .35821 L .19387 .35763 L Mistroke .19371 .35704 L .19356 .35645 L .1934 .35586 L .19324 .35527 L .19308 .35468 L .19304 .35453 L .19293 .35409 L .19277 .3535 L .19261 .35291 L .19246 .35232 L .1923 .35173 L .19214 .35114 L .19199 .35056 L .19194 .35039 L 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.31756 L .18317 .31697 L .18315 .31687 L .18302 .31638 L .18287 .31579 L .18271 .3152 L .18256 .31461 L .18241 .31403 L .18225 .31344 L .1821 .31285 L .18205 .31264 L .18195 .31226 L .18179 .31167 L .18164 .31108 L .18149 .31049 L .18134 .3099 L .18118 .30931 L .18103 .30872 L .18095 .3084 L .18088 .30813 L .18072 .30754 L .18057 .30695 L .18042 .30637 L .18027 .30578 L Mistroke .18011 .30519 L .17996 .3046 L .17985 .30416 L .17981 .30401 L .17965 .30342 L .1795 .30283 L .17935 .30224 L .1792 .30165 L .17904 .30106 L .17889 .30047 L .17875 .29992 L .17874 .29988 L .17858 .2993 L .17843 .29871 L .17828 .29812 L .17813 .29753 L .17797 .29694 L .17782 .29635 L .17767 .29576 L .17765 .29568 L .17752 .29517 L .17736 .29458 L .17721 .29399 L .17706 .2934 L .17691 .29281 L .17675 .29222 L .1766 .29164 L .17655 .29143 L .17645 .29105 L .17629 .29046 L .17614 .28987 L .17599 .28928 L .17584 .28869 L .17568 .2881 L .17553 .28751 L .17545 .28719 L .17538 .28692 L .17523 .28633 L .17507 .28574 L .17492 .28515 L .17477 .28457 L .17461 .28398 L .17446 .28339 L .17435 .28295 L .17431 .2828 L .17416 .28221 L .174 .28162 L .17385 .28103 L .1737 .28044 L .17354 .27985 L Mistroke .17339 .27926 L .17325 .27871 L .17324 .27867 L .17309 .27808 L .17293 .2775 L .17278 .27691 L .17263 .27632 L .17247 .27573 L .17232 .27514 L .17217 .27455 L .17215 .27448 L .17201 .27396 L .17186 .27337 L .17171 .27278 L .17155 .27219 L .1714 .2716 L .17125 .27101 L .17109 .27042 L .17105 .27025 L .17094 .26984 L .17079 .26925 L .17063 .26866 L .17048 .26807 L .17033 .26748 L .17017 .26689 L .17002 .2663 L .16995 .26603 L .16986 .26571 L .16971 .26512 L .16956 .26453 L .1694 .26394 L .16925 .26335 L .1691 .26277 L .16894 .26218 L .16885 .26182 L .16879 .26159 L .16863 .261 L .16848 .26041 L .16833 .25982 L .16817 .25923 L .16802 .25864 L .16786 .25805 L .16775 .25762 L .16771 .25746 L .16755 .25687 L .1674 .25628 L .16724 .2557 L .16709 .25511 L .16694 .25452 L .16678 .25393 L Mistroke .16665 .25343 L .16663 .25334 L .16647 .25275 L .16632 .25216 L .16616 .25157 L .16601 .25098 L .16585 .25039 L .16569 .2498 L .16555 .24925 L .16554 .24921 L .16538 .24862 L .16523 .24804 L .16507 .24745 L .16492 .24686 L .16476 .24627 L .16461 .24568 L .16445 .24509 L .16445 .24509 L .16429 .2445 L .16414 .24391 L .16398 .24332 L .16383 .24273 L .16367 .24214 L .16351 .24155 L .16336 .24097 L .16335 .24094 L .1632 .24038 L .16304 .23979 L .16289 .2392 L .16273 .23861 L .16257 .23802 L .16242 .23743 L .16226 .23684 L .16225 .2368 L .1621 .23625 L .16195 .23566 L .16179 .23507 L .16163 .23448 L .16147 .23389 L .16131 .23331 L .16116 .23272 L .16115 .23269 L .161 .23213 L .16084 .23154 L .16068 .23095 L .16053 .23036 L .16037 .22977 L .16021 .22918 L .16005 .22859 L .16005 .22859 L Mistroke .15989 .228 L .15973 .22741 L .15957 .22682 L .15941 .22624 L .15926 .22565 L .1591 .22506 L .15895 .22452 L .15894 .22447 L .15878 .22388 L .15862 .22329 L .15846 .2227 L .1583 .22211 L .15814 .22152 L .15798 .22093 L .15785 .22047 L .15782 .22034 L .15766 .21975 L .1575 .21917 L .15734 .21858 L .15718 .21799 L .15701 .2174 L .15685 .21681 L .15675 .21644 L .15669 .21622 L .15653 .21563 L .15637 .21504 L .15621 .21445 L .15605 .21386 L .15588 .21327 L .15572 .21268 L .15565 .21243 L .15556 .21209 L .1554 .21151 L .15523 .21092 L .15507 .21033 L .15491 .20974 L .15474 .20915 L .15458 .20856 L .15455 .20846 L .15442 .20797 L .15425 .20738 L .15409 .20679 L .15393 .2062 L .15376 .20561 L .1536 .20502 L .15345 .2045 L .15343 .20444 L .15327 .20385 L .1531 .20326 L .15294 .20267 L Mistroke .15277 .20208 L .15261 .20149 L .15244 .2009 L .15235 .20058 L .15228 .20031 L .15211 .19972 L .15194 .19913 L .15178 .19854 L .15161 .19795 L .15144 .19736 L .15128 .19678 L .15125 .19669 L .15111 .19619 L .15094 .1956 L .15078 .19501 L .15061 .19442 L .15044 .19383 L .15027 .19324 L .15015 .19283 L .1501 .19265 L .14993 .19206 L .14976 .19147 L .1496 .19088 L .14943 .19029 L .14925 .18971 L .14908 .18912 L .14905 .18901 L .14891 .18853 L .14875 .18794 L .14858 .18735 L .1484 .18676 L .14823 .18617 L .14806 .18558 L .14795 .18522 L .14789 .18499 L .14772 .1844 L .14755 .18381 L .14737 .18322 L .1472 .18264 L .14703 .18205 L .14685 .18146 L .14685 .18146 L .14668 .18087 L .14651 .18028 L .14633 .17969 L .14616 .1791 L .14598 .17851 L .1458 .17792 L .14575 .17775 L .14563 .17733 L Mistroke .14546 .17674 L .14528 .17615 L .14511 .17556 L .14493 .17498 L .14475 .17439 L .14465 .17407 L .14457 .1738 L .1444 .17321 L .14422 .17262 L .14404 .17203 L .14386 .17144 L .14368 .17085 L .14355 .17044 L .1435 .17026 L .14333 .16967 L .14315 .16908 L .14297 .16849 L .14279 .16791 L .1426 .16732 L .14245 .16684 L .14242 .16673 L .14224 .16614 L .14206 .16555 L .14188 .16496 L .1417 .16437 L .14151 .16378 L .14135 .16329 L .14132 .16319 L .14115 .1626 L .14097 .16201 L .14078 .16142 L .14059 .16083 L .1404 .16025 L .14025 .15979 L .14022 .15966 L .14004 .15907 L .13986 .15848 L .13967 .15789 L .13947 .1573 L .13928 .15671 L .13915 .15633 L .13909 .15612 L .13892 .15553 L .13873 .15494 L .13854 .15435 L .13834 .15376 L .13814 .15318 L .13805 .15292 L .13796 .15259 L .13779 .152 L Mistroke .13759 .15141 L .13739 .15082 L .13719 .15023 L .13698 .14964 L .13695 .14956 L .13683 .14905 L .13665 .14846 L .13644 .14787 L .13623 .14728 L .13602 .14669 L .13585 .14626 L .13583 .14611 L .1357 .14552 L .1355 .14493 L .13528 .14434 L .13505 .14375 L .13482 .14316 L .13475 .143 L .13461 .14257 L .13441 .14198 L .13438 .14139 L .13411 .1408 L .13384 .14021 L .13366 .1398 L .13359 .13962 L .13339 .13903 L .13318 .13845 L .13298 .13786 L .13277 .13727 L .13256 .13668 L .13256 .13666 L .13236 .13609 L .13215 .1355 L .13194 .13491 L .13173 .13432 L .13151 .13373 L .13146 .13357 L .1313 .13314 L .13109 .13255 L .13088 .13196 L .13066 .13138 L .13045 .13079 L .13036 .13054 L .12959 .13079 L .12964 .13138 L .12968 .13196 L .12972 .13255 L .12976 .13314 L .12981 .13373 L .12985 .13432 L Mistroke .12989 .13491 L .12993 .1355 L .12997 .13609 L .13001 .13668 L .12993 .13727 L .13002 .13786 L .13008 .13845 L .13014 .13903 L .13019 .13962 L .13024 .14021 L .13028 .1408 L .13033 .14139 L .13036 .14179 L .13036 .14198 L .13038 .14257 L .13042 .14316 L .13045 .14375 L .13049 .14434 L .13053 .14493 L .13058 .14552 L .13062 .14611 L .13065 .14669 L .13069 .14728 L .13073 .14787 L .13077 .14846 L .13081 .14905 L .13085 .14964 L .13089 .15023 L .13092 .15082 L .13096 .15141 L .131 .152 L .13104 .15259 L .13107 .15318 L .13111 .15376 L .13114 .15435 L .13118 .15494 L .13122 .15553 L .13125 .15612 L .13129 .15671 L .13132 .1573 L .13136 .15789 L .13139 .15848 L .13143 .15907 L .13146 .15958 L .13146 .15966 L .13149 .16025 L .13153 .16083 L .13156 .16142 L .13159 .16201 L .13163 .1626 L Mistroke .13166 .16319 L .1317 .16378 L .13173 .16437 L .13176 .16496 L .13179 .16555 L .13183 .16614 L .13186 .16673 L .13189 .16732 L .13193 .16791 L .13196 .16849 L .13199 .16908 L .13202 .16967 L .13206 .17026 L .13209 .17085 L .13212 .17144 L .13215 .17203 L .13218 .17262 L .13221 .17321 L .13225 .1738 L .13228 .17439 L .13231 .17498 L .13234 .17556 L .13237 .17615 L .1324 .17674 L .13243 .17733 L .13246 .17792 L .13249 .17851 L .13252 .1791 L .13256 .17969 L .13256 .17969 L .13259 .18028 L .13262 .18087 L .13265 .18146 L .13268 .18205 L .13271 .18264 L .13274 .18322 L .13277 .18381 L .1328 .1844 L .13283 .18499 L .13285 .18558 L .13288 .18617 L .13291 .18676 L .13294 .18735 L .13297 .18794 L .133 .18853 L .13303 .18912 L .13306 .18971 L .13309 .19029 L .13312 .19088 L .13315 .19147 L Mistroke .13317 .19206 L .1332 .19265 L .13323 .19324 L .13326 .19383 L .13329 .19442 L .13332 .19501 L .13334 .1956 L .13337 .19619 L .1334 .19678 L .13343 .19736 L .13346 .19795 L .13348 .19854 L .13351 .19913 L .13354 .19972 L .13357 .20031 L .13359 .2009 L .13362 .20149 L .13365 .20208 L .13366 .20221 L .13368 .20267 L .1337 .20326 L .13373 .20385 L .13376 .20444 L .13378 .20502 L .13381 .20561 L .13384 .2062 L .13386 .20679 L .13389 .20738 L .13392 .20797 L .13394 .20856 L .13397 .20915 L .134 .20974 L .13402 .21033 L .13405 .21092 L .13408 .21151 L .1341 .21209 L .13413 .21268 L .13416 .21327 L .13418 .21386 L .13421 .21445 L .13423 .21504 L .13426 .21563 L .13428 .21622 L .13431 .21681 L .13434 .2174 L .13436 .21799 L .13439 .21858 L .13441 .21917 L .13444 .21975 L .13446 .22034 L Mistroke .13449 .22093 L .13451 .22152 L .13454 .22211 L .13456 .2227 L .13459 .22329 L .13461 .22388 L .13464 .22447 L .13466 .22506 L .13469 .22565 L .13471 .22624 L .13474 .22682 L .13475 .22724 L .13476 .22741 L .13479 .228 L .13481 .22859 L .13484 .22918 L .13486 .22977 L .13488 .23036 L .13491 .23095 L .13493 .23154 L .13496 .23213 L .13498 .23272 L .13501 .23331 L .13503 .23389 L .13505 .23448 L .13508 .23507 L .1351 .23566 L .13513 .23625 L .13515 .23684 L .13517 .23743 L .1352 .23802 L .13522 .23861 L .13524 .2392 L .13527 .23979 L .13529 .24038 L .13531 .24097 L .13534 .24155 L .13536 .24214 L .13538 .24273 L .13541 .24332 L .13543 .24391 L .13545 .2445 L .13548 .24509 L .1355 .24568 L .13552 .24627 L .13555 .24686 L .13557 .24745 L .13559 .24804 L .13562 .24862 L .13564 .24921 L Mistroke .13566 .2498 L .13568 .25039 L .13571 .25098 L .13573 .25157 L .13575 .25216 L .13577 .25275 L .1358 .25334 L .13582 .25393 L .13584 .25452 L .13585 .25486 L .13586 .25511 L .13589 .2557 L .13591 .25628 L .13593 .25687 L .13595 .25746 L .13598 .25805 L .136 .25864 L .13602 .25923 L .13604 .25982 L .13606 .26041 L .13609 .261 L .13611 .26159 L .13613 .26218 L .13615 .26277 L .13617 .26335 L .13619 .26394 L .13622 .26453 L .13624 .26512 L .13626 .26571 L .13628 .2663 L .1363 .26689 L .13632 .26748 L .13635 .26807 L .13637 .26866 L .13639 .26925 L .13641 .26984 L .13643 .27042 L .13645 .27101 L .13647 .2716 L .1365 .27219 L .13652 .27278 L .13654 .27337 L .13656 .27396 L .13658 .27455 L .1366 .27514 L .13662 .27573 L .13664 .27632 L .13666 .27691 L .13668 .2775 L .13671 .27808 L Mistroke .13673 .27867 L .13675 .27926 L .13677 .27985 L .13679 .28044 L .13681 .28103 L .13683 .28162 L .13685 .28221 L .13687 .2828 L .13689 .28339 L .13691 .28398 L .13693 .28457 L .13695 .28515 L .13695 .28519 L .13697 .28574 L .13699 .28633 L .13701 .28692 L .13703 .28751 L .13706 .2881 L .13708 .28869 L .1371 .28928 L .13712 .28987 L .13714 .29046 L .13716 .29105 L .13718 .29164 L .1372 .29222 L .13722 .29281 L .13724 .2934 L .13726 .29399 L .13728 .29458 L .1373 .29517 L .13732 .29576 L .13734 .29635 L .13736 .29694 L .13738 .29753 L .1374 .29812 L .13742 .29871 L .13743 .2993 L .13745 .29988 L .13747 .30047 L .13749 .30106 L .13751 .30165 L .13753 .30224 L .13755 .30283 L .13757 .30342 L .13759 .30401 L .13761 .3046 L .13763 .30519 L .13765 .30578 L .13767 .30637 L .13769 .30695 L Mistroke .13771 .30754 L .13773 .30813 L .13775 .30872 L .13776 .30931 L .13778 .3099 L .1378 .31049 L .13782 .31108 L .13784 .31167 L .13786 .31226 L .13788 .31285 L .1379 .31344 L .13792 .31403 L .13794 .31461 L .13796 .3152 L .13797 .31579 L .13799 .31638 L .13801 .31697 L .13803 .31756 L .13805 .31815 L .13805 .3183 L .13807 .31874 L .13809 .31933 L .13811 .31992 L .13812 .32051 L .13814 .3211 L .13816 .32168 L .13818 .32227 L .1382 .32286 L .13822 .32345 L .13824 .32404 L .13825 .32463 L .13827 .32522 L .13829 .32581 L .13831 .3264 L .13833 .32699 L .13835 .32758 L .13836 .32817 L .13838 .32875 L .1384 .32934 L .13842 .32993 L .13844 .33052 L .13846 .33111 L .13847 .3317 L .13849 .33229 L .13851 .33288 L .13853 .33347 L .13855 .33406 L .13856 .33465 L .13858 .33524 L .1386 .33583 L Mistroke .13862 .33641 L .13864 .337 L .13865 .33759 L .13867 .33818 L .13869 .33877 L .13871 .33936 L .13873 .33995 L .13874 .34054 L .13876 .34113 L .13878 .34172 L .1388 .34231 L .13882 .3429 L .13883 .34348 L .13885 .34407 L .13887 .34466 L .13889 .34525 L .1389 .34584 L .13892 .34643 L .13894 .34702 L .13896 .34761 L .13897 .3482 L .13899 .34879 L .13901 .34938 L .13903 .34997 L .13904 .35056 L .13906 .35114 L .13908 .35173 L .1391 .35232 L .13911 .35291 L .13913 .3535 L .13915 .35409 L .13915 .35431 L .13916 .35468 L .13918 .35527 L .1392 .35586 L .13922 .35645 L .13923 .35704 L .13925 .35763 L .13927 .35821 L .13929 .3588 L .1393 .35939 L .13932 .35998 L .13934 .36057 L .13935 .36116 L .13937 .36175 L .13939 .36234 L .1394 .36293 L .13942 .36352 L .13944 .36411 L .13946 .3647 L Mistroke .13947 .36528 L .13949 .36587 L .13951 .36646 L .13952 .36705 L .13954 .36764 L .13956 .36823 L .13957 .36882 L .13959 .36941 L .13961 .37 L .13962 .37059 L .13964 .37118 L .13966 .37177 L .13967 .37236 L .13969 .37294 L .13971 .37353 L .13972 .37412 L .13974 .37471 L .13976 .3753 L .13977 .37589 L .13979 .37648 L .13981 .37707 L .13982 .37766 L .13984 .37825 L .13986 .37884 L .13987 .37943 L .13989 .38001 L .1399 .3806 L .13992 .38119 L .13994 .38178 L .13995 .38237 L .13997 .38296 L .13999 .38355 L .14 .38414 L .14002 .38473 L .14004 .38532 L .14005 .38591 L .14007 .3865 L .14008 .38709 L .1401 .38767 L .14012 .38826 L .14013 .38885 L .14015 .38944 L .14016 .39003 L .14018 .39062 L .1402 .39121 L .14021 .3918 L .14023 .39239 L .14024 .39298 L .14025 .39331 L .14026 .39357 L Mistroke .14028 .39416 L .14029 .39474 L .14031 .39533 L .14032 .39592 L .14034 .39651 L .14036 .3971 L .14037 .39769 L .14039 .39828 L .1404 .39887 L .14042 .39946 L .14044 .40005 L .14045 .40064 L .14047 .40123 L .14048 .40181 L .1405 .4024 L .14051 .40299 L .14053 .40358 L .14055 .40417 L .14056 .40476 L .14058 .40535 L .14059 .40594 L .14061 .40653 L .14062 .40712 L .14064 .40771 L .14065 .4083 L .14067 .40889 L .14069 .40947 L .1407 .41006 L .14072 .41065 L .14073 .41124 L .14075 .41183 L .14076 .41242 L .14078 .41301 L .14079 .4136 L .14081 .41419 L .14082 .41478 L .14084 .41537 L .14086 .41596 L .14087 .41654 L .14089 .41713 L .1409 .41772 L .14092 .41831 L .14093 .4189 L .14095 .41949 L .14096 .42008 L .14098 .42067 L .14099 .42126 L .14101 .42185 L .14102 .42244 L .14104 .42303 L Mistroke .14105 .42362 L .14107 .4242 L .14108 .42479 L .1411 .42538 L .14111 .42597 L .14113 .42656 L .14114 .42715 L .14116 .42774 L .14117 .42833 L .14119 .42892 L .1412 .42951 L .14122 .4301 L .14123 .43069 L .14125 .43127 L .14126 .43186 L .14128 .43245 L .14129 .43304 L .14131 .43363 L .14132 .43422 L .14134 .43481 L .14135 .4354 L .14135 .43541 L .14137 .43599 L .14138 .43658 L .1414 .43717 L .14141 .43776 L .14143 .43834 L .14144 .43893 L .14146 .43952 L .14147 .44011 L .14149 .4407 L .1415 .44129 L .14152 .44188 L .14153 .44247 L .14155 .44306 L .14156 .44365 L .14157 .44424 L .14159 .44483 L .1416 .44542 L .14162 .446 L .14163 .44659 L .14165 .44718 L .14166 .44777 L .14168 .44836 L .14169 .44895 L .14171 .44954 L .14172 .45013 L .14173 .45072 L .14175 .45131 L .14176 .4519 L Mistroke .14178 .45249 L .14179 .45307 L .14181 .45366 L .14182 .45425 L .14184 .45484 L .14185 .45543 L .14186 .45602 L .14188 .45661 L .14189 .4572 L .14191 .45779 L .14192 .45838 L .14194 .45897 L .14195 .45956 L .14196 .46014 L .14198 .46073 L .14199 .46132 L .14201 .46191 L .14202 .4625 L .14204 .46309 L .14205 .46368 L .14206 .46427 L .14208 .46486 L .14209 .46545 L .14211 .46604 L .14212 .46663 L .14213 .46722 L .14215 .4678 L .14216 .46839 L .14218 .46898 L .14219 .46957 L .1422 .47016 L .14222 .47075 L .14223 .47134 L .14225 .47193 L .14226 .47252 L .14227 .47311 L .14229 .4737 L .1423 .47429 L .14232 .47487 L .14233 .47546 L .14234 .47605 L .14236 .47664 L .14237 .47723 L .14239 .47782 L .1424 .47841 L .14241 .479 L .14243 .47959 L .14244 .48018 L .14245 .4807 L .14245 .48077 L Mistroke .14247 .48136 L .14248 .48195 L .1425 .48253 L .14251 .48312 L .14252 .48371 L .14254 .4843 L .14255 .48489 L .14256 .48548 L .14258 .48607 L .14259 .48666 L .14261 .48725 L .14262 .48784 L .14263 .48843 L .14265 .48902 L .14266 .4896 L .14267 .49019 L .14269 .49078 L .1427 .49137 L .14272 .49196 L .14273 .49255 L .14274 .49314 L .14276 .49373 L .14277 .49432 L .14278 .49491 L .1428 .4955 L .14281 .49609 L .14282 .49667 L .14284 .49726 L .14285 .49785 L .14286 .49844 L .14288 .49903 L .14289 .49962 L .1429 .50021 L .14292 .5008 L .14293 .50139 L .14294 .50198 L .14296 .50257 L .14297 .50316 L .14298 .50375 L .143 .50433 L .14301 .50492 L .14302 .50551 L .14304 .5061 L .14305 .50669 L .14306 .50728 L .14308 .50787 L .14309 .50846 L .1431 .50905 L .14312 .50964 L .14313 .51023 L Mistroke .14314 .51082 L .14316 .5114 L .14317 .51199 L .14318 .51258 L .1432 .51317 L .14321 .51376 L .14322 .51435 L .14324 .51494 L .14325 .51553 L .14326 .51612 L .14328 .51671 L .14329 .5173 L .1433 .51789 L .14331 .51848 L .14333 .51906 L .14334 .51965 L .14335 .52024 L .14337 .52083 L .14338 .52142 L .14339 .52201 L .14341 .5226 L .14342 .52319 L .14343 .52378 L .14344 .52437 L .14346 .52496 L .14347 .52555 L .14348 .52613 L .1435 .52672 L .14351 .52731 L .14352 .5279 L .14354 .52849 L .14355 .52908 L .14355 .5293 L .14356 .52967 L .14357 .53026 L .14359 .53085 L .1436 .53144 L .14361 .53203 L .14363 .53262 L .14364 .5332 L .14365 .53379 L .14366 .53438 L .14368 .53497 L .14369 .53556 L .1437 .53615 L .14372 .53674 L .14373 .53733 L .14374 .53792 L .14375 .53851 L .14377 .5391 L Mistroke .14378 .53969 L .14379 .54028 L .1438 .54086 L .14382 .54145 L .14383 .54204 L .14384 .54263 L .14385 .54322 L .14387 .54381 L .14388 .5444 L .14389 .54499 L .14391 .54558 L .14392 .54617 L .14393 .54676 L .14394 .54735 L .14396 .54793 L .14397 .54852 L .14398 .54911 L .14399 .5497 L .14401 .55029 L .14402 .55088 L .14403 .55147 L .14404 .55206 L .14406 .55265 L .14407 .55324 L .14408 .55383 L .14409 .55442 L .14411 .55501 L .14412 .55559 L .14413 .55618 L .14414 .55677 L .14416 .55736 L .14417 .55795 L .14418 .55854 L .14419 .55913 L .14421 .55972 L .14422 .56031 L .14423 .5609 L .14424 .56149 L .14425 .56208 L .14427 .56266 L .14428 .56325 L .14429 .56384 L .1443 .56443 L .14432 .56502 L .14433 .56561 L .14434 .5662 L .14435 .56679 L .14437 .56738 L .14438 .56797 L .14439 .56856 L Mistroke .1444 .56915 L .14441 .56973 L .14443 .57032 L .14444 .57091 L .14445 .5715 L .14446 .57209 L .14448 .57268 L .14449 .57327 L .1445 .57386 L .14451 .57445 L .14452 .57504 L .14454 .57563 L .14455 .57622 L .14456 .57681 L .14457 .57739 L .14458 .57798 L .1446 .57857 L .14461 .57916 L .14462 .57975 L .14463 .58034 L .14465 .58093 L .14465 .58131 L .14466 .58152 L .14467 .58211 L .14468 .5827 L .14469 .58329 L .14471 .58388 L .14472 .58446 L .14473 .58505 L .14474 .58564 L .14475 .58623 L .14477 .58682 L .14478 .58741 L .14479 .588 L .1448 .58859 L .14481 .58918 L .14483 .58977 L .14484 .59036 L .14485 .59095 L .14486 .59154 L .14487 .59212 L .14488 .59271 L .1449 .5933 L .14491 .59389 L .14492 .59448 L .14493 .59507 L .14494 .59566 L .14496 .59625 L .14497 .59684 L .14498 .59743 L Mistroke .14499 .59802 L .145 .59861 L .14502 .59919 L .14503 .59978 L .14504 .60037 L .14505 .60096 L .14506 .60155 L .14507 .60214 L .14509 .60273 L .1451 .60332 L Mfstroke .2 g .008 w .07315 .60332 m .07317 .60303 L .07319 .60273 L .07323 .60214 L .07326 .60155 L .0733 .60096 L .07334 .60037 L .07338 .59978 L .07342 .59919 L .07346 .59861 L .0735 .59802 L .07353 .59743 L .07357 .59684 L .07361 .59625 L .07365 .59566 L .07369 .59507 L .07373 .59448 L .07377 .59389 L .07381 .5933 L .07385 .59271 L .07388 .59212 L .07392 .59154 L .07396 .59095 L .074 .59036 L .07404 .58977 L .07408 .58918 L .07412 .58859 L .07416 .588 L .0742 .58741 L .07424 .58682 L .07427 .58638 L .07428 .58623 L .07432 .58564 L .07436 .58505 L .07439 .58446 L .07443 .58388 L .07447 .58329 L .07451 .5827 L .07455 .58211 L .07459 .58152 L .07463 .58093 L .07467 .58034 L .07471 .57975 L .07475 .57916 L .07479 .57857 L .07483 .57798 L .07487 .57739 L .07491 .57681 L .07495 .57622 L .07499 .57563 L Mistroke .07503 .57504 L .07507 .57445 L .07511 .57386 L .07515 .57327 L .07519 .57268 L .07523 .57209 L .07527 .5715 L .07531 .57091 L .07535 .57032 L .07537 .5701 L .07539 .56973 L .07543 .56915 L .07547 .56856 L .07551 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.07804 .53203 L .07808 .53144 L .07813 .53085 L .07817 .53026 L .07821 .52967 L .07826 .52908 L .0783 .52849 L .07834 .5279 L .07838 .52731 L .07843 .52672 L .07847 .52613 L .07851 .52555 L .07856 .52496 L .0786 .52437 L .07864 .52378 L .07867 .52345 L .07868 .52319 L .07873 .5226 L .07877 .52201 L .07881 .52142 L .07886 .52083 L .0789 .52024 L .07894 .51965 L .07899 .51906 L Mistroke .07903 .51848 L .07908 .51789 L .07912 .5173 L .07916 .51671 L .07921 .51612 L .07925 .51553 L .07929 .51494 L .07934 .51435 L .07938 .51376 L .07942 .51317 L .07947 .51258 L .07951 .51199 L .07956 .5114 L .0796 .51082 L .07964 .51023 L .07969 .50964 L .07973 .50905 L .07977 .50862 L .07978 .50846 L .07982 .50787 L .07987 .50728 L .07991 .50669 L .07995 .5061 L .08 .50551 L .08004 .50492 L .08009 .50433 L .08013 .50375 L .08018 .50316 L .08022 .50257 L .08027 .50198 L .08031 .50139 L .08036 .5008 L .0804 .50021 L .08045 .49962 L .08049 .49903 L .08054 .49844 L .08058 .49785 L .08063 .49726 L .08067 .49667 L .08072 .49609 L .08076 .4955 L .08081 .49491 L .08085 .49432 L .08087 .49413 L .0809 .49373 L .08094 .49314 L .08099 .49255 L .08103 .49196 L .08108 .49137 L .08112 .49078 L Mistroke .08117 .49019 L .08121 .4896 L .08126 .48902 L .08131 .48843 L .08135 .48784 L .0814 .48725 L .08144 .48666 L .08149 .48607 L .08153 .48548 L .08158 .48489 L .08163 .4843 L .08167 .48371 L .08172 .48312 L .08177 .48253 L .08181 .48195 L .08186 .48136 L .0819 .48077 L .08195 .48018 L .08197 .47999 L .082 .47959 L .08204 .479 L .08209 .47841 L .08214 .47782 L .08218 .47723 L .08223 .47664 L .08228 .47605 L .08232 .47546 L .08237 .47487 L .08242 .47429 L .08246 .4737 L .08251 .47311 L .08256 .47252 L .0826 .47193 L .08265 .47134 L .0827 .47075 L .08275 .47016 L .08279 .46957 L .08284 .46898 L .08289 .46839 L .08293 .4678 L .08298 .46722 L .08303 .46663 L .08306 .46618 L .08308 .46604 L .08312 .46545 L .08317 .46486 L .08322 .46427 L .08327 .46368 L .08332 .46309 L .08336 .4625 L Mistroke .08341 .46191 L .08346 .46132 L .08351 .46073 L .08355 .46014 L .0836 .45956 L .08365 .45897 L .0837 .45838 L .08375 .45779 L .0838 .4572 L .08384 .45661 L .08389 .45602 L .08394 .45543 L .08399 .45484 L .08404 .45425 L .08409 .45366 L .08413 .45307 L .08416 .45271 L .08418 .45249 L .08423 .4519 L .08428 .45131 L .08433 .45072 L .08438 .45013 L .08443 .44954 L .08448 .44895 L .08453 .44836 L .08457 .44777 L .08462 .44718 L .08467 .44659 L .08472 .446 L .08477 .44542 L .08482 .44483 L .08487 .44424 L .08492 .44365 L .08497 .44306 L .08502 .44247 L .08507 .44188 L .08512 .44129 L .08517 .4407 L .08522 .44011 L .08526 .43957 L .08527 .43952 L .08532 .43893 L .08537 .43834 L .08542 .43776 L .08547 .43717 L .08552 .43658 L .08557 .43599 L .08562 .4354 L .08567 .43481 L .08572 .43422 L Mistroke .08577 .43363 L .08582 .43304 L .08587 .43245 L .08592 .43186 L .08597 .43127 L .08602 .43069 L .08607 .4301 L .08613 .42951 L .08618 .42892 L .08623 .42833 L .08628 .42774 L .08633 .42715 L .08636 .42674 L .08638 .42656 L .08643 .42597 L .08648 .42538 L .08653 .42479 L .08659 .4242 L .08664 .42362 L .08669 .42303 L .08674 .42244 L .08679 .42185 L .08684 .42126 L .0869 .42067 L .08695 .42008 L .087 .41949 L .08705 .4189 L .0871 .41831 L .08715 .41772 L .08721 .41713 L .08726 .41654 L .08731 .41596 L .08736 .41537 L .08742 .41478 L .08746 .41424 L .08747 .41419 L .08752 .4136 L .08757 .41301 L .08763 .41242 L .08768 .41183 L .08773 .41124 L .08778 .41065 L .08784 .41006 L .08789 .40947 L .08794 .40889 L .088 .4083 L .08805 .40771 L .0881 .40712 L .08816 .40653 L .08821 .40594 L Mistroke .08826 .40535 L .08832 .40476 L .08837 .40417 L .08842 .40358 L .08848 .40299 L .08853 .4024 L .08856 .40205 L .08858 .40181 L .08864 .40123 L .08869 .40064 L .08875 .40005 L .0888 .39946 L .08886 .39887 L .08891 .39828 L .08896 .39769 L .08902 .3971 L .08907 .39651 L .08913 .39592 L .08918 .39533 L .08924 .39474 L .08929 .39416 L .08935 .39357 L .0894 .39298 L .08946 .39239 L .08951 .3918 L .08957 .39121 L .08962 .39062 L .08966 .39016 L .08968 .39003 L .08973 .38944 L .08979 .38885 L .08984 .38826 L .0899 .38767 L .08995 .38709 L .09001 .3865 L .09006 .38591 L .09012 .38532 L .09018 .38473 L .09023 .38414 L .09029 .38355 L .09034 .38296 L .0904 .38237 L .09046 .38178 L .09051 .38119 L .09057 .3806 L .09063 .38001 L .09068 .37943 L .09074 .37884 L .09076 .37857 L .09079 .37825 L Mistroke .09085 .37766 L .09091 .37707 L .09097 .37648 L .09102 .37589 L .09108 .3753 L .09114 .37471 L .09119 .37412 L .09125 .37353 L .09131 .37294 L .09137 .37236 L .09142 .37177 L .09148 .37118 L .09154 .37059 L .0916 .37 L .09165 .36941 L .09171 .36882 L .09177 .36823 L .09183 .36764 L .09186 .36729 L .09189 .36705 L .09194 .36646 L .092 .36587 L .09206 .36528 L .09212 .3647 L .09218 .36411 L .09224 .36352 L .0923 .36293 L .09235 .36234 L .09241 .36175 L .09247 .36116 L .09253 .36057 L .09259 .35998 L .09265 .35939 L .09271 .3588 L .09277 .35821 L .09283 .35763 L .09289 .35704 L .09295 .35645 L .09296 .35629 L .09301 .35586 L .09307 .35527 L .09313 .35468 L .09319 .35409 L .09325 .3535 L .09331 .35291 L .09337 .35232 L .09343 .35173 L .09349 .35114 L .09355 .35056 L .09361 .34997 L Mistroke .09367 .34938 L .09373 .34879 L .09379 .3482 L .09385 .34761 L .09391 .34702 L .09397 .34643 L .09404 .34584 L .09406 .34558 L .0941 .34525 L .09416 .34466 L .09422 .34407 L .09428 .34348 L .09434 .3429 L .09441 .34231 L .09447 .34172 L .09453 .34113 L .09459 .34054 L .09465 .33995 L .09472 .33936 L .09478 .33877 L .09484 .33818 L .0949 .33759 L .09497 .337 L .09503 .33641 L .09509 .33583 L .09515 .33524 L .09516 .33516 L .09522 .33465 L .09528 .33406 L .09534 .33347 L .09541 .33288 L .09547 .33229 L .09553 .3317 L .0956 .33111 L .09566 .33052 L .09573 .32993 L .09579 .32934 L .09585 .32875 L .09592 .32817 L .09598 .32758 L .09605 .32699 L .09611 .3264 L .09618 .32581 L .09624 .32522 L .09626 .32501 L .0963 .32463 L .09637 .32404 L .09643 .32345 L .0965 .32286 L .09656 .32227 L Mistroke .09663 .32168 L .0967 .3211 L .09676 .32051 L .09683 .31992 L .09689 .31933 L .09696 .31874 L .09702 .31815 L .09709 .31756 L .09716 .31697 L .09722 .31638 L .09729 .31579 L .09735 .3152 L .09736 .31514 L .09742 .31461 L .09749 .31403 L .09756 .31344 L .09762 .31285 L .09769 .31226 L .09776 .31167 L .09782 .31108 L .09789 .31049 L .09796 .3099 L .09803 .30931 L .09809 .30872 L .09816 .30813 L .09823 .30754 L .0983 .30695 L .09837 .30637 L .09843 .30578 L .09846 .30554 L .0985 .30519 L .09857 .3046 L .09864 .30401 L .09871 .30342 L .09878 .30283 L .09885 .30224 L .09892 .30165 L .09898 .30106 L .09905 .30047 L .09912 .29988 L .09919 .2993 L .09926 .29871 L .09933 .29812 L .0994 .29753 L .09947 .29694 L .09954 .29635 L .09956 .29619 L .09961 .29576 L .09968 .29517 L .09975 .29458 L Mistroke .09983 .29399 L .0999 .2934 L .09997 .29281 L .10004 .29222 L .10011 .29164 L .10018 .29105 L .10025 .29046 L .10032 .28987 L .1004 .28928 L .10047 .28869 L .10054 .2881 L .10061 .28751 L .10066 .28711 L .10069 .28692 L .10076 .28633 L .10083 .28574 L .1009 .28515 L .10098 .28457 L .10105 .28398 L .10112 .28339 L .1012 .2828 L .10127 .28221 L .10134 .28162 L .10142 .28103 L .10149 .28044 L .10156 .27985 L .10164 .27926 L .10171 .27867 L .10176 .27829 L .10179 .27808 L .10186 .2775 L .10194 .27691 L .10201 .27632 L .10209 .27573 L .10216 .27514 L .10224 .27455 L .10231 .27396 L .10239 .27337 L .10246 .27278 L .10254 .27219 L .10262 .2716 L .10269 .27101 L .10277 .27042 L .10285 .26984 L .10286 .26971 L .10292 .26925 L .103 .26866 L .10308 .26807 L .10315 .26748 L .10323 .26689 L Mistroke .10331 .2663 L .10339 .26571 L .10346 .26512 L .10354 .26453 L .10362 .26394 L .1037 .26335 L .10378 .26277 L .10385 .26218 L .10393 .26159 L .10396 .26138 L .10401 .261 L .10409 .26041 L .10417 .25982 L .10425 .25923 L .10433 .25864 L .10441 .25805 L .10449 .25746 L .10457 .25687 L .10465 .25628 L .10473 .2557 L .10481 .25511 L .10489 .25452 L .10497 .25393 L .10505 .25334 L .10506 .2533 L .10514 .25275 L .10522 .25216 L .1053 .25157 L .10538 .25098 L .10546 .25039 L .10555 .2498 L .10563 .24921 L .10571 .24862 L .10579 .24804 L .10588 .24745 L .10596 .24686 L .10604 .24627 L .10613 .24568 L .10616 .24545 L .10621 .24509 L .1063 .2445 L .10638 .24391 L .10646 .24332 L .10655 .24273 L .10663 .24214 L .10672 .24155 L .1068 .24097 L .10689 .24038 L .10697 .23979 L .10706 .2392 L Mistroke .10715 .23861 L .10723 .23802 L .10726 .23783 L .10732 .23743 L .10741 .23684 L .10749 .23625 L .10758 .23566 L .10767 .23507 L .10775 .23448 L .10784 .23389 L .10793 .23331 L .10802 .23272 L .10811 .23213 L .1082 .23154 L .10828 .23095 L .10836 .23044 L .10837 .23036 L .10846 .22977 L .10855 .22918 L .10864 .22859 L .10873 .228 L .10882 .22741 L .10891 .22682 L .109 .22624 L .10909 .22565 L .10918 .22506 L .10928 .22447 L .10937 .22388 L .10946 .22329 L .10946 .22328 L .10955 .2227 L .10964 .22211 L .10974 .22152 L .10983 .22093 L .10992 .22034 L .11001 .21975 L .11011 .21917 L .1102 .21858 L .1103 .21799 L .11039 .2174 L .11048 .21681 L .11056 .21634 L .11058 .21622 L .11067 .21563 L .11077 .21504 L .11087 .21445 L .11096 .21386 L .11106 .21327 L .11115 .21268 L .11125 .21209 L Mistroke .11135 .21151 L .11144 .21092 L .11154 .21033 L .11164 .20974 L .11166 .20962 L .11174 .20915 L .11184 .20856 L .11193 .20797 L .11203 .20738 L .11213 .20679 L .11223 .2062 L .11233 .20561 L .11243 .20502 L .11253 .20444 L .11263 .20385 L .11273 .20326 L .11276 .20311 L .11283 .20267 L .11294 .20208 L .11304 .20149 L .11314 .2009 L .11324 .20031 L .11335 .19972 L .11345 .19913 L .11355 .19854 L .11366 .19795 L .11376 .19736 L .11386 .1968 L .11386 .19678 L .11397 .19619 L .11407 .1956 L .11418 .19501 L .11428 .19442 L .11439 .19383 L .1145 .19324 L .1146 .19265 L .11471 .19206 L .11482 .19147 L .11493 .19088 L .11496 .1907 L .11503 .19029 L .11514 .18971 L .11525 .18912 L .11536 .18853 L .11547 .18794 L .11558 .18735 L .11569 .18676 L .1158 .18617 L .11591 .18558 L .11602 .18499 L Mistroke .11606 .18481 L .11614 .1844 L .11625 .18381 L .11636 .18322 L .11647 .18264 L .11659 .18205 L .1167 .18146 L .11681 .18087 L .11693 .18028 L .11704 .17969 L .11716 .17911 L .11716 .1791 L .11728 .17851 L .11739 .17792 L .11751 .17733 L .11763 .17674 L .11774 .17615 L .11786 .17556 L .11798 .17498 L .1181 .17439 L .11822 .1738 L .11826 .1736 L .11834 .17321 L .11846 .17262 L .11858 .17203 L .1187 .17144 L .11882 .17085 L .11894 .17026 L .11907 .16967 L .11919 .16908 L .11931 .16849 L .11936 .16828 L .11944 .16791 L .11956 .16732 L .11969 .16673 L .11981 .16614 L .11994 .16555 L .12007 .16496 L .12019 .16437 L .12032 .16378 L .12045 .16319 L .12046 .16315 L .12058 .1626 L .12071 .16201 L .12084 .16142 L .12097 .16083 L .1211 .16025 L .12123 .15966 L .12136 .15907 L .12149 .15848 L Mistroke .12156 .1582 L .12163 .15789 L .12176 .1573 L .1219 .15671 L .12203 .15612 L .12217 .15553 L .1223 .15494 L .12244 .15435 L .12258 .15376 L .12266 .15343 L .12272 .15318 L .12285 .15259 L .12299 .152 L .12313 .15141 L .12328 .15082 L .12342 .15023 L .12356 .14964 L .1237 .14905 L .12376 .14883 L .12385 .14846 L .12399 .14787 L .12414 .14728 L .12428 .14669 L .12443 .14611 L .12458 .14552 L .12472 .14493 L .12486 .1444 L .12487 .14434 L .12502 .14375 L .12517 .14316 L .12532 .14257 L .12548 .14198 L .12563 .14139 L .12578 .1408 L .12594 .14021 L .12596 .14014 L .12609 .13962 L .12625 .13903 L .12641 .13845 L .12656 .13786 L .12672 .13727 L .12688 .13668 L .12704 .13609 L .12706 .13605 L .12721 .1355 L .12737 .13491 L .12753 .13432 L .1277 .13373 L .12786 .13314 L .12803 .13255 L Mistroke .12816 .13211 L .1282 .13196 L .12837 .13138 L .12854 .13079 L .12871 .1302 L .12888 .12961 L .12905 .12902 L .12923 .12843 L .12926 .12833 L .1294 .12784 L .12958 .12725 L .12976 .12666 L .12994 .12607 L .13012 .12548 L .1303 .12489 L .13036 .12471 L .13048 .1243 L .13067 .12372 L .13085 .12313 L .13104 .12254 L .13123 .12195 L .13142 .12136 L .13146 .12124 L .13161 .12077 L .1318 .12018 L .13199 .11959 L .13219 .119 L .13239 .11841 L .13256 .11791 L .13258 .11782 L .13278 .11723 L .13299 .11665 L .13319 .11606 L .1334 .11547 L .1336 .11488 L .13366 .11473 L .13381 .11429 L .13402 .1137 L .13423 .11311 L .13445 .11252 L .13466 .11193 L .13475 .11169 L .13488 .11134 L .1351 .11075 L .13532 .11016 L .13555 .10958 L .13578 .10899 L .13585 .10878 L .136 .1084 L .13624 .10781 L Mistroke .13647 .10722 L .1367 .10663 L .13694 .10604 L .13695 .10601 L .13718 .10545 L .13743 .10486 L .13767 .10427 L .13792 .10368 L .13805 .10337 L .13817 .10309 L .13843 .1025 L .13869 .10192 L .13895 .10133 L .13915 .10086 L .13921 .10074 L .13948 .10015 L .13975 .09956 L .14002 .09897 L .14025 .09848 L .1403 .09838 L .14058 .09779 L .14087 .0972 L .14115 .09661 L .14135 .09621 L .14145 .09602 L .14175 .09543 L .14205 .09485 L .14235 .09426 L .14245 .09407 L .14267 .09367 L .14298 .09308 L .1433 .09249 L .14355 .09204 L .14363 .0919 L .14396 .09131 L .1443 .09072 L .14465 .09013 L .14465 .09012 L .145 .08954 L .14536 .08895 L .14573 .08836 L .14575 .08832 L .1461 .08778 L .14648 .08719 L .14685 .08662 L .14687 .0866 L .14727 .08601 L .14768 .08542 L .14795 .08503 L .1481 .08483 L Mistroke .14853 .08424 L .14897 .08365 L .14905 .08354 L .14942 .08306 L .14989 .08247 L .15015 .08215 L .15038 .08188 L .15087 .08129 L .15125 .08086 L .15139 .0807 L .15193 .08012 L .15235 .07966 L .15248 .07953 L .15306 .07894 L .15345 .07856 L .15367 .07835 L .1543 .07776 L .15455 .07754 L .15497 .07717 L .15565 .07661 L .15568 .07658 L .15644 .07599 L .15675 .07576 L .15725 .0754 L .15785 .075 L .15813 .07481 L .15895 .07431 L .1591 .07422 L .16005 .0737 L .16018 .07363 L .16115 .07317 L .16143 .07305 L .16225 .07271 L .16293 .07246 L .16335 .07231 L .16445 .07199 L .16494 .07187 L .16555 .07173 L .16665 .07154 L .16775 .0714 L .16885 .07133 L .16995 .07131 L .17105 .07135 L .17215 .07144 L .17325 .07158 L .17435 .07177 L .1748 .07187 L .17545 .07201 L .17655 .0723 L .1771 .07246 L Mistroke .17765 .07262 L .17875 .07299 L .17889 .07305 L .17985 .0734 L .18043 .07363 L .18095 .07385 L .1818 .07422 L .18205 .07433 L .18306 .07481 L .18315 .07485 L .18424 .0754 L .18425 .0754 L .18535 .07599 L .18535 .07599 L .18641 .07658 L .18644 .0766 L .18742 .07717 L .18754 .07724 L .1884 .07776 L .18864 .07791 L .18935 .07835 L .18974 .0786 L .19026 .07894 L .19084 .07932 L .19116 .07953 L .19194 .08006 L .19203 .08012 L .19288 .0807 L .19304 .08082 L .19372 .08129 L .19414 .0816 L .19454 .08188 L .19524 .08239 L .19535 .08247 L .19615 .08306 L .19634 .08321 L .19693 .08365 L .19744 .08404 L .19771 .08424 L .19848 .08483 L .19854 .08488 L .19924 .08542 L .19964 .08574 L .19999 .08601 L .20073 .0866 L .20074 .0866 L .20147 .08719 L .20184 .08748 L .20221 .08778 L .20294 .08836 L Mistroke .20294 .08837 L .20366 .08895 L .20404 .08926 L .20438 .08954 L .2051 .09013 L .20514 .09017 L .20582 .09072 L .20624 .09107 L .20653 .09131 L .20724 .0919 L .20734 .09199 L .20795 .09249 L .20844 .0929 L .20865 .09308 L .20936 .09367 L .20954 .09382 L .21006 .09426 L .21064 .09474 L .21077 .09485 L .21147 .09543 L .21174 .09566 L .21217 .09602 L .21284 .09658 L .21288 .09661 L .21358 .0972 L .21394 .0975 L .21429 .09779 L .215 .09838 L .21504 .09842 L .21571 .09897 L .21614 .09933 L .21642 .09956 L .21713 .10015 L .21724 .10024 L .21784 .10074 L .21834 .10114 L .21856 .10133 L .21928 .10192 L .21944 .10204 L .22001 .1025 L .22054 .10293 L .22074 .10309 L .22147 .10368 L .22164 .10382 L .2222 .10427 L .22274 .1047 L .22294 .10486 L .22369 .10545 L .22384 .10557 L .22444 .10604 L Mistroke .22494 .10643 L .2252 .10663 L .22596 .10722 L .22604 .10727 L .22673 .10781 L .22714 .10811 L .22751 .1084 L .22824 .10894 L .2283 .10899 L .22909 .10958 L .22934 .10976 L .22989 .11016 L .23044 .11056 L .23071 .11075 L .23153 .11134 L .23154 .11135 L .23236 .11193 L .23264 .11212 L .23321 .11252 L .23374 .11288 L .23407 .11311 L .23484 .11363 L .23494 .1137 L .23582 .11429 L .23594 .11436 L .23672 .11488 L .23704 .11508 L .23764 .11547 L .23813 .11578 L .23858 .11606 L .23923 .11646 L .23954 .11665 L .24033 .11713 L .24052 .11723 L .24143 .11778 L .24152 .11782 L .24253 .11841 L .24255 .11841 L .2436 .119 L .24363 .11902 L .24469 .11959 L .24473 .11961 L .24582 .12018 L .24583 .12019 L .24693 .12074 L .24699 .12077 L .24803 .12128 L .2482 .12136 L .24913 .1218 L .24946 .12195 L Mistroke .25023 .1223 L .25079 .12254 L .25133 .12277 L .25218 .12313 L .25243 .12323 L .25353 .12366 L .25366 .12372 L .25463 .12408 L .25525 .1243 L .25573 .12447 L .25683 .12485 L .25697 .12489 L .25793 .1252 L .25887 .12548 L .25903 .12553 L .26013 .12584 L .26101 .12607 L .26123 .12613 L .26233 .1264 L .26343 .12664 L .26353 .12666 L .26453 .12686 L .26563 .12707 L .26673 .12725 L .26676 .12725 L .26783 .1274 L .26893 .12754 L .27003 .12766 L .27113 .12775 L .27223 .12782 L .27256 .12784 L .27333 .12787 L .27443 .1279 L .27553 .12791 L .27663 .12789 L .27773 .12786 L .27819 .12784 L .27883 .1278 L .27993 .12773 L .28103 .12763 L .28213 .12751 L .28323 .12738 L .28411 .12725 L .28433 .12722 L .28543 .12704 L .28653 .12684 L .28746 .12666 L .28763 .12663 L .28873 .12639 L .28982 .12614 L Mistroke .29009 .12607 L .29092 .12586 L .29202 .12557 L .29234 .12548 L .29312 .12526 L .29422 .12493 L .29435 .12489 L .29532 .12459 L .29618 .1243 L .29642 .12422 L .29752 .12384 L .29789 .12372 L .29862 .12345 L .29948 .12313 L .29972 .12303 L .30082 .12261 L .30099 .12254 L .30192 .12216 L .30243 .12195 L .30302 .1217 L .30382 .12136 L .30412 .12123 L .30515 .12077 L .30522 .12074 L .30632 .12023 L .30643 .12018 L .30742 .11971 L .30768 .11959 L .30852 .11918 L .30889 .119 L .30962 .11864 L .31007 .11841 L .31072 .11808 L .31122 .11782 L .31182 .11751 L .31234 .11723 L .31292 .11693 L .31345 .11665 L .31402 .11633 L .31453 .11606 L .31512 .11573 L .31559 .11547 L .31622 .11512 L .31664 .11488 L .31732 .11449 L .31767 .11429 L .31842 .11385 L .31869 .1137 L .31952 .11321 L .31969 .11311 L Mistroke .32062 .11256 L .32068 .11252 L .32166 .11193 L .32172 .11189 L .32263 .11134 L .32282 .11122 L .32358 .11075 L .32392 .11055 L .32453 .11016 L .32502 .10986 L .32547 .10958 L .32612 .10917 L .32641 .10899 L .32722 .10847 L .32734 .1084 L .32826 .10781 L .32832 .10777 L .32917 .10722 L .32942 .10706 L .33008 .10663 L .33052 .10635 L .33099 .10604 L .33162 .10563 L .33189 .10545 L .33272 .10491 L .33278 .10486 L .33368 .10427 L .33382 .10418 L .33457 .10368 L .33492 .10345 L .33545 .10309 L .33602 .10272 L .33634 .1025 L .33712 .10199 L .33722 .10192 L .3381 .10133 L .33822 .10125 L .33898 .10074 L .33932 .10052 L .33987 .10015 L .34041 .09978 L .34074 .09956 L .34151 .09904 L .34162 .09897 L .34251 .09838 L .34261 .09831 L .34339 .09779 L .34371 .09757 L .34427 .0972 L .34481 .09684 L Mistroke .34515 .09661 L .34591 .09611 L .34604 .09602 L .34693 .09543 L .34701 .09538 L .34782 .09485 L .34811 .09465 L .34871 .09426 L .34921 .09393 L .34961 .09367 L .35031 .09321 L .35051 .09308 L .35141 .09249 L .35141 .09249 L .35232 .0919 L .35251 .09178 L .35324 .09131 L .35361 .09107 L .35416 .09072 L .35471 .09037 L .35509 .09013 L .35581 .08968 L .35603 .08954 L .35691 .08899 L .35697 .08895 L .35792 .08836 L .35801 .08831 L .35888 .08778 L .35911 .08763 L .35985 .08719 L .36021 .08697 L .36083 .0866 L .36131 .08631 L .36182 .08601 L .36241 .08566 L .36283 .08542 L .36351 .08502 L .36385 .08483 L .36461 .08439 L .36488 .08424 L .36571 .08377 L .36593 .08365 L .36681 .08316 L .36699 .08306 L .36791 .08256 L .36808 .08247 L .36901 .08198 L .36919 .08188 L .37011 .0814 L .37032 .08129 L Mistroke .37121 .08084 L .37147 .0807 L .37231 .08029 L .37266 .08012 L .37341 .07975 L .37388 .07953 L .37451 .07923 L .37513 .07894 L .37561 .07872 L .37642 .07835 L .37671 .07822 L .37776 .07776 L .37781 .07774 L .37891 .07727 L .37915 .07717 L .38001 .07682 L .3806 .07658 L .38111 .07638 L .38213 .07599 L .38221 .07596 L .38331 .07556 L .38374 .0754 L .38441 .07517 L .38546 .07481 L .38551 .0748 L .38661 .07444 L .38732 .07422 L .38771 .07411 L .38881 .07379 L .38936 .07363 L .38991 .07349 L .39101 .07321 L .39167 .07305 L .3921 .07294 L .3932 .0727 L .3943 .07247 L .39439 .07246 L .3954 .07227 L .3965 .07208 L .3976 .07191 L .39794 .07187 L .3987 .07177 L .3998 .07164 L .4009 .07153 L .402 .07145 L .4031 .07138 L .4042 .07134 L .4053 .07132 L .4064 .07131 L .4075 .07133 L Mistroke .4086 .07137 L .4097 .07143 L .4108 .07152 L .4119 .07162 L .413 .07175 L .41388 .07187 L .4141 .0719 L .4152 .07207 L .4163 .07226 L .41732 .07246 L .4174 .07247 L .4185 .07271 L .4196 .07296 L .41993 .07305 L .4207 .07324 L .4218 .07354 L .42212 .07363 L .4229 .07386 L .424 .07421 L .42405 .07422 L .4251 .07457 L .4258 .07481 L .4262 .07495 L .4273 .07536 L .42741 .0754 L .4284 .07579 L .42891 .07599 L .4295 .07623 L .43032 .07658 L .4306 .0767 L .43165 .07717 L .4317 .07719 L .4328 .0777 L .43293 .07776 L .4339 .07823 L .43415 .07835 L .435 .07877 L .43532 .07894 L .4361 .07934 L .43645 .07953 L .4372 .07992 L .43755 .08012 L .4383 .08053 L .43861 .0807 L .4394 .08115 L .43964 .08129 L .4405 .08179 L .44065 .08188 L .4416 .08245 L .44163 .08247 L Mistroke .44259 .08306 L .4427 .08312 L .44353 .08365 L .44379 .08382 L .44446 .08424 L .44489 .08452 L .44536 .08483 L .44599 .08525 L .44625 .08542 L .44709 .08599 L .44712 .08601 L .44798 .0866 L .44819 .08674 L .44883 .08719 L .44929 .08751 L .44966 .08778 L .45039 .0883 L .45049 .08836 L .4513 .08895 L .45149 .08909 L .45211 .08954 L .45259 .0899 L .4529 .09013 L .45369 .09072 L .45369 .09072 L .45447 .09131 L .45479 .09156 L .45524 .0919 L .45589 .0924 L .45601 .09249 L .45676 .09308 L .45699 .09326 L .45752 .09367 L .45809 .09412 L .45826 .09426 L .45901 .09485 L .45919 .09499 L .45974 .09543 L .46029 .09588 L .46048 .09602 L .4612 .09661 L .46139 .09676 L .46193 .0972 L .46249 .09766 L .46265 .09779 L .46337 .09838 L .46359 .09856 L .46408 .09897 L .46469 .09947 L .4648 .09956 L Mistroke .46551 .10015 L .46579 .10038 L .46622 .10074 L .46689 .1013 L .46693 .10133 L .46763 .10192 L .46799 .10222 L .46834 .1025 L .46904 .10309 L .46909 .10313 L .46975 .10368 L .47019 .10406 L .47045 .10427 L .47115 .10486 L .47129 .10498 L .47186 .10545 L .47239 .1059 L .47256 .10604 L .47327 .10663 L .47349 .10681 L .47398 .10722 L .47459 .10773 L .47469 .10781 L .4754 .1084 L .47569 .10864 L .47611 .10899 L .47679 .10954 L .47683 .10958 L .47755 .11016 L .47789 .11044 L .47828 .11075 L .47899 .11133 L .479 .11134 L .47974 .11193 L .48009 .11221 L .48048 .11252 L .48119 .11309 L .48122 .11311 L .48197 .1137 L .48229 .11395 L .48273 .11429 L .48339 .1148 L .48349 .11488 L .48427 .11547 L .48449 .11563 L .48505 .11606 L .48559 .11645 L .48585 .11665 L .48665 .11723 L .48669 .11726 L Mistroke .48747 .11782 L .48779 .11805 L .48831 .11841 L .48889 .11881 L .48916 .119 L .48999 .11956 L .49003 .11959 L .49092 .12018 L .49109 .12029 L .49183 .12077 L .49219 .12099 L .49277 .12136 L .49329 .12167 L .49374 .12195 L .49439 .12233 L .49475 .12254 L .49548 .12295 L .4958 .12313 L .49658 .12355 L .4969 .12372 L .49768 .12412 L .49806 .1243 L .49878 .12465 L .49931 .12489 L .49988 .12515 L .50066 .12548 L .50098 .12561 L .50208 .12604 L .50217 .12607 L .50318 .12643 L .5039 .12666 L .50428 .12678 L .50538 .12708 L .50608 .12725 L .50648 .12734 L .50758 .12755 L .50868 .12772 L .50978 .12783 L .50986 .12784 L .51088 .1279 L .51198 .1279 L .51308 .12786 L .51336 .12784 L .51418 .12775 L .51528 .12758 L .51638 .12736 L .51681 .12725 L .51748 .12706 L .51858 .1267 L .51869 .12666 L Mistroke .51968 .12627 L .52014 .12607 L .52078 .12577 L .52135 .12548 L .52188 .1252 L .52241 .12489 L .52298 .12455 L .52336 .1243 L .52408 .12382 L .52423 .12372 L .52503 .12313 L .52518 .12301 L .52578 .12254 L .52628 .12212 L .52648 .12195 L .52715 .12136 L .52738 .12114 L .52778 .12077 L .52838 .12018 L .52848 .12008 L .52895 .11959 L .52951 .119 L .52958 .11892 L .53004 .11841 L .53055 .11782 L .53068 .11767 L .53105 .11723 L .53153 .11665 L .53178 .11633 L .53199 .11606 L .53244 .11547 L .53288 .11489 L .53288 .11488 L .53331 .11429 L .53373 .1137 L .53398 .11334 L .53414 .11311 L .53453 .11252 L .53492 .11193 L .53508 .1117 L .5353 .11134 L .53568 .11075 L .53604 .11016 L .53618 .10994 L .5364 .10958 L .53675 .10899 L .53709 .1084 L .53728 .10808 L .53743 .10781 L .53776 .10722 L Mistroke .53809 .10663 L .53838 .1061 L .53841 .10604 L .53873 .10545 L .53904 .10486 L .53934 .10427 L .53948 .10401 L .53964 .10368 L .53994 .10309 L .54023 .1025 L .54052 .10192 L .54058 .1018 L .54081 .10133 L .54109 .10074 L .54136 .10015 L .54164 .09956 L .54168 .09947 L .54191 .09897 L .54217 .09838 L .54244 .09779 L .5427 .0972 L .54278 .09702 L .54295 .09661 L .54321 .09602 L .54346 .09543 L .54371 .09485 L .54388 .09444 L .54395 .09426 L .5442 .09367 L .54444 .09308 L .54467 .09249 L .54491 .0919 L .54498 .09173 L .54514 .09131 L .54537 .09072 L .5456 .09013 L .54583 .08954 L .54605 .08895 L .54608 .08889 L .54627 .08836 L 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Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Timing", "[", RowBox[{ RowBox[{"gbrat6", "=", RowBox[{"GroebnerBasis", "[", RowBox[{"polys6", ",", "vars", ",", RowBox[{"Prepend", "[", RowBox[{"elims", ",", "drecip"}], "]"}], ",", RowBox[{"MonomialOrder", "\[Rule]", "EliminationOrder"}], ",", RowBox[{"Sort", "\[Rule]", "True"}], ",", RowBox[{"Method", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"\"\\"", "\[Rule]", "True"}]}], "}"}]}]}], "]"}]}], ";"}], "]"}]], "Input", CellChangeTimes->{3.390413101122178*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"64.244`", ",", "Null"}], "}"}]], "Output", CellChangeTimes->{ 3.390413113012961*^9, {3.390413330908543*^9, 3.390413338964704*^9}}] }, Open ]], Cell["\<\ By using approximate arithmetic of 300 digits one can obtain the same result \ in about 24 seconds. Not quite \"real time\" but getting reasonably close...\ \>", "Text", CellChangeTimes->{{3.390570367660791*^9, 3.390570430941313*^9}}] }, Open ]] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Summary", "Section", CellChangeTimes->{{3.39031774747937*^9, 3.390317892568208*^9}, { 3.390318030169785*^9, 3.390318035219289*^9}, {3.39031807053187*^9, 3.390318078405022*^9}, {3.390318155337057*^9, 3.390318162234282*^9}, { 3.390408146813615*^9, 3.390408147890972*^9}}], Cell[CellGroupData[{ Cell["What we can do", "Subsection", CellChangeTimes->{ 3.390412129519367*^9, {3.390412178861369*^9, 3.390412182950669*^9}, { 3.390413369104902*^9, 3.39041337110238*^9}}], Cell[CellGroupData[{ Cell["\<\ Implicitization of \"difficult\" polynomial, rational, and algebraic \ parametrizations from the literature.\ \>", "Subsubsection", CellChangeTimes->{{3.39041242472722*^9, 3.390412445131837*^9}, 3.390412514851427*^9, {3.390413377750857*^9, 3.390413413363172*^9}}], Cell["\<\ Many other elimination and related problems are also amenable to effective \ handling via Gr\[ODoubleDot]bner walk computations.\ \>", "Subsubsection", CellChangeTimes->{{3.390412466909498*^9, 3.390412498525952*^9}, { 3.390412646238061*^9, 3.390412673524289*^9}, {3.390413420116177*^9, 3.390413467614485*^9}, {3.390416747810202*^9, 3.390416758781663*^9}}] }, Open ]] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"], Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Necessary tactics", "Subsection", CellChangeTimes->{ 3.390412129519367*^9, {3.390412178861369*^9, 3.390412182950669*^9}}], Cell[CellGroupData[{ Cell["Perturbation of initial weight vector.", "Subsubsection", CellChangeTimes->{{3.39041242472722*^9, 3.390412445131837*^9}, 3.390412514851427*^9}], Cell["\<\ Other than when reaching boundary of final cone, this will help to avoid \ \"large initials\" problem.\ \>", "Text", CellChangeTimes->{{3.390412466909498*^9, 3.390412498525952*^9}, { 3.390412646238061*^9, 3.390412673524289*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Always interreduce intermediate bases.", "Subsubsection", CellChangeTimes->{{3.39041242472722*^9, 3.390412445131837*^9}, 3.390412514851427*^9, {3.390412772982281*^9, 3.390412781581223*^9}}], Cell[CellGroupData[{ Cell["\<\ Failure to do so will cause huge blowup due to \"false cones\" problem.\ \>", "Text", CellChangeTimes->{{3.390412466909498*^9, 3.390412498525952*^9}, { 3.390412786988447*^9, 3.39041280663295*^9}}], Cell["\<\ It will probably also cause crop failures. At least, it has not been proven \ otherwise.\ \>", "Text", CellChangeTimes->{{3.390412466909498*^9, 3.390412498525952*^9}, { 3.390412786988447*^9, 3.390412832843391*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ When indicated, perturbation of final weight vector. Viable possibilities are\ \ \>", "Subsubsection", CellChangeTimes->{{3.39041242472722*^9, 3.390412459467746*^9}, { 3.390412500036476*^9, 3.390412507305959*^9}, {3.390412590023272*^9, 3.390412591231987*^9}, {3.390412861116661*^9, 3.390412863541564*^9}, { 3.39086214722116*^9, 3.390862148741594*^9}}], Cell["Heuristic", "Text", CellChangeTimes->{{3.390412466909498*^9, 3.390412498525952*^9}}], Cell["Simulated", "Text", CellChangeTimes->{{3.390412466909498*^9, 3.390412496193618*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Early finish when we discover we have attained an elimination ideal\ \>", "Subsubsection", CellChangeTimes->{{3.39041242472722*^9, 3.390412459467746*^9}, { 3.390412500036476*^9, 3.390412507305959*^9}, {3.390412544630309*^9, 3.390412560386238*^9}, {3.390412603859285*^9, 3.390412605648876*^9}}], Cell["\<\ Rarely hurts, never by much, and sometimes helps substantially.\ \>", "Text", CellChangeTimes->{{3.390412466909498*^9, 3.390412498525952*^9}, { 3.390412573645489*^9, 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Amrhein, O. Gloor, and W. K\[UDoubleDot]chlin. On the walk.Theoretical \ Computer Science ", StyleBox["187", FontWeight->"Bold"], ":179\[Hyphen]202. 1997." }], "Reference", CellChangeTimes->{ 3.390415167301329*^9, {3.390415247989037*^9, 3.390415319146385*^9}, { 3.390415583474064*^9, 3.390415651287279*^9}, {3.390417010442318*^9, 3.390417063641847*^9}, {3.390417163181394*^9, 3.390417189872157*^9}, { 3.390417263986499*^9, 3.390417284316946*^9}, {3.390417458913721*^9, 3.390417466954401*^9}, {3.390562872568811*^9, 3.390562919866594*^9}, { 3.390563434502754*^9, 3.390563434809415*^9}, 3.390565593429898*^9, { 3.390568887193212*^9, 3.390568943258101*^9}}], Cell[TextData[{ "S. Collart, M. Kalkbrenner, and D. Mall. Converting bases with the Gr\ \[ODoubleDot]bner walk. 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Springer\[Hyphen]Verlag, \ 2007.\ \>", "Reference", CellChangeTimes->{ 3.390415167301329*^9, {3.390415247989037*^9, 3.390415319146385*^9}, { 3.390415583474064*^9, 3.390415651287279*^9}, {3.390417010442318*^9, 3.390417063641847*^9}, {3.390417163181394*^9, 3.390417189872157*^9}, { 3.390417263986499*^9, 3.390417284316946*^9}, {3.390417458913721*^9, 3.390417466954401*^9}, {3.390574211862403*^9, 3.390574308304067*^9}, { 3.390574487985872*^9, 3.3905744998566008`*^9}}], Cell[TextData[{ "K. Fukuda, A. N. Jensen, N Lauritzen, and R. Thomas. The generic Gr\ \[ODoubleDot]bner walk. Journal of Symbolic Computation ", StyleBox["42", FontWeight->"Bold"], ":198\[Hyphen]213. 2007." }], "Reference", CellChangeTimes->{ 3.390415167301329*^9, {3.390415247989037*^9, 3.390415319146385*^9}, { 3.390415583474064*^9, 3.390415651287279*^9}, {3.390417010442318*^9, 3.390417063641847*^9}}], Cell[TextData[{ "M. Kalkbrenner. Implicitization of rational parametric curves and surfaces. \ AAECC\[Hyphen]8, Lecture Notes in Computer Science ", StyleBox["508", FontWeight->"Bold"], ":249\[Hyphen]259, S. Sakata, ed. Springer, 1990." }], "Reference", CellChangeTimes->{ 3.390415167301329*^9, {3.390415247989037*^9, 3.390415319146385*^9}, { 3.390415583474064*^9, 3.390415651287279*^9}, {3.390417578984931*^9, 3.390417581066902*^9}, {3.39041762672998*^9, 3.390417633379325*^9}, 3.39056705424378*^9, {3.390567196977797*^9, 3.390567200586813*^9}}], Cell["R. Lewis. Private communication, 2007.", "Reference", CellChangeTimes->{ 3.390415167301329*^9, {3.390415247989037*^9, 3.390415319146385*^9}, { 3.390416928905531*^9, 3.390416989593711*^9}, {3.390417092904003*^9, 3.390417144330872*^9}, 3.390417224537721*^9, {3.390565632682924*^9, 3.390565638940305*^9}, {3.390565715693172*^9, 3.390565803225297*^9}, { 3.391176929745876*^9, 3.391176943085089*^9}}], Cell[TextData[{ "D. Lichtblau. Solving finite algebraic systems using numeric \ Gr\[ODoubleDot]bner bases and eigenvalues. Proceedings of SCI 2000 ", StyleBox["10", FontWeight->"Bold"], ":555\[Hyphen]560. 2000." }], "Reference", CellChangeTimes->{ 3.390415167301329*^9, {3.390415247989037*^9, 3.390415319146385*^9}, { 3.390416928905531*^9, 3.390416989593711*^9}, {3.390417092904003*^9, 3.390417144330872*^9}, 3.390417224537721*^9, {3.390565632682924*^9, 3.390565638940305*^9}, {3.390565715693172*^9, 3.390565803225297*^9}}], Cell[TextData[{ "D. Lichtblau. Computing curves bounding trigonometric planar maps: symbolic \ and hybrid methods. Proceedings of the Workshop on Automated and Deductive \ Geometry (ADG 2004). Lecture Notes in Artificial Intelligence ", StyleBox["3763", FontWeight->"Bold"], ":70\[Hyphen]91, H. Hong and D. Wang, eds. Springer\[Hyphen]Verlag, 2006." }], "Reference", CellChangeTimes->{ 3.390415167301329*^9, {3.390415247989037*^9, 3.390415319146385*^9}, { 3.390416928905531*^9, 3.390416989593711*^9}, {3.390417092904003*^9, 3.390417144330872*^9}, 3.390417224537721*^9, {3.390565632682924*^9, 3.390565638940305*^9}, {3.390565715693172*^9, 3.390565803225297*^9}, { 3.390566865371612*^9, 3.390566869566654*^9}, {3.390566934311766*^9, 3.390567047778676*^9}, {3.390567083655286*^9, 3.390567089257838*^9}}], Cell[TextData[{ "K. Shirayanagi. Floating point Gr\[ODoubleDot]bner bases. Mathematics and \ Computers in Simulation ", StyleBox["42", FontWeight->"Bold"], ":509\[Hyphen]528. 1996." }], "Reference", CellChangeTimes->{ 3.390415167301329*^9, {3.390415247989037*^9, 3.390415319146385*^9}, { 3.390416928905531*^9, 3.390416989593711*^9}, {3.390417092904003*^9, 3.390417144330872*^9}, 3.390417224537721*^9}], Cell[TextData[{ "Q-N Tran. A fast algorithm for Gr\[ODoubleDot]bner basis conversion and its \ applications. 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