diff options
| -rw-r--r-- | figs/fit_basis_poly.pdf | bin | 16699 -> 16699 bytes | |||
| -rw-r--r-- | figs/fit_bias-variance2_poly.pdf | bin | 0 -> 6185 bytes | |||
| -rw-r--r-- | figs/fit_bias-variance_poly.pdf | bin | 5618 -> 5618 bytes | |||
| -rw-r--r-- | figs/fit_data.pdf | bin | 10408 -> 10408 bytes | |||
| -rw-r--r-- | figs/fit_data_truth.pdf | bin | 13026 -> 13026 bytes | |||
| -rw-r--r-- | figs/fit_goodfit_poly.pdf | bin | 12601 -> 12601 bytes | |||
| -rw-r--r-- | figs/fit_overfit_poly.pdf | bin | 16252 -> 16252 bytes | |||
| -rw-r--r-- | figs/fit_overparamfit_poly.pdf | bin | 0 -> 21816 bytes | |||
| -rw-r--r-- | figs/fit_truth.pdf | bin | 7720 -> 7720 bytes | |||
| -rw-r--r-- | figs/fit_underfit_poly.pdf | bin | 10837 -> 10837 bytes | |||
| -rw-r--r-- | fits.nb | 3045 | ||||
| -rw-r--r-- | ictp-saifr_colloquium.tex | 150 | ||||
| -rw-r--r-- | poly_fits.dat | 2 |
13 files changed, 2962 insertions, 235 deletions
diff --git a/figs/fit_basis_poly.pdf b/figs/fit_basis_poly.pdf Binary files differindex 0661768..ca6b718 100644 --- a/figs/fit_basis_poly.pdf +++ b/figs/fit_basis_poly.pdf diff --git a/figs/fit_bias-variance2_poly.pdf b/figs/fit_bias-variance2_poly.pdf Binary files differnew file mode 100644 index 0000000..a1b6bb1 --- /dev/null +++ b/figs/fit_bias-variance2_poly.pdf diff --git a/figs/fit_bias-variance_poly.pdf b/figs/fit_bias-variance_poly.pdf Binary files differindex dfc460f..8e32d2f 100644 --- a/figs/fit_bias-variance_poly.pdf +++ b/figs/fit_bias-variance_poly.pdf diff --git a/figs/fit_data.pdf b/figs/fit_data.pdf Binary files differindex a6ff16c..ce8eecb 100644 --- a/figs/fit_data.pdf +++ b/figs/fit_data.pdf diff --git a/figs/fit_data_truth.pdf b/figs/fit_data_truth.pdf Binary files differindex 665355b..077186e 100644 --- a/figs/fit_data_truth.pdf +++ b/figs/fit_data_truth.pdf diff --git a/figs/fit_goodfit_poly.pdf b/figs/fit_goodfit_poly.pdf Binary files differindex eeef962..c3f0a4e 100644 --- a/figs/fit_goodfit_poly.pdf +++ b/figs/fit_goodfit_poly.pdf diff --git a/figs/fit_overfit_poly.pdf b/figs/fit_overfit_poly.pdf Binary files differindex cd840cb..96812ee 100644 --- a/figs/fit_overfit_poly.pdf +++ b/figs/fit_overfit_poly.pdf diff --git a/figs/fit_overparamfit_poly.pdf b/figs/fit_overparamfit_poly.pdf Binary files differnew file mode 100644 index 0000000..367fd79 --- /dev/null +++ b/figs/fit_overparamfit_poly.pdf diff --git a/figs/fit_truth.pdf b/figs/fit_truth.pdf Binary files differindex d22a512..8ad7aab 100644 --- a/figs/fit_truth.pdf +++ b/figs/fit_truth.pdf diff --git a/figs/fit_underfit_poly.pdf b/figs/fit_underfit_poly.pdf Binary files differindex 2253ade..68ab5d2 100644 --- a/figs/fit_underfit_poly.pdf +++ b/figs/fit_underfit_poly.pdf @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 154, 7] -NotebookDataLength[ 1380591, 24637] -NotebookOptionsPosition[ 1374634, 24530] -NotebookOutlinePosition[ 1375029, 24546] -CellTagsIndexPosition[ 1374986, 24543] +NotebookDataLength[ 1530793, 27220] +NotebookOptionsPosition[ 1524362, 27105] +NotebookOutlinePosition[ 1524757, 27121] +CellTagsIndexPosition[ 1524714, 27118] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -70,8 +70,8 @@ poly_fits.dat\>\"", "]"}]}], ";"}]], "Input", 3.9481309111456833`*^9, 3.948130912383401*^9}, {3.948174686216248*^9, 3.9481746867275467`*^9}, {3.9481968999131937`*^9, 3.948196900701874*^9}, { 3.9482030689210777`*^9, 3.9482030693756723`*^9}, {3.9482664554211397`*^9, - 3.94826646086629*^9}},ExpressionUUID->"b6f65d11-1714-42cd-b279-\ -8e2c0eb8fe70"], + 3.94826646086629*^9}}, + CellLabel->"In[3]:=",ExpressionUUID->"b6f65d11-1714-42cd-b279-8e2c0eb8fe70"], Cell[CellGroupData[{ @@ -91,9 +91,9 @@ Cell[BoxData[{ CellChangeTimes->{{3.9481307549726753`*^9, 3.9481308081074133`*^9}, { 3.948212743256954*^9, 3.9482127504710007`*^9}, {3.948213380672443*^9, 3.9482133987286167`*^9}, {3.948213737030558*^9, 3.9482137384782457`*^9}}, - CellLabel->"In[37]:=",ExpressionUUID->"788c910c-c901-4771-95a4-a21a3056ef4d"], + CellLabel->"In[4]:=",ExpressionUUID->"788c910c-c901-4771-95a4-a21a3056ef4d"], -Cell[BoxData["149"], "Output", +Cell[BoxData["151"], "Output", CellChangeTimes->{{3.948213738736652*^9, 3.9482137656802483`*^9}, 3.948213799433106*^9, {3.948213830637289*^9, 3.948213862914049*^9}, 3.948213954104781*^9, 3.948214070848398*^9, {3.948214140176289*^9, @@ -113,8 +113,9 @@ Cell[BoxData["149"], "Output", 3.948221998665936*^9, 3.9482221087576323`*^9, 3.9482222090225887`*^9, 3.9482222522593613`*^9, 3.948222652533906*^9, 3.948222940411882*^9, 3.948223427004236*^9, 3.948223783260468*^9, 3.948260859491197*^9, { - 3.948260919112976*^9, 3.948260923013983*^9}, 3.9482619180749407`*^9}, - CellLabel->"Out[39]=",ExpressionUUID->"f3d671d5-5163-4ffd-ad1a-0c6d048d0caa"] + 3.948260919112976*^9, 3.948260923013983*^9}, 3.9482619180749407`*^9, + 3.948273880274291*^9}, + CellLabel->"Out[6]=",ExpressionUUID->"a5455d1f-2200-4eb8-b7ac-87cfed829af8"] }, Open ]], Cell[CellGroupData[{ @@ -132,7 +133,7 @@ Cell[BoxData[ CellChangeTimes->{{3.948261248158375*^9, 3.9482612593668957`*^9}, { 3.948261369932403*^9, 3.948261372307385*^9}, {3.948262696713688*^9, 3.9482627016733522`*^9}}, - CellLabel->"In[47]:=",ExpressionUUID->"cbba3901-f3bc-435c-9c36-ae44b4230e6a"], + CellLabel->"In[7]:=",ExpressionUUID->"cbba3901-f3bc-435c-9c36-ae44b4230e6a"], Cell[BoxData[ GraphicsBox[{{}, @@ -366,8 +367,8 @@ aA8A0XlEJQ== Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{ 3.94826125958193*^9, 3.948261372822441*^9, 3.948261919055586*^9, { - 3.948262699276074*^9, 3.948262701872097*^9}}, - CellLabel->"Out[47]=",ExpressionUUID->"d7d2b8f1-468c-4cd8-83c4-dcaf04dc40a9"] + 3.948262699276074*^9, 3.948262701872097*^9}, 3.948273880901355*^9}, + CellLabel->"Out[7]=",ExpressionUUID->"78929829-92ad-4661-b73b-c0d85ddb98cb"] }, Open ]], Cell[CellGroupData[{ @@ -390,7 +391,7 @@ Cell[BoxData[ CellChangeTimes->{{3.948261225687996*^9, 3.948261238816614*^9}, { 3.948261377452162*^9, 3.948261383060684*^9}, {3.948262705554737*^9, 3.9482627057549877`*^9}}, - CellLabel->"In[48]:=",ExpressionUUID->"28259c60-740d-4dce-ab83-46e9aa5aaa2d"], + CellLabel->"In[8]:=",ExpressionUUID->"28259c60-740d-4dce-ab83-46e9aa5aaa2d"], Cell[BoxData[ GraphicsBox[ @@ -1042,8 +1043,8 @@ OziurXbk9fj2P2KYO68= Scaled[0.02]}, {0, 0}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{{3.948261218376964*^9, 3.948261239077613*^9}, - 3.9482613835910263`*^9, 3.9482627060342903`*^9}, - CellLabel->"Out[48]=",ExpressionUUID->"fc3b1c7d-1612-478f-aa47-a5b3a1d59ced"] + 3.9482613835910263`*^9, 3.9482627060342903`*^9, 3.948273881445201*^9}, + CellLabel->"Out[8]=",ExpressionUUID->"8e055139-6bd8-4751-84b0-d76ee0bd2474"] }, Open ]], Cell[CellGroupData[{ @@ -1072,7 +1073,7 @@ Cell[BoxData[ 3.948212486614019*^9, 3.948212490612102*^9}, {3.948261269328219*^9, 3.948261280512623*^9}, {3.94826138642839*^9, 3.94826139046032*^9}, { 3.948262708914226*^9, 3.948262709162466*^9}}, - CellLabel->"In[49]:=",ExpressionUUID->"93081125-f7f5-4ec1-8522-2663d9863e0b"], + CellLabel->"In[9]:=",ExpressionUUID->"93081125-f7f5-4ec1-8522-2663d9863e0b"], Cell[BoxData[ GraphicsBox[{ @@ -1892,8 +1893,8 @@ aA8A0XlEJQ== 3.948220688463863*^9, 3.9482209729685993`*^9, 3.9482216961959887`*^9, 3.9482219993874283`*^9, 3.948222253069086*^9, 3.948260860389288*^9, { 3.948261269960252*^9, 3.948261280838236*^9}, 3.9482613908586397`*^9, - 3.948262709673897*^9}, - CellLabel->"Out[49]=",ExpressionUUID->"5bb72cd0-6313-4d2b-aacb-35b976cc8b3f"] + 3.948262709673897*^9, 3.948273881694083*^9}, + CellLabel->"Out[9]=",ExpressionUUID->"6aba4807-4f56-4e4c-91f9-44245b663beb"] }, Open ]], Cell[CellGroupData[{ @@ -1914,7 +1915,7 @@ Cell[BoxData[ CellChangeTimes->{{3.948261632439481*^9, 3.948261661903262*^9}, { 3.948261774758247*^9, 3.9482617749885273`*^9}, {3.948262713474251*^9, 3.9482627137705584`*^9}}, - CellLabel->"In[50]:=",ExpressionUUID->"28c5ddb2-5548-4f43-9824-c5195899a516"], + CellLabel->"In[10]:=",ExpressionUUID->"28c5ddb2-5548-4f43-9824-c5195899a516"], Cell[BoxData[ GraphicsBox[ @@ -4431,8 +4432,8 @@ b+Wf+/dvBtL///fL8H97WYBK Scaled[0.02]}, {0, 0}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{{3.948261641863297*^9, 3.948261662286827*^9}, - 3.948261775329072*^9, 3.948262714084161*^9}, - CellLabel->"Out[50]=",ExpressionUUID->"e810cfbd-ca29-411b-b2cd-b42bb27abee4"] + 3.948261775329072*^9, 3.948262714084161*^9, 3.948273882180984*^9}, + CellLabel->"Out[10]=",ExpressionUUID->"bd7062d2-2ab1-4ceb-a4ac-bd6a0bb3c342"] }, Open ]], Cell[CellGroupData[{ @@ -4470,7 +4471,7 @@ eCYnEH1umtbkeUB6zfZ2MB33pXIpiNY0/LYSRC836NoOouf8fLgTRPPoaewD 0RbP3PaD6E93q5YtAtm79A6YftS45gSI9t3AfxJEq95ZeX0bkDbsrHwAor9+ vvccRB9q9XkBogHSF7/7 "], - CellLabel->"In[64]:=",ExpressionUUID->"64b9d7b0-4d42-4971-a779-d26a172dddb6"], + CellLabel->"In[11]:=",ExpressionUUID->"64b9d7b0-4d42-4971-a779-d26a172dddb6"], Cell[BoxData[ GraphicsBox[{ @@ -4903,8 +4904,9 @@ aA8A0XlEJQ== 3.948220266647156*^9, 3.948220575535624*^9, 3.9482207005843573`*^9, 3.948220984475416*^9, {3.948221746067596*^9, 3.9482217619438553`*^9}, { 3.948222009167244*^9, 3.948222028298908*^9}, 3.948260864460042*^9, { - 3.948263106647544*^9, 3.9482631721112423`*^9}, 3.948263234899865*^9}, - CellLabel->"Out[64]=",ExpressionUUID->"3eb5fcf9-8f4f-4427-ae95-caddc8dc5094"] + 3.948263106647544*^9, 3.9482631721112423`*^9}, 3.948263234899865*^9, + 3.948273884419683*^9}, + CellLabel->"Out[11]=",ExpressionUUID->"076474d4-f1aa-4668-a0f1-b95f7dd8be21"] }, Open ]], Cell[CellGroupData[{ @@ -4942,7 +4944,7 @@ eCYnEH1umtbkeUB6zfZ2MB33pXIpiNY0/LYSRC836NoOouf8fLgTRPPoaewD 0RbP3PaD6E93q5YtAtm79A6YftS45gSI9t3AfxJEq95ZeX0bkJa/YfMIRKtp 7nkBouXM74Ppo4+/hm4Hma/lHAaiAefvxtQ= "], - CellLabel->"In[81]:=",ExpressionUUID->"6320da01-8775-4d5d-a006-6ebc2cd45cdf"], + CellLabel->"In[12]:=",ExpressionUUID->"6320da01-8775-4d5d-a006-6ebc2cd45cdf"], Cell[BoxData[ GraphicsBox[{ @@ -5730,8 +5732,8 @@ aA8A0XlEJQ== 3.948220984475416*^9, {3.948221746067596*^9, 3.9482217619438553`*^9}, { 3.948222009167244*^9, 3.948222028298908*^9}, 3.948260864460042*^9, { 3.948263106647544*^9, 3.948263186399065*^9}, 3.948263239350268*^9, - 3.9482641144511223`*^9}, - CellLabel->"Out[81]=",ExpressionUUID->"acad27c5-11e9-4605-b453-e6d388234131"] + 3.9482641144511223`*^9, 3.948273884720285*^9}, + CellLabel->"Out[12]=",ExpressionUUID->"fe02788d-4433-4cdf-9696-f7c15350355e"] }, Open ]], Cell[CellGroupData[{ @@ -5762,7 +5764,7 @@ Cell[BoxData[ RowBox[{"testdata", ",", RowBox[{"PlotStyle", "->", "Black"}]}], "]"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.948263198213752*^9, 3.9482632423275013`*^9}}, - CellLabel->"In[66]:=",ExpressionUUID->"8d4e6581-f6b8-48df-a676-75ca341189cb"], + CellLabel->"In[13]:=",ExpressionUUID->"8d4e6581-f6b8-48df-a676-75ca341189cb"], Cell[BoxData[ GraphicsBox[{ @@ -6986,8 +6988,2511 @@ aA8A0XlEJQ== Scaled[0.02], Scaled[0.02]}, {0, 0}}, Ticks->{Automatic, Automatic}]], "Output", - CellChangeTimes->{{3.948263202100992*^9, 3.9482632430956593`*^9}}, - CellLabel->"Out[66]=",ExpressionUUID->"a9f403e8-1dbf-4c95-9afa-f2836ea123b7"] + CellChangeTimes->{{3.948263202100992*^9, 3.9482632430956593`*^9}, + 3.9482738852959003`*^9}, + CellLabel->"Out[13]=",ExpressionUUID->"e068285f-6324-4bb0-9a30-479c6b4173d2"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Length", "[", + RowBox[{"as", "[", + RowBox[{"[", + RowBox[{"-", "31"}], "]"}], "]"}], "]"}]], "Input", + CellChangeTimes->{{3.948274025275671*^9, 3.948274142941441*^9}}, + CellLabel->"In[49]:=",ExpressionUUID->"40855202-d9c2-46f6-ae45-c3c37ee795d0"], + +Cell[BoxData["80"], "Output", + CellChangeTimes->{{3.948274026529709*^9, 3.948274143213243*^9}}, + CellLabel->"Out[49]=",ExpressionUUID->"a961f55f-4340-44b4-8a5e-96fef706b7c0"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"overparamfit", "=", + RowBox[{"Show", "[", + RowBox[{ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"as", "[", + RowBox[{"[", + RowBox[{"-", "31"}], "]"}], "]"}], ".", + RowBox[{"polyBasis", "[", + RowBox[{"Length", "[", + RowBox[{"as", "[", + RowBox[{"[", + RowBox[{"-", "31"}], "]"}], "]"}], "]"}], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", + RowBox[{"PlotRange", "->", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}]}], ",", + RowBox[{"ImageSize", "->", "200"}]}], "]"}], ",", + RowBox[{"ListPlot", "[", + RowBox[{"testdata", ",", + RowBox[{"PlotStyle", "->", "Black"}]}], "]"}]}], "]"}]}]], "Input", + CellChangeTimes->{{3.94827391272864*^9, 3.948273951753463*^9}, { + 3.948274065228917*^9, 3.948274148605711*^9}}, + CellLabel->"In[50]:=",ExpressionUUID->"af4110b9-8b7d-44d5-a091-88eb1c487999"], + +Cell[BoxData[ + GraphicsBox[{ + InterpretationBox[{ + TagBox[{{{}, {}, + TagBox[ + {RGBColor[0.24, 0.6, 0.8], AbsoluteThickness[2], Opacity[1.], + LineBox[CompressedData[" +1:eJwUV3k4lW8TllSSJElIkiiVJC0kuW1JRSlkSX5IlC1JUtkSslNJKiT7mn1f +su/7eqznHFuOc6xtKul7v7/e677meWeemWfmnpk9pnev3mJmYmIyZmVi+v/3 +wq3pzgqajnxHU417A1fSZxZlfjsy33Ewvf68LkXtDY59CI/I4VMBk+4zEa+G +AkwIiDx9uO8SZFrmT2ozVeNia392JJ82ZN4qbH+QUA+RgF3x/3brw13U5ZjB +30asXLj5xmSfEZxmLUYfejVhxrOnxiTMBAssuTOJg43QNftZ9pLPDCt7Sm+t +BjegRpm/oDrCHJIp7ou3dtVDcu+ZzG+770AtO1Srn1SLCGbjZNFYK4T09nAV +/qgB65hHzLV9tiA1ct6VC6pBMaWrtVrbDpmrXYyEDzWw0zS7YBh2Dx2dD96s +8NdiX8X3um/99uhQc5G8PFWLkSPPlQP5HOBzpgR7xusQ+oG3QvT6AzD1Zb5O +W6rHhS0pcuURjrATnUxf86sBTG6ni66NPsT0mb5L28iNyJ9rOTG/+xGWsz7f +6HrVBGsjo+znJo8hJLLzkxd7M4Tb5iWEYp9guWv/DX+VZpDOPE0tnHBGyEHs +ypBrRlA6l9iVfa4ImfdQkPvdhLO74uJoFm7I5JlyYhDxcq17x1mp7Q5eBYOv +rTON0HcdvxT43R12dzpkT5xoxPGT4oH6YU/B6Tvj23ivAVvmHJpFpT3g5P+a +Jy+tHjPxZRuX+j3A+TopYHWhDrU31quVOz2DzGzJzc1qdYjeftnbj88Tdkkp +v3WLavGk9U3NtWJPdPjF6MtcqMU1Lwrz3uteYJqd2j7+twZHzxxQnP/jBc7U +278e99aA/fs9t5IIbyzPnkg73VGDL2nFZc/PPAdJ79KbPHoNqszWrmiNPkc0 +L/3RdpFaRAqoywq5+SAg+WS0vUMtnHpCnRi7fZGkm6C8u78WWgEj+YUVvtAb +4rn482wdJFT2ffc08QPLPRvdlOI6bFyxPXaF2R96W458XpWox0ROwb1dsf7w +edfXsCmyHp+tmDJpygFo8FPeZvmvHu/2np/LmwiAj0R2sv6VBjgOvRD38AoE +hW17yUhQA668GrS8tC8IIho3rrblNkD84t5k/vogqCScLadUNIB1rfWXKYtg +xGmohyZmNcD+xuBLfZYQcL7dcsvfuwH/Fa1mfdYOQajTjytlaID69r2dovEh +0BRdLhcZrYfsvXML/t9DYFYeoX/+Zj3EWq22LJ19AbVtojGynXXYfiBEQi/s +BSrKNLc4HqwDs1euRvnUCziRnja13KvFAoVkLSL9EuJe02PnU2rQHL4ndaH/ +JdRFOnfd/1OFp6w5+335QqHGorHXlV6Og+de+GTbhSJ8g4vlHHcZurzu0obq +Q5HJFV9kfaUET2o0Lqzb/RrhTCcmouKLILJWPFXC8TV4N+eW6m0vRIsiG7te +62sUbrTv+hCbjwfu09ZPRcKwQFvanHc1D4Kf61pTnoRBEtlb9orkou5vnERP +VxhCqnce7eDNwV25Z8F/D7yBmkLv5m1Hs8H7xGRh39M3YDq206/BOgsVRbii +SXoDUoihsWVzJu4s78p+dCQcCh6DBqLqmeCSXuGK9Q5HyImY5eGhDBQ/GLzf +MhIOIa1rP8T/y8DN3MKe78ffInrbHbH83Rlg/xp2YnfAW1SUrsmn82cg7+iD +MLXxtzBOSY/QvJQBIzutn/dk38Euf+9Bv4IMrM84qvf+xTssjN+9efJgJjJm +txTVTL+D8YYDH5++yISe+BzfHN6D1SDOpYEzC0xWLY93vHkPpx+MzHOJWUhO +ThlSmHsPBZ3oPC3tbFyd9pGzPBsBybhvnVo7cvBnn0Xkq4gIsIqot5TM5yDu +1tnV0q8RiNapT2EZyYV63N7/pi5EgvJbciRuNA/fx9ZUbImJhNrZ+sOs3/IR +tYcidOpXJDRdxDqeCxRC1bj8qalmFHx4bo+a6hYhfOSxct5qFIx3pp5zYSqF +ooB+3KjOB3CqbGNzty7DjIH0Otb0D4ieZ58wnCqHIOPRzfTD0eDcX/7nxWoF +7t45Kco0HI2JQzdMHVCDGp/43tANH6HA3d4bv7UWvEnc3geOfUTcc/8NbGO1 +qJhamrrq9xE9WqNeCw/rwb3e9M2XvI/Q42MxypJtwB3RznPO1I8Ynn9269CP +BnCZZSTFy8QQfOHuxX+1CebPBPVlzWKgydnNK7zQhJKYwI3twTEQUV0q4vRo +BmfVStHNkhgsnNrJmF3fAjOqleXyVAwErCuZqS4tKGQa4g/kioWd8PVLx6da +wC50oXmPfCxuM8s26KIVxih6kn8nFpryP6TGfVqRZyQmfvF1LBrkGhLfVLWC +zfXNMLkiFpT96wOMGa0wilwf6MCIhRx/E0NrfRuySx+c2cgbB81lF8Vszjas +H56YjVSOg4hYdPjkpjYY/NGKkrobB3Yd1+Puy63I4K++VP8uDiGdpA+y/a1g +kZX6d70uDu5rr6ssJrVCT/9jxsJiHPSkgoI+2rZifkibLYY/Hs4nLr7SkGiF +txHrLS3leKiYFL6+O9kCAWrJZxbreAx/er607XULcm7e5c8PjYfnboezOvIt +uDAl/MCiLB4CSasW+mPNoNzua+edigeToITRJSJ+HLZnvJ5IJ0DFaCPrQHET +4hcWyOLGCVjmuJbbr9MEuftxsqM+CWhJ1Bd4tdgIS6dNCwqDCZA8cnjX4JFG +rPlTfmGJORFyVZrLb3oaEO5iHx97KBGMhNT99q4NkGDax6SjnYjCS5l6hhIN +qPUYMFjvkggSvSpYerIehusC8wriE3F7YNy5I7YeS88VOO+0JcLsdjjXqGU9 +fNm+WfL/TMS0D4cJ0+l6CAUm1jbvTkJEXnj+Z+56FGy5LuSilgSxg3XrApbr +cOklxxOJe0mYhl9I6VQdJrmreslvk0BiCPYHk+vg/OaB5IuqJNxuf9VwiOjX +2/gP+CvRk8B4dUkqarEOKRHDk1+3JUNNWcRqhK0eCrtDFOLlkrFsvO9kI9Ev ++j8qv792KxkOj6pJh27Uw1bk5/cNQckQirr3X8nrerAkpmgW5RP4XdWmnaR6 +vD9glGpJTobxO5ep4b0NkErbul6ANQW5bmJ2z5wa0ChRa9wqmQL1touWz3ob +YJzlVOKqT8g/fco5K9uIwHyyHTUlBSItvZWevE0QOfWq+WV3CpY3lh9KDmlC +cYnqPpWVFLCzLWwd39yM6Yr0oQSNVBjemHKr4G6Bm7LJST3HVJCeilj/imgB +Tx33i40fUsHgiON13N8K5eYnqtYLqVDwr/IPVGhDVO/5rKOv0jDY4u60+VQH +Tuj93TRekgbxmpTlSJcOtAxmmodOpMFnbKGAu7IDv8g7BH6eSAdF8xTrGpVO +hJg2OyYZpaPmsynL4Wed2Dfp2qn/PB0vJ08eTavohPbMpHcpKR0TDYpG+ie7 +QLd+S7VZ8wm0Jxvn7tl2wWNeXW73wU+YVthunB3XhcxvOYtPn3xCfMimLxWb +urHp31PDc4IZuHwYfjW13Qi/o2skrpqBQc5A7pb5boj0iBtvtc2AjFfniwTe +Hsgn998cKstA9TXFJl2LHhQlh+UVSGSiXsQt12mlB7NajNKLbZlgVgqbSxTu +w/GN/WfkxzJxQUzqMO/5PjwuryyX/JEJ+XlXe2G7Pmw48KZiu2AWXLoul4pW +9GHPqmIN2SYLPMxpH9hv90Mn6U3z/c3ZGFFbduFrIyHihoe6+Z5s1D6x9Pjv +DwljXDateieyISzL9c5CbAB3XZTaz9zIhlj06CvlpwPIlzqsKXkvG3YyxZ4D +aQNY+bKjU9grG4812hTy+wfge3W2a0N6NliYC1yaDw6iYwNJ63dFNrQzNkw2 +Xh0ET1lVD6MnGzdjeWzfPxpE7P7wvs4Vwr6pKLtW9SBmhj10azhz8N9fbdNN +U4OQfGlDyhfJwcHS/OrTG4ZQtqI0+F49B2YpoyOVKkNgyT58Pcg4BwJu1a9X +jIdwwYJ32N0hB847PUIePRlCiMDaG/d9cpD2BmJSoUPo75wduRVBnA+aeCmc +OgTB5yQjvcwcnDywOn2+YghmctXkCzU5eMR7Z19K9xBSFtONz5BywDpJFVGb +HMJiQjj1CCMHo/oxIYe+D0HG8JmpMFMues6j32jtMFy32o5zc+fiRz/L1vkt +w6ip0zPbIJaLWXu+STr/MDY5K0/+Op2L8unC2xYiw7h6VMKccTkXn1Wovx6I +DyN8ivfL6M1cdHt3bZc4NozR92tvdz7MhV9iw6EkmWGIXpmbrvbPBV+tofWq +3DD43c7JWnzMRdP8x+2+CsPgTI/2ZyvIheMMy3Fm5WGsG/o1nN6SC6/KN24h +KsP4zaolcWUsF87MrdTrZ4excDLN7dvPXJQ8NNoVSOBJs3WdbzbnQXL3wwca +BB58aSR8em8epIwXteuI/zsqCu6PyuRB7dmDH0IErp3jrH16KQ8ihWc4vAl7 +xQKWPKJmeWhLknPcReDMC9UWDY/yYNalP7KZwPFOAkVWwXk48NnqsTOB3yU8 +YNsSn4d6un91AKEvpKftenZxHoJqrh40Vh2GF7NYuk5HHiZGnoxsPz+Mx5JP +V5cn8/DT82ZIk/ow7hoNXo74k4cfQp/Vwq8MwyyAaO5b86HQQJUK0x2GQXHA +0ti+fBixtzmTjIZxeXpS2VsuH+oPz8rYWQxDhQevD1zNx7uM78pW94YhqxI+ +1WKRj2+9Xad7nIdxxH5R2s4lHzWvouyyfYchEn3Bd9urfNhG+09tDB8GX1vs +YH5SPuZ1Rw2GEofBsbJyyKA8HzGOhpoiRcNgOXjN5W93PizVNIXJzcP4pZvR +Fk3LR2Ry3661lGHMebEKqfzLR5j03o+e34eJed/k3hfuAnBwXFfQYR9B2xZu +bgmFAmhaVh6NPDOC6jM2tzp1CuDEZ3qRrjuCQqu6fAerAhSphj86eX8EsfVO ++iVhBTBao61omDYCJ7eRKLXZAkTcyv5WIzoKm/STC3TmQqQ0ymfSVEZhOhSs +GMxbCEUdtuN7zEahIa000atciBMmIQvqMaMQnk84cPNdIbT5+xav85OxYxfT +k/WZhbgftuHx0Eky2C/qtyTXFoKTNp4adJWMnwmb7i4sFOL6fZt9cs/JYPSY +VbxaX4QX0Q0BW6PJGGMu3yotUIQ5m4UtnQVktBjZ5bqcK8I+3izukXEyqgIa +1+25UYSwzgMtPMtkFBQL69bYF8GFaTTQbx0FadNPkix8imCy6bCGJQcFMTy9 +v9iiipA/sFMohYeCNyoSFz/lFOFgQfSnC4IUBNg/j7jSWIStCQ9rNUQp8Iim +zH4bLYIUe5d6/iEKHradQvi3IuTSaXI+RyngkMibbGQtRiqb3dn7JymIC5QM ++CNQjPpxV5UJWQpkZ1OlDh8thiepKJsiT0Gn+v4Bo7PF6DVxTbJVouB2Woxb +iH4xvIOYO0LPUrC6SXBflU0xNnEnXjNQoyDU6m3L16fFaBZ7N1J3gYJDzdz3 +RcOK8XIH7c6YOgVVB0P4iEUQtf8EtfMuUaDnt6nCp7wYhz2DpdU0KZijeZsX +dxXDRtmaGnuFAq/zzJsZU8UwHaxG51UKBJJdcnb9KYb0uI/mgBYF2ay/9C9v +KYHxRDlnrTYF5Pr5hGzpEjD9phyyukaB434rjYmLJTC8s412UpcC9udTX7cb +lyD3kO0fVj0ivlMm7845lGBu4xcrGoFPqY4oPPIpge+DjimyPgUd8XpfUiJK +kLSwIeOrAQXm63oChzNL8D5i28tDhhSsmF0+zlFbgt69iiOBNyh4VdM0iIES ++J3v0xL6j4KDIqpP782WINXaZN+0MQUVzyr3x64pRZP8STrNlIJr43JtPdtL +MdIrFH7gFgWzSoUO6w+WonSXrkuKBQWeMcd2ysiXotz7k+JdSwr4mTMq71wt +hVI8H+WRDQXnKuM5Wh+XIvvN4xO3HCgYFdqTtxpUihTOKx6qThQ4uEdcl4wt +BfutGZKtMwUf8SrpVXMpxgfaIoO8KJD5wHG5llyKZokG16d+FLSt+n7/8bUU +eee0DLODKfhT5q5kIFAGyd6y+vJ3FLzctTLtL1kG3kfHHr+IpkDM5WFwmUoZ +HqeWPg9JoEBHznZYyKYM378HBPzNpiCj+Lrjl7IyTDGCSNMtFKjy9wvwdZWB +6+wx9ofdFAw/ulp9YaoMwSN/u/8NULDx1HnOTxzliM5QF/gyRUF0eE0+Wbgc +FkpSyzKzFJxcxo2t0uVwv6EiZ/2VgpsFJ1Mc/ivHvgcV3sb/KPjNk62ZcL8c +teEbz+xYR0WI4+Gf/c/L8frKud53bFSUnRBROZ1Zjufshvt/cVOh/frDjHUN +Ye/YN49WPipmvvG/iCKVo0NQmddUkIoduVtH16z5DIEXTMJ1+6gwDPijPcHz +GbuP/fo9dpCKGLPJ5jrxz3j/47RetgQVX+TalZKVPoP2Xn3xhBQV4tuLivz1 +PsOWY8bf7gQV9rMxkra2nyEpJfzvlgwVBbUBiZqen5E563x852kqlByNX2/P +/Iz5kjjqCKjwuXSBfbn2Mz40Ojj9VqSidd/xZ4NDn3H9mTbLd2Uq0ujPCtvX +VkByPOFM+jkq2vqXv1ZwVEChe2zo6XkqFqttjmTzVSDd/5i06UUquDPHLGNF +KtCWdWLougYVJyN0E0KPVECVw2yTy2Uq9H1aqF6yFcS+T8vsuUKFs4Pirodn +KwDX3efstamIMs7Xu61ZAa6S4bpbulRUqh8K1b9eASmHpJDPBlRMyES3XzCv +gHjmX50QIyrWi27fJHevAltki9fQTKk4sNVP9bBzBV50jH4YtKBC/e/qU8Hn +FZh4WaPiaEOFLe1+2ZaXFdjWwPjacp+KF73Ty0yRFQhNDvGef0xFbuWN40uJ +FSg+tOPlnAcVfeldd8ezK+DUH3Zp0J+KX2/PpfaUVWAxydel6jUVAt6lU7UN +FdgfSNLMj6ZC3v6ocEF3BWZ8b16tSaPCxCjhRtJoBUp6D6r/LqLC88LOt29p +FUg6JHf0VgMVCSdDevy+VeD5E+8NW0lUNAqv43T+V4FTpbldrDQqMcc/vmjD +VomWnUfcr/2hguPPnLfR9kp48Bj3MG8Zw9EvN6suC1VCQ1hff7vIGBw/a5yS +OlkJKQ+7CM+rY3ibWuWwV7ESz9To1TSrMZS+kc7kVq9ETMH5/lrvMayx27P/ +p0klpo1ux45XjEHEMMx02roSomF/1wlTxqCqtilq4GElcr4c+dDBNI4Aoe/c +pYGVKFq4QjZXHccndkvN9PBKnFmbOSZvNY7O5VH/qNhKRHsfHbZ4MQ6ezgbm +p0WVkJ05P+xMHcfHpxELZycrEfWqjMIdPIH8MeWWdrkq0N2FfVc5ptCn9nQx +8FwVahYKbCsxhR+fynnUr1Zh1vb1rSC7KUg/OWXSYFEF0QzyPKVzCoXbjvyo +eFmFltsGT6NCvoD0yHqnW2QVlhcEHWbKv2CZnKxwJqkKEqNK/xwZXyCTJuJf +VFaF0L5rj76qTKNIhV8oe7oKQbF1why0aQym6J61+0rof+edPc9Bw2/O15YS +q1WI1CuKsDxGg+zIlryUbdUYtt+bzXhIg4GyxuBtwWrckrx3pP8NDY+T/f7t +O1CNrX+O1u/Jp6H4wboLsfLVGAvQO5E+S8PgkNJdk/PVaPk4lD28fga/Fd1D +d2tXo0byY9J5wRnwJ5UVjRhVQ2fwy6n5YzM4zfFn9P0dQj7rxdt0bgaGDjIs +Bg7VEOr57k3Sn4Hz4IMDvG7V6LhVpMdvOYMIhZxLfb7VcHXbvhjiNIPShIX7 +oaHVCNx0QAFeMxhml3h79UM1KvzNyg+EzGDF3qqcM6UaUSu3za+9nYHAQNJ4 +W2417D9dS2+JnsEZTLEGfq7GxM2wR68TZmAUv1fiYlM1VlPEeEtSZuC6yURr +Y281In/5SJ5Pn0HUvSinejJxn7BjBeqfZlDePxTpNVMN4/rR0W5CPnqGr1r5 +ezVM2R6xzqXOYDX22vQaphrct/+XlZo0A0G20M0VbDWQvKxgJhg3A3m7TinX +7TWYuP3hg14UYb+PQ09OqAaJa5fqbd4Q9uXUXX4frEFage8W+2DCfoxvTOGJ +GrjSvEwee8/gM2t9vaNCDXZqeF6McJ4BxZZl9vjFGniaNk7N3psBU68i11ed +GrAq/q7wMp+BwsdSw7tWNThZXCA0oTGDilPZixZhNchT/0yb3kH8/2GeZ9/H +GhjFvkz8sZH4f/1huYnUGgSxrznHskKDYleit3FlDUQ+x4c6UWgwlZlMFWyp +QZIGUwlbNw0eUcKdw301UFL44/O1loYqy8id+owatBWqDPKm05BDs7Iy+lED +bb+yw/IxNMTdli25yVQLTU2P5Hkiv0K/sG66w1YLVfeFYdkgGrzM+w1suWvh +1P4pWNyLBsfJ+JT7grXI9uov6HCmwdzM4beTWC2uci/ZST2gQXdc6YKrVC3+ +lVZ9vW5Lg5rp1nfP5Gphq/Aj6NptGk5RyTQf1Vqw53+KPniThoPGn04FadZi +Xc/3ELIRDTvJzr6vDGqRy8Xb+uQ6DexGFwfCzWohLUuvZtGn4e8w34Eo21pQ +2ZjHXXVpmLs+7RTrVIv8ntbQ2Ws0jA7mNyR51CL2Rzq0CHm7vhfvp4BaXDNj +nM3So6GCpHU7J6wW4k/i17MS+jN1hQsLown/3oeTrxH2P/YtbChPqUWp+OiR +CFMaXup81q3OrUUUzfV6rwUNz3oCExvKa+EY8KV91YYGBy3Dn60NtXgkfWwj +N+H/ra6D57q7aiFzRjV8iwsN1678CiMN1+KJfPYBOhG/cx31UyNTtZimXw/8 +EEyDzOWwk+MLtdDeOVgu8o4GPo1jfbMsdVgQlvB3yaKBrWXNvq8cddjw1079 +TDnBFxc6Hizz1mEfZ8SZhGYahtVstq89XAcmWZsalWkaWutP32KVrkNq9h1n +k580lKuy5W1WrMNa+R1V3wk++KCSqM2rU4foxDOCl/bPwFSB+uqwSx0E/muf +PGQ1A63PGeNSz+vQfzxWxZHIZxV512MyL+qwuU4xvjpwBqJyO7uV4uvQEPRx +4WDmDKaldbj0WusQt08yyG9pBgP5e01v9NfBsa9UQp2ZjqYTS1mm1DpU6L/Q +ithKR+qx4Cs23+vw2OJaU44EHRHZNz7a/yP8nSQLmsrREXBUfPHhxnpMsVRy +2Zynw/ZIY4jHrnrsqjZktTGh479PbyjP99cjIn1fsYY1HZqHzSUDj9bjZGW2 +s6kjHYppx91fnq4n+uHvyRg3OqQOre14c7YePc/jLm7woWNvSufuyMv1YHmi +3egTTAf3gei7Mfr1cObVUN0TRgdLku3nxJv14DfUedz8no7v+85sSbepB/P0 +xKJHNB3yY0r1fk71mP7g2egbR4d3pJrb7Wf1KPpR5mWVSEeb3iVp1aB6LAfe +o4om08HDrT2/9209KJVeTQUENmrXT1wTVw/LZV3TPQRO8PvvP/KnenBI/V65 +Sfw/d/bWjrKieuyUV9jtQeg/ucaq/V1NPaIEPz5xI+y7lto9d2qvR6Ha0qwx +cb+6h464NliP68/XOoq/poPjmPPPY5P1ENPee5QWSIfu3NOMrQv1CHYNvfrB +i47o5OcW87/rwb2wyq/nTMe0WeDu1nUNkFebattlT4fTUHiwz84GRHd1jf41 +oKMiLOqc+b4GHAgOdTh6iQ7Wq3H/lI82wHBkn2acAh1vGzLu/lNtgHfv4VPP +9tJRnFd32dG+AarONi9nxgj+D/62xayxAebZQ12sekQ+Xfxdr9jTAM8TuQbH +iH4TsJ7JfTeZON9xj7nk5Ax2uWxaGPzWAKWth64fIvjQXGZrUuG/BmRsMFsr +wzqDT195jMPYGiGc/+cd7RcN8pbCHVeEGiHT98XWlUyDt6iYz5FDjdCqdo1/ +SvBhG+WwwuaTjWDb+Sb+TgMNPBHHlmcUGvHwuGClClFPRrqnMhsuNuLwDrKv +UB4NCVy4nXCtEUnnpuo2Enw516oi5GnSCCXXfEv2BBpO+l4gmVg3osZBx+9Y +NA1uKpoheNiIBS5pHd/3NDT801Hb5dGIYAN2jh3hNHCWXGf6E9CIS36PWSZf +06DnaFJIetOIQeby4N+hNEQftbDLj2kEb9BpNiNCPs2wFgtNb4Rx6Zo2boKP +JZPsKfcKG1G857TUXoIfnG46hV+ubgRF64VvQBTBZ4KumofbGmEW77ZHK44G +1sFnrJsGGtFQ8ErJKZUGzde+FdPjjUje8/boSg4N4ZrBTnVzjbgclHZ0tIwG +6qbXknG/GiExc/S5QCPBx/Xvpp+yNIH5VtKT3F4a7D2io//b0oShS9dMY8aJ +eeNMgt4Z/ibw8tdFUpdoYP6VyrlTtAl9fJsTrNfOYGer0lccaUKoqMgOFu4Z +HP840Gt2qgnrLBels0RncOv8hvefNJrASLDuOqpO9NddUS7duk1Q0Q5+8MN4 +BmGLx42XTZrgc1PzQI7jDBremooqOTbh2AGDQ4tEv6ba/Npg4d4E124rl//K +/j/fhMz4+zXB94nq8oe+GYjPlGX0RjUh/eIEzXoTHcGyfLJ36ptwlO2s6R8i +35M4MgWCOpuQeZjjQ9U7Ir/HVP9lDzWhweVs+79COpb8HGpW5puQuxr6POUH +HdeG2i+F8DZj9Xve5VsPGBBw9r5ZcKcZlptcWkkPZnFCc5fq8P1m2J9L57ny +ehaXRHLF1rg2gyJ9555X7izcWqizF142Q0jU4b+/i7MYEzjjNFrcjB/6jO0K +t+fwZ6HbYG1tM3j6lUXSPOfAXWt5Rqy9GedHfHTCouegahPObD/ejLgl80/t +fXNILvsasI69BSkMDw0juXlUvfC7e5CnBQbtBzqhPY/BW3uuXhZqQeMes1QP +q3mwc1ze8fZ4C9pY7S+Ihc9DdGzyV5l8C5YEE7X90uchn+88PKbWAiOlT6fV +q+ZhZ5TyUfwGoX9/Uc1X2jx8pRQ9r1i0QFN79tPwyjxi1pPMHe+1gP+n+b/X +GxbQ/WmdeIVXCxqeXMpg4VvAyX/G+VqfWiA2GGX2SmYB6hoVHmcLWzB8Xj4v +Awu4+X73ZemqFgRZ2216qbqAEOnRL/x9Ldiq+sUuR2sBtLvX+cb+tmA0idez +yGoBTOXFk90bWvHb/ae1zr0F8LDzZ9dubcWMkuWadscFKCWRLiSLtsJnsYb3 +9tMFRFB0nO00WlGxVmki4PUCsiXy1Ex1W7GcoffZ7t0CGpy5t2ubtMLNatPy +xQ8L+M7bnS79oBXBFrYp35IWcOmKJnk1ohUX9AZj/itdwJqqC0qBjFYIB/1p +rJ5cAC9nCofbj1ZoxYo3atEXIGG0cciOqQ1Sa9LCVhcWYPC7/r42dxs6bTYc +TVpZQK7U2fidcm3IxXF1g+2LMI8Fa4p/G5yEf6vtUF+E82JUz/vXbchq1V41 +0lrEK6xGB35ogy2XTmexwSIqhkpP3ctpg4U1n0jinUXwcctayQy1IWjyTBO3 +zyJaPI+31R1sR/HOafvFmkXIbmlmfnGiHbdv8Swutiwi6a2J9HWFdjRZ7mDu +61nEs09B0fM67dhjQ4qWnljEgoxob5FxO1Q3anmm0RdhVF2y0dOqHeqqB9K/ +LhH6SNP2vE/bkbK6FPyFaQlJpm6JY/7tOENmqfTfsASe2e3DaWHtsGdxEl/c +vITFNcpnFdPasWVtvvo83xKMAgYebSpoxzuDvevddy+hhcfuU29lOxo6bmys +EiH0HYrcYdnfDuHVneIXJQh9+cfUj4+1I/xPH/ylluCp0OS+ymhH3AFWf9uT +S1hqMs5r+NkO2Qze6cVTS8hM+eNwfk0H+oQlDbnOLOHLvGrwp/UdUPrvKl8r +liB44mXyNvYOOETpuO9WWoL245Fqp60dkPiUIbxBZQn+n8VGR3g6wHqKr+bp +2SVUsTgsKwl0YK3qesNA1SUsn//MlbSnA3tlvvKInVvCkWC2w5v3d8Dzs5eu +JoHNe3TO2Yt3IFX7aQELgSP5Ppr0H+3Ay9UgVhXi/x4jxhM56Q7kXiBpbyb0 +b4qTDvso1wFHrwfk/5SXoETzyFyv1IFm8wyR04pLeCTR1mR1rgO/A7gHo+QJ +/+7zTXaod8BY+eac32nCv0KzfyeudkBQWs33nzTh32oG33vdDqyMLLH9PbYE +HeU/x5hudED8gfsmzyNLCPBRvXTLtANsUfIGrw8S/rW+uN1k0QHvsrqVo6JL ++MU14nHEpgN2xl8PXyfeR1JPLDLUvgN1zFmGXMT7mUfeL/j1sIPo36kH9bkI +f/azMao9OvC1aG535FrCHxud9Qd8iHjmvH8c9WcRStnRQkGBHRDybeuX/rqI +TDlpHb3wDqg+WR2Voy7iy1OPu2WRHQizV+D41L8IwfpWX+HYDpT6aqhWtS4i +4IpZOSO9A6Rt7kaUwkXcNn+x/2l1B8pPmFlf8V/Eh9RhxamGDqDXQ0jGbRF9 +C/sNL7Z1wEaWPW7EfhEqT8pDtg90IGIx4p6D/iJ2h9B/Jc91YCAkLVReZBHl +Jm7J2V870PF2U67DDiLfj23TL1km7Ld83B3ItoiIPtnCFuZOUJ0C39wj6pl3 +l5/jPE8nBvlW04xLFsCVIvb1ODrhUhWudFdzAVlPSmPOqHQi8/LUpmPKC9DU +0Lyqer4TUp9XktefXEDwwsMsXa1OfPhXrzO1cwHs0vV3H1t04q/j4YmnnfNY +V3OL8Tm4E7xRu+9WcM4j7vWv9w2hnej4zea+/GsOKhaBFzvfduL3xDY2j/E5 +eLDlpYzFdqLskJFjcMEcVjVZ7qwr7MSa3+lpOTfnECkczstR1gm3mKaW8Mtz +kPt2qIGnqhMqHml/+07P4ckbrf1iLZ3gsHvr/d/2OSyPxExeoBD+VVktRLfM +4k3Gyddak51gOTWtfblkFiefNqkYznRi80euNJ2UWTwQWYq1+daJwxYWdRa+ +s1iyVDQNYe1C3POewYCLs3gh17v17eYuvJe6Ez8lNwtJjjuVH7m68FiK/fsL +iVnYZoUI5Qh04er5JYEBrlnQf5JHeyW7UL1i9oidzEC+RXDVhZNdUNv10qir +kwH3fvmEz6e7YJHeJDlXwwBPQaRNsmoXiDP3hNMYUHK8vuJs2AWx+6w8110Z +2DzFRlk06ULQ78Sl9PsMkHSKq80tunBWRt1C4w4Dtif4/DXtu7B0SPiGrQ4D +77718Yn4dOFy8UrKnqMM3DLz/hse2IUxVjXOKjEGJHtOUDe/6oLk2/fCyUIM +1OWEJv2M7EIS00OH81sZeLFXJcA6tgsfDFKm17AxYPjq611qEnE+PPPeP2YG +Fu2vSjfndIFN1je94TsdpWNrdioUdUHhlO3cq3lif7iatZpb3gWtW99uxNLo +EJDirItqJM6XnjsZNErHl4+fk7e1d2GbtZXJnQE6srfeDfTp6YL2nmU5nx46 +1BZbte3JXdix+U5kSDMd20xcZL5MdOFV/MzMo3o6RjvEBQxnukCXpDomVNOR +rDD8r2O+CyaSf/h5KuhwyPQfP/u9C9Z2lckNpXRA6HR98e8ulLauMMqK6GAL +mUk5wtSN3OtCcd/z6ej59zYobl03AvYXe9zNpePD3fP2fJu6odTEkDiUTYcl +eVkniLMbrxe+QiyTjuOXk06t5enG6FKenPknOv6V6+5y2tkNPDd7N5FG7IcS +G9bMCnWD67lESUwqHa+j8idM9hH60llmP6TQYcxh3tB3qBsxu+7fHiL2pUOu +29MuHu2Gle2Ly9oE/jFbE1xxshtsPWzpGwlcecPh/gm5bnz/hvu/k4h9snWv +bopiN4zbnz35/z6me6Zbdve5bvD/dfDyJbBwuodgqHo31J45nBQl7M0KSDFv +vNoNJrnTfD8JXBhAnXTR7YZ3XVDkX+J+HishjUuG3Yho5OGVTqdDw1oh3cK0 +GwaSWlUfCf94h+dDhi26MTOVU3ya8H/s4geHKzbdKHHqYllLxCe95JJenX03 +wlpbfb/nEPvWodXTp526YS7YwLuViK/y+/TdmS5EPHieW2gR8yjHphtrRZ91 +48zciW3FxXTEzZQ0cQR1g5b3zH3mM7Efv7m81/JVN0I/BPV/rKJDWmX8SW14 +NwTDBk/Z1xLxjWQ77BzbjSb2KgctIj8WNfWDaYXdqCYtjzT2E/vaX8YXlfJu +PHnbcnRlkA7PFHeF6OpupNbPzkoS+cfLkrR4ra0bcSrDua8niP234IdWzXg3 +DsobCvxaIPZBM7+03bRuOJezutK/0tHFKbjuyVw3nDaVFTQQ8/Mty7P5R391 +Y0ibFCizQofEjgGOwNVuiA+vqaxdpWO52tpiem0P7pPlVqXWMBCwK5T3A0cP +WJXNU2PXMXCtaf+939t6YOp+4VbMBgZ2Pyxp1OHrQaHEvcqHGxmY3ntZOEuw +Bxe2c37as4mB7I6xx+wiPWBK05CNYmfA2cWx2+JAD2zJ4uH0zQyoHmQTr5bo +QfQrM0HWLQxw9kd6Ch7vgdNvoQtLBB54dnTk0akedFLSKpI4GYiRrD3RK9+D +l6Jrrhwk6t16RC9IUqUHl6Jlvj8g8Ek/xpT/+R6Mtk91+xGYSdodXy71gFR+ +WfE2gZvGt4Urafeg5qNbxWYCvwpJXIjU7wGjSYHlCaHf8Mzp87+MepCZNDef +QdjfN9P2UdusBwaRIuFpHAwshJn+zrjTg5PvzynfI+5frPzj6qa7xP38aXdW +CX89F3xTzR16sJywrkCb4B+NyF0sVY96ILHCzfqAleDLC1mGu9x6kBby29p4 +PQOUHyp5Tp49CHpVt5+XhQEHTWvzI8E9sHZK+LBEvIf833/lfqE9ENx/rZ+X +eK8NKa92TL3twafO53pcv+h4t7akISKuB+72ycd8loh6y994iK24B4liO1rr +x+nwuxn57NZn4n2u8Di3k+nQ5jw6XFHTg3sL+ZkVQ3RM39ELfNjeA9czH57b +dBP5vStxfmKiBwvbUv/pEvmrcO3ZyDitB9wS5i7Xy+mwD/6veWyuBz6Uow9v +Efnft4Y3kbLcg+1Mc7veEfXEevpbKPlvD4783urYTNSfrEOHxyhzLyjd/95z +EvUaNeVjNMzeC9M61aTxWDo6dt9SH9rai+zMf4edoulg1leUHeTphb2/bsnh +SIKvXu4SG9jZi09zFT4biP3QvPnXdpJQL7is6BWsb+gIZ+lb2y/aiwuW51yP +hxL1dSZ7sfdgL6Ty/BsCX9Cx4hhE7jnSi9cy8i93BBP5nmnZ2n28F1djFPN7 +Agg+o6mWdJ3qBdnuzvd6PzpeCu9N7pTvxToOnm9ffeiouf4vrEO5F0IBg9LX +nxP8Fjrk2a7Wi5G3h0WZvOkQayuwb9PohYfc/r8TnnQYbAg1br3ai9Uh9aFN +BA5QsLvUotuLN6I2OY7P6Ch/pC7XbNgLJ+XAy/sJvJAtdrDJpBffR6c1dhNY +mMHC22jeiz6D9buNCawtSl3XYNWL+CTKWjqBvY3KvtbZ9SJkqxh7JaG/8M1b +au2DXpjjPfe4Fx0zHQ/aax73YqL2Ue0V4r4CbFfLqt16sf6/rS82+xL8qCyR +WuXZS+zT5tk8/nS4OrO9rfTtxe3ulUM2gXRk5k15VwT1wu1Ufh1nCMGXc1UO +n18R/oUNcq55RQe32AfT8vBevGeSuXEmjA5VkyeaZZHE+3iaV9W8Jfjzna58 +aUwv/msW5w8j3m+YnZO/OI3wn7+9lzOByC9VxoairF7sc/Uvyif4XMGt4XtB +fi84mW4Ef8gg+HTRvTOvoheZ36ZvSxL5Zd236JPV04sUNXXS304if7a0OWYO +9OLO8TcbrUlE/qilmGWM9kLmomjRWiK/j5eYKqRP96I+6uDzKAbx/h+6fyat +9GJF0Jy+StSfxEDGZOKaPihxjWdLE/VuzBXQnbC+D67ulzLsdzBQ46mSEcfZ +hxqRezIkUYL/7uSZR4v0IcVXeW+hIgMzCuk+mw72wefqlT9f1Bg4xxuf4nik +D+M8rB7kywww14fOqcv24bG81dO1Nwj9UQGchehDRoJGseBNBsofeErtPduH +4rpfh8i3GRDQcNYOutCHns9VfHK2DDwScXD8dbkPUkVPa8SJeanvj1W4mU4f +Do7n3U16yMDx7pvF7QZ9uHo1yzzhCQMvU64Pyxr3IdajfY2gG8FPT7VW42/1 +QV0tO3W9BwOX9C8KbbXqwzv60yldTwZSJZWVnO36oCd2+MpGbwZYWU+bfXlA +nK+JT+N6zoA5Wcr76pM+iNjxUK0IXJN/MKnMvQ8T8RxrNxNYOEi4Scy7D9Gn +P+rNeRHz4C1+xiv/Pny/ZW/ESugfkePi+BfSh1OzWS1aTxmQ5WaTtAzrQ77J +6vtGFwbC6Wuu9r7vA9d+Cbabjxj4UfXrvsLHPtyT+xPF58CA9rvF16kJhL38 +IMkvNkT/uEcr4Enrg/P36S+15gxsOU8deJrVh2/Je89mGhH8LzTwh5Hfh99T +fns/EvNj08+OXXqlfZB19it7dZEBsfYGVFf2QY3ZJvOZAgPeCRUmEvV94N42 +88/6OAOKOpnxLF1EPEs/9O/iYyBKPKn+bn8fxEiBnmSin62sjaYNDvehzXXv +SBDBt4XZwYezvvSh1Ji1I6OXDh6/55cFZvugGD5yYjfBl/dN3O49X+pD5AvB +sYfEPCLBeTfvxt8+iKtSlybdCT74Yt7fwNyPmAvr1/29TdRrudGvY6z9mDni +XsykSUe8zaUzbNsI+a2V8T5+on6bD9fmi/XDWXbrzI64GTyOEf2yR6IfT/7I +nZt5NoP+R7s2Bh7rh4nNm6560xm8FNuscVO+H296/s6V7poB8cY9W7T74YBU +UW1fGn4opE7cduuH5MDWtjL5aZTG0d8/9OwHQ6e8YGH7NDxYxbW8ffshKOYl +2sL4Ao6OtMrYV/0w2pIjG/v2C/b99ylqNLEfxxUTfGkLU7jmkqWn3dGPPskz +5MmoSQhQF7fc7O3HKYrjzVsPJjGmIlV/b7AfYlK8iVLqk7BlzzkRPNGP+I9M +A+TfE/B+n8vVtNyP/KWKmugbE1D/962R9Jc4L/0pOEV6Alw3Tzz9wkyC3s51 +8Ve4JhB1MH+eZTMJIjfvK0Y0jiOvqKAFe0jgYvNw5FEcx+Ndy88u7SPBcHhU +4J/QOBSeypy+cYiEm+kbRuvXjKNFrSj58QkSBJgS+7fXjeFl2i9jX1kSmF0P +6yclj0GPU5Y3HCR0rZR4nAgaw0R/sXfeeRJ4+CyyrxmMIeX0nzM1l0gY9dpw +4bviGOw+nP7epUXCtPTW5NiDY1gxL725cIOED+JbRxX+UVHVtML/z5SEEfU8 +LWk6FT4SZ7o23ybB7FtzqzqJCu4fZQqH7EkYK3rZQ86jYlB/9eephyRs379m +xiSBiugy+Qw1ZxJqL1hxs4dTYb7HzVz3KQmneB9GkP2oEPf6vMvcmwQZ7oFb +I65ULE3/63HwJ8HVxGF+nQMVheoKAc9CiHgcT9DSt6TCNdNd+eVrEnTOl6r1 +m1Chwl35O/odCRcmX+9xM6CCzWlNdsYHEjI7bNsua1PRMaR4pzyOhIWU7pFz +l6kIg4dQazIJO8jlLrcuUmEYW9U/9ImES3dHnBPUqBDesDZ4JoeEpKLfF1nP +UTFtqaz6q5AEW9WX/56rUvGp7dnfDeUk2EV5XxEm5A5SNbk81SSo8azEdBP/ +mx8Xin7RQILsl7BnZEK/3klnf/Y2Eu5Jh/SLaVJxQYbk+LybiPfUSk6yDhWn +ZY+bMg+QMCd+ouK6IREPuRANl1ESDnGFnpIxo0JQniGzPE7CHR6zn9I2VHAq +qIncp5EQYv3DVushFcxKcVvm5kiI2TtW4OFBxTdlpj+3vxHv7347pCyIismz +hlPjv0jIL/9j8uc9FQ3nucsGWAbQMM/KZlhERfFFuyRttgHs/F1xwrqRijSN +llftWwbgwNrFYTBIRfAVT8ta/gHECvyXn7BKhbsWRUdBiJDXr/+xsHUM9jpy +iiWiAzgults+LzqGa/rfdmRJDsCR5acu5fIYBEzMaiNUBzAxcvyJfgqRf3Yq +Qg72A9C/+bX5y91xRNhHb5p/OAD5/p2ul33HEeiw8uOOywBIO1WsSmLGYeeU +2/qfzwASvj/jcewdh7S7yJOLUYT8Em/29VMTEPNwN6+LHYBfpblq45UJ8HsO +X1FMHoBdH+UB484EVp+HiknnDsCyPrRS8u0EaoJZ+oSbBrBVFzYtSxPIf2Fc +Gdk+gIPX7zkysU4i6VVpGm/vABGH3u5UgUn4v3F4xkEZwJLqHZXLKpNwftth +6zs5gJBjqt6ndQk+eC9uwEIfgOqAwZPndyZx9cOE5O/vA7gunO1zMGASKh8V +BB78GQDLmI2LU8QkTsRGbFhgGoQft+PotrRJ8CZqj05uGoQt69hVkcZJsCVn +NhpvHcQUpWfpZd8kVlLY84Z4BhEmM8WjND4J8qca/849gzj/4tFHvd+T6Jhl +YUjtHwT/WUu/QJYpVIifVQ8VH0RAXPBjZo4pZFp5pX0/Oojjf5MM8nmmEJ1S +y64rPYh3bsMGSYJTCKGtsymUG4QQY+div+gUnoqptvIpDcL/kk2/ivgU7C28 +Dz85N4ijFnxs80enYJpQFzisPohuy8ravpNTuDq5fu7M1UH0Nd3wWpGdgrLI +uUsfdAexXL6fyUR+CsdvPv/EdGMQNZfv7l+nOAWRmHoOU1NCHv+fyIzSFLip +G+5WWwwizjxHZ6vKFNYJqbWL2Axi85SBhjOBfxj5HPG2H8Sble1t4gSeimwI +/vJwEG1qaxtFlKfQN8y6oOYyiDVJ+66bE/rrd57XTPEYREradNNXwn6hgW/m +Jh/ifG+IV/vpKSS9beS0CRzE7bOlAivSUwgnbbzX9nIQlz51KTsfm4Lvjgud +R8IHIXbwSetViSk8vuZ39EXkINSiuZI9xKZg+brpxVLMIBwMRSkcwlMw6GFb +0koaRIbl7Kvf/FO4uO3i1bz0QRgo9v9W2zYFuav+2Tw5RPylOYz+sk1B/EUz +l1PhIM6c4Nqxk3kKAh2b7g+UDaJjvV5g/PIk2Leod8tWDyLo/fdj0XOTmA1o +efW3lbBXJLDpG2kSo83s34y6B2GJunParZNoY9PQriAR+G9dg1TlJD75tHI/ +Gx+EuBKl3ilxEnaeba9Zfw3izpc2c3/bSRhXc/y4szoI1dQTpgr/TeIK8+Vr +zWuHcLrulEfw5UlIubfzBHEMIdMu027jkUl8e9LxZpvIEBroQz61tAlMFHMu +Oxwg5BHsLvH9E+j9panXJzGEAEGVBzK1RD097OR9e2oIJJX1zzw+TMDpftdb +wctDkHFkWpzXnMAfy573Bx4PQbs2w+NI8ji0T954IeE2hKicpVP9oeNIWzPl +fcxzCEsjsuP67uMwCv9570zQEFynVCu/XRtHZS2/2pWYIbjfPf4+inkcz4VM +vjk1DeFZ0Ng2P+0xbOubVW/gH4Y1W8yK2BcKDiluWDUvGcZU4jdFxwri3imp ++0kVw9hXPLBtyG8Ix7k1r5yvGwazPJ1dRmcIcl/C4w51DkNx21GjERqRF4EH +Ly5MDeO7xtanU1yDsB/QCH/ENQKGp5SXghkJRfdCpQLujKBpxXi3E7Enyg/J +GP61HUGkxT7Wb809qFIZ8bJ1GMHr1MJLN173oGnHvgFNtxHccsu4+HV/D4bL +Cty2vx7BQlp+0Gb1bjCxDbVEVYxA1aKFfCi4E+di9lhk7Rgl+pa6VdyaFhwP +59hXJzAKUy4VnxthzRAK+jMxuGcUcm25P3gONeP3o15TFvFROOeU7E/QbkL6 +FV8jXYVRPL6y8wVHcgO2rVnU+Xt7FKjI/an8Xy2Yfo5wc9mOYrX61Pm9yzVg +MJq6990fxTqWS3diX9SgjhR3RdNlFH+k95iX1lXjUaaeRuyLURjuy7Ajy1aB +/F+FyvniURSuWxdgmFmOFp30tUafCf3puv5sLOUovPiuyr5mFCxhHrFjBmV4 +Ke2gENE2isa08PAXXKVwO2zyL7N7FOw9WyWT7pfAeu+l8lrSKFaYXI/eJhXj +7BYxufmxUcjHvxYyTi+C1Lrtf9ZOj0L6fXtKz64iCP5ZU8w7Owr7k+uyrV4W +YnlqSFrp5yiCfrBb3fcpQGp58LHXm8hwrXRZP5iSh/Bc56VkTjKkQl7J6SIP +nil3ssq3k3HLm0mtmpSLe9HX7Lr5yVhTY5Yh9TAXRmHKR6Z3k5ET7xtRyJ+L +iwGScysiZFiRlhvNq3Mg47ErfetBMhia03Ya93Kw1fbnwdPHyRg7lrv773A2 +Vm9O0C6fIiOcX8px9F02ZvQ7k8zkyZiMvVYlZpSN/svlFo+UyTiifil/fF82 +as6m7gtSI6Of7+fu7d+zkHU6fDJGg4ytj40HKxqyEHXUK67gKhmj739/nv6Y +Bb/99jdbdMlgYbhFBrhn4eGu/4SphmRs54kVTTHLgqmm5LVhEzLsX1fKRl/K +wqVna/z6zcmQ+ej+s+1MFmTzu8q6rMiIvkbZKiGVhX202MVWOzIUyhwP5BzK +ApfAA9HGB2RwHpKtuHIwC38vqerXPCbD+Nyh438OZ2H66Y7Az25klCdOFkWd +zEJP7nRFsScZdR936R1QyULFl6Jveb5k5PpsnfC6loVUfn+xrCAy2kW+rUbY +ZCFMw9Aw7RXhX50Ot45vFjzcD4ckhpPhTA3Rf5mcBduc1eqYSDJScuTbTrZl +QX+q/WdkDBnFMwVnhH9mQYXv46G3iWSIDccpSolkQ1Ld/r/QNDIk1KPPKulk +Q8BN+VVwFhnP1Ob9D/llY0M2d71fPhm7uTWP1VZlY3RHgcTTCjIUIfL2unwO +mi74mDrXkhGSwL1/xT0HeS76YQ+byCgd+q8htC4HAeN//tr0kOFmsm09RT8X +TjytR+8MkNHTe69hX2Iubp6PumU2Sobdjt3rg37kQjZDodVgmoyDvh6pXe/y +MP3YK+LcChkR3zSKrJbyMXPt0O2PTBTk/CIr/j5fAOOFbcy711KQndmkkPqx +ABf3Tp7gZ6XA75nrV0PNQgj7Po/k5KKA8WTtsmhsEcKF7aSDuCmQeXk99OfX +InCU6nVu2kH8v+LsmahUjF9zB9ZtEKCgQmv0nSNRT7Y+XB88BQncVx/+T7AE +E3v+yDDvoUBIprJP1rQEHdot1n9FKRg/cXpf5EgJVOdy1z8Ro8D3fXXWke2l +KH0eGb18kIIJg81ZF9VKIbXHW9bxMAV1MyvGSY6lSCy27fl6hAI167HOvx9K +IaCta3tPigLvjMoN62pK8XIWrPPHKRjufcfvNFYK1udiMdbSFFCj465x/SmF +q9BWuZlTlP9RcKXxVH5dVElkqiSlNElCKir9I9mUIklCkRBSqWQomg0pKpUk +ZU7RnCkJmbYpRJkJIXeenntvKlSk97wf1+8855y9117nnLU/3As/XY66xCiU +wc93vzuPGA+CvXGhaa5qGRyzp/uxTAbhKdMhU39RGQxSDdMOmg2CD+fYWOeC +MtgT+SZjcMsgHO2JdXGfXQYNi1I2uW0jfFVcFN+TKgPTd1c+f7Ek+6fNZ2wS +lUKB3YmAfTsGIfvb9rtLmktBl9oj93nnIKDM5yfyz0uhyMEao2wHoWGBzcyj +gaWwpWzzKRN7wsd6iTfU+lJoWma4/PueQVBqelDmJi4B5+jVX544DcKzbRm6 +UaklwB5Zdnvf/kGwGh3ibTIrgZMH1LYouA2CtdfPIeveYpioUxqtcB8Emz9K +p6O9i+G63rRXgQfJu2V95m+/4B0oJ/5z0zpM6n9b4sp8r3fwcNKIUp/3IBwb +cIhf0VoEuseo2tvHB2Fn4p+A0TVFUNRGP7/Fl+hB57DyieuFYL6xZ9Wo/yBI +uvL2h3YUQHNGM/3lqUEYCTk5R1O5ANiBpVZK5wZBM2jyDu2AfDjZnzfx/sIg +eHdXvomOfgN/t77IOxcyCOzdWjeSHuaB8pz782iXB+FeQv6Zb+m58DD0ZlNc +5CAkpM3Y0quZA7rc8HDL64PQ8/VHC38oE7a88+PnRA+ChO/U4NsWz6FpyeEH +B+8MwoOAC1l9bU/AOcrFbk7cIPxZNKD2ZnsGnNy/vTgkcRBASzayfDQZHv5V +j9r5eBBSJFhVPPlA0D2sajLp2SDErJeVujNsi4VN07/nvxiEm/HDtkZSwdiU +Nr5PLWcQ1D0HTIz+3sW/Zl3agneDkPqeG21s/wydI69/uNY8CI49Lnkfat8h +WxQabNw2CPKye+ZsvVuCAY6n9b91DIL+hy2d3ANleE3rYKJj7yBMMfpgXnCh +AgsajI9qsgZhh0Jq9gfpGpw1/ZtMzZ9BqBc9OL3gTQO2lUVd3f53ELZ2X5dk +Hm/EWJ9lU5v/kXo3+XO4iz+iUoOzZO8UGlgYTGr/GvIJ284OXzogTYPW1cl/ +TyxvwtjlMRKsaTQoME39drKxCZUi3v8VK9KAHjHJO25yC7atdb8YNJP0eYHX +35nubMFY+p8/f2aRvntvtqHtvRacaar3S0qV9HFrljC2L2jFFlHD6RvzaXAk +4g2l6NqKMamHhmcspIHRvesjVGIrzhhL+j5/KQ2Omavm58u2YcsLg4BHy2ik +jzF1u2TShjFOLWJNLRqcf31JcqVfG9pKH/fN1KGB/PbnX1+ltOH0Aimh/koa +eGz0sv9R24ZNXg+PF66mQemmd7zfwjaMnrWRb7yG4H0jLoUz29GmqtO7ah1Z +32NNssaadlQM8OdY/EcD23Grho272rFpkdzhT4Y0eL/Ya8cv73aMbnrCtDOm +wc1J7LK9oWR+sOnBbhMaWBeNTtoT244Kul9ormY02LkiyOj7o3b82BvkzthC +g/mUW9Oq7Ha8eX3GV2/StzvLVB+VL2xH6w2vXEWkT7ecsnDiVmk7ynO29p0i +ffqRwLVVheVk/r1B59///x0I31X/dhmZb36hJ4T07VOX75Wd/47M/zHbaYo9 +DbprA3YefN2Ocum5XddJH1/csc8o4Gk7Ntju2DPdiQZnfhnu3JXQjlH/WO1x +zjQwW3l047Sr7WiVHWY3z5UGiqtviV+dbEdZ1/mtaQdocFnWKGLrfjJfrmDX +Mk8aXDw33ZxlSuYX2za99KJB6vc9SclLyfyjAmu9IzRYeXvBnPOS7ThtbmTj +26M08F9GO3h3sA3raxdbbfShAXd17qax4ja8FlRSX+FLg057+ona2DaUaf/2 +vvEUDfY7Wkp9NSLfX7phvvs0DbZIvvjpLEe+19Os7jpLg0BHDcP4nlaUjt5f +QQumQdH29xWFfq04dXtt8ehVGvTU1T+7H9GCtaPuhsFRNNjerfhI3qIFI5+O +FU6+RQOr6gWXNKRbUGqK/luFWBrMo+aln5BuximYnLM0hQaVOYoDLYyP2Gts +bvn1AQ3ylj5WULb+iDnF1GDSIxroZSy5fP1NIzoXbFJSekaDg9SZWZ6XGvB1 +1tdAiTyynvrueSvV6zFyxTWF0nwaeIew53reqkOXF3pPzxTSoIqmIhX4pxZl +nlz6LCqlgc5F5+/nvrxHt5SlRv11NAgfM6/tq6zGdfM+tiU00OBtxCnOR/Nq +nJYQeNzhE9HjM50jih+rMP/u+5TGNpJ/jmdtGrcSo2b6GlztJHo+ft73TEgl +ut9WadrcTQPN4esNOaqVKHfjyL93/TQY3GS3aoNHBQ7KzEgIGiT1GVK6Ma5A +7o/IIj19Bg0eJrdrKYcj3pzi8YFiEX1/u6CjNVyOnuHTPJ9zacQH7KLfCyrH +DRJ5fw4KaNDh+G5JkWQ5KoQ4310kokEiy+YhI60M6WOTdb98I/Fv/NV72KoM +i869qrn/g9Tzhe3IdckyjB61d7UbocFVj72PoxtL8WDQ+LDCbxrc/xigkJte +iht+PI7+MEaDvvKBUvXrpeQ87lweMUGDkeDQGOXQUmSKhtF0Eh0k7izKzLxS +isU+D5zGJelQc0LHXy6pFGP424YKp9KBqdl9ygpL8ZC3+PqpaXTSd7SEX/xZ +ikbsePXV8nR4fczsQZZhGc7wMi3hK9Lh0eyjkxjRZcimce2fzqSDVOZV7fk/ +y7D0wB3KQ5kOo8/+o+08Wo6x/YYRC+bQ4Uziol0+onI8sp++oEeVDo3nfkh7 +XEY07okqiFOjwyS9vpkyyhWo5Lh2l+0iOtxlLXi1wrcCuR1fOHLqdLj1d6+U +dEsFltldCavTIPnc1KwMN6xEb5vO1yY6dBB/u9svUq9Ck4/BVn906TCldNPb +R+lVOMtKk/F2Nfn+wG6p89rVWL71jPJKA5L/tPS3k6xrMK56URb3PzoYORpM +uHJq8KhZ/dbHRnTQk0qrMrz+HpU3qZ6Zb0oHVb3N4Tlfa/H4upKeaTvosKtC +/3N/6wesaOnMLNpJh0gld+3P8Q04+8S30CO2dHAecsgK8GxEfLJM8/0eOize +9bUkbconnDUn5mSYOx2OuTCHFm5swZLfXnKjQXRQ6oid/k7QjjPuhw48OUuH +73fnXNl2qAMPrUl67XCBDiXatnf1vnbg9OPNjnlhdAj1yruR1t6JB/sMH5+4 +QYdNyZpnn5R8RjlU3MR8SIfYMLlH6/2/oPt+7Rl3M0g+9g5L7Olf8O3oFobZ +Uzr4mDSUadv34QG9c9fTXtHBvbH0WLFeP755xOh0LqDDWOCj9ISeAZQxmXg+ +7R0dwhTfyWTDV3TtnXuxqIToQXNBleTjryg9y0ZdpZIOz4vn6D9eO4j7rxT5 +tjbSQStI6mGOYBBzF7ebhTXRYWbIMWXrOTSUKhMqr26lQ9eewDixGQ1zhtVL +bnbR4efKsjfb42goeeSWtCWNDrvXSjftW0lHJ8nnvSMMOsTsejTbaDcds9Kq +sp6w/88/vVgnkI6O3aP2khQdzrsUsawK6fhqu+fD8hE6PDbxuTOxhoHrdJeY +wG863NikPyTYycByxcEvOEYHJ/tKH21vBra0u86plGBAhZrPzhdJDPzpui+6 +WpYBK0pkFJx+MTDYdK6uuQIDFDZM4R1QZOLUpZ8/1ExnwMmYHU2spUxU5TpI +1SozIEziilPETiaanLS9WL+QATu/7lJpTGZincP0eduXMOD1uj6589lMtP2v +qfDDUgbE9Gxv+FLBRM/xHT8atBgQaaZk0cZk4tVIi2Of1jBAMkVGeosOC1uS +TJzatjFgzVnH/zJyWTgsmDeDfZ8BcXk3r/5dwsW4VE5dSiID0u9ElzGMuLh2 +V36ofQoDNLxWqI7YczEgb6e44hED5rT8tY6O5KLwbFhTciYDZi/2mJgm5CJL +in1zdxUDimbHHLtdzMMrhXnmMu8ZEJvhsmGgnYdLj4aOl9cxQN/YO05SyEOP +j3N9dD8x4Lv7xObihXzsj92xQ7qbASNDYfPWhfLxovlcyfJeBvx5sWbs7n0+ +zh9hFgf2M8Bp9/snKVl83LcvRIdOZ4Ddhcved3v52Lno9bQyIQN64gP5N1cL +MLA1uPLUNwbUTxWFP98iwFmXrc7p/GDAucnngiwcBbibzeDG/2KAMH3RaYlg +AX6Lz31oM8aAlgJ66qzbAry9PdhJaoIB1p6n9qY8FOCnTJX6k5JMmLFuYK9k +lQB93Bih2lOZkJKfmN3XKkC5Gbn/Dcow4cOShqIlNAFuP7X92U5FJjh95vVx +/gqQq6FyYMpMJrTlG80/LEfh1S66SsksJjSVqe2xmkvhe8OLkVqqTLCcJsM3 +06PQS2Bp8nU+E0pq4y87bKRQMnX2yL2FTLBOTY9r3Ephug09y3oJExIu9Lo/ +20WhmUTOIUkNJoxylX24ThQOvr6woFiTxLdk8bnbHhSGHrTs9NdmQtVJv2up +Ryksq6WZD6xiQsS+3t4fZyh0OZs9HqfPBM0jslshhMIx7Qv5O9YxYfOmv2Oj +lylM+mLhM/k/Jtgp7pu/+DqFhreUNd4ZMsHx/Lmhd7coJF7si58xE3xjV/+t +u0PhmW9ZdzWBCYPzvQXW9yhUST+/o9+MCYcti+N2JFD41t5CMs6cCSaatD+1 +SRRe21EUoWbBBL3+6IDHKSSeLdoyT7aT7zN2/VR+QOHqjUlRK62ZcPTJeqv5 +aRROXiunUGDDhDT3vN3FBHfqXLxtspsJDa0xEz8Jfq4unFlnz4TVzyccmwi+ +MM8tbtdeJiwdCz+9nWAbpWaVbicmPJ/4dekoWX+JrGmi+34maKy5nqOfSuHP +Sa/n81yZUBCWAU+SKaz/veRBgDsTZOvGLtQlUpg8FLv4jyep78qot8nxFPry +JDPCDzFBpTxm8zKS72Za4DI5byY4JD+7eCSWwtk9rGd3jzFhlW5r+aHbFHJb +9uqonWDC6bvxB5fepLCkvi7zsR8TygvWVWdcozC6YsPqlSeZsEKpVp9/hcJ1 +ufPWmZxhwiRP0xNdFymUfn6joPYcE9y9D5WHn6WwN218w66LTKjwq146OZDC +S7cHNrlfYsI9y/uFkccodLi6q4J7mQmRP17LxB6iUCu0YnNAJOFDJi/3ojuF +Tb7pFuE3mBAY/CJ2bA+F82wO7358jwlX5y/Vp4BC4dbP7boJTPBcHrkZjCis +2GS5920SE5hWD7Ii11F4eKXO/to0Jiy8r35oTIvCN/IiL+4LJvSc1azNn0mh +dWPQWd1yMj935ZUehgAXVbP/5FeQ+sYoalgOCPB7sWPwpmomxBkXHanuFmDi +S8Nwm3omfEwY6aF/EiD7+t8b/m1MKHrleKurSIChlhFp+WwmaK12MqXuCLDN +zdtFj8eEQ+VjymduCVAjaIdqpoAJGxQNe2ddF2DDo5l3M74xYc8yu4+XwwSo +PJYaGfuHCc7zGV/N/AV4eOalLYp/yXm04re5+wjw3XIviah/TDgbGbrxrrcA +3Rx0zl+awoL+hu/P1noI8HlWwQl/RRZs5W1tPGEvwD/ViTrUDBYMCo/OWGsr +wJ29FzlHZrHAuc3da/pOkt/ULR4H5rKgbcvqiekWAjRfoLnwyzwWuA9YfTQw +F2D82mlf9i5gwZipb3GQmQCN3ZsdbNRZMCVT/o2FsQCjT+fNbNBgQVd5ZPUX +QwHSbt5r2rqcBSmUskT0fwJcl3H2RqU2C+Y9uXP3gIEAI9/tt9yky4KmqbeK +dq8VYHezidS7VSxYdVDu3SF9Aa5gL6lap8+CWX2rRCnkvgwZnxKau5YF8cs/ +4q+VAmxR4m7UXc8CQQI/47yuANW1G38928AC9dTVCzVWCDAIst8u3ciCboEB +jmgLsH7PnZNpm1iworRl6U8tAc7zCVw935QFigc2/lxAsE+4I3V/Mwt0cg0Y +QcsFiAlGL5S2sqByQCHrr6YAlXIWHI62IOstSlApJNjrvcRSWSsWKPCVqQyC +C74wvkZYs8Ds+FSJWoKnfa9NmbSLBQYjw9qLyHouMi/3Be9mwWwDna2vCc5e +eEvltz0Lto3ZrA4h+0sY+LcH7mWB+YPpdVdJvPY77GO+ObGA8+Exv1lHgE89 +1u/02c8Cw5a9p51Ivr/OqMpyXVkgf2l489JVArSKHq896M4C07RtGmv0BJj6 ++Ovlr54sSFD24USuIe9HcZXp/kMsOK+wZfdSwv/m1id/u46wgLaqTG3aBgHG +ca4V2x1jwdrFBr8NNwqQ8/f4mSYfFqS9wGuFJgK8qbNm6H0ACz5afBl/sE2A +A6azs80CWVB0aLxdbocA9R1/HSs7zYKzGmJo3CXAKye+LDc8xwK0Vbw64CDA +rsvlzPwLLDiwf2/3NmcBaic9eqQXwoI186u3S7kL8GLuFbfMMBZU5eV3zTss +wCX9Vt0ZESw4Grg+3eaUAKOqNubsucaCD71xSQoXiF6f6UZK32DBjL0m/usv +C7DqpOK64zEs8DSssK+LE6CO0z/ZBXeJPjZdyV/9QIB3N32jNd0j+RdWxk1+ +Tuon03Z7TTILJJZZ6rJLBfhRWHWYmcoCy19y4cN1AjRof7Pp/kMWHH6afMen +XYBTH9wT/H5C8t2wMuamgJyvtfssKnPJ95+NTnospnCGqtXCU2+I3jO3PApe +ReG5CaNhjQIWONn2p30zptDqg1rGtRJSX9ub4k/OFArcBid21bIgclvPg3Fy +X6+KOlIw8IUF96c8f6uuLsT7fk63YgZYUHxT/vKLtUL857DdazONBeN1RzYa +bhViy6IVSk/ZLHj+inq3z1uIAW9FJ04MsaDAM3UTK0uIvUlfzRf9ZIHdldaC +P+VC3BzWMr91hAUyNasCGM1CVNqR92HdOAtUvQ8KlYaEmD8YtGx8Kht2XN7z +RUtPhGq1h8ezprEh+dox3zkgwohXju0H5NnAT1ArT98pwr2nDS9Vz2TD4Lns +L0FHRVi+X8cpSJkNBmmey1+fFqGm2fzVy+ewYf23vLX+l0U4Kve3L0qNDZRp +4QnPZBG6DwnfGC9iw83M57einoqwvmsgSrSEDcfB33nxaxHqlTZ7PNRgQ/kT +2uDCEhEmPKrYYLecDZ6cC36XakQocfX19Ck6bLhi+jVxyycRHvVJZ7/VZcOv +FQuNPTpF2Lb7btmR1WxIGGQHd/WJ0Oi/K3Gqa9iQmhTemcYQYZen6vrUdWzQ +MnEQ7eWJ8FR09ufF/7HB3v2uwSmRCGcUbzn32JAN5pmL73z/LsJMVvc8LWM2 +aMZwtNtHRGg507f0lQmb3P8OJ2b9ESHLWNJttRkbDlk+U8wbF2G4d8K/vC1s +sNm+UCZ7QoQL41Y+Wr+NDZOHx5OnSoixGKs2F1uyIX7T0T0lBDsKHJmbdrAh +bPGSaR8J/qkijKjcyQYabWrXBoJjNocv32rLBpWjl5dN/idCXd85H+rt2CDW +K3+l9VeEHxIzj1nvYUOe08sjWSSew+/N5FscyX4h3PQ7oyKcPNSVZe/Mhp/q +wUNdP0T4QM1n12cXNuSG7tcPFYtwo+WkIecDbKgtrrl+ky/C7lP3Ywc8SH3S +LhybxBJhYNqKdZ5ebLg39VPU4ADhp7Gik3WYDcamJ7i63SLMGtlz5uhRNsiL +dGp5LSJk7wwr9vdlw5pt9a7VFYSPc7NdfvqzYcrwBy6nUISLnrz8e+YUG6q/ +n4y9mS1Cp/EO09CzpJ4Zlte8k0TY+FK77lY4G66ZNk4f9RGhd1e598wINmSa +KXCeuotwymQH2XtX2WBdNVom4SBCk30hO1NusuHkL15ug6EIc6Xb21/eZ4O/ +T9s978kijPO6OFj3kg2btp9rir8lRL2YmeE7stgwNCEy/RYixE8lT5c257Ah +PLV8jou/EKfOaj3clc+GkbEF867ZC/Fs5TIhs5zEyx5+QZ8vRGVhcbR3JRve +77/NvaooxNdzbfWoajasdFxUFDBJiHy/86d+1LNh1fOnz7S4xC8ubP49qZ0N +cQFuZ3PeUaioevJtSScbdOZNjVyWTWHlrNkBQd1sCOGZpMzNoFBz2n4ut58N +6ZtFD69GE/8qOZGRPsiGJ86N5+QiKIyaeHjAhUHOy5j2CjXit8Q/2F3NXKLH +lRER4uPEf4uux14XEL3kB/UVeBF/xdO12SJiQ890+0PKbhROZTZP+/uNDT5z +h7ynET9eNHDyfcEPNhS8FFXdt6PwWM/sS/4jpL5rYmilOylc0FFkrPObDfsv +CN5f2E5hS9P+X4wxNjz+6DWlnfj98A8Tb1In2KAoFfy+cjPxgzWP/BwnceCW +8bfabaYUcsrNV8ycwgF3DQ1XdxPi199x2A1TOZCvwQqU30T8V35U+pVpHKgb +9r9nSe7LieyVbibyHDix7hN9JsG5L1pUfylyQGqd9+JDBHs+PtX5eiYHamZN +zjch82enqdw5rsyBQdqX50lk/frEd9bL5nCA76rzJpDsfz7ORearKgei33xY +W0/i0739rzpBjQOnd682jiHxD1xPD7VbxIGfjfdj6ywpjLmydaO8Oge+Xj9c +4G1N4ZZQ7sh7DQ5oNtYzT9hSOHLuRl7ocg58Px60oNWB+PnAVb6GOhxQefB8 ++c19FDr7tWr/0OXA41eb4xMI3wrHAlmZqzlAvZZvEx+k8OSBYpfFBhxorHM7 +f9CPwo1W23ZIm3JAsS38cxLx1yJz3tTKzRywj3mmZUT8+EO4WXV+Kweka2/F +Coh/n2LQZiiy4oDe4u0fjhC9NC1y0+rcQ/iw15T+V0Zh2LxJzGgnDkjkbj/k +XUPh2tmP0yz3c8Bfccwts4HCBFm+Sqk7B4oTjqx41UXeJ6lbbUEHOaQfKZJz +7qPw77/V0asPk/Gd7FeNNML3cJBUxnEOHDtpKkMXUKj8bW6liy8H1mx4yrn4 +jcI6fslFlQAOnJV+1lH7k/DNctvQcooDmx71PCn5RfgenPTz+mkOvNcwi3Qc +J3z3Ps7Zco4DTTf+jt7/R/jutDj+9wIHPoTndp2eTN6rFr5mYQgHxp/H7fs5 +RYjDDbfo/pc4MD1y62wFaSH2yXV6j1/mwNzAmjNPZIRYZa0mvhrJgUxtq1b6 +NCG+uHUwaNZ1DhSsG5SrkRViTNPLsQc3OHA4/PJ+Szkhnp7+/ZJONMEKO038 +CHa1NZQpiOFA61/PixsINr8TFm12lwN0h7zlj8l8nbY65U/3OMDxDkjOI+vP +mDU92SmBA0vSjl/wIvuP2u9dwkziQNmYypviqUIciEt95pfKgRbLwMACEn9N +J3PlWBoHSsuL1+8j+b1U0c2PTOeAhmlL/mOS/x3HU0ZKTzig4HVbkET4OZtQ +XJH6jJyH7L45Jr8pdOuZZKH9ksQTdjM/ZphC83nbP+VncqD5yPyz94YoXLE/ +xt40h/CZZmS3S0jhr76F7o755LydXDhHzCB8LzjMphdwoOTvP/aXAdLPu2X5 ++L7jQNdY3p0bPRTGDm48F1HOgYTTkiu3NJH9l1z+N6OSAzbRLo729RQe8GyI +SKnmQNGVWR/WV5F6Mp1i39RzQD7azfr6WwprOUGvaG0c0Cm/N3WA9MuZWmX6 +Jzo5oPwdimXiKLx7dErRr89E3+HBkrqkH3cXxNZM7yd8LVEO9gul8I8op38T +hwNGV0pn+pL7anD16MEPPA7MCLh4lOZK9OVvwnegiN69vm0+6Uhh3PePI8eH +OJAs93H9XyvSf4/wpieNcUC278ySZaTfU/lP//6yCQ7IyPVafyd+bPzMWbXX +ElzgpA/b/9GmkFGE6caSXHCIt1EwXUZhw++p2vVSXMDFrnNriZ/LNbLJsZfh +wkRz4ZdoNQrjL9wz+CrLBZV+v8spcykMKe0rOabAhX8zHv37pkyh19+lm0em +c2EsZL1kNOknrUyO119S4sLwHNbkIEUK9UPzbBRmc2HFsMu6Z3IUzq343ZEw +hwvPZfNuLZtG7jsJs/0a87jwoHq85ttUCplm12g5alwI7ltjO02Kwsbw5iMb +F3FhQdqGQ36SFOZVq4hql3Bh62mdP+qTyXme4hZop8GF26kD75dOIusdnGPQ +qskF0cJJUoESJL7qluFd2lxIW8oABYIb1KMKmlZwweeYaYTonwD1wrec2bmK +C/sdV2apkPH7tPH/Pupx4eKWUOcrBI+bFvyyWsuFaFnPcQOyvudDv3cfDLhg +EaXaok32r/+ndd5yAxeyHwnpriS+VQfoRnVGXLg/D5RbppB6lSePbd3EBdWa +6jkhJL8/C/aU1gAX8uicM4dkiB6CFYO3bObC5D92CZdliZ766jZVmXOB23Gr +qFOe6M340oSpBRfqY+tGnKZTOPrnR6iJNRd23EjIZRP+XZyzTMtsuJAgZ9LH +n0Nh1bvDk4x3k/1DNt6cNZ/C6LM94YZ7udDiWjVes4S8ryPlEevcuSCh/J+x +hR6Fe4eu39AJ5IK8js+ZChsKS223WL84zYWXvxqZAeQ9VM8dl9c6x4VA38xk +pb3kfvb1i14WwoVM+fvr5hB9OjRp7XocxoXI7Odqp90pLF5Jn770MuFLyeZA +MbnvIyiHO4uvkfk/fTr5Rynk71C0S4si+ftL+bX7UGj7qk5p4S0unHRdvjaJ +vAcFspfaU24T/amFt206SaHaMaO4+bFcWKtUvKYs8P/v7Q+HpDiS75UUvzln +KORqZc1WjSfrNy/q23GOwnzOoniVFC7IiIyfmwVTOM+ix/HeAy7sOv20bjI5 +b2FPY+cqP+LCn8aO+6lhFLKlrHtiM8h6KSuvKIWT9/iQVNLMp6QeSvXrPS8T +vdWUO8c854KdK+/WrStEvxpn509/xQVHT8uH94gfCbms33criwtJ+XNLLkQS +/dL5KfK5XHC37Hc3u0rOw+bHrjfyyPrHJS25BOc+cl0o+5YLDY3b9p0k753K +pDlfrxVyITH0axaN4IvuLWnSxVwYN7pwa8N1Cul43T2ylAvXpCR9zhFsuWjL +EinkQtPvVZynBGeHjNMuV3LhbDWvuprgWQNv0yfXcMEUIwRtBEfLBwcX1nLh +m8Wuw58Jlt1o7uTzgej7+IoD7QRHHpVbu+QjF3SYi6QaCZ6c0KbQ1cQF3+/S +z6oIDqlN5Ea1ku8Fq7PLCf7z070aOrgQcKM84f/7nV6q9eBnFxdSXId+dBL8 +fbf47IseLtR+0N/7h2DfsAJ7tz4upN+U2WcQReqfHbxq1lculN8djr1B8OF+ +82n1NKJHzzV3Jt2gkCYnz7zIJPXbfqg1mWAXo/ZyfQ4XDrB2lLjdJH7QOymR +zSP8Hj6YZEPuU4d4j8Bkigs3Te/F+xG/2PJea5etmOw/Ksp7T/yD9U+xttR3 +LhwsPF7mcIecV/XCKcU/ueDh32W3+C55T3aHfPUd5YKzfmP7CuIvMHRr8dI/ +XKhyHzhwPp5Co2z5e93j5L7z+9asSO73gr52v1v/uNAakZ8rSKFwjVyy1ebJ +PBCF+G+a9ZDUw9Bz2egUHuwPGXe+SvyJjre2RKY0D57Ok7m7/RmFT+9/63WX +5UHo5FfT978i5+t94dvZCjxwKd4WX5pDYeqPkJiG6Tzw7iy/5ptP9Ka+7Xio +Eg8S6uS7/Yl/jrNV2LZuNg9kl66Tqy6n8GZW8ljqPB7Ra8s/O+JvZPo8u+wW +8EDCKO/OrRYKr8jqvJZezIPEt3OezPxM4YUjRYcDlvHg/lL/Pj6T+N0lna3m +ejwIe/zW5oykENm7UjJ/r+FBy4XH/+4TP+AZcvBqtgEPzGvfWvXPEuK+L0PG +czfyoMftYF21hhAt7yk+F2zlQTk0VuhakPe+ujP8oSUPfr3/1FK0S4im31Nc +9+zgwfNgZ8ZKJyH+t2vFLLTlwU3Lh6uySf+eF/xdeMqeB4fvZ3g8Jf3Hqsx3 +9Vp7eXBCITHJ46yQ9AOWIbH7eWAlt3z570ghpv83fZ+FGw+cPV5vqCT9zMLD +XWvH3XlwXNW4f2mcEJPiUhVfH+SBTNKuDpUkIapUe/EOHeZByfoZtNtpQowd +WlEz7ygPClcHt195LETFxT8eNB/nwecZTXcEz4UYZVN87oovD8JV2EuKM4Uo +FXzJwTCA5D+zM4+dI8T8Ieo3niL1WSHptzlPiF6HndK2neZBSqax3KR80h99 +qTb/dJbkN7ZBdf5bwseu1Xz7Czx47fH20HWCA2uSbvcG8+Dx8an/zAnWMJxq +4BHGgwObYjZakPkdWQG9nHAeTHFZXHGdrH9FvT/UN4IHSWeXRk7NFeK6eMtl +w1cJH59f0wpJfEy5/IYLUTyomXTiagKJPy5skf/kW4TPm9qxGRnEzw1Hzb5+ +mwfstgPXOlKF+PPoSPH0WB6E5Ll5LI8X4uMBD/f7cTxY47sxKuG2EB3sP0kt +iOdB06zzfI2rQpxSv+FVRiLhm3OU+yGY5G/82FYnhQdut/RPRJwi+b+ePpL7 +gAf2jEjuHlJPZc0Lyf894sHDXEUHIxeSfxLbtDyDB9EJ7uvXED0ETrdjmz/l +gXj01ZNNZiT/K2U3Gp/zoOrBn+2ua4R4+URcV3cWDw5ld78dmCnENfR/Fw7k +8mChRMRbcwkh0vceX8LO40FDoppLHfF7m003+/wo5IHq353X9WvJ/TXr2yTF +Kh4Yxwc8VD9B7u+r+5/F1fDAjtUz8J30K57jtdbz63gQGD3nhTzpp6pYqfFa +H3ngf8yTv4m8x+FFO1Zu6eKBerHZw6REAU5ye+Z0ls8Dp3OFTQ0v+JjbpjQx +QfHA58GDS5I3+OhuEZIRIeaBxuxeNPLhY4XeHlHsTx7E/SiR6lvFxzBJyStZ +Ezz4nl/D9Svgod5ZX+11k/gw1/qeYEkiDwepnqZiST7pP61emF3koWlXrmq9 +DB/OFOz+KGHOQ4kXbjl0JT6s8+m7Le7lYi312TdtNh8ikg23hFVw8abe7lUu +c/nQ4C4RLPeMi3OKtmR1LuCD6ferN6zOcLFvrNQndjEf1B8ucFH14GI6rNfd +tZQPfZhzb641F1fVab2q1+JDd/nJh13LuPhTNv1YxAo+hNC+vH2pzMVim/k6 +m1fxQStbPrNnChfDYuN4E3p8YLZkqfiMcHBrl8KLkrV8iPmp9vIoj4Oy8656 +n13PB5VtvgY9/RxscZXQMjDkQ03WstSKdg7ef3SOM7SRD557M7s0Gjnowvr+ +NNuED6e9IpnTajioru1z+LgZH55KW7efLOcg14e1TMucD2F23oUexRzMznVj +MbfxYUdk2qvPhRw89fPz40fb+SAod23pKODghg27vdys+RCp1bTDiYxPXGhY +On8XH/Q0i63c33GwBrcwPu/mQ5fi6sn8Ug5GSZalxznw4Y8X9/VQJQdtLdZ7 +7nbkw8ucC89O1nNQ5UbOEkVnPgwc2Lz5SAsH+5q0aA0ufCgN+jta38PBdKX0 +h1cP8MGAs9I5hslB773z3c09+VA/X03t7TcOrkqKWzTpEB8sda6prprg4M9+ +ha9lR/ggzR5zHZLn4rslVx+cP8YH7upC3Z9qXAw5JOH23wk+BPqvmrZiFRfN +X5xb8NOPDyMJShXXTbnYoueTciKIDzNdy+KjvLl4P5C1X+csqf8RrbkzQ7jo +UuQ2n3OeD4WiyxbX4rjEKexOcg/jQ+qrrxFyNVzMvtywb8FlPiiHXvw62sfF +wLotqr0RfGiuYMTdG+HiP5v1CfY3+DDPO7bk0QoeqrjNv7/tPh9iI/4+mpvM +w75HcXskE/kww5u2NLuQh+kshdkVyXygO6lXHO3g4coTEnGGj4ieOidK5RX5 +aH6RdUc3kw9v9F1G54fxUbbCbTcvmw+v90i4jyfzsUWye8bT13yQmTW5+nwh +H/ffaLi9qJAPyyerz5gl5OPJpJxbSlV8cHmiXDN7twALx5OuVtXwwcZLbX7/ +EQGOu0VeOllH9Ol8prYnWIBXl7oGtX0k+3+vu2HxTIAfIyz9wpv54ODYbvm4 +WIBK3LVH17TxoX3e3qcKnwSYkinrGvuZD1bP7/1liARIUxzZu7mXD7WH0/aY +TQhQM4Bm+72P6NU6Vf4m8ePH2z9apX8l/NH+dpapEj9nUGRuR+eD97YIiVbS +Tw3HZ5hMZvHBWiU5qIL4a6M/0RvyOHw4YKNTdNWI+E+X82s8+STegLkM9S2k +Hy0/pKsk5MPmo/ueRZN+TnbJbs0qMR9sZz3dXm9L/PFl48Unv/NhfcaXtE97 +KLzHWj5PfZgPUW6yiqn7KOy1mKXcNkrOj4fRZQMXChe9nFAI/8OHRHth0H3i +z73k+dJr/vLBeK7XIBL8wrdzEv0fH5zTcozzyPeiloqxO5MFMCgfF+brTOHa +tZnDZlICKPLdqjpC/P7Ze/HiIWkBfFgrxbEi/UD5aDjvkawAnoQ/2+BnTaGk +sy9jt4IAFp2Urju0lfjT0n39k2YIIGDcP1d/E/GfC7d+fq0kgBB76cCutRS2 +h+m1eswWQMHESqEj6UfnMuY3zpwrgHnMPzbFCyh03Sr9vnKeALQUChdNJv1k ++rPv5QELSDwPTq1bR/orzrSBoiWLBVA8tyhzz08B6vp8yGtVF8DU6zai40wB +BjTlZ15aJoBQgf6ji+0CLNB7+FRfSwDB59Nf3aoUoNnw6aQ7KwVw7+DSSx+S +BBjp6BlnpieArp0qqydFEr282xk9tEYAJlTxDzt/Ae4N0QjfvUEALiP3ot03 +C/CYdNvRmVsE4GXS6inu42PO0bKDlVsFkDOD1llZycefjc9dAywFcOfJ9mre +Ez6GxoTubt0pgAVSJ+Y5k/chTnWl4R0nAby0qLmb/p2HZSuuycz0JfmsH1e3 +pLi4vmPOp1h/ASyOaln98iMXcy8+u6N8SgBSqy6rizPJ/f2pdt7cswL4aLvL +Bk5w8Zqf1MpF4YS/4X3J9UIO2r0J373yvgA0xr+VDP9kY+N+JZWcBAEkK2+Q +GOtio/mU9F69ZAFEPS867viOjf/tqTy47qEAEjYqrtALZaPa6L+gjS8FYHWI +zZ0xg433024blWUKYGZAXnfoMAunWy76Z5IjgPg6KWbQFxZOTjS5tjlfAE8/ +BlbKvmAhxyg4aXu5AJTDXDVtdrDQnSF/oLFCAENnbtr5GrCw90bK0p3VAkip +f1O/djELP/aVZNrWC2B+VolnwSgTt0XsCGhrEICttbzDaSYTceUXA4dPAjjz +e8pSWisT80L+lDu2CcDz0/nmwmwmrlgedbmnQwCRDuez1B8w8XGzquX+zwIY +ib12aH00E+MXG7a69ZHxly9bbP2ZOOND/b3BAcL/9WhfO08mRgU4OXvSBLCn +e7T4uwMTL1adYRxiC+DHct75fxuZOHxM+jmHKwD7QdprTz0m+s6K9zkqEIDj +8a1L7JYx0cOrYNjnmwDk96e8KJvBxF75bcWi70QvD4Ju60oz0eFtZ4j/sAAy +mLq7FCYYuG3qsHTgHwEc3+wjLSVkYEX2lY/D4wJYMyK0lWMx0NBR+c6Zf0QP +YS/VPfsZqPt87bwLUyjQ1Lqm1NfEwJlWJ3XDFSlQtq8Np94w8GHldDmjmRTs +6tZ37M5koJ5hFm9oFgWqLrZ9VU8YaKPFfeqhSkHj9ZdmrvEM7E+LiFBVo4B3 +a8aXodsM9Jmz1Kt1IQUb1MKLba4xMGqq2xIzDQpMGnbe1z3LQNWQsX+/NClo +CAj8d9ePgc+HEwZytSlgvyvIjDnMwDpme/Li1RQ8PnswY749A/e6BJzv1qfg +2miMbZwlA9ntivti1lFABU7RPbOJgVOqt6tIGFGQ+r1F12kZA+8acX4WGlPw +JbygbdtcBqrnXWn3AwoGDbe8D5NloOkjjPlqTsG2/t7FVRQdm+e6+sVbULCa +5zla2UdHt5g/O3dZUXDx7mTZiUY6BocayOEuCnR2flut9ZyO8qNtvNN2FOTM +206bc4+OKb7+9av2kPwjT82yuETHYtdXEQ+cKZBx1YwJdKTjyMYlEiGHKBjN +W1VTPUbDiDflAwbeFBTnQIgbg4bKK1zKhMco+F2xpeRsAw3Xzos/7+pPQZm/ +TbF7PA39f8kPG1+goNZ5cV3GShr+83vZ/jOYgt7EI5WflWgYzbHIywyjYLnF +WR3ZX4OY2RXupxZJQct+xdL8qkHk5f/ijcVQ8Kks8cja/YN4Vvd+/Zu7FOj3 +6/Yd3TyIMo/XPjt+n4J1ARsfrtMZRM27vl5fkimYt/xLVeLoV3wrK7/l7gMK +9g2+VTvT+BXNw18s2fHo//9Lw3Gf9OgregYwB4qfUnA5K/Dmrd1fcYh7qezk +Cwq2RLjYVul+xTD3RSk6mRQce5nkME32K87oLj1Pz6ag/ZNzQhBvANN2Oe9L +ek3BJWsNozmNA8Q/jv5nl0/4uRtjN5Y9gOUm91RkCym4dcWG9NMDuLNgzXDl +OwpmTlQdywkewL6VLe3nSole8mJ8rnuT9QQzgyWRgnc6sTKcvQPo+cJe81Yl +BSuzY513WAyg5pF7zSo1FPT/Os3NNRxAnsbnsw9rKZBboXlr+qoBzKTPVdf5 +QMH6pu/nXTQG0P+hc+ObRgpEV8fMotQGcK1bSuCmJgq0lKN7r6kM4Mj8gQV1 +LRQYLr/zZqvSABb3LKqzbSf1yflR82r6AAbHe/j3dlKgnq76NENxAE33ZKh6 +dVPQJb3h+SwyPmUWq0rYS/iMvfHz64wBrGvR9DnTT0Glp002f9YARkV7z540 +SME3zR1zlecOoI31y/IoOgVe5qwyowUDOFOWOqLMosDS7EjaxqUD2FG3cuYD +Djl/vp4e37UHMCHCr3g5n9T/JTPEUH8AF076Ib9RTIH5inVaA6YDSC9fV1Az +RAFjkFdBWQ7gk4unD9j8pKA6cXCzyHYAdX/9fu3xmwK7RUKWtvsAit9u3C8Y +o0D+aXSW8pEBzDsVPCVoggLFHN/lDicG8LQ+Zk1ICGG+5Y2TVScH0FAs4XhN +UghNa1o7jM4M4HjmZgmlqULQrH88mnh+ACuOXXmRLCMEpV2qS8svDuBlrVq7 +ZXJCULfxO3OV1HcbW3o8W0EIlkMnNbrJ+LTH259smCGEol6HB3Fk/kePGzZV +SkJYn5XYnHF6AGMWfRrdMVsIvVZoIfYfQPt+xUedc4SgoWV0+ODRAVRJtrU6 +ME8IbasDLokPDGCvU+wPrhqJJ/LgtEiHAUxV6Ug5uYh8P/H8iRrRi3vH7G3j +S4SweNsVm8z/BlAj1lEcoSEEm1c17vqaA8jZlZgwfbkQfjYbZ74i9X+p8MUs +UVsIdlXJFxf+7UffRjWBuq4Qpl0NSYlh9aP+dbe4zFVCCN+ZaCf/sR9/bnu4 +ab2+EPqW0JzScvvxQtXSmO3rSfymOQvtA/vRJOyQYfsGIRhP1hCl2ffjZJNn +dJeNQlioXDy0X78fr73TMfA3FULLLfuvSdw+vJ+r33vfSgjDC0+JZln1Ye4D +0GC6CaH5aM7O4r+9+OP8D2kPDyH41063HenqxfWOzwT9B4XQpVByZdXrXiyZ +Pv3NZ28heOx28l51tBcnBFX3HY4T/pnhnSYWvWhaf/p86wkhcIp+HOzT7MXa +sAGzxpNCWHLlZp+BoAdlXGOXWQYJ4QNt459lLT24w3DbtPdnhJDzgqYnV9iD +0bP/UGbnSfwMNffRtB5sGcpqKb9I9DJ7Z+OvqB6c1eSRvzGU8FfrPqx6tgf3 +vpydUHRJCKWbNC57HOnBhMgPFwyuCKGcd1ijzakHv3gGH8iLFMJ/TzdfOWbd +gwtBf8vq60L4rFhjumxzD7rPZ2lm3hBCoJ4m/5dhD2aMJshqR5N6O9VO617b +Q94Ta9GTGCGsucLWe726B7VyJdrU7wrhof626X4re/D4zfy3afeIHiZH3fml +24PZ3t6JaglC8FPbL62/qge/masFJyYJYWDXnN2/9Hpw7ZIWd5VUITQofFFe +YdCDp/9eNr+bJoRImwd/0o16sKjnP60Z6UK48EhBvN6sB8feCuRuPRZCnvw7 +nxLLHjSJTRNPeyaERN2ljZN392CYr3175AshvHfQvdu/rwenLi9JCssWQpJM +z71rPj24XdIv5G+uEERi5Rk/g3rw5ld1z/NvhBAsm/GfTmgPNpV0bR19K4Sw +RKvpv6724MyEKO3AIpIvv0dpRUwPOgSaKAwVC+GWy7kHd+J78L7t928nysh5 +bYvdM5bagz26Tzv4KASX8yevGWb0oNo056IjVUJQDayOX/SsBw+wFFKYNSS/ +bbJ7Lr/owfTKylCPOqI/c9MDm172IDM16ODAByEMWRSc1ybjy89rW+z/KAQv +g2MMzac9eGxvv053kxDif09KnPuoBzPX3FHc0yoEevazDFZiD4oVt35vbRfC +hkaF3edIvGsEvzptuoh+14u9q6/0YFBd5rvGbsLfIl+notOE3wz3VMsvQjDR +f2+/+3AP/glVvvS+XwgnrFtP3LTvwU0u9V6bB4WQslzxiY8J4XfDRUukC6Gx +/y3rt2YPVinr6RqzhHA7oUHCTKEHLT/F/zDgk3rTaH8t2rsx6sWOz3mUEObt +WCBv+KYbP0X8K14tFsI2iZnCrXe60c7kSLj2TyEcumTcu8WyG11z1s9cMCGE +B+4ZehFPP2OB8y/FFgkRGO9XpczPfkbFqcXylyVFMOkXvSV0+2escNkkw5MR +wewLvXeCBV04V+afVIqcCMqu5rxoLO3CgDcVkrsURTBHtLnlRXQXqsua/8uf +JYJLV1rr5xt04fm3Un+PqIhAIGLd1ZHtwnb3uj/zVEUwPj2RXzbYibry1399 +mi+CDP0V1jLvOvFKodVI2EIR3HyV/Xz93U7s85T/uXaJCLL2q7T5+XWigWLT +EHupCPSyBifad3Yi22u30FpbRPg92HR+ZieazJgl+LdCBL6nJaJ6RjowvqSD +m7eK7Lc1eW7yQAd+O3yffUhfBJ/6QzcU13egpZITc+46ETgtKBJrv+3Ah2Wq +9Mb1IhixTH/bmdGBv72/fA0xFIGUyKfwUVwH2imn9usbk3H25v+OX+3Al+j2 +hWkigpda96SmXezAyccX98SbET6jYmZZn+zA/Sr0LitzEThsPbFA4lgH5ldm +dPzdJgKzQtYxyrMD5U8casvdLgIZs+qMDpcO9Jq7vOWgtQgCXZQLzjl2YFk1 +95PKLhJfsEVjkl0H+s7z+XDRQQQXf7f3Wm3vwNr3K+tWO4qg+9XDUCfzDlwU +IK6h7xPB91HvRJpJB55Ve111z0UEnj3sX682dGBL3ckKywMi0n/spV/S70Ct +U+vKxzxEkGCQPXWtdgdeWjhSku0lAmsJtRP3FnVg74fCdx5HRJB99ZZlpHIH +rgk6V6h8TARhz/Xe8qU7MGrxxrd1PqQeZ8b35f5uR0bjeN55P7L/yD3+J147 +Gp8pz115UgRdHvqRW7rbMU49LHswkNQnJODbvPftKPxklnn3DBmvLHx0JLcd +t52TfLntPMFHezK3JbXjaHPkk8xQEfiHKux0O9aOthcsMw6EE36v57/+a9uO +zzVlHylFiOBxScujsfXt6Bx8K+VslAjCf7xzWDW5HfO0diWtuCWCuc1F78c5 +bSjXMSNh4LYIBu9KHHduasNSnbi75vdEcP+8hrXCgzZU7tpzZzReBFah1een +XGvDE5fm3H6ZJIKUjXstG0+1Ya1uz03XVBHo7h/AZx5tuLA7KWrGQ5Jvva9j +9+42PH3Z5Vp1OuEr5KR+rHkbNq9aGHn6CeHr8ITfP8M21Or9eln7uQia1tWk +b1rThmERjy71vST6iN/l5LKyDRXOSFt5ZIkg/+tvtyMr2jDJ+4QSO4foK9L8 +BodgTef23mN5ZL3EgL3Vq9rwzQ7DDHG+CLjP9bvb17ah6aa044GFRO8cuMU0 +asOPq6TW/X5H+JrmbvdmSxvuW3x8PLhUBLFHOPe/7WxD9szWmskogiIVuw+w +rw1PSv5362ol0dPdp//+O9SG/36m7JGvEYH7kcQ+r4A2vMmevPBOLcGikNcW +wW04t9ubPfuDCHSEmn1OhK8nH5qykxoJ31rlbtNi23BNybozi5pE0Db3Q3ZN +YhuWZybB4xYR8L03Fn4nfO94ICGj3S6CYyOpMn8etmH37cMtWZ0Eyy3T35zW +hl6XPias6Sb5xkUbrCfzh06u8SjsJXrd90jdIroNQ7wStI37RVAT9l+2iMQj +u3diqOIr0e9SVv/rI20Yb+FVvJUuAsWCm8+X7mhDDcOG8AamCLaV3L3KWd6G +uTp6O3ZxRPCwUSx487cVN6ndn9XBI/mH/4hy+NiKDQrjX5woch5/PDydebcV +9/7zeNwvEoHlNqfhQvtWZHyr8/EcEkGSQEIhWr4V/ekrDTg/yPpndhZ4lLfg +ePvdv8dHCHY8mxV+tAVVCg9EB42JIMbssusf52bMeP5+75+/pF4GWy8q3m5C +vaQVi0IlxHDl8fj8i8WfcHvwaM41KTFY1j52OjXRiF2+rmcVZMSQsKGncmRe +I3q6V5vGypLx9LG+kvUNeHHL7dbk6WJY99TroW9QPU4zGE5crCQGGXVlsWFq +Hd7X3O/5RFkM3ep8hvhTLarPrdTRmSOGmPY4joRsLeZMW/4jW1UMmZt00hvt +36Px2M2StWpiiHuz1TY2qwbrqe+XixaK4VvktRn+qjW4Z8DJetMSMXhNv+hq +k1iN9OZy5aqlYvAPecnvXVWNfpUa/ds0xaAl83ZByJcqHM+LetKoJQZzubmu +dg+r8NrjbydsV4hhRpCSr1pIFc6+v3d950qy/pEXqluDqjD9aunEPj0x5PKo +nR0RVbjqnHrdwBrCz/hB6kROFZYcu3b7oIEYpqxt87cdqkJLF5Ej9z+yPn9f +3B6rauzY6bD4hJEYSt85yQwXVaMHFHOHjMWQ4mbtvH1jDYr0Fr8+DWIY/JQ5 +dU5zDZ5Xjzw3ZiaGuU9U8jsD3qO0MmUWZi6GGuat8JLFtRgnZScrZSEGNblt +1g3dtZjFXZCsaC2Gek85zwrHeryWGuE+YCMG5aEZ4UdXfUAvO+Gy7N2E73rt +7KUSDWgqvUcQ7ED43ucLlfUNqFZamrvTUQzP3zoNnrjSiL/8NU4vcBZDR8SS +D59Wf8T2ZTc3Cl3EcPH2oYh59R8xu/eHRNkBMXycGJ1tvOMTRt3eX3vTk9Rb +x3Zrf+EnPGxefcPlkBgW20xVPq/QhJt/6+zW9Sb1DPI1OWLdhAuzY1XGj4mh +762nVFtQE/72/POl8YQYNI4vTi680YQdczwfJfuT+XGZPe0xTZj78cPh46fE +sGFmj+HVa01485K+7sbTpD7Hjh7IP92E3usTh2TPET1KDw7fO9CE5gKJwt4L +YjD9YywdbdGEix56X3wZQvLVTD78bU0T/nFoMTt/SQwObQf/a1jWhF3TNkhb +XRFDy2/1SS+WNmFeedpH1auEf6+jql6rmzD6lHQs77oY9Iz8AgRWTXhMy8/x +3U0xMCcejC8804Rb+7vUrt8m+Owg5/WbJlwca0J3iiXnYePNHLV/TTi+7ekz +rXtEL7ILah7ubcbuMYUTv+LFwA3r6zxQ0Iz5uUFr6pPE8P1D65Qa+RaMOdQ/ +Gp9K6mex75HVphY8Pm9r2ZGHYlD/XaPbTs7vtubM8P8yCH8zp9QG3G5B9SvK +ltJPib5S//SffdWCExsuKnx+Lgbb1KzFBSUt2CNktD19Rcav/cvIJvdBfvqO +hNPZYugqnwjvfEP2c3zjuu21GMaPBbsXJregj/z8pSr5JB4tW7ry2Ra0rAzn +sgrEsN762yr2jhbUOM3PevtODLKPw3+YzW/Bfzp2pyJKxeDyvHmDRVcz9n59 +t2EPkvPncOeNWngzFsQtmdCoEkOY9NP387Y2Y+z269U/awg/zQNXVmg3o+/E +t2s1deR8XuI9fmLQjFZvnGziGsj4jKSU7hPNuMy7YpbXJzHoFqpnFDQ3o8QC +rZ61LURvjQW6x7RbsK/19gPJdjEUxdVzJQJbsChy9GB7pxjSkx/sY5a2YNzG +A9oZ/wvrABT/2O8/Lkf34g330L9w8MbuctvvP9pn3fe7FNG/S6UutELe7z8U +sIc4ywnRvyZalnkS4e8/rgtJ9sjO0L8CD/4+4uPvP3T/ZDB7ZNC/3sNlBLLm +7z8YULkljq7Pv7p4zcmB6e8/aFqrdcSCzr+WLTWPUezvP2Aaio8LlM2/ceKc +VCHv7z/Ibs9bsz3Nv0yXBBrx8e8/iKknsNXGzb8oTGzfwPTvPziS80MyIc+/ +BAHUpJD37z9E08sNXTvQv+C1O2pg+u8/sLTfxcFtz7+8aqMvMP3vP6DxX3vl +Ase/lx8L9f//7z/gTQjbu5+RP2YoVbw= + "]]}, + Annotation[#, "Charting`Private`Tag#1"]& ]}, {}}, + {"WolframDynamicHighlight", <| + "Label" -> {"XYLabel"}, "Ball" -> {"InterpolatedBall"}|>}], + StyleBox[ + DynamicBox[(Charting`HighlightActionBox["DynamicHighlight", {}, + Slot["HighlightElements"], + Slot["LayoutOptions"], + Slot["Meta"], + Charting`HighlightActionFunction["DynamicHighlight", {{{{}, {}, + Annotation[{ + Directive[ + Opacity[1.], + RGBColor[0.24, 0.6, 0.8], + AbsoluteThickness[2]], + Line[CompressedData[" +1:eJwUV3k4lW8TllSSJElIkiiVJC0kuW1JRSlkSX5IlC1JUtkSslNJKiT7mn1f +su/7eqznHFuOc6xtKul7v7/e677meWeemWfmnpk9pnev3mJmYmIyZmVi+v/3 +wq3pzgqajnxHU417A1fSZxZlfjsy33Ewvf68LkXtDY59CI/I4VMBk+4zEa+G +AkwIiDx9uO8SZFrmT2ozVeNia392JJ82ZN4qbH+QUA+RgF3x/3brw13U5ZjB +30asXLj5xmSfEZxmLUYfejVhxrOnxiTMBAssuTOJg43QNftZ9pLPDCt7Sm+t +BjegRpm/oDrCHJIp7ou3dtVDcu+ZzG+770AtO1Srn1SLCGbjZNFYK4T09nAV +/qgB65hHzLV9tiA1ct6VC6pBMaWrtVrbDpmrXYyEDzWw0zS7YBh2Dx2dD96s +8NdiX8X3um/99uhQc5G8PFWLkSPPlQP5HOBzpgR7xusQ+oG3QvT6AzD1Zb5O +W6rHhS0pcuURjrATnUxf86sBTG6ni66NPsT0mb5L28iNyJ9rOTG/+xGWsz7f +6HrVBGsjo+znJo8hJLLzkxd7M4Tb5iWEYp9guWv/DX+VZpDOPE0tnHBGyEHs +ypBrRlA6l9iVfa4ImfdQkPvdhLO74uJoFm7I5JlyYhDxcq17x1mp7Q5eBYOv +rTON0HcdvxT43R12dzpkT5xoxPGT4oH6YU/B6Tvj23ivAVvmHJpFpT3g5P+a +Jy+tHjPxZRuX+j3A+TopYHWhDrU31quVOz2DzGzJzc1qdYjeftnbj88Tdkkp +v3WLavGk9U3NtWJPdPjF6MtcqMU1Lwrz3uteYJqd2j7+twZHzxxQnP/jBc7U +278e99aA/fs9t5IIbyzPnkg73VGDL2nFZc/PPAdJ79KbPHoNqszWrmiNPkc0 +L/3RdpFaRAqoywq5+SAg+WS0vUMtnHpCnRi7fZGkm6C8u78WWgEj+YUVvtAb +4rn482wdJFT2ffc08QPLPRvdlOI6bFyxPXaF2R96W458XpWox0ROwb1dsf7w +edfXsCmyHp+tmDJpygFo8FPeZvmvHu/2np/LmwiAj0R2sv6VBjgOvRD38AoE +hW17yUhQA668GrS8tC8IIho3rrblNkD84t5k/vogqCScLadUNIB1rfWXKYtg +xGmohyZmNcD+xuBLfZYQcL7dcsvfuwH/Fa1mfdYOQajTjytlaID69r2dovEh +0BRdLhcZrYfsvXML/t9DYFYeoX/+Zj3EWq22LJ19AbVtojGynXXYfiBEQi/s +BSrKNLc4HqwDs1euRvnUCziRnja13KvFAoVkLSL9EuJe02PnU2rQHL4ndaH/ +JdRFOnfd/1OFp6w5+335QqHGorHXlV6Og+de+GTbhSJ8g4vlHHcZurzu0obq +Q5HJFV9kfaUET2o0Lqzb/RrhTCcmouKLILJWPFXC8TV4N+eW6m0vRIsiG7te +62sUbrTv+hCbjwfu09ZPRcKwQFvanHc1D4Kf61pTnoRBEtlb9orkou5vnERP +VxhCqnce7eDNwV25Z8F/D7yBmkLv5m1Hs8H7xGRh39M3YDq206/BOgsVRbii +SXoDUoihsWVzJu4s78p+dCQcCh6DBqLqmeCSXuGK9Q5HyImY5eGhDBQ/GLzf +MhIOIa1rP8T/y8DN3MKe78ffInrbHbH83Rlg/xp2YnfAW1SUrsmn82cg7+iD +MLXxtzBOSY/QvJQBIzutn/dk38Euf+9Bv4IMrM84qvf+xTssjN+9efJgJjJm +txTVTL+D8YYDH5++yISe+BzfHN6D1SDOpYEzC0xWLY93vHkPpx+MzHOJWUhO +ThlSmHsPBZ3oPC3tbFyd9pGzPBsBybhvnVo7cvBnn0Xkq4gIsIqot5TM5yDu +1tnV0q8RiNapT2EZyYV63N7/pi5EgvJbciRuNA/fx9ZUbImJhNrZ+sOs3/IR +tYcidOpXJDRdxDqeCxRC1bj8qalmFHx4bo+a6hYhfOSxct5qFIx3pp5zYSqF +ooB+3KjOB3CqbGNzty7DjIH0Otb0D4ieZ58wnCqHIOPRzfTD0eDcX/7nxWoF +7t45Kco0HI2JQzdMHVCDGp/43tANH6HA3d4bv7UWvEnc3geOfUTcc/8NbGO1 +qJhamrrq9xE9WqNeCw/rwb3e9M2XvI/Q42MxypJtwB3RznPO1I8Ynn9269CP +BnCZZSTFy8QQfOHuxX+1CebPBPVlzWKgydnNK7zQhJKYwI3twTEQUV0q4vRo +BmfVStHNkhgsnNrJmF3fAjOqleXyVAwErCuZqS4tKGQa4g/kioWd8PVLx6da +wC50oXmPfCxuM8s26KIVxih6kn8nFpryP6TGfVqRZyQmfvF1LBrkGhLfVLWC +zfXNMLkiFpT96wOMGa0wilwf6MCIhRx/E0NrfRuySx+c2cgbB81lF8Vszjas +H56YjVSOg4hYdPjkpjYY/NGKkrobB3Yd1+Puy63I4K++VP8uDiGdpA+y/a1g +kZX6d70uDu5rr6ssJrVCT/9jxsJiHPSkgoI+2rZifkibLYY/Hs4nLr7SkGiF +txHrLS3leKiYFL6+O9kCAWrJZxbreAx/er607XULcm7e5c8PjYfnboezOvIt +uDAl/MCiLB4CSasW+mPNoNzua+edigeToITRJSJ+HLZnvJ5IJ0DFaCPrQHET +4hcWyOLGCVjmuJbbr9MEuftxsqM+CWhJ1Bd4tdgIS6dNCwqDCZA8cnjX4JFG +rPlTfmGJORFyVZrLb3oaEO5iHx97KBGMhNT99q4NkGDax6SjnYjCS5l6hhIN +qPUYMFjvkggSvSpYerIehusC8wriE3F7YNy5I7YeS88VOO+0JcLsdjjXqGU9 +fNm+WfL/TMS0D4cJ0+l6CAUm1jbvTkJEXnj+Z+56FGy5LuSilgSxg3XrApbr +cOklxxOJe0mYhl9I6VQdJrmreslvk0BiCPYHk+vg/OaB5IuqJNxuf9VwiOjX +2/gP+CvRk8B4dUkqarEOKRHDk1+3JUNNWcRqhK0eCrtDFOLlkrFsvO9kI9Ev ++j8qv792KxkOj6pJh27Uw1bk5/cNQckQirr3X8nrerAkpmgW5RP4XdWmnaR6 +vD9glGpJTobxO5ep4b0NkErbul6ANQW5bmJ2z5wa0ChRa9wqmQL1touWz3ob +YJzlVOKqT8g/fco5K9uIwHyyHTUlBSItvZWevE0QOfWq+WV3CpY3lh9KDmlC +cYnqPpWVFLCzLWwd39yM6Yr0oQSNVBjemHKr4G6Bm7LJST3HVJCeilj/imgB +Tx33i40fUsHgiON13N8K5eYnqtYLqVDwr/IPVGhDVO/5rKOv0jDY4u60+VQH +Tuj93TRekgbxmpTlSJcOtAxmmodOpMFnbKGAu7IDv8g7BH6eSAdF8xTrGpVO +hJg2OyYZpaPmsynL4Wed2Dfp2qn/PB0vJ08eTavohPbMpHcpKR0TDYpG+ie7 +QLd+S7VZ8wm0Jxvn7tl2wWNeXW73wU+YVthunB3XhcxvOYtPn3xCfMimLxWb +urHp31PDc4IZuHwYfjW13Qi/o2skrpqBQc5A7pb5boj0iBtvtc2AjFfniwTe +Hsgn998cKstA9TXFJl2LHhQlh+UVSGSiXsQt12mlB7NajNKLbZlgVgqbSxTu +w/GN/WfkxzJxQUzqMO/5PjwuryyX/JEJ+XlXe2G7Pmw48KZiu2AWXLoul4pW +9GHPqmIN2SYLPMxpH9hv90Mn6U3z/c3ZGFFbduFrIyHihoe6+Z5s1D6x9Pjv +DwljXDateieyISzL9c5CbAB3XZTaz9zIhlj06CvlpwPIlzqsKXkvG3YyxZ4D +aQNY+bKjU9grG4812hTy+wfge3W2a0N6NliYC1yaDw6iYwNJ63dFNrQzNkw2 +Xh0ET1lVD6MnGzdjeWzfPxpE7P7wvs4Vwr6pKLtW9SBmhj10azhz8N9fbdNN +U4OQfGlDyhfJwcHS/OrTG4ZQtqI0+F49B2YpoyOVKkNgyT58Pcg4BwJu1a9X +jIdwwYJ32N0hB847PUIePRlCiMDaG/d9cpD2BmJSoUPo75wduRVBnA+aeCmc +OgTB5yQjvcwcnDywOn2+YghmctXkCzU5eMR7Z19K9xBSFtONz5BywDpJFVGb +HMJiQjj1CCMHo/oxIYe+D0HG8JmpMFMues6j32jtMFy32o5zc+fiRz/L1vkt +w6ip0zPbIJaLWXu+STr/MDY5K0/+Op2L8unC2xYiw7h6VMKccTkXn1Wovx6I +DyN8ivfL6M1cdHt3bZc4NozR92tvdz7MhV9iw6EkmWGIXpmbrvbPBV+tofWq +3DD43c7JWnzMRdP8x+2+CsPgTI/2ZyvIheMMy3Fm5WGsG/o1nN6SC6/KN24h +KsP4zaolcWUsF87MrdTrZ4excDLN7dvPXJQ8NNoVSOBJs3WdbzbnQXL3wwca +BB58aSR8em8epIwXteuI/zsqCu6PyuRB7dmDH0IErp3jrH16KQ8ihWc4vAl7 +xQKWPKJmeWhLknPcReDMC9UWDY/yYNalP7KZwPFOAkVWwXk48NnqsTOB3yU8 +YNsSn4d6un91AKEvpKftenZxHoJqrh40Vh2GF7NYuk5HHiZGnoxsPz+Mx5JP +V5cn8/DT82ZIk/ow7hoNXo74k4cfQp/Vwq8MwyyAaO5b86HQQJUK0x2GQXHA +0ti+fBixtzmTjIZxeXpS2VsuH+oPz8rYWQxDhQevD1zNx7uM78pW94YhqxI+ +1WKRj2+9Xad7nIdxxH5R2s4lHzWvouyyfYchEn3Bd9urfNhG+09tDB8GX1vs +YH5SPuZ1Rw2GEofBsbJyyKA8HzGOhpoiRcNgOXjN5W93PizVNIXJzcP4pZvR +Fk3LR2Ry3661lGHMebEKqfzLR5j03o+e34eJed/k3hfuAnBwXFfQYR9B2xZu +bgmFAmhaVh6NPDOC6jM2tzp1CuDEZ3qRrjuCQqu6fAerAhSphj86eX8EsfVO ++iVhBTBao61omDYCJ7eRKLXZAkTcyv5WIzoKm/STC3TmQqQ0ymfSVEZhOhSs +GMxbCEUdtuN7zEahIa000atciBMmIQvqMaMQnk84cPNdIbT5+xav85OxYxfT +k/WZhbgftuHx0Eky2C/qtyTXFoKTNp4adJWMnwmb7i4sFOL6fZt9cs/JYPSY +VbxaX4QX0Q0BW6PJGGMu3yotUIQ5m4UtnQVktBjZ5bqcK8I+3izukXEyqgIa +1+25UYSwzgMtPMtkFBQL69bYF8GFaTTQbx0FadNPkix8imCy6bCGJQcFMTy9 +v9iiipA/sFMohYeCNyoSFz/lFOFgQfSnC4IUBNg/j7jSWIStCQ9rNUQp8Iim +zH4bLYIUe5d6/iEKHradQvi3IuTSaXI+RyngkMibbGQtRiqb3dn7JymIC5QM ++CNQjPpxV5UJWQpkZ1OlDh8thiepKJsiT0Gn+v4Bo7PF6DVxTbJVouB2Woxb +iH4xvIOYO0LPUrC6SXBflU0xNnEnXjNQoyDU6m3L16fFaBZ7N1J3gYJDzdz3 +RcOK8XIH7c6YOgVVB0P4iEUQtf8EtfMuUaDnt6nCp7wYhz2DpdU0KZijeZsX +dxXDRtmaGnuFAq/zzJsZU8UwHaxG51UKBJJdcnb9KYb0uI/mgBYF2ay/9C9v +KYHxRDlnrTYF5Pr5hGzpEjD9phyyukaB434rjYmLJTC8s412UpcC9udTX7cb +lyD3kO0fVj0ivlMm7845lGBu4xcrGoFPqY4oPPIpge+DjimyPgUd8XpfUiJK +kLSwIeOrAQXm63oChzNL8D5i28tDhhSsmF0+zlFbgt69iiOBNyh4VdM0iIES ++J3v0xL6j4KDIqpP782WINXaZN+0MQUVzyr3x64pRZP8STrNlIJr43JtPdtL +MdIrFH7gFgWzSoUO6w+WonSXrkuKBQWeMcd2ysiXotz7k+JdSwr4mTMq71wt +hVI8H+WRDQXnKuM5Wh+XIvvN4xO3HCgYFdqTtxpUihTOKx6qThQ4uEdcl4wt +BfutGZKtMwUf8SrpVXMpxgfaIoO8KJD5wHG5llyKZokG16d+FLSt+n7/8bUU +eee0DLODKfhT5q5kIFAGyd6y+vJ3FLzctTLtL1kG3kfHHr+IpkDM5WFwmUoZ +HqeWPg9JoEBHznZYyKYM378HBPzNpiCj+Lrjl7IyTDGCSNMtFKjy9wvwdZWB +6+wx9ofdFAw/ulp9YaoMwSN/u/8NULDx1HnOTxzliM5QF/gyRUF0eE0+Wbgc +FkpSyzKzFJxcxo2t0uVwv6EiZ/2VgpsFJ1Mc/ivHvgcV3sb/KPjNk62ZcL8c +teEbz+xYR0WI4+Gf/c/L8frKud53bFSUnRBROZ1Zjufshvt/cVOh/frDjHUN +Ye/YN49WPipmvvG/iCKVo0NQmddUkIoduVtH16z5DIEXTMJ1+6gwDPijPcHz +GbuP/fo9dpCKGLPJ5jrxz3j/47RetgQVX+TalZKVPoP2Xn3xhBQV4tuLivz1 +PsOWY8bf7gQV9rMxkra2nyEpJfzvlgwVBbUBiZqen5E563x852kqlByNX2/P +/Iz5kjjqCKjwuXSBfbn2Mz40Ojj9VqSidd/xZ4NDn3H9mTbLd2Uq0ujPCtvX +VkByPOFM+jkq2vqXv1ZwVEChe2zo6XkqFqttjmTzVSDd/5i06UUquDPHLGNF +KtCWdWLougYVJyN0E0KPVECVw2yTy2Uq9H1aqF6yFcS+T8vsuUKFs4Pirodn +KwDX3efstamIMs7Xu61ZAa6S4bpbulRUqh8K1b9eASmHpJDPBlRMyES3XzCv +gHjmX50QIyrWi27fJHevAltki9fQTKk4sNVP9bBzBV50jH4YtKBC/e/qU8Hn +FZh4WaPiaEOFLe1+2ZaXFdjWwPjacp+KF73Ty0yRFQhNDvGef0xFbuWN40uJ +FSg+tOPlnAcVfeldd8ezK+DUH3Zp0J+KX2/PpfaUVWAxydel6jUVAt6lU7UN +FdgfSNLMj6ZC3v6ocEF3BWZ8b16tSaPCxCjhRtJoBUp6D6r/LqLC88LOt29p +FUg6JHf0VgMVCSdDevy+VeD5E+8NW0lUNAqv43T+V4FTpbldrDQqMcc/vmjD +VomWnUfcr/2hguPPnLfR9kp48Bj3MG8Zw9EvN6suC1VCQ1hff7vIGBw/a5yS +OlkJKQ+7CM+rY3ibWuWwV7ESz9To1TSrMZS+kc7kVq9ETMH5/lrvMayx27P/ +p0klpo1ux45XjEHEMMx02roSomF/1wlTxqCqtilq4GElcr4c+dDBNI4Aoe/c +pYGVKFq4QjZXHccndkvN9PBKnFmbOSZvNY7O5VH/qNhKRHsfHbZ4MQ6ezgbm +p0WVkJ05P+xMHcfHpxELZycrEfWqjMIdPIH8MeWWdrkq0N2FfVc5ptCn9nQx +8FwVahYKbCsxhR+fynnUr1Zh1vb1rSC7KUg/OWXSYFEF0QzyPKVzCoXbjvyo +eFmFltsGT6NCvoD0yHqnW2QVlhcEHWbKv2CZnKxwJqkKEqNK/xwZXyCTJuJf +VFaF0L5rj76qTKNIhV8oe7oKQbF1why0aQym6J61+0rof+edPc9Bw2/O15YS +q1WI1CuKsDxGg+zIlryUbdUYtt+bzXhIg4GyxuBtwWrckrx3pP8NDY+T/f7t +O1CNrX+O1u/Jp6H4wboLsfLVGAvQO5E+S8PgkNJdk/PVaPk4lD28fga/Fd1D +d2tXo0byY9J5wRnwJ5UVjRhVQ2fwy6n5YzM4zfFn9P0dQj7rxdt0bgaGDjIs +Bg7VEOr57k3Sn4Hz4IMDvG7V6LhVpMdvOYMIhZxLfb7VcHXbvhjiNIPShIX7 +oaHVCNx0QAFeMxhml3h79UM1KvzNyg+EzGDF3qqcM6UaUSu3za+9nYHAQNJ4 +W2417D9dS2+JnsEZTLEGfq7GxM2wR68TZmAUv1fiYlM1VlPEeEtSZuC6yURr +Y281In/5SJ5Pn0HUvSinejJxn7BjBeqfZlDePxTpNVMN4/rR0W5CPnqGr1r5 +ezVM2R6xzqXOYDX22vQaphrct/+XlZo0A0G20M0VbDWQvKxgJhg3A3m7TinX +7TWYuP3hg14UYb+PQ09OqAaJa5fqbd4Q9uXUXX4frEFage8W+2DCfoxvTOGJ +GrjSvEwee8/gM2t9vaNCDXZqeF6McJ4BxZZl9vjFGniaNk7N3psBU68i11ed +GrAq/q7wMp+BwsdSw7tWNThZXCA0oTGDilPZixZhNchT/0yb3kH8/2GeZ9/H +GhjFvkz8sZH4f/1huYnUGgSxrznHskKDYleit3FlDUQ+x4c6UWgwlZlMFWyp +QZIGUwlbNw0eUcKdw301UFL44/O1loYqy8id+owatBWqDPKm05BDs7Iy+lED +bb+yw/IxNMTdli25yVQLTU2P5Hkiv0K/sG66w1YLVfeFYdkgGrzM+w1suWvh +1P4pWNyLBsfJ+JT7grXI9uov6HCmwdzM4beTWC2uci/ZST2gQXdc6YKrVC3+ +lVZ9vW5Lg5rp1nfP5Gphq/Aj6NptGk5RyTQf1Vqw53+KPniThoPGn04FadZi +Xc/3ELIRDTvJzr6vDGqRy8Xb+uQ6DexGFwfCzWohLUuvZtGn4e8w34Eo21pQ +2ZjHXXVpmLs+7RTrVIv8ntbQ2Ws0jA7mNyR51CL2Rzq0CHm7vhfvp4BaXDNj +nM3So6GCpHU7J6wW4k/i17MS+jN1hQsLown/3oeTrxH2P/YtbChPqUWp+OiR +CFMaXup81q3OrUUUzfV6rwUNz3oCExvKa+EY8KV91YYGBy3Dn60NtXgkfWwj +N+H/ra6D57q7aiFzRjV8iwsN1678CiMN1+KJfPYBOhG/cx31UyNTtZimXw/8 +EEyDzOWwk+MLtdDeOVgu8o4GPo1jfbMsdVgQlvB3yaKBrWXNvq8cddjw1079 +TDnBFxc6Hizz1mEfZ8SZhGYahtVstq89XAcmWZsalWkaWutP32KVrkNq9h1n +k580lKuy5W1WrMNa+R1V3wk++KCSqM2rU4foxDOCl/bPwFSB+uqwSx0E/muf +PGQ1A63PGeNSz+vQfzxWxZHIZxV512MyL+qwuU4xvjpwBqJyO7uV4uvQEPRx +4WDmDKaldbj0WusQt08yyG9pBgP5e01v9NfBsa9UQp2ZjqYTS1mm1DpU6L/Q +ithKR+qx4Cs23+vw2OJaU44EHRHZNz7a/yP8nSQLmsrREXBUfPHhxnpMsVRy +2Zynw/ZIY4jHrnrsqjZktTGh479PbyjP99cjIn1fsYY1HZqHzSUDj9bjZGW2 +s6kjHYppx91fnq4n+uHvyRg3OqQOre14c7YePc/jLm7woWNvSufuyMv1YHmi +3egTTAf3gei7Mfr1cObVUN0TRgdLku3nxJv14DfUedz8no7v+85sSbepB/P0 +xKJHNB3yY0r1fk71mP7g2egbR4d3pJrb7Wf1KPpR5mWVSEeb3iVp1aB6LAfe +o4om08HDrT2/9209KJVeTQUENmrXT1wTVw/LZV3TPQRO8PvvP/KnenBI/V65 +Sfw/d/bWjrKieuyUV9jtQeg/ucaq/V1NPaIEPz5xI+y7lto9d2qvR6Ha0qwx +cb+6h464NliP68/XOoq/poPjmPPPY5P1ENPee5QWSIfu3NOMrQv1CHYNvfrB +i47o5OcW87/rwb2wyq/nTMe0WeDu1nUNkFebattlT4fTUHiwz84GRHd1jf41 +oKMiLOqc+b4GHAgOdTh6iQ7Wq3H/lI82wHBkn2acAh1vGzLu/lNtgHfv4VPP +9tJRnFd32dG+AarONi9nxgj+D/62xayxAebZQ12sekQ+Xfxdr9jTAM8TuQbH +iH4TsJ7JfTeZON9xj7nk5Ax2uWxaGPzWAKWth64fIvjQXGZrUuG/BmRsMFsr +wzqDT195jMPYGiGc/+cd7RcN8pbCHVeEGiHT98XWlUyDt6iYz5FDjdCqdo1/ +SvBhG+WwwuaTjWDb+Sb+TgMNPBHHlmcUGvHwuGClClFPRrqnMhsuNuLwDrKv +UB4NCVy4nXCtEUnnpuo2Enw516oi5GnSCCXXfEv2BBpO+l4gmVg3osZBx+9Y +NA1uKpoheNiIBS5pHd/3NDT801Hb5dGIYAN2jh3hNHCWXGf6E9CIS36PWSZf +06DnaFJIetOIQeby4N+hNEQftbDLj2kEb9BpNiNCPs2wFgtNb4Rx6Zo2boKP +JZPsKfcKG1G857TUXoIfnG46hV+ubgRF64VvQBTBZ4KumofbGmEW77ZHK44G +1sFnrJsGGtFQ8ErJKZUGzde+FdPjjUje8/boSg4N4ZrBTnVzjbgclHZ0tIwG +6qbXknG/GiExc/S5QCPBx/Xvpp+yNIH5VtKT3F4a7D2io//b0oShS9dMY8aJ +eeNMgt4Z/ibw8tdFUpdoYP6VyrlTtAl9fJsTrNfOYGer0lccaUKoqMgOFu4Z +HP840Gt2qgnrLBels0RncOv8hvefNJrASLDuOqpO9NddUS7duk1Q0Q5+8MN4 +BmGLx42XTZrgc1PzQI7jDBremooqOTbh2AGDQ4tEv6ba/Npg4d4E124rl//K +/j/fhMz4+zXB94nq8oe+GYjPlGX0RjUh/eIEzXoTHcGyfLJ36ptwlO2s6R8i +35M4MgWCOpuQeZjjQ9U7Ir/HVP9lDzWhweVs+79COpb8HGpW5puQuxr6POUH +HdeG2i+F8DZj9Xve5VsPGBBw9r5ZcKcZlptcWkkPZnFCc5fq8P1m2J9L57ny +ehaXRHLF1rg2gyJ9555X7izcWqizF142Q0jU4b+/i7MYEzjjNFrcjB/6jO0K +t+fwZ6HbYG1tM3j6lUXSPOfAXWt5Rqy9GedHfHTCouegahPObD/ejLgl80/t +fXNILvsasI69BSkMDw0juXlUvfC7e5CnBQbtBzqhPY/BW3uuXhZqQeMes1QP +q3mwc1ze8fZ4C9pY7S+Ihc9DdGzyV5l8C5YEE7X90uchn+88PKbWAiOlT6fV +q+ZhZ5TyUfwGoX9/Uc1X2jx8pRQ9r1i0QFN79tPwyjxi1pPMHe+1gP+n+b/X +GxbQ/WmdeIVXCxqeXMpg4VvAyX/G+VqfWiA2GGX2SmYB6hoVHmcLWzB8Xj4v +Awu4+X73ZemqFgRZ2216qbqAEOnRL/x9Ldiq+sUuR2sBtLvX+cb+tmA0idez +yGoBTOXFk90bWvHb/ae1zr0F8LDzZ9dubcWMkuWadscFKCWRLiSLtsJnsYb3 +9tMFRFB0nO00WlGxVmki4PUCsiXy1Ex1W7GcoffZ7t0CGpy5t2ubtMLNatPy +xQ8L+M7bnS79oBXBFrYp35IWcOmKJnk1ohUX9AZj/itdwJqqC0qBjFYIB/1p +rJ5cAC9nCofbj1ZoxYo3atEXIGG0cciOqQ1Sa9LCVhcWYPC7/r42dxs6bTYc +TVpZQK7U2fidcm3IxXF1g+2LMI8Fa4p/G5yEf6vtUF+E82JUz/vXbchq1V41 +0lrEK6xGB35ogy2XTmexwSIqhkpP3ctpg4U1n0jinUXwcctayQy1IWjyTBO3 +zyJaPI+31R1sR/HOafvFmkXIbmlmfnGiHbdv8Swutiwi6a2J9HWFdjRZ7mDu +61nEs09B0fM67dhjQ4qWnljEgoxob5FxO1Q3anmm0RdhVF2y0dOqHeqqB9K/ +LhH6SNP2vE/bkbK6FPyFaQlJpm6JY/7tOENmqfTfsASe2e3DaWHtsGdxEl/c +vITFNcpnFdPasWVtvvo83xKMAgYebSpoxzuDvevddy+hhcfuU29lOxo6bmys +EiH0HYrcYdnfDuHVneIXJQh9+cfUj4+1I/xPH/ylluCp0OS+ymhH3AFWf9uT +S1hqMs5r+NkO2Qze6cVTS8hM+eNwfk0H+oQlDbnOLOHLvGrwp/UdUPrvKl8r +liB44mXyNvYOOETpuO9WWoL245Fqp60dkPiUIbxBZQn+n8VGR3g6wHqKr+bp +2SVUsTgsKwl0YK3qesNA1SUsn//MlbSnA3tlvvKInVvCkWC2w5v3d8Dzs5eu +JoHNe3TO2Yt3IFX7aQELgSP5Ppr0H+3Ay9UgVhXi/x4jxhM56Q7kXiBpbyb0 +b4qTDvso1wFHrwfk/5SXoETzyFyv1IFm8wyR04pLeCTR1mR1rgO/A7gHo+QJ +/+7zTXaod8BY+eac32nCv0KzfyeudkBQWs33nzTh32oG33vdDqyMLLH9PbYE +HeU/x5hudED8gfsmzyNLCPBRvXTLtANsUfIGrw8S/rW+uN1k0QHvsrqVo6JL ++MU14nHEpgN2xl8PXyfeR1JPLDLUvgN1zFmGXMT7mUfeL/j1sIPo36kH9bkI +f/azMao9OvC1aG535FrCHxud9Qd8iHjmvH8c9WcRStnRQkGBHRDybeuX/rqI +TDlpHb3wDqg+WR2Voy7iy1OPu2WRHQizV+D41L8IwfpWX+HYDpT6aqhWtS4i +4IpZOSO9A6Rt7kaUwkXcNn+x/2l1B8pPmFlf8V/Eh9RhxamGDqDXQ0jGbRF9 +C/sNL7Z1wEaWPW7EfhEqT8pDtg90IGIx4p6D/iJ2h9B/Jc91YCAkLVReZBHl +Jm7J2V870PF2U67DDiLfj23TL1km7Ld83B3ItoiIPtnCFuZOUJ0C39wj6pl3 +l5/jPE8nBvlW04xLFsCVIvb1ODrhUhWudFdzAVlPSmPOqHQi8/LUpmPKC9DU +0Lyqer4TUp9XktefXEDwwsMsXa1OfPhXrzO1cwHs0vV3H1t04q/j4YmnnfNY +V3OL8Tm4E7xRu+9WcM4j7vWv9w2hnej4zea+/GsOKhaBFzvfduL3xDY2j/E5 +eLDlpYzFdqLskJFjcMEcVjVZ7qwr7MSa3+lpOTfnECkczstR1gm3mKaW8Mtz +kPt2qIGnqhMqHml/+07P4ckbrf1iLZ3gsHvr/d/2OSyPxExeoBD+VVktRLfM +4k3Gyddak51gOTWtfblkFiefNqkYznRi80euNJ2UWTwQWYq1+daJwxYWdRa+ +s1iyVDQNYe1C3POewYCLs3gh17v17eYuvJe6Ez8lNwtJjjuVH7m68FiK/fsL +iVnYZoUI5Qh04er5JYEBrlnQf5JHeyW7UL1i9oidzEC+RXDVhZNdUNv10qir +kwH3fvmEz6e7YJHeJDlXwwBPQaRNsmoXiDP3hNMYUHK8vuJs2AWx+6w8110Z +2DzFRlk06ULQ78Sl9PsMkHSKq80tunBWRt1C4w4Dtif4/DXtu7B0SPiGrQ4D +77718Yn4dOFy8UrKnqMM3DLz/hse2IUxVjXOKjEGJHtOUDe/6oLk2/fCyUIM +1OWEJv2M7EIS00OH81sZeLFXJcA6tgsfDFKm17AxYPjq611qEnE+PPPeP2YG +Fu2vSjfndIFN1je94TsdpWNrdioUdUHhlO3cq3lif7iatZpb3gWtW99uxNLo +EJDirItqJM6XnjsZNErHl4+fk7e1d2GbtZXJnQE6srfeDfTp6YL2nmU5nx46 +1BZbte3JXdix+U5kSDMd20xcZL5MdOFV/MzMo3o6RjvEBQxnukCXpDomVNOR +rDD8r2O+CyaSf/h5KuhwyPQfP/u9C9Z2lckNpXRA6HR98e8ulLauMMqK6GAL +mUk5wtSN3OtCcd/z6ej59zYobl03AvYXe9zNpePD3fP2fJu6odTEkDiUTYcl +eVkniLMbrxe+QiyTjuOXk06t5enG6FKenPknOv6V6+5y2tkNPDd7N5FG7IcS +G9bMCnWD67lESUwqHa+j8idM9hH60llmP6TQYcxh3tB3qBsxu+7fHiL2pUOu +29MuHu2Gle2Ly9oE/jFbE1xxshtsPWzpGwlcecPh/gm5bnz/hvu/k4h9snWv +bopiN4zbnz35/z6me6Zbdve5bvD/dfDyJbBwuodgqHo31J45nBQl7M0KSDFv +vNoNJrnTfD8JXBhAnXTR7YZ3XVDkX+J+HishjUuG3Yho5OGVTqdDw1oh3cK0 +GwaSWlUfCf94h+dDhi26MTOVU3ya8H/s4geHKzbdKHHqYllLxCe95JJenX03 +wlpbfb/nEPvWodXTp526YS7YwLuViK/y+/TdmS5EPHieW2gR8yjHphtrRZ91 +48zciW3FxXTEzZQ0cQR1g5b3zH3mM7Efv7m81/JVN0I/BPV/rKJDWmX8SW14 +NwTDBk/Z1xLxjWQ77BzbjSb2KgctIj8WNfWDaYXdqCYtjzT2E/vaX8YXlfJu +PHnbcnRlkA7PFHeF6OpupNbPzkoS+cfLkrR4ra0bcSrDua8niP234IdWzXg3 +DsobCvxaIPZBM7+03bRuOJezutK/0tHFKbjuyVw3nDaVFTQQ8/Mty7P5R391 +Y0ibFCizQofEjgGOwNVuiA+vqaxdpWO52tpiem0P7pPlVqXWMBCwK5T3A0cP +WJXNU2PXMXCtaf+939t6YOp+4VbMBgZ2Pyxp1OHrQaHEvcqHGxmY3ntZOEuw +Bxe2c37as4mB7I6xx+wiPWBK05CNYmfA2cWx2+JAD2zJ4uH0zQyoHmQTr5bo +QfQrM0HWLQxw9kd6Ch7vgdNvoQtLBB54dnTk0akedFLSKpI4GYiRrD3RK9+D +l6Jrrhwk6t16RC9IUqUHl6Jlvj8g8Ek/xpT/+R6Mtk91+xGYSdodXy71gFR+ +WfE2gZvGt4Urafeg5qNbxWYCvwpJXIjU7wGjSYHlCaHf8Mzp87+MepCZNDef +QdjfN9P2UdusBwaRIuFpHAwshJn+zrjTg5PvzynfI+5frPzj6qa7xP38aXdW +CX89F3xTzR16sJywrkCb4B+NyF0sVY96ILHCzfqAleDLC1mGu9x6kBby29p4 +PQOUHyp5Tp49CHpVt5+XhQEHTWvzI8E9sHZK+LBEvIf833/lfqE9ENx/rZ+X +eK8NKa92TL3twafO53pcv+h4t7akISKuB+72ycd8loh6y994iK24B4liO1rr +x+nwuxn57NZn4n2u8Di3k+nQ5jw6XFHTg3sL+ZkVQ3RM39ELfNjeA9czH57b +dBP5vStxfmKiBwvbUv/pEvmrcO3ZyDitB9wS5i7Xy+mwD/6veWyuBz6Uow9v +Efnft4Y3kbLcg+1Mc7veEfXEevpbKPlvD4783urYTNSfrEOHxyhzLyjd/95z +EvUaNeVjNMzeC9M61aTxWDo6dt9SH9rai+zMf4edoulg1leUHeTphb2/bsnh +SIKvXu4SG9jZi09zFT4biP3QvPnXdpJQL7is6BWsb+gIZ+lb2y/aiwuW51yP +hxL1dSZ7sfdgL6Ty/BsCX9Cx4hhE7jnSi9cy8i93BBP5nmnZ2n28F1djFPN7 +Agg+o6mWdJ3qBdnuzvd6PzpeCu9N7pTvxToOnm9ffeiouf4vrEO5F0IBg9LX +nxP8Fjrk2a7Wi5G3h0WZvOkQayuwb9PohYfc/r8TnnQYbAg1br3ai9Uh9aFN +BA5QsLvUotuLN6I2OY7P6Ch/pC7XbNgLJ+XAy/sJvJAtdrDJpBffR6c1dhNY +mMHC22jeiz6D9buNCawtSl3XYNWL+CTKWjqBvY3KvtbZ9SJkqxh7JaG/8M1b +au2DXpjjPfe4Fx0zHQ/aax73YqL2Ue0V4r4CbFfLqt16sf6/rS82+xL8qCyR +WuXZS+zT5tk8/nS4OrO9rfTtxe3ulUM2gXRk5k15VwT1wu1Ufh1nCMGXc1UO +n18R/oUNcq55RQe32AfT8vBevGeSuXEmjA5VkyeaZZHE+3iaV9W8Jfjzna58 +aUwv/msW5w8j3m+YnZO/OI3wn7+9lzOByC9VxoairF7sc/Uvyif4XMGt4XtB +fi84mW4Ef8gg+HTRvTOvoheZ36ZvSxL5Zd236JPV04sUNXXS304if7a0OWYO +9OLO8TcbrUlE/qilmGWM9kLmomjRWiK/j5eYKqRP96I+6uDzKAbx/h+6fyat +9GJF0Jy+StSfxEDGZOKaPihxjWdLE/VuzBXQnbC+D67ulzLsdzBQ46mSEcfZ +hxqRezIkUYL/7uSZR4v0IcVXeW+hIgMzCuk+mw72wefqlT9f1Bg4xxuf4nik +D+M8rB7kywww14fOqcv24bG81dO1Nwj9UQGchehDRoJGseBNBsofeErtPduH +4rpfh8i3GRDQcNYOutCHns9VfHK2DDwScXD8dbkPUkVPa8SJeanvj1W4mU4f +Do7n3U16yMDx7pvF7QZ9uHo1yzzhCQMvU64Pyxr3IdajfY2gG8FPT7VW42/1 +QV0tO3W9BwOX9C8KbbXqwzv60yldTwZSJZWVnO36oCd2+MpGbwZYWU+bfXlA +nK+JT+N6zoA5Wcr76pM+iNjxUK0IXJN/MKnMvQ8T8RxrNxNYOEi4Scy7D9Gn +P+rNeRHz4C1+xiv/Pny/ZW/ESugfkePi+BfSh1OzWS1aTxmQ5WaTtAzrQ77J +6vtGFwbC6Wuu9r7vA9d+Cbabjxj4UfXrvsLHPtyT+xPF58CA9rvF16kJhL38 +IMkvNkT/uEcr4Enrg/P36S+15gxsOU8deJrVh2/Je89mGhH8LzTwh5Hfh99T +fns/EvNj08+OXXqlfZB19it7dZEBsfYGVFf2QY3ZJvOZAgPeCRUmEvV94N42 +88/6OAOKOpnxLF1EPEs/9O/iYyBKPKn+bn8fxEiBnmSin62sjaYNDvehzXXv +SBDBt4XZwYezvvSh1Ji1I6OXDh6/55cFZvugGD5yYjfBl/dN3O49X+pD5AvB +sYfEPCLBeTfvxt8+iKtSlybdCT74Yt7fwNyPmAvr1/29TdRrudGvY6z9mDni +XsykSUe8zaUzbNsI+a2V8T5+on6bD9fmi/XDWXbrzI64GTyOEf2yR6IfT/7I +nZt5NoP+R7s2Bh7rh4nNm6560xm8FNuscVO+H296/s6V7poB8cY9W7T74YBU +UW1fGn4opE7cduuH5MDWtjL5aZTG0d8/9OwHQ6e8YGH7NDxYxbW8ffshKOYl +2sL4Ao6OtMrYV/0w2pIjG/v2C/b99ylqNLEfxxUTfGkLU7jmkqWn3dGPPskz +5MmoSQhQF7fc7O3HKYrjzVsPJjGmIlV/b7AfYlK8iVLqk7BlzzkRPNGP+I9M +A+TfE/B+n8vVtNyP/KWKmugbE1D/962R9Jc4L/0pOEV6Alw3Tzz9wkyC3s51 +8Ve4JhB1MH+eZTMJIjfvK0Y0jiOvqKAFe0jgYvNw5FEcx+Ndy88u7SPBcHhU +4J/QOBSeypy+cYiEm+kbRuvXjKNFrSj58QkSBJgS+7fXjeFl2i9jX1kSmF0P +6yclj0GPU5Y3HCR0rZR4nAgaw0R/sXfeeRJ4+CyyrxmMIeX0nzM1l0gY9dpw +4bviGOw+nP7epUXCtPTW5NiDY1gxL725cIOED+JbRxX+UVHVtML/z5SEEfU8 +LWk6FT4SZ7o23ybB7FtzqzqJCu4fZQqH7EkYK3rZQ86jYlB/9eephyRs379m +xiSBiugy+Qw1ZxJqL1hxs4dTYb7HzVz3KQmneB9GkP2oEPf6vMvcmwQZ7oFb +I65ULE3/63HwJ8HVxGF+nQMVheoKAc9CiHgcT9DSt6TCNdNd+eVrEnTOl6r1 +m1Chwl35O/odCRcmX+9xM6CCzWlNdsYHEjI7bNsua1PRMaR4pzyOhIWU7pFz +l6kIg4dQazIJO8jlLrcuUmEYW9U/9ImES3dHnBPUqBDesDZ4JoeEpKLfF1nP +UTFtqaz6q5AEW9WX/56rUvGp7dnfDeUk2EV5XxEm5A5SNbk81SSo8azEdBP/ +mx8Xin7RQILsl7BnZEK/3klnf/Y2Eu5Jh/SLaVJxQYbk+LybiPfUSk6yDhWn +ZY+bMg+QMCd+ouK6IREPuRANl1ESDnGFnpIxo0JQniGzPE7CHR6zn9I2VHAq +qIncp5EQYv3DVushFcxKcVvm5kiI2TtW4OFBxTdlpj+3vxHv7347pCyIismz +hlPjv0jIL/9j8uc9FQ3nucsGWAbQMM/KZlhERfFFuyRttgHs/F1xwrqRijSN +llftWwbgwNrFYTBIRfAVT8ta/gHECvyXn7BKhbsWRUdBiJDXr/+xsHUM9jpy +iiWiAzgults+LzqGa/rfdmRJDsCR5acu5fIYBEzMaiNUBzAxcvyJfgqRf3Yq +Qg72A9C/+bX5y91xRNhHb5p/OAD5/p2ul33HEeiw8uOOywBIO1WsSmLGYeeU +2/qfzwASvj/jcewdh7S7yJOLUYT8Em/29VMTEPNwN6+LHYBfpblq45UJ8HsO +X1FMHoBdH+UB484EVp+HiknnDsCyPrRS8u0EaoJZ+oSbBrBVFzYtSxPIf2Fc +Gdk+gIPX7zkysU4i6VVpGm/vABGH3u5UgUn4v3F4xkEZwJLqHZXLKpNwftth +6zs5gJBjqt6ndQk+eC9uwEIfgOqAwZPndyZx9cOE5O/vA7gunO1zMGASKh8V +BB78GQDLmI2LU8QkTsRGbFhgGoQft+PotrRJ8CZqj05uGoQt69hVkcZJsCVn +NhpvHcQUpWfpZd8kVlLY84Z4BhEmM8WjND4J8qca/849gzj/4tFHvd+T6Jhl +YUjtHwT/WUu/QJYpVIifVQ8VH0RAXPBjZo4pZFp5pX0/Oojjf5MM8nmmEJ1S +y64rPYh3bsMGSYJTCKGtsymUG4QQY+div+gUnoqptvIpDcL/kk2/ivgU7C28 +Dz85N4ijFnxs80enYJpQFzisPohuy8ravpNTuDq5fu7M1UH0Nd3wWpGdgrLI +uUsfdAexXL6fyUR+CsdvPv/EdGMQNZfv7l+nOAWRmHoOU1NCHv+fyIzSFLip +G+5WWwwizjxHZ6vKFNYJqbWL2Axi85SBhjOBfxj5HPG2H8Sble1t4gSeimwI +/vJwEG1qaxtFlKfQN8y6oOYyiDVJ+66bE/rrd57XTPEYREradNNXwn6hgW/m +Jh/ifG+IV/vpKSS9beS0CRzE7bOlAivSUwgnbbzX9nIQlz51KTsfm4Lvjgud +R8IHIXbwSetViSk8vuZ39EXkINSiuZI9xKZg+brpxVLMIBwMRSkcwlMw6GFb +0koaRIbl7Kvf/FO4uO3i1bz0QRgo9v9W2zYFuav+2Tw5RPylOYz+sk1B/EUz +l1PhIM6c4Nqxk3kKAh2b7g+UDaJjvV5g/PIk2Leod8tWDyLo/fdj0XOTmA1o +efW3lbBXJLDpG2kSo83s34y6B2GJunParZNoY9PQriAR+G9dg1TlJD75tHI/ +Gx+EuBKl3ilxEnaeba9Zfw3izpc2c3/bSRhXc/y4szoI1dQTpgr/TeIK8+Vr +zWuHcLrulEfw5UlIubfzBHEMIdMu027jkUl8e9LxZpvIEBroQz61tAlMFHMu +Oxwg5BHsLvH9E+j9panXJzGEAEGVBzK1RD097OR9e2oIJJX1zzw+TMDpftdb +wctDkHFkWpzXnMAfy573Bx4PQbs2w+NI8ji0T954IeE2hKicpVP9oeNIWzPl +fcxzCEsjsuP67uMwCv9570zQEFynVCu/XRtHZS2/2pWYIbjfPf4+inkcz4VM +vjk1DeFZ0Ng2P+0xbOubVW/gH4Y1W8yK2BcKDiluWDUvGcZU4jdFxwri3imp ++0kVw9hXPLBtyG8Ix7k1r5yvGwazPJ1dRmcIcl/C4w51DkNx21GjERqRF4EH +Ly5MDeO7xtanU1yDsB/QCH/ENQKGp5SXghkJRfdCpQLujKBpxXi3E7Enyg/J +GP61HUGkxT7Wb809qFIZ8bJ1GMHr1MJLN173oGnHvgFNtxHccsu4+HV/D4bL +Cty2vx7BQlp+0Gb1bjCxDbVEVYxA1aKFfCi4E+di9lhk7Rgl+pa6VdyaFhwP +59hXJzAKUy4VnxthzRAK+jMxuGcUcm25P3gONeP3o15TFvFROOeU7E/QbkL6 +FV8jXYVRPL6y8wVHcgO2rVnU+Xt7FKjI/an8Xy2Yfo5wc9mOYrX61Pm9yzVg +MJq6990fxTqWS3diX9SgjhR3RdNlFH+k95iX1lXjUaaeRuyLURjuy7Ajy1aB +/F+FyvniURSuWxdgmFmOFp30tUafCf3puv5sLOUovPiuyr5mFCxhHrFjBmV4 +Ke2gENE2isa08PAXXKVwO2zyL7N7FOw9WyWT7pfAeu+l8lrSKFaYXI/eJhXj +7BYxufmxUcjHvxYyTi+C1Lrtf9ZOj0L6fXtKz64iCP5ZU8w7Owr7k+uyrV4W +YnlqSFrp5yiCfrBb3fcpQGp58LHXm8hwrXRZP5iSh/Bc56VkTjKkQl7J6SIP +nil3ssq3k3HLm0mtmpSLe9HX7Lr5yVhTY5Yh9TAXRmHKR6Z3k5ET7xtRyJ+L +iwGScysiZFiRlhvNq3Mg47ErfetBMhia03Ya93Kw1fbnwdPHyRg7lrv773A2 +Vm9O0C6fIiOcX8px9F02ZvQ7k8zkyZiMvVYlZpSN/svlFo+UyTiifil/fF82 +as6m7gtSI6Of7+fu7d+zkHU6fDJGg4ytj40HKxqyEHXUK67gKhmj739/nv6Y +Bb/99jdbdMlgYbhFBrhn4eGu/4SphmRs54kVTTHLgqmm5LVhEzLsX1fKRl/K +wqVna/z6zcmQ+ej+s+1MFmTzu8q6rMiIvkbZKiGVhX202MVWOzIUyhwP5BzK +ApfAA9HGB2RwHpKtuHIwC38vqerXPCbD+Nyh438OZ2H66Y7Az25klCdOFkWd +zEJP7nRFsScZdR936R1QyULFl6Jveb5k5PpsnfC6loVUfn+xrCAy2kW+rUbY +ZCFMw9Aw7RXhX50Ot45vFjzcD4ckhpPhTA3Rf5mcBduc1eqYSDJScuTbTrZl +QX+q/WdkDBnFMwVnhH9mQYXv46G3iWSIDccpSolkQ1Ld/r/QNDIk1KPPKulk +Q8BN+VVwFhnP1Ob9D/llY0M2d71fPhm7uTWP1VZlY3RHgcTTCjIUIfL2unwO +mi74mDrXkhGSwL1/xT0HeS76YQ+byCgd+q8htC4HAeN//tr0kOFmsm09RT8X +TjytR+8MkNHTe69hX2Iubp6PumU2Sobdjt3rg37kQjZDodVgmoyDvh6pXe/y +MP3YK+LcChkR3zSKrJbyMXPt0O2PTBTk/CIr/j5fAOOFbcy711KQndmkkPqx +ABf3Tp7gZ6XA75nrV0PNQgj7Po/k5KKA8WTtsmhsEcKF7aSDuCmQeXk99OfX +InCU6nVu2kH8v+LsmahUjF9zB9ZtEKCgQmv0nSNRT7Y+XB88BQncVx/+T7AE +E3v+yDDvoUBIprJP1rQEHdot1n9FKRg/cXpf5EgJVOdy1z8Ro8D3fXXWke2l +KH0eGb18kIIJg81ZF9VKIbXHW9bxMAV1MyvGSY6lSCy27fl6hAI167HOvx9K +IaCta3tPigLvjMoN62pK8XIWrPPHKRjufcfvNFYK1udiMdbSFFCj465x/SmF +q9BWuZlTlP9RcKXxVH5dVElkqiSlNElCKir9I9mUIklCkRBSqWQomg0pKpUk +ZU7RnCkJmbYpRJkJIXeenntvKlSk97wf1+8855y9117nnLU/3As/XY66xCiU +wc93vzuPGA+CvXGhaa5qGRyzp/uxTAbhKdMhU39RGQxSDdMOmg2CD+fYWOeC +MtgT+SZjcMsgHO2JdXGfXQYNi1I2uW0jfFVcFN+TKgPTd1c+f7Ek+6fNZ2wS +lUKB3YmAfTsGIfvb9rtLmktBl9oj93nnIKDM5yfyz0uhyMEao2wHoWGBzcyj +gaWwpWzzKRN7wsd6iTfU+lJoWma4/PueQVBqelDmJi4B5+jVX544DcKzbRm6 +UaklwB5Zdnvf/kGwGh3ibTIrgZMH1LYouA2CtdfPIeveYpioUxqtcB8Emz9K +p6O9i+G63rRXgQfJu2V95m+/4B0oJ/5z0zpM6n9b4sp8r3fwcNKIUp/3IBwb +cIhf0VoEuseo2tvHB2Fn4p+A0TVFUNRGP7/Fl+hB57DyieuFYL6xZ9Wo/yBI +uvL2h3YUQHNGM/3lqUEYCTk5R1O5ANiBpVZK5wZBM2jyDu2AfDjZnzfx/sIg +eHdXvomOfgN/t77IOxcyCOzdWjeSHuaB8pz782iXB+FeQv6Zb+m58DD0ZlNc +5CAkpM3Y0quZA7rc8HDL64PQ8/VHC38oE7a88+PnRA+ChO/U4NsWz6FpyeEH +B+8MwoOAC1l9bU/AOcrFbk7cIPxZNKD2ZnsGnNy/vTgkcRBASzayfDQZHv5V +j9r5eBBSJFhVPPlA0D2sajLp2SDErJeVujNsi4VN07/nvxiEm/HDtkZSwdiU +Nr5PLWcQ1D0HTIz+3sW/Zl3agneDkPqeG21s/wydI69/uNY8CI49Lnkfat8h +WxQabNw2CPKye+ZsvVuCAY6n9b91DIL+hy2d3ANleE3rYKJj7yBMMfpgXnCh +AgsajI9qsgZhh0Jq9gfpGpw1/ZtMzZ9BqBc9OL3gTQO2lUVd3f53ELZ2X5dk +Hm/EWJ9lU5v/kXo3+XO4iz+iUoOzZO8UGlgYTGr/GvIJ284OXzogTYPW1cl/ +TyxvwtjlMRKsaTQoME39drKxCZUi3v8VK9KAHjHJO25yC7atdb8YNJP0eYHX +35nubMFY+p8/f2aRvntvtqHtvRacaar3S0qV9HFrljC2L2jFFlHD6RvzaXAk +4g2l6NqKMamHhmcspIHRvesjVGIrzhhL+j5/KQ2Omavm58u2YcsLg4BHy2ik +jzF1u2TShjFOLWJNLRqcf31JcqVfG9pKH/fN1KGB/PbnX1+ltOH0Aimh/koa +eGz0sv9R24ZNXg+PF66mQemmd7zfwjaMnrWRb7yG4H0jLoUz29GmqtO7ah1Z +32NNssaadlQM8OdY/EcD23Grho272rFpkdzhT4Y0eL/Ya8cv73aMbnrCtDOm +wc1J7LK9oWR+sOnBbhMaWBeNTtoT244Kul9ormY02LkiyOj7o3b82BvkzthC +g/mUW9Oq7Ha8eX3GV2/StzvLVB+VL2xH6w2vXEWkT7ecsnDiVmk7ynO29p0i +ffqRwLVVheVk/r1B59///x0I31X/dhmZb36hJ4T07VOX75Wd/47M/zHbaYo9 +DbprA3YefN2Ocum5XddJH1/csc8o4Gk7Ntju2DPdiQZnfhnu3JXQjlH/WO1x +zjQwW3l047Sr7WiVHWY3z5UGiqtviV+dbEdZ1/mtaQdocFnWKGLrfjJfrmDX +Mk8aXDw33ZxlSuYX2za99KJB6vc9SclLyfyjAmu9IzRYeXvBnPOS7ThtbmTj +26M08F9GO3h3sA3raxdbbfShAXd17qax4ja8FlRSX+FLg057+ona2DaUaf/2 +vvEUDfY7Wkp9NSLfX7phvvs0DbZIvvjpLEe+19Os7jpLg0BHDcP4nlaUjt5f +QQumQdH29xWFfq04dXtt8ehVGvTU1T+7H9GCtaPuhsFRNNjerfhI3qIFI5+O +FU6+RQOr6gWXNKRbUGqK/luFWBrMo+aln5BuximYnLM0hQaVOYoDLYyP2Gts +bvn1AQ3ylj5WULb+iDnF1GDSIxroZSy5fP1NIzoXbFJSekaDg9SZWZ6XGvB1 +1tdAiTyynvrueSvV6zFyxTWF0nwaeIew53reqkOXF3pPzxTSoIqmIhX4pxZl +nlz6LCqlgc5F5+/nvrxHt5SlRv11NAgfM6/tq6zGdfM+tiU00OBtxCnOR/Nq +nJYQeNzhE9HjM50jih+rMP/u+5TGNpJ/jmdtGrcSo2b6GlztJHo+ft73TEgl +ut9WadrcTQPN4esNOaqVKHfjyL93/TQY3GS3aoNHBQ7KzEgIGiT1GVK6Ma5A +7o/IIj19Bg0eJrdrKYcj3pzi8YFiEX1/u6CjNVyOnuHTPJ9zacQH7KLfCyrH +DRJ5fw4KaNDh+G5JkWQ5KoQ4310kokEiy+YhI60M6WOTdb98I/Fv/NV72KoM +i869qrn/g9Tzhe3IdckyjB61d7UbocFVj72PoxtL8WDQ+LDCbxrc/xigkJte +iht+PI7+MEaDvvKBUvXrpeQ87lweMUGDkeDQGOXQUmSKhtF0Eh0k7izKzLxS +isU+D5zGJelQc0LHXy6pFGP424YKp9KBqdl9ygpL8ZC3+PqpaXTSd7SEX/xZ +ikbsePXV8nR4fczsQZZhGc7wMi3hK9Lh0eyjkxjRZcimce2fzqSDVOZV7fk/ +y7D0wB3KQ5kOo8/+o+08Wo6x/YYRC+bQ4Uziol0+onI8sp++oEeVDo3nfkh7 +XEY07okqiFOjwyS9vpkyyhWo5Lh2l+0iOtxlLXi1wrcCuR1fOHLqdLj1d6+U +dEsFltldCavTIPnc1KwMN6xEb5vO1yY6dBB/u9svUq9Ck4/BVn906TCldNPb +R+lVOMtKk/F2Nfn+wG6p89rVWL71jPJKA5L/tPS3k6xrMK56URb3PzoYORpM +uHJq8KhZ/dbHRnTQk0qrMrz+HpU3qZ6Zb0oHVb3N4Tlfa/H4upKeaTvosKtC +/3N/6wesaOnMLNpJh0gld+3P8Q04+8S30CO2dHAecsgK8GxEfLJM8/0eOize +9bUkbconnDUn5mSYOx2OuTCHFm5swZLfXnKjQXRQ6oid/k7QjjPuhw48OUuH +73fnXNl2qAMPrUl67XCBDiXatnf1vnbg9OPNjnlhdAj1yruR1t6JB/sMH5+4 +QYdNyZpnn5R8RjlU3MR8SIfYMLlH6/2/oPt+7Rl3M0g+9g5L7Olf8O3oFobZ +Uzr4mDSUadv34QG9c9fTXtHBvbH0WLFeP755xOh0LqDDWOCj9ISeAZQxmXg+ +7R0dwhTfyWTDV3TtnXuxqIToQXNBleTjryg9y0ZdpZIOz4vn6D9eO4j7rxT5 +tjbSQStI6mGOYBBzF7ebhTXRYWbIMWXrOTSUKhMqr26lQ9eewDixGQ1zhtVL +bnbR4efKsjfb42goeeSWtCWNDrvXSjftW0lHJ8nnvSMMOsTsejTbaDcds9Kq +sp6w/88/vVgnkI6O3aP2khQdzrsUsawK6fhqu+fD8hE6PDbxuTOxhoHrdJeY +wG863NikPyTYycByxcEvOEYHJ/tKH21vBra0u86plGBAhZrPzhdJDPzpui+6 +WpYBK0pkFJx+MTDYdK6uuQIDFDZM4R1QZOLUpZ8/1ExnwMmYHU2spUxU5TpI +1SozIEziilPETiaanLS9WL+QATu/7lJpTGZincP0eduXMOD1uj6589lMtP2v +qfDDUgbE9Gxv+FLBRM/xHT8atBgQaaZk0cZk4tVIi2Of1jBAMkVGeosOC1uS +TJzatjFgzVnH/zJyWTgsmDeDfZ8BcXk3r/5dwsW4VE5dSiID0u9ElzGMuLh2 +V36ofQoDNLxWqI7YczEgb6e44hED5rT8tY6O5KLwbFhTciYDZi/2mJgm5CJL +in1zdxUDimbHHLtdzMMrhXnmMu8ZEJvhsmGgnYdLj4aOl9cxQN/YO05SyEOP +j3N9dD8x4Lv7xObihXzsj92xQ7qbASNDYfPWhfLxovlcyfJeBvx5sWbs7n0+ +zh9hFgf2M8Bp9/snKVl83LcvRIdOZ4Ddhcved3v52Lno9bQyIQN64gP5N1cL +MLA1uPLUNwbUTxWFP98iwFmXrc7p/GDAucnngiwcBbibzeDG/2KAMH3RaYlg +AX6Lz31oM8aAlgJ66qzbAry9PdhJaoIB1p6n9qY8FOCnTJX6k5JMmLFuYK9k +lQB93Bih2lOZkJKfmN3XKkC5Gbn/Dcow4cOShqIlNAFuP7X92U5FJjh95vVx +/gqQq6FyYMpMJrTlG80/LEfh1S66SsksJjSVqe2xmkvhe8OLkVqqTLCcJsM3 +06PQS2Bp8nU+E0pq4y87bKRQMnX2yL2FTLBOTY9r3Ephug09y3oJExIu9Lo/ +20WhmUTOIUkNJoxylX24ThQOvr6woFiTxLdk8bnbHhSGHrTs9NdmQtVJv2up +Ryksq6WZD6xiQsS+3t4fZyh0OZs9HqfPBM0jslshhMIx7Qv5O9YxYfOmv2Oj +lylM+mLhM/k/Jtgp7pu/+DqFhreUNd4ZMsHx/Lmhd7coJF7si58xE3xjV/+t +u0PhmW9ZdzWBCYPzvQXW9yhUST+/o9+MCYcti+N2JFD41t5CMs6cCSaatD+1 +SRRe21EUoWbBBL3+6IDHKSSeLdoyT7aT7zN2/VR+QOHqjUlRK62ZcPTJeqv5 +aRROXiunUGDDhDT3vN3FBHfqXLxtspsJDa0xEz8Jfq4unFlnz4TVzyccmwi+ +MM8tbtdeJiwdCz+9nWAbpWaVbicmPJ/4dekoWX+JrGmi+34maKy5nqOfSuHP +Sa/n81yZUBCWAU+SKaz/veRBgDsTZOvGLtQlUpg8FLv4jyep78qot8nxFPry +JDPCDzFBpTxm8zKS72Za4DI5byY4JD+7eCSWwtk9rGd3jzFhlW5r+aHbFHJb +9uqonWDC6bvxB5fepLCkvi7zsR8TygvWVWdcozC6YsPqlSeZsEKpVp9/hcJ1 +ufPWmZxhwiRP0xNdFymUfn6joPYcE9y9D5WHn6WwN218w66LTKjwq146OZDC +S7cHNrlfYsI9y/uFkccodLi6q4J7mQmRP17LxB6iUCu0YnNAJOFDJi/3ojuF +Tb7pFuE3mBAY/CJ2bA+F82wO7358jwlX5y/Vp4BC4dbP7boJTPBcHrkZjCis +2GS5920SE5hWD7Ii11F4eKXO/to0Jiy8r35oTIvCN/IiL+4LJvSc1azNn0mh +dWPQWd1yMj935ZUehgAXVbP/5FeQ+sYoalgOCPB7sWPwpmomxBkXHanuFmDi +S8Nwm3omfEwY6aF/EiD7+t8b/m1MKHrleKurSIChlhFp+WwmaK12MqXuCLDN +zdtFj8eEQ+VjymduCVAjaIdqpoAJGxQNe2ddF2DDo5l3M74xYc8yu4+XwwSo +PJYaGfuHCc7zGV/N/AV4eOalLYp/yXm04re5+wjw3XIviah/TDgbGbrxrrcA +3Rx0zl+awoL+hu/P1noI8HlWwQl/RRZs5W1tPGEvwD/ViTrUDBYMCo/OWGsr +wJ29FzlHZrHAuc3da/pOkt/ULR4H5rKgbcvqiekWAjRfoLnwyzwWuA9YfTQw +F2D82mlf9i5gwZipb3GQmQCN3ZsdbNRZMCVT/o2FsQCjT+fNbNBgQVd5ZPUX +QwHSbt5r2rqcBSmUskT0fwJcl3H2RqU2C+Y9uXP3gIEAI9/tt9yky4KmqbeK +dq8VYHezidS7VSxYdVDu3SF9Aa5gL6lap8+CWX2rRCnkvgwZnxKau5YF8cs/ +4q+VAmxR4m7UXc8CQQI/47yuANW1G38928AC9dTVCzVWCDAIst8u3ciCboEB +jmgLsH7PnZNpm1iworRl6U8tAc7zCVw935QFigc2/lxAsE+4I3V/Mwt0cg0Y +QcsFiAlGL5S2sqByQCHrr6YAlXIWHI62IOstSlApJNjrvcRSWSsWKPCVqQyC +C74wvkZYs8Ds+FSJWoKnfa9NmbSLBQYjw9qLyHouMi/3Be9mwWwDna2vCc5e +eEvltz0Lto3ZrA4h+0sY+LcH7mWB+YPpdVdJvPY77GO+ObGA8+Exv1lHgE89 +1u/02c8Cw5a9p51Ivr/OqMpyXVkgf2l489JVArSKHq896M4C07RtGmv0BJj6 ++Ovlr54sSFD24USuIe9HcZXp/kMsOK+wZfdSwv/m1id/u46wgLaqTG3aBgHG +ca4V2x1jwdrFBr8NNwqQ8/f4mSYfFqS9wGuFJgK8qbNm6H0ACz5afBl/sE2A +A6azs80CWVB0aLxdbocA9R1/HSs7zYKzGmJo3CXAKye+LDc8xwK0Vbw64CDA +rsvlzPwLLDiwf2/3NmcBaic9eqQXwoI186u3S7kL8GLuFbfMMBZU5eV3zTss +wCX9Vt0ZESw4Grg+3eaUAKOqNubsucaCD71xSQoXiF6f6UZK32DBjL0m/usv +C7DqpOK64zEs8DSssK+LE6CO0z/ZBXeJPjZdyV/9QIB3N32jNd0j+RdWxk1+ +Tuon03Z7TTILJJZZ6rJLBfhRWHWYmcoCy19y4cN1AjRof7Pp/kMWHH6afMen +XYBTH9wT/H5C8t2wMuamgJyvtfssKnPJ95+NTnospnCGqtXCU2+I3jO3PApe +ReG5CaNhjQIWONn2p30zptDqg1rGtRJSX9ub4k/OFArcBid21bIgclvPg3Fy +X6+KOlIw8IUF96c8f6uuLsT7fk63YgZYUHxT/vKLtUL857DdazONBeN1RzYa +bhViy6IVSk/ZLHj+inq3z1uIAW9FJ04MsaDAM3UTK0uIvUlfzRf9ZIHdldaC +P+VC3BzWMr91hAUyNasCGM1CVNqR92HdOAtUvQ8KlYaEmD8YtGx8Kht2XN7z +RUtPhGq1h8ezprEh+dox3zkgwohXju0H5NnAT1ArT98pwr2nDS9Vz2TD4Lns +L0FHRVi+X8cpSJkNBmmey1+fFqGm2fzVy+ewYf23vLX+l0U4Kve3L0qNDZRp +4QnPZBG6DwnfGC9iw83M57einoqwvmsgSrSEDcfB33nxaxHqlTZ7PNRgQ/kT +2uDCEhEmPKrYYLecDZ6cC36XakQocfX19Ck6bLhi+jVxyycRHvVJZ7/VZcOv +FQuNPTpF2Lb7btmR1WxIGGQHd/WJ0Oi/K3Gqa9iQmhTemcYQYZen6vrUdWzQ +MnEQ7eWJ8FR09ufF/7HB3v2uwSmRCGcUbzn32JAN5pmL73z/LsJMVvc8LWM2 +aMZwtNtHRGg507f0lQmb3P8OJ2b9ESHLWNJttRkbDlk+U8wbF2G4d8K/vC1s +sNm+UCZ7QoQL41Y+Wr+NDZOHx5OnSoixGKs2F1uyIX7T0T0lBDsKHJmbdrAh +bPGSaR8J/qkijKjcyQYabWrXBoJjNocv32rLBpWjl5dN/idCXd85H+rt2CDW +K3+l9VeEHxIzj1nvYUOe08sjWSSew+/N5FscyX4h3PQ7oyKcPNSVZe/Mhp/q +wUNdP0T4QM1n12cXNuSG7tcPFYtwo+WkIecDbKgtrrl+ky/C7lP3Ywc8SH3S +LhybxBJhYNqKdZ5ebLg39VPU4ADhp7Gik3WYDcamJ7i63SLMGtlz5uhRNsiL +dGp5LSJk7wwr9vdlw5pt9a7VFYSPc7NdfvqzYcrwBy6nUISLnrz8e+YUG6q/ +n4y9mS1Cp/EO09CzpJ4Zlte8k0TY+FK77lY4G66ZNk4f9RGhd1e598wINmSa +KXCeuotwymQH2XtX2WBdNVom4SBCk30hO1NusuHkL15ug6EIc6Xb21/eZ4O/ +T9s978kijPO6OFj3kg2btp9rir8lRL2YmeE7stgwNCEy/RYixE8lT5c257Ah +PLV8jou/EKfOaj3clc+GkbEF867ZC/Fs5TIhs5zEyx5+QZ8vRGVhcbR3JRve +77/NvaooxNdzbfWoajasdFxUFDBJiHy/86d+1LNh1fOnz7S4xC8ubP49qZ0N +cQFuZ3PeUaioevJtSScbdOZNjVyWTWHlrNkBQd1sCOGZpMzNoFBz2n4ut58N +6ZtFD69GE/8qOZGRPsiGJ86N5+QiKIyaeHjAhUHOy5j2CjXit8Q/2F3NXKLH +lRER4uPEf4uux14XEL3kB/UVeBF/xdO12SJiQ890+0PKbhROZTZP+/uNDT5z +h7ynET9eNHDyfcEPNhS8FFXdt6PwWM/sS/4jpL5rYmilOylc0FFkrPObDfsv +CN5f2E5hS9P+X4wxNjz+6DWlnfj98A8Tb1In2KAoFfy+cjPxgzWP/BwnceCW +8bfabaYUcsrNV8ycwgF3DQ1XdxPi199x2A1TOZCvwQqU30T8V35U+pVpHKgb +9r9nSe7LieyVbibyHDix7hN9JsG5L1pUfylyQGqd9+JDBHs+PtX5eiYHamZN +zjch82enqdw5rsyBQdqX50lk/frEd9bL5nCA76rzJpDsfz7ORearKgei33xY +W0/i0739rzpBjQOnd682jiHxD1xPD7VbxIGfjfdj6ywpjLmydaO8Oge+Xj9c +4G1N4ZZQ7sh7DQ5oNtYzT9hSOHLuRl7ocg58Px60oNWB+PnAVb6GOhxQefB8 ++c19FDr7tWr/0OXA41eb4xMI3wrHAlmZqzlAvZZvEx+k8OSBYpfFBhxorHM7 +f9CPwo1W23ZIm3JAsS38cxLx1yJz3tTKzRywj3mmZUT8+EO4WXV+Kweka2/F +Coh/n2LQZiiy4oDe4u0fjhC9NC1y0+rcQ/iw15T+V0Zh2LxJzGgnDkjkbj/k +XUPh2tmP0yz3c8Bfccwts4HCBFm+Sqk7B4oTjqx41UXeJ6lbbUEHOaQfKZJz +7qPw77/V0asPk/Gd7FeNNML3cJBUxnEOHDtpKkMXUKj8bW6liy8H1mx4yrn4 +jcI6fslFlQAOnJV+1lH7k/DNctvQcooDmx71PCn5RfgenPTz+mkOvNcwi3Qc +J3z3Ps7Zco4DTTf+jt7/R/jutDj+9wIHPoTndp2eTN6rFr5mYQgHxp/H7fs5 +RYjDDbfo/pc4MD1y62wFaSH2yXV6j1/mwNzAmjNPZIRYZa0mvhrJgUxtq1b6 +NCG+uHUwaNZ1DhSsG5SrkRViTNPLsQc3OHA4/PJ+Szkhnp7+/ZJONMEKO038 +CHa1NZQpiOFA61/PixsINr8TFm12lwN0h7zlj8l8nbY65U/3OMDxDkjOI+vP +mDU92SmBA0vSjl/wIvuP2u9dwkziQNmYypviqUIciEt95pfKgRbLwMACEn9N +J3PlWBoHSsuL1+8j+b1U0c2PTOeAhmlL/mOS/x3HU0ZKTzig4HVbkET4OZtQ +XJH6jJyH7L45Jr8pdOuZZKH9ksQTdjM/ZphC83nbP+VncqD5yPyz94YoXLE/ +xt40h/CZZmS3S0jhr76F7o755LydXDhHzCB8LzjMphdwoOTvP/aXAdLPu2X5 ++L7jQNdY3p0bPRTGDm48F1HOgYTTkiu3NJH9l1z+N6OSAzbRLo729RQe8GyI +SKnmQNGVWR/WV5F6Mp1i39RzQD7azfr6WwprOUGvaG0c0Cm/N3WA9MuZWmX6 +Jzo5oPwdimXiKLx7dErRr89E3+HBkrqkH3cXxNZM7yd8LVEO9gul8I8op38T +hwNGV0pn+pL7anD16MEPPA7MCLh4lOZK9OVvwnegiN69vm0+6Uhh3PePI8eH +OJAs93H9XyvSf4/wpieNcUC278ySZaTfU/lP//6yCQ7IyPVafyd+bPzMWbXX +ElzgpA/b/9GmkFGE6caSXHCIt1EwXUZhw++p2vVSXMDFrnNriZ/LNbLJsZfh +wkRz4ZdoNQrjL9wz+CrLBZV+v8spcykMKe0rOabAhX8zHv37pkyh19+lm0em +c2EsZL1kNOknrUyO119S4sLwHNbkIEUK9UPzbBRmc2HFsMu6Z3IUzq343ZEw +hwvPZfNuLZtG7jsJs/0a87jwoHq85ttUCplm12g5alwI7ltjO02Kwsbw5iMb +F3FhQdqGQ36SFOZVq4hql3Bh62mdP+qTyXme4hZop8GF26kD75dOIusdnGPQ +qskF0cJJUoESJL7qluFd2lxIW8oABYIb1KMKmlZwweeYaYTonwD1wrec2bmK +C/sdV2apkPH7tPH/Pupx4eKWUOcrBI+bFvyyWsuFaFnPcQOyvudDv3cfDLhg +EaXaok32r/+ndd5yAxeyHwnpriS+VQfoRnVGXLg/D5RbppB6lSePbd3EBdWa +6jkhJL8/C/aU1gAX8uicM4dkiB6CFYO3bObC5D92CZdliZ766jZVmXOB23Gr +qFOe6M340oSpBRfqY+tGnKZTOPrnR6iJNRd23EjIZRP+XZyzTMtsuJAgZ9LH +n0Nh1bvDk4x3k/1DNt6cNZ/C6LM94YZ7udDiWjVes4S8ryPlEevcuSCh/J+x +hR6Fe4eu39AJ5IK8js+ZChsKS223WL84zYWXvxqZAeQ9VM8dl9c6x4VA38xk +pb3kfvb1i14WwoVM+fvr5hB9OjRp7XocxoXI7Odqp90pLF5Jn770MuFLyeZA +MbnvIyiHO4uvkfk/fTr5Rynk71C0S4si+ftL+bX7UGj7qk5p4S0unHRdvjaJ +vAcFspfaU24T/amFt206SaHaMaO4+bFcWKtUvKYs8P/v7Q+HpDiS75UUvzln +KORqZc1WjSfrNy/q23GOwnzOoniVFC7IiIyfmwVTOM+ix/HeAy7sOv20bjI5 +b2FPY+cqP+LCn8aO+6lhFLKlrHtiM8h6KSuvKIWT9/iQVNLMp6QeSvXrPS8T +vdWUO8c854KdK+/WrStEvxpn509/xQVHT8uH94gfCbms33criwtJ+XNLLkQS +/dL5KfK5XHC37Hc3u0rOw+bHrjfyyPrHJS25BOc+cl0o+5YLDY3b9p0k753K +pDlfrxVyITH0axaN4IvuLWnSxVwYN7pwa8N1Cul43T2ylAvXpCR9zhFsuWjL +EinkQtPvVZynBGeHjNMuV3LhbDWvuprgWQNv0yfXcMEUIwRtBEfLBwcX1nLh +m8Wuw58Jlt1o7uTzgej7+IoD7QRHHpVbu+QjF3SYi6QaCZ6c0KbQ1cQF3+/S +z6oIDqlN5Ea1ku8Fq7PLCf7z070aOrgQcKM84f/7nV6q9eBnFxdSXId+dBL8 +fbf47IseLtR+0N/7h2DfsAJ7tz4upN+U2WcQReqfHbxq1lculN8djr1B8OF+ +82n1NKJHzzV3Jt2gkCYnz7zIJPXbfqg1mWAXo/ZyfQ4XDrB2lLjdJH7QOymR +zSP8Hj6YZEPuU4d4j8Bkigs3Te/F+xG/2PJea5etmOw/Ksp7T/yD9U+xttR3 +LhwsPF7mcIecV/XCKcU/ueDh32W3+C55T3aHfPUd5YKzfmP7CuIvMHRr8dI/ +XKhyHzhwPp5Co2z5e93j5L7z+9asSO73gr52v1v/uNAakZ8rSKFwjVyy1ebJ +PBCF+G+a9ZDUw9Bz2egUHuwPGXe+SvyJjre2RKY0D57Ok7m7/RmFT+9/63WX +5UHo5FfT978i5+t94dvZCjxwKd4WX5pDYeqPkJiG6Tzw7iy/5ptP9Ka+7Xio +Eg8S6uS7/Yl/jrNV2LZuNg9kl66Tqy6n8GZW8ljqPB7Ra8s/O+JvZPo8u+wW +8EDCKO/OrRYKr8jqvJZezIPEt3OezPxM4YUjRYcDlvHg/lL/Pj6T+N0lna3m +ejwIe/zW5oykENm7UjJ/r+FBy4XH/+4TP+AZcvBqtgEPzGvfWvXPEuK+L0PG +czfyoMftYF21hhAt7yk+F2zlQTk0VuhakPe+ujP8oSUPfr3/1FK0S4im31Nc +9+zgwfNgZ8ZKJyH+t2vFLLTlwU3Lh6uySf+eF/xdeMqeB4fvZ3g8Jf3Hqsx3 +9Vp7eXBCITHJ46yQ9AOWIbH7eWAlt3z570ghpv83fZ+FGw+cPV5vqCT9zMLD +XWvH3XlwXNW4f2mcEJPiUhVfH+SBTNKuDpUkIapUe/EOHeZByfoZtNtpQowd +WlEz7ygPClcHt195LETFxT8eNB/nwecZTXcEz4UYZVN87oovD8JV2EuKM4Uo +FXzJwTCA5D+zM4+dI8T8Ieo3niL1WSHptzlPiF6HndK2neZBSqax3KR80h99 +qTb/dJbkN7ZBdf5bwseu1Xz7Czx47fH20HWCA2uSbvcG8+Dx8an/zAnWMJxq +4BHGgwObYjZakPkdWQG9nHAeTHFZXHGdrH9FvT/UN4IHSWeXRk7NFeK6eMtl +w1cJH59f0wpJfEy5/IYLUTyomXTiagKJPy5skf/kW4TPm9qxGRnEzw1Hzb5+ +mwfstgPXOlKF+PPoSPH0WB6E5Ll5LI8X4uMBD/f7cTxY47sxKuG2EB3sP0kt +iOdB06zzfI2rQpxSv+FVRiLhm3OU+yGY5G/82FYnhQdut/RPRJwi+b+ePpL7 +gAf2jEjuHlJPZc0Lyf894sHDXEUHIxeSfxLbtDyDB9EJ7uvXED0ETrdjmz/l +gXj01ZNNZiT/K2U3Gp/zoOrBn+2ua4R4+URcV3cWDw5ld78dmCnENfR/Fw7k +8mChRMRbcwkh0vceX8LO40FDoppLHfF7m003+/wo5IHq353X9WvJ/TXr2yTF +Kh4Yxwc8VD9B7u+r+5/F1fDAjtUz8J30K57jtdbz63gQGD3nhTzpp6pYqfFa +H3ngf8yTv4m8x+FFO1Zu6eKBerHZw6REAU5ye+Z0ls8Dp3OFTQ0v+JjbpjQx +QfHA58GDS5I3+OhuEZIRIeaBxuxeNPLhY4XeHlHsTx7E/SiR6lvFxzBJyStZ +Ezz4nl/D9Svgod5ZX+11k/gw1/qeYEkiDwepnqZiST7pP61emF3koWlXrmq9 +DB/OFOz+KGHOQ4kXbjl0JT6s8+m7Le7lYi312TdtNh8ikg23hFVw8abe7lUu +c/nQ4C4RLPeMi3OKtmR1LuCD6ferN6zOcLFvrNQndjEf1B8ucFH14GI6rNfd +tZQPfZhzb641F1fVab2q1+JDd/nJh13LuPhTNv1YxAo+hNC+vH2pzMVim/k6 +m1fxQStbPrNnChfDYuN4E3p8YLZkqfiMcHBrl8KLkrV8iPmp9vIoj4Oy8656 +n13PB5VtvgY9/RxscZXQMjDkQ03WstSKdg7ef3SOM7SRD557M7s0Gjnowvr+ +NNuED6e9IpnTajioru1z+LgZH55KW7efLOcg14e1TMucD2F23oUexRzMznVj +MbfxYUdk2qvPhRw89fPz40fb+SAod23pKODghg27vdys+RCp1bTDiYxPXGhY +On8XH/Q0i63c33GwBrcwPu/mQ5fi6sn8Ug5GSZalxznw4Y8X9/VQJQdtLdZ7 +7nbkw8ucC89O1nNQ5UbOEkVnPgwc2Lz5SAsH+5q0aA0ufCgN+jta38PBdKX0 +h1cP8MGAs9I5hslB773z3c09+VA/X03t7TcOrkqKWzTpEB8sda6prprg4M9+ +ha9lR/ggzR5zHZLn4rslVx+cP8YH7upC3Z9qXAw5JOH23wk+BPqvmrZiFRfN +X5xb8NOPDyMJShXXTbnYoueTciKIDzNdy+KjvLl4P5C1X+csqf8RrbkzQ7jo +UuQ2n3OeD4WiyxbX4rjEKexOcg/jQ+qrrxFyNVzMvtywb8FlPiiHXvw62sfF +wLotqr0RfGiuYMTdG+HiP5v1CfY3+DDPO7bk0QoeqrjNv7/tPh9iI/4+mpvM +w75HcXskE/kww5u2NLuQh+kshdkVyXygO6lXHO3g4coTEnGGj4ieOidK5RX5 +aH6RdUc3kw9v9F1G54fxUbbCbTcvmw+v90i4jyfzsUWye8bT13yQmTW5+nwh +H/ffaLi9qJAPyyerz5gl5OPJpJxbSlV8cHmiXDN7twALx5OuVtXwwcZLbX7/ +EQGOu0VeOllH9Ol8prYnWIBXl7oGtX0k+3+vu2HxTIAfIyz9wpv54ODYbvm4 +WIBK3LVH17TxoX3e3qcKnwSYkinrGvuZD1bP7/1liARIUxzZu7mXD7WH0/aY +TQhQM4Bm+72P6NU6Vf4m8ePH2z9apX8l/NH+dpapEj9nUGRuR+eD97YIiVbS +Tw3HZ5hMZvHBWiU5qIL4a6M/0RvyOHw4YKNTdNWI+E+X82s8+STegLkM9S2k +Hy0/pKsk5MPmo/ueRZN+TnbJbs0qMR9sZz3dXm9L/PFl48Unv/NhfcaXtE97 +KLzHWj5PfZgPUW6yiqn7KOy1mKXcNkrOj4fRZQMXChe9nFAI/8OHRHth0H3i +z73k+dJr/vLBeK7XIBL8wrdzEv0fH5zTcozzyPeiloqxO5MFMCgfF+brTOHa +tZnDZlICKPLdqjpC/P7Ze/HiIWkBfFgrxbEi/UD5aDjvkawAnoQ/2+BnTaGk +sy9jt4IAFp2Urju0lfjT0n39k2YIIGDcP1d/E/GfC7d+fq0kgBB76cCutRS2 +h+m1eswWQMHESqEj6UfnMuY3zpwrgHnMPzbFCyh03Sr9vnKeALQUChdNJv1k ++rPv5QELSDwPTq1bR/orzrSBoiWLBVA8tyhzz08B6vp8yGtVF8DU6zai40wB +BjTlZ15aJoBQgf6ji+0CLNB7+FRfSwDB59Nf3aoUoNnw6aQ7KwVw7+DSSx+S +BBjp6BlnpieArp0qqydFEr282xk9tEYAJlTxDzt/Ae4N0QjfvUEALiP3ot03 +C/CYdNvRmVsE4GXS6inu42PO0bKDlVsFkDOD1llZycefjc9dAywFcOfJ9mre +Ez6GxoTubt0pgAVSJ+Y5k/chTnWl4R0nAby0qLmb/p2HZSuuycz0JfmsH1e3 +pLi4vmPOp1h/ASyOaln98iMXcy8+u6N8SgBSqy6rizPJ/f2pdt7cswL4aLvL +Bk5w8Zqf1MpF4YS/4X3J9UIO2r0J373yvgA0xr+VDP9kY+N+JZWcBAEkK2+Q +GOtio/mU9F69ZAFEPS867viOjf/tqTy47qEAEjYqrtALZaPa6L+gjS8FYHWI +zZ0xg433024blWUKYGZAXnfoMAunWy76Z5IjgPg6KWbQFxZOTjS5tjlfAE8/ +BlbKvmAhxyg4aXu5AJTDXDVtdrDQnSF/oLFCAENnbtr5GrCw90bK0p3VAkip +f1O/djELP/aVZNrWC2B+VolnwSgTt0XsCGhrEICttbzDaSYTceUXA4dPAjjz +e8pSWisT80L+lDu2CcDz0/nmwmwmrlgedbmnQwCRDuez1B8w8XGzquX+zwIY +ib12aH00E+MXG7a69ZHxly9bbP2ZOOND/b3BAcL/9WhfO08mRgU4OXvSBLCn +e7T4uwMTL1adYRxiC+DHct75fxuZOHxM+jmHKwD7QdprTz0m+s6K9zkqEIDj +8a1L7JYx0cOrYNjnmwDk96e8KJvBxF75bcWi70QvD4Ju60oz0eFtZ4j/sAAy +mLq7FCYYuG3qsHTgHwEc3+wjLSVkYEX2lY/D4wJYMyK0lWMx0NBR+c6Zf0QP +YS/VPfsZqPt87bwLUyjQ1Lqm1NfEwJlWJ3XDFSlQtq8Np94w8GHldDmjmRTs +6tZ37M5koJ5hFm9oFgWqLrZ9VU8YaKPFfeqhSkHj9ZdmrvEM7E+LiFBVo4B3 +a8aXodsM9Jmz1Kt1IQUb1MKLba4xMGqq2xIzDQpMGnbe1z3LQNWQsX+/NClo +CAj8d9ePgc+HEwZytSlgvyvIjDnMwDpme/Li1RQ8PnswY749A/e6BJzv1qfg +2miMbZwlA9ntivti1lFABU7RPbOJgVOqt6tIGFGQ+r1F12kZA+8acX4WGlPw +JbygbdtcBqrnXWn3AwoGDbe8D5NloOkjjPlqTsG2/t7FVRQdm+e6+sVbULCa +5zla2UdHt5g/O3dZUXDx7mTZiUY6BocayOEuCnR2flut9ZyO8qNtvNN2FOTM +206bc4+OKb7+9av2kPwjT82yuETHYtdXEQ+cKZBx1YwJdKTjyMYlEiGHKBjN +W1VTPUbDiDflAwbeFBTnQIgbg4bKK1zKhMco+F2xpeRsAw3Xzos/7+pPQZm/ +TbF7PA39f8kPG1+goNZ5cV3GShr+83vZ/jOYgt7EI5WflWgYzbHIywyjYLnF +WR3ZX4OY2RXupxZJQct+xdL8qkHk5f/ijcVQ8Kks8cja/YN4Vvd+/Zu7FOj3 +6/Yd3TyIMo/XPjt+n4J1ARsfrtMZRM27vl5fkimYt/xLVeLoV3wrK7/l7gMK +9g2+VTvT+BXNw18s2fHo//9Lw3Gf9OgregYwB4qfUnA5K/Dmrd1fcYh7qezk +Cwq2RLjYVul+xTD3RSk6mRQce5nkME32K87oLj1Pz6ag/ZNzQhBvANN2Oe9L +ek3BJWsNozmNA8Q/jv5nl0/4uRtjN5Y9gOUm91RkCym4dcWG9NMDuLNgzXDl +OwpmTlQdywkewL6VLe3nSole8mJ8rnuT9QQzgyWRgnc6sTKcvQPo+cJe81Yl +BSuzY513WAyg5pF7zSo1FPT/Os3NNRxAnsbnsw9rKZBboXlr+qoBzKTPVdf5 +QMH6pu/nXTQG0P+hc+ObRgpEV8fMotQGcK1bSuCmJgq0lKN7r6kM4Mj8gQV1 +LRQYLr/zZqvSABb3LKqzbSf1yflR82r6AAbHe/j3dlKgnq76NENxAE33ZKh6 +dVPQJb3h+SwyPmUWq0rYS/iMvfHz64wBrGvR9DnTT0Glp002f9YARkV7z540 +SME3zR1zlecOoI31y/IoOgVe5qwyowUDOFOWOqLMosDS7EjaxqUD2FG3cuYD +Djl/vp4e37UHMCHCr3g5n9T/JTPEUH8AF076Ib9RTIH5inVaA6YDSC9fV1Az +RAFjkFdBWQ7gk4unD9j8pKA6cXCzyHYAdX/9fu3xmwK7RUKWtvsAit9u3C8Y +o0D+aXSW8pEBzDsVPCVoggLFHN/lDicG8LQ+Zk1ICGG+5Y2TVScH0FAs4XhN +UghNa1o7jM4M4HjmZgmlqULQrH88mnh+ACuOXXmRLCMEpV2qS8svDuBlrVq7 +ZXJCULfxO3OV1HcbW3o8W0EIlkMnNbrJ+LTH259smCGEol6HB3Fk/kePGzZV +SkJYn5XYnHF6AGMWfRrdMVsIvVZoIfYfQPt+xUedc4SgoWV0+ODRAVRJtrU6 +ME8IbasDLokPDGCvU+wPrhqJJ/LgtEiHAUxV6Ug5uYh8P/H8iRrRi3vH7G3j +S4SweNsVm8z/BlAj1lEcoSEEm1c17vqaA8jZlZgwfbkQfjYbZ74i9X+p8MUs +UVsIdlXJFxf+7UffRjWBuq4Qpl0NSYlh9aP+dbe4zFVCCN+ZaCf/sR9/bnu4 +ab2+EPqW0JzScvvxQtXSmO3rSfymOQvtA/vRJOyQYfsGIRhP1hCl2ffjZJNn +dJeNQlioXDy0X78fr73TMfA3FULLLfuvSdw+vJ+r33vfSgjDC0+JZln1Ye4D +0GC6CaH5aM7O4r+9+OP8D2kPDyH41063HenqxfWOzwT9B4XQpVByZdXrXiyZ +Pv3NZ28heOx28l51tBcnBFX3HY4T/pnhnSYWvWhaf/p86wkhcIp+HOzT7MXa +sAGzxpNCWHLlZp+BoAdlXGOXWQYJ4QNt459lLT24w3DbtPdnhJDzgqYnV9iD +0bP/UGbnSfwMNffRtB5sGcpqKb9I9DJ7Z+OvqB6c1eSRvzGU8FfrPqx6tgf3 +vpydUHRJCKWbNC57HOnBhMgPFwyuCKGcd1ijzakHv3gGH8iLFMJ/TzdfOWbd +gwtBf8vq60L4rFhjumxzD7rPZ2lm3hBCoJ4m/5dhD2aMJshqR5N6O9VO617b +Q94Ta9GTGCGsucLWe726B7VyJdrU7wrhof626X4re/D4zfy3afeIHiZH3fml +24PZ3t6JaglC8FPbL62/qge/masFJyYJYWDXnN2/9Hpw7ZIWd5VUITQofFFe +YdCDp/9eNr+bJoRImwd/0o16sKjnP60Z6UK48EhBvN6sB8feCuRuPRZCnvw7 +nxLLHjSJTRNPeyaERN2ljZN392CYr3175AshvHfQvdu/rwenLi9JCssWQpJM +z71rPj24XdIv5G+uEERi5Rk/g3rw5ld1z/NvhBAsm/GfTmgPNpV0bR19K4Sw +RKvpv6724MyEKO3AIpIvv0dpRUwPOgSaKAwVC+GWy7kHd+J78L7t928nysh5 +bYvdM5bagz26Tzv4KASX8yevGWb0oNo056IjVUJQDayOX/SsBw+wFFKYNSS/ +bbJ7Lr/owfTKylCPOqI/c9MDm172IDM16ODAByEMWRSc1ybjy89rW+z/KAQv +g2MMzac9eGxvv053kxDif09KnPuoBzPX3FHc0yoEevazDFZiD4oVt35vbRfC +hkaF3edIvGsEvzptuoh+14u9q6/0YFBd5rvGbsLfIl+notOE3wz3VMsvQjDR +f2+/+3AP/glVvvS+XwgnrFtP3LTvwU0u9V6bB4WQslzxiY8J4XfDRUukC6Gx +/y3rt2YPVinr6RqzhHA7oUHCTKEHLT/F/zDgk3rTaH8t2rsx6sWOz3mUEObt +WCBv+KYbP0X8K14tFsI2iZnCrXe60c7kSLj2TyEcumTcu8WyG11z1s9cMCGE +B+4ZehFPP2OB8y/FFgkRGO9XpczPfkbFqcXylyVFMOkXvSV0+2escNkkw5MR +wewLvXeCBV04V+afVIqcCMqu5rxoLO3CgDcVkrsURTBHtLnlRXQXqsua/8uf +JYJLV1rr5xt04fm3Un+PqIhAIGLd1ZHtwnb3uj/zVEUwPj2RXzbYibry1399 +mi+CDP0V1jLvOvFKodVI2EIR3HyV/Xz93U7s85T/uXaJCLL2q7T5+XWigWLT +EHupCPSyBifad3Yi22u30FpbRPg92HR+ZieazJgl+LdCBL6nJaJ6RjowvqSD +m7eK7Lc1eW7yQAd+O3yffUhfBJ/6QzcU13egpZITc+46ETgtKBJrv+3Ah2Wq +9Mb1IhixTH/bmdGBv72/fA0xFIGUyKfwUVwH2imn9usbk3H25v+OX+3Al+j2 +hWkigpda96SmXezAyccX98SbET6jYmZZn+zA/Sr0LitzEThsPbFA4lgH5ldm +dPzdJgKzQtYxyrMD5U8casvdLgIZs+qMDpcO9Jq7vOWgtQgCXZQLzjl2YFk1 +95PKLhJfsEVjkl0H+s7z+XDRQQQXf7f3Wm3vwNr3K+tWO4qg+9XDUCfzDlwU +IK6h7xPB91HvRJpJB55Ve111z0UEnj3sX682dGBL3ckKywMi0n/spV/S70Ct +U+vKxzxEkGCQPXWtdgdeWjhSku0lAmsJtRP3FnVg74fCdx5HRJB99ZZlpHIH +rgk6V6h8TARhz/Xe8qU7MGrxxrd1PqQeZ8b35f5uR0bjeN55P7L/yD3+J147 +Gp8pz115UgRdHvqRW7rbMU49LHswkNQnJODbvPftKPxklnn3DBmvLHx0JLcd +t52TfLntPMFHezK3JbXjaHPkk8xQEfiHKux0O9aOthcsMw6EE36v57/+a9uO +zzVlHylFiOBxScujsfXt6Bx8K+VslAjCf7xzWDW5HfO0diWtuCWCuc1F78c5 +bSjXMSNh4LYIBu9KHHduasNSnbi75vdEcP+8hrXCgzZU7tpzZzReBFah1een +XGvDE5fm3H6ZJIKUjXstG0+1Ya1uz03XVBHo7h/AZx5tuLA7KWrGQ5Jvva9j +9+42PH3Z5Vp1OuEr5KR+rHkbNq9aGHn6CeHr8ITfP8M21Or9eln7uQia1tWk +b1rThmERjy71vST6iN/l5LKyDRXOSFt5ZIkg/+tvtyMr2jDJ+4QSO4foK9L8 +BodgTef23mN5ZL3EgL3Vq9rwzQ7DDHG+CLjP9bvb17ah6aa044GFRO8cuMU0 +asOPq6TW/X5H+JrmbvdmSxvuW3x8PLhUBLFHOPe/7WxD9szWmskogiIVuw+w +rw1PSv5362ol0dPdp//+O9SG/36m7JGvEYH7kcQ+r4A2vMmevPBOLcGikNcW +wW04t9ubPfuDCHSEmn1OhK8nH5qykxoJ31rlbtNi23BNybozi5pE0Db3Q3ZN +YhuWZybB4xYR8L03Fn4nfO94ICGj3S6CYyOpMn8etmH37cMtWZ0Eyy3T35zW +hl6XPias6Sb5xkUbrCfzh06u8SjsJXrd90jdIroNQ7wStI37RVAT9l+2iMQj +u3diqOIr0e9SVv/rI20Yb+FVvJUuAsWCm8+X7mhDDcOG8AamCLaV3L3KWd6G +uTp6O3ZxRPCwUSx487cVN6ndn9XBI/mH/4hy+NiKDQrjX5woch5/PDydebcV +9/7zeNwvEoHlNqfhQvtWZHyr8/EcEkGSQEIhWr4V/ekrDTg/yPpndhZ4lLfg +ePvdv8dHCHY8mxV+tAVVCg9EB42JIMbssusf52bMeP5+75+/pF4GWy8q3m5C +vaQVi0IlxHDl8fj8i8WfcHvwaM41KTFY1j52OjXRiF2+rmcVZMSQsKGncmRe +I3q6V5vGypLx9LG+kvUNeHHL7dbk6WJY99TroW9QPU4zGE5crCQGGXVlsWFq +Hd7X3O/5RFkM3ep8hvhTLarPrdTRmSOGmPY4joRsLeZMW/4jW1UMmZt00hvt +36Px2M2StWpiiHuz1TY2qwbrqe+XixaK4VvktRn+qjW4Z8DJetMSMXhNv+hq +k1iN9OZy5aqlYvAPecnvXVWNfpUa/ds0xaAl83ZByJcqHM+LetKoJQZzubmu +dg+r8NrjbydsV4hhRpCSr1pIFc6+v3d950qy/pEXqluDqjD9aunEPj0x5PKo +nR0RVbjqnHrdwBrCz/hB6kROFZYcu3b7oIEYpqxt87cdqkJLF5Ej9z+yPn9f +3B6rauzY6bD4hJEYSt85yQwXVaMHFHOHjMWQ4mbtvH1jDYr0Fr8+DWIY/JQ5 +dU5zDZ5Xjzw3ZiaGuU9U8jsD3qO0MmUWZi6GGuat8JLFtRgnZScrZSEGNblt +1g3dtZjFXZCsaC2Gek85zwrHeryWGuE+YCMG5aEZ4UdXfUAvO+Gy7N2E73rt +7KUSDWgqvUcQ7ED43ucLlfUNqFZamrvTUQzP3zoNnrjSiL/8NU4vcBZDR8SS +D59Wf8T2ZTc3Cl3EcPH2oYh59R8xu/eHRNkBMXycGJ1tvOMTRt3eX3vTk9Rb +x3Zrf+EnPGxefcPlkBgW20xVPq/QhJt/6+zW9Sb1DPI1OWLdhAuzY1XGj4mh +762nVFtQE/72/POl8YQYNI4vTi680YQdczwfJfuT+XGZPe0xTZj78cPh46fE +sGFmj+HVa01485K+7sbTpD7Hjh7IP92E3usTh2TPET1KDw7fO9CE5gKJwt4L +YjD9YywdbdGEix56X3wZQvLVTD78bU0T/nFoMTt/SQwObQf/a1jWhF3TNkhb +XRFDy2/1SS+WNmFeedpH1auEf6+jql6rmzD6lHQs77oY9Iz8AgRWTXhMy8/x +3U0xMCcejC8804Rb+7vUrt8m+Owg5/WbJlwca0J3iiXnYePNHLV/TTi+7ekz +rXtEL7ILah7ubcbuMYUTv+LFwA3r6zxQ0Iz5uUFr6pPE8P1D65Qa+RaMOdQ/ +Gp9K6mex75HVphY8Pm9r2ZGHYlD/XaPbTs7vtubM8P8yCH8zp9QG3G5B9SvK +ltJPib5S//SffdWCExsuKnx+Lgbb1KzFBSUt2CNktD19Rcav/cvIJvdBfvqO +hNPZYugqnwjvfEP2c3zjuu21GMaPBbsXJregj/z8pSr5JB4tW7ry2Ra0rAzn +sgrEsN762yr2jhbUOM3PevtODLKPw3+YzW/Bfzp2pyJKxeDyvHmDRVcz9n59 +t2EPkvPncOeNWngzFsQtmdCoEkOY9NP387Y2Y+z269U/awg/zQNXVmg3o+/E +t2s1deR8XuI9fmLQjFZvnGziGsj4jKSU7hPNuMy7YpbXJzHoFqpnFDQ3o8QC +rZ61LURvjQW6x7RbsK/19gPJdjEUxdVzJQJbsChy9GB7pxjSkx/sY5a2YNzG +A9oZ/wvrABT/2O8/Lkf34g330L9w8MbuctvvP9pn3fe7FNG/S6UutELe7z8U +sIc4ywnRvyZalnkS4e8/rgtJ9sjO0L8CD/4+4uPvP3T/ZDB7ZNC/3sNlBLLm +7z8YULkljq7Pv7p4zcmB6e8/aFqrdcSCzr+WLTWPUezvP2Aaio8LlM2/ceKc +VCHv7z/Ibs9bsz3Nv0yXBBrx8e8/iKknsNXGzb8oTGzfwPTvPziS80MyIc+/ +BAHUpJD37z9E08sNXTvQv+C1O2pg+u8/sLTfxcFtz7+8aqMvMP3vP6DxX3vl +Ase/lx8L9f//7z/gTQjbu5+RP2YoVbw= + "]]}, "Charting`Private`Tag#1"]}}, {}}, <| + "HighlightElements" -> <| + "Label" -> {"XYLabel"}, "Ball" -> {"InterpolatedBall"}|>, + "LayoutOptions" -> <| + "PanelPlotLayout" -> <||>, + "PlotRange" -> {{0., 0.9999999795918367}, {-1.5, 1.5}}, + "Frame" -> {{False, False}, {False, False}}, + "AxesOrigin" -> {0, 0}, "ImageSize" -> {200, 200/GoldenRatio}, + "Axes" -> {True, True}, "LabelStyle" -> {}, "AspectRatio" -> + GoldenRatio^(-1), "DefaultStyle" -> { + Directive[ + Opacity[1.], + RGBColor[0.24, 0.6, 0.8], + AbsoluteThickness[2]]}, + "HighlightLabelingFunctions" -> <|"CoordinatesToolOptions" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), + "ScalingFunctions" -> {{Identity, Identity}, { + Identity, Identity}}|>, "Primitives" -> {}, "GCFlag" -> + False|>, + "Meta" -> <| + "DefaultHighlight" -> {"Dynamic", None}, "Index" -> {}, "Function" -> + Plot, "GroupHighlight" -> False|>|>]]& )[<| + "HighlightElements" -> <| + "Label" -> {"XYLabel"}, "Ball" -> {"InterpolatedBall"}|>, + "LayoutOptions" -> <| + "PanelPlotLayout" -> <||>, + "PlotRange" -> {{0., 0.9999999795918367}, {-1.5, 1.5}}, + "Frame" -> {{False, False}, {False, False}}, + "AxesOrigin" -> {0, 0}, "ImageSize" -> {200, 200/GoldenRatio}, + "Axes" -> {True, True}, "LabelStyle" -> {}, "AspectRatio" -> + GoldenRatio^(-1), "DefaultStyle" -> { + Directive[ + Opacity[1.], + RGBColor[0.24, 0.6, 0.8], + AbsoluteThickness[2]]}, + "HighlightLabelingFunctions" -> <|"CoordinatesToolOptions" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), + "ScalingFunctions" -> {{Identity, Identity}, { + Identity, Identity}}|>, "Primitives" -> {}, "GCFlag" -> + False|>, + "Meta" -> <| + "DefaultHighlight" -> {"Dynamic", None}, "Index" -> {}, "Function" -> + Plot, "GroupHighlight" -> False|>|>], + ImageSizeCache->{{4.503599627370496*^15, -4.503599627370496*^15}, { + 4.503599627370496*^15, -4.503599627370496*^15}}], + Selectable->False]}, + Annotation[{{{{}, {}, + Annotation[{ + Directive[ + Opacity[1.], + RGBColor[0.24, 0.6, 0.8], + AbsoluteThickness[2]], + Line[CompressedData[" +1:eJwUV3k4lW8TllSSJElIkiiVJC0kuW1JRSlkSX5IlC1JUtkSslNJKiT7mn1f +su/7eqznHFuOc6xtKul7v7/e677meWeemWfmnpk9pnev3mJmYmIyZmVi+v/3 +wq3pzgqajnxHU417A1fSZxZlfjsy33Ewvf68LkXtDY59CI/I4VMBk+4zEa+G +AkwIiDx9uO8SZFrmT2ozVeNia392JJ82ZN4qbH+QUA+RgF3x/3brw13U5ZjB +30asXLj5xmSfEZxmLUYfejVhxrOnxiTMBAssuTOJg43QNftZ9pLPDCt7Sm+t +BjegRpm/oDrCHJIp7ou3dtVDcu+ZzG+770AtO1Srn1SLCGbjZNFYK4T09nAV +/qgB65hHzLV9tiA1ct6VC6pBMaWrtVrbDpmrXYyEDzWw0zS7YBh2Dx2dD96s +8NdiX8X3um/99uhQc5G8PFWLkSPPlQP5HOBzpgR7xusQ+oG3QvT6AzD1Zb5O +W6rHhS0pcuURjrATnUxf86sBTG6ni66NPsT0mb5L28iNyJ9rOTG/+xGWsz7f +6HrVBGsjo+znJo8hJLLzkxd7M4Tb5iWEYp9guWv/DX+VZpDOPE0tnHBGyEHs +ypBrRlA6l9iVfa4ImfdQkPvdhLO74uJoFm7I5JlyYhDxcq17x1mp7Q5eBYOv +rTON0HcdvxT43R12dzpkT5xoxPGT4oH6YU/B6Tvj23ivAVvmHJpFpT3g5P+a +Jy+tHjPxZRuX+j3A+TopYHWhDrU31quVOz2DzGzJzc1qdYjeftnbj88Tdkkp +v3WLavGk9U3NtWJPdPjF6MtcqMU1Lwrz3uteYJqd2j7+twZHzxxQnP/jBc7U +278e99aA/fs9t5IIbyzPnkg73VGDL2nFZc/PPAdJ79KbPHoNqszWrmiNPkc0 +L/3RdpFaRAqoywq5+SAg+WS0vUMtnHpCnRi7fZGkm6C8u78WWgEj+YUVvtAb +4rn482wdJFT2ffc08QPLPRvdlOI6bFyxPXaF2R96W458XpWox0ROwb1dsf7w +edfXsCmyHp+tmDJpygFo8FPeZvmvHu/2np/LmwiAj0R2sv6VBjgOvRD38AoE +hW17yUhQA668GrS8tC8IIho3rrblNkD84t5k/vogqCScLadUNIB1rfWXKYtg +xGmohyZmNcD+xuBLfZYQcL7dcsvfuwH/Fa1mfdYOQajTjytlaID69r2dovEh +0BRdLhcZrYfsvXML/t9DYFYeoX/+Zj3EWq22LJ19AbVtojGynXXYfiBEQi/s +BSrKNLc4HqwDs1euRvnUCziRnja13KvFAoVkLSL9EuJe02PnU2rQHL4ndaH/ +JdRFOnfd/1OFp6w5+335QqHGorHXlV6Og+de+GTbhSJ8g4vlHHcZurzu0obq +Q5HJFV9kfaUET2o0Lqzb/RrhTCcmouKLILJWPFXC8TV4N+eW6m0vRIsiG7te +62sUbrTv+hCbjwfu09ZPRcKwQFvanHc1D4Kf61pTnoRBEtlb9orkou5vnERP +VxhCqnce7eDNwV25Z8F/D7yBmkLv5m1Hs8H7xGRh39M3YDq206/BOgsVRbii +SXoDUoihsWVzJu4s78p+dCQcCh6DBqLqmeCSXuGK9Q5HyImY5eGhDBQ/GLzf +MhIOIa1rP8T/y8DN3MKe78ffInrbHbH83Rlg/xp2YnfAW1SUrsmn82cg7+iD +MLXxtzBOSY/QvJQBIzutn/dk38Euf+9Bv4IMrM84qvf+xTssjN+9efJgJjJm +txTVTL+D8YYDH5++yISe+BzfHN6D1SDOpYEzC0xWLY93vHkPpx+MzHOJWUhO +ThlSmHsPBZ3oPC3tbFyd9pGzPBsBybhvnVo7cvBnn0Xkq4gIsIqot5TM5yDu +1tnV0q8RiNapT2EZyYV63N7/pi5EgvJbciRuNA/fx9ZUbImJhNrZ+sOs3/IR +tYcidOpXJDRdxDqeCxRC1bj8qalmFHx4bo+a6hYhfOSxct5qFIx3pp5zYSqF +ooB+3KjOB3CqbGNzty7DjIH0Otb0D4ieZ58wnCqHIOPRzfTD0eDcX/7nxWoF +7t45Kco0HI2JQzdMHVCDGp/43tANH6HA3d4bv7UWvEnc3geOfUTcc/8NbGO1 +qJhamrrq9xE9WqNeCw/rwb3e9M2XvI/Q42MxypJtwB3RznPO1I8Ynn9269CP +BnCZZSTFy8QQfOHuxX+1CebPBPVlzWKgydnNK7zQhJKYwI3twTEQUV0q4vRo +BmfVStHNkhgsnNrJmF3fAjOqleXyVAwErCuZqS4tKGQa4g/kioWd8PVLx6da +wC50oXmPfCxuM8s26KIVxih6kn8nFpryP6TGfVqRZyQmfvF1LBrkGhLfVLWC +zfXNMLkiFpT96wOMGa0wilwf6MCIhRx/E0NrfRuySx+c2cgbB81lF8Vszjas +H56YjVSOg4hYdPjkpjYY/NGKkrobB3Yd1+Puy63I4K++VP8uDiGdpA+y/a1g +kZX6d70uDu5rr6ssJrVCT/9jxsJiHPSkgoI+2rZifkibLYY/Hs4nLr7SkGiF +txHrLS3leKiYFL6+O9kCAWrJZxbreAx/er607XULcm7e5c8PjYfnboezOvIt +uDAl/MCiLB4CSasW+mPNoNzua+edigeToITRJSJ+HLZnvJ5IJ0DFaCPrQHET +4hcWyOLGCVjmuJbbr9MEuftxsqM+CWhJ1Bd4tdgIS6dNCwqDCZA8cnjX4JFG +rPlTfmGJORFyVZrLb3oaEO5iHx97KBGMhNT99q4NkGDax6SjnYjCS5l6hhIN +qPUYMFjvkggSvSpYerIehusC8wriE3F7YNy5I7YeS88VOO+0JcLsdjjXqGU9 +fNm+WfL/TMS0D4cJ0+l6CAUm1jbvTkJEXnj+Z+56FGy5LuSilgSxg3XrApbr +cOklxxOJe0mYhl9I6VQdJrmreslvk0BiCPYHk+vg/OaB5IuqJNxuf9VwiOjX +2/gP+CvRk8B4dUkqarEOKRHDk1+3JUNNWcRqhK0eCrtDFOLlkrFsvO9kI9Ev ++j8qv792KxkOj6pJh27Uw1bk5/cNQckQirr3X8nrerAkpmgW5RP4XdWmnaR6 +vD9glGpJTobxO5ep4b0NkErbul6ANQW5bmJ2z5wa0ChRa9wqmQL1touWz3ob +YJzlVOKqT8g/fco5K9uIwHyyHTUlBSItvZWevE0QOfWq+WV3CpY3lh9KDmlC +cYnqPpWVFLCzLWwd39yM6Yr0oQSNVBjemHKr4G6Bm7LJST3HVJCeilj/imgB +Tx33i40fUsHgiON13N8K5eYnqtYLqVDwr/IPVGhDVO/5rKOv0jDY4u60+VQH +Tuj93TRekgbxmpTlSJcOtAxmmodOpMFnbKGAu7IDv8g7BH6eSAdF8xTrGpVO +hJg2OyYZpaPmsynL4Wed2Dfp2qn/PB0vJ08eTavohPbMpHcpKR0TDYpG+ie7 +QLd+S7VZ8wm0Jxvn7tl2wWNeXW73wU+YVthunB3XhcxvOYtPn3xCfMimLxWb +urHp31PDc4IZuHwYfjW13Qi/o2skrpqBQc5A7pb5boj0iBtvtc2AjFfniwTe +Hsgn998cKstA9TXFJl2LHhQlh+UVSGSiXsQt12mlB7NajNKLbZlgVgqbSxTu +w/GN/WfkxzJxQUzqMO/5PjwuryyX/JEJ+XlXe2G7Pmw48KZiu2AWXLoul4pW +9GHPqmIN2SYLPMxpH9hv90Mn6U3z/c3ZGFFbduFrIyHihoe6+Z5s1D6x9Pjv +DwljXDateieyISzL9c5CbAB3XZTaz9zIhlj06CvlpwPIlzqsKXkvG3YyxZ4D +aQNY+bKjU9grG4812hTy+wfge3W2a0N6NliYC1yaDw6iYwNJ63dFNrQzNkw2 +Xh0ET1lVD6MnGzdjeWzfPxpE7P7wvs4Vwr6pKLtW9SBmhj10azhz8N9fbdNN +U4OQfGlDyhfJwcHS/OrTG4ZQtqI0+F49B2YpoyOVKkNgyT58Pcg4BwJu1a9X +jIdwwYJ32N0hB847PUIePRlCiMDaG/d9cpD2BmJSoUPo75wduRVBnA+aeCmc +OgTB5yQjvcwcnDywOn2+YghmctXkCzU5eMR7Z19K9xBSFtONz5BywDpJFVGb +HMJiQjj1CCMHo/oxIYe+D0HG8JmpMFMues6j32jtMFy32o5zc+fiRz/L1vkt +w6ip0zPbIJaLWXu+STr/MDY5K0/+Op2L8unC2xYiw7h6VMKccTkXn1Wovx6I +DyN8ivfL6M1cdHt3bZc4NozR92tvdz7MhV9iw6EkmWGIXpmbrvbPBV+tofWq +3DD43c7JWnzMRdP8x+2+CsPgTI/2ZyvIheMMy3Fm5WGsG/o1nN6SC6/KN24h +KsP4zaolcWUsF87MrdTrZ4excDLN7dvPXJQ8NNoVSOBJs3WdbzbnQXL3wwca +BB58aSR8em8epIwXteuI/zsqCu6PyuRB7dmDH0IErp3jrH16KQ8ihWc4vAl7 +xQKWPKJmeWhLknPcReDMC9UWDY/yYNalP7KZwPFOAkVWwXk48NnqsTOB3yU8 +YNsSn4d6un91AKEvpKftenZxHoJqrh40Vh2GF7NYuk5HHiZGnoxsPz+Mx5JP +V5cn8/DT82ZIk/ow7hoNXo74k4cfQp/Vwq8MwyyAaO5b86HQQJUK0x2GQXHA +0ti+fBixtzmTjIZxeXpS2VsuH+oPz8rYWQxDhQevD1zNx7uM78pW94YhqxI+ +1WKRj2+9Xad7nIdxxH5R2s4lHzWvouyyfYchEn3Bd9urfNhG+09tDB8GX1vs +YH5SPuZ1Rw2GEofBsbJyyKA8HzGOhpoiRcNgOXjN5W93PizVNIXJzcP4pZvR +Fk3LR2Ry3661lGHMebEKqfzLR5j03o+e34eJed/k3hfuAnBwXFfQYR9B2xZu +bgmFAmhaVh6NPDOC6jM2tzp1CuDEZ3qRrjuCQqu6fAerAhSphj86eX8EsfVO ++iVhBTBao61omDYCJ7eRKLXZAkTcyv5WIzoKm/STC3TmQqQ0ymfSVEZhOhSs +GMxbCEUdtuN7zEahIa000atciBMmIQvqMaMQnk84cPNdIbT5+xav85OxYxfT +k/WZhbgftuHx0Eky2C/qtyTXFoKTNp4adJWMnwmb7i4sFOL6fZt9cs/JYPSY +VbxaX4QX0Q0BW6PJGGMu3yotUIQ5m4UtnQVktBjZ5bqcK8I+3izukXEyqgIa +1+25UYSwzgMtPMtkFBQL69bYF8GFaTTQbx0FadNPkix8imCy6bCGJQcFMTy9 +v9iiipA/sFMohYeCNyoSFz/lFOFgQfSnC4IUBNg/j7jSWIStCQ9rNUQp8Iim +zH4bLYIUe5d6/iEKHradQvi3IuTSaXI+RyngkMibbGQtRiqb3dn7JymIC5QM ++CNQjPpxV5UJWQpkZ1OlDh8thiepKJsiT0Gn+v4Bo7PF6DVxTbJVouB2Woxb +iH4xvIOYO0LPUrC6SXBflU0xNnEnXjNQoyDU6m3L16fFaBZ7N1J3gYJDzdz3 +RcOK8XIH7c6YOgVVB0P4iEUQtf8EtfMuUaDnt6nCp7wYhz2DpdU0KZijeZsX +dxXDRtmaGnuFAq/zzJsZU8UwHaxG51UKBJJdcnb9KYb0uI/mgBYF2ay/9C9v +KYHxRDlnrTYF5Pr5hGzpEjD9phyyukaB434rjYmLJTC8s412UpcC9udTX7cb +lyD3kO0fVj0ivlMm7845lGBu4xcrGoFPqY4oPPIpge+DjimyPgUd8XpfUiJK +kLSwIeOrAQXm63oChzNL8D5i28tDhhSsmF0+zlFbgt69iiOBNyh4VdM0iIES ++J3v0xL6j4KDIqpP782WINXaZN+0MQUVzyr3x64pRZP8STrNlIJr43JtPdtL +MdIrFH7gFgWzSoUO6w+WonSXrkuKBQWeMcd2ysiXotz7k+JdSwr4mTMq71wt +hVI8H+WRDQXnKuM5Wh+XIvvN4xO3HCgYFdqTtxpUihTOKx6qThQ4uEdcl4wt +BfutGZKtMwUf8SrpVXMpxgfaIoO8KJD5wHG5llyKZokG16d+FLSt+n7/8bUU +eee0DLODKfhT5q5kIFAGyd6y+vJ3FLzctTLtL1kG3kfHHr+IpkDM5WFwmUoZ +HqeWPg9JoEBHznZYyKYM378HBPzNpiCj+Lrjl7IyTDGCSNMtFKjy9wvwdZWB +6+wx9ofdFAw/ulp9YaoMwSN/u/8NULDx1HnOTxzliM5QF/gyRUF0eE0+Wbgc +FkpSyzKzFJxcxo2t0uVwv6EiZ/2VgpsFJ1Mc/ivHvgcV3sb/KPjNk62ZcL8c +teEbz+xYR0WI4+Gf/c/L8frKud53bFSUnRBROZ1Zjufshvt/cVOh/frDjHUN +Ye/YN49WPipmvvG/iCKVo0NQmddUkIoduVtH16z5DIEXTMJ1+6gwDPijPcHz +GbuP/fo9dpCKGLPJ5jrxz3j/47RetgQVX+TalZKVPoP2Xn3xhBQV4tuLivz1 +PsOWY8bf7gQV9rMxkra2nyEpJfzvlgwVBbUBiZqen5E563x852kqlByNX2/P +/Iz5kjjqCKjwuXSBfbn2Mz40Ojj9VqSidd/xZ4NDn3H9mTbLd2Uq0ujPCtvX +VkByPOFM+jkq2vqXv1ZwVEChe2zo6XkqFqttjmTzVSDd/5i06UUquDPHLGNF +KtCWdWLougYVJyN0E0KPVECVw2yTy2Uq9H1aqF6yFcS+T8vsuUKFs4Pirodn +KwDX3efstamIMs7Xu61ZAa6S4bpbulRUqh8K1b9eASmHpJDPBlRMyES3XzCv +gHjmX50QIyrWi27fJHevAltki9fQTKk4sNVP9bBzBV50jH4YtKBC/e/qU8Hn +FZh4WaPiaEOFLe1+2ZaXFdjWwPjacp+KF73Ty0yRFQhNDvGef0xFbuWN40uJ +FSg+tOPlnAcVfeldd8ezK+DUH3Zp0J+KX2/PpfaUVWAxydel6jUVAt6lU7UN +FdgfSNLMj6ZC3v6ocEF3BWZ8b16tSaPCxCjhRtJoBUp6D6r/LqLC88LOt29p +FUg6JHf0VgMVCSdDevy+VeD5E+8NW0lUNAqv43T+V4FTpbldrDQqMcc/vmjD +VomWnUfcr/2hguPPnLfR9kp48Bj3MG8Zw9EvN6suC1VCQ1hff7vIGBw/a5yS +OlkJKQ+7CM+rY3ibWuWwV7ESz9To1TSrMZS+kc7kVq9ETMH5/lrvMayx27P/ +p0klpo1ux45XjEHEMMx02roSomF/1wlTxqCqtilq4GElcr4c+dDBNI4Aoe/c +pYGVKFq4QjZXHccndkvN9PBKnFmbOSZvNY7O5VH/qNhKRHsfHbZ4MQ6ezgbm +p0WVkJ05P+xMHcfHpxELZycrEfWqjMIdPIH8MeWWdrkq0N2FfVc5ptCn9nQx +8FwVahYKbCsxhR+fynnUr1Zh1vb1rSC7KUg/OWXSYFEF0QzyPKVzCoXbjvyo +eFmFltsGT6NCvoD0yHqnW2QVlhcEHWbKv2CZnKxwJqkKEqNK/xwZXyCTJuJf +VFaF0L5rj76qTKNIhV8oe7oKQbF1why0aQym6J61+0rof+edPc9Bw2/O15YS +q1WI1CuKsDxGg+zIlryUbdUYtt+bzXhIg4GyxuBtwWrckrx3pP8NDY+T/f7t +O1CNrX+O1u/Jp6H4wboLsfLVGAvQO5E+S8PgkNJdk/PVaPk4lD28fga/Fd1D +d2tXo0byY9J5wRnwJ5UVjRhVQ2fwy6n5YzM4zfFn9P0dQj7rxdt0bgaGDjIs +Bg7VEOr57k3Sn4Hz4IMDvG7V6LhVpMdvOYMIhZxLfb7VcHXbvhjiNIPShIX7 +oaHVCNx0QAFeMxhml3h79UM1KvzNyg+EzGDF3qqcM6UaUSu3za+9nYHAQNJ4 +W2417D9dS2+JnsEZTLEGfq7GxM2wR68TZmAUv1fiYlM1VlPEeEtSZuC6yURr +Y281In/5SJ5Pn0HUvSinejJxn7BjBeqfZlDePxTpNVMN4/rR0W5CPnqGr1r5 +ezVM2R6xzqXOYDX22vQaphrct/+XlZo0A0G20M0VbDWQvKxgJhg3A3m7TinX +7TWYuP3hg14UYb+PQ09OqAaJa5fqbd4Q9uXUXX4frEFage8W+2DCfoxvTOGJ +GrjSvEwee8/gM2t9vaNCDXZqeF6McJ4BxZZl9vjFGniaNk7N3psBU68i11ed +GrAq/q7wMp+BwsdSw7tWNThZXCA0oTGDilPZixZhNchT/0yb3kH8/2GeZ9/H +GhjFvkz8sZH4f/1huYnUGgSxrznHskKDYleit3FlDUQ+x4c6UWgwlZlMFWyp +QZIGUwlbNw0eUcKdw301UFL44/O1loYqy8id+owatBWqDPKm05BDs7Iy+lED +bb+yw/IxNMTdli25yVQLTU2P5Hkiv0K/sG66w1YLVfeFYdkgGrzM+w1suWvh +1P4pWNyLBsfJ+JT7grXI9uov6HCmwdzM4beTWC2uci/ZST2gQXdc6YKrVC3+ +lVZ9vW5Lg5rp1nfP5Gphq/Aj6NptGk5RyTQf1Vqw53+KPniThoPGn04FadZi +Xc/3ELIRDTvJzr6vDGqRy8Xb+uQ6DexGFwfCzWohLUuvZtGn4e8w34Eo21pQ +2ZjHXXVpmLs+7RTrVIv8ntbQ2Ws0jA7mNyR51CL2Rzq0CHm7vhfvp4BaXDNj +nM3So6GCpHU7J6wW4k/i17MS+jN1hQsLown/3oeTrxH2P/YtbChPqUWp+OiR +CFMaXup81q3OrUUUzfV6rwUNz3oCExvKa+EY8KV91YYGBy3Dn60NtXgkfWwj +N+H/ra6D57q7aiFzRjV8iwsN1678CiMN1+KJfPYBOhG/cx31UyNTtZimXw/8 +EEyDzOWwk+MLtdDeOVgu8o4GPo1jfbMsdVgQlvB3yaKBrWXNvq8cddjw1079 +TDnBFxc6Hizz1mEfZ8SZhGYahtVstq89XAcmWZsalWkaWutP32KVrkNq9h1n +k580lKuy5W1WrMNa+R1V3wk++KCSqM2rU4foxDOCl/bPwFSB+uqwSx0E/muf +PGQ1A63PGeNSz+vQfzxWxZHIZxV512MyL+qwuU4xvjpwBqJyO7uV4uvQEPRx +4WDmDKaldbj0WusQt08yyG9pBgP5e01v9NfBsa9UQp2ZjqYTS1mm1DpU6L/Q +ithKR+qx4Cs23+vw2OJaU44EHRHZNz7a/yP8nSQLmsrREXBUfPHhxnpMsVRy +2Zynw/ZIY4jHrnrsqjZktTGh479PbyjP99cjIn1fsYY1HZqHzSUDj9bjZGW2 +s6kjHYppx91fnq4n+uHvyRg3OqQOre14c7YePc/jLm7woWNvSufuyMv1YHmi +3egTTAf3gei7Mfr1cObVUN0TRgdLku3nxJv14DfUedz8no7v+85sSbepB/P0 +xKJHNB3yY0r1fk71mP7g2egbR4d3pJrb7Wf1KPpR5mWVSEeb3iVp1aB6LAfe +o4om08HDrT2/9209KJVeTQUENmrXT1wTVw/LZV3TPQRO8PvvP/KnenBI/V65 +Sfw/d/bWjrKieuyUV9jtQeg/ucaq/V1NPaIEPz5xI+y7lto9d2qvR6Ha0qwx +cb+6h464NliP68/XOoq/poPjmPPPY5P1ENPee5QWSIfu3NOMrQv1CHYNvfrB +i47o5OcW87/rwb2wyq/nTMe0WeDu1nUNkFebattlT4fTUHiwz84GRHd1jf41 +oKMiLOqc+b4GHAgOdTh6iQ7Wq3H/lI82wHBkn2acAh1vGzLu/lNtgHfv4VPP +9tJRnFd32dG+AarONi9nxgj+D/62xayxAebZQ12sekQ+Xfxdr9jTAM8TuQbH +iH4TsJ7JfTeZON9xj7nk5Ax2uWxaGPzWAKWth64fIvjQXGZrUuG/BmRsMFsr +wzqDT195jMPYGiGc/+cd7RcN8pbCHVeEGiHT98XWlUyDt6iYz5FDjdCqdo1/ +SvBhG+WwwuaTjWDb+Sb+TgMNPBHHlmcUGvHwuGClClFPRrqnMhsuNuLwDrKv +UB4NCVy4nXCtEUnnpuo2Enw516oi5GnSCCXXfEv2BBpO+l4gmVg3osZBx+9Y +NA1uKpoheNiIBS5pHd/3NDT801Hb5dGIYAN2jh3hNHCWXGf6E9CIS36PWSZf +06DnaFJIetOIQeby4N+hNEQftbDLj2kEb9BpNiNCPs2wFgtNb4Rx6Zo2boKP +JZPsKfcKG1G857TUXoIfnG46hV+ubgRF64VvQBTBZ4KumofbGmEW77ZHK44G +1sFnrJsGGtFQ8ErJKZUGzde+FdPjjUje8/boSg4N4ZrBTnVzjbgclHZ0tIwG +6qbXknG/GiExc/S5QCPBx/Xvpp+yNIH5VtKT3F4a7D2io//b0oShS9dMY8aJ +eeNMgt4Z/ibw8tdFUpdoYP6VyrlTtAl9fJsTrNfOYGer0lccaUKoqMgOFu4Z +HP840Gt2qgnrLBels0RncOv8hvefNJrASLDuOqpO9NddUS7duk1Q0Q5+8MN4 +BmGLx42XTZrgc1PzQI7jDBremooqOTbh2AGDQ4tEv6ba/Npg4d4E124rl//K +/j/fhMz4+zXB94nq8oe+GYjPlGX0RjUh/eIEzXoTHcGyfLJ36ptwlO2s6R8i +35M4MgWCOpuQeZjjQ9U7Ir/HVP9lDzWhweVs+79COpb8HGpW5puQuxr6POUH +HdeG2i+F8DZj9Xve5VsPGBBw9r5ZcKcZlptcWkkPZnFCc5fq8P1m2J9L57ny +ehaXRHLF1rg2gyJ9555X7izcWqizF142Q0jU4b+/i7MYEzjjNFrcjB/6jO0K +t+fwZ6HbYG1tM3j6lUXSPOfAXWt5Rqy9GedHfHTCouegahPObD/ejLgl80/t +fXNILvsasI69BSkMDw0juXlUvfC7e5CnBQbtBzqhPY/BW3uuXhZqQeMes1QP +q3mwc1ze8fZ4C9pY7S+Ihc9DdGzyV5l8C5YEE7X90uchn+88PKbWAiOlT6fV +q+ZhZ5TyUfwGoX9/Uc1X2jx8pRQ9r1i0QFN79tPwyjxi1pPMHe+1gP+n+b/X +GxbQ/WmdeIVXCxqeXMpg4VvAyX/G+VqfWiA2GGX2SmYB6hoVHmcLWzB8Xj4v +Awu4+X73ZemqFgRZ2216qbqAEOnRL/x9Ldiq+sUuR2sBtLvX+cb+tmA0idez +yGoBTOXFk90bWvHb/ae1zr0F8LDzZ9dubcWMkuWadscFKCWRLiSLtsJnsYb3 +9tMFRFB0nO00WlGxVmki4PUCsiXy1Ex1W7GcoffZ7t0CGpy5t2ubtMLNatPy +xQ8L+M7bnS79oBXBFrYp35IWcOmKJnk1ohUX9AZj/itdwJqqC0qBjFYIB/1p +rJ5cAC9nCofbj1ZoxYo3atEXIGG0cciOqQ1Sa9LCVhcWYPC7/r42dxs6bTYc +TVpZQK7U2fidcm3IxXF1g+2LMI8Fa4p/G5yEf6vtUF+E82JUz/vXbchq1V41 +0lrEK6xGB35ogy2XTmexwSIqhkpP3ctpg4U1n0jinUXwcctayQy1IWjyTBO3 +zyJaPI+31R1sR/HOafvFmkXIbmlmfnGiHbdv8Swutiwi6a2J9HWFdjRZ7mDu +61nEs09B0fM67dhjQ4qWnljEgoxob5FxO1Q3anmm0RdhVF2y0dOqHeqqB9K/ +LhH6SNP2vE/bkbK6FPyFaQlJpm6JY/7tOENmqfTfsASe2e3DaWHtsGdxEl/c +vITFNcpnFdPasWVtvvo83xKMAgYebSpoxzuDvevddy+hhcfuU29lOxo6bmys +EiH0HYrcYdnfDuHVneIXJQh9+cfUj4+1I/xPH/ylluCp0OS+ymhH3AFWf9uT +S1hqMs5r+NkO2Qze6cVTS8hM+eNwfk0H+oQlDbnOLOHLvGrwp/UdUPrvKl8r +liB44mXyNvYOOETpuO9WWoL245Fqp60dkPiUIbxBZQn+n8VGR3g6wHqKr+bp +2SVUsTgsKwl0YK3qesNA1SUsn//MlbSnA3tlvvKInVvCkWC2w5v3d8Dzs5eu +JoHNe3TO2Yt3IFX7aQELgSP5Ppr0H+3Ay9UgVhXi/x4jxhM56Q7kXiBpbyb0 +b4qTDvso1wFHrwfk/5SXoETzyFyv1IFm8wyR04pLeCTR1mR1rgO/A7gHo+QJ +/+7zTXaod8BY+eac32nCv0KzfyeudkBQWs33nzTh32oG33vdDqyMLLH9PbYE +HeU/x5hudED8gfsmzyNLCPBRvXTLtANsUfIGrw8S/rW+uN1k0QHvsrqVo6JL ++MU14nHEpgN2xl8PXyfeR1JPLDLUvgN1zFmGXMT7mUfeL/j1sIPo36kH9bkI +f/azMao9OvC1aG535FrCHxud9Qd8iHjmvH8c9WcRStnRQkGBHRDybeuX/rqI +TDlpHb3wDqg+WR2Voy7iy1OPu2WRHQizV+D41L8IwfpWX+HYDpT6aqhWtS4i +4IpZOSO9A6Rt7kaUwkXcNn+x/2l1B8pPmFlf8V/Eh9RhxamGDqDXQ0jGbRF9 +C/sNL7Z1wEaWPW7EfhEqT8pDtg90IGIx4p6D/iJ2h9B/Jc91YCAkLVReZBHl +Jm7J2V870PF2U67DDiLfj23TL1km7Ld83B3ItoiIPtnCFuZOUJ0C39wj6pl3 +l5/jPE8nBvlW04xLFsCVIvb1ODrhUhWudFdzAVlPSmPOqHQi8/LUpmPKC9DU +0Lyqer4TUp9XktefXEDwwsMsXa1OfPhXrzO1cwHs0vV3H1t04q/j4YmnnfNY +V3OL8Tm4E7xRu+9WcM4j7vWv9w2hnej4zea+/GsOKhaBFzvfduL3xDY2j/E5 +eLDlpYzFdqLskJFjcMEcVjVZ7qwr7MSa3+lpOTfnECkczstR1gm3mKaW8Mtz +kPt2qIGnqhMqHml/+07P4ckbrf1iLZ3gsHvr/d/2OSyPxExeoBD+VVktRLfM +4k3Gyddak51gOTWtfblkFiefNqkYznRi80euNJ2UWTwQWYq1+daJwxYWdRa+ +s1iyVDQNYe1C3POewYCLs3gh17v17eYuvJe6Ez8lNwtJjjuVH7m68FiK/fsL +iVnYZoUI5Qh04er5JYEBrlnQf5JHeyW7UL1i9oidzEC+RXDVhZNdUNv10qir +kwH3fvmEz6e7YJHeJDlXwwBPQaRNsmoXiDP3hNMYUHK8vuJs2AWx+6w8110Z +2DzFRlk06ULQ78Sl9PsMkHSKq80tunBWRt1C4w4Dtif4/DXtu7B0SPiGrQ4D +77718Yn4dOFy8UrKnqMM3DLz/hse2IUxVjXOKjEGJHtOUDe/6oLk2/fCyUIM +1OWEJv2M7EIS00OH81sZeLFXJcA6tgsfDFKm17AxYPjq611qEnE+PPPeP2YG +Fu2vSjfndIFN1je94TsdpWNrdioUdUHhlO3cq3lif7iatZpb3gWtW99uxNLo +EJDirItqJM6XnjsZNErHl4+fk7e1d2GbtZXJnQE6srfeDfTp6YL2nmU5nx46 +1BZbte3JXdix+U5kSDMd20xcZL5MdOFV/MzMo3o6RjvEBQxnukCXpDomVNOR +rDD8r2O+CyaSf/h5KuhwyPQfP/u9C9Z2lckNpXRA6HR98e8ulLauMMqK6GAL +mUk5wtSN3OtCcd/z6ej59zYobl03AvYXe9zNpePD3fP2fJu6odTEkDiUTYcl +eVkniLMbrxe+QiyTjuOXk06t5enG6FKenPknOv6V6+5y2tkNPDd7N5FG7IcS +G9bMCnWD67lESUwqHa+j8idM9hH60llmP6TQYcxh3tB3qBsxu+7fHiL2pUOu +29MuHu2Gle2Ly9oE/jFbE1xxshtsPWzpGwlcecPh/gm5bnz/hvu/k4h9snWv +bopiN4zbnz35/z6me6Zbdve5bvD/dfDyJbBwuodgqHo31J45nBQl7M0KSDFv +vNoNJrnTfD8JXBhAnXTR7YZ3XVDkX+J+HishjUuG3Yho5OGVTqdDw1oh3cK0 +GwaSWlUfCf94h+dDhi26MTOVU3ya8H/s4geHKzbdKHHqYllLxCe95JJenX03 +wlpbfb/nEPvWodXTp526YS7YwLuViK/y+/TdmS5EPHieW2gR8yjHphtrRZ91 +48zciW3FxXTEzZQ0cQR1g5b3zH3mM7Efv7m81/JVN0I/BPV/rKJDWmX8SW14 +NwTDBk/Z1xLxjWQ77BzbjSb2KgctIj8WNfWDaYXdqCYtjzT2E/vaX8YXlfJu +PHnbcnRlkA7PFHeF6OpupNbPzkoS+cfLkrR4ra0bcSrDua8niP234IdWzXg3 +DsobCvxaIPZBM7+03bRuOJezutK/0tHFKbjuyVw3nDaVFTQQ8/Mty7P5R391 +Y0ibFCizQofEjgGOwNVuiA+vqaxdpWO52tpiem0P7pPlVqXWMBCwK5T3A0cP +WJXNU2PXMXCtaf+939t6YOp+4VbMBgZ2Pyxp1OHrQaHEvcqHGxmY3ntZOEuw +Bxe2c37as4mB7I6xx+wiPWBK05CNYmfA2cWx2+JAD2zJ4uH0zQyoHmQTr5bo +QfQrM0HWLQxw9kd6Ch7vgdNvoQtLBB54dnTk0akedFLSKpI4GYiRrD3RK9+D +l6Jrrhwk6t16RC9IUqUHl6Jlvj8g8Ek/xpT/+R6Mtk91+xGYSdodXy71gFR+ +WfE2gZvGt4Urafeg5qNbxWYCvwpJXIjU7wGjSYHlCaHf8Mzp87+MepCZNDef +QdjfN9P2UdusBwaRIuFpHAwshJn+zrjTg5PvzynfI+5frPzj6qa7xP38aXdW +CX89F3xTzR16sJywrkCb4B+NyF0sVY96ILHCzfqAleDLC1mGu9x6kBby29p4 +PQOUHyp5Tp49CHpVt5+XhQEHTWvzI8E9sHZK+LBEvIf833/lfqE9ENx/rZ+X +eK8NKa92TL3twafO53pcv+h4t7akISKuB+72ycd8loh6y994iK24B4liO1rr +x+nwuxn57NZn4n2u8Di3k+nQ5jw6XFHTg3sL+ZkVQ3RM39ELfNjeA9czH57b +dBP5vStxfmKiBwvbUv/pEvmrcO3ZyDitB9wS5i7Xy+mwD/6veWyuBz6Uow9v +Efnft4Y3kbLcg+1Mc7veEfXEevpbKPlvD4783urYTNSfrEOHxyhzLyjd/95z +EvUaNeVjNMzeC9M61aTxWDo6dt9SH9rai+zMf4edoulg1leUHeTphb2/bsnh +SIKvXu4SG9jZi09zFT4biP3QvPnXdpJQL7is6BWsb+gIZ+lb2y/aiwuW51yP +hxL1dSZ7sfdgL6Ty/BsCX9Cx4hhE7jnSi9cy8i93BBP5nmnZ2n28F1djFPN7 +Agg+o6mWdJ3qBdnuzvd6PzpeCu9N7pTvxToOnm9ffeiouf4vrEO5F0IBg9LX +nxP8Fjrk2a7Wi5G3h0WZvOkQayuwb9PohYfc/r8TnnQYbAg1br3ai9Uh9aFN +BA5QsLvUotuLN6I2OY7P6Ch/pC7XbNgLJ+XAy/sJvJAtdrDJpBffR6c1dhNY +mMHC22jeiz6D9buNCawtSl3XYNWL+CTKWjqBvY3KvtbZ9SJkqxh7JaG/8M1b +au2DXpjjPfe4Fx0zHQ/aax73YqL2Ue0V4r4CbFfLqt16sf6/rS82+xL8qCyR +WuXZS+zT5tk8/nS4OrO9rfTtxe3ulUM2gXRk5k15VwT1wu1Ufh1nCMGXc1UO +n18R/oUNcq55RQe32AfT8vBevGeSuXEmjA5VkyeaZZHE+3iaV9W8Jfjzna58 +aUwv/msW5w8j3m+YnZO/OI3wn7+9lzOByC9VxoairF7sc/Uvyif4XMGt4XtB +fi84mW4Ef8gg+HTRvTOvoheZ36ZvSxL5Zd236JPV04sUNXXS304if7a0OWYO +9OLO8TcbrUlE/qilmGWM9kLmomjRWiK/j5eYKqRP96I+6uDzKAbx/h+6fyat +9GJF0Jy+StSfxEDGZOKaPihxjWdLE/VuzBXQnbC+D67ulzLsdzBQ46mSEcfZ +hxqRezIkUYL/7uSZR4v0IcVXeW+hIgMzCuk+mw72wefqlT9f1Bg4xxuf4nik +D+M8rB7kywww14fOqcv24bG81dO1Nwj9UQGchehDRoJGseBNBsofeErtPduH +4rpfh8i3GRDQcNYOutCHns9VfHK2DDwScXD8dbkPUkVPa8SJeanvj1W4mU4f +Do7n3U16yMDx7pvF7QZ9uHo1yzzhCQMvU64Pyxr3IdajfY2gG8FPT7VW42/1 +QV0tO3W9BwOX9C8KbbXqwzv60yldTwZSJZWVnO36oCd2+MpGbwZYWU+bfXlA +nK+JT+N6zoA5Wcr76pM+iNjxUK0IXJN/MKnMvQ8T8RxrNxNYOEi4Scy7D9Gn +P+rNeRHz4C1+xiv/Pny/ZW/ESugfkePi+BfSh1OzWS1aTxmQ5WaTtAzrQ77J +6vtGFwbC6Wuu9r7vA9d+Cbabjxj4UfXrvsLHPtyT+xPF58CA9rvF16kJhL38 +IMkvNkT/uEcr4Enrg/P36S+15gxsOU8deJrVh2/Je89mGhH8LzTwh5Hfh99T +fns/EvNj08+OXXqlfZB19it7dZEBsfYGVFf2QY3ZJvOZAgPeCRUmEvV94N42 +88/6OAOKOpnxLF1EPEs/9O/iYyBKPKn+bn8fxEiBnmSin62sjaYNDvehzXXv +SBDBt4XZwYezvvSh1Ji1I6OXDh6/55cFZvugGD5yYjfBl/dN3O49X+pD5AvB +sYfEPCLBeTfvxt8+iKtSlybdCT74Yt7fwNyPmAvr1/29TdRrudGvY6z9mDni +XsykSUe8zaUzbNsI+a2V8T5+on6bD9fmi/XDWXbrzI64GTyOEf2yR6IfT/7I +nZt5NoP+R7s2Bh7rh4nNm6560xm8FNuscVO+H296/s6V7poB8cY9W7T74YBU +UW1fGn4opE7cduuH5MDWtjL5aZTG0d8/9OwHQ6e8YGH7NDxYxbW8ffshKOYl +2sL4Ao6OtMrYV/0w2pIjG/v2C/b99ylqNLEfxxUTfGkLU7jmkqWn3dGPPskz +5MmoSQhQF7fc7O3HKYrjzVsPJjGmIlV/b7AfYlK8iVLqk7BlzzkRPNGP+I9M +A+TfE/B+n8vVtNyP/KWKmugbE1D/962R9Jc4L/0pOEV6Alw3Tzz9wkyC3s51 +8Ve4JhB1MH+eZTMJIjfvK0Y0jiOvqKAFe0jgYvNw5FEcx+Ndy88u7SPBcHhU +4J/QOBSeypy+cYiEm+kbRuvXjKNFrSj58QkSBJgS+7fXjeFl2i9jX1kSmF0P +6yclj0GPU5Y3HCR0rZR4nAgaw0R/sXfeeRJ4+CyyrxmMIeX0nzM1l0gY9dpw +4bviGOw+nP7epUXCtPTW5NiDY1gxL725cIOED+JbRxX+UVHVtML/z5SEEfU8 +LWk6FT4SZ7o23ybB7FtzqzqJCu4fZQqH7EkYK3rZQ86jYlB/9eephyRs379m +xiSBiugy+Qw1ZxJqL1hxs4dTYb7HzVz3KQmneB9GkP2oEPf6vMvcmwQZ7oFb +I65ULE3/63HwJ8HVxGF+nQMVheoKAc9CiHgcT9DSt6TCNdNd+eVrEnTOl6r1 +m1Chwl35O/odCRcmX+9xM6CCzWlNdsYHEjI7bNsua1PRMaR4pzyOhIWU7pFz +l6kIg4dQazIJO8jlLrcuUmEYW9U/9ImES3dHnBPUqBDesDZ4JoeEpKLfF1nP +UTFtqaz6q5AEW9WX/56rUvGp7dnfDeUk2EV5XxEm5A5SNbk81SSo8azEdBP/ +mx8Xin7RQILsl7BnZEK/3klnf/Y2Eu5Jh/SLaVJxQYbk+LybiPfUSk6yDhWn +ZY+bMg+QMCd+ouK6IREPuRANl1ESDnGFnpIxo0JQniGzPE7CHR6zn9I2VHAq +qIncp5EQYv3DVushFcxKcVvm5kiI2TtW4OFBxTdlpj+3vxHv7347pCyIismz +hlPjv0jIL/9j8uc9FQ3nucsGWAbQMM/KZlhERfFFuyRttgHs/F1xwrqRijSN +llftWwbgwNrFYTBIRfAVT8ta/gHECvyXn7BKhbsWRUdBiJDXr/+xsHUM9jpy +iiWiAzgults+LzqGa/rfdmRJDsCR5acu5fIYBEzMaiNUBzAxcvyJfgqRf3Yq +Qg72A9C/+bX5y91xRNhHb5p/OAD5/p2ul33HEeiw8uOOywBIO1WsSmLGYeeU +2/qfzwASvj/jcewdh7S7yJOLUYT8Em/29VMTEPNwN6+LHYBfpblq45UJ8HsO +X1FMHoBdH+UB484EVp+HiknnDsCyPrRS8u0EaoJZ+oSbBrBVFzYtSxPIf2Fc +Gdk+gIPX7zkysU4i6VVpGm/vABGH3u5UgUn4v3F4xkEZwJLqHZXLKpNwftth +6zs5gJBjqt6ndQk+eC9uwEIfgOqAwZPndyZx9cOE5O/vA7gunO1zMGASKh8V +BB78GQDLmI2LU8QkTsRGbFhgGoQft+PotrRJ8CZqj05uGoQt69hVkcZJsCVn +NhpvHcQUpWfpZd8kVlLY84Z4BhEmM8WjND4J8qca/849gzj/4tFHvd+T6Jhl +YUjtHwT/WUu/QJYpVIifVQ8VH0RAXPBjZo4pZFp5pX0/Oojjf5MM8nmmEJ1S +y64rPYh3bsMGSYJTCKGtsymUG4QQY+div+gUnoqptvIpDcL/kk2/ivgU7C28 +Dz85N4ijFnxs80enYJpQFzisPohuy8ravpNTuDq5fu7M1UH0Nd3wWpGdgrLI +uUsfdAexXL6fyUR+CsdvPv/EdGMQNZfv7l+nOAWRmHoOU1NCHv+fyIzSFLip +G+5WWwwizjxHZ6vKFNYJqbWL2Axi85SBhjOBfxj5HPG2H8Sble1t4gSeimwI +/vJwEG1qaxtFlKfQN8y6oOYyiDVJ+66bE/rrd57XTPEYREradNNXwn6hgW/m +Jh/ifG+IV/vpKSS9beS0CRzE7bOlAivSUwgnbbzX9nIQlz51KTsfm4Lvjgud +R8IHIXbwSetViSk8vuZ39EXkINSiuZI9xKZg+brpxVLMIBwMRSkcwlMw6GFb +0koaRIbl7Kvf/FO4uO3i1bz0QRgo9v9W2zYFuav+2Tw5RPylOYz+sk1B/EUz +l1PhIM6c4Nqxk3kKAh2b7g+UDaJjvV5g/PIk2Leod8tWDyLo/fdj0XOTmA1o +efW3lbBXJLDpG2kSo83s34y6B2GJunParZNoY9PQriAR+G9dg1TlJD75tHI/ +Gx+EuBKl3ilxEnaeba9Zfw3izpc2c3/bSRhXc/y4szoI1dQTpgr/TeIK8+Vr +zWuHcLrulEfw5UlIubfzBHEMIdMu027jkUl8e9LxZpvIEBroQz61tAlMFHMu +Oxwg5BHsLvH9E+j9panXJzGEAEGVBzK1RD097OR9e2oIJJX1zzw+TMDpftdb +wctDkHFkWpzXnMAfy573Bx4PQbs2w+NI8ji0T954IeE2hKicpVP9oeNIWzPl +fcxzCEsjsuP67uMwCv9570zQEFynVCu/XRtHZS2/2pWYIbjfPf4+inkcz4VM +vjk1DeFZ0Ng2P+0xbOubVW/gH4Y1W8yK2BcKDiluWDUvGcZU4jdFxwri3imp ++0kVw9hXPLBtyG8Ix7k1r5yvGwazPJ1dRmcIcl/C4w51DkNx21GjERqRF4EH +Ly5MDeO7xtanU1yDsB/QCH/ENQKGp5SXghkJRfdCpQLujKBpxXi3E7Enyg/J +GP61HUGkxT7Wb809qFIZ8bJ1GMHr1MJLN173oGnHvgFNtxHccsu4+HV/D4bL +Cty2vx7BQlp+0Gb1bjCxDbVEVYxA1aKFfCi4E+di9lhk7Rgl+pa6VdyaFhwP +59hXJzAKUy4VnxthzRAK+jMxuGcUcm25P3gONeP3o15TFvFROOeU7E/QbkL6 +FV8jXYVRPL6y8wVHcgO2rVnU+Xt7FKjI/an8Xy2Yfo5wc9mOYrX61Pm9yzVg +MJq6990fxTqWS3diX9SgjhR3RdNlFH+k95iX1lXjUaaeRuyLURjuy7Ajy1aB +/F+FyvniURSuWxdgmFmOFp30tUafCf3puv5sLOUovPiuyr5mFCxhHrFjBmV4 +Ke2gENE2isa08PAXXKVwO2zyL7N7FOw9WyWT7pfAeu+l8lrSKFaYXI/eJhXj +7BYxufmxUcjHvxYyTi+C1Lrtf9ZOj0L6fXtKz64iCP5ZU8w7Owr7k+uyrV4W +YnlqSFrp5yiCfrBb3fcpQGp58LHXm8hwrXRZP5iSh/Bc56VkTjKkQl7J6SIP +nil3ssq3k3HLm0mtmpSLe9HX7Lr5yVhTY5Yh9TAXRmHKR6Z3k5ET7xtRyJ+L +iwGScysiZFiRlhvNq3Mg47ErfetBMhia03Ya93Kw1fbnwdPHyRg7lrv773A2 +Vm9O0C6fIiOcX8px9F02ZvQ7k8zkyZiMvVYlZpSN/svlFo+UyTiifil/fF82 +as6m7gtSI6Of7+fu7d+zkHU6fDJGg4ytj40HKxqyEHXUK67gKhmj739/nv6Y +Bb/99jdbdMlgYbhFBrhn4eGu/4SphmRs54kVTTHLgqmm5LVhEzLsX1fKRl/K +wqVna/z6zcmQ+ej+s+1MFmTzu8q6rMiIvkbZKiGVhX202MVWOzIUyhwP5BzK +ApfAA9HGB2RwHpKtuHIwC38vqerXPCbD+Nyh438OZ2H66Y7Az25klCdOFkWd +zEJP7nRFsScZdR936R1QyULFl6Jveb5k5PpsnfC6loVUfn+xrCAy2kW+rUbY +ZCFMw9Aw7RXhX50Ot45vFjzcD4ckhpPhTA3Rf5mcBduc1eqYSDJScuTbTrZl +QX+q/WdkDBnFMwVnhH9mQYXv46G3iWSIDccpSolkQ1Ld/r/QNDIk1KPPKulk +Q8BN+VVwFhnP1Ob9D/llY0M2d71fPhm7uTWP1VZlY3RHgcTTCjIUIfL2unwO +mi74mDrXkhGSwL1/xT0HeS76YQ+byCgd+q8htC4HAeN//tr0kOFmsm09RT8X +TjytR+8MkNHTe69hX2Iubp6PumU2Sobdjt3rg37kQjZDodVgmoyDvh6pXe/y +MP3YK+LcChkR3zSKrJbyMXPt0O2PTBTk/CIr/j5fAOOFbcy711KQndmkkPqx +ABf3Tp7gZ6XA75nrV0PNQgj7Po/k5KKA8WTtsmhsEcKF7aSDuCmQeXk99OfX +InCU6nVu2kH8v+LsmahUjF9zB9ZtEKCgQmv0nSNRT7Y+XB88BQncVx/+T7AE +E3v+yDDvoUBIprJP1rQEHdot1n9FKRg/cXpf5EgJVOdy1z8Ro8D3fXXWke2l +KH0eGb18kIIJg81ZF9VKIbXHW9bxMAV1MyvGSY6lSCy27fl6hAI167HOvx9K +IaCta3tPigLvjMoN62pK8XIWrPPHKRjufcfvNFYK1udiMdbSFFCj465x/SmF +q9BWuZlTlP9RcKXxVH5dVElkqiSlNElCKir9I9mUIklCkRBSqWQomg0pKpUk +ZU7RnCkJmbYpRJkJIXeenntvKlSk97wf1+8855y9117nnLU/3As/XY66xCiU +wc93vzuPGA+CvXGhaa5qGRyzp/uxTAbhKdMhU39RGQxSDdMOmg2CD+fYWOeC +MtgT+SZjcMsgHO2JdXGfXQYNi1I2uW0jfFVcFN+TKgPTd1c+f7Ek+6fNZ2wS +lUKB3YmAfTsGIfvb9rtLmktBl9oj93nnIKDM5yfyz0uhyMEao2wHoWGBzcyj +gaWwpWzzKRN7wsd6iTfU+lJoWma4/PueQVBqelDmJi4B5+jVX544DcKzbRm6 +UaklwB5Zdnvf/kGwGh3ibTIrgZMH1LYouA2CtdfPIeveYpioUxqtcB8Emz9K +p6O9i+G63rRXgQfJu2V95m+/4B0oJ/5z0zpM6n9b4sp8r3fwcNKIUp/3IBwb +cIhf0VoEuseo2tvHB2Fn4p+A0TVFUNRGP7/Fl+hB57DyieuFYL6xZ9Wo/yBI +uvL2h3YUQHNGM/3lqUEYCTk5R1O5ANiBpVZK5wZBM2jyDu2AfDjZnzfx/sIg +eHdXvomOfgN/t77IOxcyCOzdWjeSHuaB8pz782iXB+FeQv6Zb+m58DD0ZlNc +5CAkpM3Y0quZA7rc8HDL64PQ8/VHC38oE7a88+PnRA+ChO/U4NsWz6FpyeEH +B+8MwoOAC1l9bU/AOcrFbk7cIPxZNKD2ZnsGnNy/vTgkcRBASzayfDQZHv5V +j9r5eBBSJFhVPPlA0D2sajLp2SDErJeVujNsi4VN07/nvxiEm/HDtkZSwdiU +Nr5PLWcQ1D0HTIz+3sW/Zl3agneDkPqeG21s/wydI69/uNY8CI49Lnkfat8h +WxQabNw2CPKye+ZsvVuCAY6n9b91DIL+hy2d3ANleE3rYKJj7yBMMfpgXnCh +AgsajI9qsgZhh0Jq9gfpGpw1/ZtMzZ9BqBc9OL3gTQO2lUVd3f53ELZ2X5dk +Hm/EWJ9lU5v/kXo3+XO4iz+iUoOzZO8UGlgYTGr/GvIJ284OXzogTYPW1cl/ +TyxvwtjlMRKsaTQoME39drKxCZUi3v8VK9KAHjHJO25yC7atdb8YNJP0eYHX +35nubMFY+p8/f2aRvntvtqHtvRacaar3S0qV9HFrljC2L2jFFlHD6RvzaXAk +4g2l6NqKMamHhmcspIHRvesjVGIrzhhL+j5/KQ2Omavm58u2YcsLg4BHy2ik +jzF1u2TShjFOLWJNLRqcf31JcqVfG9pKH/fN1KGB/PbnX1+ltOH0Aimh/koa +eGz0sv9R24ZNXg+PF66mQemmd7zfwjaMnrWRb7yG4H0jLoUz29GmqtO7ah1Z +32NNssaadlQM8OdY/EcD23Grho272rFpkdzhT4Y0eL/Ya8cv73aMbnrCtDOm +wc1J7LK9oWR+sOnBbhMaWBeNTtoT244Kul9ormY02LkiyOj7o3b82BvkzthC +g/mUW9Oq7Ha8eX3GV2/StzvLVB+VL2xH6w2vXEWkT7ecsnDiVmk7ynO29p0i +ffqRwLVVheVk/r1B59///x0I31X/dhmZb36hJ4T07VOX75Wd/47M/zHbaYo9 +DbprA3YefN2Ocum5XddJH1/csc8o4Gk7Ntju2DPdiQZnfhnu3JXQjlH/WO1x +zjQwW3l047Sr7WiVHWY3z5UGiqtviV+dbEdZ1/mtaQdocFnWKGLrfjJfrmDX +Mk8aXDw33ZxlSuYX2za99KJB6vc9SclLyfyjAmu9IzRYeXvBnPOS7ThtbmTj +26M08F9GO3h3sA3raxdbbfShAXd17qax4ja8FlRSX+FLg057+ona2DaUaf/2 +vvEUDfY7Wkp9NSLfX7phvvs0DbZIvvjpLEe+19Os7jpLg0BHDcP4nlaUjt5f +QQumQdH29xWFfq04dXtt8ehVGvTU1T+7H9GCtaPuhsFRNNjerfhI3qIFI5+O +FU6+RQOr6gWXNKRbUGqK/luFWBrMo+aln5BuximYnLM0hQaVOYoDLYyP2Gts +bvn1AQ3ylj5WULb+iDnF1GDSIxroZSy5fP1NIzoXbFJSekaDg9SZWZ6XGvB1 +1tdAiTyynvrueSvV6zFyxTWF0nwaeIew53reqkOXF3pPzxTSoIqmIhX4pxZl +nlz6LCqlgc5F5+/nvrxHt5SlRv11NAgfM6/tq6zGdfM+tiU00OBtxCnOR/Nq +nJYQeNzhE9HjM50jih+rMP/u+5TGNpJ/jmdtGrcSo2b6GlztJHo+ft73TEgl +ut9WadrcTQPN4esNOaqVKHfjyL93/TQY3GS3aoNHBQ7KzEgIGiT1GVK6Ma5A +7o/IIj19Bg0eJrdrKYcj3pzi8YFiEX1/u6CjNVyOnuHTPJ9zacQH7KLfCyrH +DRJ5fw4KaNDh+G5JkWQ5KoQ4310kokEiy+YhI60M6WOTdb98I/Fv/NV72KoM +i869qrn/g9Tzhe3IdckyjB61d7UbocFVj72PoxtL8WDQ+LDCbxrc/xigkJte +iht+PI7+MEaDvvKBUvXrpeQ87lweMUGDkeDQGOXQUmSKhtF0Eh0k7izKzLxS +isU+D5zGJelQc0LHXy6pFGP424YKp9KBqdl9ygpL8ZC3+PqpaXTSd7SEX/xZ +ikbsePXV8nR4fczsQZZhGc7wMi3hK9Lh0eyjkxjRZcimce2fzqSDVOZV7fk/ +y7D0wB3KQ5kOo8/+o+08Wo6x/YYRC+bQ4Uziol0+onI8sp++oEeVDo3nfkh7 +XEY07okqiFOjwyS9vpkyyhWo5Lh2l+0iOtxlLXi1wrcCuR1fOHLqdLj1d6+U +dEsFltldCavTIPnc1KwMN6xEb5vO1yY6dBB/u9svUq9Ck4/BVn906TCldNPb +R+lVOMtKk/F2Nfn+wG6p89rVWL71jPJKA5L/tPS3k6xrMK56URb3PzoYORpM +uHJq8KhZ/dbHRnTQk0qrMrz+HpU3qZ6Zb0oHVb3N4Tlfa/H4upKeaTvosKtC +/3N/6wesaOnMLNpJh0gld+3P8Q04+8S30CO2dHAecsgK8GxEfLJM8/0eOize +9bUkbconnDUn5mSYOx2OuTCHFm5swZLfXnKjQXRQ6oid/k7QjjPuhw48OUuH +73fnXNl2qAMPrUl67XCBDiXatnf1vnbg9OPNjnlhdAj1yruR1t6JB/sMH5+4 +QYdNyZpnn5R8RjlU3MR8SIfYMLlH6/2/oPt+7Rl3M0g+9g5L7Olf8O3oFobZ +Uzr4mDSUadv34QG9c9fTXtHBvbH0WLFeP755xOh0LqDDWOCj9ISeAZQxmXg+ +7R0dwhTfyWTDV3TtnXuxqIToQXNBleTjryg9y0ZdpZIOz4vn6D9eO4j7rxT5 +tjbSQStI6mGOYBBzF7ebhTXRYWbIMWXrOTSUKhMqr26lQ9eewDixGQ1zhtVL +bnbR4efKsjfb42goeeSWtCWNDrvXSjftW0lHJ8nnvSMMOsTsejTbaDcds9Kq +sp6w/88/vVgnkI6O3aP2khQdzrsUsawK6fhqu+fD8hE6PDbxuTOxhoHrdJeY +wG863NikPyTYycByxcEvOEYHJ/tKH21vBra0u86plGBAhZrPzhdJDPzpui+6 +WpYBK0pkFJx+MTDYdK6uuQIDFDZM4R1QZOLUpZ8/1ExnwMmYHU2spUxU5TpI +1SozIEziilPETiaanLS9WL+QATu/7lJpTGZincP0eduXMOD1uj6589lMtP2v +qfDDUgbE9Gxv+FLBRM/xHT8atBgQaaZk0cZk4tVIi2Of1jBAMkVGeosOC1uS +TJzatjFgzVnH/zJyWTgsmDeDfZ8BcXk3r/5dwsW4VE5dSiID0u9ElzGMuLh2 +V36ofQoDNLxWqI7YczEgb6e44hED5rT8tY6O5KLwbFhTciYDZi/2mJgm5CJL +in1zdxUDimbHHLtdzMMrhXnmMu8ZEJvhsmGgnYdLj4aOl9cxQN/YO05SyEOP +j3N9dD8x4Lv7xObihXzsj92xQ7qbASNDYfPWhfLxovlcyfJeBvx5sWbs7n0+ +zh9hFgf2M8Bp9/snKVl83LcvRIdOZ4Ddhcved3v52Lno9bQyIQN64gP5N1cL +MLA1uPLUNwbUTxWFP98iwFmXrc7p/GDAucnngiwcBbibzeDG/2KAMH3RaYlg +AX6Lz31oM8aAlgJ66qzbAry9PdhJaoIB1p6n9qY8FOCnTJX6k5JMmLFuYK9k +lQB93Bih2lOZkJKfmN3XKkC5Gbn/Dcow4cOShqIlNAFuP7X92U5FJjh95vVx +/gqQq6FyYMpMJrTlG80/LEfh1S66SsksJjSVqe2xmkvhe8OLkVqqTLCcJsM3 +06PQS2Bp8nU+E0pq4y87bKRQMnX2yL2FTLBOTY9r3Ephug09y3oJExIu9Lo/ +20WhmUTOIUkNJoxylX24ThQOvr6woFiTxLdk8bnbHhSGHrTs9NdmQtVJv2up +Ryksq6WZD6xiQsS+3t4fZyh0OZs9HqfPBM0jslshhMIx7Qv5O9YxYfOmv2Oj +lylM+mLhM/k/Jtgp7pu/+DqFhreUNd4ZMsHx/Lmhd7coJF7si58xE3xjV/+t +u0PhmW9ZdzWBCYPzvQXW9yhUST+/o9+MCYcti+N2JFD41t5CMs6cCSaatD+1 +SRRe21EUoWbBBL3+6IDHKSSeLdoyT7aT7zN2/VR+QOHqjUlRK62ZcPTJeqv5 +aRROXiunUGDDhDT3vN3FBHfqXLxtspsJDa0xEz8Jfq4unFlnz4TVzyccmwi+ +MM8tbtdeJiwdCz+9nWAbpWaVbicmPJ/4dekoWX+JrGmi+34maKy5nqOfSuHP +Sa/n81yZUBCWAU+SKaz/veRBgDsTZOvGLtQlUpg8FLv4jyep78qot8nxFPry +JDPCDzFBpTxm8zKS72Za4DI5byY4JD+7eCSWwtk9rGd3jzFhlW5r+aHbFHJb +9uqonWDC6bvxB5fepLCkvi7zsR8TygvWVWdcozC6YsPqlSeZsEKpVp9/hcJ1 +ufPWmZxhwiRP0xNdFymUfn6joPYcE9y9D5WHn6WwN218w66LTKjwq146OZDC +S7cHNrlfYsI9y/uFkccodLi6q4J7mQmRP17LxB6iUCu0YnNAJOFDJi/3ojuF +Tb7pFuE3mBAY/CJ2bA+F82wO7358jwlX5y/Vp4BC4dbP7boJTPBcHrkZjCis +2GS5920SE5hWD7Ii11F4eKXO/to0Jiy8r35oTIvCN/IiL+4LJvSc1azNn0mh +dWPQWd1yMj935ZUehgAXVbP/5FeQ+sYoalgOCPB7sWPwpmomxBkXHanuFmDi +S8Nwm3omfEwY6aF/EiD7+t8b/m1MKHrleKurSIChlhFp+WwmaK12MqXuCLDN +zdtFj8eEQ+VjymduCVAjaIdqpoAJGxQNe2ddF2DDo5l3M74xYc8yu4+XwwSo +PJYaGfuHCc7zGV/N/AV4eOalLYp/yXm04re5+wjw3XIviah/TDgbGbrxrrcA +3Rx0zl+awoL+hu/P1noI8HlWwQl/RRZs5W1tPGEvwD/ViTrUDBYMCo/OWGsr +wJ29FzlHZrHAuc3da/pOkt/ULR4H5rKgbcvqiekWAjRfoLnwyzwWuA9YfTQw +F2D82mlf9i5gwZipb3GQmQCN3ZsdbNRZMCVT/o2FsQCjT+fNbNBgQVd5ZPUX +QwHSbt5r2rqcBSmUskT0fwJcl3H2RqU2C+Y9uXP3gIEAI9/tt9yky4KmqbeK +dq8VYHezidS7VSxYdVDu3SF9Aa5gL6lap8+CWX2rRCnkvgwZnxKau5YF8cs/ +4q+VAmxR4m7UXc8CQQI/47yuANW1G38928AC9dTVCzVWCDAIst8u3ciCboEB +jmgLsH7PnZNpm1iworRl6U8tAc7zCVw935QFigc2/lxAsE+4I3V/Mwt0cg0Y +QcsFiAlGL5S2sqByQCHrr6YAlXIWHI62IOstSlApJNjrvcRSWSsWKPCVqQyC +C74wvkZYs8Ds+FSJWoKnfa9NmbSLBQYjw9qLyHouMi/3Be9mwWwDna2vCc5e +eEvltz0Lto3ZrA4h+0sY+LcH7mWB+YPpdVdJvPY77GO+ObGA8+Exv1lHgE89 +1u/02c8Cw5a9p51Ivr/OqMpyXVkgf2l489JVArSKHq896M4C07RtGmv0BJj6 ++Ovlr54sSFD24USuIe9HcZXp/kMsOK+wZfdSwv/m1id/u46wgLaqTG3aBgHG +ca4V2x1jwdrFBr8NNwqQ8/f4mSYfFqS9wGuFJgK8qbNm6H0ACz5afBl/sE2A +A6azs80CWVB0aLxdbocA9R1/HSs7zYKzGmJo3CXAKye+LDc8xwK0Vbw64CDA +rsvlzPwLLDiwf2/3NmcBaic9eqQXwoI186u3S7kL8GLuFbfMMBZU5eV3zTss +wCX9Vt0ZESw4Grg+3eaUAKOqNubsucaCD71xSQoXiF6f6UZK32DBjL0m/usv +C7DqpOK64zEs8DSssK+LE6CO0z/ZBXeJPjZdyV/9QIB3N32jNd0j+RdWxk1+ +Tuon03Z7TTILJJZZ6rJLBfhRWHWYmcoCy19y4cN1AjRof7Pp/kMWHH6afMen +XYBTH9wT/H5C8t2wMuamgJyvtfssKnPJ95+NTnospnCGqtXCU2+I3jO3PApe +ReG5CaNhjQIWONn2p30zptDqg1rGtRJSX9ub4k/OFArcBid21bIgclvPg3Fy +X6+KOlIw8IUF96c8f6uuLsT7fk63YgZYUHxT/vKLtUL857DdazONBeN1RzYa +bhViy6IVSk/ZLHj+inq3z1uIAW9FJ04MsaDAM3UTK0uIvUlfzRf9ZIHdldaC +P+VC3BzWMr91hAUyNasCGM1CVNqR92HdOAtUvQ8KlYaEmD8YtGx8Kht2XN7z +RUtPhGq1h8ezprEh+dox3zkgwohXju0H5NnAT1ArT98pwr2nDS9Vz2TD4Lns +L0FHRVi+X8cpSJkNBmmey1+fFqGm2fzVy+ewYf23vLX+l0U4Kve3L0qNDZRp +4QnPZBG6DwnfGC9iw83M57einoqwvmsgSrSEDcfB33nxaxHqlTZ7PNRgQ/kT +2uDCEhEmPKrYYLecDZ6cC36XakQocfX19Ck6bLhi+jVxyycRHvVJZ7/VZcOv +FQuNPTpF2Lb7btmR1WxIGGQHd/WJ0Oi/K3Gqa9iQmhTemcYQYZen6vrUdWzQ +MnEQ7eWJ8FR09ufF/7HB3v2uwSmRCGcUbzn32JAN5pmL73z/LsJMVvc8LWM2 +aMZwtNtHRGg507f0lQmb3P8OJ2b9ESHLWNJttRkbDlk+U8wbF2G4d8K/vC1s +sNm+UCZ7QoQL41Y+Wr+NDZOHx5OnSoixGKs2F1uyIX7T0T0lBDsKHJmbdrAh +bPGSaR8J/qkijKjcyQYabWrXBoJjNocv32rLBpWjl5dN/idCXd85H+rt2CDW +K3+l9VeEHxIzj1nvYUOe08sjWSSew+/N5FscyX4h3PQ7oyKcPNSVZe/Mhp/q +wUNdP0T4QM1n12cXNuSG7tcPFYtwo+WkIecDbKgtrrl+ky/C7lP3Ywc8SH3S +LhybxBJhYNqKdZ5ebLg39VPU4ADhp7Gik3WYDcamJ7i63SLMGtlz5uhRNsiL +dGp5LSJk7wwr9vdlw5pt9a7VFYSPc7NdfvqzYcrwBy6nUISLnrz8e+YUG6q/ +n4y9mS1Cp/EO09CzpJ4Zlte8k0TY+FK77lY4G66ZNk4f9RGhd1e598wINmSa +KXCeuotwymQH2XtX2WBdNVom4SBCk30hO1NusuHkL15ug6EIc6Xb21/eZ4O/ +T9s978kijPO6OFj3kg2btp9rir8lRL2YmeE7stgwNCEy/RYixE8lT5c257Ah +PLV8jou/EKfOaj3clc+GkbEF867ZC/Fs5TIhs5zEyx5+QZ8vRGVhcbR3JRve +77/NvaooxNdzbfWoajasdFxUFDBJiHy/86d+1LNh1fOnz7S4xC8ubP49qZ0N +cQFuZ3PeUaioevJtSScbdOZNjVyWTWHlrNkBQd1sCOGZpMzNoFBz2n4ut58N +6ZtFD69GE/8qOZGRPsiGJ86N5+QiKIyaeHjAhUHOy5j2CjXit8Q/2F3NXKLH +lRER4uPEf4uux14XEL3kB/UVeBF/xdO12SJiQ890+0PKbhROZTZP+/uNDT5z +h7ynET9eNHDyfcEPNhS8FFXdt6PwWM/sS/4jpL5rYmilOylc0FFkrPObDfsv +CN5f2E5hS9P+X4wxNjz+6DWlnfj98A8Tb1In2KAoFfy+cjPxgzWP/BwnceCW +8bfabaYUcsrNV8ycwgF3DQ1XdxPi199x2A1TOZCvwQqU30T8V35U+pVpHKgb +9r9nSe7LieyVbibyHDix7hN9JsG5L1pUfylyQGqd9+JDBHs+PtX5eiYHamZN +zjch82enqdw5rsyBQdqX50lk/frEd9bL5nCA76rzJpDsfz7ORearKgei33xY +W0/i0739rzpBjQOnd682jiHxD1xPD7VbxIGfjfdj6ywpjLmydaO8Oge+Xj9c +4G1N4ZZQ7sh7DQ5oNtYzT9hSOHLuRl7ocg58Px60oNWB+PnAVb6GOhxQefB8 ++c19FDr7tWr/0OXA41eb4xMI3wrHAlmZqzlAvZZvEx+k8OSBYpfFBhxorHM7 +f9CPwo1W23ZIm3JAsS38cxLx1yJz3tTKzRywj3mmZUT8+EO4WXV+Kweka2/F +Coh/n2LQZiiy4oDe4u0fjhC9NC1y0+rcQ/iw15T+V0Zh2LxJzGgnDkjkbj/k +XUPh2tmP0yz3c8Bfccwts4HCBFm+Sqk7B4oTjqx41UXeJ6lbbUEHOaQfKZJz +7qPw77/V0asPk/Gd7FeNNML3cJBUxnEOHDtpKkMXUKj8bW6liy8H1mx4yrn4 +jcI6fslFlQAOnJV+1lH7k/DNctvQcooDmx71PCn5RfgenPTz+mkOvNcwi3Qc +J3z3Ps7Zco4DTTf+jt7/R/jutDj+9wIHPoTndp2eTN6rFr5mYQgHxp/H7fs5 +RYjDDbfo/pc4MD1y62wFaSH2yXV6j1/mwNzAmjNPZIRYZa0mvhrJgUxtq1b6 +NCG+uHUwaNZ1DhSsG5SrkRViTNPLsQc3OHA4/PJ+Szkhnp7+/ZJONMEKO038 +CHa1NZQpiOFA61/PixsINr8TFm12lwN0h7zlj8l8nbY65U/3OMDxDkjOI+vP +mDU92SmBA0vSjl/wIvuP2u9dwkziQNmYypviqUIciEt95pfKgRbLwMACEn9N +J3PlWBoHSsuL1+8j+b1U0c2PTOeAhmlL/mOS/x3HU0ZKTzig4HVbkET4OZtQ +XJH6jJyH7L45Jr8pdOuZZKH9ksQTdjM/ZphC83nbP+VncqD5yPyz94YoXLE/ +xt40h/CZZmS3S0jhr76F7o755LydXDhHzCB8LzjMphdwoOTvP/aXAdLPu2X5 ++L7jQNdY3p0bPRTGDm48F1HOgYTTkiu3NJH9l1z+N6OSAzbRLo729RQe8GyI +SKnmQNGVWR/WV5F6Mp1i39RzQD7azfr6WwprOUGvaG0c0Cm/N3WA9MuZWmX6 +Jzo5oPwdimXiKLx7dErRr89E3+HBkrqkH3cXxNZM7yd8LVEO9gul8I8op38T +hwNGV0pn+pL7anD16MEPPA7MCLh4lOZK9OVvwnegiN69vm0+6Uhh3PePI8eH +OJAs93H9XyvSf4/wpieNcUC278ySZaTfU/lP//6yCQ7IyPVafyd+bPzMWbXX +ElzgpA/b/9GmkFGE6caSXHCIt1EwXUZhw++p2vVSXMDFrnNriZ/LNbLJsZfh +wkRz4ZdoNQrjL9wz+CrLBZV+v8spcykMKe0rOabAhX8zHv37pkyh19+lm0em +c2EsZL1kNOknrUyO119S4sLwHNbkIEUK9UPzbBRmc2HFsMu6Z3IUzq343ZEw +hwvPZfNuLZtG7jsJs/0a87jwoHq85ttUCplm12g5alwI7ltjO02Kwsbw5iMb +F3FhQdqGQ36SFOZVq4hql3Bh62mdP+qTyXme4hZop8GF26kD75dOIusdnGPQ +qskF0cJJUoESJL7qluFd2lxIW8oABYIb1KMKmlZwweeYaYTonwD1wrec2bmK +C/sdV2apkPH7tPH/Pupx4eKWUOcrBI+bFvyyWsuFaFnPcQOyvudDv3cfDLhg +EaXaok32r/+ndd5yAxeyHwnpriS+VQfoRnVGXLg/D5RbppB6lSePbd3EBdWa +6jkhJL8/C/aU1gAX8uicM4dkiB6CFYO3bObC5D92CZdliZ766jZVmXOB23Gr +qFOe6M340oSpBRfqY+tGnKZTOPrnR6iJNRd23EjIZRP+XZyzTMtsuJAgZ9LH +n0Nh1bvDk4x3k/1DNt6cNZ/C6LM94YZ7udDiWjVes4S8ryPlEevcuSCh/J+x +hR6Fe4eu39AJ5IK8js+ZChsKS223WL84zYWXvxqZAeQ9VM8dl9c6x4VA38xk +pb3kfvb1i14WwoVM+fvr5hB9OjRp7XocxoXI7Odqp90pLF5Jn770MuFLyeZA +MbnvIyiHO4uvkfk/fTr5Rynk71C0S4si+ftL+bX7UGj7qk5p4S0unHRdvjaJ +vAcFspfaU24T/amFt206SaHaMaO4+bFcWKtUvKYs8P/v7Q+HpDiS75UUvzln +KORqZc1WjSfrNy/q23GOwnzOoniVFC7IiIyfmwVTOM+ix/HeAy7sOv20bjI5 +b2FPY+cqP+LCn8aO+6lhFLKlrHtiM8h6KSuvKIWT9/iQVNLMp6QeSvXrPS8T +vdWUO8c854KdK+/WrStEvxpn509/xQVHT8uH94gfCbms33criwtJ+XNLLkQS +/dL5KfK5XHC37Hc3u0rOw+bHrjfyyPrHJS25BOc+cl0o+5YLDY3b9p0k753K +pDlfrxVyITH0axaN4IvuLWnSxVwYN7pwa8N1Cul43T2ylAvXpCR9zhFsuWjL +EinkQtPvVZynBGeHjNMuV3LhbDWvuprgWQNv0yfXcMEUIwRtBEfLBwcX1nLh +m8Wuw58Jlt1o7uTzgej7+IoD7QRHHpVbu+QjF3SYi6QaCZ6c0KbQ1cQF3+/S +z6oIDqlN5Ea1ku8Fq7PLCf7z070aOrgQcKM84f/7nV6q9eBnFxdSXId+dBL8 +fbf47IseLtR+0N/7h2DfsAJ7tz4upN+U2WcQReqfHbxq1lculN8djr1B8OF+ +82n1NKJHzzV3Jt2gkCYnz7zIJPXbfqg1mWAXo/ZyfQ4XDrB2lLjdJH7QOymR +zSP8Hj6YZEPuU4d4j8Bkigs3Te/F+xG/2PJea5etmOw/Ksp7T/yD9U+xttR3 +LhwsPF7mcIecV/XCKcU/ueDh32W3+C55T3aHfPUd5YKzfmP7CuIvMHRr8dI/ +XKhyHzhwPp5Co2z5e93j5L7z+9asSO73gr52v1v/uNAakZ8rSKFwjVyy1ebJ +PBCF+G+a9ZDUw9Bz2egUHuwPGXe+SvyJjre2RKY0D57Ok7m7/RmFT+9/63WX +5UHo5FfT978i5+t94dvZCjxwKd4WX5pDYeqPkJiG6Tzw7iy/5ptP9Ka+7Xio +Eg8S6uS7/Yl/jrNV2LZuNg9kl66Tqy6n8GZW8ljqPB7Ra8s/O+JvZPo8u+wW +8EDCKO/OrRYKr8jqvJZezIPEt3OezPxM4YUjRYcDlvHg/lL/Pj6T+N0lna3m +ejwIe/zW5oykENm7UjJ/r+FBy4XH/+4TP+AZcvBqtgEPzGvfWvXPEuK+L0PG +czfyoMftYF21hhAt7yk+F2zlQTk0VuhakPe+ujP8oSUPfr3/1FK0S4im31Nc +9+zgwfNgZ8ZKJyH+t2vFLLTlwU3Lh6uySf+eF/xdeMqeB4fvZ3g8Jf3Hqsx3 +9Vp7eXBCITHJ46yQ9AOWIbH7eWAlt3z570ghpv83fZ+FGw+cPV5vqCT9zMLD +XWvH3XlwXNW4f2mcEJPiUhVfH+SBTNKuDpUkIapUe/EOHeZByfoZtNtpQowd +WlEz7ygPClcHt195LETFxT8eNB/nwecZTXcEz4UYZVN87oovD8JV2EuKM4Uo +FXzJwTCA5D+zM4+dI8T8Ieo3niL1WSHptzlPiF6HndK2neZBSqax3KR80h99 +qTb/dJbkN7ZBdf5bwseu1Xz7Czx47fH20HWCA2uSbvcG8+Dx8an/zAnWMJxq +4BHGgwObYjZakPkdWQG9nHAeTHFZXHGdrH9FvT/UN4IHSWeXRk7NFeK6eMtl +w1cJH59f0wpJfEy5/IYLUTyomXTiagKJPy5skf/kW4TPm9qxGRnEzw1Hzb5+ +mwfstgPXOlKF+PPoSPH0WB6E5Ll5LI8X4uMBD/f7cTxY47sxKuG2EB3sP0kt +iOdB06zzfI2rQpxSv+FVRiLhm3OU+yGY5G/82FYnhQdut/RPRJwi+b+ePpL7 +gAf2jEjuHlJPZc0Lyf894sHDXEUHIxeSfxLbtDyDB9EJ7uvXED0ETrdjmz/l +gXj01ZNNZiT/K2U3Gp/zoOrBn+2ua4R4+URcV3cWDw5ld78dmCnENfR/Fw7k +8mChRMRbcwkh0vceX8LO40FDoppLHfF7m003+/wo5IHq353X9WvJ/TXr2yTF +Kh4Yxwc8VD9B7u+r+5/F1fDAjtUz8J30K57jtdbz63gQGD3nhTzpp6pYqfFa +H3ngf8yTv4m8x+FFO1Zu6eKBerHZw6REAU5ye+Z0ls8Dp3OFTQ0v+JjbpjQx +QfHA58GDS5I3+OhuEZIRIeaBxuxeNPLhY4XeHlHsTx7E/SiR6lvFxzBJyStZ +Ezz4nl/D9Svgod5ZX+11k/gw1/qeYEkiDwepnqZiST7pP61emF3koWlXrmq9 +DB/OFOz+KGHOQ4kXbjl0JT6s8+m7Le7lYi312TdtNh8ikg23hFVw8abe7lUu +c/nQ4C4RLPeMi3OKtmR1LuCD6ferN6zOcLFvrNQndjEf1B8ucFH14GI6rNfd +tZQPfZhzb641F1fVab2q1+JDd/nJh13LuPhTNv1YxAo+hNC+vH2pzMVim/k6 +m1fxQStbPrNnChfDYuN4E3p8YLZkqfiMcHBrl8KLkrV8iPmp9vIoj4Oy8656 +n13PB5VtvgY9/RxscZXQMjDkQ03WstSKdg7ef3SOM7SRD557M7s0Gjnowvr+ +NNuED6e9IpnTajioru1z+LgZH55KW7efLOcg14e1TMucD2F23oUexRzMznVj +MbfxYUdk2qvPhRw89fPz40fb+SAod23pKODghg27vdys+RCp1bTDiYxPXGhY +On8XH/Q0i63c33GwBrcwPu/mQ5fi6sn8Ug5GSZalxznw4Y8X9/VQJQdtLdZ7 +7nbkw8ucC89O1nNQ5UbOEkVnPgwc2Lz5SAsH+5q0aA0ufCgN+jta38PBdKX0 +h1cP8MGAs9I5hslB773z3c09+VA/X03t7TcOrkqKWzTpEB8sda6prprg4M9+ +ha9lR/ggzR5zHZLn4rslVx+cP8YH7upC3Z9qXAw5JOH23wk+BPqvmrZiFRfN +X5xb8NOPDyMJShXXTbnYoueTciKIDzNdy+KjvLl4P5C1X+csqf8RrbkzQ7jo +UuQ2n3OeD4WiyxbX4rjEKexOcg/jQ+qrrxFyNVzMvtywb8FlPiiHXvw62sfF +wLotqr0RfGiuYMTdG+HiP5v1CfY3+DDPO7bk0QoeqrjNv7/tPh9iI/4+mpvM +w75HcXskE/kww5u2NLuQh+kshdkVyXygO6lXHO3g4coTEnGGj4ieOidK5RX5 +aH6RdUc3kw9v9F1G54fxUbbCbTcvmw+v90i4jyfzsUWye8bT13yQmTW5+nwh +H/ffaLi9qJAPyyerz5gl5OPJpJxbSlV8cHmiXDN7twALx5OuVtXwwcZLbX7/ +EQGOu0VeOllH9Ol8prYnWIBXl7oGtX0k+3+vu2HxTIAfIyz9wpv54ODYbvm4 +WIBK3LVH17TxoX3e3qcKnwSYkinrGvuZD1bP7/1liARIUxzZu7mXD7WH0/aY +TQhQM4Bm+72P6NU6Vf4m8ePH2z9apX8l/NH+dpapEj9nUGRuR+eD97YIiVbS +Tw3HZ5hMZvHBWiU5qIL4a6M/0RvyOHw4YKNTdNWI+E+X82s8+STegLkM9S2k +Hy0/pKsk5MPmo/ueRZN+TnbJbs0qMR9sZz3dXm9L/PFl48Unv/NhfcaXtE97 +KLzHWj5PfZgPUW6yiqn7KOy1mKXcNkrOj4fRZQMXChe9nFAI/8OHRHth0H3i +z73k+dJr/vLBeK7XIBL8wrdzEv0fH5zTcozzyPeiloqxO5MFMCgfF+brTOHa +tZnDZlICKPLdqjpC/P7Ze/HiIWkBfFgrxbEi/UD5aDjvkawAnoQ/2+BnTaGk +sy9jt4IAFp2Urju0lfjT0n39k2YIIGDcP1d/E/GfC7d+fq0kgBB76cCutRS2 +h+m1eswWQMHESqEj6UfnMuY3zpwrgHnMPzbFCyh03Sr9vnKeALQUChdNJv1k ++rPv5QELSDwPTq1bR/orzrSBoiWLBVA8tyhzz08B6vp8yGtVF8DU6zai40wB +BjTlZ15aJoBQgf6ji+0CLNB7+FRfSwDB59Nf3aoUoNnw6aQ7KwVw7+DSSx+S +BBjp6BlnpieArp0qqydFEr282xk9tEYAJlTxDzt/Ae4N0QjfvUEALiP3ot03 +C/CYdNvRmVsE4GXS6inu42PO0bKDlVsFkDOD1llZycefjc9dAywFcOfJ9mre +Ez6GxoTubt0pgAVSJ+Y5k/chTnWl4R0nAby0qLmb/p2HZSuuycz0JfmsH1e3 +pLi4vmPOp1h/ASyOaln98iMXcy8+u6N8SgBSqy6rizPJ/f2pdt7cswL4aLvL +Bk5w8Zqf1MpF4YS/4X3J9UIO2r0J373yvgA0xr+VDP9kY+N+JZWcBAEkK2+Q +GOtio/mU9F69ZAFEPS867viOjf/tqTy47qEAEjYqrtALZaPa6L+gjS8FYHWI +zZ0xg433024blWUKYGZAXnfoMAunWy76Z5IjgPg6KWbQFxZOTjS5tjlfAE8/ +BlbKvmAhxyg4aXu5AJTDXDVtdrDQnSF/oLFCAENnbtr5GrCw90bK0p3VAkip +f1O/djELP/aVZNrWC2B+VolnwSgTt0XsCGhrEICttbzDaSYTceUXA4dPAjjz +e8pSWisT80L+lDu2CcDz0/nmwmwmrlgedbmnQwCRDuez1B8w8XGzquX+zwIY +ib12aH00E+MXG7a69ZHxly9bbP2ZOOND/b3BAcL/9WhfO08mRgU4OXvSBLCn +e7T4uwMTL1adYRxiC+DHct75fxuZOHxM+jmHKwD7QdprTz0m+s6K9zkqEIDj +8a1L7JYx0cOrYNjnmwDk96e8KJvBxF75bcWi70QvD4Ju60oz0eFtZ4j/sAAy +mLq7FCYYuG3qsHTgHwEc3+wjLSVkYEX2lY/D4wJYMyK0lWMx0NBR+c6Zf0QP +YS/VPfsZqPt87bwLUyjQ1Lqm1NfEwJlWJ3XDFSlQtq8Np94w8GHldDmjmRTs +6tZ37M5koJ5hFm9oFgWqLrZ9VU8YaKPFfeqhSkHj9ZdmrvEM7E+LiFBVo4B3 +a8aXodsM9Jmz1Kt1IQUb1MKLba4xMGqq2xIzDQpMGnbe1z3LQNWQsX+/NClo +CAj8d9ePgc+HEwZytSlgvyvIjDnMwDpme/Li1RQ8PnswY749A/e6BJzv1qfg +2miMbZwlA9ntivti1lFABU7RPbOJgVOqt6tIGFGQ+r1F12kZA+8acX4WGlPw +JbygbdtcBqrnXWn3AwoGDbe8D5NloOkjjPlqTsG2/t7FVRQdm+e6+sVbULCa +5zla2UdHt5g/O3dZUXDx7mTZiUY6BocayOEuCnR2flut9ZyO8qNtvNN2FOTM +206bc4+OKb7+9av2kPwjT82yuETHYtdXEQ+cKZBx1YwJdKTjyMYlEiGHKBjN +W1VTPUbDiDflAwbeFBTnQIgbg4bKK1zKhMco+F2xpeRsAw3Xzos/7+pPQZm/ +TbF7PA39f8kPG1+goNZ5cV3GShr+83vZ/jOYgt7EI5WflWgYzbHIywyjYLnF +WR3ZX4OY2RXupxZJQct+xdL8qkHk5f/ijcVQ8Kks8cja/YN4Vvd+/Zu7FOj3 +6/Yd3TyIMo/XPjt+n4J1ARsfrtMZRM27vl5fkimYt/xLVeLoV3wrK7/l7gMK +9g2+VTvT+BXNw18s2fHo//9Lw3Gf9OgregYwB4qfUnA5K/Dmrd1fcYh7qezk +Cwq2RLjYVul+xTD3RSk6mRQce5nkME32K87oLj1Pz6ag/ZNzQhBvANN2Oe9L +ek3BJWsNozmNA8Q/jv5nl0/4uRtjN5Y9gOUm91RkCym4dcWG9NMDuLNgzXDl +OwpmTlQdywkewL6VLe3nSole8mJ8rnuT9QQzgyWRgnc6sTKcvQPo+cJe81Yl +BSuzY513WAyg5pF7zSo1FPT/Os3NNRxAnsbnsw9rKZBboXlr+qoBzKTPVdf5 +QMH6pu/nXTQG0P+hc+ObRgpEV8fMotQGcK1bSuCmJgq0lKN7r6kM4Mj8gQV1 +LRQYLr/zZqvSABb3LKqzbSf1yflR82r6AAbHe/j3dlKgnq76NENxAE33ZKh6 +dVPQJb3h+SwyPmUWq0rYS/iMvfHz64wBrGvR9DnTT0Glp002f9YARkV7z540 +SME3zR1zlecOoI31y/IoOgVe5qwyowUDOFOWOqLMosDS7EjaxqUD2FG3cuYD +Djl/vp4e37UHMCHCr3g5n9T/JTPEUH8AF076Ib9RTIH5inVaA6YDSC9fV1Az +RAFjkFdBWQ7gk4unD9j8pKA6cXCzyHYAdX/9fu3xmwK7RUKWtvsAit9u3C8Y +o0D+aXSW8pEBzDsVPCVoggLFHN/lDicG8LQ+Zk1ICGG+5Y2TVScH0FAs4XhN +UghNa1o7jM4M4HjmZgmlqULQrH88mnh+ACuOXXmRLCMEpV2qS8svDuBlrVq7 +ZXJCULfxO3OV1HcbW3o8W0EIlkMnNbrJ+LTH259smCGEol6HB3Fk/kePGzZV +SkJYn5XYnHF6AGMWfRrdMVsIvVZoIfYfQPt+xUedc4SgoWV0+ODRAVRJtrU6 +ME8IbasDLokPDGCvU+wPrhqJJ/LgtEiHAUxV6Ug5uYh8P/H8iRrRi3vH7G3j +S4SweNsVm8z/BlAj1lEcoSEEm1c17vqaA8jZlZgwfbkQfjYbZ74i9X+p8MUs +UVsIdlXJFxf+7UffRjWBuq4Qpl0NSYlh9aP+dbe4zFVCCN+ZaCf/sR9/bnu4 +ab2+EPqW0JzScvvxQtXSmO3rSfymOQvtA/vRJOyQYfsGIRhP1hCl2ffjZJNn +dJeNQlioXDy0X78fr73TMfA3FULLLfuvSdw+vJ+r33vfSgjDC0+JZln1Ye4D +0GC6CaH5aM7O4r+9+OP8D2kPDyH41063HenqxfWOzwT9B4XQpVByZdXrXiyZ +Pv3NZ28heOx28l51tBcnBFX3HY4T/pnhnSYWvWhaf/p86wkhcIp+HOzT7MXa +sAGzxpNCWHLlZp+BoAdlXGOXWQYJ4QNt459lLT24w3DbtPdnhJDzgqYnV9iD +0bP/UGbnSfwMNffRtB5sGcpqKb9I9DJ7Z+OvqB6c1eSRvzGU8FfrPqx6tgf3 +vpydUHRJCKWbNC57HOnBhMgPFwyuCKGcd1ijzakHv3gGH8iLFMJ/TzdfOWbd +gwtBf8vq60L4rFhjumxzD7rPZ2lm3hBCoJ4m/5dhD2aMJshqR5N6O9VO617b +Q94Ta9GTGCGsucLWe726B7VyJdrU7wrhof626X4re/D4zfy3afeIHiZH3fml +24PZ3t6JaglC8FPbL62/qge/masFJyYJYWDXnN2/9Hpw7ZIWd5VUITQofFFe +YdCDp/9eNr+bJoRImwd/0o16sKjnP60Z6UK48EhBvN6sB8feCuRuPRZCnvw7 +nxLLHjSJTRNPeyaERN2ljZN392CYr3175AshvHfQvdu/rwenLi9JCssWQpJM +z71rPj24XdIv5G+uEERi5Rk/g3rw5ld1z/NvhBAsm/GfTmgPNpV0bR19K4Sw +RKvpv6724MyEKO3AIpIvv0dpRUwPOgSaKAwVC+GWy7kHd+J78L7t928nysh5 +bYvdM5bagz26Tzv4KASX8yevGWb0oNo056IjVUJQDayOX/SsBw+wFFKYNSS/ +bbJ7Lr/owfTKylCPOqI/c9MDm172IDM16ODAByEMWRSc1ybjy89rW+z/KAQv +g2MMzac9eGxvv053kxDif09KnPuoBzPX3FHc0yoEevazDFZiD4oVt35vbRfC +hkaF3edIvGsEvzptuoh+14u9q6/0YFBd5rvGbsLfIl+notOE3wz3VMsvQjDR +f2+/+3AP/glVvvS+XwgnrFtP3LTvwU0u9V6bB4WQslzxiY8J4XfDRUukC6Gx +/y3rt2YPVinr6RqzhHA7oUHCTKEHLT/F/zDgk3rTaH8t2rsx6sWOz3mUEObt +WCBv+KYbP0X8K14tFsI2iZnCrXe60c7kSLj2TyEcumTcu8WyG11z1s9cMCGE +B+4ZehFPP2OB8y/FFgkRGO9XpczPfkbFqcXylyVFMOkXvSV0+2escNkkw5MR +wewLvXeCBV04V+afVIqcCMqu5rxoLO3CgDcVkrsURTBHtLnlRXQXqsua/8uf +JYJLV1rr5xt04fm3Un+PqIhAIGLd1ZHtwnb3uj/zVEUwPj2RXzbYibry1399 +mi+CDP0V1jLvOvFKodVI2EIR3HyV/Xz93U7s85T/uXaJCLL2q7T5+XWigWLT +EHupCPSyBifad3Yi22u30FpbRPg92HR+ZieazJgl+LdCBL6nJaJ6RjowvqSD +m7eK7Lc1eW7yQAd+O3yffUhfBJ/6QzcU13egpZITc+46ETgtKBJrv+3Ah2Wq +9Mb1IhixTH/bmdGBv72/fA0xFIGUyKfwUVwH2imn9usbk3H25v+OX+3Al+j2 +hWkigpda96SmXezAyccX98SbET6jYmZZn+zA/Sr0LitzEThsPbFA4lgH5ldm +dPzdJgKzQtYxyrMD5U8casvdLgIZs+qMDpcO9Jq7vOWgtQgCXZQLzjl2YFk1 +95PKLhJfsEVjkl0H+s7z+XDRQQQXf7f3Wm3vwNr3K+tWO4qg+9XDUCfzDlwU +IK6h7xPB91HvRJpJB55Ve111z0UEnj3sX682dGBL3ckKywMi0n/spV/S70Ct +U+vKxzxEkGCQPXWtdgdeWjhSku0lAmsJtRP3FnVg74fCdx5HRJB99ZZlpHIH +rgk6V6h8TARhz/Xe8qU7MGrxxrd1PqQeZ8b35f5uR0bjeN55P7L/yD3+J147 +Gp8pz115UgRdHvqRW7rbMU49LHswkNQnJODbvPftKPxklnn3DBmvLHx0JLcd +t52TfLntPMFHezK3JbXjaHPkk8xQEfiHKux0O9aOthcsMw6EE36v57/+a9uO +zzVlHylFiOBxScujsfXt6Bx8K+VslAjCf7xzWDW5HfO0diWtuCWCuc1F78c5 +bSjXMSNh4LYIBu9KHHduasNSnbi75vdEcP+8hrXCgzZU7tpzZzReBFah1een +XGvDE5fm3H6ZJIKUjXstG0+1Ya1uz03XVBHo7h/AZx5tuLA7KWrGQ5Jvva9j +9+42PH3Z5Vp1OuEr5KR+rHkbNq9aGHn6CeHr8ITfP8M21Or9eln7uQia1tWk +b1rThmERjy71vST6iN/l5LKyDRXOSFt5ZIkg/+tvtyMr2jDJ+4QSO4foK9L8 +BodgTef23mN5ZL3EgL3Vq9rwzQ7DDHG+CLjP9bvb17ah6aa044GFRO8cuMU0 +asOPq6TW/X5H+JrmbvdmSxvuW3x8PLhUBLFHOPe/7WxD9szWmskogiIVuw+w +rw1PSv5362ol0dPdp//+O9SG/36m7JGvEYH7kcQ+r4A2vMmevPBOLcGikNcW +wW04t9ubPfuDCHSEmn1OhK8nH5qykxoJ31rlbtNi23BNybozi5pE0Db3Q3ZN +YhuWZybB4xYR8L03Fn4nfO94ICGj3S6CYyOpMn8etmH37cMtWZ0Eyy3T35zW +hl6XPias6Sb5xkUbrCfzh06u8SjsJXrd90jdIroNQ7wStI37RVAT9l+2iMQj +u3diqOIr0e9SVv/rI20Yb+FVvJUuAsWCm8+X7mhDDcOG8AamCLaV3L3KWd6G +uTp6O3ZxRPCwUSx487cVN6ndn9XBI/mH/4hy+NiKDQrjX5woch5/PDydebcV +9/7zeNwvEoHlNqfhQvtWZHyr8/EcEkGSQEIhWr4V/ekrDTg/yPpndhZ4lLfg +ePvdv8dHCHY8mxV+tAVVCg9EB42JIMbssusf52bMeP5+75+/pF4GWy8q3m5C +vaQVi0IlxHDl8fj8i8WfcHvwaM41KTFY1j52OjXRiF2+rmcVZMSQsKGncmRe +I3q6V5vGypLx9LG+kvUNeHHL7dbk6WJY99TroW9QPU4zGE5crCQGGXVlsWFq +Hd7X3O/5RFkM3ep8hvhTLarPrdTRmSOGmPY4joRsLeZMW/4jW1UMmZt00hvt +36Px2M2StWpiiHuz1TY2qwbrqe+XixaK4VvktRn+qjW4Z8DJetMSMXhNv+hq +k1iN9OZy5aqlYvAPecnvXVWNfpUa/ds0xaAl83ZByJcqHM+LetKoJQZzubmu +dg+r8NrjbydsV4hhRpCSr1pIFc6+v3d950qy/pEXqluDqjD9aunEPj0x5PKo +nR0RVbjqnHrdwBrCz/hB6kROFZYcu3b7oIEYpqxt87cdqkJLF5Ej9z+yPn9f +3B6rauzY6bD4hJEYSt85yQwXVaMHFHOHjMWQ4mbtvH1jDYr0Fr8+DWIY/JQ5 +dU5zDZ5Xjzw3ZiaGuU9U8jsD3qO0MmUWZi6GGuat8JLFtRgnZScrZSEGNblt +1g3dtZjFXZCsaC2Gek85zwrHeryWGuE+YCMG5aEZ4UdXfUAvO+Gy7N2E73rt +7KUSDWgqvUcQ7ED43ucLlfUNqFZamrvTUQzP3zoNnrjSiL/8NU4vcBZDR8SS +D59Wf8T2ZTc3Cl3EcPH2oYh59R8xu/eHRNkBMXycGJ1tvOMTRt3eX3vTk9Rb +x3Zrf+EnPGxefcPlkBgW20xVPq/QhJt/6+zW9Sb1DPI1OWLdhAuzY1XGj4mh +762nVFtQE/72/POl8YQYNI4vTi680YQdczwfJfuT+XGZPe0xTZj78cPh46fE +sGFmj+HVa01485K+7sbTpD7Hjh7IP92E3usTh2TPET1KDw7fO9CE5gKJwt4L +YjD9YywdbdGEix56X3wZQvLVTD78bU0T/nFoMTt/SQwObQf/a1jWhF3TNkhb +XRFDy2/1SS+WNmFeedpH1auEf6+jql6rmzD6lHQs77oY9Iz8AgRWTXhMy8/x +3U0xMCcejC8804Rb+7vUrt8m+Owg5/WbJlwca0J3iiXnYePNHLV/TTi+7ekz +rXtEL7ILah7ubcbuMYUTv+LFwA3r6zxQ0Iz5uUFr6pPE8P1D65Qa+RaMOdQ/ +Gp9K6mex75HVphY8Pm9r2ZGHYlD/XaPbTs7vtubM8P8yCH8zp9QG3G5B9SvK +ltJPib5S//SffdWCExsuKnx+Lgbb1KzFBSUt2CNktD19Rcav/cvIJvdBfvqO +hNPZYugqnwjvfEP2c3zjuu21GMaPBbsXJregj/z8pSr5JB4tW7ry2Ra0rAzn +sgrEsN762yr2jhbUOM3PevtODLKPw3+YzW/Bfzp2pyJKxeDyvHmDRVcz9n59 +t2EPkvPncOeNWngzFsQtmdCoEkOY9NP387Y2Y+z269U/awg/zQNXVmg3o+/E +t2s1deR8XuI9fmLQjFZvnGziGsj4jKSU7hPNuMy7YpbXJzHoFqpnFDQ3o8QC +rZ61LURvjQW6x7RbsK/19gPJdjEUxdVzJQJbsChy9GB7pxjSkx/sY5a2YNzG +A9oZ/wvrABT/2O8/Lkf34g330L9w8MbuctvvP9pn3fe7FNG/S6UutELe7z8U +sIc4ywnRvyZalnkS4e8/rgtJ9sjO0L8CD/4+4uPvP3T/ZDB7ZNC/3sNlBLLm +7z8YULkljq7Pv7p4zcmB6e8/aFqrdcSCzr+WLTWPUezvP2Aaio8LlM2/ceKc +VCHv7z/Ibs9bsz3Nv0yXBBrx8e8/iKknsNXGzb8oTGzfwPTvPziS80MyIc+/ +BAHUpJD37z9E08sNXTvQv+C1O2pg+u8/sLTfxcFtz7+8aqMvMP3vP6DxX3vl +Ase/lx8L9f//7z/gTQjbu5+RP2YoVbw= + "]]}, "Charting`Private`Tag#1"]}}, {}}, <| + "HighlightElements" -> <| + "Label" -> {"XYLabel"}, "Ball" -> {"InterpolatedBall"}|>, + "LayoutOptions" -> <| + "PanelPlotLayout" -> <||>, + "PlotRange" -> {{0., 0.9999999795918367}, {-1.5, 1.5}}, + "Frame" -> {{False, False}, {False, False}}, "AxesOrigin" -> {0, 0}, + "ImageSize" -> {200, 200/GoldenRatio}, "Axes" -> {True, True}, + "LabelStyle" -> {}, "AspectRatio" -> GoldenRatio^(-1), "DefaultStyle" -> { + Directive[ + Opacity[1.], + RGBColor[0.24, 0.6, 0.8], + AbsoluteThickness[2]]}, + "HighlightLabelingFunctions" -> <|"CoordinatesToolOptions" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), + "ScalingFunctions" -> {{Identity, Identity}, { + Identity, Identity}}|>, "Primitives" -> {}, "GCFlag" -> False|>, + "Meta" -> <| + "DefaultHighlight" -> {"Dynamic", None}, "Index" -> {}, "Function" -> + Plot, "GroupHighlight" -> False|>|>, "DynamicHighlight"]], {{}, + InterpretationBox[{ + TagBox[ + TagBox[ + {GrayLevel[0], PointSize[0.012833333333333334`], AbsoluteThickness[2], + PointBox[CompressedData[" +1:eJxTTMoPSmViYGDQAGIQDQO1ISmtesIr9vMtcZRa4jjLfu7zaH+/Q+vtZcH8 +VfZ3FarfL/h3wl7IeqOw9cbN9pe2aClwHrxtbwWW32W/yuzS6q+OD+w72TIn +sGUesK9aIK9oEf/QXhKs/rD9J/HEVX/mvbJvzf85Lf/nMfuXyzinPzd+bS8G +1n/KnnXu/N9bTF7ZL7vROfdG51n7+uPrpghs/gA174K9h/K26WEqn+wvKvBe +AiJ744SLdRK2b6HmX7af6vV2q+bl1/b+oSBw1f7rUqPrAi2v7aeD7btmf8Z8 +RZLipNf2D0DGz71h//Wvy5a1oQ+h9t+y77NV4Pyi/cw+bt/T6H1Pb9tzWPT1 +it1+CHXPXftq95tbOfZetr/zSfc+ENm/8HafqGW62X4S2H0P7KsjZRaWntxh +v1YY5KCH9tUv1xl9K7m8H+LeR/aTU9JOLwjdu/8rWPsj+yOlW+vrBB7tFwC7 +/7E9gzfbzt8SL/ebeDQD0RP73t7nZ6+kvdkfAfbPU/sps/9L/9Z4vb84Sb0s +Sf2ZfWXl8fLtR97th/jvmb2l9Ox6Wc83+3fXnN5ec/q5/RrHM3Xx697svw72 +7wt75/2TW93r3uz/PQ2k4aW97cL7ggLr3u6H+P+VvXzNX1XBfc/3W4GcI/za +/uuLQEFhgzf7IeHx2v6Fj9lGOfsn+ytBxm9/Y5/WHXs9ve/efnBodr61T3fe +7nXF/ub+gyDl0e/sk8/0NLhYXdkPCa/39iK+n3VaSw/th6S2D/YxJx8w+SyZ +aA8A0XlEJQ== + "]]}, + Annotation[#, "Charting`Private`Tag#1"]& ], + {"WolframDynamicHighlight", <| + "Label" -> {"XYLabel"}, "Ball" -> {"IndicatedBall"}|>}], + StyleBox[ + DynamicBox[(Charting`HighlightActionBox["DynamicHighlight", {}, + Slot["HighlightElements"], + Slot["LayoutOptions"], + Slot["Meta"], + Charting`HighlightActionFunction["DynamicHighlight", {{ + Annotation[{ + Directive[ + PointSize[0.012833333333333334`], + AbsoluteThickness[2], + GrayLevel[0]], + Point[CompressedData[" +1:eJxTTMoPSmViYGDQAGIQDQO1ISmtesIr9vMtcZRa4jjLfu7zaH+/Q+vtZcH8 +VfZ3FarfL/h3wl7IeqOw9cbN9pe2aClwHrxtbwWW32W/yuzS6q+OD+w72TIn +sGUesK9aIK9oEf/QXhKs/rD9J/HEVX/mvbJvzf85Lf/nMfuXyzinPzd+bS8G +1n/KnnXu/N9bTF7ZL7vROfdG51n7+uPrpghs/gA174K9h/K26WEqn+wvKvBe +AiJ744SLdRK2b6HmX7af6vV2q+bl1/b+oSBw1f7rUqPrAi2v7aeD7btmf8Z8 +RZLipNf2D0DGz71h//Wvy5a1oQ+h9t+y77NV4Pyi/cw+bt/T6H1Pb9tzWPT1 +it1+CHXPXftq95tbOfZetr/zSfc+ENm/8HafqGW62X4S2H0P7KsjZRaWntxh +v1YY5KCH9tUv1xl9K7m8H+LeR/aTU9JOLwjdu/8rWPsj+yOlW+vrBB7tFwC7 +/7E9gzfbzt8SL/ebeDQD0RP73t7nZ6+kvdkfAfbPU/sps/9L/9Z4vb84Sb0s +Sf2ZfWXl8fLtR97th/jvmb2l9Ox6Wc83+3fXnN5ec/q5/RrHM3Xx697svw72 +7wt75/2TW93r3uz/PQ2k4aW97cL7ggLr3u6H+P+VvXzNX1XBfc/3W4GcI/za +/uuLQEFhgzf7IeHx2v6Fj9lGOfsn+ytBxm9/Y5/WHXs9ve/efnBodr61T3fe +7nXF/ub+gyDl0e/sk8/0NLhYXdkPCa/39iK+n3VaSw/th6S2D/YxJx8w+SyZ +aA8A0XlEJQ== + "]]}, "Charting`Private`Tag#1"]}}, <| + "HighlightElements" -> <| + "Label" -> {"XYLabel"}, "Ball" -> {"IndicatedBall"}|>, + "LayoutOptions" -> <| + "PanelPlotLayout" -> <||>, + "PlotRange" -> {{0, 1.}, {-0.961513265556092, 1.1338716436605}}, + "Frame" -> {{False, False}, {False, False}}, + "AxesOrigin" -> {0, 0}, "ImageSize" -> {360, 360/GoldenRatio}, + "Axes" -> {True, True}, "LabelStyle" -> {}, "AspectRatio" -> + GoldenRatio^(-1), "DefaultStyle" -> { + Directive[ + PointSize[0.012833333333333334`], + AbsoluteThickness[2], + GrayLevel[0]]}, + "HighlightLabelingFunctions" -> <|"CoordinatesToolOptions" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), + "ScalingFunctions" -> {{Identity, Identity}, { + Identity, Identity}}|>, "Primitives" -> {}, "GCFlag" -> + False|>, + "Meta" -> <| + "DefaultHighlight" -> {"Dynamic", None}, "Index" -> {}, + "Function" -> ListPlot, "GroupHighlight" -> False|>|>]]& )[<| + "HighlightElements" -> <| + "Label" -> {"XYLabel"}, "Ball" -> {"IndicatedBall"}|>, + "LayoutOptions" -> <| + "PanelPlotLayout" -> <||>, + "PlotRange" -> {{0, 1.}, {-0.961513265556092, 1.1338716436605}}, + "Frame" -> {{False, False}, {False, False}}, + "AxesOrigin" -> {0, 0}, "ImageSize" -> {360, 360/GoldenRatio}, + "Axes" -> {True, True}, "LabelStyle" -> {}, "AspectRatio" -> + GoldenRatio^(-1), "DefaultStyle" -> { + Directive[ + PointSize[0.012833333333333334`], + AbsoluteThickness[2], + GrayLevel[0]]}, + "HighlightLabelingFunctions" -> <|"CoordinatesToolOptions" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), + "ScalingFunctions" -> {{Identity, Identity}, { + Identity, Identity}}|>, "Primitives" -> {}, "GCFlag" -> + False|>, + "Meta" -> <| + "DefaultHighlight" -> {"Dynamic", None}, "Index" -> {}, "Function" -> + ListPlot, "GroupHighlight" -> False|>|>], + ImageSizeCache->{{4.503599627370496*^15, -4.503599627370496*^15}, { + 4.503599627370496*^15, -4.503599627370496*^15}}], + Selectable->False]}, + Annotation[{{ + Annotation[{ + Directive[ + PointSize[0.012833333333333334`], + AbsoluteThickness[2], + GrayLevel[0]], + Point[CompressedData[" +1:eJxTTMoPSmViYGDQAGIQDQO1ISmtesIr9vMtcZRa4jjLfu7zaH+/Q+vtZcH8 +VfZ3FarfL/h3wl7IeqOw9cbN9pe2aClwHrxtbwWW32W/yuzS6q+OD+w72TIn +sGUesK9aIK9oEf/QXhKs/rD9J/HEVX/mvbJvzf85Lf/nMfuXyzinPzd+bS8G +1n/KnnXu/N9bTF7ZL7vROfdG51n7+uPrpghs/gA174K9h/K26WEqn+wvKvBe +AiJ744SLdRK2b6HmX7af6vV2q+bl1/b+oSBw1f7rUqPrAi2v7aeD7btmf8Z8 +RZLipNf2D0DGz71h//Wvy5a1oQ+h9t+y77NV4Pyi/cw+bt/T6H1Pb9tzWPT1 +it1+CHXPXftq95tbOfZetr/zSfc+ENm/8HafqGW62X4S2H0P7KsjZRaWntxh +v1YY5KCH9tUv1xl9K7m8H+LeR/aTU9JOLwjdu/8rWPsj+yOlW+vrBB7tFwC7 +/7E9gzfbzt8SL/ebeDQD0RP73t7nZ6+kvdkfAfbPU/sps/9L/9Z4vb84Sb0s +Sf2ZfWXl8fLtR97th/jvmb2l9Ox6Wc83+3fXnN5ec/q5/RrHM3Xx697svw72 +7wt75/2TW93r3uz/PQ2k4aW97cL7ggLr3u6H+P+VvXzNX1XBfc/3W4GcI/za +/uuLQEFhgzf7IeHx2v6Fj9lGOfsn+ytBxm9/Y5/WHXs9ve/efnBodr61T3fe +7nXF/ub+gyDl0e/sk8/0NLhYXdkPCa/39iK+n3VaSw/th6S2D/YxJx8w+SyZ +aA8A0XlEJQ== + "]]}, "Charting`Private`Tag#1"]}}, <| + "HighlightElements" -> <| + "Label" -> {"XYLabel"}, "Ball" -> {"IndicatedBall"}|>, + "LayoutOptions" -> <| + "PanelPlotLayout" -> <||>, + "PlotRange" -> {{0, 1.}, {-0.961513265556092, 1.1338716436605}}, + "Frame" -> {{False, False}, {False, False}}, "AxesOrigin" -> {0, 0}, + "ImageSize" -> {360, 360/GoldenRatio}, "Axes" -> {True, True}, + "LabelStyle" -> {}, "AspectRatio" -> GoldenRatio^(-1), + "DefaultStyle" -> { + Directive[ + PointSize[0.012833333333333334`], + AbsoluteThickness[2], + GrayLevel[0]]}, + "HighlightLabelingFunctions" -> <|"CoordinatesToolOptions" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), + "ScalingFunctions" -> {{Identity, Identity}, { + Identity, Identity}}|>, "Primitives" -> {}, "GCFlag" -> False|>, + "Meta" -> <| + "DefaultHighlight" -> {"Dynamic", None}, "Index" -> {}, "Function" -> + ListPlot, "GroupHighlight" -> False|>|>, + "DynamicHighlight"]], {{}, {}}}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + ImageSize->200, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{0., 0.9999999795918367}, {-1.5, 1.5}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, {0, 0}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{{3.948273942078746*^9, 3.948273952675535*^9}, { + 3.948274067409328*^9, 3.948274149377993*^9}}, + CellLabel->"Out[50]=",ExpressionUUID->"eaa9a4dd-4bdb-4a04-9840-d5957524e949"] }, Open ]], Cell[CellGroupData[{ @@ -7030,7 +9535,7 @@ Cell[BoxData[ 3.948264089290145*^9}, {3.9482644010883017`*^9, 3.948264402230794*^9}, { 3.9482644325136557`*^9, 3.948264433328302*^9}, {3.948264522108773*^9, 3.9482645225078363`*^9}}, - CellLabel->"In[99]:=",ExpressionUUID->"f6f545cf-927d-43c1-af6d-713c7a209a9d"], + CellLabel->"In[25]:=",ExpressionUUID->"f6f545cf-927d-43c1-af6d-713c7a209a9d"], Cell[BoxData[ GraphicsBox[{{}, @@ -7369,8 +9874,8 @@ XeWlqg== CellChangeTimes->{{3.948263812698069*^9, 3.948263832514358*^9}, 3.9482638859955683`*^9, 3.948264033645093*^9, {3.948264084133428*^9, 3.948264094565215*^9}, 3.948264407583634*^9, 3.948264438687293*^9, - 3.948264527768785*^9}, - CellLabel->"Out[99]=",ExpressionUUID->"4558eca3-abe8-4b93-8bbd-b8a6a370b459"] + 3.948264527768785*^9, 3.948273998661524*^9}, + CellLabel->"Out[25]=",ExpressionUUID->"97c48afc-a508-455f-a069-6e9a7516ab1b"] }, Open ]], Cell[CellGroupData[{ @@ -12115,46 +14620,83 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"ListLogPlot", "[", - RowBox[{ + RowBox[{"biasVarianceCurve2", "=", + RowBox[{"ListLogPlot", "[", RowBox[{ RowBox[{ RowBox[{ - FractionBox["1", "1000"], - RowBox[{"Sum", "[", + RowBox[{"{", RowBox[{ - SuperscriptBox[ - RowBox[{"(", + RowBox[{"Length", "[", "#", "]"}], ",", + RowBox[{ + FractionBox["1", "1000"], + RowBox[{"Sum", "[", RowBox[{ - RowBox[{"#", ".", - RowBox[{"polyBasis", "[", - RowBox[{"Length", "[", "#", "]"}], "]"}]}], "-", - RowBox[{"Sin", "[", - RowBox[{"2", "\[Pi]", " ", "x"}], "]"}]}], ")"}], "2"], ",", - RowBox[{"{", - RowBox[{"x", ",", "0", ",", "1", ",", - RowBox[{"1", "/", "1000"}]}], "}"}]}], "]"}]}], "&"}], "/@", - RowBox[{"Join", "[", - RowBox[{ - RowBox[{"as", "[", - RowBox[{"[", - RowBox[{";;", - RowBox[{"Length", "[", "testdata", "]"}]}], "]"}], "]"}], ",", - RowBox[{"Reverse", "@", + SuperscriptBox[ + RowBox[{"(", + RowBox[{ + RowBox[{"#", ".", + RowBox[{"polyBasis", "[", + RowBox[{"Length", "[", "#", "]"}], "]"}]}], "-", + RowBox[{"Sin", "[", + RowBox[{"2", "\[Pi]", " ", "x"}], "]"}]}], ")"}], "2"], ",", + RowBox[{"{", + RowBox[{"x", ",", "0", ",", "1", ",", + RowBox[{"1", "/", "1000"}]}], "}"}]}], "]"}]}]}], "}"}], "&"}], "/@", + RowBox[{"Join", "[", + RowBox[{ RowBox[{"as", "[", RowBox[{"[", - RowBox[{ + RowBox[{";;", + RowBox[{"Length", "[", "testdata", "]"}]}], "]"}], "]"}], ",", + RowBox[{"Reverse", "@", + RowBox[{"as", "[", + RowBox[{"[", RowBox[{ - RowBox[{"Length", "[", "testdata", "]"}], "+", "1"}], ";;"}], - "]"}], "]"}]}]}], "]"}]}], ",", - RowBox[{"Joined", "->", "True"}], ",", - RowBox[{"PlotRange", "->", "All"}]}], "]"}]], "Input", - CellChangeTimes->{{3.948213593242156*^9, 3.9482136694857197`*^9}, { - 3.948213772579567*^9, 3.948213776296318*^9}, {3.948213818203815*^9, - 3.94821382625779*^9}, {3.9482139633127813`*^9, 3.948213963520137*^9}, { - 3.948214498223065*^9, 3.948214505726357*^9}, {3.948220586592793*^9, - 3.9482206081052313`*^9}, {3.948220906413961*^9, 3.948220931102378*^9}}, - CellLabel->"In[41]:=",ExpressionUUID->"7c9d6eb3-c96d-4f11-913b-3d4f12b217fa"], + RowBox[{ + RowBox[{"Length", "[", "testdata", "]"}], "+", "1"}], ";;"}], + "]"}], "]"}]}]}], "]"}]}], ",", + RowBox[{"Joined", "->", "True"}], ",", + RowBox[{"PlotRange", "->", "All"}], ",", + RowBox[{"ImageSize", "->", "250"}], ",", + RowBox[{"AxesLabel", "->", + RowBox[{"{", + RowBox[{"N", ",", "\"\<MSE\>\""}], "}"}]}], ",", + RowBox[{"LabelStyle", "->", "Black"}], ",", + RowBox[{"Prolog", "->", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"40", ",", + RowBox[{"Log", "[", + RowBox[{"4", " ", + SuperscriptBox["10", + RowBox[{"-", "1"}]]}], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"40", ",", + RowBox[{"Log", "[", + SuperscriptBox["10", "18"], "]"}]}], "}"}]}], "}"}], "]"}]}], ",", + + RowBox[{"Epilog", "->", + RowBox[{"Text", "[", + RowBox[{"\"\<\!\(\*StyleBox[\"M\",FontSlant->\"Italic\"]\)\>\"", ",", + RowBox[{"{", + RowBox[{"40", ",", + RowBox[{"Log", "[", + RowBox[{"1", " ", + SuperscriptBox["10", + RowBox[{"-", "2"}]]}], "]"}]}], "}"}]}], "]"}]}]}], + "]"}]}]], "Input", + CellChangeTimes->CompressedData[" +1:eJxTTMoPSmViYGAQBmIQvW+/+up5WW8dWbrXbwHRF7onHQTRBdWch0D08la3 +4yD6or3HCRDtx5R1E0R/W1IApiOV3WXmA+lAO3NZEK35I0h0EZDmi2OWANHa +9r62IHqdW7IDiD6w/u6SPUCaiTl0JYju3nZsLYjms7qzCUSXZffsAtEbts/c +DaJb/V1OgOh3XjNPgWiDFYGXQHQw+8KrIHpl+4kHINrjkM1TEB0RJfISRO/s +aXsPoo0uL/sMor90rAfTBtqcP0F0QdLt3yD66NWzjHuBdLX+ZyYQnWbMzg6i +RRRvcYBo3jp1XhC9e/YbMA0AEeSiIg== + "], + CellLabel->"In[75]:=",ExpressionUUID->"7c9d6eb3-c96d-4f11-913b-3d4f12b217fa"], Cell[BoxData[ GraphicsBox[{{}, @@ -12163,39 +14705,39 @@ Cell[BoxData[ TagBox[ {RGBColor[0.24, 0.6, 0.8], PointSize[0.009166666666666668], AbsoluteThickness[2], LineBox[CompressedData[" -1:eJw91A0w1Hkcx/G9HKGuQ1HytKU8lkOen/YjIaRl12LX0+7Kpek8LJKUa1Vi -unPDDJV00qNK5aGnu4Sl0HPpukslcRc6iWo6EV3Xjf+XmR3z8vm//7/x351d -IE3ixU1jsVjFn1///578ec0JULtUmWPZ18j8AYUjA47GW8YYq4Jbmh9klkzW -QGLPn0723nMUk56DCSWxbyiHPA/laZ0tNvpzGevDUpNbpW5AZqPebcSzYyZ5 -IayyTs2dXqnDeBEiBKoLtfeTTWDA/jTQHkk2g0TaumvBlC0ws+e926nD2oyX -oL/55pWeg2QriGXLO7OndmsIjQ/4q6eQbZAZvGveemuyLaTzm8qzOeRlaMhI -rfvFhWyH7t3Tkg2VyPboHRSJysa0GDsgW/lt3+xEDcaOWFRuKeO6ajJ2wrfp -pkkJL1UZOyNHNqB6oZnsgpsHxU3+87uZ5+0Kn8af68fdP3Im7YZ8veQGpdOq -mLQ7JJx11TeEmow9cNfmzNq/5VqMOcj8YYAtkxkxBqxlS/TYVexJy4H8WLN0 -YdZiZvcE63aFt7edKbN7wuFB3YZ7tdbMvhzpnXH3a0Q2zL4co69Sm0vz7Jnd -Cy+eun0ReMaR2b2QYPh7pGaHC7OvQF1ba4BpP5h9Bcbu7VCf6Opm/j9v7M1u -43b8wVjuDeeqGIMWYyXm+fjgEX/wookZY7kP7hktSsj8+DWz++J9HnvixQRj -uS80i/3eNOfR81+JdxyZ70myfCUep22Nie2i3Q8ecSr8Nd20+2FlTrkwgEXv -rz/ila/U237JWO4Pr7daqgFRtAeg8ll9Y42Y9gB43WkqG+PSvgrHjZ92N/Np -X4V90e5N+mRWIORNw3W64bQH4mrfu4lrdD/WaqSInLw9JLSvhmA8KNEylnYu -ZEVxLxzIci42Jgk19Kf6IDS6y/Q7qUcQFibZFdwW0fVBuCDsO5lP1yuCYPaV -l9lmup4VDMMhtxa1DOqDwX7ysrVqE/XBOFax66fC49QHY7Nj8/VHR6jn4fbW -jn8NzlPPQ4vH7GUXT1LPQ+q73GvdNdTzsPSSR2dRNfV8jNtPjOadpZ6PHkWO -3R26v5wPzYTUod4K6vkYLVOadYjMCoFK/FbOaTJCcD+7teBwCfUh2Fkyu8yl -lPoQcGbo+hXtp16A4sylx/UPUC+A86vcq7JC6gXYoj+Ysm439QLksvf0O2ZT -HwqhlrxkezH1ofB17zm7aTP1oagR9B+12EF9KJQvWBiGplAfhmqdhlNWG6gP -g9/Wyt60dOrDPn9etgdcJivCwP2woiN+6v0Lx1376pqSNdSHIyz9hPa5FdSH -wzR9rWspWRGObQmtD/eRWUIEd+UUGpIhRIPj4naBG/VC5Od+k93rQb0QagZH -PVebUC/CgzlPWjXMqRfhsFGpT5sB9SKcGPTUrSUrRDAZnlnQbkZ9BKJstwlc -LamPwJNHSbzoJdRHwOvH/DSvpdRH4B832ekhuh8rEnWFGT0OZETCWz3heaUe -9ZHY2ZtwKkeX+khkHJJ/mDaP+ijYFn53LImuRxQmDGOHfOl6eRR0+s7tMjCm -Pgq/GSlPz7KgPhq3bCvU2u2oj0YO6wjrlTP10dibF2P+jKyIxoj1Nt1b9HxZ -MSi6vKXPiIwYBDxWTmx1pz4GtVXcI+ZkRQwq9MxNN031YphdOm+eSmaLIfrL -RVFL50GM9DfHrMZcGYvFONpW6Hp+6v5ibDRsiwWHcbkYMQ9jw8PJCjHOJr1f -f92XcbcY55QtjXv96HwJ1nVo3GgKpPMlCLaHDXsVnS9BS9P42i30fSmWILH/ -g+qtYDpfAtbz4dM8+r4sl8Cpd/8MJR6dL0HYaxV+F7lbArWR+JTvqWdJ8Wz0 -9fsCMluKaVp7mvTpekgxq8hQJTuEzpciWee+UhhZLsWey8Mq2kI6X4pfs3Tb -Pn3e/wMy+6Ka +1:eJw91Ak41Hkcx/H/skS1GyqlHFPKWRY5cs5HkpU0rsGMa45selrHUNJhG5Xy +tGsfnkeptNKpQo5UuwlDobu0bamksRvaEtXTOqJt28f/O57H43n5/t6/L/Of +Z+ZIkoLj1BiGKfj8/f/P8a83XH/ti6VZ1j0N7C+QN/jS2XTLCGst8ApzAi2S +yTpI7PpzsaPPNMW4p2FMXeQbxiXPRPG6jmY7wxmsDWGty6uYaETmoM590Kt9 +MnkubDLKZkwo1Wc9D5F8rbnTD5LNYMT59LItimwBsaRl9xyVrTC5a8i97Oh0 +1gvQ23Tjctdhsg1EsiUdmaq5LQSmh5ZPTCHbYVPQ7plrbcn2kMxqLM7kkheh +Pj219ldXsgOUe9WSjdXJjujuEwqLRvRYOyFT413P1EQd1s6YV2wt47npsl6M +79LMkxJeabF2QZbspdb5JrIrbhwWNS6fpWRfbzcsa/ilbtTjI3fc7siZnVyv +Xq6FcXtAzF1TeV2gy9oTd+zOrP5brseai00/vuTIZCasAVvZgtmcCs645UCO +1CJNkDGfnXuBuVXi4+Ngzs694HS/dv3dalt2vgRpHXH3qoR27HwJhl+nNhVm +O7Jzb7x46v5FwBlndu6NBOM/onTbXdn5UtS2tvib94K1H2q2j2HUaQp73g+P +Tz2ocyczyzFyd8fEsU7l+P8vX459ma289gesGX+4VMQaNZuqj79+cn88Cum7 +YGbBmlmBuybzEjZ9nMLOV2AomzP2Yow1EwDdPX5vm7LZ5yMPwHuuzPc0mVmJ +x+u2xko7ab4SnnGaIauUNOfh26xigT/DPn85D/Eal+vsv6T3QyC83+lp+Uez +RiBKn9U1VIno/Of57caiER5rRSBOmj5VNoVQH4QDMR6NhmQEQd44UGsQQX0Q +rvS8H7tK9ymCkCJc7OMppj4Y/NHARGsp9cGQ5ce9cCLLg7EhSaBjqOqD0eAh +M+xQ9SGYm+SQe0tIfQjOC3pO56j+/hBYfOVtsZnOK0Jg3O/erJ1OfSg4T161 +VGykPhQnSnb/nHeS+lBsdm669ugY9aG4tbX9X6Nz1PPR7Dl10YXT1POR+n7X +VWUV9XwsvOjZkV9JPR+jjmPD2WepD0OXIsvhNt2PMOgmpPZ3l1AfhuEi9a+P +kBVh0Izfyi0nM+G4l9mSe3Q/9eHYuX9qkWsh9eHgTjLwyz9IfTj2bFp40vAQ +9RFweb3riiyP+ghsMexLWbOX+gjs4hT0OmdSHwGBnnz/9j3UC+Dr0XV242bq +Baji9x632kG9ABrnrYzDUqgXoFK/vsxmPfVC+G0t7V6XRr3w8/tlu/8lslwI +3oel7fGq5yfEHcfKqv2rqI9EeNqp6TVLqY+Eedpqt0KyPBLbEloeHiArIhHU +mZVnTGaiUO88v43vTn0UcnZ9k9ntSX0UtI2Oe600oz4K96c9adGxpD4aR00K +l7UaUR+NU31eBtVkeTTMBibntllQH41o+218N2vqY/DkUVJwzALqY+D9U846 +74XUx+Afd1l5P92niEFtXnqXE5mJhc/EhOels6mPxc7uhLIsA+pjkX5E/kFt +JvWxsM/7/kQSnWdEGDOW9vvSeY4I+j01u41M6T4RfjfRmJBhxVokwk37Eu02 +B7pfhCzmGPPahXWxCPuyYy2fkRUiDNpuM7hJr69ShPxLW3pMyIwY/o81Els8 +aL8Y1RW8Y5ZkiFEy29J8I50XiWFx8ZxlKlkuhvAvV0W1ar8YaW9P2Iy40X4x +jrfmuZ2j+5RibDBulYJL+yWIfSiNiCBzJDibNLT2mi/tl6BGw9q024/2S7Cm +Xed6YwDtlyDIEXacFbRfgubG0dVbVJ+XEiT2ftC6GUT7JWCeD5QHqz4/pVjc +fXCSejDtlyL8jWZIJxlSaA/Gp/xAvUiKZ8NvhnLJcinU9AoaDel8sRRf5xtr +ZobSfimS9e+ph5OVUhRcGtCcLqD9q/BbhkHrp8/z/wCmd69O "]]}, Annotation[#, "Charting`Private`Tag#1"]& ]}, {"WolframDynamicHighlight", <| @@ -12213,50 +14755,51 @@ Pn3e/wMy+6Ka RGBColor[0.24, 0.6, 0.8], AbsoluteThickness[2]], Line[CompressedData[" -1:eJw91A0w1Hkcx/G9HKGuQ1HytKU8lkOen/YjIaRl12LX0+7Kpek8LJKUa1Vi -unPDDJV00qNK5aGnu4Sl0HPpukslcRc6iWo6EV3Xjf+XmR3z8vm//7/x351d -IE3ixU1jsVjFn1///578ec0JULtUmWPZ18j8AYUjA47GW8YYq4Jbmh9klkzW -QGLPn0723nMUk56DCSWxbyiHPA/laZ0tNvpzGevDUpNbpW5AZqPebcSzYyZ5 -IayyTs2dXqnDeBEiBKoLtfeTTWDA/jTQHkk2g0TaumvBlC0ws+e926nD2oyX -oL/55pWeg2QriGXLO7OndmsIjQ/4q6eQbZAZvGveemuyLaTzm8qzOeRlaMhI -rfvFhWyH7t3Tkg2VyPboHRSJysa0GDsgW/lt3+xEDcaOWFRuKeO6ajJ2wrfp -pkkJL1UZOyNHNqB6oZnsgpsHxU3+87uZ5+0Kn8af68fdP3Im7YZ8veQGpdOq -mLQ7JJx11TeEmow9cNfmzNq/5VqMOcj8YYAtkxkxBqxlS/TYVexJy4H8WLN0 -YdZiZvcE63aFt7edKbN7wuFB3YZ7tdbMvhzpnXH3a0Q2zL4co69Sm0vz7Jnd -Cy+eun0ReMaR2b2QYPh7pGaHC7OvQF1ba4BpP5h9Bcbu7VCf6Opm/j9v7M1u -43b8wVjuDeeqGIMWYyXm+fjgEX/wookZY7kP7hktSsj8+DWz++J9HnvixQRj -uS80i/3eNOfR81+JdxyZ70myfCUep22Nie2i3Q8ecSr8Nd20+2FlTrkwgEXv -rz/ila/U237JWO4Pr7daqgFRtAeg8ll9Y42Y9gB43WkqG+PSvgrHjZ92N/Np -X4V90e5N+mRWIORNw3W64bQH4mrfu4lrdD/WaqSInLw9JLSvhmA8KNEylnYu -ZEVxLxzIci42Jgk19Kf6IDS6y/Q7qUcQFibZFdwW0fVBuCDsO5lP1yuCYPaV -l9lmup4VDMMhtxa1DOqDwX7ysrVqE/XBOFax66fC49QHY7Nj8/VHR6jn4fbW -jn8NzlPPQ4vH7GUXT1LPQ+q73GvdNdTzsPSSR2dRNfV8jNtPjOadpZ6PHkWO -3R26v5wPzYTUod4K6vkYLVOadYjMCoFK/FbOaTJCcD+7teBwCfUh2Fkyu8yl -lPoQcGbo+hXtp16A4sylx/UPUC+A86vcq7JC6gXYoj+Ysm439QLksvf0O2ZT -HwqhlrxkezH1ofB17zm7aTP1oagR9B+12EF9KJQvWBiGplAfhmqdhlNWG6gP -g9/Wyt60dOrDPn9etgdcJivCwP2woiN+6v0Lx1376pqSNdSHIyz9hPa5FdSH -wzR9rWspWRGObQmtD/eRWUIEd+UUGpIhRIPj4naBG/VC5Od+k93rQb0QagZH -PVebUC/CgzlPWjXMqRfhsFGpT5sB9SKcGPTUrSUrRDAZnlnQbkZ9BKJstwlc -LamPwJNHSbzoJdRHwOvH/DSvpdRH4B832ekhuh8rEnWFGT0OZETCWz3heaUe -9ZHY2ZtwKkeX+khkHJJ/mDaP+ijYFn53LImuRxQmDGOHfOl6eRR0+s7tMjCm -Pgq/GSlPz7KgPhq3bCvU2u2oj0YO6wjrlTP10dibF2P+jKyIxoj1Nt1b9HxZ -MSi6vKXPiIwYBDxWTmx1pz4GtVXcI+ZkRQwq9MxNN031YphdOm+eSmaLIfrL -RVFL50GM9DfHrMZcGYvFONpW6Hp+6v5ibDRsiwWHcbkYMQ9jw8PJCjHOJr1f -f92XcbcY55QtjXv96HwJ1nVo3GgKpPMlCLaHDXsVnS9BS9P42i30fSmWILH/ -g+qtYDpfAtbz4dM8+r4sl8Cpd/8MJR6dL0HYaxV+F7lbArWR+JTvqWdJ8Wz0 -9fsCMluKaVp7mvTpekgxq8hQJTuEzpciWee+UhhZLsWey8Mq2kI6X4pfs3Tb -Pn3e/wMy+6Ka +1:eJw91Ak41Hkcx/H/skS1GyqlHFPKWRY5cs5HkpU0rsGMa45selrHUNJhG5Xy +tGsfnkeptNKpQo5UuwlDobu0bamksRvaEtXTOqJt28f/O57H43n5/t6/L/Of +Z+ZIkoLj1BiGKfj8/f/P8a83XH/ti6VZ1j0N7C+QN/jS2XTLCGst8ApzAi2S +yTpI7PpzsaPPNMW4p2FMXeQbxiXPRPG6jmY7wxmsDWGty6uYaETmoM590Kt9 +MnkubDLKZkwo1Wc9D5F8rbnTD5LNYMT59LItimwBsaRl9xyVrTC5a8i97Oh0 +1gvQ23Tjctdhsg1EsiUdmaq5LQSmh5ZPTCHbYVPQ7plrbcn2kMxqLM7kkheh +Pj219ldXsgOUe9WSjdXJjujuEwqLRvRYOyFT413P1EQd1s6YV2wt47npsl6M +79LMkxJeabF2QZbspdb5JrIrbhwWNS6fpWRfbzcsa/ilbtTjI3fc7siZnVyv +Xq6FcXtAzF1TeV2gy9oTd+zOrP5brseai00/vuTIZCasAVvZgtmcCs645UCO +1CJNkDGfnXuBuVXi4+Ngzs694HS/dv3dalt2vgRpHXH3qoR27HwJhl+nNhVm +O7Jzb7x46v5FwBlndu6NBOM/onTbXdn5UtS2tvib94K1H2q2j2HUaQp73g+P +Tz2ocyczyzFyd8fEsU7l+P8vX459ma289gesGX+4VMQaNZuqj79+cn88Cum7 +YGbBmlmBuybzEjZ9nMLOV2AomzP2Yow1EwDdPX5vm7LZ5yMPwHuuzPc0mVmJ +x+u2xko7ab4SnnGaIauUNOfh26xigT/DPn85D/Eal+vsv6T3QyC83+lp+Uez +RiBKn9U1VIno/Of57caiER5rRSBOmj5VNoVQH4QDMR6NhmQEQd44UGsQQX0Q +rvS8H7tK9ymCkCJc7OMppj4Y/NHARGsp9cGQ5ce9cCLLg7EhSaBjqOqD0eAh +M+xQ9SGYm+SQe0tIfQjOC3pO56j+/hBYfOVtsZnOK0Jg3O/erJ1OfSg4T161 +VGykPhQnSnb/nHeS+lBsdm669ugY9aG4tbX9X6Nz1PPR7Dl10YXT1POR+n7X +VWUV9XwsvOjZkV9JPR+jjmPD2WepD0OXIsvhNt2PMOgmpPZ3l1AfhuEi9a+P +kBVh0Izfyi0nM+G4l9mSe3Q/9eHYuX9qkWsh9eHgTjLwyz9IfTj2bFp40vAQ +9RFweb3riiyP+ghsMexLWbOX+gjs4hT0OmdSHwGBnnz/9j3UC+Dr0XV242bq +Baji9x632kG9ABrnrYzDUqgXoFK/vsxmPfVC+G0t7V6XRr3w8/tlu/8lslwI +3oel7fGq5yfEHcfKqv2rqI9EeNqp6TVLqY+Eedpqt0KyPBLbEloeHiArIhHU +mZVnTGaiUO88v43vTn0UcnZ9k9ntSX0UtI2Oe600oz4K96c9adGxpD4aR00K +l7UaUR+NU31eBtVkeTTMBibntllQH41o+218N2vqY/DkUVJwzALqY+D9U846 +74XUx+Afd1l5P92niEFtXnqXE5mJhc/EhOels6mPxc7uhLIsA+pjkX5E/kFt +JvWxsM/7/kQSnWdEGDOW9vvSeY4I+j01u41M6T4RfjfRmJBhxVokwk37Eu02 +B7pfhCzmGPPahXWxCPuyYy2fkRUiDNpuM7hJr69ShPxLW3pMyIwY/o81Els8 +aL8Y1RW8Y5ZkiFEy29J8I50XiWFx8ZxlKlkuhvAvV0W1ar8YaW9P2Iy40X4x +jrfmuZ2j+5RibDBulYJL+yWIfSiNiCBzJDibNLT2mi/tl6BGw9q024/2S7Cm +Xed6YwDtlyDIEXacFbRfgubG0dVbVJ+XEiT2ftC6GUT7JWCeD5QHqz4/pVjc +fXCSejDtlyL8jWZIJxlSaA/Gp/xAvUiKZ8NvhnLJcinU9AoaDel8sRRf5xtr +ZobSfimS9e+ph5OVUhRcGtCcLqD9q/BbhkHrp8/z/wCmd69O "]]}, "Charting`Private`Tag#1"]}}, <| "HighlightElements" -> <| "Label" -> {"XYLabel"}, "Ball" -> {"IndicatedBall"}|>, "LayoutOptions" -> <| "PanelPlotLayout" -> <||>, - "PlotRange" -> {{0, 149.}, {-8.876053103180046, + "PlotRange" -> {{0, 160.}, {-8.876053103180046, 33.805886718807834`}}, "Frame" -> {{False, False}, {False, False}}, "AxesOrigin" -> {0, -8.876053103180046}, - "ImageSize" -> {360, 360/GoldenRatio}, "Axes" -> {True, True}, - "LabelStyle" -> {}, "AspectRatio" -> GoldenRatio^(-1), + "ImageSize" -> {250, 250/GoldenRatio}, "Axes" -> {True, True}, + "LabelStyle" -> { + GrayLevel[0]}, "AspectRatio" -> GoldenRatio^(-1), "DefaultStyle" -> { Directive[ PointSize[0.009166666666666668], @@ -12276,13 +14819,13 @@ Pn3e/wMy+6Ka "Label" -> {"XYLabel"}, "Ball" -> {"IndicatedBall"}|>, "LayoutOptions" -> <| "PanelPlotLayout" -> <||>, - "PlotRange" -> {{0, 149.}, {-8.876053103180046, + "PlotRange" -> {{0, 160.}, {-8.876053103180046, 33.805886718807834`}}, "Frame" -> {{False, False}, {False, False}}, "AxesOrigin" -> {0, -8.876053103180046}, - "ImageSize" -> {360, 360/GoldenRatio}, "Axes" -> {True, True}, - "LabelStyle" -> {}, "AspectRatio" -> GoldenRatio^(-1), - "DefaultStyle" -> { + "ImageSize" -> {250, 250/GoldenRatio}, "Axes" -> {True, True}, + "LabelStyle" -> { + GrayLevel[0]}, "AspectRatio" -> GoldenRatio^(-1), "DefaultStyle" -> { Directive[ PointSize[0.009166666666666668], RGBColor[0.24, 0.6, 0.8], @@ -12308,49 +14851,50 @@ Pn3e/wMy+6Ka RGBColor[0.24, 0.6, 0.8], AbsoluteThickness[2]], Line[CompressedData[" -1:eJw91A0w1Hkcx/G9HKGuQ1HytKU8lkOen/YjIaRl12LX0+7Kpek8LJKUa1Vi -unPDDJV00qNK5aGnu4Sl0HPpukslcRc6iWo6EV3Xjf+XmR3z8vm//7/x351d -IE3ixU1jsVjFn1///578ec0JULtUmWPZ18j8AYUjA47GW8YYq4Jbmh9klkzW -QGLPn0723nMUk56DCSWxbyiHPA/laZ0tNvpzGevDUpNbpW5AZqPebcSzYyZ5 -IayyTs2dXqnDeBEiBKoLtfeTTWDA/jTQHkk2g0TaumvBlC0ws+e926nD2oyX -oL/55pWeg2QriGXLO7OndmsIjQ/4q6eQbZAZvGveemuyLaTzm8qzOeRlaMhI -rfvFhWyH7t3Tkg2VyPboHRSJysa0GDsgW/lt3+xEDcaOWFRuKeO6ajJ2wrfp -pkkJL1UZOyNHNqB6oZnsgpsHxU3+87uZ5+0Kn8af68fdP3Im7YZ8veQGpdOq -mLQ7JJx11TeEmow9cNfmzNq/5VqMOcj8YYAtkxkxBqxlS/TYVexJy4H8WLN0 -YdZiZvcE63aFt7edKbN7wuFB3YZ7tdbMvhzpnXH3a0Q2zL4co69Sm0vz7Jnd -Cy+eun0ReMaR2b2QYPh7pGaHC7OvQF1ba4BpP5h9Bcbu7VCf6Opm/j9v7M1u -43b8wVjuDeeqGIMWYyXm+fjgEX/wookZY7kP7hktSsj8+DWz++J9HnvixQRj -uS80i/3eNOfR81+JdxyZ70myfCUep22Nie2i3Q8ecSr8Nd20+2FlTrkwgEXv -rz/ila/U237JWO4Pr7daqgFRtAeg8ll9Y42Y9gB43WkqG+PSvgrHjZ92N/Np -X4V90e5N+mRWIORNw3W64bQH4mrfu4lrdD/WaqSInLw9JLSvhmA8KNEylnYu -ZEVxLxzIci42Jgk19Kf6IDS6y/Q7qUcQFibZFdwW0fVBuCDsO5lP1yuCYPaV -l9lmup4VDMMhtxa1DOqDwX7ysrVqE/XBOFax66fC49QHY7Nj8/VHR6jn4fbW -jn8NzlPPQ4vH7GUXT1LPQ+q73GvdNdTzsPSSR2dRNfV8jNtPjOadpZ6PHkWO -3R26v5wPzYTUod4K6vkYLVOadYjMCoFK/FbOaTJCcD+7teBwCfUh2Fkyu8yl -lPoQcGbo+hXtp16A4sylx/UPUC+A86vcq7JC6gXYoj+Ysm439QLksvf0O2ZT -HwqhlrxkezH1ofB17zm7aTP1oagR9B+12EF9KJQvWBiGplAfhmqdhlNWG6gP -g9/Wyt60dOrDPn9etgdcJivCwP2woiN+6v0Lx1376pqSNdSHIyz9hPa5FdSH -wzR9rWspWRGObQmtD/eRWUIEd+UUGpIhRIPj4naBG/VC5Od+k93rQb0QagZH -PVebUC/CgzlPWjXMqRfhsFGpT5sB9SKcGPTUrSUrRDAZnlnQbkZ9BKJstwlc -LamPwJNHSbzoJdRHwOvH/DSvpdRH4B832ekhuh8rEnWFGT0OZETCWz3heaUe -9ZHY2ZtwKkeX+khkHJJ/mDaP+ijYFn53LImuRxQmDGOHfOl6eRR0+s7tMjCm -Pgq/GSlPz7KgPhq3bCvU2u2oj0YO6wjrlTP10dibF2P+jKyIxoj1Nt1b9HxZ -MSi6vKXPiIwYBDxWTmx1pz4GtVXcI+ZkRQwq9MxNN031YphdOm+eSmaLIfrL -RVFL50GM9DfHrMZcGYvFONpW6Hp+6v5ibDRsiwWHcbkYMQ9jw8PJCjHOJr1f -f92XcbcY55QtjXv96HwJ1nVo3GgKpPMlCLaHDXsVnS9BS9P42i30fSmWILH/ -g+qtYDpfAtbz4dM8+r4sl8Cpd/8MJR6dL0HYaxV+F7lbArWR+JTvqWdJ8Wz0 -9fsCMluKaVp7mvTpekgxq8hQJTuEzpciWee+UhhZLsWey8Mq2kI6X4pfs3Tb -Pn3e/wMy+6Ka +1:eJw91Ak41Hkcx/H/skS1GyqlHFPKWRY5cs5HkpU0rsGMa45selrHUNJhG5Xy +tGsfnkeptNKpQo5UuwlDobu0bamksRvaEtXTOqJt28f/O57H43n5/t6/L/Of +Z+ZIkoLj1BiGKfj8/f/P8a83XH/ti6VZ1j0N7C+QN/jS2XTLCGst8ApzAi2S +yTpI7PpzsaPPNMW4p2FMXeQbxiXPRPG6jmY7wxmsDWGty6uYaETmoM590Kt9 +MnkubDLKZkwo1Wc9D5F8rbnTD5LNYMT59LItimwBsaRl9xyVrTC5a8i97Oh0 +1gvQ23Tjctdhsg1EsiUdmaq5LQSmh5ZPTCHbYVPQ7plrbcn2kMxqLM7kkheh +Pj219ldXsgOUe9WSjdXJjujuEwqLRvRYOyFT413P1EQd1s6YV2wt47npsl6M +79LMkxJeabF2QZbspdb5JrIrbhwWNS6fpWRfbzcsa/ilbtTjI3fc7siZnVyv +Xq6FcXtAzF1TeV2gy9oTd+zOrP5brseai00/vuTIZCasAVvZgtmcCs645UCO +1CJNkDGfnXuBuVXi4+Ngzs694HS/dv3dalt2vgRpHXH3qoR27HwJhl+nNhVm +O7Jzb7x46v5FwBlndu6NBOM/onTbXdn5UtS2tvib94K1H2q2j2HUaQp73g+P +Tz2ocyczyzFyd8fEsU7l+P8vX459ma289gesGX+4VMQaNZuqj79+cn88Cum7 +YGbBmlmBuybzEjZ9nMLOV2AomzP2Yow1EwDdPX5vm7LZ5yMPwHuuzPc0mVmJ +x+u2xko7ab4SnnGaIauUNOfh26xigT/DPn85D/Eal+vsv6T3QyC83+lp+Uez +RiBKn9U1VIno/Of57caiER5rRSBOmj5VNoVQH4QDMR6NhmQEQd44UGsQQX0Q +rvS8H7tK9ymCkCJc7OMppj4Y/NHARGsp9cGQ5ce9cCLLg7EhSaBjqOqD0eAh +M+xQ9SGYm+SQe0tIfQjOC3pO56j+/hBYfOVtsZnOK0Jg3O/erJ1OfSg4T161 +VGykPhQnSnb/nHeS+lBsdm669ugY9aG4tbX9X6Nz1PPR7Dl10YXT1POR+n7X +VWUV9XwsvOjZkV9JPR+jjmPD2WepD0OXIsvhNt2PMOgmpPZ3l1AfhuEi9a+P +kBVh0Izfyi0nM+G4l9mSe3Q/9eHYuX9qkWsh9eHgTjLwyz9IfTj2bFp40vAQ +9RFweb3riiyP+ghsMexLWbOX+gjs4hT0OmdSHwGBnnz/9j3UC+Dr0XV242bq +Baji9x632kG9ABrnrYzDUqgXoFK/vsxmPfVC+G0t7V6XRr3w8/tlu/8lslwI +3oel7fGq5yfEHcfKqv2rqI9EeNqp6TVLqY+Eedpqt0KyPBLbEloeHiArIhHU +mZVnTGaiUO88v43vTn0UcnZ9k9ntSX0UtI2Oe600oz4K96c9adGxpD4aR00K +l7UaUR+NU31eBtVkeTTMBibntllQH41o+218N2vqY/DkUVJwzALqY+D9U846 +74XUx+Afd1l5P92niEFtXnqXE5mJhc/EhOels6mPxc7uhLIsA+pjkX5E/kFt +JvWxsM/7/kQSnWdEGDOW9vvSeY4I+j01u41M6T4RfjfRmJBhxVokwk37Eu02 +B7pfhCzmGPPahXWxCPuyYy2fkRUiDNpuM7hJr69ShPxLW3pMyIwY/o81Els8 +aL8Y1RW8Y5ZkiFEy29J8I50XiWFx8ZxlKlkuhvAvV0W1ar8YaW9P2Iy40X4x +jrfmuZ2j+5RibDBulYJL+yWIfSiNiCBzJDibNLT2mi/tl6BGw9q024/2S7Cm +Xed6YwDtlyDIEXacFbRfgubG0dVbVJ+XEiT2ftC6GUT7JWCeD5QHqz4/pVjc +fXCSejDtlyL8jWZIJxlSaA/Gp/xAvUiKZ8NvhnLJcinU9AoaDel8sRRf5xtr +ZobSfimS9e+ph5OVUhRcGtCcLqD9q/BbhkHrp8/z/wCmd69O "]]}, "Charting`Private`Tag#1"]}}, <| "HighlightElements" -> <| "Label" -> {"XYLabel"}, "Ball" -> {"IndicatedBall"}|>, "LayoutOptions" -> <| "PanelPlotLayout" -> <||>, - "PlotRange" -> {{0, 149.}, {-8.876053103180046, 33.805886718807834`}}, + "PlotRange" -> {{0, 160.}, {-8.876053103180046, 33.805886718807834`}}, "Frame" -> {{False, False}, {False, False}}, "AxesOrigin" -> {0, -8.876053103180046}, - "ImageSize" -> {360, 360/GoldenRatio}, "Axes" -> {True, True}, - "LabelStyle" -> {}, "AspectRatio" -> GoldenRatio^(-1), "DefaultStyle" -> { + "ImageSize" -> {250, 250/GoldenRatio}, "Axes" -> {True, True}, + "LabelStyle" -> { + GrayLevel[0]}, "AspectRatio" -> GoldenRatio^(-1), "DefaultStyle" -> { Directive[ PointSize[0.009166666666666668], RGBColor[0.24, 0.6, 0.8], @@ -12368,9 +14912,18 @@ Pn3e/wMy+6Ka "DynamicHighlight"]], {{}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, - AxesLabel->{None, None}, + AxesLabel->{ + FormBox[ + TagBox["N", HoldForm], TraditionalForm], + FormBox[ + TagBox["\"MSE\"", HoldForm], TraditionalForm]}, AxesOrigin->{0, -8.876053103180046}, DisplayFunction->Identity, + Epilog->InsetBox[ + FormBox[ + "\"\\!\\(\\*StyleBox[\\\"M\\\",FontSlant->\\\"Italic\\\"]\\)\"", + TraditionalForm], + NCache[{40, -Log[100]}, {40, -4.605170185988092}]], Frame->{{False, False}, {False, False}}, FrameLabel->{{None, None}, {None, None}}, FrameTicks->{{ @@ -12380,6 +14933,8 @@ Pn3e/wMy+6Ka GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], + ImageSize->250, + LabelStyle->GrayLevel[0], Method->{ "AxisPadding" -> Scaled[0.02], "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { @@ -12447,13 +15002,18 @@ Pn3e/wMy+6Ka Part[#, 1]], (Exp[#]& )[ Part[#, 2]]}& )}}, - PlotRange->{{0, 149.}, {-8.876053103180046, 33.805886718807834`}}, + PlotRange->{{0, 160.}, {-8.876053103180046, 33.805886718807834`}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.02], Scaled[0.05]}}, + Prolog->LineBox[ + NCache[{{40, -Log[ + Rational[5, 2]]}, {40, + Log[1000000000000000000]}}, {{40, -0.9162907318741551}, { + 40, 41.44653167389282}}]], Ticks->FrontEndValueCache[{Automatic, Charting`ScaledTicks[{Log, Exp}, {Log, Exp}, "Nice", WorkingPrecision -> 15.954589770191003`, RotateLabel -> 0]}, {Automatic, {{0., @@ -12566,8 +15126,13 @@ Pn3e/wMy+6Ka 3.948220757553961*^9, {3.948220926295884*^9, 3.948220951198298*^9}, 3.94822105768297*^9, 3.948221596008532*^9, 3.948222092860569*^9, 3.948222160512904*^9, 3.948260896298966*^9, 3.9482609695374937`*^9, - 3.9482619704036713`*^9}, - CellLabel->"Out[41]=",ExpressionUUID->"82706fc6-8940-4675-bd62-6cef3dba3ea1"] + 3.9482619704036713`*^9, {3.9482750112208643`*^9, 3.948275040866067*^9}, + 3.948275077650091*^9, 3.948275117481819*^9, 3.948275188884832*^9, + 3.948275307230934*^9, 3.948275396037715*^9, 3.948275520683762*^9, + 3.948275594593666*^9, {3.948275637196106*^9, 3.948275665184217*^9}, + 3.948275703371668*^9, 3.948275757839251*^9, 3.948275805212986*^9, + 3.948275847617524*^9}, + CellLabel->"Out[75]=",ExpressionUUID->"1cb0d51f-f5b2-4f14-a301-4582947dec07"] }, Open ]], Cell[CellGroupData[{ @@ -17800,13 +20365,23 @@ figs/fit_overfit_poly.pdf\>\"", ",", "overfit"}], "]"}], ";"}], "\[IndentingNewL RowBox[{ RowBox[{"Export", "[", RowBox[{"\"\<~/doc/professional/presentations/2025/ictp-saifr_colloquium/\ +figs/fit_overparamfit_poly.pdf\>\"", ",", "overparamfit"}], "]"}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Export", "[", + RowBox[{"\"\<~/doc/professional/presentations/2025/ictp-saifr_colloquium/\ figs/fit_bias-variance_poly.pdf\>\"", ",", "biasVarianceCurve"}], "]"}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Export", "[", + RowBox[{"\"\<~/doc/professional/presentations/2025/ictp-saifr_colloquium/\ +figs/fit_bias-variance2_poly.pdf\>\"", ",", "biasVarianceCurve2"}], "]"}], ";"}]}], "Input", CellChangeTimes->{{3.948261396853858*^9, 3.948261456102914*^9}, { 3.948262002062767*^9, 3.948262010053669*^9}, {3.948263254535993*^9, - 3.948263278400828*^9}, {3.948264466456936*^9, 3.9482644798256807`*^9}}, - CellLabel-> - "In[100]:=",ExpressionUUID->"89df9a87-bbde-4eed-acbd-026f71c05d25"], + 3.948263278400828*^9}, {3.948264466456936*^9, 3.9482644798256807`*^9}, { + 3.948273980266115*^9, 3.948273987450266*^9}, {3.9482758400977917`*^9, + 3.9482758469938517`*^9}}, + CellLabel->"In[76]:=",ExpressionUUID->"89df9a87-bbde-4eed-acbd-026f71c05d25"], Cell[CellGroupData[{ @@ -24528,7 +27103,7 @@ eWfvqdeUqv7g6n5IaH2wf/2t9v+0tZv2AwBCPagc "Out[239]=",ExpressionUUID->"d4b981b1-8a57-45b0-a635-08df48bc2861"] }, Open ]] }, -WindowSize->{1024.5, 561}, +WindowSize->{1440, 796.5}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"14.2 for Linux x86 (64-bit) (December 26, 2024)", StyleDefinitions->"Default.nb", @@ -24547,97 +27122,105 @@ CellTagsIndex->{} Notebook[{ Cell[554, 20, 544, 15, 23, "Input",ExpressionUUID->"2bf7a7a4-5fb8-45e5-93d8-d867014a08f2"], Cell[1101, 37, 971, 22, 23, "Input",ExpressionUUID->"5af352c6-8896-4a1b-b393-d7f34eecf643"], -Cell[2075, 61, 575, 12, 23, "Input",ExpressionUUID->"b6f65d11-1714-42cd-b279-8e2c0eb8fe70"], +Cell[2075, 61, 596, 12, 23, "Input",ExpressionUUID->"b6f65d11-1714-42cd-b279-8e2c0eb8fe70"], +Cell[CellGroupData[{ +Cell[2696, 77, 710, 16, 57, "Input",ExpressionUUID->"788c910c-c901-4771-95a4-a21a3056ef4d"], +Cell[3409, 95, 1574, 22, 25, "Output",ExpressionUUID->"a5455d1f-2200-4eb8-b7ac-87cfed829af8"] +}, Open ]], +Cell[CellGroupData[{ +Cell[5020, 122, 576, 13, 23, "Input",ExpressionUUID->"cbba3901-f3bc-435c-9c36-ae44b4230e6a"], +Cell[5599, 137, 10272, 233, 150, "Output",ExpressionUUID->"78929829-92ad-4661-b73b-c0d85ddb98cb"] +}, Open ]], Cell[CellGroupData[{ -Cell[2675, 77, 711, 16, 57, "Input",ExpressionUUID->"788c910c-c901-4771-95a4-a21a3056ef4d"], -Cell[3389, 95, 1549, 21, 25, "Output",ExpressionUUID->"f3d671d5-5163-4ffd-ad1a-0c6d048d0caa"] +Cell[15908, 375, 728, 18, 23, "Input",ExpressionUUID->"28259c60-740d-4dce-ab83-46e9aa5aaa2d"], +Cell[16639, 395, 36941, 651, 150, "Output",ExpressionUUID->"8e055139-6bd8-4751-84b0-d76ee0bd2474"] }, Open ]], Cell[CellGroupData[{ -Cell[4975, 121, 577, 13, 23, "Input",ExpressionUUID->"cbba3901-f3bc-435c-9c36-ae44b4230e6a"], -Cell[5555, 136, 10251, 233, 150, "Output",ExpressionUUID->"d7d2b8f1-468c-4cd8-83c4-dcaf04dc40a9"] +Cell[53617, 1051, 1011, 24, 23, "Input",ExpressionUUID->"93081125-f7f5-4ec1-8522-2663d9863e0b"], +Cell[54631, 1077, 45693, 819, 150, "Output",ExpressionUUID->"6aba4807-4f56-4e4c-91f9-44245b663beb"] }, Open ]], Cell[CellGroupData[{ -Cell[15843, 374, 729, 18, 23, "Input",ExpressionUUID->"28259c60-740d-4dce-ab83-46e9aa5aaa2d"], -Cell[16575, 394, 36920, 651, 150, "Output",ExpressionUUID->"fc3b1c7d-1612-478f-aa47-a5b3a1d59ced"] +Cell[100361, 1901, 666, 16, 23, "Input",ExpressionUUID->"28c5ddb2-5548-4f43-9824-c5195899a516"], +Cell[101030, 1919, 146040, 2516, 150, "Output",ExpressionUUID->"bd7062d2-2ab1-4ceb-a4ac-bd6a0bb3c342"] }, Open ]], Cell[CellGroupData[{ -Cell[53532, 1050, 1012, 24, 23, "Input",ExpressionUUID->"93081125-f7f5-4ec1-8522-2663d9863e0b"], -Cell[54547, 1076, 45672, 819, 150, "Output",ExpressionUUID->"5bb72cd0-6313-4d2b-aacb-35b976cc8b3f"] +Cell[247107, 4440, 1305, 33, 23, "Input",ExpressionUUID->"64b9d7b0-4d42-4971-a779-d26a172dddb6"], +Cell[248415, 4475, 22662, 433, 102, "Output",ExpressionUUID->"076474d4-f1aa-4668-a0f1-b95f7dd8be21"] }, Open ]], Cell[CellGroupData[{ -Cell[100256, 1900, 666, 16, 23, "Input",ExpressionUUID->"28c5ddb2-5548-4f43-9824-c5195899a516"], -Cell[100925, 1918, 146018, 2516, 150, "Output",ExpressionUUID->"e810cfbd-ca29-411b-b2cd-b42bb27abee4"] +Cell[271114, 4913, 1320, 33, 23, "Input",ExpressionUUID->"6320da01-8775-4d5d-a006-6ebc2cd45cdf"], +Cell[272437, 4948, 44278, 787, 102, "Output",ExpressionUUID->"fe02788d-4433-4cdf-9696-f7c15350355e"] }, Open ]], Cell[CellGroupData[{ -Cell[246980, 4439, 1305, 33, 23, "Input",ExpressionUUID->"64b9d7b0-4d42-4971-a779-d26a172dddb6"], -Cell[248288, 4474, 22636, 432, 102, "Output",ExpressionUUID->"3eb5fcf9-8f4f-4427-ae95-caddc8dc5094"] +Cell[316752, 5740, 974, 26, 23, "Input",ExpressionUUID->"8d4e6581-f6b8-48df-a676-75ca341189cb"], +Cell[317729, 5768, 68968, 1224, 104, "Output",ExpressionUUID->"e068285f-6324-4bb0-9a30-479c6b4173d2"] }, Open ]], Cell[CellGroupData[{ -Cell[270961, 4911, 1320, 33, 23, "Input",ExpressionUUID->"6320da01-8775-4d5d-a006-6ebc2cd45cdf"], -Cell[272284, 4946, 44256, 787, 102, "Output",ExpressionUUID->"acad27c5-11e9-4605-b453-e6d388234131"] +Cell[386734, 6997, 278, 6, 23, "Input",ExpressionUUID->"40855202-d9c2-46f6-ae45-c3c37ee795d0"], +Cell[387015, 7005, 174, 2, 25, "Output",ExpressionUUID->"a961f55f-4340-44b4-8a5e-96fef706b7c0"] }, Open ]], Cell[CellGroupData[{ -Cell[316577, 5738, 974, 26, 23, "Input",ExpressionUUID->"8d4e6581-f6b8-48df-a676-75ca341189cb"], -Cell[317554, 5766, 68940, 1223, 104, "Output",ExpressionUUID->"a9f403e8-1dbf-4c95-9afa-f2836ea123b7"] +Cell[387226, 7012, 1049, 28, 23, "Input",ExpressionUUID->"af4110b9-8b7d-44d5-a091-88eb1c487999"], +Cell[388278, 7042, 145116, 2452, 102, "Output",ExpressionUUID->"eaa9a4dd-4bdb-4a04-9840-d5957524e949"] }, Open ]], Cell[CellGroupData[{ -Cell[386531, 6994, 1555, 38, 68, "Input",ExpressionUUID->"f6f545cf-927d-43c1-af6d-713c7a209a9d"], -Cell[388089, 7034, 14486, 338, 133, "Output",ExpressionUUID->"4558eca3-abe8-4b93-8bbd-b8a6a370b459"] +Cell[533431, 9499, 1555, 38, 45, "Input",ExpressionUUID->"f6f545cf-927d-43c1-af6d-713c7a209a9d"], +Cell[534989, 9539, 14508, 338, 133, "Output",ExpressionUUID->"97c48afc-a508-455f-a069-6e9a7516ab1b"] }, Open ]], Cell[CellGroupData[{ -Cell[402612, 7377, 1023, 26, 23, "Input",ExpressionUUID->"bbf26ddc-fe38-479d-a3c9-6d8e7eb05a56"], -Cell[403638, 7405, 79640, 1394, 171, "Output",ExpressionUUID->"259cf64a-f845-402c-9036-7198c08c5ee1"] +Cell[549534, 9882, 1023, 26, 23, "Input",ExpressionUUID->"bbf26ddc-fe38-479d-a3c9-6d8e7eb05a56"], +Cell[550560, 9910, 79640, 1394, 171, "Output",ExpressionUUID->"259cf64a-f845-402c-9036-7198c08c5ee1"] }, Open ]], Cell[CellGroupData[{ -Cell[483315, 8804, 812, 23, 23, "Input",ExpressionUUID->"ee92f7cf-efbe-4a88-99e0-b631a8475400"], -Cell[484130, 8829, 187767, 3242, 176, "Output",ExpressionUUID->"3e3e6643-166f-47a6-a8d0-c67de6c2e4be"] +Cell[630237, 11309, 812, 23, 23, "Input",ExpressionUUID->"ee92f7cf-efbe-4a88-99e0-b631a8475400"], +Cell[631052, 11334, 187767, 3242, 176, "Output",ExpressionUUID->"3e3e6643-166f-47a6-a8d0-c67de6c2e4be"] }, Open ]], Cell[CellGroupData[{ -Cell[671934, 12076, 887, 27, 45, "Input",ExpressionUUID->"0e06d7b5-aef2-4721-9794-4d08e86b51b0"], -Cell[672824, 12105, 264, 6, 26, "Output",ExpressionUUID->"d9e07b9d-4c99-4596-8430-98b40a9824db"] +Cell[818856, 14581, 887, 27, 45, "Input",ExpressionUUID->"0e06d7b5-aef2-4721-9794-4d08e86b51b0"], +Cell[819746, 14610, 264, 6, 26, "Output",ExpressionUUID->"d9e07b9d-4c99-4596-8430-98b40a9824db"] }, Open ]], Cell[CellGroupData[{ -Cell[673125, 12116, 1570, 40, 68, "Input",ExpressionUUID->"7c9d6eb3-c96d-4f11-913b-3d4f12b217fa"], -Cell[674698, 12158, 19159, 411, 178, "Output",ExpressionUUID->"82706fc6-8940-4675-bd62-6cef3dba3ea1"] +Cell[820047, 14621, 2799, 77, 73, "Input",ExpressionUUID->"7c9d6eb3-c96d-4f11-913b-3d4f12b217fa"], +Cell[822849, 14700, 20203, 434, 133, "Output",ExpressionUUID->"1cb0d51f-f5b2-4f14-a301-4582947dec07"] }, Open ]], Cell[CellGroupData[{ -Cell[693894, 12574, 650, 17, 23, "Input",ExpressionUUID->"9112ed8c-b092-4553-8c70-b3cf97baaf69"], -Cell[694547, 12593, 48762, 871, 171, "Output",ExpressionUUID->"128a43ca-5a2f-4258-a468-df2dc1caa86b"] +Cell[843089, 15139, 650, 17, 23, "Input",ExpressionUUID->"9112ed8c-b092-4553-8c70-b3cf97baaf69"], +Cell[843742, 15158, 48762, 871, 171, "Output",ExpressionUUID->"128a43ca-5a2f-4258-a468-df2dc1caa86b"] }, Open ]], Cell[CellGroupData[{ -Cell[743346, 13469, 1166, 30, 23, "Input",ExpressionUUID->"048b0258-5171-4ae8-971c-7cda8b5e5a39"], -Cell[744515, 13501, 113415, 1937, 171, "Output",ExpressionUUID->"e4b6b211-4660-48b8-8c93-495e75216299"] +Cell[892541, 16034, 1166, 30, 23, "Input",ExpressionUUID->"048b0258-5171-4ae8-971c-7cda8b5e5a39"], +Cell[893710, 16066, 113415, 1937, 171, "Output",ExpressionUUID->"e4b6b211-4660-48b8-8c93-495e75216299"] }, Open ]], Cell[CellGroupData[{ -Cell[857967, 15443, 1072, 27, 23, "Input",ExpressionUUID->"644bc450-35b3-4346-a518-939a37f73a1e"], -Cell[859042, 15472, 64148, 1138, 171, "Output",ExpressionUUID->"f13c5692-112d-4db3-b926-5a0e63510020"] +Cell[1007162, 18008, 1072, 27, 23, "Input",ExpressionUUID->"644bc450-35b3-4346-a518-939a37f73a1e"], +Cell[1008237, 18037, 64148, 1138, 171, "Output",ExpressionUUID->"f13c5692-112d-4db3-b926-5a0e63510020"] }, Open ]], Cell[CellGroupData[{ -Cell[923227, 16615, 879, 24, 23, "Input",ExpressionUUID->"77011a3f-25f7-4ebc-8867-077913d64174"], -Cell[924109, 16641, 43162, 781, 171, "Output",ExpressionUUID->"82a5d709-d14e-409d-9dc3-a3709bead9b5"] +Cell[1072422, 19180, 879, 24, 23, "Input",ExpressionUUID->"77011a3f-25f7-4ebc-8867-077913d64174"], +Cell[1073304, 19206, 43162, 781, 171, "Output",ExpressionUUID->"82a5d709-d14e-409d-9dc3-a3709bead9b5"] }, Open ]], Cell[CellGroupData[{ -Cell[967308, 17427, 887, 27, 45, "Input",ExpressionUUID->"ce01a5ff-e386-49cd-932e-f969de5ec286"], -Cell[968198, 17456, 306, 7, 26, "Output",ExpressionUUID->"2b9abaf1-daa3-4fd3-8c60-190b388e81e3"] +Cell[1116503, 19992, 887, 27, 45, "Input",ExpressionUUID->"ce01a5ff-e386-49cd-932e-f969de5ec286"], +Cell[1117393, 20021, 306, 7, 26, "Output",ExpressionUUID->"2b9abaf1-daa3-4fd3-8c60-190b388e81e3"] }, Open ]], Cell[CellGroupData[{ -Cell[968541, 17468, 1808, 44, 68, "Input",ExpressionUUID->"defda054-10ca-447b-b647-94d42a909770"], -Cell[970352, 17514, 11393, 253, 179, "Output",ExpressionUUID->"890b6588-ab8c-4d16-ae4b-440a9b9a42e2"] +Cell[1117736, 20033, 1808, 44, 45, "Input",ExpressionUUID->"defda054-10ca-447b-b647-94d42a909770"], +Cell[1119547, 20079, 11393, 253, 179, "Output",ExpressionUUID->"890b6588-ab8c-4d16-ae4b-440a9b9a42e2"] }, Open ]], -Cell[981760, 17770, 1924, 38, 142, "Input",ExpressionUUID->"89df9a87-bbde-4eed-acbd-026f71c05d25"], +Cell[1130955, 20335, 2457, 48, 176, "Input",ExpressionUUID->"89df9a87-bbde-4eed-acbd-026f71c05d25"], Cell[CellGroupData[{ -Cell[983709, 17812, 1434, 30, 23, "Input",ExpressionUUID->"f1af494d-9d96-4899-b3af-8673ddf60d9f"], -Cell[985146, 17844, 122458, 2096, 179, "Output",ExpressionUUID->"958a8029-3a5b-4cb5-8c98-6c2d8a901d8d"] +Cell[1133437, 20387, 1434, 30, 23, "Input",ExpressionUUID->"f1af494d-9d96-4899-b3af-8673ddf60d9f"], +Cell[1134874, 20419, 122458, 2096, 179, "Output",ExpressionUUID->"958a8029-3a5b-4cb5-8c98-6c2d8a901d8d"] }, Open ]], Cell[CellGroupData[{ -Cell[1107641, 19945, 744, 20, 23, "Input",ExpressionUUID->"28a73a8c-aea0-47e2-b622-44374c6b6c73"], -Cell[1108388, 19967, 144539, 2459, 171, "Output",ExpressionUUID->"de41f093-c137-461b-9d53-da822c3f3f15"] +Cell[1257369, 22520, 744, 20, 23, "Input",ExpressionUUID->"28a73a8c-aea0-47e2-b622-44374c6b6c73"], +Cell[1258116, 22542, 144539, 2459, 171, "Output",ExpressionUUID->"de41f093-c137-461b-9d53-da822c3f3f15"] }, Open ]], -Cell[1252942, 22429, 602, 13, 23, "Input",ExpressionUUID->"b480bdb4-aea4-4095-b875-8b69fc641458"], -Cell[1253547, 22444, 535, 14, 40, "Input",ExpressionUUID->"e6f0b190-e1d7-423d-9ac0-1bea376c509f"], +Cell[1402670, 25004, 602, 13, 23, "Input",ExpressionUUID->"b480bdb4-aea4-4095-b875-8b69fc641458"], +Cell[1403275, 25019, 535, 14, 40, "Input",ExpressionUUID->"e6f0b190-e1d7-423d-9ac0-1bea376c509f"], Cell[CellGroupData[{ -Cell[1254107, 22462, 1435, 30, 23, "Input",ExpressionUUID->"22daee6f-134b-4508-8577-f887ddf00b51"], -Cell[1255545, 22494, 119073, 2033, 171, "Output",ExpressionUUID->"d4b981b1-8a57-45b0-a635-08df48bc2861"] +Cell[1403835, 25037, 1435, 30, 23, "Input",ExpressionUUID->"22daee6f-134b-4508-8577-f887ddf00b51"], +Cell[1405273, 25069, 119073, 2033, 171, "Output",ExpressionUUID->"d4b981b1-8a57-45b0-a635-08df48bc2861"] }, Open ]] } ] diff --git a/ictp-saifr_colloquium.tex b/ictp-saifr_colloquium.tex index 2d621f2..dc152f8 100644 --- a/ictp-saifr_colloquium.tex +++ b/ictp-saifr_colloquium.tex @@ -227,7 +227,7 @@ \frametitle{Machine learning is just curve fitting} \begin{columns} - \begin{column}{0.8\textwidth} + \begin{column}{0.9\textwidth} Number of data points $M$ is big: all images on the internet \medskip @@ -243,15 +243,157 @@ \medskip - $\chi^2(\pmb a\mid\text{data})$ is called \emph{cost} or \emph{objective function} + $\chi^2(\pmb a\mid\text{data})$ is called the \emph{cost} or \emph{loss function} \medskip - $\chi^2(\pmb a^*\mid\text{data})$ is call the \emph{training error} + $\chi^2(\pmb a^*\mid\text{data})$ is called the \emph{training error} \medskip - MSE is called \emph{test} or \emph{generalization error} + MSE is called the \emph{test} or \emph{generalization error} + + \bigskip + + \textbf{BUT:} machine learning uses many more parameters $N$ than data points $M$ + \end{column} + \end{columns} +\end{frame} + +\begin{frame} + \frametitle{Curve fitting: the bad, the good, the ugly, and the weird} + \begin{columns} + \begin{column}{0.25\textwidth} + \centering + $M=40$, $N=2$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_underfit_poly.pdf} + + \bigskip + + Underfit + + \smallskip + + $\chi^2$ is large + + \smallskip + + Best fit has \emph{high bias} \phantom{variance} + \end{column} + \begin{column}{0.25\textwidth} + \centering + $M=40$, $N=7$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_goodfit_poly.pdf} + + \bigskip + + Good fit! + + \smallskip + + $\chi^2$ is moderate + + \smallskip + + Best fit has \emph{low variance} and \emph{low bias} + \end{column} + \begin{column}{0.25\textwidth} + \centering + $M=40$, $N=40$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_overfit_poly.pdf} + + \bigskip + + Overfit + + \smallskip + + $\chi^2$ is zero + + \smallskip + + Best fit has \emph{high variance} + \end{column} + \begin{column}{0.25\textwidth} + \centering + $M=40$, $N=80$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_overparamfit_poly.pdf} + + \bigskip + + Good fit? + + \smallskip + + $\chi^2$ is zero + + \smallskip + + Best fit has \emph{low variance} and \emph{low bias} + \end{column} + \end{columns} +\end{frame} + +\begin{frame} + \frametitle{Curve fitting: the bad, the good, the ugly, and the weird} + + \begin{columns} + \begin{column}{0.5\textwidth} + \centering + $M=40$, $N=80$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_overparamfit_poly.pdf} + \end{column} + \begin{column}{0.5\textwidth} + \centering + \includegraphics[width=\textwidth]{figs/fit_bias-variance2_poly.pdf} + + \bigskip + + Bias--variance trade-off is blown up! + \end{column} + \end{columns} +\end{frame} + +\begin{frame} + \frametitle{Overparamaterized curve fitting} + \begin{columns} + \begin{column}{0.5\textwidth} + Underparameterized fitting ($M>N$) has a unique minimizing solution + + \medskip + + Overparameterized fits are not unique: $M$ constraints + \[ + 0=y_i-\hat f(x_i\mid\pmb a)\qquad\text{for all $1\leq i\leq M$} + \] + plus $N$ unknowns $\pmb a=[a_1,\ldots, a_N]$ gives a manifold of $N-M$ dimensions + + \medskip + + What leads to the `good' solutions instead of `bad' ones? + \end{column} + \begin{column}{0.5\textwidth} + \centering + $M=40$, $N=80$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_overparamfit_poly.pdf} \end{column} \end{columns} \end{frame} diff --git a/poly_fits.dat b/poly_fits.dat index 8b24681..c852533 100644 --- a/poly_fits.dat +++ b/poly_fits.dat @@ -148,3 +148,5 @@ 0.0156992609950267 -0.855990654518181 -0.0487481000745383 1.16526081049727 0.0115277702897213 -0.41170348113494 -0.0277528012501371 -0.133089717088096 0.0499212777564621 -0.163208300822234 -0.0918303208298792 -0.0212634736101883 0.11892778805798 -0.0726148615560329 -0.0257757683323649 -0.28855282845615 -0.0933442918708437 -0.269730974027386 0.0516344008860471 -0.0800827898377909 -0.0824934474712395 0.366261054573152 0.10852720274791 0.152551891488986 -0.0151591274206862 -0.3101038968827 0.0171049269714861 -0.275199948777986 -0.177558067860056 0.013314309874632 0.184169384863041 0.069263456944367 -0.047979183181397 -0.248145475996162 -0.12893748815333 -0.449349007035541 0.177488475336076 0.144672525257065 -0.114120630040306 0.393411524368455 0.103135411129222 -0.337385367297853 -0.178826390493433 -0.392860827965247 0.156916741864721 0.509963912383838 -0.116839426396639 -0.0818323806659801 0.0504921008087951 -1.05813420175425 -0.0195168530979508 0.69601728625912 0.108440006169425 1.97065702278657 0.0157011750212708 -1.47265718741318 -0.0487491472878755 0.324784202520371 0.0115316778330241 -0.537421319619236 -0.0277578292231692 0.879416758676714 0.0499189692849963 1.4480559282375 -0.0918336469652153 1.13618613010888 0.118927436204161 0.135136365798039 -0.0257782335995401 -0.372109879702366 -0.0933502579464975 0.407493169961186 0.0516289027042208 1.33210400272092 -0.0824931417085299 1.17773387170451 0.108531936883484 -0.470556907321667 -0.0151563480278765 -1.08566358272376 0.0170937119396583 0.741330284535738 -0.17755948698266 2.31460342007802 0.184164305231105 1.00544737610829 -0.0479708156142459 -1.15571316222327 -0.12895145655675 -0.294914706313337 0.177485570892503 2.3951858748892 -0.114116375037234 1.30485944594152 0.103140669896743 -2.10959404473414 -0.178840166192846 -0.323764335068271 0.156913536696162 4.11157344228129 -0.116826825804998 0.776604784965629 0.0504793955269988 -6.4162474684845 -0.0195378147977744 -5.21974767682956 0.108507760290167 0.00836086194721252 -1.47258120196202 -0.0766418534313989 0.32489190224214 -0.00891920685402311 -0.537396451947032 -0.0145934854104207 0.879297965472762 0.0972631642326662 1.44785244978115 -0.0389197514390108 1.13603408068545 0.144870990363605 0.135117847119193 -0.0289879728712142 -0.372066278244718 -0.0927264162862545 0.407443072748128 0.0844349464743901 1.33192421548264 -0.0363389925413266 1.17759388996824 0.120092319634288 -0.470497166213846 -0.0437349967508779 -1.08552728438572 0.00940754590353577 0.741246456656251 -0.120777980423517 2.31429654757286 0.251110837396278 1.00529608758788 -0.0477997419467728 -1.15555793286671 -0.157318593247708 -0.294871027376391 0.217666708777024 2.39486404934543 -0.0420711994085414 1.30468198744714 0.0869379708208069 -2.10930361050267 -0.22878081871129 -0.323709713947386 0.227675630588069 4.11102324437483 -0.0213544547928814 0.776492077555783 -0.0563536442705833 -6.41538396691822 -0.247397724116167 -5.2190370510797 +0.0083464321088261 -0.259045606978447 -0.0767327482838297 2.42433613639978 -0.00896769404150989 0.532254896733201 -0.0145736052476122 -1.66305791966046 0.0974002498981976 -6.00706452330201 -0.0387661521446207 -9.03930028495489 0.144952437061279 -7.46241287025206 -0.0290093021195982 -1.32136805636478 -0.0927550998643551 3.99964591302567 0.0845084683795553 1.87757756663877 -0.0361880933075889 -6.33831837543809 0.120155285050558 -11.2142350175853 -0.0438077382255349 -4.78594650312355 0.00932203257410406 5.9159631451035 -0.120607880587521 4.78148306519606 0.251303193353683 -9.04690567714601 -0.047751920245287 -15.1787017960394 -0.157483969086387 -1.78658812968893 0.217774404535616 10.6240028086073 -0.041812022576882 -2.09896649254381 0.0869177471644478 -21.4256667613624 -0.22901783422761 -9.09513839491435 0.227884646615107 25.5867185366696 -0.0209799346896165 35.7570391043719 -0.0567574931274445 15.2558199208748 -0.248249781125227 +0.0148822083085583 -0.259146814722491 -0.0469653427409659 2.42413595471842 0.0246561642249715 0.532117835861584 -0.0267378699447054 -1.66280124115861 -0.0212187119708147 -6.00614845196186 -0.273176148134555 -9.03790886552455 -0.114221846983822 -7.46126743526478 -0.167676176889528 -1.32117330621003 -0.0526487952415103 3.99903819523348 0.175851689267966 1.8772912617348 -0.105278162562738 -6.33732185611541 -0.152166356733099 -11.2125171425002 -0.290751848374689 -4.78522630831028 0.0242125768763595 5.91507489300003 0.0410597846362137 4.78075866467834 0.185937306592611 -9.04553179394344 -0.421995287284564 -15.1763741025325 -0.42382185635511 -1.78631058144966 0.350253943822395 10.6223768702851 0.0909189712190791 -2.09864153600621 -0.272294690444556 -21.4223755935745 -0.701290133149344 -9.09373100735653 0.47599483511028 25.5828044008482 0.926760544474678 35.7515405095308 0.744819515683356 15.2534614845216 |