(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 6.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[     92613,       2074]
NotebookOptionsPosition[     87515,       1898]
NotebookOutlinePosition[     88570,       1934]
CellTagsIndexPosition[     88442,       1928]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[TextData[{
 StyleBox["M",
  FontSize->12],
 StyleBox["athematica",
  FontSize->12,
  FontSlant->"Italic"],
 StyleBox["l and visualizaton packages: ",
  FontSize->12],
 StyleBox["Mathematica",
  FontSize->12,
  FontSlant->"Italic"]
}], "MainTitle",
 CellMargins->{{24.375, 31.375}, {4., 4.}},
 CellChangeTimes->{{3.3991807872930174`*^9, 3.3991809225074463`*^9}, {
   3.3992213137786493`*^9, 3.3992213656832848`*^9}, {3.399307715630843*^9, 
   3.399307715630843*^9}, {3.4063082555888815`*^9, 3.406308278361627*^9}, {
   3.4063083791665773`*^9, 3.4063083851952467`*^9}, {3.4063084779586334`*^9, 
   3.4063084969859934`*^9}, {3.406308528010605*^9, 3.406308549841997*^9}, {
   3.4063086072144947`*^9, 3.4063086153061295`*^9}, {3.4063086512478113`*^9, 
   3.406308683844683*^9}, {3.406308715990907*^9, 3.4063088223238063`*^9}, {
   3.4063088667677135`*^9, 3.4063092195950546`*^9}, {3.406309421555459*^9, 
   3.406309470836322*^9}, {3.406309518414736*^9, 3.4063095560588655`*^9}, {
   3.4063156648929377`*^9, 3.406315673835797*^9}, 3.406315844120654*^9, {
   3.494181972140625*^9, 3.494181972625*^9}, {3.562090305313267*^9, 
   3.5620903203204937`*^9}, {3.562091373483588*^9, 3.5620913744351892`*^9}, {
   3.5782025474521894`*^9, 3.5782025478421907`*^9}},
 TextAlignment->Center,
 TextJustification->0.],

Cell["Recursion and Iteration", "Subtitle"],

Cell["\<\
Here we give a short summary of the tools for recursions and iterations. \
Then, in the next projects we consider several examples.\
\>", "Text",
 CellChangeTimes->{{3.4133983260731506`*^9, 3.41339837614515*^9}, {
  3.413653048904213*^9, 3.4136530493448467`*^9}}],

Cell[CellGroupData[{

Cell["\<\
Functions for recursions (conditional definitions of functions)\
\>", "MainSection"],

Cell[TextData[{
 "Conditional, piecewise functions are very common. We considered them in an \
the project, when we studied the ",
 ButtonBox["conditions in patterns",
  BaseStyle->"Hyperlink",
  ButtonData->{"CAM-2-typecheck.nb", None}],
 ". Here we give examples how they can be used for recursive functions."
}], "Text",
 CellChangeTimes->{{3.413396936785453*^9, 3.413396994167965*^9}, {
   3.4133970500683455`*^9, 3.4133970765764627`*^9}, {3.4134033067149615`*^9, 
   3.413403421920619*^9}, {3.413403454026786*^9, 3.413403454026786*^9}, {
   3.414265188959501*^9, 3.414265197682043*^9}, 3.5628433882220144`*^9}],

Cell[CellGroupData[{

Cell["Using test in patterns", "Section"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "f", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"f", "[", 
   RowBox[{"x_", "?", "Positive"}], "]"}], ":=", 
  RowBox[{"x", " ", "+", " ", 
   RowBox[{"f", "[", 
    RowBox[{"x", "-", "1"}], "]"}], "+", 
   RowBox[{"f", "[", 
    RowBox[{"x", "-", "2"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"f", "[", 
   RowBox[{"x_", "?", "NonPositive"}], "]"}], ":=", "0"}]}], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"?", "f"}]], "Input"],

Cell[CellGroupData[{

Cell["Global`f", "Print", "PrintUsage",
 CellChangeTimes->{3.399662555717131*^9},
 CellTags->"Info3399669754-6520538"],

Cell[BoxData[
 InterpretationBox[GridBox[{
    {GridBox[{
       {
        RowBox[{
         RowBox[{"f", "[", 
          RowBox[{"x_", "?", "Positive"}], "]"}], ":=", 
         RowBox[{"x", "+", 
          RowBox[{"f", "[", 
           RowBox[{"x", "-", "1"}], "]"}], "+", 
          RowBox[{"f", "[", 
           RowBox[{"x", "-", "2"}], "]"}]}]}]},
       {" "},
       {
        RowBox[{
         RowBox[{"f", "[", 
          RowBox[{"x_", "?", "NonPositive"}], "]"}], ":=", "0"}]}
      },
      BaselinePosition->{Baseline, {1, 1}},
      GridBoxAlignment->{
       "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
        "RowsIndexed" -> {}},
      GridBoxItemSize->{"Columns" -> {{
           Scaled[0.999]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
        "RowsIndexed" -> {}}]}
   },
   BaselinePosition->{Baseline, {1, 1}},
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}}],
  Definition["f"],
  Editable->False]], "Print",
 CellChangeTimes->{3.399662555837304*^9},
 CellTags->"Info3399669754-6520538"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Evaluate", "[", 
    RowBox[{"f", "[", "x", "]"}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "1"}], ",", "4"}], "}"}], ",", 
   RowBox[{"PlotRange", "->", "All"}]}], "]"}]], "Input"],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxF0wlUTdsfwPHTrXvPbVJE6d7GW1JdvPLSpOxfphQKqYciEkL/eIgkVEoD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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{All, All},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.3996625588316097`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell["The derivative", "Subsection"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "'"}], "[", "x", "]"}]], "Input"],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["f", "\[Prime]",
   MultilineFunction->None], "[", "x", "]"}]], "Output",
 CellChangeTimes->{3.3996625637887373`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Evaluate", "[", 
    RowBox[{
     RowBox[{"f", "'"}], "[", "x", "]"}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "1"}], ",", "5"}], "}"}], ",", 
   RowBox[{"PlotRange", "->", "All"}], ",", 
   RowBox[{"PlotPoints", "->", "100"}]}], "]"}]], "Input"],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxE23c41e//OPAjKXsVGSUrqwjJSp4vJYSsCmUkohJJJEVllJBKkswSMkJC
ZZVXVlb2HpW9OcceB+d3n++v6/P2j+txvda9ns/7eV8uQrYuJvZbCASCKgOB
QP3daOXxl0Ih4oR/P99G9tUErfznNJe2zztm/7Ofr0Kw+MB/PvR+TsGw/D9H
TF0PfhP4ny29Lh8+yvGfxyPNn9wVnvmfz9x8FVWze+p/trrbynpVZeK/+30C
x/0ujP3PVftei920GvmfT6ym1GTdG/qfd17b0VR6a+B/vtIzr2Z8u+9/zlnI
2Gup+Pt/jv1jmq0i9p8DqgjHd3H/5/OxZxyaF3v/Z1rN9QydL//5zEs91cMK
/3lJbuIMq3zP/9zHHz4yKfSfa+jUPas5/vNn4ihDCs1/ftP1IubhbDd+MI7s
+sxOpziw7Ii0bX833iT52uPMRFDxzczhYmjqxkf1t9Mqi0cVa/uqDKx96sY5
raE6rSK1WP7aoFtnfDf+SWVP5qc/H4t3n31K9zW0G+8MvlfV45VTTJLol3C9
gexgkTEQnl8c2RjoMnqwG7/2nEnV06602K9QnqZiL/I22vmC8bJip6TesAQ2
5Htr6WSXimLMU/arFbELv3ZtfM8D76ri8b2d6y0fu3AT7UqagFf1xaou4sE/
pLvw2AclQ9V2bcVRjgzPPwl04Z9kl17P87YXr9hPvoxn68Ir+qX09jS2F3+1
zIrzme3Ep4+HZ99Q6yyW11XKxr504ur0l+/v4uopfnGC96tsciduUhAjp1Hb
U0zCyIWCrztxB8fGIUff3uKPSng54U4nHvpLRa94+nex1D7tzh9qnfgNnW0h
8nZ9xUGCkr8/SXfi5Ph4e+3ivuIxfqaBeIFO/NGqKljy9hcnczZM+hA68agP
LnOPGvqL6VizSTdmO3ARWsZf0VIDxZcYXi7aDHTgmRZJ77MeDRQLE8woWHkH
XsLcZd51ZLDYl6y8Ve5LB65n7yY/EzFY3LfExyCU3IG3fWdhpp0bLIa5dRaO
1x24DXfq8K5TQ8Vvpv9w0gR24Ld2mx0nl/8p3hj7sWvWswPfpV91U8qzudhy
KGF3/9UOvHtmONAhM7+Yv8dBrESvA1cSHdrUvt6sfrddZ3+2WgcevnCzgafo
j3p3k5TsO+kOfMcAoXHBf1g9smpGxZetA1ft0m60HSOp7/zqcUqjpR1/ndYe
f+jwhjrziwD3kvPt+IF9a/GOo4ywrpVcWnK1DV8cYBIK+MELhhO5CRvn23Dz
H8oc7r58kPC0xE9Fvw0viLOnsT3GDydbe49ly7ThruZ4/9Hy3RBxcUdZ/Hwr
PlF3M2Gxci+MbxVK7B1qxZPbDKtdNQVBLVXGn6e9FTfTdCgZSxKEgZmTx0Pz
W/F8oZfZ7fZCcNDbp+zBvVbco3fqRc6oMPjtfZZYdL0VF9OjDZbUEYH20hj/
5QuteFMBr198qghIOqTZHTJuxX0lZO/uYhAFb4a84y7HWvFDr7VuPrsqCg0Z
5SLph1pxN8st0pePi4KwUTPtqGgrru3dH7siJgS35v8OCnO34irKvrw7uXZD
VcR0mfX2Vnz4Nqwq9nIBvyo5MXqlBd/jQs7O1WKD67/pH7aPt+BuM7ddV1u3
AJeoqKbBrxZcSUdNfUplrNg2+3z50Rct+FxQPX3OBD/+5cyVpDt+Lfi+fYHh
lRxCOP3KrYdf3FpwQ7o0UUUZUfyj+gtNadMWPLliQnPHZSmcXFtZvpu/BWcV
ySt1cDqEh48oVJCTmvG3iaq0Qn8AHw069l4pohnvDnq/78BXDFeVNnrk9rgZ
Hy7JrNa+p4H3u107MXm1GZ+WK+Z4wHQcl6FJqOiWacYZOf++mxbXwiv52X4W
5DfhJs2CpTU2+jhz+EHjz6lNeK7LNq0W5VO4CbNR78fIJpyRZaq6h90A/7Me
Opfoia5r5zVN/TDERW9l33tzpQn3v1n/4a6+Ee443UQfZd6Ey2iUTN3PN8IX
f3PufabchAf9Sb7xONQYVzU99CFQoglXzYzKebJujPvUnz7sz9OED3mFLDy/
YoL/1HL/cY++CX+u+0AxvNUEZ8bD9TxXGnFl3puekdhp3ETpS/vNsUZ8cPRS
YWzGaTwyq+2ic2cj/uyr2Xo8zxn8j/jS1OWqRvy1r4uq/RYTXCSe29M2vxEP
Sq1t8w01xK/wKNFapTbiw6fyFVV26+EfQ82emUU24oHzSa9JKVq4qm9kkr5n
I554bz2n+P4R3NiWr0lRGb0vXe0Js7YgbOqoneG+0YDvp3xm2dp9GoJV7jky
GTXg5hnqVhI7TYFLqtiHINuAR52rytA3MIcDTFjmBLEe3/65R+9VqSWcrzu+
DXepx28q0Jx42WYLX4318i+71OGG4+L+osXX4NixkHpLwzp8GJ/6oNjjBHXy
dUPGB+tw/4jsZp0VZxjaYcihRvyF/3m354Ui7w3gbDdxZHf5hXMZpvSdP30T
3vx86UNn+Au/WBi0MNh/EyTzWiPWZH7hn/Y50TvfcAMs0rRsaKYW11uXlX3w
1B1czp/fXXC9Fr+fVvggsdIDhpyZeFuManEPC+eRBP3bcN73G9e0fC3uyCJ4
KqHpNjSEO3Nu56rFbfHm3HemnqCZKsAmtFyDn3d9xPeuxxMKixqYjnTV4HWX
5XuHsdtwsMGH/mxRDT4r/ztR9fgt4FsaoAl6UIMbVMsfGtJ2hecM4ZsJF2vw
cYmiRdfw67B1zwnyt+M1uCzO/og/yhGIx1MWSNtr8NHJosTrCbZQ/uLaqHlo
NR4gGUafknoYVN/vHrp5sxrn1PJb5bkkimfl1/WFnKnGzykz0thsO4FH/z3Y
/YOnGi8vlSkLunEed5Fe+CXxrgrnpNdIerPPGeer9s5Zya7EM6Vqdkr63MdD
e6WzOMMr8W9Zz8Um1H1wOtKf9AMelbikbmEpftQXJ3FrvLdRrcTJ99nIjkf8
8YpLdJFVpT/xtLGCayWKj3FVz6/hA0k/cW7/oe2vDwfin55cfrEe8BO/t4ct
yUkhCI/OqQ6W1fuJm5lc6t0l/wS/QXh2L7KlAl8tYj11Xfo5PrwD7uZ8qcAV
0mMXhLhD8fPiJI9frytwx5Xs0pBXofgJA5MbBMsKvDWs19o2/AVeeJHWmU+9
Amfqmz1QtyMMl731+aqCYAWuJr2drPQyDOeL5ba7MlSOf6iUe80S9hIPzaq8
4PezHP+9U9vekyMcpyvztIxNLce5bC0PDYaG43fbJc99DS7HdbNcaQzYX+Gk
8e6zjU7luPd6QEP+81e4/cYTkwmDcjz3ZGycCFsE3s1+1HCrXDnenZnJlaka
gRuJzugJ7CjH2XuJNYt54XiF0lsd5cUyXJFR3kf98EtccPFWTENrGU65HVvP
GvYCv5ujP+PwuQx3r2VRLf79HJeVXnv5yq0Mj/LLc6MYofESPvt3brYUN+vn
qqd18cSvszB5ZM6U4HYOsZfmlrygqqa/SrO+BM8zu/OqU8MXRALz+XszS/B9
3kkrSoEPoXOLQwmjcwnOX7FWvLTzCRxb+cF8ZfIH/jC9ZZ/qrnA48HNa60Qj
jucLYF0WkfHQj8VMuT3H8c5Rxpz5q+8gokgnLMEAx5c/tQU/OZIAhOzE35Rf
xbji8WtqRX8SoTXmnHth9Xc853LEW759KRDEvZ1vPPA7Xi970TNnKQXUX3zG
d+l8x6dW9xvrVqVCagAb062f3/D9ISVb7l77AFY03z8lPvqG658N6eE4mg6c
3o6mzZrf8MsCZp/TWDPA27Xi3cGyIjzl05R9V3YmyE3d1Lb2K8Ir7uSpu/p/
hBEHwekQjSJ85JjfLoazWRDTXxdWRCjCCQFinkY7PoGRpZfyBF6IT3QVr/S/
+wh0HRJ/eB4U4pSp1/4Hb2VAoXG7v7Z6Ic5KcGW9p/MBRLXlGpK+FeBHxERE
eYjvoavkj3uLVwFuoLL+0b40EZ6phfBtOVKA2+u3qeS+egcrcqP2Fwry8Z3D
rG9jPaOhbnfcOu/XPDyE/HGSQ8wPTJRWWT098nAxruNHCMpu0Gl8VqhdMQ8/
H6uxOiSgAUMBLFpheV/x4coA/cNbfPA10r3njAVf8M8nrI+pc0XhYhXWwuSi
XPz9Vt3vpW8y8Yy/hQrnvHPxTps6We2SLFxujVs7Ty0XD7GWaB6e/YSrHWy4
5vY9B/9ZmH7CcWcufjoKvkwWZ+PybjkH3M7l4YQeLDTfPwvfNYSvPRzEcSb2
1c/uW7Nwnmos2u7uD5z7RHaX7KOPuFi8UN5W2hJcOktIJC0gEz9mMEjS2lmK
Kw91adtvz8SN95WzjMWW4pq8YU5CgRm41XqSVNC+MtzQQPfFb/oM3KnlkbbU
xzL8vP+Wr1FB6fidDw6XahXLcfv8wu6zjOl4oK+2rxNejt+YvknhePIBd41k
kTr6sgz3Et4vWs/0Ad96aKU/YEspHmA2qBMckoa/qhuIanT9gb8IiXHWYknD
9RqjExVKv+OxJafDtjxLxV3pbuyoii/Ec/eX99x9noKXu/DNz1h9xottvAlK
7Cn4SBLR1k8tG695pbBvPjQZ3/s56P1+xQy8j5J0/VrYe/wqx/fqOZu3OHPr
IxrLV4m4aSxRuf1LGPxaeWZwV/EtPnk0jK07/zvI3fWp5T35Bl/oVxcXNvkB
EWRXnQKLOJyU9Fmro7IEbDbPHFvxicGnpOIfaeSWwwItv6JH7Wt8SPE2LXdw
DexmS9lz0yYUv5oS9uAvfwvkm87Vvkk2x8/jmFdg9R9g696pKP3uON4VT2a0
e/gXkuZumf3kUgApDYu6N3v7gC61nfzD/CKkC3Nb3enug9yjLR+v+N2GtOEn
3jJGAxAcaByo9joYkq7dLoo8MgyLmey3koViIfq2gYoz5yQ4/J7V2i0SByE3
POlKb09CJ3MLT5joG/C8mtDE/XsS/nzR/VO8Ix7OWSxd/ZEyBSU7Wfw+cCcA
H7yJ3nF0Bu5mbDjav04ARuUqhysJMyCvOXNakCcRyLJz8t+3EyHJrWFfBG8S
dAtr1To0E+Fx84tq393JcIp2eaM3lwSYo1+OWlwyVFCYLj0eIcEKjVvM8p4U
OLouWCPHOwuOcmecnfemgsyibkTA/VkQqdY0lYhPhZTZC+uy2bPQa3MYBgXT
QGDG3bZncBZereyTePMuDSImgqoecc+BQSg3xznhD8Ay+kZG9uQcbJfYvrYj
8QM8HswN7/aagx/48kC9SDqYC/x09wufA0+zsdqgpHTYIWi5fsR/DuSInZ81
92XAL6E5/0XXOZgIqI6jvM+AAJFApiybOUgQKAwoFMsEjX0CL68YzsFOgxhz
WYmP8FVCN6HnwBzUDT/RmEz9CNel+iRf8c9BwD1vqWTJLBA/4JFtwDgH3u0y
m0+5PsGbgwk/SkZnYZqOvZF2VzY8Ulz7k5IwC42Xmt2IvLlwWvMDvzvPLLwW
Niv6uTcPFi8wvmLeSoJ4CaJtt0UeaB3e7981SoRUmceMM6/zIPGDRm9UJREK
VfPOcbHng9Wr68/4HhPhj8muFTtCAbQ4Vs3xbyPCqHnW29tqBaDQ90evd3gG
SNba2k88CyDs7GJSbMUM0Fy7HZFDKgA9TNhsz6MZYHRlU/95oBCyvih/+n1p
Bjhvpwx3XSkExv2GDG80Z4D/HjydTioEl3h7W2vRGRD171Cg6S+Eci7vIoGt
MyAd5NK7c08RhJRkxxvRzoDi8+0PJc4Vweqd0VZ3thlQf/V2v9qrIrCR38MQ
xT8D2jFKLYZNRVA1YXL0u/gMGL1ruGvH8g1kEwNd+w/NgHnKZeHbJ7/BS4vi
93TYDDjmvnZ9U/IN7H9JshqYz8CnQbOPRxKK4d3zjiyXghkoGCeeNfxTDNt0
WIZeov6VEh9v2PLh4EE4zpPfNAMt5Dz94DAc1F0/+hAmZoDMEHLLSeMHdJk8
Mn7BRwQB4akdRXIlwMN9aD7HiwjC+/JHyw1L4EH9FfEONL7iEg+L6p1LoC/g
jQX5JRFkZXbbDaSVQPYyQ/nxDCJoqOrnMAiXwpmuvvDWXiJcMskwMucsA00D
bX6yAAn8003qh+TL4E7QBvfzfSRI2Lqq53q6DHLKczlFDpCg/+sJ7eDwMthz
RJBRT4UEBPapcu4vZWDg0U73F0ggeDXsWGJbGTzODqFx0yIBlCr/OLhUBvlT
xza2nSKBNf/fo9+4y2FWfHUl+jQJ7rk/KtJRKofKe6l2DedIEFu3X6XNrBxC
mdKDk8xIUCTW/PWiZzlYRGVm3zlLgu4HngozkeUgJf6p0wA9v9opkHO3oBxW
PudQRIxJwCNfcXB7dzmUHfsitmpAArMhjv2C/BVwwbrQPVGXBB5H81MzjlTA
/qlvMZ46JIiIsBZTsayApTt46SnU3laddCGTuAoIfVXOvqJBAqNMTZ6He39C
6a/6DH3UX12P23RjIpUgfmRwaFGcBFcb9vi7a1bCctUwUy0ar0CJcgKNfSXg
pmPy8SIkqOxmX+dNrgSLm9M+untJoAkf5vQkquB52vLut9wksIs0utGpUwXn
ldaOu+8kgd/s0vSlq1UgUbHueJKTBCWJx8fvfaiCij6agnkWEqjT//6bdaAa
Zncxn9WhI4HVRX8rtVPVUP2e1XsPLQm8CyV7qpyr4cUhjsQ5Aho/J4/2/o/V
oPvmwIDKKhG6K3afud5QDSMFcrJDC0RYEyhrWiNWw902xfvPSERQbmKr2yFX
A0XMGnyDKJ7NpL7qxhvXgKGE1pWng0Tw8LesOnCzBiaO631V+kuEV71btArC
auDxBaOtA91E+Hw4rexEbg3s8TprEtJOhJZnhhrNLTXwIeJ8vCLKv3Oji8XW
CzVwXo8iJ1tPBE6NWLXJnbVwMXeh3LiBCHLRxwpvH64FC/4JM7dGIlxJfOHr
dLYW6sr2vX/eRIQ3GX06F2/VgrrTxbl09D5m/H6H7pdaOPC9M2SolQhjg4UL
ew7/AoYLlSVnu4gQL33oYLlCHeQkJO1XHiBCh6LfUv6ZOhDS6/M8g/rDijV9
z3Svg5fz/D9vDBHB28RF//XnOgjSfGmTNkIE89vpVx0V6sFmxPcV3yQR2EtE
ktgVGmC71AXK+jwRtGtuXqM70wDezdH6vItEuN9SIr/m1gDzd9ujDi8RYWr4
QslgbgMM1p5SuL6C4o3OwKWHtxEKndWu/l0nAiF4sblNshGUuD2/kjeIEMMa
p9io0ggJxbm0PBQiNO+a2ig/1wi1j7kMU9F8YlLBIR+jGuFzZ8h43xYS9H6U
I6WmNQIxQ4rdBc3/7UNdpxMLGkHat0pxA5kz3ycvrroRLpx1sHqC8vVHNQn+
yK5GsJErlt2K1o9uScP9sPFG4BY5e2wcXR8+cXsgZLURWnZOna5H3m34M82X
twlUV3hvRyLntzizeEs2wfL4p8B7yKfNuVw9VJrgY492tC1y8MVLytfONcFe
/Nb3A8jLblsqz0Q1weqjJtoS1B6BUdc8tVR03YEymIKseb4/RTSvCXS1pMuf
IYdhPwIXWpsgclvQQ0vkAyz3dcPZm+HwY4xuBfXXJnm1ruVxM9wIzNp2EDmA
92pxUUQzRFz5PcKFnBnS+THxfTP80GGqXKchwdrNvOduZc2wg+Hy4xrkcLhl
vIPSDJlBAvQOyFWdpFYTjxYYCH7KEIfGd0bPpkL1UQswXisa90fmwhu+CIe3
wGG98WpHZNv3HyPmslvAh+lEsDJyII/A4+4fLfB+8qbjXuSsJ09vlza0QFNt
vO425HVXJ/Ow6RbAeFa5UtF8Cg/36Nxdb4GQzjPtt5BPmuup2DK1Qmfkp4jj
yDdqCyV1+VpB/hyzGQdyhLoUn7xkK9zmvbLr7yYRvmdHMfIpt8LxYKaDX5CH
RBnINNqt8CGU70QRMmOk5+T42VYQfC1pUYIsxzTW03SpFQLilF0rkc3vm/0q
cGuF1UTtx3XI92d/fnvn1wqOH0zjWpB/dbyPc41vBf0892rq9xyS7C5w9LbC
RuMnoRXk6KN/B4xOt4HvVslmCdS++p4jEnft2mDuyrVrB5G33I10TnRrA4+6
zK2KyI5fjVcWX7aBdoS8ErV/qgfLWWJa20BAQi3WCrlbME15+Gw71OoZOoQh
s+J091kd2uHEpxeUSORjVrZlSh7t8Hlna+Rb5A9R/AbBEe3w9Ld5bQbyXc5n
dgc72sHexVa2Evnjp4lU89F2aG9Jqq5DHjDQnvFdbgcz5VHbVmTdJ4Q7rbs6
4CSN06t+ZN6tbs/umHfAzpe31sjI+gkNLQlXOqCK3HOSBs2fD3aA95dnB2xK
34vYivz5T6D1YmAHqNkIDG5HHvMeThSI6oCuHlNBRuTd/MfGtdM6IHjpDpEB
2ajgjYxrQQcc44grpjp/0aygrKsDMrUGLameevl5c2q8Ay5d3HaAakF5Dk3u
tQ7g95Yk01PX1/Wa+it8nfAg2yWKavNRtSEWi064tHu9jfr9kEdRkkrXOoFL
ae97qn+ILF238eqERuNj7lRL2GSt5sR0wtHHgZxUr3QKsZn3dgLP3E5D6vqM
rNmmmmDVBY2V0lXU/pmZ7WcucOqCnoxn0VRzDxn+afDqgv4XRCeqwzci/Tai
uoBkkc1Bdajs/lrz9i7gISlY0CIbfjeMcxlGbnslTTWrrrtLwEIX7Ctcomyh
ttfu+47PnN2g+DA/ieqgCENLNsNuOMejNkMdbx0Rdxkx626w3Ij9QTX9p0jC
UeduuDKwEUZ1QHV/kuOTbriXgStRfcJ0223f6G7wfyHISPXWQamTkWnd8NjD
t5eA7LfuNl1R2Q1x2HFfqjWCIvHe9m5I2Jd0mmoC9/cX88Pd8ImRToxqPKHf
jnGxG7b+3193SHD/4DZFoa09MEeh/hBhXcew20C4B7b8u37XNvK+N/bfdUeZ
/vhxuV6Y/2eLNckyU5HfQP7n/JdaCV/W/8DiPz+JyMYYr/X9733s4ZyU+mv9
QPx3PeKF2/eXTgPQ/89VoTVp7O4D0PvPa8+FIp56/ecDzz39GP0HYPSfrZ41
XH8cPADXjos0U/3sqZjF1rABMD0WfpvqHyH3tH2jBkBXg24P1aJP9gt6pQ4A
O4xe3kQ2DfZjXskagEPq5ixUPw7qWnHPGwDpo9U5G8gTjx83Xf85AHOq6Rvr
yNkPB/1shwaAqOjykhpPA/6qLn8nB6DscJ8y1Tv9X1hYzg/ADwXjP2vInr6g
YLplEMLlD0lSrX4/Zvik4CBYySwXryD/un1aR85yEGjEHkwsIm96fFD4aDcI
c6Kk51TLetAI7b82CAyiFw9T/dI9a1X07iAwCh/3WUA+78qUzhM5CPie7dzz
yCE3bF+/ejsICbs9i+aQi10K/DlTBiGUf9yGaqHrly2Zvw7Ca97a9FnkMccy
FkLrIGhzPdcgIfM58q159wyCyU7CKJGaL666jqwODILRDtcQqrMu78XnZ9F1
jtMdM8h9Dh7pN1YHYQt7uTfVnA51r6cJQ8DFdliYao9LXjdG2YZgknmX8zRy
ql2z5aVdQ9DIFMhJdZet5Ml+gSGgZ1rNm0JmtPU5bC02BA0MjlZUq13sEOqR
HoJf9D1bqL5uI8NqfngI6rfrp04ix194tNaqNgR1m7/1qP1ptu4dMdYcgpJK
tavLyLTWh1rq9YagJzQmgDqf3+YIjlOn0fd7InZQ49P9cT2B0XIIzhP/2tEh
D326KnPCaQhOcd/cyoz8kzY+qChkCI5fijjBixycxoyl1g3BHsLfykPIx9S7
2yvahiB2hwSPEjK5OcV58PcQSIu7XlFFdlo/FiMwMwScBrQMGsinDO8shbMO
A3usuK4BNR4WhzN8DYdhVOnGryvIVUG5x9+aDYOtXsFuJ2RfAd/ubxeGYdp6
i7ML8pz2bvoVl2HoexTO4oHcGm1idz10GNpa8g2o+3nIQcG1J5HDoDFK8zaA
mj/Kp0PT4ofh95ouMQj563Rg8dCnYcgX+v08FPm6n+nZLQXDAIfF+l4ii+0S
ndpbMgw5Oi6yr5FfYzivRdMw/HChaaLWD0ZtIZ88u4ZBwl9X6B01fzme147o
H4Z3ES9dk6j5eVP8T+74MHAXLMtEIHu+XHRvmh0GufrzLXeRZSXKmIirw6A+
+P32BeTxb6EJzFtG4PyK4G5N5PMj+xu1OUfgmvDoJRZkTq9VB3u+EWByCecc
QvNXy1a54Sc8AljUeYtM6vpQsd1fLD8Cl6ZHpgBZICQyQOH0CLBGUNjs0X7e
q9948IDFCBw29TY/iBzDQt8lYjcCn7lX41dRPcrz/Pb+HW4jwPV6Tu4ZMkeY
aeNs2AiciBw+nYfq162RO/mymkfAObr2NQOZCKXm+mXJ3SPw6rxOX8saEXx4
Hzq9GRiBPr4KiTfIG9HzxU/nRiAgprhAHnkprtnOiXMUgmKzeyzQ+WQ8MTRT
0mQUWt683vtxGcXDpSpTofOjwHZh5xVPZId9BAKv7Sjo7n3x6RjyQLKLCf3N
Uch+G6zRgert+MspZMqdUVi8sD34HfIFib9Jy76jcEPwYfM1ZIFxbgNi0ChE
9hH4FZF70wyWR16MwmT8PTsCcrRjQPyfqFGoy/+gWIhsvr/4ZPu7UWjQXCtu
Q9/jnlqcq0sbhf7Gk9qzqJ5vy5COrcgeBWGrqAZm1J/6LGaNpKZRcH7aQbq7
Sc03mhMxXaPgxit+JwKNv56c98uX/aNQZlJEOEddzzmTw36zo9D4hzHIHdWj
JV9qgi9yjAHzclpUOqp/PxcFtgoYj4Gx+FghLz2qH9xENZ+aj0Hcd9vFOORv
+3/kki+Mwdrp3weFGUhQHrMc1nl9DCJ9mpOkGEnQ4uVgHBYyBoNd354dYUbx
cUSznq5qDK6FvLC1YifB0vzfo+4NY1AkzBzXj7yW7pU50D4G9AUBHfYcJNiy
OzcEHx6DtGEv/evoPMqxLqR3h3YcNtUdFB+g8+rOz98LRxnH4Uhb3w1aLnT+
djonZco5DveuWaQ/RhbsDWU4JDQOhyONBEPReVc0/MCddxLj4CtTe37nLlSf
6FeNscmOQ0f5iVeRyAe2XjK/rzQOuy1+NOzmQfHwjVI5pT4Ot2ZVGd8hK7jH
KFlojQPvq0RrUWTlA0op1afGYSaPNVkSvV9tqJlb+ew41HTfmZZB7cNirwck
W45D0saQggJqv+YZxqWdl8YhTNDIWwX1V4c52d7/2jhcPV5Ups6K6hfv35o2
d8dBPOiFyUk0ftfVikpavoxDPbTxj6LzcsY3j6LCAxNwKUaFIfQLERQZg9qq
FSbg4JOnNCeyiVBiFkPsVJtAcdm/uppBhPY5XGRZfwLenQ+asEsiAo0kQ8gh
Z3Sdr6tW6SVaHx78ycduTUAPg3T51DO0vsqlfxjfm4BXqz7f3gWj/fyCyYLL
0wmw65LIZPJD+/GrGMuMzAl4Hen57O8NtL8MZHoUfZlA56FfAeFORLgm+yO0
5vsEnPYUfHDyCoq/2qHysboJoDevcsm9gPYP3uU/y20T0Ky9+8oVC3R+d2BY
3fZnAvKUbtjsMSOC4Gf+HdwjExAiXm7ebILqbRoZ6X0z6H27eIwfGxBBwRDT
VliagLQoAUFRdB2PNbl4fHMCqkYW8vej9+tOXPIy2TYJtYdqjQ+h9rQq3X51
kXUS2nzeTajeQfH4KCjrBvck0NXf9j8WgOqH5pjqBwKTsMhnsFsXjQfF+cdG
nMwkqH9ZO3UukwjBRc27MhWRtzSN2BSi+oFhWO6b+iRIGKY8uFJJBKkkBodu
g0mwGT+dfbufCGe6Teq5XSah7JkpYy2av1St4TfPsyaBryzLeVydBPLhy/lv
8ibh7TifqvMJEnzvZ2jJxCdBlT1g26weCZq9Zbb/akDvt7J8u2JOgo2c2y70
pEm4uEzftN2NBCZ7GTFf2SlI32+rIJZCAuFLPoLbladg4AxwHslE8ZW6RHgK
UyB2fzfJMBedZ+UHSyINpiChsT39Do7Oj7fPJQiYTkHfam7QswrUnm8NfklW
6H6RF5cTa1G8nvh2/JPTFHy8pSdS10GCpGB5UUX3KZh6I0Ez8Bvtxw2pW795
TYFkFd3fpUG0nnfuHdbwnwKH2YFvTBMoHs+9qqgMnoIUvh/RgiS0X8cxJZ8K
m4Le43Geh5dQPhnwDWiJmgJe57umuuskeCi+4nDu3RScjzBTuLBlFs44Xdf+
mzoFFQIf7h2eR/GaPSRu/2kK+NTNTFjR9xYWz9NP5qHvWW0VH21G54EH2tVL
P6dgMca6MTKHBG1hgnqsw1Owj3eHyLorCUwLmg2OCk1Dq9hK6CM0P2KbOgfL
JKbBxt5EVakE5f9jONtJ2WmYTMwYHItH9e6v9MYzMA37hC4q6tsQoePvQxMn
q2lI4K/p4fw7A+bblExjoqZBjj1WLL53GiT0MhWF3k1Ds8FSg/G3aVh5LrIr
JXUafJ4a3aGNnYZIXvbOnLxp8Gak++VgMQ1dB8bP1bRNw+jW667S3ajfp2Os
VjlmwHUVvhV2TIJsuZfROd4ZkHH9fIItfxK2HbY8XiA4A5ljEg12kZOQw71H
8s7BGRjt4BhgPjcJgY83+LsUZyDWMODaRZVJsF75zaqiPgNClWsLX3gnQeFq
MU3UiRloU3e5z7g2AYzdbxZW9GfA+evg9gvdE9Cn+2DU/MwMSB7Rtx9ZnICv
RRe68y1mYGY7jW6VySSEHMDqeOxmoKf1i8wHtI5t4wR/eDrOwNN3jjtCmKdA
mZUmt9N1Bh5f37vifHUKWB/0v1e+MwOXjrT2GqJ5KbJJeLLyeAbOtx1N3uEz
DWFNfvfNn88AbcJc8CIavyvH7FzzI1D7rqe4dKjMwE5RUTPP9zMQSc+hEjM/
A06j74VXSmeAWWDO/sUhdL69nlawvDED7sYVKzwpszD3JyjDjA7Fed7eyaC2
WagydHybx4zygMDd32u0c+Aut//RbX4Up5Mypb02c/BrIcNoWRnlrYeRT+L5
5uGe16fRJTciuORfE5B4tgB/AvO4lsaJoLmXU1Pp1jKoPmfNXZolQm512EpM
yjK8fmVvtIzqBHP3HZmE7mWQaAo6sb6VBLrVO7lr1Fdg4LeSzwbK+3fcdo1Z
0q+C6fLLRYoCCXIqd4f4xazBw7ugSVBB+8zNOGy0bg1yNybCCEdJ8Gm3wKIe
gQzsW4/J0qC88M11rzWXPRmq2UmOW86SoJNfWDZVZh3UpPT7tt4iAe8N8da6
kg1wzFyWobtDAi++1ED5hQ2Ikk28R3ePBIwVEkdfi23CkuIa37ZHaB/jk0q2
ebIJWcdTz25/hfax8gOe82co8Ofn6aTtUSQou555wPwxBZh1KXPb40hwiVem
/1sBBa4YmYbSvyeBZN6ufcfZCJiw1dZahi8kOMLM+4zZnYAZ9WXxMhaQ4MHF
c2PqTwnYAzuLK4zfSVD4NeqYazIB672aQ8eE8oz+Rb7ltk4CxjhtdYapGsX9
1/PG9HMETPkGQyJTHeovU0y6KhMN5jD/eZapiQQsF3vonEVpsFceNhhzG3r+
K7/N26M0WPkq03PmLhJkWO7IvKxLg8155/1mRnnJdeqZSaMGDSZIsDvA0o/2
dW/GFWUVGszAn9WLZZgE/UwBce9kaTDvbYXVLOMoL8bQHGeUoMHSg+x5WKdJ
YLD/3tjNvTQYfei3L6yLqG7XdT+kyUqDdbFGX65ZQecGD8f92DYa7MPT27wB
KG8dTLQRUdskYPpP5O9t0M5CMll/h8IMAXsRkKo5xTkLnhn75kXqCRjfvfCW
atlZEGHtyKF9RsAmya6PHinMgpVq3QfKIwL27a6hkobyLMQ5lCWQ7xGwC56M
MfkwC/R4Vti8MwFLcvOxTTGYhTaXwJuDpwiYtKPT7EOnWXjQpCKPTobY5tjJ
ROzGLOAbB6VwOgLWeFn87LrbLPSf1tf0IFPgpv1AvpvXLBRu3Sfq0EOBrzbm
PrbBs+Dh0D54IoYCj/8elhd4NguVxaUtR59QwNx6x1DXi1kw3ZVVdtiLAmSL
em3jqFmgq3qcuM+CAr+601eZ42YhQdD95R49Crw5F5ReFT8LTHds/LmOUAAz
02TDUmfht6SKHR0/BTjahUrI6bOg4rfv9AYjBe1TlJt5WbNg2fgu79jmJuS2
9Iq65c7CN++Lf/W2UuChSWG7TN4s2EgKbT+L7j/b9DpwonAWytv6ZKzZKSBm
dEs1uXgWjvrFm17mpkD1Kdk3e37OAm/P3uQ7whSI/sVi1FWN2vf4b52fBAWc
9CZpXtXNAovC28UnMhRgPZlsz4zyxHiIwIk3qhQw0dwtTR6chQr1PUOlJhQY
YTmssH1sFiR0PadPnaOAV8epIzumZuHJ2ZalzgsUSHJ8cHL/wixEOwUxEJ0o
sBQ6YG+xdQ7cohdl+FH8RP9OfVMkOgc7l+ruuBVRQCal5H2lxBx400j6b5ZQ
oOxGd0bLgTn4w/wwJKiKAlO0zEWTCnNAFFF9+7aNAupSLh38J+ag2ji5vJaI
xsvjMLu3/Rx8McW3c3ISMA/MYFfg1Tlw7XUKMeMiYEyMlwXCneeA15aPI46H
gCnERR7IuDUHsc63+CT2ErAqh+xD+Xfm4NS88FtnYQJmJVujWn5vDpjvNIrk
7iNgc6sDGo2+6Hub91JXJAhYQBlZp/fRHAQ/3C+tfgCt36c7jcaC5mB6IcmM
HznLVNps4ekc1C/fvrR9PwHTFNSyJoTNQe2aruu8JAHrHLe2Z46Yg08be+7/
Re9zyr3txBM9B+8Js8G14gSM5l6om+ibOXhGW/46T4yASbGX+qolz4EDg2P2
c1ECVtzVHajzYQ6smY8We4kQsNOJ88/PfJwDLTb22suo/d6K+944fZ0DUa6v
QyBIwOotAwtjf87Bb8EtPCR+AuaWZjC/PjIHmsrR9412ELAP16OsyifmoIDQ
32SAxm/g0FDlk5k5YKgW33eKA+Wv4juxfEtzkHbuS+1JlN9kWpJOKNPNA61X
I89xJgI2tr722k1kHjK+b8s9TEvA9pae2HJEfB4oj05tU9hCwEwfhzpt2T8P
jgbh5+RpCFgFh5jGC/l56Pt+nGC9SYEEMeOJjxrz0Ey4G220RIGuyZgzHifm
4fiL7RqnFijAnj1SfPTkPMwLvRo9OUeBB0e8X/4ymgfz458Ujs+geCVUbrw8
Mw+SrUd7YIoCMxUcVyzM5yHqUq2v2gQF9j2xbBa2nAds0VxCZYwClkYpahMX
5sG6QbNeZ5QCL7nmkrPt5uGIktjJBuSabjWOO5fnQebt9vKz6H4V++bh7S7z
MH69psB2nALcdzee7buP3s9q9N57kgKNiaf7bWLn4eMpC+9PaD2eWKY86uic
h/JaVymeFQr4ND9YfdI7DyunPbbEIhdmUpywvnlY7LnbvXcVrf9LlNNpo/Nw
Yso/WHyNAruaNoW8lubhK3PEhOI6ir+M+68Ors0Dzavo0kLkkMeb9EMb88C0
5220+gYFCOqbRH26BbCUTtXVQuM5/mHju8DOBegTs2qTIhAw0YB7ci27FoBw
7UKJE7L1xY2kx/wLQJd1MfMjcvOujSck4QVQVXJ4RJ0f5nlvSpLYAmh6XXF1
R9aqX795TmoBzuCOVl+RfdK8R1hkFuASrfPJFeSih+vnSuUWwF7b5bAqmu+l
C951HocX4OYTVyFvZNkj69h+lQXwynhS4onsyO39+a/aAswz6mo6ISfNksXD
sQVwvkpfeQH5zy+vGB3NBVis/HnyNDJPKpl1Q3sB3MQe/dJCfmpNXrQ3XACz
QZpmaeQqFa+rfKcXgKTx44wQ8hYucm+96QK4xN/v2InsUbtWpmS9AJetyL1k
1N4LymsvGJwXwLhjYbQaWY5zVTozGPW3dnTDHrmtYsl+oWIBDuXWSb6hjs9k
tsxq9QIM7CiOC0Vu5HBe3qhbgPfuHzn8kX9ZDQZub1+AucPPVy8jly42pPON
LMC9fKNqOeQf/E/c904sgCyvxlFR5O8aWkdFZxag/Y5cNjdy/tNv9dJLaDw9
ROWXKWg9595+Lb+2AG+V6Ph6kXO75G2UNhegY2WYpgT54760WWzbIrzzSmkK
Rs7Qu1R4gnERZtQCC1yQ01z3+uuyLoJmPEvDeeTk1916hpyLsLpFapc1ctL3
VzvPcC+Cjr3WhYvICYNGv835FoGpyjblEnI8A3OylcAiREk9IF5Gjjnrp3RZ
bBEiiHkPriNHeh0lOEktAmbSWumKHPFupeqGzCJ0fCax3UIOm75+/q7iInDe
lYz3Qg58ZHHvqdYiCG+N+RGIHJDOrRWmuwi1Dnn0Icj+TU2srw0Wwbi6xeg5
8v09OvHxposQ+Iy5/xXyrS8KZbkOi3CP5z5NIrLtMAtDd8AiyEtfPPYd2Yap
uulP8CLUPb8X/APZSu5h9OCzRVCai2ouQza/t7Z/OmIRfPKabWuQDbhGDQgp
i5CuoenfgXzkxI9wscpFYDAVL59F7nXI/DFSswjiCmqtC8jegdFTyfWLwMtp
PESdn2+17pri7YvQXXd36yay5fTFG6Ndi9Dfph1MQPO5wWoYm/J7Eco1TTi3
IL+RVau63L8IlbmW0bTI6iaSC+LDi2C+f5mbDvmPG7fg2Ngi0O88SaD6wSta
/dSpRXi1Hj2+lbp+On8nSiyg+atT/0a1xoWw05K0S+BzI+Ai1QM+Dx6Mb1sC
pXOdulT7JTilpzEuwYCGlALVpcNatFKcS6C4o34b1ZpO5BwpoSVo+cKVQW2P
9p1LnAdgCejJSUvU9o5FG6tPHVuCzMGlv1QHflN3zNBagnO/dKqprqLwlB4w
WIKcuKkYqnUD6lylrZZAB1PQoPrUS8UmGa8lePKo7AkN8sxnkY2Z+0tw6DrX
LaqftbNLZvktQa/pZWuq63knfQ4GLwG3BJMc1Ubxb2Vlo5agosaknTqepJIQ
S1LsEjjnJlH/pwd7MXgn8FP8EvDHLqVS3Sx2pk82dQnsnKO9qL6po8E8m74E
XKZTl6jmdJRRzs5aggJ1dQOqc57wX3LNXQIL8VAlqk9n0ofK5S0BM/uAINVf
eeU4jhUtgZyCAT3VfAHnwkxwNJ7/9/catD7nfHfYlS3Bn38esP4Q7la5BPX/
nKZEjghvWIIf/3yDXT/qS8cSbP4zpWQ6bnl06d/fgyjwzO15gsrKEnT+c0Z7
c/p3nmVY+ecaFe4vGirL/7t/GyGu8uTdZWj7Z42fIt3GRcsw8c+7drTuoz2y
8j9PX3jo+rlwBeL/+SHmrXt8aeV//dkt5C7SLLcKdP//36Wwg3tebh5XWYW0
f9eP8eZ0fcFWYeif9V9rVF7XXAWFHxojVJ/lavosrrMKOa+VQ6i2fmmT0Ke3
CidcDspTfYWD9DzKcBWeaol1UuPl5vMH90xOrwKfwJ77VHuxsF1jMluF14s7
RKl+xiCjdc96FcqTaG5sIH+mcVq3cV4F0pbf29eRix+Qx3ldV+Fwd0smGbly
I7ij2X0VvmbXnKa6ezUtR9N7FUps8t+uIRPmRq9IPFmFsuKXSqvIegN2bcTU
Vai8q3t5CZknXYZnNWMV7mIf6Kgecls9vyV7FdroGJMWqfNN97xvZ8Eq3Ait
7qPmgxyJwkmV6lWgvNc5P4/8YPahzPG6VTh6LXVljjo+hYau+k2r8EOW/jXV
w3rDS9Zdq2BQVNlCzS88LuxbHo6vwlqj1ikS9bpSj+bT6VXgjkieJFLfT0h+
HDG7ChEW24Kp1gs7wpK2ugrnRyp+zlCft9hmlLOxCh3p++ypHhJpCiuiWYND
ro9oqb7/xYGnnmENWsia2DT1+ftyFh0sa6BRkvRnivq89npcH8caJAdsvUf1
MFtl3zjXGvzVu8RPdU7nC5F53jVw4CgvmKT2752lw/qeNbC15oiktlffUTyN
TngNZoajDlLz4TD5mwyP1Bpk3z17kBr/OeWPXYVk1sCzmNeLms/uPzX5LCW/
Boe3/PmJAgrj2TumclR1DfqCHKzZkPWP7Thhq7sG8lG3n+6mPh941SLDcQ3+
5EVNKlLzIRd3IJa+BiULv1OuUfNJF6cMXdYa8H2OLrpOrWfesLVW56zBWTez
BldqfhVnEDxduAZ+s41Lt5HXldfz7KvXQGCm7MRDZKeNFSupujW4melz7jFy
T8kiLbFxDW47HXVGCRwr1CUaenauwa+Jr+HU/V6KbWpRrXcN1tLcUl8iR7WM
xdD0rYHgVdlvEcielgOjwaNrcGU0bTCWmj8F/z41nFyD98kOy2+RzYZ7Du0k
rkGWvQhTIvLPtM6uzrk1iOk+lEO14vW2B3FLa7C1yFuX+v1k+eZ9tmtrYBJT
MXADmXu5vlZsE/Xfi9XLDHnxQdWuT3RkuKgWn06tJy5pVnx3ZyBD7e5xVI4T
sFb6UjsVFjIcXrPLH6TGz4uirNKdZHD1esx7nxp/iR+120TIoHG/vicH1YsD
l9Ono8TJ8EfdhtkH2fhA6kvr/WRIocyqnUKW/fLu76g8GTZ9uN6MonqT+DP8
9poGGar8LW12IztN3E3Za0OGI0ETQ4/Qebr34+1TQ3ZkENH15kIBCXpu7vOp
l8nwkpFVSxBZat0Z5F3IMPVELqUQ1btjLBc7NO+TofmZ51Uiqoft5bS3O8aS
4Vj4thlzVC93Mt35yh9PBslJAwFxZN2RD/Z1iWSo10BVwzJqXwxruWw6GWKJ
4lkvkBNuYW4DH8lwU+vG3wvIXEY3hcNzyMARl88mg7y2td1nuYAMw7onb9Sg
84bT3+2yad/J8Obdi/hI5L8FKn/Pl5AhYaWr0QHZJPzaM+YKMpgbCtMcRi6/
Hne0uIoMysmOcrTIiicbplx+kaHrMeuvCOQ0EZpYoUYyPPbanxeHvrd7U16v
pYUM0S46CUmo/c86L6097CCDj53903TUX0JuRJpiDxkUzfw8c9B4uD2tMh/7
Q4Ytem/tCtB4mR87kKc3QoZ++S6VSjTewhnzbpyLZFDxFXObpe5XD/ym33Ku
w1ej6L0sdARM4vznWGPudfhQI/EqFDlGYUSPlm8d/DXzGHduQ/X7+MkPDkLr
cFO5dZFvO9q/T3NclpZdhyOCrL8kGAjYX7H4vsJT65BO9PXUZCFgJjTNz52M
1yH1KvtMJXJ5Dy0InF2HmME3dnqs6PwYejnO13Id7ncUGZig86H7msx5nWvr
cABfFLVB58eRVhuGtevrIKiC6jLkc1lh+ek314E9l5P9Mjpvql9a4ma7uw4L
yQfJzug8Sl//vaUtcB2Kn11t8kLnd/V5qc6OkHVoqypyZeRG7+eJ7O0KXYfZ
LaycUcgfjtL194Svw5ajNjniuwhYn+3N4d+R6Hu3c0y+InMH/h3/G7sOkL11
XhOd//Uz9Wf649fBatL0ZQuyX3PB3GDSOtD4jfSqovvzlsWWh1PX0b6Rq8eD
vj+1O5w8moHaa+tbuIjaK3yMhjDxaR2Ymw0kW9hRPRPSQz+Tvw7j2ePbnjET
MAehUL6lqnUYdt1bSruVgMVqbQis/FqHuf4p2X50vmi+5iiy1ojGN9Ed7qF4
VP+qeWCzcx0c7T6szaH1w623enTb+DpoDXK5/hmmQIW77UVuhg3gHJyy+lKG
1m9Ugz0PywbsKnt85AaO1j+u5sjHsQHiicK8+4soEMuwy02AdwP47Mxb43Mo
4P6m9qGY5AZkDJTphryjwIcy5SAJ6Q0oKrWW0I6jQN/Y+6dSchuQkrBKtyUK
5fdDPhEyKhvwyfZgye1QCohWKaQqntwAi4FoJbsHFDg//S5D+dQGBJQe5hLw
okAoJ1u2qjFyQuNcpwcF1i3HC9TPbYC17baPBtcpIO9nWoxZbQDTsXdPGBxR
PZBSVnrs4gYoCKtdLbenQMtsXK3W1Q1gHXAVVbWiAP0upkYd5w3YUcq8ZdEc
jY+aZ6uuK3o+IeVv1hnUn4vDnfq3NmDS99h3RyPUnwCT3wZ3NmCC0LzNTB/1
Jx3vN7q3AfdnZgv1z6HxbDowYuK7AVK9HC7HHCjgx7+daBq0AUZ5xh3SPhSw
UEs23fl0Azg+nP14IoQCClYniptCN0Az7twjq0i0v73xf6ofuQGS/hcPPf1E
AR1hwoFjKRugY+j6fKqPAiySq1ekKzbAw60qsU0QrfeTkY0TVRsg6Kz7vF+M
gBU7Kimn/tqAJw6/7k4fIGA3Mm5tF2ndgLhzjcZ0Kmg9HJx7zzO4Ae9RBahg
TMAiFScHaGk24TnTmEW4L7rfLFi3ZOsmcNE5asc/JmAnPSVz7tNvgvfmpHzG
UwK2VnDZd5VtE8JmiQzlUQTM6ujQXqIAcsdy3nw22l+s/R9nCG8CU9OdREoe
AWN9IEy8KrYJ4TXkZ0zF6Hzxw6Z4SHoTor5T7EVq0PrW/G3ZrbYJoYnbd54e
IGDkS97lr7FNYI8LoliPof3lEf+Bs5qbEBTBNOk4Q8AykgtfcupsAmPo03aP
BQL2qPIcuUFvEzyD2Er91tD+PLZi+9QQXfd/kfmMQIMpMkTW6J7ehIvDZjv2
rhAwNikleXqzTbARdkhnQ+8f022Pqji/CbYX3I8TOlH7rt2i8bdG74v16yFV
ov03ZOdVzHYT7LpC3fpRf3TrTZSLrm7Cu9OZiaWvCVimcUP7J89N+Kw9QvvI
DF3/nvay2HsTzK7IJezWQvMj8dDolw/qT5A39lmBgAkQVGpGAzfhbg3nPWp+
evYx4btA1CZoRN+f8kfzf53JIymkYBPk38s2bfiiftw2uhj9fRMujfxkkb6w
CckDUgKpJZvQKm6la4nG7U/B39dl1ZuAfwgqK1zaAIMrJ5+sdW3CYtbAl9vX
NkCmYvfNK2ubUF4YHj17Zh1qZJdlPDY34dS6VIeg/Do4xDZN+m9B5/SjJTuM
2NbhjVuA/VtGdA7+MR3ysZoMqn9thDNZKZBL87D6dzIZ2nWP/C3kpIDMcb5t
LA/JwCpMMm/no0B+hdaDa+pk+PC0hmtIgAJs238XRfOTQWs1qXlWGJ0zdNxW
qlfWYODSg+cUMRQ3QQyHV9vW4H7jOX2W/RSQ663n3MZMBj41BQb+gxR49z61
SugmGb6msP6UOITi2sXv/tFOMszcLwPNIxQQ2KI44Y7yaPBE3LoxUCCxli0+
lHEDxEw9Cy4cR+eIV+NnM26gvCAtfchLjwIHJeJKBtF41fdEiOVYUIDOYGuU
SRsFspQdWQS9UR2vPy7C40+DGRTeaeFDcYq/bxNT+kKDzRwJiuJ6iM7dmyWS
pqM02AFI3ceE4jY0K/pguN4WLPXEyNGlGAo0c+gfYd9Ji8Wb2F7/hfLiw/aP
JvTvt2KhTucbPNG+2nTB3Xfl53bs4MzVV24oD+/Mt3m4a3U7Npr3TToP5ek5
9lOPFffTYwEqv+az0T7KV7rvqftzeqxcbfJBCtoHPUQ7IklmDBh2XDIybA+6
Pq7yaWyMEVM2el915SgBs79J+dPJyIp1sWr9Pg4ELKy949trFVbsbt3IrIAG
AetU/RRteoUV+6Yrwd+mScC8aS+atlawYnAi3VlDn4CFhJfWNfiwYX20+n67
DdA+tBKd/iyLDfMpnYpYNiRgzFZuQaf+sGGlIPMj8zQBq+MMSxjew45pqWZz
8lkQsKs9x6ztvNix0RVj8UVLAvaU5WBdaRg7Fpg3d6TRmoAVAb+a8Ad2rEZB
wT7AloBNJ87z9neyY9fmW+9cvETARNr/BmIkdow559YzNQcCBvS/lt9u58Ay
bnAn7rqCzs2q+Q4UAQ7s1MG8vLmrBMzLKanNWpEDm5k2+1V3Db2fvm/4wSkO
7FnGSl+qMwEbKAvAH5/gwA5ei1r0dyFg4/elo54f5cAaJVUZL7gSMAbV1puv
D3NgrmPdAqpuBGz34l39t9IcGGeK1yGuWwRs/ychsZR9HNgZ0e+WtZ4EzFzM
pesrFwe2OGDlmnwX1fX9XLnFLBxYxLvNR77eBOxO7LeQn3QcWKcAlqXkg/IU
JyPWvsiOWfCW0SShPLq0mZS82MaO2bJWJ3tHELDwjm43hQh2zHWllST9mYDV
B2qx5nCzY+6WO2TlvqK65wvTNRZWdszjh7GLQj4B+zTQWHmFjh3zDqyfVv1G
wGo9v26BMTYsgKdqQrsc1R19f8d4E9mwQO9tUno/Ud2u4pjQ+IINe9KnedWg
CuXRlwsWj9H8hqaWjJ75RcD8tRkaFqzYsDBmgrh5PQGTf/cyMF2fDXt1Q93B
opGACZL3HLM9woZFtnq/t25GefFMKplHig2LVi4authKwFI/yn9p4GHDYmNX
RezbUZ1H//16wHa2/0e0nYdT+bwBA3cOZ+Xssp1DQs6hIlLa6KYFSYqi7ESh
xb4kZUnaU1Qo2UKyi+xbQoiS0KaUry1JEiKpd57f2/W+f36u8zwz99wzcz8z
uYIkobUHXFEdNRR+FEURYkCqs3/q4bdovj/UZVwkMiCtufjTsV4huF9RV02j
MSBj+Q957w9CsOdmXVcUhwH3r2o4+H1EddK77gtLhgF5+/I+nBgQAieVOmkJ
PgMKqsZkQ4aEQIVQtzJuBQOK5JfZhqM6/vdjrYGMFgPKRu69OzcmBFZxtX5y
egx4HJjy+gb6TsiTal8oWzOgqbdPMn4GxdNfM5LpyIBmkLNMQN+FCzU1f1Vd
GfCMfLs79bcQzPnVrFD3Y8DruOud+SI4eDtQfV47igFjZWfbWsRx4FxfpWf4
mAHjvCbRdgkc6CRW7WttYcD3UBHjDikcDB6v8tjRwYAZw7CWHh4ONmpU3dn1
ngFCb4Ka/lPCgXhy5dy+nwxYNHe0bkELB691378uXsSEEauthR/W4ICvJnG0
RooJVVW81Nq1ONgua4pr5jLBOfTp6bCNOCiar1N5t4QJa/tTfZ10cTAxOlc9
oIT2z5Ygl82AA7m3mmbjfCZ8TN9toaSPA4eWw0M/VZlQTFIxIGzBQa74prhb
y9H+dBNaO7QVvR/3yvnWMibYPH0leGKAAytZT41b6HmRqEjqeWMcSCuntMYL
mLBHYqBdzBwHp7WFF+JQf4LAypqve3DQV3m7JU6RCb/fROc/s8CBKWjdjFNg
QtodvWtXrXDwzdBFPU6eCVNKSXvEnXAQZPXEMZbHhOurrN5xvVB/Jy823RBn
gusNjbbf3jiowinF3OAwYeNPcvV7XxwoRlbZ32AzYaCiNDEpEAfPr3ydvc5k
gpb+IifFUBzoJ5suuy7GhJe7OkZUo9B3/zHnarQIEzIe3Hsjeg0HUQY5NtHC
TAgSD2kdi8bB96dbVKLxTFB4vSIn7yYOKrr86q8JMcHb/qKHZiIOdNvyPy+Z
Y8C2R04OnGQcCHV/DF+C5ktGcf3uqRQc5L9n8ZZMo3o4NKJZko6Ddd98dsp/
Z8BNwzrF2Hs4aPuZNrz4GwPcs2LFA+/j4INQT+jirwzQFfMg7M/GgSWFJLP4
CwPYx7bNrMvFAY+9tkjuMwMM/SpZm/Nx4PX7t4nkMANOBq9csaMQfZfIJWqZ
yA9OpxvuLcLBV44HYx3a/yMXZJzt0Hcqd7FgogVZLjoq5FApDg4v+9Rhhdrb
Ey9y27McBxztW4VfkGvvjb8Ir8aBy04xHxrqfyrvwNeLtTjgWjWaJyKrlrwm
33iExudySkt9DI2noX7TvUa0Xk9OTO9C8R/5dDP3aTsOZrO7Aq+j8aWOiLZ0
PUfjKb28f+kEA159Cx14/wIHUo+3rS9B1v/jzp3oxoHP27L5Vyg/0txN58U/
4ECTcucUdwrtxz3DzrbjaLwHXSJSZxnw29om9OAEDnZ7y7msQvnXOPDitsck
Dn6ffLW1ATnBq7IzbAYHe28YkYZ+McDnShRk/MHByOMVF1QWGJB5Q8QmXwgP
Tc+H3CuQPyQcDyjD48HzXZKx8R8GbM8+kNdKxEPGJIt29C8D5Ju1ed/oeMhm
zhu8RvNv8TxHe5aJh8s3LcvkcUy42LPEHMfBgwuvWOCGXPf+5jHqIjxsT2XG
FyLPDIhe4EjigS04SvmFvHwsNJ0njYfB3Jbj+mh9Of2YrlvKxYPstQavcOS4
X+69arJ4uFVxrMwXuR338af2YjzoD0j9PYiMp+zl6C3BQz3t8db9yGuZrWrb
FVF/2kcvGSOnyRW72PDxYH3hkfRK5KAN516GquPhxkp3rTnUf2F7rE+oBh5u
/sVVfkEesb/HCV2Fh9vP4vU+IFtENJmHaOPh1ZGWnY+RV7WLdJ3chAf5+wK3
y8hjdmFdQaZ46FoyfGcJsuL3q75Bu/EwMHFKSRzZ6nSyeJA5Ht7VSmQTkZvv
1e45bokHJbttZV9Q/tInFroC7PFw9FZ650Nku/Cgbl8PPJA5zqTtyDfEL/j5
euFBqn/+8kbktoz4Rb4+eOAXxoirI69/WrbXJwAPJqaPl4gje9k2T3sfx8Mh
OetMInLmt1c3vE/gQfTdoO0kmj9J8Z/dXiF42CS5NbAKeWcG0d8rDA/OD33P
pCBHrpWQ8DqNh3zztOhI5OrWpSWeZ/Dw8PvLpMPIUzarLTzP4uG1UK6RNfKy
b1tmPM7j4XnMlst2yE5he256XMTDkHJvhyNyR7pPz7EotD52iO5zRSatPe1/
7BoeDval3sba022NljgWgwcH7/V9x5Bzxgstjsai+Y9zO+iHfE57oudwEh7K
/nviG46s13LklWs+HnqDIq4lIG/fv0hlWyEelp4Xv5OEbPa5OkixCM13bFpm
KhYPhSH3oQQP/xU11GYiRxgVOpvX4OHpmMh4MXJzy/R3nXY8FNmd2d6Oxbs/
cTP3OR6eHVlk0YH85vO2G7MdeBA/ke74EnmUEre2qAsPhbGNgW+QxbavDxH0
onx1EO4NIou/7e8gfMDDlw83Howgy7pfVPivDw8LY0trviCrXehtvPMfHuIo
27q/I+9qPSXG+YIHW/1I4T/I+6z4dhNjeNgvuHhWCM2f4+jz/PZxPHiom9Pw
yO5BgbjsCTycXcONEcbqL3WJ+blJtN4kIiQJyEG3WtJcpvCQ6/dTCPNpVe8Z
/Rm0n7vcR0WQr29/HL8whwda9O5qzAlvD395O4+H8YmGDMzp7uI6ZQt4SDdd
exVzyQWXj944YdCnLT6A+XUriT9CFgb7c2NkzB+tCgIbqcKwZth+Eovn8+i+
1lQxYfi69eU7zL+oWUdtmcJwXrgiDzPPeEdxp6Qw1Jw6uwezw9OretXKwiDn
p5CMja9V6FV1vUAYHBkFZzFrrZFd36wqDFfu63hgpqTc13ypJgzLPuzTxfzA
v17x8xph2GQQ1YvD2s8hJ4+vFYbAT7wGzJGfdvKm1gtD4YmsbMxWO96J/9UV
BoOCxiDMwgpThEUGwqAj/VsK8zHL9eEyRsJwsei8EObXl0L/LDYWhl4TyRFs
PnJ+iv1UNRWGfeGapZglVpj7rNwtDOm8ukTMoU7x31abo+dLTCIx72lfOgKW
wnDoi+tezDX4I87b9gtD9pmZjZgFax98NLYWhm+LI5QwRx+dtdltKwxaFSwx
zAupum8s7IVB7H9//mFCJ+3pC8cDwoD754xAy9Yjh4RB5J8Nn1dcaTgrDIv+
+ctSOXNepjCQ/9nmsggjfEAYxP/52dRo67C8CPzf/1/FAI8qBRk5GxEg/fud
GWHltidWBDj/vNP4vOK+2yJA++eL7LL31kkioPDPqv7PK2xTRP5fvM1vhmLt
74pA6JWSeqz9Qzp/fB3RPS+7of84ZmLKIrMD90TAeZ6ugTldZIW6y30RiNbY
MILthy2uW8QOZYuAseuhJMxh6j5N7vkiINxdS8P8u7pjvXepCDTkeY7+Rr69
ZETSt1wE1AYTUjCvP/N3yq9SBGa5LfswB+xQyz9eKwI3zi15Mo88+faiYtgT
ETjn1Hn3F/Lwz21iV1+h+CW0bGexemht9/naGxHw2uEgjlmp1q8p5p0IzIVf
evoTqy+RaaGxfSLw9NvAOsy94vjpxGERuNxyQ2IG+USgdGfyZxSvUH37NLJM
78r81C8icGnNeARmy7v2bhnfRMD27rYfU8idGtXvc3+KwOqTP5//QPa60VWR
PycCZUWKZzEz577EFs6LgNaoqS5mkzoZs4d/RaDLIjMHq+9jiprqpTgCXL7c
dQDzhbNGYuXCBGA0CHExN+8MbKoiESBn5f7zWP059CDqbg2FAAaHzgBmosS9
0DpRAjy6U/hzAjnteI1tPY0Ae0Z3HcF+3/y+e30DgwBJUistsfH1w1fJJhYB
Hmxj6GP5DE0TmX7CIUDU+gCJ/633w6vyn0oSoMfVAofVI7X2/3SypQlwwKZu
Bwk5Ue162wUuAX6ZqsZRkE99n/pstJgAG7X/qNGRNwWUKDUrE+A6IcNGErku
fN2thtUESE+dLlVBXjnwWZCmTQDHm/bCy5GTt94qPb2OAF3nW3aqYfuRPN+l
r0MAvtedQU1kuFLFeLSFAImbtnKw7+mj+E1nqs0JENZ7/dhOZM35b5w7ewmw
oeNP+S7kVJvk1GBLAnQ+diWYI4cvxtVtsCYAPntjgiWyfnr9r3InAtw5PtDi
gNUjos/5eGcCCI7uXHQAWcFVUer4QQLUOZQ5uCDjl0WsXutOgMWGl366IdcX
bPUs8SLATQmtpT5Y/+yZPzd8CCBBTfT0w/r3ybjs50eA8gVSVQAyu9uCtzeA
ADbfvUhBWDxrSNlaxwkwPvDOLBh5MrZ0nfgJAgj1lJPckZ3mDjX/CCbA47tf
FmHxbq5qHnwQSoCyTaaaGsjFssd9o8MJcJwWBnLISiEqwt4RaH7ePdgpiiyi
f0Fe4xwBDo8v72lF89vwxNg6P4oA4baVBquQbz6LFy+9htr/W6xNRXbtHm6v
iSEAITWP/wmdH0X/Ow3PYgmwbyiFFIVs9qdy6dckNF6Pc09G0Xnzo9byCdUC
tN7C9hqk/kbn9Q1B9zUfEOCzoqn2ceQI/Wan9cUEWNZkyN+FzN/l3G1URoBm
6kbSn3kGHDucUOFah9ZPjMKT/cgLKWJnMjoI8CL92zYWOu8+y7TSzeskwC7D
z2tG0Hk4OT/z58MuAtiP9ivXIm+p3uLe+JoAquo9xKPIEg3Riu1v0fy/eD6z
GXmk9WNvVy8BYnxahmSQL70ONh34SADJsqqmZnT+tutrJY/1E0DHqqQkCXnl
kFT9jwECnPydn+GPjP968MT8EAEsLt5I1Ufvv/xRrCX8mQAZpF/2XBRf2i/8
OPULAaJP28lOIfvjdt9jfyXAu7/1b9vQeGQYX6UVvhPAY/bi3lMoX2OLNrxU
+YHWg+8E2xLls4Z3/pLGNAFkvu/pUEf5d1Rd+hfmCHBv6kq6J3b+22o7YI8j
guZXS3kFdP5dE9yed4dFBNqHz4vOEND3lF4ydptDBEtf/6BvyL1Jiaq3FhGh
kCrct5+Izg+PPTJuShNhrTYvU43EhA4qOzFqCRF8ru5c/5qMziPxFpfDNIjw
Rr/Ibhm6T+os2/Q0ZBURJN9senwDmVnNp5xaTQRnjza+EI0JpR9nI4LWEUEk
YXCiC/mC96f6wA1EWKfpvXcTHZ1/RVqFAnSIcKv5T/l9ZBHB7WAfPSIoT0ue
PsVgwqvy0xVem4ngeTFteAQ5y/jIrMdWItQu0dhhju63p97vWXPMgAjssuqC
auTdHjq+R4yIsG3n9kUCFlrfOOUH7sZESBroOR6NPBtNn3A1IcJI0IEPv5Gf
Kv1cccgU5Ys1oX8I3Z8TS/oOu+wmgrZ2VZU+spdh8/0D5kQwGuwgZKP2t7wt
GHbcSwSTmMGdHBTPl4WwA3b7iXDkG/3Tf6LoPrJVydrSkQgX7jkSsHx3vnTd
buRFhPPq9IQr6H5H+v5dsOIaET5O3K2JrUHn31AfKUoMEUoSBEpJleh8yJwm
DV4nwiaj3PMZZQy4pT47lBBHhLspJXsePmDA8mN/0sSSiUAybxntzGDAi4WQ
6yMpaD7+mOx6exetp8u4iIa7RDDP7nz4KRndZ3NEDgTfI8IL4d7QiVtoP36h
LhnLIwLr4bgEPYoBM0GXmM0FRFBx9AledAl9T6l0obQHRLChzX7inWcA3Ir6
FlJMBPmKYAOlSAYMqLD6rEuI8MsFl7vsNAPOl0c/0y4jggE7kr0qFJ13jcRr
OBVEsKuhBq4/ib5vr2/kfqskQrF71Hu9IPQ9dpW887SaCJPvb/q2nmIAbzbu
0r1aIlSK7R59dpYBdWdlgk8/IoLTBlGHl1cZQL0na72hkQjecSHGvanofjuo
KJ3dRgRpc1eF8SYUn186+ewzIqonCnGTzxkwKMKfdeogAq6gl/bzNYpHSfWV
TBc2nt1zf0cZ8Mhp5Y0L74ggMcAbOYfW91DfRpb7KJq/REIt9u87K9/upaiQ
SXCA8+pIjQ/aPww/xRVUEswUjjBTA5mwcct1HQ0xEmTu+lV85iQTjPI6vdYx
SZB8WXZhx1lUf8NN3xpJkWCQ5Hz53S0muJYemzKRIcGpDD+N2iQmeIxdppvx
SCC69Wx3ahoTgi3a9K3kSaAdniXrnofq+8UvNnYKJHgsX/XIpIgJ5+qoAU5K
JNCvbXfRKGPClWmVaweVSfDbto+yqBrdF1WNst0FJDjzeyJ39hE639u7Nh5T
JYGc1B5l4kP0Pbl+ts97OQkmtt3Ip2QyIe9PI+fEShI8TJOsZ15B57VO/eCL
a0nQbs8blrNC5/egjSY5hiRIyDF28h9ggFCB9aGC7SSwpj7zPdmK1u9gUFjx
DhKQXXedjShA9x/T8odVu0ggobg3JzqYASsU18i17yPBtXi7mTxxBjrvq3/7
6kqCwkivC8Nb6HBQyJQy6U4CnYEfCeOqdDiy+pjizBEUn55//jSTDseTciz/
eJJgxUJQl/B7GkT7qNTRj5OgwCdCTt6PBnGZhm/ZJ0iw7wVRg29Ng6T3h6Yk
TpJgjfr5zWp6NMgxyBAsDiOB6uhl1400GjRyFa+pnydBlEPsg33pYpCw850N
6yIJxmLOV0lfFgPfsBjBj0skeNt0oumtrxjsKDae6rpCgidzRztu24iB0rBw
XclVEoitcHhrs0UMfktXXYyLJsGsvdmA7HIxeLnD1zLoOgkCnvwYdl8iBlkh
yxVtbpJg3UOr8UhXMQh/MDCuE0cC0t1HU6n5YmA1mFCx+BbyNcF8zYwYaErt
jcQlkODSqSjcOx0afDrZKNuYRAJJK1s6p40GYJSxY8c9lC/WHP/0CB2kgu2k
1O6TgPvXXi1JnQETeRIDjGwSjIw1aVX6MyBJ/OyJl3kkkHduTT6O6v+fvkNZ
ViUkyN4Ul1t4lQlV/ipkt0YSFM+serIklwXX7396uf0JCU4fPdSa38GCI73x
SctbSBA2cKtdZ4oFXH2q9kQbmt9OXNf+DWwIon1xCegiQWnu84/XWtignZbz
+Mx/JIh2PvwLN8SBBy/UQ1JxZKjqTF3RLycBF6PCnwcJk+HUx256tZ4EOJt0
LzYnkGHLOHki1lkCJFuC6oQpZCikeDwwyZKA4LpGnAuTDJWwQbt8tSRszbeO
4C8mQ0reS7i6QwrkjuZ1/ZUng2UVUeGwhxTMquKWvlYgw/bWdcLboqUgKyOj
8ZwyGR4NJjXOv5ICeuJ34ugKMpTwjmw/dEAa3e/Ons/ZSIbWCyJ7dINkoHD7
2zcRumTwidNeLX1HBi6QV6jaAhm2ZbhLTNXKgE5EZyttCxnSHnW8vk/gQuoJ
WTEPYzLkzybYLrrGhRPrPG0MTMhgQezQnSjiwp6f9TmLTckgEBeWf9rDBaKP
q0mHGRkS1N36Q3k8OOxedEXDigwXD64+NHaPB1sExD6KDRk8fF0Nn7TyQG5o
n3q/LRmUwm+rpH7lQYfjn+fRjmRouIMbs1wlC/cX75Y/fIAMgdla7ZoWshD+
/q7nZhcycMsP5dGOy4L17Zk67iEyPGm6FTVyWxa09huxplxRf13tno9rZIEm
meDY5k4G434hs8RPsjDUNV6YdoQMq89fi301Lgt10Xr4k8fIYBZ4feV0vyzE
77putteTDMxDsS3sV7LgTR9OXeFNBmmLW04rn8rCjrZ1Pwi+aLxb78yb1MrC
H4O+mJIAMvQp3F1x/p4srMt+Ti89TobgKnPRtFuy4EuvO196As2/hcjnmsuy
MNqVHFIWQgaH8y5pUz6y0O3odLjiLBlUJ/hcB5CFnBOD+jWxZPCvziFrv+HB
8Ifu6pp4Mqy0tB3a3cYDBf2mtbW3yfB8gtZwpJYHceR7anVJZNBQ8ghJTefB
6RuuMvX3yFB6QWOG5s0Dq/wv3xtLyTBgWfLfAJUHN9i9R5rK0Xx+P/jo7wIX
OvzahpsqyZB4UTJJ5jsXtm3Mff+klgy5NYFWu15xQaPlWEvLEzJoL93wovIu
F44st9/S2kIGsdoveT03uZARZVrb+pQM1fsSLn0/zwWexcqHT5+T4c/FBQO+
Jxcsy+VXtr0gw+2leUv1D3AhmsfKbntJBvNaO2FbCy60h+CU27vJQN3P+BRg
xAXyf9+T21+RIeOj+dsoXS5s3tbPffaGDDccnz9038yFU/c7bz57h9Zn//Zr
Ww258MOj6NLzPjKcG9AznN/NhQ+/fQNfDJPBdES95KALFx5KzJp2/ySD3oRo
tM4lLtQHhAUXzaF8/0hY33iVC89eU+9fmyeD5syK/3bc4MLQLVn8zr9kWPLb
VMsmkQuSizcXNxEpsJx8vSeogAvH+VekyhZRQFyexy3r4kLkOcmtNyUpsFIx
9/GmN2h8n5O9fKUpwFXWPfLkPReysotaV8pSQGm5Q3XPEBfeqb8Jvq9EAcO1
afbTs1zQWav06dYqCjjsWp6mKcuD7fG5tOOrKWBkXr2jYgkPLH6tWW+pTYHV
Fjun9ZR5cKzKKIazgQLWNp7bdqvzIEj2Ze33jRSQsMd9e72KB5GnbMae61JA
0yk61mEtD6L7BqXygALrXBRhZCMPksBj6yV9CgS7Fo946PEgJ2XWy30LBcq9
Umix+jwow4cnGm6jgEVn6IwU+r3hgOhTZUMK/NB06Lu1Ce3Phus/RbZTwD5m
UzNPlwe9S+WU/jOmwKIpucJE1P5I5L1dj0wocHrPn3j5DTzAGVXcP7mbAvmL
qg8roXjoWZt7rM0pYOCfsCdjDQ9kRNvx6/dSYLDnhI5gNQ802/usZ/ZRQC5u
PWO5Jg8O7CbQPRwocEym7MGq5Txo3L/L28GDAvqLi+b05dHzDgEtB70okJa0
pDVNjgfJBxPlj/qgfMtfvUVE+Qz2GXt2PIACT+SPbmiV5oHW5XPLYkIokKTA
P7mbw4O0urqBxigKXF56W8iByAP2k+ENbdcoMJJOefFIhAeh7fSYzhgK7FQO
TFEU5oHNWxu9vlgK6PD36g//5QJnavbObBIFqgWMiGNzXAj9tXj6TwoF8PdP
7un4yYVxIYMdhDT0vMqYkuYMF1ppN36xMinAUG1pnJ7kwlrxqt1SWWj+s7Rv
WqL9lyHzX6ZcDsqHasbB8m9cEF9CFVqaR4GT2eLa3HEuhPM1LJcVoOffMD6H
feXCxIp9eRoPKPD10ueFr8h2WiGEtcUUsIXHbCv0/Hq99qItZRTg3PPfqIna
m7RyY9rVUYDt9z6qf4ILjldSWq52oHhZ2Ws2T3EBplkbZyYoEGi4LUJkngsh
cy+2vJ2kgLbUBy835JqFayY1UxR4OOxn/wxZh8i2j5ylwPGz6evjfqP+JNnh
EkJUGG4U+b7sDxeCuJ0XfuGocPZGwoeryOWLo2M+CFNh1lmrbRp5rYCdnkGi
Qo2I871alM/V69jNaxhUsN382NYcxwNfnc4OGRYVlDjWxmXIxXrRb/6wqZDd
P7lWFs+DH1vN+vvFqXDpwQXlcGTN7ewvTRJUkAtXEB9G9t7Z+SNLigqvdlfg
dqD5KzSL/n1FhgpGS8y+FSBPWJgRfHhUaOYYh5Ygr7Rm0y3lqBCftcbxLrKH
fafEBnkq6Oop6F9FzjsQvXixAhUUX9MUTyKvOMLWGF5KhQLC4IAFsupJ9p6A
FVTId4hxpSK7hXXaWKuj+H6eMvqJ4sk8E+2ySYMKmlfcVQeQ+VfYAaTVVOiu
1BurRlZKYt+K3UiFCYkJDy/kxY/YH0uNqUBs3xHwGo1fnMA5MuuG2ltHjMwQ
4sHe60fnOg9TodiwpykG+aZic2TuUSqUW2aQwpAl9U+mOHlR4a7ftvPWyDIh
wz1tgaj9wshLTGRrur7zvSAqGD6yaF9A+U+4k/A9LJgKrh3K9C/IclW7xbRD
qbBjvCmqEdneOCeeFU4F5sLNjgfIyW+J/LHTVDgjdoiVjPzRzbG46QwVbnO1
zS4jL5mr1Es5S4UTYyuKIpCdzkk8P3GeCm3W/rORyKmSXjYWF6lQ2Vqjcx5Z
aY1ygGgUFUIyTZux9wU+V3P8blLB1Nnr/U1kta/OktvTqZD+rph0H9kjuDZN
6R4VErYv7MhGLhCV0fybSYWK8q3Rucgaqs93FOdQQSW2h4fFq3VoXbhcMRXE
zWc1KpHXf6J9nayngkvrBpt25BOerkHtDVS4uC4i5Tly1d96UmYTFfZltg29
QNaRC1SwbaWCRaStVw8yWPdbPnlBhSa9kMg+ZIPukvrbH6nofFJf8B15lJIf
lNiP8nNYlz+FfEn3nmbKABUKZSvuzCB33ItNzRhB8YQXXphH9u6Nsro/it7X
WoH7g7yIdY6dM0YFt6HMACE0X2VbQ1vzxqngH6c0jke2CgoML5ygQtz2ZGcC
8u88z/XFkyhfBSrJJOSk/1wnS6aocN+w4ARmfSnHrPIZKth9WmOJeWDHfqeq
WSqwgqo1MUeG7Zap/UWFUPYWOmaVEqPOR79R/rJbPxORjy1er/9ESBQce18l
Y2bu0fzVghcFZT+7YMxF51QftImIQj1t0BLz7HcZhU6yKJTqTtIxhzfM494z
RWFRithJLN6bbtWPJuVFwfyg3n4R5LWJD49PK6Dn/zzRwvyuM1djVkkUNsTu
ZGKW35iYsiAQhehm6yfCyFn0kDCyhijUqfqvxlxTBHpyeqLw8FsWC8uPw8ja
OfnNonD8nMZXHLKwrEah4lZRWLGkrBmzYeSSJSpGoqBn1hiCebRC+s0yY1Fo
HzW2xnz5G+uamoko+J3uXIO5cx8ep7VbFK4W933F5sP38q+yNeaoPZODLZgl
6yc91+1F8Q2OpWGumBkVbLQUBY1TPqGYbZb991F3vyioSf6yxvzH/l2cnrUo
nM4P1cacfP3lri226HlDEgezfstTsoG96L+/V/BgcOFxnZGjKBj9s8OO0UmL
O6JA+efeW8ylzm9EQfWfL9/4kuUvIwZm/6x7tWnleWsxEPxzXrVNddAJMRj7
399H0H7/Mml05LbYv7+/8GDapMrp8B0x2PDPbQVnTrgnicGBf77LMb3uliIG
ov8c5C+V63pXDJa+efsUa2/3m0+Nh9A9lCV8KgqzYGP2h4P3xMB5xRJzzD04
XaZLthgcCzv0Flvvuc4kFedcMYjKpiZijnjSoXcA3SOLu3MdMWtePuDjWCQG
iSpTI1i9uiJ1vse2Ugw+vgj9+RvZ5YTZN5tqMZD+rViJeeMHLtmmVgymlz45
hXn0bt46q8diMHucRsS8Tb0rweKpGLgp3BLH9t/frYsPmL4TgyTvIo055MyM
sBXL34tB/psDc7PIu0gDP8l9YpAC4o8wJzdnXqrvF4MLdL9dmPWNNUtWj4qB
U9Yaj59Yf9nXQ9ljYqDGGl6DOUbs5/ZvX8XAPjD2D7b/B9or+zK/i4HFttnL
mCN3baXw5sRg7lN5zjRW7wrvvZz9JQbPDN19Mb9iURO7f4vBg3yZjZgFL59p
RgnRoP7kiadYfelYpbFwGE+DLwPLYjAHXo95YihCgyzjXivMLXv32eDJNLgq
rTP6A6s3JRXKfRQaBIV+LcQsIyn7vVIU/T585zjm+oCQyjgaDdQDt5zB7P76
0xk/Bg3WOqSZYeNhr9uyy4xFgxcGIvJY/irjM2TUOTQYVXf+is2XmPXh/BEJ
Grj/VTyH7f/iyvbjjVI0UB4+vZeKbMtbuSVVhgY/nv2nQMfW4/up19ZyKJ7E
u9WLkE0dTuGfL6WBrY7iDyXkaJdrex9q0eD1CQW7zcjSnqXzYWY02DIrrxWK
rORfOhG5hwZG86HmEchqwaWDFy1ocGTho/c5bD+dK31+w4oGafiUwqvI7sml
d+870SBYbIl6CrafM0rj8pzR+BhhO9ORT+WUXi46SIMh1qej97H+y0oDqt1p
8E4iJacQOaGm9Ej9ERqESuPaHiJnNJQ6PjlGAwLP8Us5tv87So1feNNAd8kS
1Xrkhp5S6PGlQapimFET8rPe0tXv/Gkgq/zJtRX5dX+p6sdAGnQK9M49Q+4f
KV08GEQDLQfvF0XIY+Ol4qPBNNiewWi+hjwzVUr5dgq9P5ZT44Esiiv7MRtO
g8mA4exlyBKkspGFCBp8ro5IpWD1k1b2Hn+WBnXCCvHY+VVLuuyJ2EUaxETZ
RN5FttEouy0fQ4PD9144cJEPapddXXqDBuu+HrOcQ+c1T52yM6qxNHBZJbbz
FXKEUZmH1m0aLK/dtiEGOcexbLPhXRp86KlcJIq8cK3si0cRDfYQM1p/ofMh
Oa7so+9DGhju2PzoNTI7saz7eCkN5q99LC1BVs4qqz1dSQNpOW66N/LO+rKY
2Mc0KFt9NWQUnTcTJ8s21L5E69ElSOvtL3S+nNndn9JNA829e45WIO/9NXou
4hUN3c/VMm4hi+Fle4ze0eCPUr+kNfIIoSR4+XsaLIhX7dqA/JhiqsjoQ+0R
bp7nIifSRlq+f6SB6LRH/Tw6zwexwjy7+mnAHjSaf4dssUhGsnSABrxuRa0q
ZA3pour4IRr8+hi+HrD+ZHc4B4/QgPFXYmYY609+kGo/SoM4XnZhFIq/QelU
od4YDXzWbzqqjcaXJJDcpzROg2nLl4I+ZIuVRumfv9PAN2Y+SQ3lT1Or37jt
Bw2kCqOse5Bpa09M5k3TgPVcUfIUmp+GTbmbfOdoYELdcaUdza+mKevtHyE6
GIYlBB9B50/asTd0cSYdXDx09meR0f3My/vhDIsO05deiJtR0Hr0E7V5w6FD
apZLxxxy0Emd+4mSdMAPXTYwEkXPX0rZrLKYDgs2H1aP0NDz2W6Bump0mNwe
wlZG96fkfPziJSvpUOHKedaOfKLodqOwJh28Iu+d9xNH8VS2s1tW0+HBo+dC
jYvQ860aueY6dChfK//tgBS6nz1rNV+ziQ6FFsVZouh+Ztl54JeUHh2UfQ0P
FiHT394w+LAFPZ/v+R7PRd/n92rjddvosKddJD4LufHTk+t3DVF8o3F7zHio
vc9zn1x3oHiUHz1NQfe//YEraPo76eC8/NGGbeh+uIbkuJa7iw53NR9ljyJz
bl4/MLWbDvJTWl0F6PkJpeYr7eZ0ePXGI3c9ar+9aL48Yy8d7GuzIhtQvFn6
6oMhlnRQSh+03ynBA2eHmxs0rekQ5WnNdmLxQO9by0FRWzp82Hvzyxc6D+RO
LVwbsKPDpQ0vGvzE0P6+7Txy04kO74gGAedJPDB+pXlj3g3l/45mb8ECqucH
D9Z1HUbzd/row/VovYhMx3/JPUoHMbfMKw2z6P7Fxuk7eNFhYpWc3usfaH3s
fD7eEEiHqlZKxt/PqH43Hja8cpYOV39+9NjZw4Wf5kk+h87TYcV7rtHrl1zo
6u9MhIt0kHpsoeD0An0/hdZPT16hg8GVti6/Ni7gN5JTLW/S4YlS2bo79Vzo
a93QvjKODkbUH2x+HToP7/eYpdyiw+qJFWMF1VzwD+jZWXWHDtsr7yY2lKHv
3YO0efl0OrTtjhIey+PCE73Xyr8y6HBFu7XXL4cLaR2iZi8z6bBXllDy9z66
r457Z57JoYP7SJArJ50LG05mvLTLo4Pcs4d6d1K5ICX29o92AR3KiiZk+Mlc
6FTR2ztaRAdSyMH29be5kF/mG/r4IR1OOKdkNMSh87VBZnZCKR30tveG7LzJ
Bbeedz1+5XSoV5fc/zoGfe9dGHjTSjqcX2Sm6XSNC4pT+isE1XSYye5vrEEW
Ou2/D1dLh53LHXdqx3Ohl5V1+m0dHUpy+nryUf/lye/ziurpoLXCzl6QyYXZ
rjyRhw10eDjwQW9zARfWUEKtSpro8PK2vZIdykexlwKxvJUODlTHzzHNXMjT
P2Rb00kH3+EDPn9HuHB3YEK0pZ8OlSluZ3tUUL2XqndsHaBD1r5Rt+8aqF6b
xJQ+HULtMw7vEFvPg8SHqw88G6VD+KkjLP3tPIiLDKp4OUmHBGuP27nu6Lwn
EHH7gGfAqUV++RHZ6Lxm013TJ8KAF23T15KKeEC9liH+iciAV6f9fSsqeXBu
zrDuPyoD8iYD1k08Refz1suSn9kMCHoe9Nh6jAd1f+yOjoozIClyPt1/igd/
NVc+/iLBAIpu8Llrv9F+u915bFyGAY9zTpo8EZOFyud3G77xGPDrwB/1fnFZ
+CXsJ/NdjgHC3BD2Ak8WAo5INv1QYID9+dBXmitkoSR5hDutxIAfgKswWS0L
U13lXjPKDDCeDUtw1ZGFVZSLT34KGLDdYfejY8jeOjayc6oM2M1JzR/my0KB
1wqfX8sZ4Ns0eceBLQvf0v80z6sxIPv45ktvUHxH6Cm+fzQZIPNxwPXpC2z/
erf+1WLAoZjVlluqePDZf7M8TpsB4dsit1Zn8OBg3+BT4Q0MqMzhK+Sf4IFj
gaoiZTMDWo67v4teygPv/uuqI1sYsLr4q2Qw2u/h4n81nmxjgNe45x4XtH9T
A1/Cme0MMDsQ0K7dzYV+CLbDmTGgbEdEbW8Euv++aI+fc2DA08WJd5UHZMBb
eG3KaycGmFst+cjokIHw1amZpc4MuHs9jTdXKQOp8f6lfq4MiKZk33gaIwP9
jou7v3ugfP4oPeu5WQacJj2Zo6cYsKHpxeGKVGnwVnon2RKKxi+0N/PuFWkI
t9i6ODOcAbwNrwcuBUlDaoW02sFIBrzL/2BrbyYND8ZOr956DrU36njLUFca
6uXGNypdYMBlpcEeDVVp6A+vN+6/zIA18V9MRfDSMFm83PxRFAMuvTx26etX
KcAP37RKvsaAFfTJ5p43UsCWxjmFxDDglqEfoa5RChSMD7vZ3UDr6dp/76/2
S4HmyW5PnVgGSHzf1HhCVhr08zcF8uIZQN6dkHNwnzQ4ccTPvk1gwGnm3hMb
n6HxbD11pTwRte9Z6MSnoPwEjNyIS2ZAz3PadvYWlJ93VWkWaQyQj2qSGilH
+bnrUt+ZzYAK2tqSGFRPnLRKF1orGGAoyv0+GiwLXaK16p1VaL6Af7GpSha2
/dfk+KaGAdp+q5am/pYFleiexuF6Brj1Ge/fHywHE9+mL4s8ZQD9QfCjJycW
w8lsLTnddwy4uPyboVm1PMQpPNAtnGdAQ+cuafUqBaD+KvcsW2CA5leLIV6v
AgS/eJRa+5cBqSTbIupvBVhZ5yo8jGNC9EY3k6ENisDxCDw0TWCCeEZY2J1K
RXjbFqvOpjPh1PEHn0UrleDQuZ5aYzkm/LdYvGKkXBmSy/m3ty9mQla/NOi9
UYa3o4H+RvJMOJm+uCl+Vhl2mnBXGCgwYdWyZZ3btfmgxXa4pa/MBJM1+qM5
xXw4trnQT4/PhN1zBp6ELj7c88XvBgETxitNZmx/8EHmVRpJV5UJMXr78QxN
AQglfPZdp8aErh2eMl75Aljfvn7XWnUmxDH8k1ueCcDnz8Vl2iuZsK/zhLLC
uACGHNT6tTSZMGR5VvPlchWQjw6pXrWKCQ9lLpct26ECVo874jS1mBDwPlo3
4rAKXJ9a4quxGsWfHNfQe0EF2pf6mK5cw4Tjm41rnt5RAaJlg6q6NhPy5U9k
cGNUAM4tIqqtZcLMQtaVw+dUoHi0tGrZeiZcKaPai/qowK383yp8XSYMrGj9
u91QBbo+mhCUNzGBLfpr+JaOCtDYSR+VgAm+Iyodo5oqEOqrF6ugz4S/qeeT
L8iqwKF1kSJy25igKWWk1zopAK3HjD7xnUxIxjeHG90RQHuPwnW8HRNuvmok
GE7yYSISDCfssP+3Q1+0a4QPbG273+/tmbBLep/Svg98sIiNdy53ZILAelTf
tZUPgQalUvecmMAIXmXmWceH2z+72q4fYMJUQrBjYAkfPloyV3u6MKH5Az30
XCof8GS1z7YHmXDrr2XU1Tg+KJUZ3zE+hMYrn5IYd4UP21zddq9zZYK33mhu
cgQf3KTOEvhuTDBwWlWdGcSHS81p5eLuTFh3OritwJMPeYH1R/GHmaCV1viu
7CAfOgQfl0wg5wln9U3a8WHy9UL3+yNMeKf5936REx/Ez3MvPD3KBEOnPb6+
6Pk169bplh9jQvG1+7qr3flwIt4347onE2wmzF+WePFBxOqLv7EvE27kZv4u
D+WDxLvXkuUnmLBaYGZal8iHtRdnnmYEM+Gw5T3pMDQ+qw3ioddPMqEu8vd/
ehl8SLptOuIRwoSjgxmBj3P5ILBpKlM+zYRnqfMpTVV8WP++aP/1C0yIkk2f
anvLB5vLL2jhF5lwf8evmsso36d0vj3yuMQE6WDT8zv7+fD4jqqq8RUm3Hs7
J9vxmQ877FJ+4aKZ0BS70+DlLB/s+67c9ohnwm32bPwbCQFoOs07e91C+8V2
57UvMgIgDh5S87nNBKHMtHMLcgLIGYVH/neYYKWzO2AJXwAhR3MvBCYyQeHc
vWOrlgnAbEJ6T1ASEyo7F1y2qgtgqU+kbHAy2i+ye2wtVwlgdnpy6GQKE1a4
Zu1x0xbA00D7gpBUJvDNs4plkBPnnx4Pu8uEzzE5zo9XC8Dr1NrNp9OYEN+V
J35ESwBbcOliZ9KZoL+osEEctScZweqJzGCCmEWRb7WGAEaJp5LO3UP77eZD
pYMrBXBNzFLz0n1UX6QqIkpXCMA56vH85Swm/NxXpeWwXABr2Ssbo7KZcCy+
ZoCM4v8gSdkXk4v2j8zjLVYCAagqVp68VYjF3yayoCCAx+sWt2SWM0Fb8UOE
vpQAblZdjM6qYALO+aPWF5Q/902z1jmVqL6l9Q/ELBIAc+uL8fxqJsgrD28Z
ZAvAZtdp8dJHqJ4IJkTO0QSg/vLb+7J6NN9uk8UrxQSAt7C5V/GYCUZZU85v
qALItF69vqaRCYHL5hpUyQKYPjhs39jCBB81/Jl2vACaP5urPGlF+fcQWe2P
E0DCkbrJ5qdMKMsnDsoJCUDfO/5MWzsTVDVEt3ou8GHRNMH02TMm9HrRpqV+
82EkwFuq4zkTzj5gpD/6xYcrJ42zX75gwvAqcQIHrQ9HoTLf7k4m1PtKPKyc
QfX0tJLuq5dMgIdSLs7TfCARr5HedDGBOCOziDbFh7fnFjredqP5WyPb+BDV
h1xR91u9PajeBSz2s/vOh9ArPQc+vELrWeN5yekJPuxhbV7x8TUTEh5yTd4j
86/nz3x6wwSPda7/rUHP998Yiet8i+YnJPP0BeTE2CUbHr9jgkPjiOIHZInb
MSFp79Hvu92cz6D+iKkB5EOfmODs5j74EtXzgfxNMmMjTLCIPzLsieJPLgys
6v3MBKe+nLMNyDZFhXbto+h7sPQrX+onH16WKN7NG2OCY+FR11rk+mrScq8J
1F7Lsc+0OT6kPH2uM/MTrf85zy9Z8+j9dvLHoVkmbN9UePEPstRzvfBXc0yw
PPN9mRnK79XOoqayeSbsYHkfmUMOfRNreuIvqr8qPl8N/vBh47uO74eFWGDn
UXT5NvJsL+W6DY4Fux7+WPEN2ePjidc6wiyw1vM9dvMvH+yG7R2FSCww2e/3
bQDNr8znOOHvyHpJD6PWovnvGX2R/omM2hucVr+EHD1GNeyksMB12ZqOPmST
8c2j9VQW6Hr5e65C64c8EXypSJQF+0pLmGeRG74/VEsTY8HBhZmCt8ihP8Y7
rtNYIPflzFcFYQFsnOb7nKGzQOfc7UUc5NkZh0X+DBZILC3UEUYuno0vPchk
Abe+yeUHen/5b9HfBmwWaP7+/vAlMld4IoIqwQKKp6HFdeR92/3dZpAX8Qye
RSBfv/bbpF+SBbTmrdv8kOnyFMkKaRb8WLx5jQWykI7CfTdZFpx/riMhhTzg
v6e9WYkFPWqrem6j8cnXvC0sXsqCxrcaO7Hx2xIcbyYrs9D5fWVTMJafmKP2
gQL0/ocVJbbIzQWR3/nL0fiuCG4uxmH1rWzR2VUsiPgqa3EX5XdEY9Mvby0W
+MXznsUgLz3e+MFuNZqfrdxtEciJpM57a7RZIH9Hao0L8lWlL+uG1rPgxQ6O
BB+57bCXXOcGFjyaZV2RRKYU/cTXbGTBgzQmkYwcrifSdkOXBUd/02ZG0PzW
nrtQELaJBfaZYsfeIP9+zrxxFFiwdo/oUAvyWsnY4/v1WKAvRLWrQPazk7Xb
qs+C3TnknizkB+l39TU2s+CnJWnnbeTxMRW+7BbUf8Dq3njkZVoFopStLJA9
2VKN/e56Ys3EFLJ+uG3SHeS0+qquj9tYMHD2e2gS8ifK5vI2AxaIXj7jlIJs
FWcanmbEgvrY3KXpyDf7ug9e3c6CkQQ90j3kl8o2xsHGLIDU7pFM5B0PXcX3
mLDgW85Cdg6ybmdYhvBuFmysN9EsRl4+ZpEsbIba7/60sQRZmrj8lrA5Cy4O
+xmUIU+t67ksvJcFn8QSbaqQ76eo+gnvZ0GL5XhkA7K418vNwo4s8Px65V0X
Mv5ipo6wEwvEhRSHepC/pZ3UFj7Agtfs0onXyK2v+cuEXdD+WdtHeI8cAsFs
YTcUf7j6ykHkUcbST3gvFgRLdURMI79W+fUW782Czcuco34iN25+3oX3YcFT
ndn4OeTkgOPNeD8WrDogn7+AfPnaznq8PwvG/IrL/yIHZStW4QNYUH3OsAGH
5tu1cfYhPpAFird7nwkj7+1rz8cfZ4FynucbAlav51Lv44PQfj44uI2IvJIT
eBd/ggUG9CwBZtkVJnfwwSyIKTlGxUw1UIjFn2TBWbtVY9j7sw4/r+JPoXwT
Z9sxDwa1XcCHsICcX5WPuS7P/xQ+jAUuf7f6YM5rNg7Eh7Pg8j3qXsy3++W9
8adZUGP6fA1mf4mnLvgzaD8n7/slgrz81GIT/HkWVMHhMMyxJs1c/DUWmIZf
jcLGc2zIbXwCuafZ2gfzlhDRR33RLEhh8C0xTxTsPFh9nQWFCdVymA3FuwsC
41iwrHQ0F4/F//bT1m9JLBCMbWnD8vXM57TUh2QW9GoyCzCniS390pbCgsDj
72Iw79J1vZp1F7VP9LbGfD9l/K3LPTQfS5JGhZBD11/N3ZOJ6sEh92eYLV5q
hG6+zwKHvNUPMOMJfkuXZLMgfUPbccyv70jMMnJY4BUea4s5b01Z6x/kt81O
epgjnu+/8zWXBbcYaksxW7nOe/Tmof4s5siYV+Lu6D/NZ0HC//6ehL5Ht3QX
VRSw4NI/92p+HM4sZMGZf37wNKwi9gGqN/9st9Bg71fMgsh/pqqTCeYlLLj+
z07RV0zpFSyI/+fKafFbLdUsCP3nI1VL1KGRBXH/zDut1lDShubrn3/92FDP
+fr/+3vlbFTnSWPDhX9ufTD0KnMZG67+c41QxLePRmyw++ckh7jpCmM2+Pxz
aF3O/HUTNlj+s+dEyZ+wnWyI+mcH+Uc4D1M2HPnnXbueitjsYoPFP+uFdpOM
drNBpTxqFLNmQR91jRkb6MuaqjErfPxMUzRnw++E31cx4+EPZ2EPG9JD3bQx
N/xVli/cx4avBpsj/iAXq2soJu5nw/3y45aY0+03KF+0YkPGsgJVzJG1pstd
bNgQzZB9ge1Xg5DAtdIObHjZMyOLufVPy66wQ2zwdskqnUeuUOsyP+aK4n/1
8QLmbLsPFtZubFhmJGmH+VLNpM3qw2xoXx4hgtnkFNft8zE26E/Z7v6F3LFw
JGy3PxuET7O+zCLXrQiI0A1gQ/2UQQ3mAtuws8sC2VB98NQ1zNeqb1wmBLHB
YfsXbcxmJ2viy0+yIZHVGIHVH/3c5oSMU2woOT1viXnV+86kmBA2+E1rLMMs
rjOcfjSMDUOvE1/MIIsc/Z5pFc6G2e3daZinEuazDU6z4VmVaCDmgTZCvlYE
G2LV9I0xd/9mPFhyBs1PcqAcZv+/rq0KkWxYc/6/r1g9lMLX9yueZUPuXwkF
rL9yEe680jnU3p8Pbth4rUi+HOXzbJhYyCjE8jlPaV/Gv8CG9QvH5rD9kSCm
vEVwkQ2bf6/Rw+rHB9ZrX9XLbKj61dRBRQ4R17i87AobGuauSNGR5SUvpC+P
YgN+zsKBhXyAt7FH7Robtv8c+oZ9T0eUk7VX3WCD5BSRsRT5vMqcqdZNNpj9
eGYhQFZdbua6OpYNVpM3E5chH9UQideOZ0PNhLKaJvLkBtdfG+6wQfPrNpNN
yPO7VlZvSWfD4uHIi/uxeM3Pd2/NYANnaOdLG2Rdi/6v2+6h3wcluA5YfbG+
Lmd0nw2n/svIOogscnA2xCSXDWofm1p8kNNdd8ftzGODed8VVgDytsNZBab5
bLj8wWJ/EBavp82n3YUont6hkVBk+ok6fYuHbMh7QyRfQc4/KW1tWcKGjtfP
TK9h9S7U22dfKRvevboZex2LP/zpxf1lbOC+suuLRY45o5RmVc4G9R5l/m1k
rXMnq6wr2HCse/xYInLPhZ4um0q0/rtKSlKQAy6rf7WtYsPCy1N/0pClrp4j
2Fezwf1J+Wesv/LoT7IONWyw1jfv8sfq3Y31axxr2dBcPVZjjeXn1tjBA4/Y
oFq8+DqW/yXpu5oPNbKhNfmMbjma/yxl/3LLJjaEUUt+YucJrczbWQZP2CDn
O1QQiWyYPXSJ34LyZWCguAerH4XBu4fb0H78SiZj59+66sy3B7vY8GT9pRdK
yNs3PXtq0c1G9/eqC6LIXXU/qrb1sEGE/nXzJLrfjDzWTVJ+jdbbJ5OSWmRG
a9eBoXdov5xl3LZCtusR+uryHxuedkU7X8XuP5bKH/YOsOGw7mPZAGTvN8bP
tw6yofbejx5b5Mjem4VLh9H6OLHHaBlybv9y/8FRNqQukVBrQuf9Nc5mh7q/
sIF/cdtwDnLdYMC+xjE0f1P+yTHIXSP169PH0XppfsV2RLZzH1l24xsbijXI
bQbII19osmcm0Pq4vfaMGrL30VV0v+9seC3iprsI+ff4vr/Ok2zIPhb/cx7d
zyI9T03s+cEGpz0trMPod+bk3U9bptgQ+TkyeAJZaXr8sdIMG45z8GbzKF7j
+YhzA3NscDw0+5uJ8nuLVMhyxnEghDFothGd17utl0q54jng6nxwpA2ZWRAv
d0SYA9fKh0/aigjgzL7wZb4EDmg5j2aeIgjA87751ggKBx6VfftTR0Lr2Xgm
MI3FAX2nX1lb0f01LMk9JJPNAZvSE9CDXPXjw5kcDgfOiC10H0T3XY2EJ9HF
izggXPpX6BxdALyvcTkN0uh3UYJlKxN9n/VoRc0yHJhyiByzYqH7+42w8jYu
B1aXkMK/IBN13Zu6ZDmg6kDNFeMI4PuVDR8HlnAA95AhbIru28v/yx8aUeDA
Muq1uD7kg9pKX8cUOeBuz1bzRPfzlItxPyaUOHC6OOaxkKQAevvEfk0t5UAv
ZdH+a8gSWmFCc8ocGLG7Ob4E3e93n5smLvA5sLhYMuIB8qVeNxpOhQM9EV1i
D9DzTSs/cAiqHHh4THj+LOoPd8ZMhrKMA9H7ND/bovg2vmmSpy3nQKi+46tV
KP7CsPwVi9Q4ICpRW9SH8pPQGWqwVJMDmtVBR7RRvl8pT5uorOIA4d59Kxq6
37BPuO1ZocWBwauvDf9D83dW0cxx9RoOODuvWRqFrRdfxRNb13Pggujk+yF0
/zWUaMpz0efARis305ufUP0vOPvTeTMHnRueWPr3ofuFkRE4b+HA+talDhbv
0fo92fbCaRsH1q7v95R4g9bPQOeU/XYOWMtYR9/s4MPHk9d17I3R+jArv+X/
jA+3JS0i7XZw4NIFybsWbXxgG7+RtN2J+v/1skiimQ9CD/rWW5lxoOztju6b
tXyoMk45vd+cA7ns7Pf+1XwIGHRq27eHA8+3U4YsKtH9RGrI1tICja+icUai
FNWLB/cyLCw5gP+h+HemmA8uO9y+7d3HgVrVcNKrB+j8FDIWuseKA99u6UrF
5vEhTjqvxdyaA5IvE+QDcvhgXuTBNrdB8yU6L7DM4gPdRMPazJYDrM37NbQz
0fd9aPLubjsO7DjbLyGXwYczocVju+w5kLRrXOwaeh9k/FfvcuDAE+lfeJEi
PpSazDXtdOJAYA7r22c0Hu/hCsbOAxxI9JMdtGnig1pY8D4TZw406Kq8e47y
kVb897PxQQ54v4AnD1E+o7lEmpE7B7bPeCSF/eDDsc9s883eHHCEZ6bSfAEo
n1nepx3OgYKuCwWGVwTQeqdCSPk02g/J5LId19F5usRQQTwC5ftIZO2uWwIo
GXZ2mTjDgUMi4c/2ZQjAYPudL5nnOSCrdXzMtUYAY07LaLEXOKAs9PPHkQZ0
Hz1RrnbmIgfs2nznPVvR+Tan28vxMgfknD2px3sEENx4IMb0Ctpv6uOsk73o
e/vhe/H/qbjOg6quojiAF5LAPDa7DbIUE8j78ePB44fgCAnZVyiojGAEKjTU
gRwSRWgqYsmXCJpsKrIvsggOIPYETCRAthcgqz7mPSBKNhGQvWJfHt3+/Mzc
f86555x7z7vXaL42z+hFjtJ9RUtzVS+R1nuSPxszx0KdzdZTvUGgfvIFl7DI
ogwC+2XqEXM/28R1Fp7eVV+OJRFsrwwfTHnFDGvfOIt6kmn8N9ZSjVfpvhwr
y21Iof7Ax4SdpPtOgW+jOJVgc6WhXNjPIlYmUo5Lp/3jc6XTroqF5aw6E5ZB
UKc9432wmEXPa1ku/pk0vxK3Cad0Fvq2D2OdsgmMzXYruYWyKM2Y197MJchY
vG17yo6+lxXnrafyCNKK1JoDWBaL7TzP/nwCg6OBR4JpPztsmqb9WkAwWr8v
MGLVFJ3HT74VWETwRZzkVmIVrc89UrNBMYHCaESjzo7ep8OJw533aD7l72dJ
WNo/XrNnq8vo/Pi5mG3TNYXoslpZagVB0WyQk2yVgdbLQ/vdKglUf1OETlUx
sBJXODY8Ilhwe3NM5x0GlzKuhTXVEbiO1/4gMWUwEH227Pd6gqYffXjBOgyi
jzGGbY0EL0tyrNv+5eMP5x1eHU0E7niv5ftRPiyth+O6JATDvUPexlI++lUz
16TNBE93GEVGiPkQLoZYyVrovMtsfIO9ycfFIQ//3laCISvfYlkcH33tVjn9
jwkutyo5RIbzYVGpIR9oI6jxKXgiPM1HZP4U71k7jc8779nr9HxvfKvjUAdB
UPoonj/iwzy0MGykk+a/z6Tw/gIfF/wiy553Eejr+KtE72Eg//T4xItugmrP
kgDPzxgIDtgbTj6h8yVpusskhoFMeyluRkrraVdwcvMcA7bua/8lOYGUF2ak
Uk3/z7ruhiqDBDavxtnHupuBryz0UhsisEVXztEoM4TPq8Xzhgk6RVpK5pVm
MGmRrGmNEphsJj3uMBAg9Ftbue44gfJKtpfGhABvdxvGC+YIUmfEQdfPWyA4
anbNVUHfi/6egtQ7HBKvLDV6UgcvajnPlHKoSNiKOUa9c5fr5KFfOCymaeif
ps75qNVi9h6HsLvCA9HUtjU1D5wecLgoDwyv/v98TmHrQj2HFNO5dWabIOWr
kOmP5RwqLZabhNTdF+4n5PVy6N+riN1H7XVzgVvu46DvoGngSL27N+C7/AEO
Oe6W9j7UyS4ntlaGOBSHnYtIoq4VfKh1e4pDmyjEKZOacblUvj7NYSpKxMun
lvg1ebjPcrC4ejVLTB2d7ZC+Mc+h/Ja4po16p+ZeoyNLHHqKKqOeUvsJzkmK
lml8d+sO91FLnUtPba1w2P+w+88x6sCf+HeK1zl8XttbME29leX7iWKDQ2jj
4Jl/qE9V5c55bHHIaBm3WaPOkP11vUTBobpjbmObWvtvPZvtbQ7/AR7Occ8=

     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{All, All},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.399662569246586*^9}]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Important", "Section"],

Cell[TextData[{
 StyleBox["In the conditional definitions:\n- the definition of the recursive \
part must be delayed. Use \":=\" !!!\n- the definition for the initial value \
must work after final steps of the recursion",
  FontColor->RGBColor[1, 0, 0]],
 "\n\n",
 StyleBox["In the program development phase, after a modification of the \
definition of a function, multiple definition can appear!\n\nUse Clear to \
avoid such a bug!!!!!",
  FontColor->RGBColor[1, 0, 0]]
}], "Text-Framed",
 CellMargins->{{53.04861166300595, 66.27083518770002}, {2., 2.}},
 CellChangeTimes->{{3.5628434249681163`*^9, 3.562843445370283*^9}}]
}, Closed]],

Cell[CellGroupData[{

Cell["Which statement", "Section",
 CellChangeTimes->{{3.4133971632510943`*^9, 3.4133971634814253`*^9}}],

Cell[TextData[{
 StyleBox["Which",
  FontFamily->"Courier New"],
 " gives piecewise definition of functions. You can also use the ",
 StyleBox["Piecewise",
  FontFamily->"Courier New"],
 " statement. Such functions can be differentiated and integrated."
}], "Text",
 CellChangeTimes->{{3.413397240792594*^9, 3.4133973303213296`*^9}, {
  3.414265238130205*^9, 3.414265238310464*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"g", "[", "x_", "]"}], ":=", 
  RowBox[{"Which", "[", 
   RowBox[{
    RowBox[{"x", ">", "0"}], ",", 
    RowBox[{"x", " ", "+", " ", 
     RowBox[{"g", "[", 
      RowBox[{"x", "-", "1"}], "]"}], "+", 
     RowBox[{"g", "[", 
      RowBox[{"x", "-", "2"}], "]"}]}], ",", "True", ",", "0"}], 
   "]"}]}]], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Evaluate", "[", 
    RowBox[{"g", "[", "x", "]"}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "1"}], ",", "5"}], "}"}], ",", 
   RowBox[{"PlotRange", "->", "All"}]}], "]"}]], "Input"],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxF1Wk81GsbwPGxzPzHWGZQHYxlZEmGkmQpuq9ClEI1oY4kxbFWtIlStMmR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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{All, All},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.399662630945304*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell["The derivative", "Subsection"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"g", "'"}], "[", "x", "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"Which", "[", 
  RowBox[{
   RowBox[{"x", ">", "0"}], ",", 
   RowBox[{"1", "+", 
    RowBox[{
     SuperscriptBox["g", "\[Prime]",
      MultilineFunction->None], "[", 
     RowBox[{"x", "-", "2"}], "]"}], "+", 
    RowBox[{
     SuperscriptBox["g", "\[Prime]",
      MultilineFunction->None], "[", 
     RowBox[{"x", "-", "1"}], "]"}]}], ",", "True", ",", "0"}], 
  "]"}]], "Output",
 CellChangeTimes->{3.399662636803728*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Evaluate", "[", 
    RowBox[{
     RowBox[{"g", "'"}], "[", "x", "]"}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "1"}], ",", "5"}], "}"}], ",", 
   RowBox[{"PlotRange", "->", "All"}]}], "]"}]], "Input"],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxFz3swFAgcB/D1XJb16shjdUTr0SWDlnLYdE1ZsSXndTOSK631yG3cFRFl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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{All, All},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.3996626386463776`*^9}]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Piecewise statement", "Section",
 CellChangeTimes->{{3.4133971672868977`*^9, 3.41339716758733*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Which", "[", 
  RowBox[{
   RowBox[{"x", ">", "0"}], ",", 
   RowBox[{"x", " ", "+", " ", 
    RowBox[{"g", "[", 
     RowBox[{"x", "-", "1"}], "]"}], "+", 
    RowBox[{"g", "[", 
     RowBox[{"x", "-", "2"}], "]"}]}], ",", "True", ",", "0"}], 
  "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"Which", "[", 
  RowBox[{
   RowBox[{"x", ">", "0"}], ",", 
   RowBox[{"x", "+", 
    RowBox[{"g", "[", 
     RowBox[{"x", "-", "1"}], "]"}], "+", 
    RowBox[{"g", "[", 
     RowBox[{"x", "-", "2"}], "]"}]}], ",", "True", ",", "0"}], 
  "]"}]], "Output",
 CellChangeTimes->{3.3996626530570993`*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"h", "[", "x_", "]"}], ":=", 
  RowBox[{"Piecewise", "[", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"x", " ", "+", " ", 
        RowBox[{"g", "[", 
         RowBox[{"x", "-", "1"}], "]"}], "+", 
        RowBox[{"g", "[", 
         RowBox[{"x", "-", "2"}], "]"}]}], ",", 
       RowBox[{"x", ">", "0"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"0", ",", "True"}], "}"}]}], "}"}], "]"}]}]], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"?", "h"}]], "Input"],

Cell[CellGroupData[{

Cell["Global`h", "Print", "PrintUsage",
 CellChangeTimes->{3.399662658274602*^9},
 CellTags->"Info3399669857-6408941"],

Cell[BoxData[
 InterpretationBox[GridBox[{
    {GridBox[{
       {
        RowBox[{
         RowBox[{"h", "[", "x_", "]"}], ":=", 
         RowBox[{"\[Piecewise]", GridBox[{
            {
             RowBox[{"x", "+", 
              RowBox[{"g", "[", 
               RowBox[{"x", "-", "1"}], "]"}], "+", 
              RowBox[{"g", "[", 
               RowBox[{"x", "-", "2"}], "]"}]}], 
             RowBox[{"x", ">", "0"}]},
            {"0", "True"}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
           
           GridBoxItemSize->{
            "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{1.}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.84]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}]}]}]}
      },
      BaselinePosition->{Baseline, {1, 1}},
      GridBoxAlignment->{
       "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
        "RowsIndexed" -> {}},
      GridBoxItemSize->{"Columns" -> {{
           Scaled[0.999]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
        "RowsIndexed" -> {}}]}
   },
   BaselinePosition->{Baseline, {1, 1}},
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}}],
  Definition["h"],
  Editable->False]], "Print",
 CellChangeTimes->{3.3996626583747454`*^9},
 CellTags->"Info3399669857-6408941"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Evaluate", "[", 
    RowBox[{"h", "[", "x", "]"}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "1"}], ",", "5"}], "}"}], ",", 
   RowBox[{"PlotRange", "->", "All"}]}], "]"}]], "Input"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxTTMoPSmViYGBQAGIQ3bXXad///+/3M0CB35vsGW8+IPiC0lOLbj5E8GdU
PFfbfBjBX2bc05/WjuAfXHk14Swfgv9jagbzbNl3cH56Xp+HmfUbOL+uTnmf
q+oLOD/Kwd92acgTOF/Z2VdQd/oDON/LS3OhtOBNOP9m4VOj2rqLcP729Rlm
ipMPwfnfvH6ErQlC8E2etZebCyH4m2SW7/CdeBDOX9f51Kqq/wCc73n8SN0y
8b1wvor+jglcnFvh/EWp1y8qdGyB8xXmfBMyZ0fwpTlNpyazbobzhR5vnLmH
cSOc/0833PXul5Vwfsbv6kte6yfD+U56R257n5sI55sdkjg181Y/nD+n1/L9
3LAOOP+Cx7cin7lFcH6Ohp7BQqM0OP9a+7FfFyLi4XwAmICOVQ==
      "]], LineBox[CompressedData["
1:eJxF1Xk81Gv7wPGxzHynscwgHoxlrMlQSJai+yqKjkI1RR3ZThxrRZsoa4vj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      "]]}, {}}, {{}, {}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{All, All},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.3996626605478706`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell["The derivative", "Subsection"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"h", "'"}], "[", "x", "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"\[Piecewise]", GridBox[{
    {"0", 
     RowBox[{"x", "<", "0"}]},
    {
     RowBox[{"1", "+", 
      RowBox[{"Which", "[", 
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"-", "2"}], "+", "x"}], ">", "0"}], ",", 
        RowBox[{"1", "+", 
         RowBox[{
          SuperscriptBox["g", "\[Prime]",
           MultilineFunction->None], "[", 
          RowBox[{
           RowBox[{"(", 
            RowBox[{
             RowBox[{"-", "2"}], "+", "x"}], ")"}], "-", "2"}], "]"}], "+", 
         RowBox[{
          SuperscriptBox["g", "\[Prime]",
           MultilineFunction->None], "[", 
          RowBox[{
           RowBox[{"(", 
            RowBox[{
             RowBox[{"-", "2"}], "+", "x"}], ")"}], "-", "1"}], "]"}]}], ",", 
        "True", ",", "0"}], "]"}], "+", 
      RowBox[{"Which", "[", 
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"-", "1"}], "+", "x"}], ">", "0"}], ",", 
        RowBox[{"1", "+", 
         RowBox[{
          SuperscriptBox["g", "\[Prime]",
           MultilineFunction->None], "[", 
          RowBox[{
           RowBox[{"(", 
            RowBox[{
             RowBox[{"-", "1"}], "+", "x"}], ")"}], "-", "2"}], "]"}], "+", 
         RowBox[{
          SuperscriptBox["g", "\[Prime]",
           MultilineFunction->None], "[", 
          RowBox[{
           RowBox[{"(", 
            RowBox[{
             RowBox[{"-", "1"}], "+", "x"}], ")"}], "-", "1"}], "]"}]}], ",", 
        "True", ",", "0"}], "]"}]}], 
     RowBox[{"x", ">", "0"}]},
    {"Indeterminate", 
     TagBox["True",
      "PiecewiseDefault",
      AutoDelete->False,
      DeletionWarning->True]}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxItemSize->{
    "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[0.84]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}]}]], "Output",
 CellChangeTimes->{3.399662667778267*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Evaluate", "[", 
    RowBox[{
     RowBox[{"h", "'"}], "[", "x", "]"}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "1"}], ",", "5"}], "}"}], ",", 
   RowBox[{"PlotRange", "->", "All"}]}], "]"}]], "Input"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxTTMoPSmViYGBQA2IQ3bXXad///+/3M0CB35vsGW8+IPiC0lOLbj5E8GdU
PFfbfBjBX2bc05/WjuAfXHk14Swfgv9jagbzbNl3cH56Xp+HmfUbOL+uTnmf
q+oLOD/Kwd92acgTOF/Z2VdQd/oDON/LS3OhtOBNOP9m4VOj2rqLcP729Rlm
ipMPwfnfvH6ErQlC8E2etZebCyH4m2SW7/CdeBDOX9f51Kqq/wCc73n8SN0y
8b1wvor+jglcnFvh/EWp1y8qdGyB8xXmfBMyZ0fwpTlNpyazbobzhR5vnLmH
cSOc/0833PXul5Vw/q9ZU49zfl4B539lv+Jp9nE5nP/mYYBf/9ulCP9P9Qp3
fLYQzs/4XX3Ja/1kON9J78ht73MT4XyzQxKnZt7qh/Pn9Fq+nxvWAef7fz7J
uGBKC5zPFBklsuhSA5x/weNbkc/cIjg/R0PPYKFRGpx/rf3YrwsR8XA+AL/W
qjQ=
      "]], LineBox[CompressedData["
1:eJxFzntMUwcYBfBLKa8LhSKBCRTHy9KimQSQsTihczM+CKKAUjApSBi2l4ek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      "]]}, {}}, {{}, {}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{All, All},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.3996626712632785`*^9}]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Nesting", "MainSection"],

Cell["\<\
The most important tool for iterations, finding fixed points, and solving \
difference equations are the Nest statements. They are structural operations \
and do not use loops!\
\>", "Text",
 CellChangeTimes->{{3.41339738005284*^9, 3.413397443674323*^9}, {
  3.413398017569544*^9, 3.4133980435168543`*^9}, {3.413398313865597*^9, 
  3.4133983149571667`*^9}, {3.4142652683736925`*^9, 3.414265268904456*^9}}],

Cell[TextData[{
 ButtonBox["Nest",
  BaseStyle->"RefGuideLink"],
 StyleBox["[func, init, step]\n",
  FontFamily->"Courier"],
 ButtonBox["NestList",
  BaseStyle->"RefGuideLink"],
 StyleBox["[func,init, step]\n",
  FontFamily->"Courier"],
 ButtonBox["NestWhile",
  BaseStyle->"RefGuideLink"],
 StyleBox["[func, init, cond,...]\n",
  FontFamily->"Courier"],
 ButtonBox["NestWhileList",
  BaseStyle->"RefGuideLink"],
 StyleBox["[func, init, cond,...]",
  FontFamily->"Courier"]
}], "Text-Framed",
 CellMargins->{{49.86111206037023, 203.375}, {7., 7.}}],

Cell[CellGroupData[{

Cell["Important", "Section"],

Cell["\<\
The nested function is not an expression with variables!
The structure of the input and output must be the same!\
\>", "Text-Framed",
 CellMargins->{{50.09027866080952, 110.313}, {7., 7.}},
 CellChangeTimes->{{3.413397451235195*^9, 3.413397452807456*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell["Examples", "Section"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Nest", "[", 
  RowBox[{"f", ",", "x0", ",", "0"}], "]"}]], "Input"],

Cell[BoxData["x0"], "Output",
 CellChangeTimes->{3.399662718210786*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Nest", "[", 
  RowBox[{"f", ",", "x0", ",", "1"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"f", "[", "x0", "]"}]], "Output",
 CellChangeTimes->{3.3996627182808867`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Nest", "[", 
  RowBox[{"f", ",", "x0", ",", "3"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"f", "[", 
  RowBox[{"f", "[", 
   RowBox[{"f", "[", "x0", "]"}], "]"}], "]"}]], "Output",
 CellChangeTimes->{3.3996627184110737`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"NestList", "[", 
  RowBox[{"f", ",", "x0", ",", "5"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"x0", ",", 
   RowBox[{"f", "[", "x0", "]"}], ",", 
   RowBox[{"f", "[", 
    RowBox[{"f", "[", "x0", "]"}], "]"}], ",", 
   RowBox[{"f", "[", 
    RowBox[{"f", "[", 
     RowBox[{"f", "[", "x0", "]"}], "]"}], "]"}], ",", 
   RowBox[{"f", "[", 
    RowBox[{"f", "[", 
     RowBox[{"f", "[", 
      RowBox[{"f", "[", "x0", "]"}], "]"}], "]"}], "]"}], ",", 
   RowBox[{"f", "[", 
    RowBox[{"f", "[", 
     RowBox[{"f", "[", 
      RowBox[{"f", "[", 
       RowBox[{"f", "[", "x0", "]"}], "]"}], "]"}], "]"}], "]"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.3996627185012035`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"NestWhileList", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"#", "^", "2"}], "&"}], ",", "0.9", ",", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"#", ">", "0.2"}], ")"}], "&"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.399662751939285*^9, 3.399662764337112*^9}, {
  3.399662798556317*^9, 3.3996627988166914`*^9}, {3.3996629100065746`*^9, 
  3.399663059832013*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "0.9`", ",", "0.81`", ",", "0.6561000000000001`", ",", 
   "0.43046721000000016`", ",", "0.18530201888518424`"}], "}"}]], "Output",
 CellChangeTimes->{{3.3996629824707727`*^9, 3.3996630606031218`*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"NestWhileList", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"#", "^", "2"}], "&"}], ",", "0.9", ",", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"#1", "-", "#2"}], ")"}], ">", "0.01"}], ")"}], "&"}], ",", 
   StyleBox["2",
    FontColor->RGBColor[1, 0, 0]]}], "]"}]], "Input",
 CellChangeTimes->{{3.399662751939285*^9, 3.399662764337112*^9}, {
  3.399662798556317*^9, 3.3996627988166914`*^9}, {3.3996629100065746`*^9, 
  3.399663059832013*^9}, {3.399688283708954*^9, 3.3996882849206963`*^9}, {
  3.399688318619152*^9, 3.399688353228918*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "0.9`", ",", "0.81`", ",", "0.6561000000000001`", ",", 
   "0.43046721000000016`", ",", "0.18530201888518424`", ",", 
   "0.03433683820292518`", ",", "0.001179018457773862`", ",", 
   "1.390084523771456`*^-6"}], "}"}]], "Output",
 CellChangeTimes->{{3.399688349193115*^9, 3.399688354420632*^9}}]
}, Open  ]]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell["Fixed points", "MainSection"],

Cell[TextData[{
 "A combination of nesting with a test can be used to find fixed point of a \
mapping. It is known that under some conditions (like the Banach's fixed \
point theorem for contractive mappings), the solution of the equation ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"F", "(", "x", ")"}], "=", "x"}], TraditionalForm]]],
 " can be found by successive approximation, i.e., as the limit of the \
sequence "
}], "Text",
 CellChangeTimes->{{3.4133974838420815`*^9, 3.413397535886918*^9}, {
  3.413397589624189*^9, 3.41339774307484*^9}, {3.4133979833102818`*^9, 
  3.413397999473523*^9}, {3.4133980875601854`*^9, 3.413398098015219*^9}, {
  3.4142653568208733`*^9, 3.414265370079939*^9}}],

Cell[TextData[{
 " ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SubscriptBox["x", 
     RowBox[{"n", "+", "1"}]], "=", 
    RowBox[{
     RowBox[{"F", "(", 
      SubscriptBox["x", "n"], ")"}], "=", 
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{"F", "(", 
         RowBox[{"F", "(", 
          SubscriptBox["x", "n"], ")"}], ")"}], "=."}], ".."}], "=", 
      RowBox[{
       SuperscriptBox["F", 
        RowBox[{"(", "n", ")"}]], "(", 
       SubscriptBox["x", "0"], ")"}]}]}]}], TraditionalForm]]]
}], "Text",
 CellChangeTimes->{{3.4133974838420815`*^9, 3.413397535886918*^9}, {
  3.413397589624189*^9, 3.4133978452117057`*^9}, {3.4133978773278866`*^9, 
  3.41339791998923*^9}},
 TextAlignment->Center,
 TextJustification->0.],

Cell[TextData[{
 "where ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["F", 
    RowBox[{"(", "n", ")"}]], TraditionalForm]]],
 " is the ",
 StyleBox["n",
  FontSlant->"Italic"],
 "'th iterate of ",
 StyleBox["F",
  FontSlant->"Italic"],
 "."
}], "Text",
 CellChangeTimes->{{3.4133974838420815`*^9, 3.413397535886918*^9}, {
   3.413397589624189*^9, 3.413397861545192*^9}, 3.413397923764659*^9, {
   3.413398221653002*^9, 3.413398253679053*^9}}],

Cell[TextData[{
 ButtonBox["FixedPoint",
  BaseStyle->"RefGuideLink"],
 StyleBox["[func, init, stepno]\n",
  FontFamily->"Courier"],
 ButtonBox["FixedPointList",
  BaseStyle->"RefGuideLink"],
 StyleBox["[func,init, stepno]\nFixedPoint[func, init, \
stepno,SameTest->compfunc]\nFixedPointList[func,init, \
stepno,SameTest->compfunc]",
  FontFamily->"Courier"]
}], "Text-Framed",
 CellMargins->{{50.41666759384999, 70.88889012513334}, {7., 7.}}],

Cell[CellGroupData[{

Cell["Example", "Section"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FixedPointList", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"#", "+", 
       RowBox[{"2", "/", "#"}]}], ")"}], "/", "2"}], " ", "&"}], ",", "1.", 
   ",", "20", ",", 
   RowBox[{"SameTest", "->", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"Abs", "[", 
        RowBox[{"#1", "-", "#2"}], "]"}], "<", 
       RowBox[{"10", "^", 
        RowBox[{"-", "6"}]}]}], "&"}], ")"}]}]}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "1.`", ",", "1.5`", ",", "1.4166666666666665`", ",", "1.4142156862745097`", 
   ",", "1.4142135623746899`", ",", "1.414213562373095`"}], "}"}]], "Output",
 CellChangeTimes->{3.399662724770218*^9, 3.3996883691418*^9}]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]]
},
WindowToolbars->{"RulerBar", "EditBar"},
WindowSize->{1021, 842},
WindowMargins->{{116, Automatic}, {Automatic, 13}},
DockedCells->(FrontEndExecute[{
   FrontEnd`NotebookApply[
    FrontEnd`InputNotebook[], #, Placeholder]}]& ),
ShowSelection->True,
ShowCellTags->True,
Magnification->1.8000000715255737`,
FrontEndVersion->"9.0 for Microsoft Windows (64-bit) (January 25, 2013)",
StyleDefinitions->"Modelstyle-EN.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
 "Info3399669754-6520538"->{
  Cell[3526, 104, 118, 2, 169, "Print",
   CellTags->"Info3399669754-6520538"],
  Cell[3647, 108, 1117, 33, 210, "Print",
   CellTags->"Info3399669754-6520538"]},
 "Info3399669857-6408941"->{
  Cell[67542, 1322, 118, 2, 169, "Print",
   CellTags->"Info3399669857-6408941"],
  Cell[67663, 1326, 1745, 47, 149, "Print",
   CellTags->"Info3399669857-6408941"]}
 }
*)
(*CellTagsIndex
CellTagsIndex->{
 {"Info3399669754-6520538", 88060, 1915},
 {"Info3399669857-6408941", 88252, 1920}
 }
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[567, 22, 1301, 27, 73, "MainTitle"],
Cell[1871, 51, 43, 0, 76, "Subtitle"],
Cell[1917, 53, 273, 5, 81, "Text"],
Cell[CellGroupData[{
Cell[2215, 62, 94, 2, 104, "MainSection"],
Cell[2312, 66, 615, 11, 111, "Text"],
Cell[CellGroupData[{
Cell[2952, 81, 41, 0, 70, "Section"],
Cell[2996, 83, 436, 12, 214, "Input"],
Cell[CellGroupData[{
Cell[3457, 99, 44, 1, 108, "Input"],
Cell[CellGroupData[{
Cell[3526, 104, 118, 2, 169, "Print",
 CellTags->"Info3399669754-6520538"],
Cell[3647, 108, 1117, 33, 210, "Print",
 CellTags->"Info3399669754-6520538"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[4813, 147, 271, 8, 108, "Input"],
Cell[5087, 157, 3977, 70, 790, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9101, 232, 36, 0, 91, "Subsection"],
Cell[CellGroupData[{
Cell[9162, 236, 72, 2, 108, "Input"],
Cell[9237, 240, 158, 4, 84, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9432, 249, 338, 10, 108, "Input"],
Cell[9773, 261, 46647, 770, 783, "Output"]
}, Open  ]]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[56481, 1038, 28, 0, 47, "Section"],
Cell[56512, 1040, 623, 12, 498, "Text-Framed"]
}, Closed]],
Cell[CellGroupData[{
Cell[57172, 1057, 104, 1, 47, "Section"],
Cell[57279, 1060, 382, 9, 147, "Text"],
Cell[57664, 1071, 348, 11, 108, "Input"],
Cell[CellGroupData[{
Cell[58037, 1086, 271, 8, 108, "Input"],
Cell[58311, 1096, 4947, 86, 790, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[63295, 1187, 36, 0, 91, "Subsection"],
Cell[CellGroupData[{
Cell[63356, 1191, 72, 2, 108, "Input"],
Cell[63431, 1195, 450, 14, 84, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[63918, 1214, 292, 9, 108, "Input"],
Cell[64213, 1225, 1940, 37, 790, "Output"]
}, Open  ]]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[66214, 1269, 105, 1, 47, "Section"],
Cell[CellGroupData[{
Cell[66344, 1274, 287, 9, 108, "Input"],
Cell[66634, 1285, 322, 10, 84, "Output"]
}, Open  ]],
Cell[66971, 1298, 477, 15, 108, "Input"],
Cell[CellGroupData[{
Cell[67473, 1317, 44, 1, 108, "Input"],
Cell[CellGroupData[{
Cell[67542, 1322, 118, 2, 169, "Print",
 CellTags->"Info3399669857-6408941"],
Cell[67663, 1326, 1745, 47, 149, "Print",
 CellTags->"Info3399669857-6408941"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[69457, 1379, 271, 8, 108, "Input"],
Cell[69731, 1389, 5070, 88, 790, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[74838, 1482, 36, 0, 91, "Subsection"],
Cell[CellGroupData[{
Cell[74899, 1486, 72, 2, 108, "Input"],
Cell[74974, 1490, 2245, 68, 444, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[77256, 1563, 292, 9, 108, "Input"],
Cell[77551, 1574, 2094, 40, 790, "Output"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[79718, 1622, 30, 0, 68, "MainSection"],
Cell[79751, 1624, 415, 7, 145, "Text"],
Cell[80169, 1633, 548, 18, 320, "Text-Framed"],
Cell[CellGroupData[{
Cell[80742, 1655, 28, 0, 126, "Section"],
Cell[80773, 1657, 265, 5, 203, "Text-Framed"]
}, Open  ]],
Cell[CellGroupData[{
Cell[81075, 1667, 27, 0, 126, "Section"],
Cell[CellGroupData[{
Cell[81127, 1671, 91, 2, 108, "Input"],
Cell[81221, 1675, 71, 1, 84, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[81329, 1681, 91, 2, 108, "Input"],
Cell[81423, 1685, 100, 2, 84, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[81560, 1692, 91, 2, 108, "Input"],
Cell[81654, 1696, 157, 4, 84, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[81848, 1705, 95, 2, 108, "Input"],
Cell[81946, 1709, 621, 19, 84, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[82604, 1733, 385, 10, 108, "Input"],
Cell[82992, 1745, 243, 5, 84, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[83272, 1755, 598, 15, 108, "Input"],
Cell[83873, 1772, 337, 7, 156, "Output"]
}, Open  ]]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell[84271, 1786, 35, 0, 68, "MainSection"],
Cell[84309, 1788, 707, 14, 255, "Text"],
Cell[85019, 1804, 744, 25, 90, "Text"],
Cell[85766, 1831, 444, 16, 90, "Text"],
Cell[86213, 1849, 443, 12, 313, "Text-Framed"],
Cell[CellGroupData[{
Cell[86681, 1865, 26, 0, 126, "Section"],
Cell[CellGroupData[{
Cell[86732, 1869, 470, 16, 162, "Input"],
Cell[87205, 1887, 258, 5, 84, "Output"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]]
}
]
*)

(* End of internal cache information *)
