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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 387088, 23563]*) (*NotebookOutlinePosition[ 388295, 23601]*) (* CellTagsIndexPosition[ 388251, 23597]*) (*WindowFrame->Normal*) Notebook[{ Cell["Math 225: Calculus III Solution 10", "Subsection", Evaluatable->False, PageBreakWithin->Automatic, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Initialization"], "Subsubsection", Evaluatable->False, PageBreakWithin->Automatic, AspectRatioFixed->True], Cell[TextData["<Automatic, InitializationCell->True, AspectRatioFixed->True], Cell[TextData["i = {1, 0, 0}; j = {0, 1, 0}; k = {0, 0, 1};"], "Input", PageBreakWithin->Automatic, InitializationCell->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Problem 1 "], "Subsubsection", Evaluatable->False, PageBreakWithin->Automatic, AspectRatioFixed->True], Cell[TextData[{ "Compute ", StyleBox["Div[F]", FontFamily->"Courier", FontWeight->"Bold"], ", ", StyleBox["Curl[F]", FontFamily->"Courier", FontWeight->"Bold"], ", and ", StyleBox["Div[Curl[F]]", FontFamily->"Courier", FontWeight->"Bold"], " for the following vector fields.\n", StyleBox["a)", FontSlant->"Italic"], " ", StyleBox["F = (x^2 y + z) i + (y^2 z + x) j + (z^2 x + y) k", FontFamily->"Courier", FontWeight->"Bold"], "\n", StyleBox["b)", FontSlant->"Italic"], " ", StyleBox["F = Cos[x+y] i + Sin[x-y] j", FontFamily->"Courier", FontWeight->"Bold"], "\n", StyleBox["c)", FontSlant->"Italic"], " ", StyleBox["F = y E^z i + z E^x j + x E^y k\n", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["d)", FontSlant->"Italic"], " \"Prove\" using ", StyleBox["Mathematica", FontSlant->"Italic"], " that for an arbitrary vector field,\n", StyleBox[" F = m[x,y,z]i + n[x,y,z]j + p[x,y,z]k\n", FontFamily->"Courier", FontWeight->"Bold"], " we always get ", StyleBox["Div[Curl[F]] == 0", FontFamily->"Courier", FontWeight->"Bold"], ". 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y + z)dx + (3x y^2 - x + 2y z)dy + (y^2 + x + 2z)dz", FontFamily->"Courier", FontWeight->"Bold"], "\nover the curve ", StyleBox["C", FontFamily->"Courier", FontWeight->"Bold"], " defined by ", StyleBox["t^2 i + t j + (t^3-1)k, 0 <= t <= 1", FontFamily->"Courier", FontWeight->"Bold"], ",\n(using ", StyleBox["Integrate[]", FontFamily->"Courier", FontWeight->"Bold"], ", or ", StyleBox["FlowIntegrate[]", FontFamily->"Courier", FontWeight->"Bold"], ").\n", StyleBox["b)", FontSlant->"Italic"], " Find a function ", StyleBox["f[x,y,z]", FontFamily->"Courier", FontWeight->"Bold"], " such that\n", StyleBox[ "Grad[f[x,y,z]] == \n (y^3 - y + z)i + (3x y^2 - x + 2y z)j + (y^2 + x + \ 2z)k", FontFamily->"Courier", FontWeight->"Bold"], "\n", StyleBox["c)", FontSlant->"Italic"], " Use the Fundamental Theorem of Line Integrals to evaluate the the \ integral in ", StyleBox["a)", FontSlant->"Italic"], " using the result of ", StyleBox["b)", FontSlant->"Italic"], "." }], "Text", CellMargins->{{Inherited, 3}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True], Cell[TextData["Solution"], "Subsubsection", Evaluatable->False, PageBreakWithin->Automatic, AspectRatioFixed->True], Cell[TextData[StyleBox["a)", FontSlant->"Italic"]], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "FlowIntegrate[\n {y^3 - y + z, 3x y^2 - x + 2y z, y^2 + x + 2z},\n \ {t^2, t, t^3-1}, {t,0,1}]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ -1\ \>", "\<\ -1\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ StyleBox["b)", FontSlant->"Italic"], " We must find a function ", StyleBox["f[x,y,z]", FontFamily->"Courier", FontWeight->"Bold"], " that satisfies the equations\n", StyleBox[ " D[f[x,y,z],x] == y^3 - y + z\n D[f[x,y,z],y] == 3x y^2 - x + 2y z\n \ D[f[x,y,z],z] == y^2 + x + 2z\n", FontFamily->"Courier", FontWeight->"Bold"], "Integrate the first equations iwth respect to ", StyleBox["x", FontFamily->"Courier", FontWeight->"Bold"], ", adding a \"constant\" of integration that could depend on ", StyleBox["y", FontFamily->"Courier", FontWeight->"Bold"], " and ", StyleBox["z", FontFamily->"Courier", FontWeight->"Bold"], ":" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["Clear[f,g,h]"], "Input", AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["f[x_,y_,z_] = Integrate[y^3 - 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FontFamily->"Courier", FontWeight->"Bold"], " equals the double integral over ", StyleBox["R", FontFamily->"Courier", FontWeight->"Bold"], " of" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["g = D[x^2 y,x] - D[2x y^2,y]", "Input", PageBreakWithin->Automatic, AspectRatioFixed->True], Cell[BoxData[ \(\(-2\)\ x\ y\)], "Output"] }, Open ]] }, Open ]], Cell[TextData[{ "The region ", StyleBox["R", FontFamily->"Courier", FontWeight->"Bold"], " is described horizontally by\n", StyleBox[" y^3 <= x <= 1\n 0 <= y <= 1\n", FontFamily->"Courier", FontWeight->"Bold"], "so the value of the original line integral equals" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["Integrate[g,{y,0,1},{x,y^3,1}]", "Input", AspectRatioFixed->True], Cell[BoxData[ \(\(-\(3\/8\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Problem 5"], "Subsubsection", Evaluatable->False, PageBreakWithin->Automatic, AspectRatioFixed->True], Cell[TextData[ "Produce a plot of a surface that you think has interesting features. The \ surface does not have to be the graph of a function and can be done in any \ coordinate system you wish. Explain what features of the surface are \ interesting and why."], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["Solution"], "Subsubsection", Evaluatable->False, PageBreakWithin->Automatic, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ StyleBox["The Moebius Band. ", FontWeight->"Bold"], "The Moebius band is an example of a surface for which a unit normal vector \ ", StyleBox["cannot", FontSlant->"Italic"], " be assigned to every point on the surface in a continuous way since the \ surface has only one \"side\". If you start with a unit vector pointing up at \ one point, say, and then slide this vector around the surface and come back \ to the same point, the vector will be pointing down.\nThe surface is built \ starting with a horizontal circle and then adding a band that twists 180 \ degrees as we go around the complete circle. We'll use a horizontal circle of \ radius three:" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["u = {Cos[t], Sin[t], 0}"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {Cos[t], Sin[t], 0}\ \>", "\<\ {Cos[t], Sin[t], 0}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["circ = 3 u"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {3*Cos[t], 3*Sin[t], 0}\ \>", "\<\ {3 Cos[t], 3 Sin[t], 0}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ "The band is built out of multiples of a vector pointing away from the \ circle and spinning around on its own. This vector can be written as a \ combination of ", StyleBox["u", FontFamily->"Courier", FontWeight->"Bold"], " and ", StyleBox["k", FontFamily->"Courier", FontWeight->"Bold"], ". The factor of ", StyleBox["1/2", FontFamily->"Courier", FontWeight->"Bold"], " in the trig functions assures that as we move around the horizontal \ circle the band gets only a half twist." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["v = u Cos[t/2] + k Sin[t/2]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {Cos[t/2]*Cos[t], Cos[t/2]*Sin[t], Sin[t/2]}\ \>", "\<\ t t t {Cos[-] Cos[t], Cos[-] Sin[t], Sin[-]} 2 2 2\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ "We paramaterize the surface using the angle ", StyleBox["t", FontFamily->"Courier", FontWeight->"Bold"], " for the horizontal circle and the spinning vector ", StyleBox["v", FontFamily->"Courier", FontWeight->"Bold"], ", and we use another parameter ", StyleBox["s", FontFamily->"Courier", FontWeight->"Bold"], " to thicken the circle into a band in the direction of ", StyleBox["v", FontFamily->"Courier", FontWeight->"Bold"], " as we go around the circle. 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r F P s P p .002 w .23899 .52256 m .23895 .51504 L .28352 .55806 L p .949 .721 .56 r F P s P p .002 w .28352 .55806 m .28243 .56587 L .23899 .52256 L p .949 .721 .56 r F P s P p .002 w .20362 .39127 m .20205 .38408 L .23849 .43456 L p .985 .711 .404 r F P s P p .002 w .23849 .43456 m .23853 .4417 L .20362 .39127 L p .985 .711 .404 r F P s P p .002 w .23903 .53012 m .23899 .52256 L .28243 .56587 L p .953 .726 .557 r F P s P p .002 w .28243 .56587 m .28133 .57372 L .23903 .53012 L p .953 .726 .557 r F P s P p .002 w .20519 .39849 m .20362 .39127 L .23853 .4417 L p .987 .714 .396 r F P s P p .002 w .23853 .4417 m .23857 .44888 L .20519 .39849 L p .987 .714 .396 r F P s P p .002 w .23907 .53772 m .23903 .53012 L .28133 .57372 L p .957 .731 .555 r F P s P p .002 w .28133 .57372 m .28022 .5816 L .23907 .53772 L p .957 .731 .555 r F P s P p .002 w .78269 .57295 m .77571 .56724 L .82512 .50022 L p .61 .629 .845 r F P s P p .002 w .82512 .50022 m .83396 .50355 L .78269 .57295 L p .61 .629 .845 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.28324 .48378 m .27333 .46016 L .29452 .48797 L p .915 .572 .111 r F P s P p .002 w .29452 .48797 m .30002 .51013 L .28324 .48378 L p .915 .572 .111 r F P s P p .002 w .28324 .48378 m .30002 .51013 L p .29477 .50821 L .864 .538 .021 r F P s P p .002 w .28957 .49833 m .28806 .50104 L p .29468 .5099 L .689 .569 .715 r F P s P p .002 w .28806 .50104 m .27545 .52373 L p .29077 .51271 L .689 .569 .715 r F P s P p .29077 .51271 m .29468 .5099 L .28806 .50104 L .689 .569 .715 r F P p .002 w .28979 .49793 m .28957 .49833 L p .2952 .50953 L .689 .569 .715 r F P s P p .29468 .5099 m .2952 .50953 L .28957 .49833 L .689 .569 .715 r F P p .2952 .50953 m .29475 .5082 L .28979 .49793 L .689 .569 .715 r F P p .29477 .50821 m .29326 .50766 L .29369 .50593 L .864 .538 .021 r F P p .28774 .49331 m .29326 .50766 L .28324 .48378 L .864 .538 .021 r F P p .002 w .33168 .48331 m .30843 .46439 L .28979 .49793 L p .689 .569 .715 r F P s P p .30002 .51013 m .29731 .51586 L .2952 .50953 L .864 .538 .021 r F P p .29477 .50821 m .2952 .50953 L .29475 .5082 L .864 .538 .021 r F P p .30002 .51013 m .2952 .50953 L .29477 .50821 L .864 .538 .021 r F P p .002 w .30002 .51013 m .30561 .5326 L .29731 .51586 L p .864 .538 .021 r F P s P p .2952 .50953 m .30521 .53034 L .29534 .50943 L .689 .569 .715 r F P p .29319 .51097 m .29838 .51933 L .29712 .51547 L .689 .569 .715 r F P p .29319 .51097 m .29712 .51547 L .29468 .5099 L .689 .569 .715 r F P p .002 w .29712 .51547 m .29731 .51586 L p .29746 .51624 L .763 .471 0 r F P s P p .002 w .29731 .51586 m .30561 .5326 L p .30455 .53222 L .763 .471 0 r F P s P p .29468 .5099 m .29712 .51547 L .2952 .50953 L .689 .569 .715 r F P p .002 w .29731 .51586 m .29326 .50766 L p .29475 .5082 L .864 .538 .021 r F P s P p .29712 .51547 m .30521 .53034 L .2952 .50953 L .689 .569 .715 r F P p .29838 .51933 m .29987 .52173 L .29712 .51547 L .689 .569 .715 r F P p .30455 .53222 m .30445 .53219 L .29731 .51586 L .763 .471 0 r F P p .002 w .30433 .53191 m .30319 .53393 L p .30472 .53317 L .694 .563 .703 r F P s P p .30324 .53408 m .30472 .53317 L .30319 .53393 L .694 .563 .703 r F P p .002 w .30561 .5326 m .31127 .55541 L .30927 .54942 L p .763 .471 0 r F P s P p .002 w .31127 .55541 m .33195 .57533 L p .32056 .57778 L .979 .692 .399 r F P s P p .002 w .30303 .53421 m .2942 .5938 L p .31409 .56702 L .656 .555 .729 r F P s P p .31409 .56702 m .31418 .56691 L .31388 .56605 L .656 .555 .729 r F P p .31409 .56702 m .31388 .56605 L .30303 .53421 L .656 .555 .729 r F P p .32056 .57778 m .31442 .56658 L .31127 .55541 L .979 .692 .399 r F P p .002 w .31373 .56531 m .31368 .56511 L p .31442 .56658 L .979 .692 .399 r F P s P p .002 w .31368 .56511 m .31127 .55541 L p .31442 .56658 L .979 .692 .399 r F P s P p .002 w .33195 .57533 m .33275 .59849 L .32287 .58597 L p .979 .692 .399 r F P s P p .002 w .33275 .59849 m .33195 .57533 L .36019 .58975 L p .89 .65 .57 r F P s P p .002 w .36019 .58975 m .35714 .61415 L .33275 .59849 L p .89 .65 .57 r F P s P p .002 w .32243 .59492 m .32542 .59504 L p .32469 .59242 L .657 .542 .712 r F P s P p .002 w .2942 .5938 m .32243 .59492 L .32346 .58865 L p .656 .555 .729 r F P s P p .002 w .32346 .58865 m .32357 .58798 L p .32259 .58584 L .656 .555 .729 r F P s P p .002 w .32248 .58548 m .32287 .58597 L p .32287 .58638 L .981 .708 .322 r F P s P p .002 w .32287 .58597 m .33275 .59849 L p .3289 .59987 L .981 .708 .322 r F P s P p .3289 .59987 m .32683 .59525 L .32287 .58597 L .981 .708 .322 r F P p .32881 .5999 m .32663 .59508 L .32287 .58597 L .981 .708 .322 r F P p .002 w .32357 .58798 m .32243 .59492 L p .32527 .59178 L .657 .542 .712 r F P s P p .002 w .33275 .59849 m .35714 .61415 L p .33548 .62138 L .924 .687 .561 r F P s P p .33548 .62138 m .335 .62154 L .33487 .62025 L .924 .687 .561 r F P p .33548 .62138 m .33487 .62025 L .33275 .59849 L .924 .687 .561 r F P p .002 w .35405 .63889 m .35714 .61415 L .38614 .62459 L p .835 .632 .629 r F P s P p .002 w .38614 .62459 m .3815 .65118 L .35405 .63889 L p .835 .632 .629 r F P s P p .002 w .35714 .61415 m .35405 .63889 L .3359 .62395 L p .924 .687 .561 r F P s P p .35714 .61415 m .3359 .62395 L .335 .62154 L .924 .687 .561 r F P p .002 w .32429 .60425 m .33263 .64611 L p .33706 .63391 L .621 .532 .732 r F P s P p .33706 .63391 m .33401 .62132 L .32429 .60425 L .621 .532 .732 r F P p .33866 .6295 m .33345 .61904 L .32429 .60425 L .621 .532 .732 r F P p .002 w .33275 .59849 m .33345 .61904 L p .32881 .5999 L .981 .708 .322 r F P s P p .002 w .32243 .59492 m .32429 .60425 L p .33264 .61521 L .621 .532 .732 r F P s P p .002 w .33345 .61904 m .33275 .59849 L p .335 .62154 L .924 .687 .561 r F P s P p .33264 .61521 m .34024 .62516 L .32967 .60722 L .621 .532 .732 r F P p .33264 .61521 m .32967 .60722 L .32243 .59492 L .621 .532 .732 r F P p .35405 .63889 m .34496 .64214 L .33866 .6295 L .959 .727 .543 r F P p .002 w .3359 .62395 m .33642 .62438 L p .33866 .6295 L .959 .727 .543 r F P s P p .002 w .33642 .62438 m .35405 .63889 L p .33866 .6295 L .959 .727 .543 r F P s P p .002 w .37681 .67805 m .3815 .65118 L .41276 .65808 L p .792 .618 .665 r F P s P p .002 w .3815 .65118 m .37681 .67805 L .35243 .66479 L p .865 .663 .628 r F P s P p .002 w .35243 .66479 m .35091 .66397 L p .35208 .66348 L .865 .663 .628 r F P s P p .3815 .65118 m .35243 .66479 L .35208 .66348 L .865 .663 .628 r F P p .002 w .41276 .65808 m .40956 .68657 L .37681 .67805 L p .792 .618 .665 r F P s P p .002 w .37208 .70519 m .37681 .67805 L .40956 .68657 L p .815 .64 .664 r F P s P p .002 w .40956 .68657 m .40634 .71521 L .37208 .70519 L p .815 .64 .664 r F P s P p .34348 .65341 m .35258 .67807 L .33263 .64611 L .596 .536 .758 r F P p .002 w .35366 .68377 m .33263 .64611 L p .35258 .67807 L .596 .536 .758 r F P s P p .34656 .65548 m .35051 .66715 L .34348 .65341 L .596 .536 .758 r F P p .34741 .65605 m .34906 .66194 L .34656 .65548 L .596 .536 .758 r F P p .34906 .66194 m .35051 .66715 L .34656 .65548 L .596 .536 .758 r F P p .35051 .66715 m .35668 .68916 L .34348 .65341 L .596 .536 .758 r F P p .002 w .30766 .6541 m .33263 .64611 L .35833 .69212 L p .604 .551 .768 r F P s P p .002 w .35405 .63889 m .35091 .66397 L .34906 .66194 L p .959 .727 .543 r F P s P p .35405 .63889 m .34906 .66194 L .34878 .66094 L .959 .727 .543 r F P p .35405 .63889 m .34864 .66149 L .3443 .64237 L .959 .727 .543 r F P p .002 w .35091 .66397 m .35405 .63889 L .3815 .65118 L p .865 .663 .628 r F P s P p .002 w .35783 .63804 m .37717 .67607 L p .34656 .65548 L .596 .536 .758 r F P s P p .002 w .33263 .64611 m .34225 .64303 L p .34656 .65548 L .596 .536 .758 r F P s P p .002 w .33263 .64611 m .3443 .64237 L p .33866 .6295 L .621 .532 .732 r F P s P p .33706 .63391 m .33866 .6295 L .33401 .62132 L .621 .532 .732 r F P p .33866 .6295 m .33438 .64592 L .3359 .62395 L .959 .727 .543 r F P p .34496 .64214 m .3443 .64237 L .33866 .6295 L .959 .727 .543 r F P p .002 w .34225 .64303 m .3443 .64237 L p .34656 .65548 L .596 .536 .758 r F P s P p .3443 .64237 m .33438 .64592 L .33866 .6295 L .959 .727 .543 r F P p .002 w .3443 .64237 m .35783 .63804 L p .34864 .65227 L .596 .536 .758 r F P s P p .34656 .65548 m .3443 .64237 L .34864 .65227 L .596 .536 .758 r F P p .002 w .33521 .67019 m .33438 .64592 L .34864 .66149 L p .99 .769 .51 r F P s P p .002 w .34864 .66149 m .34906 .66194 L p .34884 .66207 L .99 .769 .51 r F P s P p .34884 .66207 m .33521 .67019 L .34864 .66149 L .99 .769 .51 r F P p .002 w .34906 .66194 m .35091 .66397 L p .34998 .66434 L .99 .769 .51 r F P s P p .002 w .35091 .66397 m .35051 .66715 L p .34998 .66434 L .99 .769 .51 r F P s P p .002 w .35091 .66397 m .35243 .66479 L p .35158 .66923 L .895 .695 .624 r F P s P p .002 w .35051 .66715 m .35091 .66397 L p .35158 .66923 L .895 .695 .624 r F P s P p .002 w .35243 .66479 m .37681 .67805 L p .36003 .6846 L .895 .695 .624 r F P s P p .36003 .6846 m .35954 .68479 L .35243 .66479 L .895 .695 .624 r F P p .35954 .68479 m .35158 .66923 L .35243 .66479 L .895 .695 .624 r F P p .002 w .37681 .67805 m .37208 .70519 L .36443 .70023 L p .895 .695 .624 r F P s P p .37681 .67805 m .36443 .70023 L .36112 .68975 L .895 .695 .624 r F P p .36003 .6846 m .36112 .68975 L .35954 .68479 L .895 .695 .624 r F P p .37681 .67805 m .36112 .68975 L .36003 .6846 L .895 .695 .624 r F P p .36185 .69325 m .35986 .69261 L .36141 .69113 L .551 .507 .759 r F P p .35954 .68479 m .35668 .68916 L .35051 .66715 L .596 .536 .758 r F P p .36052 .6867 m .36021 .6869 L .35954 .68479 L .596 .536 .758 r F P p .36021 .6869 m .35668 .68916 L .35954 .68479 L .596 .536 .758 r F P p .002 w .35668 .68916 m .35366 .68377 L p .35258 .67807 L .596 .536 .758 r F P s P p .002 w .35833 .69212 m .35947 .69115 L p .35986 .69261 L .551 .507 .759 r F P s P p .002 w .35947 .69115 m .36112 .68975 L p .35986 .69261 L .551 .507 .759 r F P s P p .002 w .36443 .70023 m .3639 .69988 L p .36112 .68975 L .895 .695 .624 r F P s P p .36112 .68975 m .3639 .69988 L .36306 .69717 L .895 .695 .624 r F P p .002 w .37208 .70519 m .40634 .71521 L p .3742 .72953 L .835 .658 .663 r F P s P p .36851 .71925 m .36965 .72187 L .33973 .70798 L .567 .525 .768 r F P p .002 w .38224 .75062 m .37574 .7441 L p .36965 .72187 L .567 .525 .768 r F P s P p .002 w .37574 .7441 m .33973 .70798 L p .36965 .72187 L .567 .525 .768 r F P s P p .36889 .7194 m .33973 .70798 L .36283 .69728 L .567 .525 .768 r F P p .36375 .69978 m .36283 .69728 L .36306 .69717 L .567 .525 .768 r F P p .36889 .7194 m .36283 .69728 L .36375 .69978 L .567 .525 .768 r F P p .002 w .33973 .70798 m .35833 .69212 L .36306 .69717 L p .567 .525 .768 r F P s P p .002 w .32136 .72365 m .33973 .70798 L .38224 .75062 L p .577 .537 .773 r F P s P p .002 w .35833 .69212 m .33973 .70798 L .30766 .6541 L p .604 .551 .768 r F P s P p .002 w .34451 .71519 m .34773 .6894 L .36375 .69978 L p .923 .725 .618 r F P s P p .002 w .36375 .69978 m .37208 .70519 L p .36648 .70722 L .923 .725 .618 r F P s P p .002 w .3639 .69988 m .36375 .69978 L p .36306 .69717 L .895 .695 .624 r F P s P p .002 w .36306 .69717 m .36479 .69901 L p .36889 .7194 L .567 .525 .768 r F P s P p .002 w .37208 .70519 m .36936 .72078 L p .36899 .71944 L .923 .725 .618 r F P s P p .37208 .70519 m .36899 .71944 L .36648 .70722 L .923 .725 .618 r F P p .002 w .36936 .72078 m .37208 .70519 L p .3742 .72953 L .835 .658 .663 r F P s P p .002 w .40634 .71521 m .40311 .74402 L .37907 .73636 L p .835 .658 .663 r F P s P p .002 w .37907 .73636 m .37656 .73556 L p .37856 .73419 L .835 .658 .663 r F P s P p .40634 .71521 m .37907 .73636 L .37856 .73419 L .835 .658 .663 r F P p .002 w .40311 .74402 m .40634 .71521 L .4472 .71757 L p .77 .617 .69 r F P s P p .002 w .4472 .71757 m .44847 .74675 L .40311 .74402 L p .77 .617 .69 r F P s P p .002 w .39985 .77299 m .40311 .74402 L .44847 .74675 L p .782 .627 .688 r F P s P p .36936 .72078 m .38224 .75062 L .36851 .71925 L .567 .525 .768 r F P p .002 w .37656 .73556 m .37907 .73636 L p .37783 .73815 L .852 .675 .661 r F P s P p .002 w .37907 .73636 m .40311 .74402 L p .38405 .75166 L .852 .675 .661 r F P s P p .38365 .75073 m .38405 .75166 L .38224 .75062 L .494 .472 .762 r F P p .40311 .74402 m .38973 .76956 L .38414 .75194 L .852 .675 .661 r F P p .38406 .75165 m .38414 .75194 L .38405 .75166 L .852 .675 .661 r F P p .40311 .74402 m .38414 .75194 L .38406 .75165 L .852 .675 .661 r F P p .002 w .37202 .77228 m .38224 .75062 L .3824 .75074 L p .512 .488 .767 r F P s P p .38327 .7534 m .37202 .77228 L .3824 .75074 L .512 .488 .767 r F P p .38983 .77491 m .37202 .77228 L .38414 .75194 L .512 .488 .767 r F P p .002 w .38224 .75062 m .37202 .77228 L .32136 .72365 L p .577 .537 .773 r F P s P p .002 w .39658 .80213 m .39985 .77299 L .44973 .77597 L p .793 .635 .686 r F P s P p .002 w .44973 .77597 m .45101 .80523 L .39658 .80213 L p .793 .635 .686 r F P s P p .002 w .39329 .83144 m .39658 .80213 L .45101 .80523 L p .801 .642 .684 r F P s P p .002 w .39408 .78678 m .37202 .77228 L p .39083 .77626 L .512 .488 .767 r F P s P p .002 w .39658 .80213 m .35758 .7883 L p .39083 .77626 L .867 .689 .658 r F P s P p .002 w .39985 .77299 m .39718 .7968 L p .39083 .77626 L .867 .689 .658 r F P s P p .002 w .39718 .7968 m .39658 .80213 L p .39083 .77626 L .867 .689 .658 r F P s P p .39031 .77498 m .39083 .77626 L .37202 .77228 L .512 .488 .767 r F P p .002 w .39554 .78774 m .39408 .78678 L p .39083 .77626 L .512 .488 .767 r F P s P p .002 w .42462 .78004 m .42303 .8058 L .39554 .78774 L p .512 .488 .767 r F P s P p .002 w .38839 .7691 m .39985 .77299 L p .39074 .77629 L .867 .689 .658 r F P s P p .42462 .78004 m .39554 .78774 L .39031 .77498 L .512 .488 .767 r F P p .002 w .35758 .7883 m .36246 .76031 L .38782 .76891 L p .867 .689 .658 r F P s P p .002 w .38782 .76891 m .38839 .7691 L p .388 .76935 L .867 .689 .658 r F P s P p .388 .76935 m .35758 .7883 L .38782 .76891 L .867 .689 .658 r F P p .002 w .40311 .74402 m .39985 .77299 L .38973 .76956 L p .852 .675 .661 r F P s P p .002 w .3824 .75074 m .38414 .75194 L p .38327 .7534 L .512 .488 .767 r F P s P p .002 w .38414 .75194 m .38224 .75062 L p .38405 .75166 L .494 .472 .762 r F P s P p .002 w .38973 .76956 m .36246 .76031 L p .38405 .75166 L .852 .675 .661 r F P s P p .002 w .44847 .74675 m .44973 .77597 L .39985 .77299 L p .782 .627 .688 r F P s P p .002 w .38414 .75194 m .42462 .78004 L p .38983 .77491 L .512 .488 .767 r F P s P p .39074 .77629 m .35758 .7883 L .38839 .7691 L .867 .689 .658 r F P p .002 w .38418 .75197 m .38414 .75194 L p .38405 .75166 L .494 .472 .762 r F P s P p .38405 .75166 m .38396 .75169 L .38365 .75073 L .852 .675 .661 r F P p .38405 .75166 m .38365 .75073 L .37907 .73636 L .852 .675 .661 r F P p .002 w .42623 .754 m .42462 .78004 L .38418 .75197 L p .494 .472 .762 r F P s P p .42623 .754 m .38418 .75197 L .38365 .75073 L .494 .472 .762 r F P p .37656 .73556 m .38224 .75062 L .36936 .72078 L .567 .525 .768 r F P p .002 w .38306 .74888 m .38236 .75037 L p .37656 .73556 L .567 .525 .768 r F P s P p .002 w .38236 .75037 m .38224 .75062 L p .37656 .73556 L .567 .525 .768 r F P s P p .40634 .71521 m .37605 .73425 L .3742 .72953 L .835 .658 .663 r F P p .38365 .75073 m .38242 .75064 L .38313 .7491 L .494 .472 .762 r F P p .002 w .38224 .75062 m .38236 .75037 L p .38242 .75064 L .494 .472 .762 r F P s P p .002 w .38236 .75037 m .39259 .72868 L p .38242 .75064 L .494 .472 .762 r F P s P p .38396 .75169 m .36246 .76031 L .37783 .73815 L .852 .675 .661 r F P p .38306 .74888 m .37783 .73815 L .37907 .73636 L .852 .675 .661 r F P p .38396 .75169 m .37783 .73815 L .38306 .74888 L .852 .675 .661 r F P p .40634 .71521 m .37656 .73556 L .37605 .73425 L .835 .658 .663 r F P p .002 w .38392 .74705 m .38306 .74888 L p .36936 .72078 L .567 .525 .768 r F P s P p .3742 .72953 m .37484 .73501 L .37336 .7299 L .835 .658 .663 r F P p .37605 .73425 m .37484 .73501 L .3742 .72953 L .835 .658 .663 r F P p .002 w .36246 .76031 m .36729 .73261 L .37656 .73556 L p .852 .675 .661 r F P s P p .37783 .73815 m .36246 .76031 L .37656 .73556 L .852 .675 .661 r F P p .002 w .39259 .72868 m .42623 .754 L p .38365 .75073 L .494 .472 .762 r F P s P p .38365 .75073 m .38313 .7491 L .39259 .72868 L .494 .472 .762 r F P p .002 w .39259 .72868 m .38392 .74705 L p .3742 .72953 L .567 .525 .768 r F P s P p .37049 .72003 m .3742 .72953 L .36851 .71925 L .567 .525 .768 r F P p .39259 .72868 m .3742 .72953 L .37049 .72003 L .567 .525 .768 r F P p .002 w .37656 .73556 m .37484 .73501 L p .37605 .73425 L .835 .658 .663 r F P s P p .002 w .37484 .73501 m .36729 .73261 L p .37336 .7299 L .835 .658 .663 r F P s P p .002 w .36479 .69901 m .39259 .72868 L p .37049 .72003 L .567 .525 .768 r F P s P p .37049 .72003 m .36899 .71944 L .36576 .70374 L .567 .525 .768 r F P p .37049 .72003 m .36576 .70374 L .36479 .69901 L .567 .525 .768 r F P p .36899 .71944 m .36889 .7194 L .36479 .69901 L .567 .525 .768 r F P p .36648 .70722 m .36899 .71944 L .36572 .70749 L .923 .725 .618 r F P p .36648 .70722 m .34451 .71519 L .36375 .69978 L .923 .725 .618 r F P p .002 w .36729 .73261 m .34451 .71519 L p .36572 .70749 L .923 .725 .618 r F P s P p .002 w .36936 .72078 m .36729 .73261 L p .36572 .70749 L .923 .725 .618 r F P s P p .002 w .36729 .73261 m .36936 .72078 L p .3742 .72953 L .835 .658 .663 r F P s P p .002 w .40307 .70646 m .39259 .72868 L .36306 .69717 L p .551 .507 .759 r F P s P p .002 w .36306 .69717 m .35833 .69212 L p .36185 .69325 L .551 .507 .759 r F P s P p .002 w .36375 .69978 m .36314 .69939 L p .36112 .68975 L .895 .695 .624 r F P s P p .40307 .70646 m .36306 .69717 L .36185 .69325 L .551 .507 .759 r F P p .002 w .36112 .68975 m .37717 .67607 L p .36141 .69113 L .551 .507 .759 r F P s P p .35986 .69261 m .36112 .68975 L .36141 .69113 L .551 .507 .759 r F P p .002 w .37717 .67607 m .35833 .69212 L .35668 .68916 L p .596 .536 .758 r F P s P p .35954 .68479 m .36112 .68975 L .34773 .6894 L .895 .695 .624 r F P p .002 w .36314 .69939 m .34773 .6894 L p .36112 .68975 L .895 .695 .624 r F P s P p .36357 .6938 m .36185 .69325 L .36224 .69034 L .551 .507 .759 r F P p .36185 .69325 m .36141 .69113 L .36224 .69034 L .551 .507 .759 r F P p .37717 .67607 m .36052 .6867 L .35909 .68334 L .596 .536 .758 r F P p .35127 .65865 m .35909 .68334 L .34741 .65605 L .596 .536 .758 r F P p .37717 .67607 m .35909 .68334 L .35127 .65865 L .596 .536 .758 r F P p .36052 .6867 m .35051 .66715 L .34741 .65605 L .596 .536 .758 r F P p .35954 .68479 m .34773 .6894 L .35158 .66923 L .895 .695 .624 r F P p .34998 .66434 m .33521 .67019 L .34906 .66194 L .99 .769 .51 r F P p .002 w .34773 .6894 m .33521 .67019 L p .34998 .66434 L .99 .769 .51 r F P s P p .002 w .35051 .66715 m .34773 .6894 L p .34998 .66434 L .99 .769 .51 r F P s P p .002 w .34773 .6894 m .35051 .66715 L p .35158 .66923 L .895 .695 .624 r F P s P p .002 w .37717 .67607 m .40307 .70646 L p .36357 .6938 L .551 .507 .759 r F P s P p .36357 .6938 m .36224 .69034 L .37717 .67607 L .551 .507 .759 r F P p .002 w .34906 .66194 m .34864 .66149 L p .34878 .66094 L .959 .727 .543 r F P s P p .002 w 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.712 r F P s P p .32527 .59178 m .35833 .55524 L .32357 .58798 L .657 .542 .712 r F P p .3289 .59987 m .32881 .5999 L .32683 .59525 L .981 .708 .322 r F P p .32881 .5999 m .32865 .59996 L .32663 .59508 L .981 .708 .322 r F P p .002 w .35082 .59604 m .32663 .59508 L p .34024 .62516 L .621 .532 .732 r F P s P p .002 w .32357 .58798 m .32398 .58545 L p .32263 .58583 L .656 .555 .729 r F P s P p .002 w .32287 .58597 m .32248 .58548 L p .32268 .58527 L .979 .692 .399 r F P s P p .2942 .5938 m .32398 .58545 L .31442 .56658 L .656 .555 .729 r F P p .002 w .32243 .59492 m .2942 .5938 L .30766 .6541 L p .626 .549 .748 r F P s P p .002 w .32284 .60202 m .31701 .57855 L .32248 .58548 L p .981 .708 .322 r F P s P p .32287 .58638 m .32284 .60202 L .32248 .58548 L .981 .708 .322 r F P p .002 w .35082 .59604 m .35833 .55524 L p .32527 .59178 L .657 .542 .712 r F P s P p .32559 .59255 m .35082 .59604 L .32527 .59178 L .657 .542 .712 r F P p .002 w .32248 .58548 m .31701 .57855 L p .32014 .57787 L .979 .692 .399 r F P s P p .002 w .31701 .57855 m .31373 .56531 L p .31442 .56658 L .979 .692 .399 r F P s P p .32056 .57778 m .32014 .57787 L .31442 .56658 L .979 .692 .399 r F P p .32014 .57787 m .31701 .57855 L .31442 .56658 L .979 .692 .399 r F P p .002 w .32398 .58545 m .33065 .54471 L p .31442 .56658 L .656 .555 .729 r F P s P p .002 w .31127 .55541 m .31373 .56531 L p .31167 .55555 L 0 0 .25 r F P s P p .002 w .30927 .54942 m .31127 .55541 L p .31167 .55555 L 0 0 .25 r F P s P p .30561 .5326 m .30927 .54942 L .30904 .54861 L .763 .471 0 r F P p .002 w .30524 .53505 m .30335 .53433 L p .30927 .54942 L .656 .555 .729 r F P s P p .30472 .53317 m .30445 .53219 L .30433 .53191 L .694 .563 .703 r F P p .30561 .5326 m .30912 .54897 L .30445 .53219 L .763 .471 0 r F P p .002 w .33065 .54471 m .35489 .5022 L p .30472 .53317 L .694 .563 .703 r F P s P p .30324 .53408 m .30524 .53505 L .30472 .53317 L .694 .563 .703 r F P p .002 w .30335 .53433 m .30524 .53505 L p .30324 .53408 L .694 .563 .703 r F P s P p .002 w .30912 .54897 m .30886 .54819 L p .30513 .53465 L .763 .471 0 r F P s P p .30472 .53317 m .30912 .54897 L .30513 .53465 L .763 .471 0 r F P p .30445 .53219 m .30436 .532 L .29731 .51586 L .763 .471 0 r F P p .30445 .53219 m .29746 .51624 L .29731 .51586 L .763 .471 0 r F P p .002 w .30303 .53421 m .30436 .53186 L p .29319 .51097 L .689 .569 .715 r F P s P p .002 w .30886 .54819 m .30339 .5318 L p .30445 .53219 L .763 .471 0 r F P s P p .30445 .53219 m .30886 .54819 L .30445 .53219 L .763 .471 0 r F P p .002 w .33065 .54471 m .30524 .53505 L p .30927 .54942 L .656 .555 .729 r F P s P p .31418 .56691 m .31546 .56518 L .30927 .54942 L .656 .555 .729 r F P p .31546 .56518 m .33065 .54471 L .30927 .54942 L .656 .555 .729 r F P p .002 w .31363 .55622 m .30339 .5318 L .30872 .54778 L p 0 0 .25 r F P s P p .002 w .30927 .54942 m .30912 .54897 L p .30904 .54861 L .763 .471 0 r F P s P p .002 w .30872 .54778 m .30912 .54897 L p .30934 .54932 L 0 0 .25 r F P s P p .30934 .54932 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m .44373 .74047 L .42786 .72768 L p .117 .208 .683 r F P s P p .002 w .43323 .7188 m .44478 .74763 L .44447 .74555 L p .762 .41 0 r F P s P p .002 w .44447 .74555 m .44373 .74047 L p .44015 .73309 L .762 .41 0 r F P s P p .43323 .7188 m .44447 .74555 L .44015 .73309 L .762 .41 0 r F P p .002 w .4295 .70106 m .43748 .71187 L p .43449 .71679 L .117 .208 .683 r F P s P p .002 w .42943 .70222 m .4295 .70106 L p .43449 .71679 L .117 .208 .683 r F P s P p .002 w .5247 .60292 m .49529 .60176 L .48766 .59647 L p .653 .78 .941 r F P s P p .002 w .46118 .60495 m .48766 .59647 L .49529 .60176 L p .607 .876 .992 r F P s P p .002 w .33779 .74536 m .33692 .7199 L .34124 .74134 L p .833 .729 .203 r F P s P p .002 w .34124 .74134 m .33792 .76786 L .33779 .74536 L p .833 .729 .203 r F P s P p .002 w .79741 .61371 m .82863 .61495 L .80754 .72604 L p .64 .63 .824 r F P s P p .002 w .32769 .84976 m .33115 .82207 L .34766 .84517 L p .999 .834 .531 r F P s P p .002 w .34766 .84517 m .34262 .87406 L .32769 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m .68285 .62874 L .6771 .63728 L p .328 .198 .548 r F P s P p .65408 .63894 m .67412 .63947 L .65496 .64026 L .272 .649 .967 r F P p .66962 .63782 m .67412 .63947 L .65408 .63894 L .272 .649 .967 r F P p .67389 .61166 m .6771 .63728 L .67122 .63771 L .328 .198 .548 r F P p .66853 .63754 m .67122 .63771 L .66845 .63791 L .328 .198 .548 r F P p .67389 .61166 m .67122 .63771 L .6686 .63717 L .328 .198 .548 r F P p .002 w .67524 .63906 m .67122 .63771 L p .673 .63807 L .208 .667 .945 r F P s P p .002 w .70232 .64813 m .67524 .63906 L .67519 .63807 L p .289 .691 .973 r F P s P p .002 w .67519 .63807 m .67518 .63796 L p .67545 .63806 L .289 .691 .973 r F P s P p .67545 .63806 m .70232 .64813 L .67519 .63807 L .289 .691 .973 r F P p .68723 .63873 m .68743 .63885 L .67518 .63796 L .289 .691 .973 r F P p .68743 .63885 m .70232 .64813 L .6796 .63962 L .289 .691 .973 r F P p .68743 .63885 m .6796 .63962 L .67518 .63796 L .289 .691 .973 r F P p .002 w .64329 .65818 m .65789 .6727 L .70239 .67079 L p .331 .627 .959 r F P s P p .002 w .62848 .64345 m .64329 .65818 L .68043 .65809 L p .26 .599 .951 r F P s P p .002 w .70239 .67079 m .68043 .65809 L .64329 .65818 L p .331 .627 .959 r F P s P p .002 w .68043 .65809 m .65829 .64529 L .63037 .64357 L p .26 .599 .951 r F P s P p .002 w .63037 .64357 m .62848 .64345 L p .62957 .64376 L .26 .599 .951 r F P s P p .68043 .65809 m .63037 .64357 L .62957 .64376 L .26 .599 .951 r F P p .64794 .63931 m .6389 .6584 L .64122 .64094 L .346 .143 .455 r F P p .64794 .63931 m .64122 .64094 L .64132 .64024 L .346 .143 .455 r F P p .002 w .70239 .67079 m .68043 .65809 L .70232 .64813 L p .386 .677 .975 r F P s P p .002 w .68043 .65809 m .65829 .64529 L .67524 .63906 L p .343 .668 .975 r F P s P p .002 w .67524 .63906 m .70232 .64813 L .68043 .65809 L p .343 .668 .975 r F P s P p .002 w .69199 .64617 m .66881 .67385 L p .67957 .63926 L .375 .218 .537 r F P s P p .002 w .67659 .63805 m .68285 .62874 L p .67996 .63801 L .375 .218 .537 r F P s P p .002 w .67524 .63906 m .67412 .63947 L p .66962 .63782 L .272 .649 .967 r F P s P p .6686 .63717 m .67122 .63771 L .66853 .63754 L .328 .198 .548 r F P p .002 w .64815 .62998 m .67122 .63771 L p .66962 .63782 L .272 .649 .967 r F P s P p .002 w .67122 .63771 m .67524 .63906 L p .66962 .63782 L .272 .649 .967 r F P s P p .66845 .63791 m .67122 .63771 L .66477 .65562 L .328 .198 .548 r F P p .002 w .6771 .63728 m .6767 .63788 L p .67122 .63771 L .328 .198 .548 r F P s P p .67122 .63771 m .6767 .63788 L .67518 .63796 L .328 .198 .548 r F P p .002 w .64655 .62649 m .67482 .631 L .67518 .63796 L p .208 .667 .945 r F P s P p .002 w .67518 .63796 m .67524 .63906 L p .673 .63807 L .208 .667 .945 r F P s P p .002 w .67659 .63805 m .66477 .65562 L p .67122 .63771 L .328 .198 .548 r F P s P p .64655 .62649 m .67518 .63796 L .673 .63807 L .208 .667 .945 r F P p .002 w .6767 .63788 m .67659 .63805 L p .67518 .63796 L .328 .198 .548 r F P s P p .002 w .67518 .63796 m .67516 .63756 L p .68723 .63873 L .289 .691 .973 r F P s P p .68285 .62874 m .68718 .63869 L .67996 .63801 L .375 .218 .537 r F P p .002 w .67516 .63756 m .67482 .631 L p .68718 .63869 L .289 .691 .973 r F P s P p .68718 .63869 m .68723 .63873 L .67516 .63756 L .289 .691 .973 r F P p .002 w .68285 .62874 m .68804 .63863 L p .68718 .63869 L .375 .218 .537 r F P s P p .67996 .63801 m .68718 .63869 L .67957 .63926 L .375 .218 .537 r F P p .68743 .63885 m .68874 .63858 L .70232 .64813 L .289 .691 .973 r F P p .002 w .68285 .62874 m .68938 .59592 L p .69153 .63736 L .298 .249 .633 r F P s P p .69153 .63736 m .69084 .63761 L .68285 .62874 L .298 .249 .633 r F P p .002 w .70331 .63554 m .70315 .6375 L p .68874 .63858 L .289 .691 .973 r F P s P p .002 w .70315 .6375 m .70232 .64813 L p .68874 .63858 L .289 .691 .973 r F P s P p .68804 .63863 m .70331 .63554 L .68743 .63885 L .289 .691 .973 r F P p .69456 .6369 m .70331 .63554 L .68804 .63863 L .289 .691 .973 r F P p .002 w .70298 .63549 m .70331 .63554 L p .69153 .63736 L .289 .691 .973 r F P s P p .002 w .70132 .66397 m .69199 .64617 L .69482 .63683 L p .327 .253 .618 r F P s P p .002 w .69482 .63683 m .69559 .63428 L p .70102 .63517 L .327 .253 .618 r F P s P p .002 w .68938 .59592 m .7031 .60953 L .6954 .63491 L p .298 .249 .633 r F P s P p .002 w .6954 .63491 m .69482 .63683 L p .69456 .63485 L .298 .249 .633 r F P s P p .68938 .59592 m .6954 .63491 L .69456 .63485 L .298 .249 .633 r F P p .002 w .73202 .64012 m .70331 .63554 L .70323 .63551 L p .209 .697 .926 r F P s P p .70328 .63552 m .73202 .64012 L .70323 .63551 L .209 .697 .926 r F P p .002 w .71219 .63605 m .71711 .62343 L p .71576 .63613 L .349 .255 .606 r F P s P p .71509 .63623 m .71576 .63613 L .73202 .64012 L .209 .697 .926 r F P p .002 w .71711 .62343 m .72879 .63502 L p .71576 .63613 L .349 .255 .606 r F P s P p .002 w .72176 .63526 m .7224 .63557 L p .71576 .63613 L .209 .697 .926 r F P s P p .002 w .7224 .63557 m .73202 .64012 L p .71576 .63613 L .209 .697 .926 r F P s P p .68938 .59592 m .69482 .63683 L .69153 .63736 L .298 .249 .633 r F P p .002 w .69863 .63479 m .70102 .63517 L p .69153 .63736 L .289 .691 .973 r F P s P p .002 w .70102 .63517 m .70298 .63549 L p .69482 .63683 L .289 .691 .973 r F P s P p .70102 .63517 m .69482 .63683 L .69153 .63736 L .289 .691 .973 r F P p .70227 .63484 m .70226 .63523 L .70102 .63517 L .327 .253 .618 r F P p .70102 .63517 m .70103 .63541 L .69944 .6356 L .327 .253 .618 r F P p .002 w .70185 .63531 m .70102 .63517 L p .70183 .63531 L .15 .673 .881 r F P s P p .002 w .7031 .60953 m .71711 .62343 L .71276 .63459 L p .327 .253 .618 r F P s P p .70183 .63531 m .70226 .63526 L .70331 .63554 L .15 .673 .881 r F P p .002 w .70242 .63525 m .70331 .63554 L p .70226 .63526 L .15 .673 .881 r F P s P p .002 w .7032 .6355 m .70242 .63525 L p .71624 .63649 L .209 .697 .926 r F P s P p .002 w .71276 .63459 m .71219 .63605 L p .70242 .63525 L .327 .253 .618 r F P s P p .002 w .70242 .63525 m .7024 .63524 L p .70305 .6353 L .209 .697 .926 r F P s P p .70305 .6353 m .71624 .63649 L .70242 .63525 L .209 .697 .926 r F P p .70226 .63526 m .70242 .63525 L .70132 .66397 L .327 .253 .618 r F P p .7031 .60953 m .71276 .63459 L .70242 .63525 L .327 .253 .618 r F P p .7031 .60953 m .70242 .63525 L .70226 .63523 L .327 .253 .618 r F P p .70491 .63536 m .71034 .6359 L .7024 .63524 L .209 .697 .926 r F P p .71034 .6359 m .71624 .63649 L .70305 .6353 L .209 .697 .926 r F P p .71034 .6359 m .70305 .6353 L .7024 .63524 L .209 .697 .926 r F P p .70226 .63523 m .70242 .63525 L .70226 .63526 L .327 .253 .618 r F P p .71497 .6362 m .71624 .63649 L .70182 .63505 L .209 .697 .926 r F P p .002 w .70323 .63551 m .7032 .6355 L p .70328 .63552 L .209 .697 .926 r F P s P p .71624 .63649 m .73202 .64012 L .7032 .6355 L .209 .697 .926 r F P p .002 w .70232 .64813 m .72938 .6572 L .70239 .67079 L p .386 .677 .975 r F P s P p .002 w .72938 .6572 m .70232 .64813 L .70331 .63554 L p .337 .7 .982 r F P s P p .002 w .70331 .63554 m .73202 .64012 L .72938 .6572 L p .337 .7 .982 r F P s P p .002 w .71219 .63605 m .70132 .66397 L p .70242 .63525 L .327 .253 .618 r F P s P p .002 w .7024 .63524 m .70242 .63525 L p .70226 .63526 L .15 .673 .881 r F P s P p .70226 .63523 m .70132 .66397 L .70102 .63517 L .327 .253 .618 r F P p .69153 .63736 m .69456 .6369 L .68804 .63863 L .289 .691 .973 r F P p .002 w .68812 .63878 m .68483 .63251 L p .69159 .63844 L .298 .249 .633 r F P s P p .002 w .68483 .63251 m .68285 .62874 L p .68649 .63278 L .298 .249 .633 r F P s P p .69159 .63844 m .68483 .63251 L .68649 .63278 L .298 .249 .633 r F P p .002 w .67482 .631 m .69863 .63479 L p .69862 .6348 L .289 .691 .973 r F P s P p .002 w .67499 .6311 m .69861 .6348 L p .68743 .63885 L .289 .691 .973 r F P s P p .002 w .64815 .62998 m .64655 .62649 L p .673 .63807 L .208 .667 .945 r F P s P p .002 w .63888 .62774 m .63887 .61289 L .64944 .58638 L p .165 .035 .446 r F P s P p .002 w .64944 .58638 m .65316 .60316 L .63888 .62774 L p .165 .035 .446 r F P s P p .002 w .63885 .58413 m .63886 .59836 L .61713 .62713 L p .106 0 .292 r F P s P p .002 w .62104 .6209 m .64815 .62998 L .63596 .63238 L p .137 .595 .925 r F P s P p .002 w .61713 .62713 m .61858 .61659 L .63885 .58413 L p .106 0 .292 r F P s P p .002 w .61345 .61937 m .62104 .6209 L p .63186 .62922 L .137 .595 .925 r F P s P p .002 w .63596 .63238 m .63172 .62993 L p .63186 .62922 L .137 .595 .925 r F P s P p .002 w .63172 .62993 m .61345 .61937 L p .63186 .62922 L .137 .595 .925 r F P s P p .002 w .62104 .6209 m .61851 .62202 L p .64815 .62998 L .059 .597 .855 r F P s P p .002 w .64655 .62649 m .64815 .62998 L p .63252 .62578 L .059 .597 .855 r F P s P p .002 w .61851 .62202 m .63281 .6243 L p .63252 .62578 L .059 .597 .855 r F P s P p .002 w .63281 .6243 m .64655 .62649 L p .63252 .62578 L .059 .597 .855 r F P s P p .002 w .67482 .631 m .64655 .62649 L .63186 .62777 L p .06 .62 .795 r F P s P p .002 w .63186 .62777 m .65736 .62834 L .67482 .631 L p .06 .62 .795 r F P s P p .002 w .67482 .631 m .65736 .62834 L p .70012 .63504 L .15 .673 .881 r F P s P p .70012 .63504 m .70183 .63531 L .69925 .6349 L .15 .673 .881 r F P p .70012 .63504 m .69925 .6349 L .67482 .631 L .15 .673 .881 r F P p .002 w .70102 .63517 m .67482 .631 L p .70183 .63531 L .15 .673 .881 r F P s P p .7031 .60953 m .70227 .63484 L .70102 .63517 L .327 .253 .618 r F P p .002 w .69559 .63428 m .7031 .60953 L p .70102 .63517 L .327 .253 .618 r F P s P p .002 w .65736 .62834 m .68326 .62892 L .7024 .63524 L p .15 .673 .881 r F P s P p .65736 .62834 m .7024 .63524 L .70183 .63531 L .15 .673 .881 r F P p .69944 .6356 m .70132 .66397 L .69482 .63683 L .327 .253 .618 r F P p .70103 .63541 m .70132 .66397 L .69944 .6356 L .327 .253 .618 r F P p .002 w .7024 .63524 m .70182 .63505 L p .70491 .63536 L .209 .697 .926 r F P s P p .71576 .63613 m .71509 .63623 L .71219 .63605 L .349 .255 .606 r F P p .002 w .70182 .63505 m .68326 .62892 L p .71497 .6362 L .209 .697 .926 r F P s P p .002 w .73143 .63764 m .73143 .63764 L p .71576 .63613 L .349 .255 .606 r F P s P p .002 w .73143 .63764 m .71085 .68215 L p .71574 .63627 L .349 .255 .606 r F P s P p .71576 .63613 m .73143 .63764 L .71574 .63627 L .349 .255 .606 r F P p .002 w .72879 .63502 m .73143 .63764 L p .71576 .63613 L .349 .255 .606 r F P s P p .71576 .63613 m .71574 .63627 L .71509 .63623 L .349 .255 .606 r F P p .002 w .68326 .62892 m .70958 .62951 L .72176 .63526 L p .209 .697 .926 r F P s P p .68326 .62892 m .72176 .63526 L .71509 .63623 L .209 .697 .926 r F P p .002 w .71085 .68215 m .70132 .66397 L .71219 .63605 L p .349 .255 .606 r F P s P p .71574 .63627 m .71085 .68215 L .71219 .63605 L .349 .255 .606 r F P p .002 w .69482 .63683 m .69199 .64617 L p .69153 .63736 L .298 .249 .633 r F P s P p .002 w .68804 .63863 m .69199 .64617 L p .67957 .63926 L .375 .218 .537 r F P s P p .69153 .63736 m .69159 .63844 L .69084 .63761 L .298 .249 .633 r F P p .002 w .69199 .64617 m .68812 .63878 L p .69159 .63844 L .298 .249 .633 r F P s P p .002 w .66881 .67385 m .66477 .65562 L .67659 .63805 L p .375 .218 .537 r F P s P p .67996 .63801 m .66881 .67385 L .67659 .63805 L .375 .218 .537 r F P p .002 w .67122 .63771 m .64815 .62998 L p .673 .63807 L .208 .667 .945 r F P s P p .64815 .62998 m .66962 .63782 L .65408 .63894 L .272 .649 .967 r F P p .002 w .66477 .65562 m .66132 .64 L p .66845 .63791 L .328 .198 .548 r F P s P p .002 w .65829 .64529 m .64976 .64036 L p .65527 .64074 L .272 .649 .967 r F P s P p .002 w .66477 .65562 m .63892 .67424 L p .65951 .63996 L .411 .182 .454 r F P s P p .002 w .66132 .64 m .66477 .65562 L p .65951 .63996 L .411 .182 .454 r F P s P p .002 w .63892 .67424 m .6389 .6584 L .65833 .64012 L p .411 .182 .454 r F P s P p .65951 .63996 m .63892 .67424 L .65833 .64012 L .411 .182 .454 r F P p .002 w .65833 .64012 m .65777 .64065 L p .65775 .64015 L .346 .143 .455 r F P s P p .002 w .64976 .64036 m .64794 .63931 L p .65527 .64074 L .272 .649 .967 r F P s P p .65527 .64074 m .64794 .63931 L .65139 .63906 L .272 .649 .967 r F P p .002 w .63596 .63238 m .64815 .62998 L p .65527 .64074 L .272 .649 .967 r F P s P p .002 w .65777 .64065 m .6389 .6584 L p .64794 .63931 L .346 .143 .455 r F P s P p .64794 .63931 m .64132 .64024 L .64323 .63966 L .346 .143 .455 r F P p .002 w .6389 .6584 m .63889 .6429 L .64092 .64036 L p .346 .143 .455 r F P s P p .64132 .64024 m .6389 .6584 L .64092 .64036 L .346 .143 .455 r F P p .002 w .64794 .63931 m .63596 .63238 L p .65139 .63906 L .272 .649 .967 r F P s P p .002 w .64092 .64036 m .63889 .6429 L p .63975 .6405 L .265 .094 .453 r F P s P p .63624 .64092 m .63934 .6382 L .6338 .64087 L .128 .537 .919 r F P p .002 w .63596 .63238 m .61345 .62851 L p .64207 .63922 L .128 .537 .919 r F P s P p .002 w .64613 .63826 m .63596 .63238 L p .64207 .63922 L .128 .537 .919 r F P s P p .002 w .63889 .6429 m .63889 .64098 L p .63975 .6405 L .265 .094 .453 r F P s P p .002 w .63889 .6429 m .61257 .66022 L p .62833 .64076 L .353 .07 .338 r F P s P p .002 w .63889 .64098 m .63889 .6429 L p .62833 .64076 L .353 .07 .338 r F P s P p .002 w .61345 .62851 m .62626 .64125 L p .63934 .6382 L .128 .537 .919 r F P s P p .62833 .64076 m .62811 .64104 L .62626 .64125 L .353 .07 .338 r F P p .002 w .61345 .62851 m .58688 .61529 L p .62516 .64121 L .056 .429 .87 r F P s P p .62542 .64122 m .61345 .62851 L .62516 .64121 L .056 .429 .87 r F P p .62275 .64164 m .62178 .64086 L .61559 .64246 L .191 .51 .913 r F P p .002 w .61257 .66022 m .61413 .64894 L .62262 .64166 L p .353 .07 .338 r F P s P p .60634 .64288 m .60127 .64304 L .59868 .64293 L .292 0 .164 r F P p .002 w .59992 .64423 m .59941 .64309 L p .59868 .64293 L .099 .376 .838 r F P s P p .59868 .64293 m .59823 .64291 L .59811 .64294 L .099 .376 .838 r F P p .002 w .6061 .64324 m .58115 .65717 L p .59823 .64291 L .292 0 .164 r F P s P p .002 w .59347 .6299 m .59941 .64309 L p .615 .64262 L .191 .51 .913 r F P s P p .61583 .64259 m .61549 .6424 L .615 .64262 L .191 .51 .913 r F P p .61549 .6424 m .59347 .6299 L 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