{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": "true" }, "source": [ "# Table of Contents\n", "

1  Runge-Kutta methods for ODE integration in OCaml
1.1  Preliminary
1.2  Runge-Kutta method of order 1, or the Euler method
1.3  Runge-Kutta method of order 2
1.4  Runge-Kutta method of order 4, \"RK4\"
1.5  Comparisons
1.6  Conclusion
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Runge-Kutta methods for ODE integration in OCaml\n", "\n", "- I want to implement and illustrate the [Runge-Kutta method](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods) (actually, different variants), in the [OCaml programming language](https://www.ocaml.org/).\n", "\n", "- The Runge-Kutta methods are a family of numerical iterative algorithms to approximate solutions of [Ordinary Differential Equations](https://en.wikipedia.org/wiki/Ordinary_differential_equation). I will simply implement them, for the mathematical descriptions, I let the interested reader refer to the Wikipedia page, or [any](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods#References) [good](https://www.directtextbook.com/isbn/9780521007948) [book](https://www.decitre.fr/livres/analyse-numerique-et-equations-differentielles-9782868838919.html) or [course](https://courses.maths.ox.ac.uk/node/4294) on numerical integration of ODE.\n", "- I will start with the order 1 method, then the order 2 and the most famous order 4.\n", "- They will be compared on different ODE." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Preliminary" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The OCaml toplevel, version 4.04.2\n" ] }, { "data": { "text/plain": [ "- : int = 0\n" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Sys.command \"ocaml -version\";;" ] }, { "cell_type": "code", "execution_count": 147, "metadata": {}, "outputs": [], "source": [ "#thread ;;\n", "#require \"jupyter.notebook\" ;;\n", "#require \"jupyter.archimedes\" ;;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I don't want to try to find a reference implementation of an Ordinary Differential Equations solver in OCaml. I'm sure there is, just don't care." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I will use as a first example the one included in [the scipy (Python) documentation for this `odeint` function](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.odeint.html).\n", "\n", "$$\\theta''(t) + b \\theta'(t) + c \\sin(\\theta(t)) = 0.$$\n", "\n", "If $\\omega(t) := \\theta'(t)$, this gives\n", "$$ \\begin{cases}\n", "\\theta'(t) = \\omega(t) \\\\\n", "\\omega'(t) = -b \\omega(t) - c \\sin(\\theta(t))\n", "\\end{cases} $$\n", "\n", "Vectorially, if $y(t) = [\\theta(t), \\omega(t)]$, then the equation is $y' = f(t, y)$ where $f(t, y) = [y_2(t), -b y_2(t) - c \\sin(y_1(t))]$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We assume the values of $b$ and $c$ to be known, and the starting point to be also fixed:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "val b : float = 0.25\n" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val c : float = 5.\n" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let b = 0.25 ;;\n", "let c = 5.0 ;;" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val y0 : float array = [|3.04156; 0.|]\n" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let y0 = [| 3.14156 -. 0.1; 0.0 |];;" ] }, { "cell_type": "code", "execution_count": 148, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val f_pend : float array -> float -> float array = \n" ] }, "execution_count": 148, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let f_pend (y : float array) (_ : float) : float array =\n", " [|\n", " y.(1);\n", " (-.b) *. y.(1) +. (-.c) *. sin(y.(0))\n", " |]\n", ";;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "## Runge-Kutta method of order 1, or the Euler method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The approximation is computed using this update:\n", "$$y_{n+1} = y_n + (t_{n+1} - t_n) f(y_n, t_n).$$\n", "\n", "The math behind this formula are the following: if $g$ is a solution to the ODE, and so far the approximation is correct, $y_n \\simeq g(t_n)$, then a small step $h = t_{n+1} - t_n$ satisfy $g(t_n + h) \\simeq g(t_n) + h g'(t_n) \\simeq y_n + h f(g(t_n), t_n) + \\simeq y_n + h f(y_n, t_n)$." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val rungekutta1 :\n", " (float array -> float -> float array) ->\n", " float array -> float array -> float array array = \n" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let rungekutta1 (f : float array -> float -> float array) (y0 : float array) (t : float array) =\n", " let d = Array.length y0 in\n", " let n = Array.length t in\n", " let y = Array.make_matrix n d 0. in\n", " for j = 0 to d-1 do\n", " y.(0).(j) <- y0.(j);\n", " done;\n", " for i = 0 to n-2 do\n", " let h = t.(i+1) -. t.(i) in\n", " let fyt = f y.(i) t.(i) in\n", " for j = 0 to d-1 do\n", " y.(i+1).(j) <- y.(i).(j) +. h *. fyt.(j);\n", " done;\n", " done;\n", " y\n", ";;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have to redefine ourselfves most of the useful functions:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val linspace : float -> float -> int -> float array = \n" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let linspace (a : float) (b : float) (n : int) =\n", " let t = Array.make n a in\n", " let h = (b -. a) /. (float_of_int n) in\n", " for i = 0 to n-1 do\n", " t.(i) <- a +. (float_of_int i) *. h;\n", " done;\n", " t\n", ";;" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "val t : float array =\n", " [|0.; 0.0990099009900990146; 0.198019801980198029; 0.297029702970297071;\n", " 0.396039603960396058; 0.495049504950495045; 0.594059405940594143;\n", " 0.69306930693069313; 0.792079207920792117; 0.891089108910891103;\n", " 0.99009900990099009; 1.08910891089108919; 1.18811881188118829;\n", " 1.28712871287128716; 1.38613861386138626; 1.48514851485148514;\n", " 1.58415841584158423; 1.68316831683168333; 1.78217821782178221;\n", " 1.8811881188118813; 1.98019801980198018; 2.07920792079207928;\n", " 2.17821782178217838; 2.27722772277227747; 2.37623762376237657;\n", " 2.47524752475247523; 2.57425742574257432; 2.67326732673267342;\n", " 2.77227722772277252; 2.87128712871287162; 2.97029702970297027;\n", " 3.06930693069306937; 3.16831683168316847; 3.26732673267326756;\n", " 3.36633663366336666; 3.46534653465346532; 3.56435643564356441;\n", " 3.66336633663366351; 3.76237623762376261; 3.86138613861386171;\n", " 3.96039603960396036; 4.05940594059405946; 4.15841584158415856;\n", " 4.25742574257425765; 4.35643564356435675; 4.45544554455445585;\n", " 4.55445544554455495; 4.65346534653465405; 4.75247524752475314;\n", " 4.85148514851485135; 4.95049504950495045; 5.04950495049504955;\n", " 5.14851485148514865; 5.24752475247524774; 5.34653465346534684;\n", " 5.44554455445544594; 5.54455445544554504; 5.64356435643564414;\n", " 5.74257425742574323; 5.84158415841584144; 5.94059405940594054;\n", " 6.03960396039604; 6.13861386138613874; 6.23762376237623783;\n", " 6.33663366336633693; 6.43564356435643603; 6.53465346534653513;\n", " 6.63366336633663423; 6.73267326732673332; 6.83168316831683242;\n", " 6.93069306930693063; 7.02970297029703; 7.12871287128712883;\n", " 7.22772277227722793; 7.32673267326732702; 7.42574257425742612;\n", " 7.52475247524752522; 7.62376237623762432; 7.72277227722772341;\n", " 7.82178217821782251; 7.92079207920792072; 8.01980198019802;\n", " 8.11881188118811892; 8.21782178217821802; 8.31683168316831711;\n", " 8.41584158415841621; 8.51485148514851531; 8.61386138613861441;\n", " 8.7128712871287135; 8.8118811881188126; 8.9108910891089117;\n", " 9.00990099009901; 9.10891089108911; 9.20792079207920899;\n", " 9.30693069306930809; 9.40594059405940719; 9.50495049504950629;\n", " 9.60396039603960361; 9.70297029702970271; 9.8019801980198018;\n", " 9.9009900990099009|]\n" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let t = linspace 0. 10. 101 ;;" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val sol : float array array =\n", " [|[|3.04156; 0.|]; [|3.04156; -0.0494385678472543874|];\n", " [|3.03666509229235126; -0.097653408767596539|];\n", " [|3.02699643795892603; -0.147085318849099422|];\n", " [|3.01243353510257972; -0.200051306879579782|];\n", " [|2.99262647501549273; -0.258862071967601193|];\n", " [|2.96699656689988878; -0.325927783092890666|];\n", " [|2.93472648936593927; -0.403855500959909908|];\n", " [|2.89474079620159186; -0.495539222697703119|];\n", " [|2.84567750682558174; -0.604239966604331213|];\n", " [|2.78585176755782626; -0.73364756279708776|];\n", " [|2.71321339500365921; -0.887906266173617|];\n", " [|2.62530188350132088; -1.07157049578384078|];\n", " [|2.51920579480985163; -1.28943151630173158|];\n", " [|2.39153930804730397; -1.54611693249596316|];\n", " [|2.23845842364176306; -1.84531096455946542|];\n", " [|2.05575436774478604; -2.18838313254248|];\n", " [|1.83908277046335211; -2.57218281242493196|];\n", " [|1.5844112048767256; -2.98585479258093889|];\n", " [|1.28878201749247401; -3.40695111899184289|];\n", " [|0.951460124522985; -3.79811412259147829|];\n", " [|0.575409221296105611; -4.1072023706189853|];\n", " [|0.168755521234819572; -4.27493407456400387|];\n", " [|-0.254505278226963338; -4.25226525047144666|];\n", " [|-0.675521639659780293; -4.02237420284389824|];\n", " [|-1.07377651122848161; -3.61325381198249129|];\n", " [|-1.43152441340496628; -3.08866463882397024|];\n", " [|-1.7373327934865479; -2.52195643825148741|];\n", " [|-1.98703145073917065; -1.97133136657366337|];\n", " [|-2.18221277416230564; -1.46975502925005852|];\n", " [|-2.3277330740880533; -1.0280107170053443|];\n", " [|-2.42951631339551311; -0.642692161055145705|];\n", " [|-2.49314920062869572; -0.303315136253584139|];\n", " [|-2.52318040223796158; 0.00317609544709579472|];\n", " [|-2.52286593734220954; 0.29009856550137425|];\n", " [|-2.49414330709454868; 0.570045824573125581|];\n", " [|-2.43770312644374432; 0.85452682168123717|];\n", " [|-2.35309651043570112; 1.15376510886464168|];\n", " [|-2.23886234124118211; 1.47634220367394819|];\n", " [|-2.09268984582791973; 1.82842342496740917|];\n", " [|-1.91165782355391944; 2.21231233647640257|];\n", " [|-1.69261699816021594; 2.62411996065747877|];\n", " [|-1.4328031406693762; 3.05054720612826546|];\n", " [|-1.13076876382499325; 3.46538219564712158|];\n", " [|-0.787661615741119592; 3.82749645947745609|];\n", " [|-0.408701570248301838; 4.08360074067417056|];\n", " [|-0.00438466523105685; 4.17926318538280217|];\n", " [|0.409403768965260539; 4.07798669623058441|];\n", " [|0.813164827997992; 3.77998581698302|];\n", " [|1.18742084948145621; 3.32678533270321619|];\n", " [|1.51680553588771549; 2.78532662951843868|];\n", " [|1.79258044970142261; 2.22205475687363219|];\n", " [|2.01258587117405963; 1.68412936790090439|];\n", " [|2.17933135314444648; 1.19492419674890016|];\n", " [|2.29764067955522888; 0.759165492009172826|];\n", " [|2.37280557975415718; 0.370436101655445|];\n", " [|2.40948242150222125; 0.0170768149151984128|];\n", " [|2.41117319525620122; -0.314257086424339|];\n", " [|2.38005863224389058; -0.636766636731305624|];\n", " [|2.31701243058732631; -0.962605357601812539|];\n", " [|2.22170496943863194; -1.30227496505272144|];\n", " [|2.09276685408687735; -1.66386893711239425|];\n", " [|1.92802735536287773; -2.05181197311360775|];\n", " [|1.72487765505459967; -2.46482092024770427|];\n", " [|1.48083597978254944; -2.89299512443404883|];\n", " [|1.19440081894749484; -3.31443400560251211|];\n", " [|0.866239036214572544; -3.69278741132267418|];\n", " [|0.500616520242030294; -3.97855919213080167|];\n", " [|0.106699768545910956; -4.1176871798846113|];\n", " [|-0.300992031442664787; -4.06848572681177778|];\n", " [|-0.703812400433926677; -3.82101440440216811|];\n", " [|-1.08213065829552768; -3.40607400666509186|];\n", " [|-1.41936570846038856; -2.88465631149967239|];\n", " [|-1.70497524425243552; -2.32386963189152063|];\n", " [|-1.9350613464199129; -1.77574835044584578|];\n", " [|-2.1108780147808881; -1.26922692614652322|];\n", " [|-2.236544047072623; -0.813222952841671676|];\n", " [|-2.3170611711163529; -0.403759425509745029|];\n", " [|-2.35703735185989194; -0.0302852883400764328|];\n", " [|-2.36003589525989943; 0.320222039037892758|];\n", " [|-2.32833074287991026; 0.66100133863006616|];\n", " [|-2.26288506578782433; 1.00430942404913726|];\n", " [|-2.16344848914929599; 1.36059620737647924|];\n", " [|-2.02873599336944643; 1.73754293425696282|];\n", " [|-1.85670203948261836; 2.13857666169778726|];\n", " [|-1.64496177594818382; 2.56059536373928109|];\n", " [|-1.39143748250865085; 2.99090290597198161|];\n", " [|-1.0953084819173653; 3.40397871344527214|];\n", " [|-0.758280886526744; 3.75985523320688042|];\n", " [|-0.386017992149824796; 4.00722235732067755|];\n", " [|0.0107366966938070019; 4.0944210195236419|];\n", " [|0.416124916448623372; 3.98775887032095389|];\n", " [|0.810952527371490373; 3.68894350003373317|];\n", " [|1.1761944580678998; 3.23875004120867871|];\n", " [|1.49686277897965048; 2.70157816128681105|];\n", " [|1.76434576524567155; 2.14101030581653617|];\n", " [|1.97632698364334858; 1.60220920537008604|];\n", " [|2.13496155843246349; 1.1076529482996047|];\n", " [|2.24463016717499864; 0.661901511814660393|];\n", " [|2.31016497032496515; ...|]; ...|]\n" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let sol = rungekutta1 f_pend y0 t ;;" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val column : 'a array array -> int -> 'a array = \n" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let column sol i =\n", " Array.map (fun x -> x.(i)) sol\n", ";;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let see a first plot!" ] }, { "cell_type": "code", "execution_count": 151, "metadata": {}, "outputs": [ { "data": { "image/png": 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xkJqKoyOWlmzciLIybdpQvfq761y/Ll/o0wcdHZyc+OorqlQp4KSCIAglVIk5gpWezpo1/Y8dmx8Wxpo1pKcD3LnDnDl89x0//8zTp/I1IyL43/+4cIGUFAnzFlflypWztLSUOkXRlpmJpydVqsirK0BDg6pVP7j+Dz9w+DBNm7JrF97eDB+Ohsa2xYvLFlhg4X3m5uaGhoZSp/goY2OCgxXc5qxZLFiQ+0vNmlGwQzONjY3FVZxCvioZBVZsLLa2nDpVedy4iPr18fenfn3mzMHenufPsbHh7l1q1+bwYYYNo2FDVq9m4kSqV8fXl/R0li6lfXsaNWLoUO7ff91sTIx82LCQZ1WqVClp4xwVIjoaQ0PKlaNcOY4f59499u7FwIC+fT+9rY0NDRrQpQsNGxIZiY0NgwbVrVOnZPzuF1bu7u7NmjWTOsXbzMy4ejUft01MZN06Ro3KfZMJE5g+/TN7/ywODg7fffddQfYolDQl4xThtGl06cLChcD1S5f6L1+Omxvz53PvHiYm8nX696ddOzp3JjQUbW2A69fp0oUff6RmTTw80NXF35/mzdmyhUuXWLkSDQ2SkujenUWLyPlnNOcwmIGBNLspFF8VKnDvHtnZHDvG8OF4efH11wB5mWmhZ0/5QlQUCQmkpODkFNO0qWX+pRWEXHh707at/Nv1fY6ODB/O48eIo0pCcVEy/os9fJgxY3IWzZ884do10tORyUhJ4cEDHjzg2TOqVCEjgx49Xv/+169PkyakpuLrS7t2NGzI5Mns3EmPHgQHExJCdDSxsRgb07o1+/dTvTrW1lhbU706R49KtrNCMaWjg5YWP/1E7dro6KCnh54e6ur/rZEOHVi0iLg4tfzJKBRioaG0b4+eHtbW7Nnz7qsjRxITg5MTlpZs2yZ/8sIFrK3R0WHgQDIz5U/GxuLqiqEhlpYsW5b7tjNmYGGBtja2tgQEyDc8ehR7+w92V7o0jRvncssnQSiySsYRrMRE/p3yx/XUKe7e5dEjUlP5+mv5Ob7ERJ4/JzOTgQNxd0dTEwMD9PW5fBmZjLlz0denQgVMTVFR4eVLFiyQH/rS0mLBAvz9GToUX1/510dAAAMGIJMRHc3OnURGUrUq7u506CDVGyAUD6tXY2WVywWDeWRujrk5wLZtFTt3VmAuodDLysLJiW7dOHqUy5fp3Jlq1bC1fb3C2rUcOsSBAzRs+PrJXbs4fRplZVq1Ys8eevdGJsPZmebNefSI2Fg6dMDKKpdtra25cgUDAzZvxtWVsDA0NAgKwsPjY91ZW3PzZn6/E4JQYEpGgWVtzaVLODgAS3v1Wr58OaNHs2sXd+++XicqCgsL9u7FxoaUFJ4949kz/vyT0qV58YLwcGJjiYwkNJSsLNq1w9ISCwuqVKFGDR4/pmnT1/+c2duzejUDBlCnDtOmYWHBzZt8/z0DBjB1KnFxhISgo0ONGqiJAwlCXsXFyYv5v/+mXr3PaWHwYID4eKpUMQgJUapbV7EBhULs+nViYpgxA1VV7Ozo0YMdO94qsHI1ZQrGxgDOzly/Tu/eBAVx6xbnzqGigoUFo0fj4yM/Xf2mXr3kC0OHMncud+9iY0N8/AfPD+bQ1ubhw8/bP0EohEpGgTVpEiNHsncvNWsChIRw8iSZmRw8SM5N8bKy2LKF0qV59IhOnQCqVSMtDZkMGxvmzn3d1Lp1jBnDiRM8eUJ4OHfvsm8fMTGcOIG5OVZW1KpFgwYkJJCQwO+/y0soKytataJ2bcLD5TESE0lJYc0aOnYs+PdDKIpmzKB3b2rVolatL2pHT4/evR9Pm2Z5+LCCkgmFX1QUpqao/vuFb2nJrVuf3urVENUyZXj8GCA8nLS01z+C6em5F/vbtrFqFTExqKgQFSUfnKqnR3Lyx7pLTkZXNy97IwhFQskosHr3JjWVNm0wNp4UGcmuXcybR61auLkxaxYWFgQFYWnJkSO4uXH6NG3bEhfH5s20aMG5c2zezMCBKCtz6xZeXpQqRdmyWFvLG09LY98+vL1p3Ji7dwkK4uRJjh1DJqNVK+rXp1EjWrWicmV0dLh+nbt35ecrz53D1ZWjR6lblwcPiI/H2lp+b15BeNvt2/j4EBKimNZcXKKGDbP086NdO8U0KBR2JiZERpKZKa+xwsIwNX13nVzvBvAOc3N0dbl9+90T1W9ue+8e7u6cPUudOgCVK5NzQ7a6dbl7l1c3V36/u9u36dYtr3skCIVeyRjkDri58egRW7d6f/UVjx7h5kaTJvz5J+vW0a8fBw7g54eDA7du4eDAH38QF8f69fj44OfH9u3o6GBsTLt2jBqFpyetWrFtG8HBHD6MgwNmZty/j4UF7dszYQI7dmBtTd26LFxItWr8/jt2dlSsyMOH1KpFUpI8kp0dHh5Mm0bNmjg64u6OpSVTp5KRIek7JRQu0dEA48czfTqKunmgmppszpzsiRN58YL58xXTplCo1a+PkRFz55KRwfnz8gFV7zA0JDT0E+3Y2FCpEh4ePH9OVhYhIVy58u62SUloalKtGsDhw6/P+nXu/HrA+/vdpadz5YoYqCoUK7ISxt3d/XM2S0mRRUe/fnj2rKxbN1nt2rKOHWXbt8sePJBVrCgbPVp25ozs9GnZqFEyfX1Zq1ZvtbBvn0xFRdali8zERGZhIRsxQnbihOyXX2RqajI/P/k6sbGyzp1l48Z97s4VAYmJideuXZM6RZERGyurWFF25IisRg1ZerrCmj137lxGRkbLlrLly2UmJgprVsi7W7duxcbGFmiXd+7I2rSR6ejIqleXeXvnsoKvr8zMTKarK9uwQSaTyYyMZH/9JX9p9mzZ8OHy5ZgYWZ8+MiMjma6urEkT2YkTuWw7YYKsRg1Zx46yKVNktWvLfv9dJpPJ4uNlFSrIkpNz787XV+bomF/7npvo6Ojbt28XZI8l3MyZM6WOUNCUZDkHb0uMsWPHLl++XPHtJiayeDHnzyOT0bIlY8bQoQP29nh6oqfHgwcMGcLFi7x4gZISd+7Ir6D54w80Ndm0iU6dKFMGkE8YceYMW7YQGoqpKb175wzPLx6SkpJCQ0Pr168vdZCiISqKRo3Q02PxYvngQIUIDAxs2rTp9euqXbvKexEKWEhIiIGBQWGfzF3hZs2iVCmmTMnlpWbN8PL6zMs3PktMTExCQkKNGjUKrMcSztPTs6TNMl1iThHmNx0d5szh9GnOnGHOHAwN8fcnPR1LS3R1adaM9u2pVYsdOwCqV2fSJAICUFenaVM2bcLEBBcX/vc/dHXR0qJdO4yMGDUKW1uGDmXSJKl3T5BMSgoVKiiyugJSU1UePlQyMKB2bZKS5JPBPXjweqojQcgXM2bkXl0BFy8WZHUlCAWgZAxyl0S5cnh54eVFYiI6OgBff03nzpw5Q9u2JCSwYQNlyjB8OM7OJCTg68vs2QwbRlQUu3bh6ipvp08fbG359lsK2401hHyzeze+vgDJySQloaIi/3GYNIlGjRTQ/pEjRocOKSspkZZGSgpt26KsjKoq69bRurUC2hcEQRBEgZX/cqoroG5dQkJYv57Dh9HRYdYsIiPx8sLJCV1dBg9m8GAGDGDXLkaNYssWhgyha1fKlqVfP44eJTqaixcBmjena9fPn25SKPQaN5ZfYuXjg5qafP4qFZWP3dH5P+nWLWrJkoqqqqpRUVStypQpDB+umJYFQRCEHKLAKlhly751vi8jg2PHaNaM4cPR08PPj0OH6NABHx/27WP5cn74galTUVdn9Wr8/fn2W4AlS1ixgkOHxJwOxVWlSlSqRHY2kyZRtizdu+djX5qaeHmJAksQBEHBxBgsSampcfAgHh5cusSOHZiY4OvL3buUKkXv3vIpuHx9mTGDUqU4dYqJE5k4kcBAqlZlxgyp0wv56+BBDA0pVSofu1BSQl2d1FQuXcrHXgRBEEogUWAVAi4ubNyIry8//kibNpibM3o0KSkAzZvToQNZWfJp4leu5OVLlJSYNo29e6XOLeSvFSv4/nvats3HLoyN2bOH4cPx8srHXgRBEEogUWAVPj4+pKVhZkajRlSowMGDqKhw8iQHD3L6NDVrcuAAJiY8fcqJE/TvT9u2jBjBX39JnVtQpOBgQkPp2ZNt2/KxFyUlmjdn0CAOH+aff/KxI0EQhJJGFFiFj54ev/xCWBheXty8iZ8fVaty8yb167N/P7/+yvTp2Nmhrs64cbRuzbRpWFnRsSO//CJ1dEFhfv6Z778voLuB6+ri5JS/lZwgCEJJIwqswkpHh4YN5beyHzWKMWPk90yxt+foUR49IjkZBwe6d6dNG8aP5+xZpkzh2TNpUwsK8c8/HDzIkCEF1+N33+HlRXZ2wfUoCLNmsWBB7i81a0ZQUMGmEQRFEwVWUTByJF26UK8enTrRqRMNG1K9OuPG8ewZdety5AhAlSo0a8bZs1JnFRRg3Tq6dVPYnQfzokkTdHXx9y+4HoUSLjGRdesYNUr+0MyMq1dfvzphAtOnS5JLEBRGFFhFgZISP/5IcDDu7ri7ExyMjQ0VK7J7Nxs3MnYsI0eSmoquLs+fA6SnS51Y+HwZGWzY8PoPT4ERQ92Ln40bWbFC6hAf4O1N27Zoa+f+qqMjgYE8flywmQRBoUSBVXSUL0/HjnTsiKEhdepw7hxA27bcuEFSEg0acOYMT55Qty56eujo0KMH4eFShxb+sz17sLambt2C7rd3bwICiIws6H6F/PPs2SeuXQgNpX179PSwtmbPHvmTxsasXYuVFVpaTJhARAT29mhp4egov7gZiI3F1RVDQywtWbZM/mRwMI0bo6NDly4MGfL6pjgzZmBhgbY2trYEBMifPHoUe3v58siRxMTg5ISlpXwsYOnSNG7MiROKeicEQQKiwCqaevXi2jUWLyYzE21t1qxBX5/oaBYtYuVKEhN59Ij69WneXNzItwi5dYtbt1i5End3CXovU4aePdm0SYKuBUlkZeHkRLNmxMayYQODB3Pjhvylffu4cIGgIDZvpkcPVq0iJoa4OPmPh0yGszMVK/LoEQEBrFvH0aNkZeHsTI8exMUxcSLe3q87srbmyhUSEhg5EldXXr4ECAqienX5CmvXYmzMoUOEhdG//+utbt4soLdCEPKDKLCKJi0t/P0JCJAfzTIzo2ZNtLTQ02PNGlJS0NHBw4M+fV7/dykUenv3smwZcXEKvrVz3o0axYYN9O0rxvIVbS4uGBhgYMDs2fz8s3y5Y8d3V7t+nZgY+TTGdnb06CG/GT0wZQoGBlSujJ0dbdpQty5aWri4yCuwoCBu3WLhQtTVsbBg9Gh8fLh2jaQkxo1DRQUHBzp0eN1Rr14YGaGiwtChaGhw9y5AfPwHzw/m0NYmIUFh74kgFDxxq5wiy9KSI0dISODxYypX5tEjzpzhxg3c3WncmH37qFWLr78WE74XITIZly4xZoz8RoQFz9qaKlW4e5fERGkCCAqxfj2pqQBr15KSIr87V+nS764WFYWpKar//hGwtOTWLflyzuXLgKbmW8s5gzzDw0lLo1Yt+fPp6dSrR1QUJiavf3TNzV93tG2b/BiYigpRUTx9CqCnR3Lyx/YiORld3f+y24JQyIgCq4jT1ZV/CamokJGBhgYbNvDbb7Rty969ZGS8/voUCr3kZB48YMAAKTOMGMHYsVIGEL6cgYF8oWxZlJUxM8t9NRMTIiPJzJR/SYSFYWqap/bNzdHV5fbtt+44f/kyUVFkZ8trrIgIatQAuHcPd3fOnqVOHYDKlZHJAOrW5e5d7Ozkm7//T8Xt23Trlqc8glA4ib++xUWVKqSnc+UKjRvTrx+mpnz7LXXq0KoVGRmEhJCURK1alCsndVDhXbVry0fKJScjk2FpCWBiQnBwwWVITmbxYtLTycoiLo41azh/HqBePXr2LLgYQkGqXx8jI+bOZepUrlxhzx7OnMnThjY2VKqEhwczZqChwZ07PH9OgwZoa7NsGWPHcu4cJ0/KC6ykJDQ1qVYN4PBhHj6UN9K5M1EarBcAACAASURBVAEBDB4sf2hoSGgoDRvKH+Z8mW3YoMDdFYSCJsZgFRfKyqxcibMzv/5KRAT6+jg4cPYskZFUr07//kydSrVqTJggJnEobK5c4f597t5FQ4MBA7h/n/v3uXatQDMoKaGtjZ4eBgbo6BATg54eenr5e6tpQVoqKhw8yNmzlC/P4MGsX0/9+nnaUFmZAweIiqJqVQwMcHMjIQFVVXx92bULPT2WLMHVVX5SskEDevXC1pZOnbhwgdq15Y307o2fn/ycIzB1KpMmoafHxo0AR47QosVb5xkFochRkuUcri0xxo4du3z5cqlT5Jtr15g9mxs30NWlUydsbenblx492L4dIC4ONzfMzVm1SqqASUlJoaGh9fP4RV6SHD/O4MEMHYqnZ773FRgY2LRpU9UPnD5u1Yp794iKeusEkKBYISEhBgYGhoaGUgfJL05OODoydOjH1pk1i1KlXs/m8KZmzfDyol69fEoHEBMTk5CQUCPnOJuQ/zw9PT0L4NutMBGnCIuXBg04cOD1Qzc3fvqJw4dxc2PDBsqVY8sWKlVi/ny0tKRLKeRiyxZsbaUOAYCuLioqXLv2+nyNIORFYCBWVpQvz/Hj+Puzdu0n1v/IFTgXLyo2miBIQJwiLNbu3MHBgZMnefyYPn3IykJPDzMzwsKkTia8JS6OkycZP56vv5Y6Cujq0r49O3dKnUMoZE6f5vTpt55JS2Px4tcP//6bunUpV45Jk/D2/uDgekEoIUSBVazp6vLkCdra8gkdRo5EJuPpU/T0pE4mvGXHDjp3pk0bGjWSOgps24aHB7t2kZUldRShMAkIeD0Pe45nz3hzwMWQIcTEEB9PcDBOTgWcThAKHVFgFWtdu7JyJZmZlCrF/v0EB8snYM7j1dhCQdmyhUGDpA7xhho1MDKS341JEARB+AxiDFaxNmgQJ0/SqBFDh6KrS6VK7N4tn+bo0SNCQzE1pVo1yea1FAC4eZNnz2jTRuocb+vVi507cXCQOocgteho+c1t/vmHlBQCAkhLIzkZAwOePiU9nQcPAFRVMTMT3yWC8JoosIo1VVV8fDh6lKNHSUzE1pYff6RDB06fJjKSmjUJD6dcOTZtkuDewsK/tmxhwIBC95epZ0/q12fVKjFTQwl18iTt2qGsTLduxMTw8iWxsQDe3mRnk52NqioyGZmZNGqEjg5KSmzYQNu23L+PqSnq6lLvgCBIrZB9qQv54euvWbuWHTuYOJHq1TEw4O5dNmzg1ClCQ/n+ezp1Ii5O6pQlVHo6O3dKPHt7rszNsbbm5EmpcwgSGTSImBiAY8fo0gVlZVxdmT6d9HQyM8nOJj2d8HCMjGjenPLlOXKEtm0BJkzg1ClpswtCoSAKrBLm8mXS0/HzY8gQAgMB+vWjXTtxzZhUDh2iVi2qVJE6R25yzhIKJdnJk9SpQ3Q0f/1F9eq5rKCiwqFDDB6MvT0LF5KVJT++JQiCKLBKmDt3aNCAxo3Zto3u3QkNBWjYkDt3pE5WQhW24e1v6t6do0dfz7UtlCgyGR4eDBrE6tXs2YOeHkpK7849m/NQSYlhw7hyhRMnsLMjJUWSvIJQ6IgCq4TR0+PJE4CvvuLHH+nendRUnjwREzdIIiqKS5dwcZE6xwcYGNC8OUeOSJ1DKCinTqGvT7ly6OkRHc2ePbx4wYABLFsG4OaGm9tb6xsZyY9xxsTQsydJSTx+zOnTjBhBw4Y0bMjkyRLshSAUEmKQewnj4MDQody4ga0to0Zx6RLDh3P69FvzvwsFYt48srNxcUFTU+ooH5ZzllDc77mEaN2a0FCysujWjatX+eMPjI0B+X0f3r8zoLIyrVoBGBnh5SU/M+jmxsOHrF9PhQqUL1+Q8QWhcCkmR7DS09NHjx5dpUoVTU1NGxubQ4cOSZ2osCpblvXr6dgRDw927qRqVby9adw4r3d5FRRnzRq2bi285wdzdO1KQADPnkmdQygQysro6bF4Maqq6OigoyO/57ea2ic2VFLC1pYGDWjQAAsL+XD4mjWpWLFAcgtCoVRMCqy0tDQlJaXdu3eHhYWNHDnS1dU1NGd0kfC+rl25dg11dQ4fJiUFb2/OnuXWLaljlTjp6WRn07Sp1Dk+SlubDh1Yv57166WOIhSIgwfZvZtdu76okW++wcoKd3cFZRKEoqmYnCLU1tZetWpVzvLw4cOXLl16/fr1qlWrSpuq8DIz46efXj/MyMDJCQcHrl4FaN6cGTOoUEGqdMVYRgYREfLllBR69ODhQwAjI8qUkTDXx/TqhacnFhYMHy51FCF/pKXx9Cmmpty9y7BhHD2KgQETJqCv/zmtffUV1arxyy80bcovvzB4MEB6uphQTShxiskRrDfFxMSEhYXVqVNH6iBFh60t0dFcvsxvv/HbbxgaUr8+f/8tdaxiKDCQ9u1p35527Xj5koMH5Q+3bpU62Yd16sTDh6SmSp1DyDenTjFqFMnJdO3K/Pk0bAgwfjylS39Oa6NGUaMGWlrs3csPP3D9OqdO0b+/YiMLQhGgJJPJpM6gSGlpaR07dqxVq9bq1avff3Xbtm0D3p7SsW7duitWrCiodIVU7enTE2xsjE6ejO7SJcrJCTDdt0/vxo3g2bOljlZs+fsbLlxYw9v7sr5+mtRZPujZs1LPnpUGli+3SkxUnTkzBFBTy65USVyIX6xcuKB/5IhJ6dLZ2toZ48ffVWDL588brFpVdciQh6dPG86d+5cCWxYKv++//z44OPjNZ7Zt29avXz+p8hS8YlVgZWRkdOvWrXTp0jt37lRRUcl1nbFjxy5/8/7vAqCry4MHxMXRogX/+x8NGvDsGVWrEh+v8K6SkpJCQ0Prl/gx9Y6OnD9PcDAmJhL0HhgY2LRpU1XVT4wQGDOGCxcAoqOJjaVePQBlZQ4eFCeQv1RISIiBgYGhoaHUQQAOH2bKFLS0OHv2M49afcTEiZw5Q4UKHD6s4Ja/UExMTEJCQo0aNaQOUlJ4enp6enpKnaJAFZMxWEBmZmbPnj1lMtmOHTs+VF0JucvIoHRpqlZlxQoGDpQPgc/IkDpWsfX0KefPo6Hx7rSNhc3KlfKFAwfo0YMDBzAzkzSQoFDTpnHlCkB4OPfv07y5/JY427ZhZKSA9jds4No1srN5+JD79+Vj+EqXZtYsdHUV0L4gFHLFpMDKysrq27dvfHz8/v37s7KysrKy1NTURJmVVw0bcuwY3brRsye7d7NgATVrygdiCPlg926+/pqRI+WTDBV+KioYGbFvH2PGSB1FUJwBA2jdGpmMQYOoXJmZMwHU1RU2eVWlSvKFzEx++w1LS/T1UVZW/EEyQSicikmBFRERsXv3bkD33/+Mli1bNnbsWElDFR2zZtGrF8rKODmxYgV161KqFD4+UscqtrZvx9OTZs2kzpFnSkqYmODrKwqsYsXKCisrfvuNMmWoXp127RTcfvv28oUKFbh4kaAgcWtLoWQpJgWWpaVlcRpMVtDs7fHxYdIk+vdHJsPYGHV17OykjlU83b/Pw4e0bSt1jv+idWtMTGjbluhoMfqqWHn5kunT+e47zp/P346qVOHCBQIDadkyfzsShMKjGE7TIHyOFi24cIG4OOLjuXcPfX28vKTOVDz99hu9e/Op8eWFS5ky1K9P584cPCh1FEGhli6lSRMcHeV3vMkn5ctjYcGsWUyciPhHWCg5RIElvKFUKUqVQlmZTZv46afXc2IKirNzJ336SB3is7i44OsrdQhBcZ48YcUK5s6lZk0mTszHjpo2Ze1a+vUjK4vdu/OxI0EoVESBJeTGyopRo/jqKxo1wsQEe3v27ZM6U3Fw6RLKyjRoIHWOz9KxI3/8wdOnUucQFGTaNAYNosBueKGszJIlTJ7MixcF1KMgSEsUWEJuZDIuXCAyEicnrl1jyhR++okff5Q6VpG3Ywd9+0od4nNpatKuXaGbzUj4PCEhHDrElCkF2qm9PQ0b8u9dzQShmBMFlpCbI0dISODkSdasQVWVTp04fZoNG8RJwy+RmcnevfTuLXWOLyDOEhYD06dz/TrjxjF9OuXKFXTvS5awZAkxMUyfzsuXBd27IBQkUWAJuQkIwMWFJk3o00c+OqNcOezt5RN7C5/l+HGsrF5PDlQUdelCYCCJiVLnEL7AzZscPEh4uDR3765cmb59mTWLzZvz41YRglCIiAJLyE1Wlvw6t1mzOH2ay5cB1NTIypI2V5G2fXtRHd7+irY2dnYcPSp1DuELyGRs3cqSJaipSRNgxgx8fcnMlKZ3QSgwosASctOkCUeOAJQpw6xZjBvH8+ecOUPjxlInK5KuX2fyZE6coHt3qaN8MXGWsChKT8fXFx8ffHwICgJ4+RIfH/mtcgoyxvXrPHhAv34kJBAUxLVrXLtGcnKBxhAk8fff1vv3Sx2iYIkCS8hNt26kpDB4MBER8u/CZs1wdCy4K46Kl8hIfv+d1q3R05M6yhdzcuLUKVJSpM4h/BfJyfICa/duIiPR1ZUXW/k9v+g7Ll5k2DCGD+f0aTIyGD2a4cMZPpzt2ws0hiCJmBijmzelDlGwitR0h0KBUVXFz49Zs2jShGfPMDAgM5Ply6WOVYQ9fsz06VKHUIRy5WjSRH7vSqGo0NfH2xvg1185e5bZs3F0lCCGvT1Xr8qXdXWpVInff5cghlAAEhPR0ZE6hNTEESzhA7S1WbyYqCiePycyknr12LxZ6kxFzJUr8uMEx4+TkEBqKj4++PqSni51si8jzhIWUTIZS5dSpYrUOQDQ1CQoiOBgqXMI+cPWln/+AbhyBT8//Px48sTwwQP5cgGfm5aKOIIlfErOUNjFi+nQgb59xX8leXfmjPz/9T/+oFQpDhwAUFfHwQF9fWmjfZGuXfHwoEULjh7l37ur51l6OvfuUbYs5ub5Ek74sGPHUFPDxIRSpaSOAsrKDBrE4sVs3Sp1FCEfpKWRkQGwZAmhoTx+zNOn1mlpREcDlCtXIub0FwWWkDd169K5M4sWMXeu1FGKjMmT5QtVqmBjw549kqZRHENDbGz46y9evPhogZUzpDkykqpVsbEhK4v581m6FFNTEhPR08PLixYtAF68IDkZI6OC2oMSatEiJk+mUyfKlpU6Cuzfj5UVVasSHo6FhdRphHyQlMSRI9y6hbo6c+awfXtgmzZ2np5SxypAosAS8mzOHOrW5ZtviItDT486ddDUlDpTEXD7NomJ1KwpdQ6FcnHhjz8+usaFC7i5oa2NhQVBQZiZUaMGd+7w11+YmQEcPoyLC+vWsWIFV69SpgzATz8xbBhKSgWwCyXNlSuEh9OtW2G50XijRgBubixbJoZ3FhM3b7J2LUBmJk+eYGODpSU1azJoEE5OeHuXuFl+CsevmlAk6OlhYYG9PQ4OxMcTGcnKlTg7Sx2rsPP2xsEBmUzqHIoQHs6uXQBJSbx8yapV8iNYDg40afLGerGxODvzyy906QKQnc28eXh6EhFBhQrydRwdGTCA3r1ZvZpTp1BWJiSEgQOJi+OHHwp2t0qExYsZP76wVFevjB1L7dpMn160T5oLOSpUoFEj4uNZswZlZX74ARMTgGrVAJSVZSoq0gYsaIXst00ozNzdsbQkMpIFC7Cx4do1nJwwMXn7T6vwFpmMnTvZvbuYTHCRmvp69u2cisjaGuD5czh3Tj7Rf/PmXLvGN9/IqysgIwNbW1RUWLwYJSUePkRfn5o1uXiRcuVwc5OvVrMmvr7Y2DB+PMCDB5iaFoqzWUVfaChnz/Lrr1LneE+FCri4sHo1M2dKHUX4XOHhBAbSpw+GhjRtSpcuDB3K2rUMGyYvsHI0bnz5++9bSxdTAqLAEvImOZk9e3j0iO3bmTSJkydp0ICpU/HyEgXWR1y6hJoaDRpInUNBqldnwQL5spcXurosWAAvX9K3LyEhfPMNwLBhZGQwahRRUaxZg7c30dFUqEBWFjdv0qkTzZoRF8etW1y/Tno65cpRsyYtWjB6NObmGBoyaBCHDlGxIpGR2NuzapUYpPOFlizhu+/kp2ELGw8PmjdnwgS0tKSOInyWoCB276ZPH/z86NOHn3+mTx/5ucI3qaun/udrYoo4MU2DkDfh4ZibU7Ysw4bx6JF8+hpbW+7dkzpZobZzZ9G+u/NHqKtz/DjZ2TB7NioqBAWxYAELFhAUhEzG/PnUqSMf5pqSwsOHaGjQvDkTJ9KtG8OGsWwZGhoMGcK9e8ydi0yGrS0DBhAWRkYGjx8TEsLTp7RsSZs2YmLTL/HkCT4+jBoldY4PqFIFOzsxCUyRt2ULffuyZ4/8hmCNGomKWRzBEvKoXDmePCE7G1VVZszA05P27YmJEUMnPiIzEx8fzp6VOkf+MDBAJuPyZZrt2MHvv6OmRnY2R4+yciXx8fI7odSuLV/73DnU1dmwgdRU2rYlIQEvL/T0+Ocf9PWxt8fenunTGTKE9HSiojh3DkdH1NSYPJkrV9i5kyFDJN3dIikhga5dadmSXr0oX17qNB/m4YGLC8rKqKjw3XdSpxHyJimJp08BYmIIDubmTX777fVYiJxZaUo4cQRLyBsTE6pUkf+b2aMH//yDnx8//8y330qdrPA6dQoLC/kAz+Ln1i26dWP/foiJwdKSR49o2ZK5cxk6lMePUVamXTsmT5aPxXB1ZedO/voLNTVWrODAAQYP5vp1wsNxccHPj6tXWbuW48dp04bBg5kyhSZNyLmzhp0df/0l9e4WSS9ecPcuGzYwbpzUUT6qUSOqVcPfn9hYqaMIeTZ+PO3b074948cTHo6SEiNGYG8vn+lKQBzBEv6DzZvp1Al/f9q2xdaWrl1xcaF/f6ljFV7e3sX0/GBoKOvXc/euc+mmrhfHLapYkQ0bmDOHiROZMAElJW7epHJljh5l715u3aJmTebPlx/snDfvraYCA1mzhoULiY/H1pZ58zh5Ejc3Bg1i+3Y6dMDTk8REtLS4c4eLFwGaNaN6dQn2umh68YKvvioss7d/hIcHffpQp47UOYQ827QJ4NAhhg6lRQuOH5c6UOEjCiwhz2rU4NYttmzh4kXMzNDWZvhwlMVB0Ny9fMnhwyxaJHUOhfP2Ztw4vvuOwYNtw8Ky9v/zl2GVOpMmcfAgHToAJCUxfjyDB1Ot2qcnXChVinHjXh9gefoUT0/u36dKFfr1w86OHj0ICcHenjZtaN8eYNo0nJ1ZsYKSds13nl29yqlTAAkJJCdjaMjChaio0KNHYZw/f+NG4uIA0tI4dEg+uV7OpQ5CIXf3LkOHMmUKp09LHaVQEgWW8F9oar4eK1ulCgsWcOiQpIEKr8OHadSo2E1OnpCAuzsBAfKJUx8/7rogcP8/Let0VmfQINq1QybDz4/u3Zk48XPaNzBg/nxatWLSJOrX5+FDkpPR0uLUKQ4fpl07gORkXFxYtEhMl/UhCQny2TSCglBSokwZ+cPnz6XNlbt//iEpCaBCBcLC5FGzStyclEXP8+c4OzN/PoaGosDKnSiwhM/l5sa8efz5J/XqSR2lMCqe5wfPnKFJE3l1dewYbm7O3ywZc3DIjDppLFnCxYvIZEyf/kXjzoYMoXFjVq9m/37MzFi6lDFj8PCgb188PBg7Fm1tlizBxUUUWB/Srp28FrW3p2zZ1zNrFE5Tp8oX1NRYvpyBA6lRQ9JAwkedPEm9epQvz+DBtGqFmxsJCYX6EgoJiQJL+Fzq6kyYwNy5+PhIHaXQiY/nzJnieBfbpCT5UKr9+xk1Ch+fFs1bxu5MefBItXLVqgqbTbVuXTZseP3w0SNGjsTZmZ49uXaNrVupXp1HjxTTV/F1/778NnBFhYoK9euzdi0rV0odRfiw1asZOpSQEMLD2bYNQFdXTIaYOzGARvgCw4dz7hzBwVLnKFxWr2bVKjp0QEdH6igKZ23N5cv4+TFiBIcP07KlsjJdyl8+kNI+HzutUIGHD7Gw4MwZEhLo3Zv799+aIlrIzbp19O5dlH4ItbSwt2fHDvkZQ6HQCgpi5Ur27qV0aamjFG6iwBK+gKYmY8awaBGpqfzzj9RpCouTJ/HxKY7nB4GGDSlTBicnduygQQOys1m3zjlp6/6o/PwHtm9fpk4lI4PSpfH1JTmZr76iV6987LHoS0vjt9/4/nuCgqSOkmcTJzJrFq1bs2OH1FGED3v5kqVL8faW37Rd+AhRYAlfpm1bdu2iXDlq1cLUlE2bisltjb9Aairh4XTqJHUOhUhMZNIk6talYkUcHdm1i4gImjWjRw9atMDcnJ072/hNvfW3Sj7OYDR9Oqqq1K6NhwczZhAaSkYGd+/y449UqYK6OnXqsGkT2dn5lqDo2bsXGxuqVUNNTeoo/9GoUaxZI3UI4W3R0ZQujZISSkr4+REfj4MDSkp06yZ1ssJNFFjCF3j4kG++oWNH+vThyROOH2fduuI4M8GnyWTcuMG1a1y7RmgotWsTHMy1a0V8pFB8PI0akZLCjh2cP4+dHf360b8/p05x9y6LF3PxIgEBpetW79iRgwfzLUbp0uzeza+/oq+Pvj6//kpoKH5+7NzJ0aMkJrJpE1u2MHZsviUoetatY8QIqUN8ltatUVbmzBmpcwhvqFCBtDRkMtauRU+PgweRyZDJ2LtX6mSFmyiwhC+wbBkjRvDrr+zbR3g4deqwbx8LF5KWJnWyghYby8iRDB/O8OE8esSjR/Ll1aulTvYlVqzAwYG1a+XzP3p58cMP7N5Ndjb6+jRvTsWKOSs6O+f/nTGaNWPyZCZPpnlzjh+ndm0sLVm0CDU1mjTh+HH27OHBg3wOUTQEB/PwIY6OUuf4XCNGiINYhVFMDDNnYmODkpLUUYoIUWAJX+DGDdq2pVw5hg5l6VKAihUxMiqBf+eMjbl4katX2b4dNTXWrOHqVa5eLeKH886exdUVIDaWNm2YOJHZs1FTe//z7dSJ8+dJSCioYBcu4OzM4cM8fCg/UKOtjYMDly8XVIJCbd06hgxBtcheI96/P6dP8/ix1DmEt40dy9ChaGtLnaPoEAWW8AVKl+bFC4CxY9mxQz5F4IsXRenScEXz9sbUtLjMb5+ZKb+Fc9++9Owpn2NWTe39WSBzrv+aOZM9ewokmJIS2dloanLkCNevy4t7mUz8Zw28eMGuXbi5SZ3jC2hp0bv3WzN1fExGBiEhXLxYgAV+SXTiBJcvM3Uqo0bRqJHUaYqI4vF3QJBI+/b8+iuAsTGOjmzciL8/ampYWkqbS0K7dmFuXlwKrCZNOHKE+fNJT8fTE+DOHeLjc72znbMzfn6EhBRIsJYt2b+f7GzKlOHQIZYvZ+9ezpyhWbMC6b5Q27EDO7tXJ2+Lqu+/Z8OGD4w1yMh4vXzyJNbWdO/OhAlUqYKHBxkZnDhB585YWdG6NRs3iqsfvtzLl4wcyerVlCnDV19hbCx1oCKiePwdECQyejT37tG9O6dP8/XXzJtHr154eZXYAwmXL6OiwqZNtG0rdRSFGD+erVtZsIA1a5DJ8PfHyYk5c3I9+eTkxIMHZGYWSLBvvkFDg27duHkTLS08POjdGycnLCwKpPtCKjGRxETWr2f4cKmjfLFq1ahTh507mTz5jWf376dePXR00NWlZ0+OHWPAADZt4tYtLlzgzh35bSvHjMHNjaNHmTYNb2+6dROXNn+28HCAn36iSRO+/lrqNEVNkT1LLxQGZcpw/jwrVzJnDnFxaGjg4SG/I2+JtHMnvXrlenynaFJXp3RprK2xsyM9nWrVWLiQrl3fWev0aZ4+BdDW5swZ+cT+Bga0bp1vwZSV+d//+Pln+vQhIoLq1endmytXSEmhTBmyskrmfaBXrSIykvh4+U23i7pRo5g7l6iofwcyenmxYgVeXtjZ8fw569bRrRseHjg4yDcwMGDhQmrX5sED+UH0atWwt6dJE375hZMnOX8eoEUL5s79ors5lRixsdjZ8b//8csv3LwpdZoiSBRYwpcpXZpJk5g0CeDgQebPL7FXy2dlsWcPAQFS5/hCKSn8/Te6ulha4uaGq6t8hFN6OqVK5bqFtzeJiQAqKty6JS+wdHTys8ACSpfmhx/euh2hmxsdO/LiBSEhaGrSsSMLF5aoyRAzM7l8mWHDiskZakdHvh+ZlZEqIzEFTU1mziQwECsrAF1dpkxh5UoCAli0iBs3iIqibFkSElBTY+5cqlbFwAA7O6ysaNECd3fmzWPZMgBfX1q25PhxKlSQdgcLv6wssrIYPpw5c8StEz6HKLAExXF0ZMIELl4smUNh/P0xNy/K/xhnZvLTT6xeTeXKJCSQkoKeHrt3y1/9QHUFbNwoX5gwgXXr8PaW6Pq1Bg3YuZPevbl4kefP8fKiaVOuXi05A0bS0rh9m0GDpM7xxZ4+JTwwgvnz28W32pXufM3sGxo3RqNlTXMrjfh4Nm8mIIA//+TJE5KSsLGhc2fMzHj+nP/9j8uXMTAgPp5bt5g5kzJlePqUmjUZNUr+czlmDFpaTJvG5s1S72gRkJJCVhZDh0qdo2gSBZagOMrKuLuzfHnJLLB27aJnT6lDfIkpUwgO5vZtjI25cYM2bXj6lDt35JNg5YG2Nrq6nD1Lmzb5GjQ3OdXhiRP07o2/Px07Mm0a8fH8/HMRnyrj03r25NkzgBs3UFWlTx8AY2N++03aXJ9v/87U9RMTMPJ8Wbl8aojSkMr+Kn+GqyQ8W9p7acuz83ByYuBA6tVj5Uq2bWPx4tdnhO/cAZg5U34hc878v40a8c8/GBnx1VcMGkT79nz7LWPHqjx6VG7vXjIysLKiVy90dSXb4UJm61a2bwd4/pykJJSU+OorgFmzSuZX++cTBZagUAMH8tNPPHpU5K9i+o9SUzlwgFmzpM7x2VJS2LSJ0FAMDHj+nJ49WbeOiAhWrnx9hOpTVFWpVYv9+6UosEJD0dOjVSt278bFhQsXqFyZLl2YObPAoxS0ceNITgbo0UM+GysU7cmKhpbaOtT5NLt2RUVRtSqDW90bfX8cvUkwJAAAIABJREFUx45BV0JCMDKSr5ecjLExTZowbBh6evj5ceQIHTvy7bfyA7FxcWzZAnD1KunpHDmCuztGRkybRnq6/tdfJ3bujK0tFy8yZw7bt+fzWe0io107TE0Bli6ldGlmz5Y/X7u2hKGKJFFgCQqlrc3AgaxaxeLFUkcpUEePUr++/FupSAoLw8wMAwOAMWNo1YoePTh//j9N0O7uTpcudOnCypUFfiGpior8CsYWLfjhB/r14+zZEjLavUkTgL/+IiuLZs1o107qQF/u1i1atAC4ckUz3WrDJuXRq114/pwzZzh+nDZtSEhg7VoCA7l8mYAA/vc/4uOxteXWLTQ1WbaMFi3kU/T16UOrVhw7Rr9+DBvG4MFs24arKxkZCatXP7Gx0atRA+DMGfr04d49NDWl3PHCwdQUU1PCwrh8GV3dYvETJRFRYAmKNno0jRoxcyZaWlJHKTg51w8WYdraxMUhkxEQgL8/t24BxMVRtux/aiPnIvorV+R/9QtOlSqkpXH1Kg0bMmYMR46wcCFhYbRqVbA5JPPLL9SrV2QnSHn6lPnzCQwEaNkSFRWePGHyZOXfftfQvZCmX+1SrWpNdQ4wbRr79jF9Orq6dOrEH39QtizffMM337zVmocHHh4kJcl/ev/4A0dH0tLktybOzCQ9nQYNdL//XqVZM5Yto3JlHByoUYOAgOJyk3YF+PFH3NzYuVPqHEWZKLAERbO0pEULhg3D3BxTU7p2LfanC5OSOHWKTZukzvElKlbk/+ydd1RT2deGn9AFaQoqUmyIHVTEBuiooOLYFdBRsfc69t7HsSv2MvaCiGLvDRXrWMDesYAKFgREOvf7g/upvxlHQZPcBPOsWWuSmJz9BjHZ95y9312gAFu2MHky/v4YGZGZyaJF//zqygYtW7Jjh9ITLC0t5s+neXOmT6duXUaP5tdfsbT8SZrL09IICGDCBPUs6H/wgNq1aduWhQsBtm5l7VoSE/n110LXjxyMzrN/PytmxVU/f5716xk6NLvLfrw2cHHh6FFGjRKbnV1dadqUmjVfeXlp+/tTvTqTJtG7N7a2xMQo4O2pJdevc/Qo4eHiPqCG7yNXtPNqUClOneLsWfbuJV8+7t7FxYVVq6TWpFi2b6duXfWvkf3rL3r2JCkJYN06XF3R0fmO9qEWLdi+Xf7qvk3r1gQHs2ULVavSrx916og+Xj8Be/dSpgx9+tCypdRSvoNRoxgyhNmzqVqVypWxtCQ9nXz5uHmTbdvKPTvYOd5/505ipyzC3Pw7Q5Qvz549xMYSG8vevVSpwvXrgpHR6z59uHiR9etp0YKrV8nIwNubkiVxcWHcOBIT5fo+1YkRIxg7loIFWbJEainqjCbB0iBXkpJo25bNmylThrJlWbyYc+cYM4Y7d6RWphDS09m8Wf3PB7PIlw89PVq0YM0aTpxg4ED27kVXN6fLVK5MRgY3bihC4reoWpW9e4mM5OZN9u2jUiXGjJFCh7JZu5ZOnaQW8d0cPYqfH8C9e9SoQUgIZ8+Smsry5Vy+jL+/RdzDBg1lmzN85Rbxt9/YuVM/y7OuaFFOnODtW27dYtgwPDzYv5+lS3n+HBcX4uPlFlR9OHWKO3c01gxyQHNEqEGuhIRQujQeHrx6xbx5NGlC8eL4+bFtG2PHSi1O/sTEMGQIqam5YohEv36MGCEeo/wYzZsTHKwCPUdLluDkhCAQEcG7dzg5MWxY7rMejYnh1Cmxr14tSUnB0JDz52nRgvHj6dWLpCRSUqhT52NbX/fjDBokThuXA4UKsW2bSceOBubmlC3LlSuYm2NigkzG69eUKIGWFqtW0aUL/v6MGyenqGrDyJH88cdPsvmrWDQ7WBrkSnQ0trYArVtz/z7XrwPY2REdLa0uxZGURNOm5MkjtY4fJCiIyEh5ufC3aMGOHXJZ6cfIkwdTU5Yvx9eXSZMwM8PZmdOnpZYlZzZsoEULNfRl+Di3snJlZsygWTNWr6Z3b2QyjhyhUqXPn1unDikpnD8vv+ju7q9DQl4NGkSDBqxdy5o1mJoSHs6xY3h6ip9XbdsSEiK/kKpOdDTR0WzfTmIivvLbLvyZ0SRYGuRKsWLcugWgq0uPHixdCnDzJsWKSatLcWQdiqofgsCGDTRoQPnyNG1K374sXfodB4JfxNWV6GgePZLLYj/A0qU4ONC5MwcPUrs2kyaxdi09ekgtS86sX69W54Pp6SxciL09hoYULsywYbi48McfjBoldvAdOEDfvkyc+PmLZDK6dcu+I1u2EPT0Pri40L49Li6kp6Onh7U1R45Qsyaurjx8iL6+sqaXqwTLl7N0KePGMXNmLpm2JDman6IGueLqSmIiixYhCHTrRmAge/eyfbuae5z/k2nTkMmQybC2JjWVBg3Eu4cPS60s22i3b8/SpQwYQGAgqakkJ3PunLwW19KiSZMcWWgphoMH6daNWbM4f14svPfyIiGBx48lFiY/Ll0iMRF3d6l1ZJ8+fQgOZvt2kpM5f55Tp1i6lOXLWbsWU1NMTRk1inXr/m2+1KkTO3aIUy/lj709r1/z4AHa2kyZwvDh1KrFmjVUqQKQlqawwCpEZiZXrlCokOjbruHH0SRYGuSKjg67drFxI5UrM3o02tp06kRgYC6bFDp6NIKAIDB8OEZG4m1BoH59qZVlD7OLF7l9m5AQfv2VlBTCwzl3jhkzePlSXiFatCA4WF6LfS8fPmBigqEh69fTvz9v3wKYmuam1vO1a+nYUX3sr+7fZ+9e9u3DyQmZjEWLeP8eZ2fy5iUsjGfPePaMsDDq1fv3Sy0tqV9fYaVmurpMnEizZpw9iyDQvj3167N+PTY2eHlhZkaRIhQrxtq1igmvEqSnc/Ik06ZJrSMXoUmwNMgbe3vOnWPxYmrXZuRIChTIxQModu1Sy+ors8uXBR8f9PTIzKR3b/78k3LlcHeXY31S3brcuiXHhO27cHQkq1OsWjW8vRk+nOfPef6c4sUllSU3UlIIDBQ78NSDixf55RcMDcnMpEsXzpzh9GlatuTCBQATk68b2/bowYoVLFnCvXsK0NavHxMm0K0bxsYULEhcHP7+DB2KtTWxsbx7x7Zt+PszZ44CYktJgwZUqUKVKixcSGoq/fpRpYpmE0s+aLoINSgAmYyaNalZE2D1ak6epHZtqTXJn/Bw3r9HT09qHTlHKy1NHAmycSO6unTsCGBoSEqKvELo6dGoETt30quXvJbMOYMG4e6OvT2+vkydSunSXLjAoEHiJGA1584drl2jYkWKFJFaSvb5ONFo0CAiIjhyBEPD7E80qlOH5GQCArC1xcFBAfJ8fPDxISkJfX1xdH23buzfz4oV9OuHszM7duDsTP/+avnP/j9YuJCEBFJT8fCgcWNGjgQ1n2WpOmh2sDQomN69c6tXXUAA7dsze7bUOnLOewcH2dGjJCczfjyzZiGTkZLCqVNUrizHKC1asG0b/fvLcckc4uDA/v3Mm4eFBZUqER+fNYBFOkHyxNOT5cvVqrwdcHUlJISxYzl1il27xOxq27ZsTjSSyejaladPFSwyTx6xxvvKFdq35/RpFi0Si+6LFqVAAR4+VLACpeLggLMzFy5QtCjlyuHsjLOzYvLXnw9NgqVBwXTowNGjvHghtQ45IwgEBtKunVq2EL6uV48nT2jYkIoVqVGDyEh8fXF1pWxZOUbx8uLiRbZtk+OSOcfZmfPnuXePQ4eIi8PdnRkzJBUkN9LSuHKFFi2k1pEjbG2pWpVZsxg+nKQkzp+nSRMsLGjc+OuvEwTCwrh8GWdnnj/nxg0uX+byZSIjFalWX5+kJIoW5fRptm/njz8AcX8rd5GSwuzZuLlJrSPXoTki1KBgTEzw9WXlSsaPl1qKPDl3DiMjKlSQWsd3kamrm7F9u06lSmhpUagQKSkMHCieDcgPQ0NcXcXqGonJl498+QAWLqRiRXx85JtKSkJSEk2aiCe9qsurV0yYwMGDvHtHxYrUr8/ly8yZw/LlDBmCtTXt2tGv3zer9KOj6dmTjAwAmYx588SuUDc35s9XmPh69Vi/nvr1sbTk2DF++YVnz9DSyn2mM6tWUbmyes5ZUm00CZYGxdOvH56ejBolL5slVSAgQL2tJ7SWL6drV/z9ef2aggXlu/jLl+KonOLFOX6co0cBtLWpWhUjI/mGyiFWVowfT5cutGjBgwdYW6tXsnX2LBMmiLcTErhxA09PgHbtVPKs8PVrqlbF25ujRzE3Z/lyxoxh3Dj69aNfvxytVKjQp0y9Rg1iYrh0Sf56/0n//ri58dtv9OmDmRm+vkyZQu/eZGQQEsK9e1hbU7euutcrpaYycyZbt1K1qtRSch2aBEuD4ilblhIl2LMn11wiZWQQFMSZM1Lr+F4MXr7U2rCBGzfQ1pZ7dgUcPMimTQCJiaSmMm2aWMQ8aZLY+SAlRYty5QqGhvz2G0+e4OHB0KEMHiy1rGzh5MTIkQgC9+5x4gSjRpE/P4Cjo9TKvsj8+TRuzMyZADdvMn8+ixczeTLjxmWzqv2LWFry+DGXLokeVQokb17On2fuXEaNEnfgjhyhQwd27sTWlkqV2LePfv1YsUK0SFVP1q+ndGlNdqUYhJ+MgQMHSi3hpyQgQPDwEN6+jX/y5PLly1Kr+VEOHhSqVZNaxA8QXb9+xoQJSggUFSXo6wtBQUoIlT0SEoSCBYVNm4QCBYSXLwVBEF68EKythfBwJQu5efNmdHT0d7980CDB2FiIipKjIgVQu7Zw7JggCMLTp4KtrbB5syAIQokSwt27P7Jq06aCn5/Qs+ePqnvx4sXt27dz9prUVKFIEcHMTNiyRXzk3DnB0lJ4+vRH1UhEerpQsqRw6pQyYk1QymeOSqEpctegFPLmJSSEokXzOjmV9fbm0CGpBf0QAQFqWdtOfDzx8Vy9anblSubvvysnZp48YrmMShASgpMTv/1G167i4MVChfDzU43RidklPZ3AQHUwYBMEZDKSk2nZkv79xX8zPzyEZfZsJk5k61YSEuSgMWecPo2VFadPM2gQu3YBVK+Ory9btihdinzYtAkbG7WaBKBWaBIsDYrnwAH69MHXl86dE548eTZsGN27c/Cg1LK+k+Rk9uzB21tqHTniyBEcHbG1xdaWWrVe16mjnGIoLS0MDTl4kORkJUTLBm/eYGUFMG4cf/8tzjaysuLNG2l15YgjRyhWDF9fzMyklvJ1XF3ZuZPevbG3Z9gwgOvXSUigRIkfWbVkSYoVo1YtgoLkIzMHPH1KqVKUL8/evfTowYkTAKVKKd46Qv48f05GBtOmMW6c1FJyL5oES4PimTKFJUv48082bpR9+JBQtSpLljBlitSyvpN9+6hUSa1m/xw6RJcuzJpFXByBgZiZWYSEyI4cUULkQoU4fpyKFVVmSqO9PVevAuTJw+LF9O1LSgphYdjbS60sB2zaRLt2LFig8i2Ev//Ohg3s38/kySQmsns3TZsyY8aPFGB9pHt3Oc9+zhZWVuIgS2dngoJo04awMCIi1OrjQKRGDVatIl++XDxoQ3o0CZYGxRMWRt262Nri7q6TddVZt674PaeGqN/54OTJLFlCgwZkZjJyJAsXPhg8WGvqVOUEL1WKVq1U5pSwRg309Jg8mYwMGjSgXDk6d2b/fn77TWpl2SUxkf378fGRWkd2uHsXHR3q1KFOHQoWZOZMVq6U12QfLy+ePyc8XC6LZZvatYmIYPdugFq1WLAALy/WrVO3DW2A9HTmzfvUlKpBEWi6CDUoHgMDEhMxNKR3b70RI3B1JTFRHUpI/klSEgkJHD3KihVSS8kRV6+K03M3bcLYmObN3x09Kps8WWnxW7dmwgRSU1VgvoiWFjt30q0b9vY4OnLvHg8eEByMhYXUyrJLcDDu7qqq9+JFJk8mPBwzM9zc2LWL9etp2FARobS06NSJ1avx91fE8v+BgQFBQfj6sno1lSoREcH795iZYWFBWpo4ItHBQS38aJKTyZ9fbebTqymaHSwNisfTkzVrsm7I4uONbt5k9WrRwEetmDuXPn2oXVs0rVQbshLctDQmTWLaNEA7OVmZCW6hQpQuzfHjSgv4VaytOXCAAwfo2pVNmxg3jtWrpdaUA7LOB1WRbdto0QIfH86dY906du4kNZXq1RUXsEsXNm9Wenlf1arcuoWvL4KAmxsPHuDtTfXq2NqKowzt7Fi3Trmassvff4safXx49w4DA3x98fFR3xp9VUezg6VB8UyfTq1aPH+Ot3d63bpFJk4kNZVTp6SWlWPS0ggLEwdmqBMeHqxbh5kZxYtn9QsVOHBAqFv3G+bZcqVlS4KDFbSX8V2ULk3p0gDly+PoyL59/Pqr1Jq+TXQ0f/+tki2PmZn8/ju7donmVJMnU706lpbMny9O8VMARYrg7ExwsNIPePPk+Z8qgSpVWLWK6tU5cAAtLW7cwNsbfX0VdCIuWRJfXzIzCQ8XBztmXStqTLAUhGYHS4PiKVaMa9cwMGDECO2rV/Wjojh1Sh3HTXz4QGTkN8emqR7TpzNvHkOG4OPD+fMMHmwdFJQ5bZoyJbRqxY4dpKcrM2b20NNj/nwGDVKZRsevsWkTLVqo5On6w4fo6YnZ1V9/ceYM69fj46Po6yhpSt3/wezZBAWRksLQoQDly7NkCbNmSS3rC5iZ0aoV3t6cO4eJCU2a4O2NtzdFikitLJeiSbA0KAVzc6ZPJzQ08fjx2Hr1xCpRNaFnT3FTfeNGDAzo3BkfH3r2lFpW9ilenCFDyJ+fVasYNAht7Str1gjKTXCLFqVIEU6fVmbMbNOwIUWK4OiImRlmZjRqxLVrUmv6Mqp7PpiRgY4OwLVrjB7Njh0YG6OrK44PVBhNm3LnDhcucOyYQuN8lVu3qFWLnTs5fFicjFijBrduSSfoG1y+zIMHGBhIreMnQHNEqEHZvG7dOt+sWQwY8M0JrypCq1bExQGcOEGFCmLDkKmptKJyQkoK/v4EBX08CUgPDVW+iqxeQlXsCT9/nvBwkpM5c4YiRdi+nfr12bWLatWkVvY/3L5NdDS1akmt44vY2xMbS1gYbdsybx4ODgB79ij6Z6iri58fM2eSliY2ckiAiQlv31K4MPv34+pK0aJUrYqJiURqvs2MGQwezJUrqqwxl6BJsDQom/dOTujrc/Ikv/witZZskdVo8/w5iYn88osadmSvXImTk+R1Fq1bi43tP2zlLW/GjWP+fJ48Ydw4du2iSxf09Rk7FqVYhWWfjRtp314uHlIKQEeHqVOpXZuaNfHxITaWpUvZskUJM5l79MDFRdIZl02asHAhf/6JnR27dtGwIQ0bqmwlwaNHhISwejUDB0ot5SdAk2BpkILu3Vm2TF0SrCy2bKFMGVX9evsKyclMn64KZ7IlS2JpyblzuLpKLeUfnDtHcDD6+jg6sncvjRvTpAm9ekkt6xOvXhEWRkCAOJ1FRcmTBxMTXrzAzAw9Pby8OHeOQoUUHbZECWxsiI5WdJz/Zto06tTh0SNatwZwcCAggHPnpBP0NWbNolcv8uaVWsfPgapdS34/CQkJbdq0MTIysrGxWbZs2RefExtLSoqKmx//HLRvz5EjvHwptY4csHUrDRpQqpTUOnLK8uW4uFC5stQ6AFVyHP0cLS0yM9HTY+FCBg4kKYnMTJXaZzt/nokTMTGhQgWppXyOIBARQWgo0dHcu8eQIezfT1gY794RG8vmzdjaKjR+u3bky0e+fNy/z+XL4m1LS168UGjYf1GwIFev4upKUBBBQXh7M3MmHTuydi0tW1KtGu3aceGCcjV9mZgYtm6lXz+pdfw05J4drMGDB8fExDx+/PjOnTuNGjUqV66c+78mWC5aRHi4ZqylCmBiQuvWrF7N6NFSS8kWERFERDB5sljIq+okJbFrF/fuUaAAM2eyf7/UgkRataJRI+bMUbHqO3d3goLo1g1PT5ydmTEDGxvc3KSW9T9ERtK/v9QiPufWLXr04Nkz7Oy4fZvMTMaOFRNAZdlsrl3L+/cAe/bQvTtHjlC8OLq6UmzP6OszYAADBnx6ZOVK+vdnxQpKlCA8HB8fhg6V/K9wwQLatqVAAWlV/ESo0FXaj5CWlhYQEDBx4kRLS0t3d3dfX991X7J6y8ggM/N/PtoFQWUbhnI7ffqwfLmim4zkxZYteHurSXZ18SJly7JpExkZ/PUXb99y+7bUmkTKl8fIiIYNxSG5qsK0aYwZw7x5REYydCizZzNyJMq1sfg66em8fKlKtkrv3lG/Pp068fgxp0/j7Y2FBTt3IgjKVKGri7m5+J+NDdu3Y26uGodfx48jk1GnDkeOULUq3bsTGsrkycTESCgqMZGVKxk0SEIJPx25JMF6/PhxYmJixYoVs+5WrFjx5s2b2XlhdDSNGilSmYb/wsmJAgXEL7Y9e0hLk1rQ19i6VU2mv6Wk4O2Nvz979jB8OFFRbN3KgAE8eCC1MpGWLXn0SNx4UBWcnDh7losXqVmTVq0oWZLy5XFykloWrVsjkyGT0bIlqanY2iKTYWSk9COwf7N5M7/8QrduyGTs2MHhw1y4wOvX/P23VIqKFGHNGpX5FDl8mN9+IyCA69fJGvppa4urq1Q+JfHxhIWxciV16qjXWHO1Ry0uyb/N+/fvAWNj46y7pqamCQkJH/80q6kFuHHjQ0yMu5HRAx2dOB2ddyVLjrG0dEpNXRQe/j+eJU+f6hcokGZgkKm8N/DTkJ6enpSUFB4ebhoSYnv3bubjx+8aNsyzZYvuwIGPZ8xIzuruVjEeP9Z//ryEsfEtZU+WzTnG584VtLR8UKQI4eEF1qzJU7HiEzu7wg0bpi9YENO168enZWRk3LhxQybFQV2FCnnmzbOPiHgSHh6v/OhfY+TIrP/L0tMdfHxezpsXV7eu4qIlJiYmJia++GquNG4c48YBdOxYMilJtnXrvazHY2Kk3QrBOjQ0xc7udXi43osXJbt3j1iw4MPTp3b29gmHD8fq6ytfT548us2aGSYkWPj7v/b0jMvmq1JTU9PS0sIV8K/a+tmzFGvr1w8e6E6fbu/n91Imi23c2C49PeHu3VgpPkROnTLZti3/vXsGc+c+Dg9PUlrcP/744+nTpx/vRkVFOTs7N2nSRGkCJCeXJFh58+YFEhISTExMgLi4uI/JFjB8OO/eAaxcqX38eJSpqUVkZDFr63eVKi2rUUP70iVtOzu7z1cbNSpvx44p9euryNVQruLDhw9RUVFFwWTq1PfbtuVt105v2LA0W1vZ9u0lhw+PO39eBQYC/5OAAINWrTKLFrX79lOlRi80VNfBwc7OTvb+venmzQl799rZ2emXL6/94IHBZ7/k8fHxNjY22kpsiYyPl/n7G2RmAqSlaQUH2zx6lAE4OGS0bZuqNBnZJG3+fLu+feN9fQWFmaY/efLE1NTUzMzsm89MSJDdv5+nRo30f3xMSUgea+u8gmBobW3cq1fagAEWXl5A3uRk3eLFjaUQaWeHszNGRrKNG627ds2uQ93bt28TExNtFVCJr1ejhun+/YZ2dtjZJQcH2zRpYl66tNG1a9qjRkny87Gw0I2NzVOqVGbDhpbKjDtw4MBXr159vBsYGPjvwujcTS5JsIoWLWpoaHjt2jU3NzcgPDy8XLlyH/80a34DEBqq/+TJvfPnG86fz8KF+bduzf/XX2RkUL68uZkZefIwdy61aqGjg6Ghrrn5p/UzM4mPJxsfhhq+gba2to6OjunBg7RrZ1y/Ph06mG7dytSpdOvGmjXmN25IZxf4n+zezZo1mJtLcGmeY8qUYeNGPXNzli3D09Mky/vq2TNKltT/7BdaJpOZmZnpKLGmTF8fa2txVI6pKe/e6VpZ6QJFi2JubqQ0GdmlSRO2bDGbP5+6dYmKwt4ed3f59hW+ePHCyMjI/PNPmf9g1y6cnLI+kb79ZCXh44O3t4FMhoGBztixebS0uH6dsDDdX3+V0IG3QwfGjOHtW/MSJbL1/JSUlLS0NIX8VLt2ZdEi8/nzGTWKatVYtcrY2xs3NxOJHEqMjHj8mDlztJX8K+T68f2+ecP06c6hoWaNGuHqysiR5M+vTCVSkUsSLF1d3bZt206ePDkwMPDu3btbt27du3fvV57v55c19JboaNq145dfCAkhPp7gYLS0vlCpefgwK1YQHKywN/CzERkpGh706kXt2owbh74+JUsSGSm1sn9y7RrJyZKbdGYbd3fevGH5cvz9xUry8+cJDOTyZWl1GRoyZIh4e98+IiIYMUJSQd+kaVN++43QUMqWZdkyBIFNmyRx6QgIoFMnVGb3CgAXF+rUYfZs0Zr1yhVWrGDxYmnnG+jr4+fHypVMny6hCgDy5OHECQYPxsICCwvevKFBA65cISKCS5cIC8PUlAYNFF3n1707x48DxMaSmCg6u2lrc/IkVlYKjfy/PHxI7dr4+Bxu0KBr165s24aTEydPks1EWJ3JJQkWMG/evG7dutnY2Jiams6YMeOLW5GVKnHlShSIjinA8+cYGrJpEy9f4ulJUBArV5KUxKlTFCyIsTHu7syfT1qaSs6pVV8KF+bhQwAHBypUICiI9u15+JD27aVW9k8CA/HxUTFbga+gq8vOnXh4kJHB0qVERHD1KmvXKtqRKEeYmZGWxvXrKubq9DlRUfTvT58+3LnDX38BLF9O8+Zcv67kVtLoaP7+m507VWzAc1wcJ08yfTrPnrFhA6VKcf68Koxv796dWrWYPFkFCg2srAgIIDWVFy+wsUFbm7FjKVOG6tWpX5/Xr2ncGF9fZs1S3IfLzJli8XGjRhQuLJoNa2srN7sCRo3i998ZMuTZxInUqEGNGlhZMWoUW7cqV4cE5J4Ey9jYODAw8OvPadaMEyeuf/GPChZkwwbRNKBPH6ysePiQx48pW5Zjx8j8Ur17z57MmaMaXcFqR5s2VKtG5844OtKvH3/+iZ4eUVGo2Am9IBAYyLZtUuvIEUXl2qgXAAAgAElEQVSKkJnJn3+SlESdOnh48Fk9oipQuDAeHgQFqXCCFRCAtzfz5uHsLHaQ9uzJ6tWEhip5/MDWrTRpohrZVVSU2CTo4sKQIfz6K0OHSq3pnzg4UK4cO3eqTM+vnh5Fioi3z5/HxQUtLYYORU+PceOoXZugIMVpzTKwuHSJ2FiqVqV4cQXF+RZHj7J4MWCWVQoNdOyoUjYoiiOX2DR8N+bmdOwIIJNRsSLOzjg7U7AgXbty/Trdu3PtWla9AcePU68ePj60bcvr1wB79xKvYo1QakOxYixbRoMGtG3L2bOEhzN0KNu3I0UL0le4dAkdHf7f/UNNWLKE2rXp1o3+/WnRQtWyK2DZMgYOJChIah1f4ckTypRBR4fFixkyRPx3XqYMT54oWUhAAG3bKjnmvxAExoyhUiXWrWPdOsqU4cQJZs6UWtaX6dGDFSukFvFvoqMJC+P4cfLlo3NnBAFjY0aMICBA0ZFnz6ZJE0n34JOTMTIiPLzrqlXiI0ZGpKRIJ0h5/OwJVp48X8ukW7Vi7FiWLaNrV8zMuHOHs2fR1v5PF5+MDHUxzlQBWrbkxg0aN8bMDG9vatemUiWpNf0PgYEEBODrK7WOHJGYyNy5YnO/ClOlCikpXP/ybrIKULCgmEu5ueHlxahRAE+eKGGy3uc8esTDh3h4KDPml/D35+RJbt5kxw5mzkRPD2trli+XWtaXadGCGze4f19qHf8gJgYrK3R12bCBp08ZPBjAzk7RMxQjIjh2jN9/l3REfaVKLFlCgwYHPnpOHj2qap/2CiL3HBHKES8vsZjVxQUXFwADA6Ki2L2bI0dYsAAnJ+ztiY/n+HHxI7dUKWxtmTsXYNgw6aSrF/nz064dQGwsJUoQE6NSQxyyPgOPHpVaR45YuhR3d8qXl1rHN5DJaN2abdtU9ZTQxwd3d3r0oGRJZs2ifHmKF+fhQ2rVUqYKVZkfsHw5GzdiaUlaGh06MHky1arRvr1qmoLr6dGxIytX4uSEr68K/PSysLXl2TM+fMDQkL17qVePiROxsVF04dr8+XTtSrlyfNZVr3hu3mTJEu7fx9qadu1o2ZLhwxk//lZW+9ihQ/Tty8fdrFyNivz2qRa9e//nH5makpxMlSq8esWHD3TpgrU1Njb06UPbtiQmKlFlbsLcnBYtWL36o9mjKpCaiqUlZcpIrSP7fPjAnDkcPiy1jmzh7U3HjkyaJLWOL+LgwKxZuLnRrBlFi2Jry6hRHDmi5GKogAD+Y2y9cnn0SEzZx4yhYEF69yY1lYgIqWX9J9274+qKtjZ16lC4sNRqsjAzo1Ejfv+dhQsxNeXAAapXJzZWocPP375l40al7xOvWcPo0QweTPPmPH5M5868fcvMmaxfP/LuXebPx86O1avx9FSuLGnQJFjZwtZWLMSpWpUjR8QHra3Zto1du1i1is2bsbREENSn3UzV6N+fZs0YOlRlLjlJSqJZM6lFZIeQEA4cIC6O16+pUUNVN4X+iYsLqancuKGq221+ftSrx+7dREbSowf58nHqFLVrKy1+eDjx8dSsqbSA/02BAkRGcv8+W7Zw5QoyGZGRKrXZ/A/s7alQgStXpNbxD5Yto0sXSpfGzY24OOLj0dHh9m1u3+bgQd69w8mJ4cPl2PC7dCnNmik3xXz7luHDOXuWkiUBdu8mLY18+ahenSFD5o8aNXLkSGm9PJSMqnyZqTgVK3650rlIEaZPR1+f8+dp04bkZAoX5sMHtLQwNmbMGOLj6diRHTuUrljtqFgRW1v27KFFCwlVHDlC/fqf7k6fLnrqzJypkie/mZl06cK5c3Tpgq0tw4aRPz937lC6tNTKskXLlgQFqWqCBVhbf9rN9vCgcmW8vZX2s92yhd9+U40LNl9fRo7kzBkCA7GwIDOTiRNVpk/vy/TsSYcOUov4ByYmbNuW5ciKqSmrVhETQ6VKlCnDlCmYmXH8OFWqsHWrXPL4lBQWL1b6dnZICDVqiNnV+vWMGsWhQ+zcyf79uLom6+v/VNkVmiL3H0Fbm6xZI3Z21K3L0KGUKsXr16xZQ0QEBQsCvH/PxYvSylQf+vVj0SJpJXh6IggIAidOoKtLVJR4VxWzK2D9eh484No1RowgPZ1GjRg/ns9mDqo43t6q3Uv4OTY2TJhAjx48fMiOHRw/zmfTTuWOIKhG/2AWEyaIhpWhofz5Jy4uxMSo5uHu4cPieGwfH1JSsLZGJkNLi1mzpFb2kQoV6NCBpk2xsODAAWrVIiaGzEzc3ZkwgXXrRD/QH2bjRipWVPrVy/v3ZJnFz5zJ+PEcP46TE+bmKjbdXXlodrC+n7NnxSzq4zdacjKApyfTp/PHH2Rm0rChZPLUj5YtGTKEW7coW1ZqKQQFqYb50NfZvp3Bg9HXJymJWbPYtw9HR8aO5cULpZsJfg8uLqSkqPAp4T/w82PSJJydqVuXd++4c4fZs/ntN7nHefGCu3cxMsLRUe5rfxfz51OxIkOGEBoKMGUKH9vBVIz69T/N4TAxwcdHtIlVUQ4dYvBgChSgUSOMjPDwoGFDunfn8WOKFv3uVR88oHBh5s5l4UL5Sf06GRmkpGBoSLlyTJlCv36cPs2ZM1hbA4SGqkArrDRoEqzvx8bmy4+7ujJ7NoGBLFjAuHEkJrJ1q7jVX7s2BQqQloaurjKVqgl6enTvzowZ+PpiZoaTE0bSTKnLzGTHDgwMJAmeE968EbtYly+nWjXxGLtgQd68UYsEC2jVSrVPCT+nf39q1ODsWRYtonBhbt6kYUPs7HBzk2+cPn1ITxf7a6UhIoIVK8QusDJlWLqUy5exslLZvOqLGBoSHMz8+SrsBf3hA8bGODsTHEzLlvz1F02aYGLChw8/suqQIVSqhIEBdevKS+h/c/8+Q4eKvdbW1oweTUICO3Zw8aI4fHTBAv7+m9WrFS9FFdEcEcoTKyvxe+3WLW7coGxZ7O1JSqJ3b1asYPt2nj8H8PMTd9w1/A9JSTx4wMaNzJ8vHrgqssXmK4SGYmXFnDlYKnX2fM6xtycsjKQkZs9mwgSA+HiePftkHq3yqM0pYVwcO3eyaRO9ejFgAEC5cowZowg7qPR0Tp+mTRu5L5w9AgOpXh0dHdq2pUAB+venVi11ydc/R1ubmjXZsEFqHV/B0ZGQEABXV/bvp0cP5s3j+fMf9FwXBIKDP43+VCDPnlGrFnXr8uYNiYksXky/flha0qgRZcvi5ETBghw5wrFjKpzkKhjhJ2PgwIHKDBcVJRQuLKxbJ1hZCR06CNHRgiAITZoIu3crU4UKERcXd/ny5S//Wbdugq+v0Lq14O8vCIJw+bJQuLBw7pwy5WXRt6/w55/KD5tzzp0TChcWBg0SvL0FQRDi4wVfX6F792++7vTp02lpaQqXlz2KFxeuX5daxDe5fl0oX14QBCE5WShVSggKEgRBOHNGqFnz+9a7efNmdNbHwb+oVk0oXfo7Zf4o794Jlpbi30dmptC4sdC/v1CkiHDxokSCvp8tW4QjR4SyZYXMzC8/4cWLF7dv31auqP/l3j2hQAFh82ZR4sGDgr6+0KiREBoq+PgIlSoJjRsLAQH/+Qb+A3d3wcJCSE1ViOT/YdAgYfRo8XZEhFC6tNCjh5A/v5CaKiQkCGFhwuvXnz99woQJitekWmh2sJSBnx+3b5M/PxUqsHTppyoBDZ+IjycoiBUrGDSIJUsQBCpXZvRoli5VspCs88HWrZUc9ruoXp2ZM1mwgAcP+PVX7O0xNcXfX2pZOaNlSxYuVHnzeQsLXr4kMxN9fdato18/oqJ4/lxem5wxMTRsiKcnnp6EhZGQIN5W9o8lJAQXF/HI1t+fV6+YMwc/P/bsUa4OOeDrS716ACdPSi3lvyhZkgMHWLiQ/PkpXpx27Rgxgr//pnFjGjRg1Sq6dmXePPz8vrnSy5dUq0aVKlSpwvnzADVqUKWKgr1gL1+mQQOAixdxc6NvX5Yvx8KCBw/ImxcnJ/LnV2R4NUBTg6VYdHU/jdfLk4fGjZk+nehokpI4cwagTBlxGOLPztOn2NpiYoKrK4aGHDpEw4ZUqsTmzUoWcuYMBQpgb6/ksN/L06e0bs2AAbx7h6OjHE10lIa3N61bq/zAx0KFKFuWxYvp359q1ejTBz8/EhIYOFAuy+fPz4gRYq1wSAjt24tlwVlVwsrj3TssLADOnGH6dM6dQ1cXS0vVGz2TLWQy+vZl8WIlT+jOCZUrc/YssbG8e0eRIrx6xcKFWFtz4wadO1OpEl5eODtz7JiYLf4HBQuyfDkZGURF0bo1Q4eKvz8KcSv78AF9fbS10dUlOZkVKxg3jpUradoUICUFPT0FRFVLNAmWYrG05OpVAF1dLCwwNcXBgQULOHMGfX3c3cUL4JgYwsN/Em/b/yBfPqKjycxES4vBg5kzh4YNeflS+ddAQUGSzu3KEfHxzJ/P6dM4OEgt5fvJ6iVUpOmBnFi9mkaNOHaMunXJzOTsWSpXllcXYZbtOBAUhLk5rq4S9V2VKcOMGURG4uvLmjXiIJcLF3B1lUKNHOjQgXHjiIpSeqqaI8zNRXeDU6f45RdWr6ZxY7p0YcUK9PVp25YjR76eYMlk4iXK6tUULUrZsjg7K0Dnpk1MmkRUFICHB+XL07cvBgafPoKy+kx/rIYsN6E5IlQ4Wc5qhoYMHsyIEYwYgbMzS5aQmMiRIzg5AVy4oMSWWtWkcGFKlhSbqn19uXePCxeYM4dWrZSpIjOT7duVHPMHmD8fLy/1za4uXiQoiG3bKFqUu3cJCiIoiO3bSUuTWtkXKVGC69dp3pxHj8jMZONG7t/nxg35BgkIkDQVcHHBwoJq1ejeHS8vBIG//uLkSZWx5Moxxsa0a6eyk6n/RXIyRkaYmXH4MLGx1KlDVBR584oOQN8iJoaAAIWNN5w/n+nTWb+exETevKFiRZYuJSYGR0diY7l7l8WLad2aRYtUwx5XJdDsYEmDhQXHjjF9OlWqsHSpaFj6s7N6NV5eHD9OvXpUqICnJ61aKdmP+exZLC3FUd+qzrt3LF7M2bNS6/h+QkK4dAkgJYVXr8R2wjx5+OUXVS3e0NOjU6dPdxMSaNuWM2d49Ij4eMqVE8/Xvpe4OI4fZ9AgRY8A/m9kMooXJyKCxYs5downT7C15dAhzMwkEiQH+vShbl3GjlWHk6tKlRg7ltRUDA3ZsYMFC3Bxwc4OHx+6dBH3h9zcmDTpi8UAixbRpg3lyyvgEyw1lalTuXhR3J06cYJly3Bzo3x5LCwYMIC4OCpV4uhRNfFcURKaBEsCrK2xsEBbmzFjqF+fdu2wsVEHW0tFU6oUN2+ybh1//03JkoSGMmECWkrdZA0KUvERIMD/10DMmUPTppQoIbWa72f4cPHGnj20bcuoUVSqJKmgnNKpE3/9hZ0dxYtjasr16/j5MWPGd3+TBwdTrx4TJ8pV5Dc5doxDh8RZeNraXLzIrVskJnL/PjY2FC2q7hsSpUtTrhzbtinCFFbelC9P1aq0a8eiRRQsSPfu/P03W7Zw4wYjRzJyJEBQEC4uHDtGuXKfvzQxkeXLOXNGMfWjDx9iaUnx4qSmMmUKa9eyfTuZmYwdy6lTjB+vgJC5Ac0RoQQsXUqNGgCtW1O1Kvfvc+IE+/eLQx6MjHjxQmqJUpEnD716sWIF8+bRpw/z5ikzeGYmwcGqfT64aRMODlhaYmzMzJm0by+1ILlRuDBbtkgtIqdcusT9+xgYMGsWISE8eMDjxwwe/N3rbdmiXPurjAz8/OjbF0tLXFzYtYt+/Zg9G2NjChXC3Z1ixdQ9u8oiq9Q9JoaYGKmlfJP16ylVCgcHbGywtEQmw80NKyvOn8fCAgcHxoxh4kRGj/7H61au5Jdf5JddffjA+PHY25MnD46O7NxJcrJYd3jtGn//jZsbycnqsCsoKVL7RCgbJftgZZPduwVHR8HGRh3tZnLG13yw/sHz50K+fMKbNwpW9InQUMHJSWnRcs68eUL58qIx2JAhgpubYGUlPH36HSuplA+WIAgHDgj16gl2djl1/JGaTp0Ef3/hyBHBxka0/ImNFUxNhYSEb7703z5Y0dGCubnw4YOCtH6J1asFNzchJUUMb2cn9O0r1KihRAVKIj1dKFpU6NlTmDTp04PS+2B9hcxMITJSNLMyMRFiYoShQ4VixYTQUEEQhDdvBFNTQRCEmBjh6lUhLi41VShSRLh0SU7R09MFNzehTRvh9m0hKUk4e1aoWlXQ0xMsLEQHuCz8/ISpU7O/qsYHS4NkFCkiNrru2iU+4ubGu3eSapIWKytatmTJEqUFDApSYfurrBqIXbuoXp2YGNauJSCAzp2VvMmnIOrXZ/t2jI1FCx+14d49qlTBwwMfH7p2JTMTMzNsbHj8+DsWCwykSRPllgoEB/P77+jpkZ6Ojw8dO4qearluC11bmx49uHiRzEyppWQTmQxra3GkWno6efIwaxZz59KmDR068Po1qanUr0/ZsnTujK1tgOfqksXS5dY5uGMHMhmbN1O6NAYGvHolDiERBGJiuHuXCxfo2JErV8SpBhr+A02CpUI0bMjBg/TvLxZhRET84Ewq9WfIEBYvzmYHzY+QkUFsLDt2qPD54McaCGD6dLFwr0EDsUpczdHSwtQUX191OyU0MxPPnP78kzdvmDABQeDVK/Ll+47FAgKU3quXNctSEOjZE2NjJk5ES0ucZZnr6N6d27dJSpJax3dQrRr79gE0b86dOxQpgrMzaWnUr8/Ll1y9KkRGzbrecETC2O8PER5Oo0aYmWFmRqNG7N5N06bIZNy7h7c3w4axcSMtWjB8OKGhNGvGgAGUKMGFCxgby+td5ko0Re4qgYuLeK3i5ERoKL/+mis/4nJO6dJUrcq6dfTsqdA4R44wfTqmppQpo9A4P0CWpx/w+DEbNnD9OpDLaiDatKF2bebOVZ+m2hYt8PencWP09AgOplo13ryhaFEKF87pSo8f8+DB162OFEDJkly9yr593LjB8eNoaREXp16zLLODlxevXgHIZCxbxrFjAFZWrFwpra5sM3ky3t5kZtKyJTo6lC0LkC8fixen2xbbTqu8efPq2hl5xAezoxq7dhEejpkZDRsyaNAnn+t/8Pw5Dx5gbU3x4ly4QPPmTJtGQADA9u30709KCq1bc/o0/fuzYQMGBixZgp3dp84UDdlAk2CpBIUK0bAhwJMnbNlC69Zs2kRMDP7+4sVw7dpUry6tRokYNoxOnShaVOxyKl1aEUHS0nj2TLUt9UuUQBA4c4alS+nXj0KFADZtEu0pcwUlS1K4MCdPUreu1FKySefOHD2KszM9emBigqMjy5ezadN3rJT1rz7rKkt59OlDgwaYmXHpEkZGxMfTvTu+vrlsW2LePBITAaZN4/BhFi9GRwcjI6llZR83N3bvZvhwuncHcHGhUSNcXXF0jOn7x+AHte2LZw4facoGOzp1YsIEBg0iNpZly6hRg8OHWbaMAweIj8fJidGjsbCgXz9OnqR0aZ4+pVAhZDLmzKFdOzGcjQ3587NtG3Pnsm6d+JN6946QEGbOlOyHoJ5oEizVIjmZ2FiA5s2ZN4/AQLy90db+ic8KHz7k6VNGjKB0aYYNw82NFSvkPptdEHjxQrUN3GUyFi+maVMyMggJ4cIFlizhyhUWLZJamTxp04bAQPVJsLS12bKFAwfYt4/4eGrVok0bhg2jcmVOn+b+faytad48O/OLAgKUYjWcns6OHYSFYWpKgwY8eYKODikpNG2KmRmXL9OyZe6o6vucjxdlFSoQFsb9+2L37cuXEorKIS4unDhBejqAjg5jxhAbyy+/cNA9tXx65NNY78G2xMfSsSO//y42ftapg48PFSpQrx4zZ2JqyokT1K1L/vw0asTTp+jrIwisXUvXrgQG8vAhR46wYgXp6YwdS58+nDpF3boULcqVKwwdSocOuWxrUwloEizVolQppk8Xb2/aRPnyPHzI1q3o/Jx/USdPMm4cc+eyaRNbtpCcTN++9OnD+vVyWX76dK5cAbh7l7Q0JkwA0NJi0aIfNIxUDL/+SsmSZGbSpg2mpvz6K0uXYmgotSx54uODszOLFil9L+dH8PLCy+vT3RMnqFCBZs1wdub2baZO5c8/6dLlKwvcvElsLG5uCtb55AlNmlCgAHXr8vo1np4kJnL2LA4OhIcTG4ujo2oPlJEDNWsyezbt2qmn+8THr4Fff8XPj8GD0TZ+n6o9cXYh7QKL8fXlwgVKlKBDB2rVwsEBQ0NkMjZuFF9Vvjx6evTvz4wZor9gXBympshkVKqEnh6enkydipcXcXEMG4azM23a8OwZpUoxcOCnLS4N2ebn/N5WGxYvpm9fOnZk/Xq0tcWCWoXM71RNVqxg7Fi6dWPhQk6fxt2dBQuwthY/F34YDw/Rp3POHCwtxR0sAwO5rK0A9u8nIYHw8FycbtvZUaoUR47QqJHUUr6PpCT27cPNDW1thg9HJmPoUGrWxNX1K+7aW7bg66t4S92uXWnfXqyhCQtj7Vqsrbl7Fyenn6T+oFo1qlbl2jWOHlXvwa/TQmqOefgAE/Fuv370w1uHFvvn6ngWCGfDBqZO5c4dYmLQ1+e33yhVCisrYmM5fRqgWTPS04mJ4f59atakQAGKFPmfDt5t23BzY/Tof7ttacgRmi5C1cXcHGNjgoOJjRV7wJctY9kyqWUpk4gIKlRAS4uhQ8WdPSMjbG159kwuy1epgrc33t5ERuLgIN5u0kQlt08yMhgxgunTc3F2lUXWKaG6EhJCqVLs20dEBH/8AVC8OH5+4higfxEfT/PmbNmieJPx6GjCwhgyBODRIxo3ZulSpkwR65p/Dry8aNSIIUOYNUtqKT/G6NEIAsKx4y2KXDXR+SD06y+EX0szL+Dp8AQnJ2bP5sQJXrygcGFq1MDLi9RULl/m7VvMzdHSonZtBgwQJwkePEjTpty4wbx5REby7Bnz5jFmDNOmSf0ucwOaBEt1uXGDfPnQ02PbNiIiGDiQzEz18XGRC5aWREYCdOzI7ducPUtGBi9eYGkpxyDXrpGWhonJt58pJevWkT8/TZpIrUPh+PqyZ496ttMD0dHY2mJgwI4d/PWXeD1kZ0d09Bef/v49Z86go6P4GUExMVhZoa3NvXt4eDB2LK1afUVYLqZtW+7e5epVqXX8MA/s6p5OrGRkacjChTg6MmoULVsSHg6Qns6KFbx9S9mydOjAH3+wfDkzZjBsGKmp1KmDlxdVq2JgwNu3HDzIxo1cvEjNmtSsycWLnDmDk5PU7y83kMuvhnMHhobs2YOHB9raNGggtRpl0qYNM2bQqBFGRowfz8iRNG+OoyMFC8oxyI4dNGgg3Xjdr/DhA6GhREVha8vEieq8sZMDLC1xdmb/fhX2JPsKRYty6xaAlRUnT+LhQWIiDx9+ZYJJUpJS7K+y9n1DQ/HxYdIksR/t5k2V/L1XLLq69O/P3Llqv481ZQpdunyqsGLYMPEaLDmZxERcXdm9m/btKV2a7t3R0+Pvv+nWjY4dadSIbt2oVImICBYupGtXmjeneXMp30wuRZNgqQENG/L6Nenp3LrFzZvs3QtgYcHBg1IrUzRt2nD+POXK0aEDpqZcvcqTJ4SEyDfIzp0sWIC7u3xX/WGOHaNrV0qUoEgRDh4kJUUlC+8Vgq8vgYFUrqyG3/5ubiQmsmgR/fpRpAinTlGzpljs8uABFy4AVKt2O80+KMg8b948aWkkJSGTsWIFWlo0bSrXCsuQEDZvJioKe3v69MHZGU9P1q7F1xfgwQOmTmXNGvnFUxt69KB4cX7/XVt9W0QePmT/fu7cwdHxs0e7dKFLF16/xthYdMA6eZLBgxkxAh0d8udnwgT8/Hj6lBUrCAzExobt23FxkehN5H40CZYa4O/P+/cA8+ezYwedOlGjhtydClQSmQx/fzp04OBBXrygc2fOnqVoUTlGiIjgxQtq1pTjkvIgKoq2bQkKonZtXr1izx4GDqRZM65dy/U1WEDLlgwdytmzXL4s381KxaOjw65dtGvH6tVUrEhEBBkZFCpE06Y8fy76Twwbdr/K5Jv6LQ3y6GTNpImMFE/CXVzkl2ANHcquXQweTPPmhIVRvTqZmVSrxqhR7NtHXBznz/PHH7nJRy37mJjQuTMrVhgOGqSuhs7TptG3L/nzf6m37/MrMQcH9u4lLY0PHz4179jZMXWqcnT+5OT+D+tcwMf2oxIlaNOGqVM5c0Zsf/spqFKFKlUABIHq1dm5kxYt5LV2cDDNmqmedXhAAN7e1K4NMHEifn6MH8/evZw5Iz6Yq8mXD3d3zpwhI0NqKd+BvT3nznHuHPfu0bYtbm7MmMG8eXh7i/tUcXFNW7WqXvI2I0b0758nb16WL5e3hnPn2LGDq1fF0sKICPT1SUlhxw4iI0UfrFWrfp490X8zaBAVKuTp2lU7IkL9NkqfPmX3bu7dy/YLdHVVtTU6l6MpclczbGwYN46WLUVv4p8LmYxJkxg3To5fvDt2yDFbkx9PnohTe27dIihIbJYuW/b7pgirI76+alvnDmhp4epK5854epInD5s3c+AAt2/TsyeZmZiaMmeO2fbtKSmyw4cVM9157178/DAxQRAYM4aFC7lwAVdXTp6kQgU6dKBp0585uwKsrfHwSFm7Np86XrD88Qe9emFuLrUODd9Ck2CpE9WqUa0afftSubJYpQo/z3cuAA0bki8fmzfLZbHoaG7dUslDkoIFefoUQaBPHyZOJH9+QJxrkas5exZPTzw9Wb2a5GRatxbvrl0rtbIf4ckTqlTh0CEePaJpU6KjKV1a9/nzw4f1HB3l5xQbGUlwMMHBREaSkEC+fDx5gqcnJ08SGkqRIuTPT3y8nILlBnr1SgwKMs1yR1cjnj5l+3YGDZJah4ZsoDkiVCc++kUvXUqtWsydS7t21KrF06eSylIy06bRoQPe3rx5Q4ECP2JatXMnXmmwXdoAACAASURBVF7/OQ5VSry9qVULCwsSE8VB1wcPcv8+tWpJrUyxODoyYoR4+8wZypfHx0d8XI0pVIjHj3Fw4NAh5szB0ZHhw9MtLHb+8aTzu7UtEtbjkI+BA+nV6zvPqjMzGTOG1atFM/jevalcmcuXmTqV3r0ZNw5tbTIzOX+eAQPk+87UmrJl04sVS713T22+BK9dA1i+nO7dxWsuDSqO2vxuafgcAwO2baN6dWxt1bNO5UdwdkZbG3Nz8ucnNpYWLZg9+/u2dnbu/PoIE+koVYrx4xkwgJYtmT2bK1c4e5YtWxRznqRC5M2Lh8en29eusWKFpILkQrt2jB3Lpk3o6jJiBO7uNGyYkGp0OtN+05VBJmVmcf06gwZx/fp3+gj7+xMayq1b4rfunTu4uhIXx5AhjB+PlhaJiQwdip0dzs7yfWdqyrp1bNxIamq+d++EuDg8PMTJOZMnU6OG1OL+m+BgEhLYsoU7d6SWoiF7aBIsdcXOjq1badVKPYdq/QgdOlCsGB8+cO8eMpnYCXX1KgYGOVomLo6zZ9m6VUEqf5iwMLp0oWJFnj2jQQNWrfo5Gkc/YWBARATqWIP8T8aPp107KlakWTOAnTtxcAi8X8cz9ZjJEy3K21GxIvv2YW/P0KHExYlF6O7u/9lC+fw5a9Zw7x7W1rRpw/LlbN4sZldBQfTvT9OmnDzJ5ctYWWFnx/37tGypwr/rysbTE2tr3r59HxWVPHx44WrVqFMHHR0qVJBa2bc4c4YuXeRrtKxBgWgSLLUk6woMyJuXiAi1uQKTAzducOkS9+/z228sWcLQoUydyrVrbNlCp045WmnfPmrXxthYMTp/kLNnOXiQmzdV3mBegbRoQUYGmzYxdqzUUn4QAwO2b+fUKc6cAVi2jB07NsT07tf2JX3a4uXF0KHY21OzJj4+vH9PrVq8e0ffvkyYQJ8+HDnCoUPExlKxIl27cvQo3bvTti316vH4MV5eREdTtix79uDvz4sX7N1LhQqYmvLoES9fEhmJvT1mZlL/FFSIwoUpXJiXL1Pv3ftgakpQEJMmqYH/yfv3XLvGzp1S69CQbVT+d0rDl/DwEMfev3mDnx82NrRvD1C+vLS6FM/Vq7i7o6vLlCn88gvdumFmRt26hIXldCVV7B8UBID0dHr1Yu7cnzm7AhYt4uJFOnZU/wQri1q1PpbQPd146s6rgrUHGDMqnD//xNWVihW5fBlnZy5eFL/qnzyhbl22b+fFC7p2pWxZjh1j1iwSEzl0SDQuAdq2pXRpihXDzo7+/fHxQU+Phw9FQ61ChXJ9Y8QPoq+PrS3r1tG1q9RS/oNixf6nk8nKCqBkyZzYNGiQCE0XoVpibY2HBx4euLtjbs7+/eTLh4eHqu7HyBEDA9GgonRpWrX6v/buPS7n+//j+OMqOkc5VEiliDmvnEbkzJzHhMlhzWkYc5oY+1mG2RjmfJzjKGcJc2zO5pTDclhIkRyjROfr90fXlu/GVrq6PnVdr/vNbbfrqs/1eT+bdL16f96f1xt/f4DExJwuTkpKYv/+/LSz39mztGhBkSIUKUKVKhQpQteuSmdSXp06qNWcOaN0Dm1bn9y5s8WuwkZp2NgwfTpRUbz/Po8fExZGQIDmphVnZ7y9uXRJs0mznx/r1tGpExkZ1KpFairnzjFoEHXrUqwYVlacOIGvLyYmZGTwf/+nadcu/pW1dcYHH/Dtt0yeTHKy0mne4NYt1Gpu3MDCgtGjUatRq6W6KhikwCrwjI359ls++YTUVKWj6ECjRhw+rOl7PXUqO3cSGsr69VlLo7Nn7148PPJNJ6Djx2nbll69iI3l9GliY7l+nRMnlI6VL3z00Su7remLdecr+5QJtenTh99+48EDQkNZtAg7Ow4e5OlT3n2XChVo3pyQENRq1q8nNJTjx1m1ips3SUigfHmKFqVnT0qX5soV/P1JTcXTkylTmDIFT08eP2bSJKW/ygLA3Dxj3jxq16Zatfx+O8WYMdSvj6Wl0jlETsglwoKtaFE6dcLPj02bmD5dXy6m/At7eyZOpGFDJk7Ew4Pu3WnThs6dadYs++fo2ZMnT/LT9cGJE5k9m+7dAfz9GTsWV1cmTmT/fqWTKa93b+rV4/vvc9OOI38JD+fZM8psH5iyY5vJp59y5w4VKjBmDF98QcWK/PgjM2YQGcnt2/TqhaUlBw5w+zbJybi74+iIkREzZtCmDSYmmjNevsyoUbi7c+QIwLRptG6t4BdYEE2dSuvW+Pnl0wrm5ElOn6ZXL6VziBySAqtgs7Rk/nyAZcvw8KBjxwJwI0xuDR9O7dr8+CNz5+LoSMWKOV16Fh/PiRP56RfWU6c0K1e3bePaNYKCSE7O6iRr2FxccHNj3z7atFE6ipasXs1HH6EyKfRi0CCrr77K+kRQENOmMXEiJia4u1OyJCkptG/P0qVZx8TFsWwZJ07Qrp3mIxs28MsvzJhB8eK0aqXTr0SPVKtGgwbMm5fVhi3/UKsZPZpp06hSRekoIoekwNITpUszeTJ9+nDqFBs34uWFk5PSmfJO/fpZ+zPfukWdOvj44OqazVc/foy9PWXL5lW6HDMyIj2de/cYPJiNGzExITEx/+2PqBhfX9at05MCS60mMJAdO173uRUr6NiRffto2pSnTwkKomNHQkI4fZratQHi4xkwgJ49uXKFcuWoXp1btzAzIyRE+k7m3jff0KABAwfmuxsug4J48YIePTCSFT0FjRRY+qNfPzZtYsYMTpzA2lqvC6xXlSvH6NEMHsyePf9yVHw806drmrKGh1O2rGZ9fJUq+WDi3dubwEA2b2bQIBo0AAgK0vum7dnXrRvjx5OQUODv4Vi1imvXsLamWjXCw//x6TJl+O03goMJC8PFhf37qVyZ7dvp0oVSpbC15dw5unZl5kzMzLh5k6tXcXSkalV549UKd3fatWPWLOLj6d6dunWVDgRASgrjx7N8ufwlF0hSYOkPlYqlS6lVy/BmkkeNYs0amjfn/n2ABg346itKl371kMze75kF1osXlC+v2So1X7xnT51K/fqULMmCBdy6xcaNzJzJgQNKx8ovihWjcWO2bKFPH6Wj5M6tW+zdS8+ebz7CyIiOHTX9SDN17EirVly8SFwc1atr7tEHXF2zP2Ursun//o9atahViwcPlI7yp3nzqFKFxo2VziHeihRY+uPZM6ytGTeOSZN49oy4OAAzM73fXgX++IPYWKKi2L2bIkXYvBlPTw4dolKlvw6xtGT0aICwMCZPxs8vP/VoSErC1JR336VlS4AGDTh1ChcXhVPlJ76+LFpU4Aus9HSuXMl5/wQzM+rUyZNA4n+5uODjw969SucAwNubVauYPp1Dh5SOIt6WFFh64t493n2XlBSAhAT69cPCAqB9e1atUjZa3hs/nkmTCA9n7VoWLqRaNUqUYNw4tm7957HBwW/cgESnnj4lIgJHR6ys8PVl2TI6dVI6U/7Vrh0DB7J7NyVLZrXYLCg2b+bxY4A9ezA317x/JyVZZ942KvKDly9Zt46MDFxciIxkyxbu3QNwdc1pBxitiYhg2jS6dKFyZWUCiNyTAktPlCpFbKzmcZMmhIVx82a+W62ZVw4dYvlyjI2pUgVfXxo0oEePN7Ws2LGDypUpVkzHEV8RF8fIkWzbhpsb0dGoVDRrJtXVvzM1pXNnZs2ifv2CV2CdPEl8PEBEBEWLcvYsQGqqRffuhrZPe/6VnExYmKaVoJUVe/ZommAouNNrejqbNnHlimIBRO5JgaWHrK2pW5cpU/j+e6Wj6EZqKqamWFqyYAG+vpw+jZkZaWn/PDAmhshITpxQdN+xDz+kUiXu3MHSkp9+4ssvOXKE+HgD3xjnP/n64uOTdfNoAZL5z/DRI1avZtAgpk0DCA+/D/mk0a3AxoZ58zSP79whLIz27bNaYehMdDQ//6x5/OQJDRrw008ALVrg4aHrMCL35M4E/dSzJytXcuuW0jl0o1Ytdu8G6NCBHj3o1o2QkNdOdAQH07q1otXVmTPcucPcuVhaEhHB2LHs2UODBqxfr1ymgqFhQ5KT89Hq45z6+Wfc3TE1VTqH+C/GxgwZwpAhJCToeujEROLiiIvj9GnS06lYUfP0yRNdJxFaITNYemj8eCpVIioKf38CA5VOowMBAZouMR068NVX1KtHv36EhPzzwB076NtX5/FeFR5OvXoYGfH8OV27EhBA9eq89x6//65orHzNzY2bNzWPFy5k4ULNByMiFAyVYytXUru2FFgFgLk5dety4wZffsmPP+p06EqV+PZbHj2iRg2KFfvnzdCigJEZLD1Urx42NowcyalTHD2qdBod8PZm0yZmzsTGhuLFMTHB2pqHD/92VGIix44pvYmItTVPnpCayocfUrs2gwYBPHlC0aKKxsrXbtzQbHA7bBgWFiQloVYXsOrq0iWePGHuXEaOVDqK+C+rV9OsGT/8wNatHD+uQIAhQzTbdouCTmaw9Ja5OZMnM3o0J04ouVRTR+rX59gxzV2UJiZcuEDLljx8yJEj3L2LuztDh/4SUf2995RufNW4MQMG4OODiQkLFgA8e8aaNaxbp2isgsHWFjs7goP58EOlo+TQ8uX06WMADVP0QuYsY9GizJjBoEGcPavTfTDXr+fSJVatIjhY5jsLPJnB0me+vqSnExSEWs2zZ0qn0QETE83vfTVqUK0aw4fTsCFff8077/D++8EzryvW++r5c2JiAGxtqVOHkBA8Pdm7lwUL8PSkSxfq1VMoWQHj4cHy5UqHyKGUFNavp3dvpXOIHOrWjXLl+P57zp5lzBhdjHjvHiNGsGoVZmaEh8sGSAWezGDpM5WKGTP4+GMsLFi5ks2blQ6kM0eOEB1N797s3s3AgXh7Z7TvuLui9aT5cWCr0yRhYQwfzvnzWFuTmoqXF7dvc+wY69Yxfz5lyrB8Od7eOo1UYH34Ie3b07o1t2/j7Kx0mmzbuZPKlXFzUzqHyLm5c/H0xMaGa9fycJR797hwgdat6d+fQYM0O08KPSAzWHrO25saNdiyRdPixVDs3o2vL/Pn8/Bh5m3xx2Ndy1jHO9/UbVPkiAhat8bPj2fPuHuXMWPYtYu2baldm9mzCQlhyRKprrKvalU8PenRQ3PvekGxcqXSt1aIt+XkxMSJmvsq8s6ZMyxYwPLlxMTw5Zd5O5bQJZnB0n/Tp1OnjoFdg0pMxMEBExM2bsTLC3Pz4NgR7ZwvkZio0xizZzN4sGaHlz17+OEHdu+mc2cCAmR5xVvr14/27fnqq4Kx/e39+xw9mtXcSBQghw9z9Sqmpjx8yNOnLFkCYGpK9+7a/+f78iXjxnHwoE7Xe4m8VhB+RIm39d13+PgwYQIWFhw9io8PPj707q3ZuEOfVa3K4cMAZcpw+DCLFweveNjhyUqqVdNpjLAwmjYFCA2lTx+2bKFJE0qV4sYNncbQL9WrY2+fXzaM+09r19KpE1ZWSucQOXfhAmfPcu4c5ctz7x4hIZw9y8mT2v81Ta0mLIxRo6haVctnFsqSGSx91rgx5coBODiwcCHNm2Nri5GR0nfS6cBHH/Htt3z3HSNGULbsH/N+SWiV6uF0ETs7vviCsDBsbGjdmr5983YaxNyc589ZsoSvvmL9et57D+D5c80+keJt9evH8uVKd9zInpUrmT9f6RDirXz2meZBcDBTp3LqFIcO8c47Wjt/165s2pT11N8ff3/Mzblxg1KltDaKUJDMYOmzOnXo2pWuXWnRAicn/viDrl3p0sUAOqxYWnLwIMeOUbIkVatub7ukQ6XrKitL3NxQqRgzhq5dWbeO5s1JTtbmuH/8gZ8fnp40a8b339OkCSNGMGMGoaGaqax9+zA3x8VFm4Mano8+4uDBAtDV/fRpEhNp2FDpHCLXSpZk1ixatSI6Wmvn3LgRtZoZMyhThpYtNc3eXryQ6kp/SIFlKNzc+OknHj1SOofOODuzfTu3bxMYGFxncvuZjUlLo3Jlrl6lYUO6dmX/fqysWLRIayPu3YuXF5Urs3Qp48dz7BjTpxMTQ4UK3L7NqVNMmULPntoc0VBZWdGxI6tXK53jX7VuzZIl+PkZQBc6fWdqiokJPXoweDBt2vD0KcCECbx8mdszz5nD4sVMnSprMvWTFFgGoUwZ6talSxfmzlU6im7FZRSt1r3KxctGjV2jSEjgxAkKF6ZjRxISUKkYMECziWHuqdUMHsyGDYwejYcHjo5cuUKpUowZQ6tW/PADw4dz5w6nTtGkiXZGNGyffMKyZajVSud4s4sX2bpV2l/pgxYtNDeu+vvTtCkffEByMj/9RFzc25xt9GhOnwZYvpxZs9i3D1vdto4ROiNrsAyChwceHty8SZ06jBxpQPuyvHzJnTs0b45ZagI2NpiYEBjIsGFUrcrs2djZkZDA/Pns3s2zZ9SsyZgxODll9+ypqYSFcfcu5ctjYUFqqqZ4CgnBz4+pUylThpkz2bePYcPy7ms0TA0aYGzMsWNUrYqNjdJpXicpiWrVcvDdJPItlSpr3eqsWfj45KrvxvXrxMayahUBARw6hLMzFhbS5V8/SYFlQFxdadOGhQvx91c6ig4lJ9OuHbi6cucOsbE4ODB/Pt26MWgQajWPHrFrF59+StGiHDpE7doEBWWrN9XJk/j5YWaGszOXLmFnh4kJly4xdiwREWzaRMOGHDmi5TVe4hWffMK8eZw6xa1bSkf50927WZuMP39O6dKae/vr1KFmTQVzCe1ISeHSJUaOZPBgnj7l4kXu3QNwd8/ZnUOHD7N+PQcP4uoKULIkzZvnSWChLCmwDIu/P82aMXy4nv/C9Ouvmkt/z56RlMS5c1y5Ym5cdfvHHUeV3zgNJycaNeLrr+nVC7Wa2rVp2RITExo2pG5dBg5k/XrmzeP6dcqUwdeXdu3IyCAwULN1tpcXTZrQqROLF9OxI0BGBmPHMnMmTZowZgxbt2qWVOzfL++readXLwIC8td38rNnnD0LEB9PWhoqleap3NWgH06cYNQozeOXL/HxwdkZU1M++YRPPyUwEKBbt6zjU1P56ScGDCA5mXXrSEsDCAvjwAHGjCE0lAcP8PLS+ZchdEUKLMNSuTINGrB0qZ5fsypcWLOsISoKIyNKlwagXSPjuCvUrImDA0+fYm9PjRoMGkRQELVrM2MGTZvSqhUPHtCmDePG8fHHREYyfjybN2saDvr4ACxZwrhxtGypqa6ePWP6dFauxNKSYsVo0wZTU9LTWbGCxYs5eVKx/wv6rmRJGjXS9DvLJypXZvFigNGjsbRkxow/v/eEXvD25swZzePSpenfnwULGDRIc8XwypW/H//wIV9/zYABJCZy+jR37nD6NE+eULs29+5x755m9yyhr6TAMjjjx9OpE4MG6XOzhvr1qV8f4JNPsLRk7NjMD6tgEFP6ERFB0aKUKoWXFxUqsHs3QUGMG0dUFC1a8OwZ27fTrh2AlxedO1OmDN7ebNumOfvgwVSrxvXrrFrFgQPs2UOHDly4wPjxGBnx/vukppKYSL16HDggcxd5YfNmzWzBgwckJGjqXmNjvviCd99VNhpAYiKrVmFpqXQOkZdUKgYOZMAARo2iShVmz/63gyMiiIggMpKZM9mwgQEDUGzjeaFDUmAZHA8PqlZl9WoOHmTxYj1vOrp/P2Zm//uhQoWoVEnzuHp1QkPx8tI0uY+KYuxY1Gp8fWnRgg4dNB1pUlIwMeHsWQoVIjKS/fuJiSEuDicnmjcnIEBTRcXEMHw4K1bw4AHW1vnr2pV+qVaNjAyAJ084c4Zq1TR/pY6OyubSWLsWLy/Cw+Xee32mUqFSUbo0/frh7s7gwWRk4OZGRgbm5lhb06ABL16QnEzbtly4wNixDBpE4cKa3w2EIdCTAislJWXkyJG7d+++d+9ehQoVJk+e3KFDB6VD5V/jx/Pxx7x4QUKCPhdYv/8OaJaRvt6IETRsiKsrPXqgUpGczJkzVK/OgQMEBxMcrLkP++VLQkO5eZO0NOztad6cH3+kVy9mz866AnT8OJcuaVbH29nl8Vdm6NzdcXcHiIlh7FjOnWPiRKUz/UmtZt485szBy0ufJ4lFSAgODgCBgTx7Rr16HD1KWBjXr5OQQFISKpWmd2hoKCYm/N//UakSLVpgaiqVt6HQkwIrOTlZpVIFBgY6OTlt3brVx8fn8uXL5cuXVzpXPuXlRenSXLqkdI48FhxMx478+OObj8i8Pjh0KEOGYGNDQgJ+fmzeTNGi9O2bdSt20aL068fUqVkvPHECBwc8Penbl3LlOHeObdtYtUr2nNM9CwuOH+fq1ax5SWUdPIhaTZMm0l9Uz9WooXmwdKnmwaRJWf/NFBND7drcvfs/L1y7VipvQ6EnjUatra3nzp1bq1YtOzu7gQMHOjk5nTt3TulQ+dHjx2zcyMaNNGpEfDzBwZqnERFKJ8sDu3bRps1/HfTuuxw7xq1bHDrEw4d89x2VK/PJJ5q5q9RUpk7FzIzdu7P2yIiKYsgQvv6a0FAsLTl7lgoVuHyZVq3y9MsR/2RtTaNGDBjAvHlKR/nTvHl89plUV+KNTE3l28NQ6MkM1qtiY2MjIyOrVaumdJD8KDKSjRs1j9VqVqzA2VnzVM/m+x4/5uJFGjfO3tE2NlndKtev58svcXLC0ZG7d2nWjNOnCQrCw4PMb6rMZlf9+wNMmJAX4UU2WVuzYQOxsVSpQkAAxYopnCcykqNHWbtW4RhCEYX08O1U5IpKnZ83m8i55OTk1q1bV6lSZd7rfqU9c+bMxIkTnf+qKaBUqVK9evXSYcB85N13XapUSV679p4uB01OTn769Km9vX1eD7Rtm9Uvv1guXHj/7V6uSk0tFBWV7uCQ8efNYEbx8abh4UBy5coZRYpoLagS7ty5U7p0aSMjPZnABvz9Szo5pQ4e/FTZGN9+WwxU/v6P//PIR48eWVhYWFhY6CCVeK3ExMSkpKTixYtr64QvX6oAc/Ost9T0dH791aJp0xfaGqJgWbNmzb17We8vZ86cWbRoUa1atRSMpGMFuORetGjRp59+Cnh7e4eGhgKpqak+Pj4lS5acM2fOa19ibm5uampq+8rOT7a2toUM9fcOMzP1tWsmUVFmrq5pOhs0PT0d0MH/89BQq+bNk95+oEKF1BUrGr16Eb1YsVQvL8BIL66sFypUSJ8KrP79n/fsaTdwYKKpqWK/MSYlqbZsKbJtW2x2vuuMjIyMjIwM9odPfqD1v4J/3jBUqBAtW6YU6PfZ3LC1tU1KSvrrqbm5ubmB3VutPzNYaWlp3bp1S01N3bx5c+HChd902Oeffz773zuWGAwXFzp2xNiYH37Q3aDx8fEREREeHh55OkpaGnZ2XL4sbR5f7+jRo/Xq1dOzd/fWrenRgz59FAuwdCk7d7J9e7YODg8PL1GihJ3ccKqc2NjYp0+fVsonN0cYgEmTJk169RYAA6AnP2HT09N9fX3j4uK2bt2anp6enp5euHBhY2NjpXPla+fO8fw5Hh4EBOjb3W9HjlC+vFRXhmXUKEaOpHdvBVYQnzzJmjUcPcrMmboeWgiRb+nJNYLo6OjAwMBDhw7Z2NhkzkPOnTtX6VD5XbFimk359G9NbkgIbdsqHULoVosWGBuzf78CQz98SFgYqak0a6bA6EKI/ElPZrBcXFz05lqnjn32GUOHMnCgXt05vHMnP/+sdAihc59/zg8/sG8f3brh6anToW/dYuJEvfpHJITIJT0psMRba9wYlYrQUJo0UTqKlkREkJCQL/akEzrWowdffklSEg0b6qLA2r+fmzcBjh3jwQPS0liyBCMjevaUfZKEEPpyiVC8NZWKoUPzUZ/G3Nu5kzZtZC7BEJmaMmSIpujRgRs3OHuWs2c5dAhLSy5f5uxZLl4kOVlHAYQQ+ZnMYAl8fZkwgagonJyUjqINISEMHap0CKFbKSkEB5ORgYMDMTHs3Uvm7eFly1KvXl4NOnAgwPXrBAZSvz6LF+fVQEKIgkgKLIGVFb16sXAh06YpHSXX4uP57TeaN1c6h9CthAS2biUlBcDMjM2buX8foF69PCywMk2YQMeOmq2VhBDiL1JgCYChQ6lfHw8PTEzo2FHpNG/r4kX27sXLiz+7rwtDUbx41s2w77/PyZNMnIgOtss6c4bjx1myhFWr8nwsIUTBImuwBICbG56erFvH+fNKR8mFLVtYu1YaNBi6woXx8WHECF2M5e/PpEm0acOaNboYTghRgEiBJTQ++4xTp5QOkTtqNRERtGmjdA6hqMxZ2Pv3CQnJ24H27iU6mr59NYMKIcSr5BKh4MwZnj6lUCFevODUKU2rxuLFC16ngzt3sLLCxUXpHEJRK1ZgbY2JCUOH0rIlb943K1fUasaPZ9o09GvDISGE1sjPBsF332mW6BYuzLFjpKUB2NoSFKRsruwqV47IyKynmQ0aKlTg+nWFAglFFSkC0Lw55cqxcCHDhuXJKEFBGBvzwQd5cnIhhB6QAktkFVJjx/LjjwQFYWuraKAcunVL88Deng4dWLpU0TQi35g1C29vevakeHFtnnbAAHr2ZMIEFi+WdmtCiDeSNVgii7k5bm6sX690jrdy+zaJibLBs8hSqRI+PgQEcPMmq1dr7bSxsWzYQPnyNG2qtXMKIfSPFFgii7ExtWoV1H6J27dTsaLMKIj/ERBAYCC7d7Npk9bOmZ5OUBBTpmjthEIIvSSXCEWWoUPJyKB2bc6dw8ND6TQ5tHMnvXrRuLHSOUR+YmuLvz8rV1KqVK7Ok5jIwoWkpwOcPk3Rouzbx759VKxIp05aSSqE0DdSYIksmUuv/PxYvryAFViZDdy3bpUWoyLLkyc8fUqbNkyfTmqqZo9CY2OcnXN8qvR04uJITyc6midPqFVLc19IQoKWMwsh9IYUWOLv+valZk2+/x4LC6WjZNuePdLAXfzd2LEcPAiQnMzFizRpQqFCGBvz6685ntAqzEH8TgAAESxJREFUUoQpU4iMpH596tTh009p3z4vIgsh9IeswRJ/5+hIvXraXLOiAzt2FOAdfkQeWbqUGze4cYNVq3jnHaytOXOG69ff8nLhy5d8+CHjx1OihLaDCiH0kRRY4jU++YTly5UOkW3p6fzyizRwF//GzY1WrejUiaSknL3w2TMAtZq+falalaFDsbbG2jovMgoh9IoUWOI12rcnIoIrV5TOkT1HjlCuHGXKKJ1D5FeZ95bOmIGzM927a9aqBwZqeur+i4cPNfsZBARw547mBtt16+ReCiHEf5MCS7xGoUL06sXKlUrnyJ7gYFkQI/6NtzeTJ6NSsXw5L17w2WcAI0fy4MF/vDA1leRktm1j6VI2bsTUVAdhhRB6Qgos8Xr9+7N6NampSufIhuBgOnRQOoTIx6ytqVEDoHBhNm3i5EmmT3/NYfHxxMf//YNpaQwcyNat0sNWCJEzcheheD03NypWZMcO7O3x8lI6zZtdvUpyMtWrK51DFBBFirBzJ15evHz590/9+CPAhAns2EFICMCNGzx8SNOmLFvGsmUMHqwp1IQQ4j9JgSXeqF8/Fizg2jXu3FE6yptlXh+UBu4iO/bto2XLrKd/rdv77jvGjMlaklWuHGlp7NtHWhoWFvj4ABgZ5bZbqRDCoMglQvFGXbpw/vx/LwRW1o4dcn1QZFeLFqjVmj+lSrF4Me3aUaQIp08THExGBikpzJlDu3Zcu8b8+Zqm7QMGMGAA/fphZ6f0FyCEKDhkBku8kbk5HTuyebPSOd7s0SMuX8bbW+kcogBSqWjXjgED6NyZCxf45RcSEwFKlsTZmXLlaN+emBilUwohCiwpsMRrzJmjWY/y8iUJCbi5aT6+dClNmyqY6+927aJ5c7m3S+TKF1/w/DnA/PmoVAweDGBlpflv7dpKZhNCFFxSYInX6NdP0/jgwQMaNmTSJBo0AHByUjbX/9i/n+3bZatd8ZamT6dkSYB69TQfOXoUoHnzrGOKFGHbNp0nE0LoBSmwxGtYWuLqCmBmhqUlu3fTq5fSmf6hd28SEzW9H4XIKV9fpRMIIfSaFFjiP5ibs2cPcXHY2iod5X+lpFC5smwMJ7RGmn0IIbRICizxb4oX5/PPuXiRn39myBCl0/yvpCRatFA6hNAjnTsrnUAIoUekTYP4N6amjB2bj/Z+PnAANzfNn8REli/XPJ49W+lkQgghxCtkBkv8tyZNiI/n/HnNxrfKJtm/H7Wac+fo0YPNmzWtiRwdFQ4mhBBCvEpmsMR/U6no3ZsVK5TOAUZGlCuHqyvHjmFujpMTrq64umJionQyIYQQ4hVSYIls8fNj/frXbN+mCLWaLVswN1c6hxBCCPEGUmCJbHF0pFYttm9XOgcAx45hY8OYMRQvrnQUIYQQ4nWkwBLZ5eeXL64SAhs30rUro0dLD3chhBD5lBRYIrs6deLCBW7eVDhGRgabN/PhhwrHEEIIIf6FFFgiu0xM6N6d1asVjnHsGCVLUqmSwjGEEEKIfyFtGkQO9OtH27ZYWtKuHe+8o0yGzOuDQgghRH4mM1giB6pVw86OLVuIiFAmQOb1QSmwhBBC5HNSYImc8fMjOlqx0Y8cwd6eChUUCyCEEEJkh1wiFNmSkcHRo6SkUKYM9+9z4oSmDZWLC+XL6y6GXB8UQghRIEiBJbLl4UOmTCEjA8DYmNWrOX0aoHZtpk7VUYaMDLZs4fBhHQ0nhBBCvDUpsES22Nvzyy+axw0bEhHBL79gpNsrzIcPU7q0TifMhBBCiLcja7BEjtnaYmXF3r26HleuDwohhCgopMASOWZkRNu2zJ+vuxFfvuT6dbZulf6iQgghCga5RChybNYsbG1xd+fmTVxddTHiwYNMnUqZMri56WI4IYQQIpdkBkvkWLly2NjQty+LFuloxIwM7t6V64NCCCEKDCmwxFsaMoSffuLFC12MlZFBbCxduuhiLCGEECL35BKheEvOztSrx4YN+Pnl1RCff87RowD37pGWRrduAMbGbN+Og0NeDSqEEELknhRY4u0NGcK4cXlYYI0aRa9eAH37YmnJ4sUAxsbY2+fViEIIIYRWyCVC8fZateLFC06cyKvzly2LpyclShAVRYUKeHri6UnNmqhUeTWiEEIIoRVSYIm3p1IxaFCe92uYP59mzTA2zttRhBBCCC2SAkvkyscfs2sXly/nVd/Rly9ZuZLBg2ndOk/OL4QQQuQFWYMlcsXGhg8/ZPp0nj2jZUvtn3/tWt57j+bNad5c+ycXQggh8ojMYIncGjaM3bs1+0Br3bx5fPZZnpxZCCGEyDtSYIncqloVe3vu39f+mX/9ldRUmjXT/pmFEEKIPCUFlnh7XbqgUqFSER7OmTOax6am3LunnfPPm8eQIXLPoBBCiIJHCizx9jZvRq1GrWb7dooWZcsW1GqSkylVSgsnv3uXgwc1fbCEEEKIgkUKLKEFKhWVK+PvT2qq1s45fz69e1OkiNZOKIQQQuiMFFhCO0qUwMWFJUu0cKqICJ4+5aef+PRTLZxNCCGE0D1p0yC0oE4dTE1xcKBVK3r1yu2006hRuLri4YG7u5byCSGEELolM1hCC+ztadmS6tVp3Zrvvsvt2dRqdu6U7gxCCCEKMCmwhDZ98w2LFhEdnauTPHnCixd50rZUCCGE0A0psIQ2lSnDgAFMmpTjF8bGUrcutWpRqxa//UZKCnXqUKsWI0ZoP6QQQgiR12QNltCyceOoWJHz55k+naVLsbbO1qvs7Vm8mPR0tm3j6lW++IKmTQHs7PI0rBBCCJEnpMASWmZtzbhxfPklFy6QkJDdAkulomZNIiJYvJhatahUCU/PPA4qhBBC5Bm5RCi0b9AgIiJITs7Zq5KT8fFhyhTpfSWEEKLAkxksoU2PHnHoEED79syZw44dFC8OUKPGf/dc8PfH1ZX+/UlJkQYNQgghCjbDmsFasWLF77//rnQKfRYdzcaNbNyouZHw66/ZsIGNGwkP1xxw48aNSa+sgU9PJyQEYPdutmzR9CkdMoSKFXUc3LB8/vnnyTmdYBRaNWfOnBMnTiidwqCFhoYuXLhQ6RRCnxnWDFZUVFRCQoLSKfTZu+8SFKR5XKYMjRoRE8OOHRQtqvngkydPIiMj/zr+/n0GDOD8efr1Y+1aihXTdWDDdPXq1aSkJEtLS6WDGK7o6OgHDx4oncKgxcbG3rlzR+kUQp8Z1gyW0LEZM6hTBy8v7t4FmD2bzZvL/vMwPz/69aNJE13HE0IIIfKIYc1gCV0qXBgTE77/HkdHGjVizx6ePiUxsfDfDnv+nIcPmTBBkYxCCCFEnpAZLJFXwsIoWRJg+HDGjaNJE2JjNZ+aNAlra8zNcXYmPp5r17C3p1gx9u1TMK8QQgihNQY3gxUfHz99+nSlUxiWEyfeTUkxtbcvvmzZO2ZmxZOSQq9cSbO1ja9c+Y/ixeP27m34+efLMo88ezbp3DllwxqKhQsXFi7899lEoTPx8fFnzpx58uSJ0kEM17Vr1+Li4uTtQGeOHTumdARdU6nVaqUz6M6FCxeAGjVqKB3EsMycycOHAEePkp6eXrr0zQoVKpQsyahRxMRQu7ZmhZbQmbVr1/bs2VOlUikdxHAdPHjQ3d3d0dFR6SCGKzIyMjo6umHDhkoHEXrLsAosoazM/gyv7lQoBZYQQgi9JGuwhJJKlGDiRKVDCCGEENpmcGuwhIJsbP7+ERMTBg1SIooQQgiRl+QSoRBCCCGElsklQiGEEEIILZMCSwghhBBCywyowEpISOjevbulpaWjo+OiRYuUjmNwUlJShg4d6ubmZmFhUaNGjR07diidyHBFRkZaWFi0bt1a6SAGavXq1RUrVjQ1Na1YseLp06eVjmOIwsPDmzZtam1tXapUqdGjR2dkZCidSOghA1rkPnLkyAcPHkRGRl69erVNmzZVqlSRDii6lJycrFKpAgMDnZyctm7d6uPjc/ny5fLlyyudyxB99tlnnp6eSqcwUDt37vziiy+WLl1at27dqKioEiVKKJ3IEPn6+np4eOzcufPu3bstWrSoWLFi//79lQ4l9I2hLHJPTU21tbXdtWtXo0aNgH79+gHLli1TOpfhcnd3/+abb3x8fJQOYnC2bdu2YsWK+vXrh4aG7tmzR+k4BsfDw2PYsGF9+/ZVOohBs7W13b59e+bbQf/+/S0tLWfPnq10KKFvDOUSYWRkZGJiYs2aNTOf1qxZ8/fff1c2kiGLjY2NjIysVq2a0kEMTmJi4tixY+W9RCnJyclhYWGxsbFlypQpVarUsGHDkpKSlA5liEaMGLFmzZoXL15EREQcOHBALpeLvGAoBdbz588Ba2vrzKdFixZNSEhQNJHhSk5O7tGjx4ABA9555x2lsxicgICAjz76yNXVVekgBuru3btqtTokJOTcuXO//fbbr7/+Om3aNKVDGaI2bdocOXLE0tKyQoUKbdu2lQJL5AVDKbCsrKyAv4qqZ8+e/VVsCV1KTU318fEpWbLknDlzlM5icMLDw7dt2zZ27Filgxguc3NzYPTo0fb29mXLlh02bNiuXbuUDmVwXrx40bp16969e798+TIqKurs2bPffPON0qGEHjKUAsvFxcXCwuLixYuZTy9cuFClShVlIxmgtLS07t27q9XqdevWGRsbKx3H4Bw+fPjOnTsuLi4ODg5Tpkw5dOiQi4uL0qEMS6lSpUqUKCHbbCsrJibm8ePHw4YNMzMzK1u27EcffSSLEUVeMJQCq3Dhwj169AgICIiLizt58mRQUFCfPn2UDmVY0tPTfX194+Li1qxZk56enpSUlJ6ernQow9KnT58bN26EhYWFhYUNHz68QYMGp06dUjqUwfn4449nzJjx6NGjmJiYefPmtWvXTulEBsfFxcXOzm7+/Pmpqan37t3bsGFDjRo1lA4l9JChFFjArFmzbG1tHR0dO3fuPH36dOnRoGPR0dGBgYGHDh2ysbExNzc3NzefO3eu0qEMi7m5ucOfrKysTExM7O3tlQ5lcCZPnlyxYkU3NzcPDw9vb29/f3+lExmcQoUK7dixY8eOHcWLF69Ro4aLi8uUKVOUDiX0kKG0aRBCCCGE0BkDmsESQgghhNANKbCEEEIIIbRMCiwhhBBCCC2TAksIIYQQQsukwBJCCCGE0DIpsIQQ+YiLi8uZM2eUTiGEELklBZYQQteSkpJUr7N27dqAgABnZ2dtDeTo6CjlmhBCEYWUDiCEMDhmZmYvX77MfOzo6LhmzZomTZoAJiYmRkbyW58QQh/IzzIhhALM/gQULlw487GRkdFflwgdHBwWLFjg7u5uZWU1atSo6Ohob29vKyur9u3bJyYmZp7k/v37Pj4+dnZ2Li4us2bN+tsQgwcPjo2N7dChg4uLy+rVq3X8BQohDJwUWEKIfGrLli3Hjx+/ePHiihUrunXrNnfu3NjY2CdPnixbtgxQq9UffPCBk5NTVFTUr7/+umjRopCQkFdfvmDBAgcHhx07dkRGRvbu3VuhL0IIYaDkEqEQIp/y9/cvUaJEiRIlGjZsWL169erVqwNdunQ5f/48cPHixd9///3IkSPGxsbOzs5Dhw7duHFj27ZtlU4thBAgBZYQIt9ycHDIfGBhYfHq4+fPnwO3b99OTk6uUqVK5sdTUlJq1qypSE4hhPgnKbCEEAVS2bJlbWxsrly5olKp3nSMLJkXQihFfvoIIQqkGjVqlCtXbuzYsc+fP09PTw8PD//tt9/+doydnV1ERIQi8YQQBk4KLCFEgWRkZLRt27aYmJjy5cuXKFHCz8/v6dOnfztm/PjxY8aMsbW1Xbp0qSIhhRAGS6VWq5XOIIQQQgihV2QGSwghhBBCy6TAEkIIIYTQMimwhBBCCCG07P8BaCmm4X8BQ0wAAAAASUVORK5CYII=" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 151, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let vp = A.init ~w:800. ~h:360. [\"jupyter\"] in\n", "A.Axes.box vp ;\n", "A.Viewport.xlabel vp \"Time t\";\n", "A.Viewport.title vp \"Solution to the pendulum ODE with Runge-Kutta 1\";\n", "A.set_color vp A.Color.red ;\n", "A.Viewport.text vp 7. 3. \"o theta(t)\" ;\n", "A.Array.xy ~style:(`Linesmarkers \"o\") vp t (column sol 0);\n", "A.set_color vp A.Color.blue ;\n", "A.Viewport.text vp 7. 2.5 \"+ omega(t)\" ;\n", "A.Array.xy ~style:(`Linesmarkers \"+\") vp t (column sol 1);\n", "A.close vp;;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the same number of points, the Euler method (*i.e.* the Runge-Kutta method of order 1) is less precise than the reference `solve` method. With more points, it can give a satisfactory approximation of the solution:" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val t : float array =\n", " [|0.; 0.00999000999000999; 0.01998001998001998; 0.0299700299700299683;\n", " 0.03996003996003996; 0.0499500499500499517; 0.0599400599400599365;\n", " 0.0699300699300699352; 0.07992007992007992; 0.0899100899100899;\n", " 0.0999000999000999; 0.109890109890109888; 0.119880119880119873;\n", " 0.129870129870129858; 0.13986013986013987; 0.149850149850149855;\n", " 0.15984015984015984; 0.169830169830169825; 0.17982017982017981;\n", " 0.189810189810189822; 0.199800199800199807; 0.209790209790209792;\n", " 0.219780219780219777; 0.229770229770229761; 0.239760239760239746;\n", " 0.249750249750249759; 0.259740259740259716; 0.269730269730269756;\n", " 0.279720279720279741; 0.289710289710289726; 0.29970029970029971;\n", " 0.309690309690309695; 0.31968031968031968; 0.329670329670329665;\n", " 0.33966033966033965; 0.349650349650349634; 0.359640359640359619;\n", " 0.369630369630369604; 0.379620379620379644; 0.389610389610389629;\n", " 0.399600399600399614; 0.409590409590409599; 0.419580419580419584;\n", " 0.429570429570429568; 0.439560439560439553; 0.449550449550449538;\n", " 0.459540459540459523; 0.469530469530469508; 0.479520479520479492;\n", " 0.489510489510489533; 0.499500499500499517; 0.509490509490509447;\n", " 0.519480519480519431; 0.529470529470529416; 0.539460539460539512;\n", " 0.549450549450549497; 0.559440559440559482; 0.569430569430569467;\n", " 0.579420579420579451; 0.589410589410589436; 0.599400599400599421;\n", " 0.609390609390609406; 0.61938061938061939; 0.629370629370629375;\n", " 0.63936063936063936; 0.649350649350649345; 0.65934065934065933;\n", " 0.669330669330669314; 0.679320679320679299; 0.689310689310689284;\n", " 0.699300699300699269; 0.709290709290709254; 0.719280719280719238;\n", " 0.729270729270729223; 0.739260739260739208; 0.749250749250749304;\n", " 0.759240759240759289; 0.769230769230769273; 0.779220779220779258;\n", " 0.789210789210789243; 0.799200799200799228; 0.809190809190809213;\n", " 0.819180819180819197; 0.829170829170829182; 0.839160839160839167;\n", " 0.849150849150849152; 0.859140859140859137; 0.869130869130869121;\n", " 0.879120879120879106; 0.889110889110889091; 0.899100899100899076;\n", " 0.909090909090909061; 0.919080919080919; 0.929070929070929;\n", " 0.939060939060939; 0.949050949050949; 0.959040959040959;\n", " 0.96903096903096908; 0.979020979020979065; 0.989010989010989;\n", " 0.999000999000999; 1.00899100899100902; 1.01898101898101889;\n", " 1.02897102897102899; 1.03896103896103886; 1.04895104895104896;\n", " 1.05894105894105883; 1.06893106893106893; 1.07892107892107902;\n", " 1.0889110889110889; 1.09890109890109899; 1.10889110889110887;\n", " 1.11888111888111896; 1.12887112887112884; 1.13886113886113893;\n", " 1.14885114885114881; 1.1588411588411589; 1.16883116883116878;\n", " 1.17882117882117887; 1.18881118881118875; 1.19880119880119884;\n", " 1.20879120879120872; 1.21878121878121881; 1.22877122877122869;\n", " 1.23876123876123878; 1.24875124875124865; 1.25874125874125875;\n", " 1.26873126873126862; 1.27872127872127872; 1.28871128871128882;\n", " 1.29870129870129869; 1.30869130869130879; 1.31868131868131866;\n", " 1.32867132867132876; 1.33866133866133863; 1.34865134865134872;\n", " 1.3586413586413586; 1.36863136863136869; 1.37862137862137857;\n", " 1.38861138861138866; 1.39860139860139854; 1.40859140859140863;\n", " 1.41858141858141851; 1.4285714285714286; 1.43856143856143848;\n", " 1.44855144855144857; 1.45854145854145845; 1.46853146853146854;\n", " 1.47852147852147842; 1.48851148851148851; 1.49850149850149861;\n", " 1.50849150849150848; 1.51848151848151858; 1.52847152847152845;\n", " 1.53846153846153855; 1.54845154845154842; 1.55844155844155852;\n", " 1.56843156843156839; 1.57842157842157849; 1.58841158841158836;\n", " 1.59840159840159846; 1.60839160839160833; 1.61838161838161843;\n", " 1.6283716283716283; 1.63836163836163839; 1.64835164835164827;\n", " 1.65834165834165836; 1.66833166833166824; 1.67832167832167833;\n", " 1.68831168831168821; 1.6983016983016983; 1.7082917082917084;\n", " 1.71828171828171827; 1.72827172827172837; 1.73826173826173824;\n", " 1.74825174825174834; 1.75824175824175821; 1.76823176823176831;\n", " 1.77822177822177818; 1.78821178821178828; 1.79820179820179815;\n", " 1.80819180819180825; 1.81818181818181812; 1.82817182817182822;\n", " 1.83816183816183809; 1.84815184815184819; 1.85814185814185806;\n", " 1.86813186813186816; 1.87812187812187803; 1.88811188811188813;\n", " 1.898101898101898; 1.9080919080919081; 1.91808191808191797;\n", " 1.92807192807192807; 1.93806193806193816; 1.94805194805194803;\n", " 1.95804195804195813; 1.968031968031968; 1.9780219780219781;\n", " 1.98801198801198797; 1.99800199800199807; 2.00799200799200817;\n", " 2.01798201798201804; 2.02797202797202791; 2.03796203796203779;\n", " 2.0479520479520481; 2.05794205794205798; 2.06793206793206785;\n", " 2.07792207792207773; 2.08791208791208804; 2.09790209790209792;\n", " 2.10789210789210779; 2.11788211788211767; 2.12787212787212798;\n", " 2.13786213786213786; 2.14785214785214773; 2.15784215784215805;\n", " 2.16783216783216792; 2.1778221778221778; 2.18781218781218767;\n", " 2.19780219780219799; 2.20779220779220786; 2.21778221778221774;\n", " 2.22777222777222761; 2.23776223776223793; 2.2477522477522478;\n", " 2.25774225774225767; 2.26773226773226755; 2.27772227772227787;\n", " 2.28771228771228774; 2.29770229770229761; 2.30769230769230749;\n", " 2.31768231768231781; 2.32767232767232768; 2.33766233766233755;\n", " 2.34765234765234787; 2.35764235764235774; 2.36763236763236762;\n", " 2.37762237762237749; 2.38761238761238781; 2.39760239760239768;\n", " 2.40759240759240756; 2.41758241758241743; 2.42757242757242775;\n", " 2.43756243756243762; 2.4475524475524475; 2.45754245754245737;\n", " 2.46753246753246769; 2.47752247752247756; 2.48751248751248744;\n", " 2.49750249750249731; 2.50749250749250763; 2.5174825174825175;\n", " 2.52747252747252737; 2.53746253746253725; 2.54745254745254757;\n", " 2.55744255744255744; 2.56743256743256731; 2.57742257742257763;\n", " 2.58741258741258751; 2.59740259740259738; 2.60739260739260725;\n", " 2.61738261738261757; 2.62737262737262744; 2.63736263736263732;\n", " 2.64735264735264719; 2.65734265734265751; 2.66733266733266738;\n", " 2.67732267732267726; 2.68731268731268713; 2.69730269730269745;\n", " 2.70729270729270732; 2.7172827172827172; 2.72727272727272707;\n", " 2.73726273726273739; 2.74725274725274726; 2.75724275724275714;\n", " 2.76723276723276701; 2.77722277722277733; 2.7872127872127872;\n", " 2.79720279720279708; 2.80719280719280739; 2.81718281718281727;\n", " 2.82717282717282714; 2.83716283716283701; 2.84715284715284733;\n", " 2.85714285714285721; 2.86713286713286708; 2.87712287712287695;\n", " 2.88711288711288727; 2.89710289710289715; 2.90709290709290702;\n", " 2.91708291708291689; 2.92707292707292721; 2.93706293706293708;\n", " 2.94705294705294696; 2.95704295704295683; 2.96703296703296715;\n", " 2.97702297702297702; ...|]\n" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val sol : float array array =\n", " [|[|3.04156; 0.|]; [|3.04156; -0.00498830704552716622|];\n", " [|3.04151016676278196; -0.00996415578174981824|];\n", " [|3.04141062474698032; -0.0149300540462087225|];\n", " [|3.04126147335790709; -0.0198884971903821491|];\n", " [|3.04106278707228883; -0.0248419693190828489|];\n", " [|3.04081461555061949; -0.0297929445205624109|];\n", " [|3.04051698373722745; -0.0347438880877792081|];\n", " [|3.04016989194813858; -0.0396972577312808828|];\n", " [|3.0397733159468272; -0.0446555047841474054|];\n", " [|3.03932720700792469; -0.0496210753994339171|];\n", " [|3.03883149196896918; -0.0545964117405467325|];\n", " [|3.03828607327026257; -0.059583953164978172|];\n", " [|3.0376908289829; -0.0645861374018181639|];\n", " [|3.0370456128250396; -0.0696054017234524758|];\n", " [|3.03635025416646354; -0.0746441841118481442|];\n", " [|3.03560455802149; -0.0797049244198173|];\n", " [|3.0348083050302832; -0.0847900655276403459|];\n", " [|3.03396125142860829; -0.0899020544954184653|];\n", " [|3.03306312900607677; -0.0950433437115140861|];\n", " [|3.03211364505291492; -0.10021639203742537|];\n", " [|3.03111248229529817; -0.105423665949428341|];\n", " [|3.03005929881928; -0.110667640677305584|];\n", " [|3.02895372798334295; -0.115950801340466647|];\n", " [|3.0277953783196021; -0.121275644081749304|];\n", " [|3.02658383342368031; -0.126644677199174549|];\n", " [|3.02531865183327886; -0.132060422275910555|];\n", " [|3.02399936689545745; -0.137525415308682619|];\n", " [|3.02262548662264363; -0.143042207834846169|];\n", " [|3.02119649353738051; -0.148613368058319567|];\n", " [|3.01971184450582886; -0.154241481974550704|];\n", " [|3.01817097056002925; -0.159929154494668657|];\n", " [|3.01657327670893372; -0.165679010568946294|];\n", " [|3.01491814173821515; -0.171493696309673593|];\n", " [|3.01320491799885781; -0.177375880113513379|];\n", " [|3.01143293118453714; -0.183328253783381329|];\n", " [|3.00960148009779; -0.189353533649860462|];\n", " [|3.00770983640498413; -0.195454461692126963|];\n", " [|3.00575724438008773; -0.201633806658328057|];\n", " [|3.00374292063724724; -0.207894365185315|];\n", " [|3.00166605385217933; -0.214238962917594228|];\n", " [|2.99952580447238315; -0.220670455625315509|];\n", " [|2.99732130441618638; -0.227191730321072205|];\n", " [|2.99505165676063134; -0.233805706375238592|];\n", " [|2.99271593541822156; -0.240515336629518517|];\n", " [|2.99031318480254216; -0.247323608508324466|];\n", " [|2.98784241948277884; -0.254233545127548088|];\n", " [|2.98530262382715916; -0.261248206400220451|];\n", " [|2.98269275163534875; -0.268370690138495627|];\n", " [|2.98001172575983908; -0.275604133151319375|];\n", " [|2.97725843771636933; -0.282951712337071504|];\n", " [|2.97443174728343163; -0.290416645770390724|];\n", " [|2.97153048209092; -0.298002193782306302|];\n", " [|2.96855343719799; -0.305711660032710719|];\n", " [|2.96549937466020053; -0.313548392574114043|];\n", " [|2.9623670230860335; -0.321515784905517|];\n", " [|2.9591550771828814; -0.329617277015135157|];\n", " [|2.95586219729262023; -0.337856356410588754|];\n", " [|2.95248700891689; -0.346236559135054911|];\n", " [|2.94902810223222422; -0.354761470767747611|];\n", " [|2.94548403159518379; -0.363434727406955427|];\n", " [|2.94185331503767156; -0.372260016633721047|];\n", " [|2.9381344337526194; -0.381241078454092552|];\n", " [|2.93432583157026095; -0.390381706217713731|];\n", " [|2.93042591442522893; -0.39968574751034619|];\n", " [|2.92643304981473618; -0.409157105017733391|];\n", " [|2.92234556624812525; -0.418799737358020729|];\n", " [|2.91816175268810518; -0.428617659879740431|];\n", " [|2.91387985798401195; -0.438614945422150737|];\n", " [|2.90949809029747719; -0.448795725034487669|];\n", " [|2.90501461652090898; -0.459164188650442|];\n", " [|2.9004275616892361; -0.469724585713915843|];\n", " [|2.89573500838540099; -0.480481225751838|];\n", " [|2.89093499614012783; -0.491438478889528|];\n", " [|2.88602552082654595; -0.502600776303792296|];\n", " [|2.88100453405028434; -0.513972610608612324|];\n", " [|2.87586994253571282; -0.525558536167942347|];\n", " [|2.87061960750906; -0.537363169329777|];\n", " [|2.86525134407919202; -0.549391188575263811|];\n", " [|2.85976292061690174; -0.56164733457624072|];\n", " [|2.85415205813362283; -0.574136410154152621|];\n", " [|2.84841642966055453; -0.58686328013286|];\n", " [|2.8425536596292571; -0.599832871077383589|];\n", " [|2.83656132325485766; -0.613050170910138359|];\n", " [|2.83043694592308803; -0.62652022839569621|];\n", " [|2.82417800258247187; -0.640248152484572786|];\n", " [|2.81778191714306558; -0.654239111505968|];\n", " [|2.81124606188326576; -0.668498332198795|];\n", " [|2.804567756866295; -0.68303109856970845|];\n", " [|2.79774426936809606; -0.697842750566194492|];\n", " [|2.7907728133184837; -0.712938682552101|];\n", " [|2.7836505487575236; -0.728324341572281098|];\n", " [|2.77637458130924886; -0.744005225392280645|];\n", " [|2.76894196167496043; -0.759986880298231471|];\n", " [|2.76134968514850465; -0.776274898641312|];\n", " [|2.75359469115608402; -0.792874916110307359|];\n", " [|2.74567386282331372; -0.8097926087149383|];\n", " [|2.73758402657241495; -0.827033689461742272|];\n", " [|2.72932195175261727; -0.844603904703366326|];\n", " [|2.72088435030702902; ...|]; ...|]\n" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let t = linspace 0. 10. 1001 ;;\n", "let sol = rungekutta1 f_pend y0 t ;;" ] }, { "cell_type": "code", "execution_count": 153, "metadata": {}, "outputs": [ { "data": { "image/png": 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jI5aWbNiAsjKtW1O9+rvrXL0qX+jdGx0dnJz4+muqVCngpIIgCCVUiTmClZbG6tX9jh6dFxbG6tWkpQHcvs3s2Xz/Pb/8wpMn8jUjIvjf/zh3juRkCfMWV+XKlbO0tJQ6RdGWkYGnJ1WqyKsrQEODqlU/uP6PP3LoEE2bsnMn3t4MG4aGxtZFi8oWWGDhfebm5oaGhlKnKNGMjY2/9CpOY2Nu3FBQnP/MnMn8+Tm/1KwZYvRqkVIyCqzYWGxtOXGi8tixEfXrExBA/frMno29Pc+fY2PDnTvUrs2hQwwdSsOGrFrFhAlUr46vL2lpLFlCu3Y0asSQIdy797rZmBj5sGEhz6pUqVLSxjkqRHQ0hoaUK0e5chw7xt277NmDgQF9+nx8WxsbGjSgc2caNiQyEhsbBg6sW6dOyfjdL6zc3d2bNWsmdYoSzcHB4fvvv/+0bczMuHz5M/vLy7aJiaxdy8iROW8yfjzTpn1m74IUSsYpwqlT6dyZBQuAqxcu9Fu2DDc35s3j7l1MTOTr9OtH27Z06kRoKNraAFev0rkzP/1EzZp4eKCrS0AAzZuzeTMXLrBiBRoaJCXRrRsLF5L9ZTT7MJiBgTS7KRRfFSpw9y5ZWRw9yrBheHnxzTcAeZlpoUcP+UJUFAkJJCfj5BTTtKll/qUVBOFzeHvTpo38H9D7HB0ZNoxHjxDTpxURJeNb7KFDjB6dvWj++DFXrpCWhkxGcjL373P/Pk+fUqUK6el07/76h7t+fZo0ISUFX1/atqVhQyZNYscOunfnxg1CQoiOJjYWY2O++op9+6heHWtrrK2pXp0jRyTbWaGY0tFBS4uff6Z2bXR00NNDTw919U9rpH17Fi4kLk4tfzIKQlEWGkq7dujpYW3N7t3vvjpiBDExODlhacnWrfInz53D2hodHQYMICND/mRsLK6uGBpiacnSpTlvO306FhZoa2NrS2CgfMMjR7C3/2B3pUvTuHEOd8USCquScQQrMZH/pvxxPXGCO3d4+JCUFL75Rn6OLzGR58/JyGDAANzd0dTEwAB9fS5eRCZjzhz09alQAVNTVFR4+ZL58+WHvrS0mD+fgACGDMHXV/67ERhI//7IZERHs2MHkZFUrYq7O+3bS/UGCMXDqlVYWeVwwWAemZtjbg6wdWvFTp0UmEsQir7MTJyc6NqVI0e4eJFOnahWDVvb1yusWcPBg+zfT8OGr5/cuZOTJ1FWplUrdu+mVy9kMpydad6chw+JjaV9e6ysctjW2ppLlzAwYNMmXF0JC0NDg+BgPDxy687amuvX8/udEBSlZBRY1tZcuICDA7CkZ89ly5YxahQ7d3Lnzut1oqKwsGDPHmxsSE7m6VOePuWvvyhdmhcvCA8nNpbISEJDycykbVssLbGwoEoVatTg0SOaNn39zcPenlWr6N+fOnWYOhULC65f54cf6N+fKVOIiyMkBB0datRATRxIEPIqLk5ezP/zD/XqfU4LgwYBxMdTpYpBSIhS3bqKDSgIRdnVq8TEMH06qqrY2dG9O9u3v1Vg5WjyZIyNAZyduXqVXr0IDubmTc6cQUUFCwtGjcLHR35G/009e8oXhgxhzhzu3MHGhvj4D54fzKatzYMHn7d/QsErGQXWxImMGMGePdSsCRASgp8fGRkcOED2TfEyM9m8mdKlefiQjh0BqlUjNRWZDBsb5sx53dTatYwezfHjPH5MeDh37rB3LzExHD+OuTlWVtSqRYMGJCSQkMAff8hLKCsrWrWidm3Cw+UxEhNJTmb1ajp0KPj3QyiKpk+nVy9q1aJWrS9qR0+PXr0eTZ1qeeiQgpIJQjEQFYWpKar//U+0tOTmzY9v9WoUb5kyPHoEEB5Oaurr39K0tJy/D23dysqVxMSgokJUlHz8rp4ez57l1t2zZ+jq5mVvhMKgZBRYvXqRkkLr1hgbT4yMZOdO5s6lVi3c3Jg5EwsLgoOxtOTwYdzcOHmSNm2Ii2PTJlq04MwZNm1iwACUlbl5Ey8vSpWibFmsreWNp6aydy/e3jRuzJ07BAfj58fRo8hktGpF/fo0akSrVlSujI4OV69y5478fOWZM7i6cuQIdety/z7x8Vhby+/NKwhvu3ULHx9CQhTTmotL1NChlv7+tG2rmAYFocgzMSEykowMeY0VFoap6bvr5HjDhHeYm6Ory61b757Lf3Pbu3dxd+f0aerUAahcmex71tWty507vLr/9Pvd3bpF16553SNBaiVjkDvg5sbDh2zZ4v311zx8iJsbTZrw11+sXUvfvuzfj78/Dg7cvImDA3/+SVwc69bh44O/P9u2oaODsTFt2zJyJJ6etGrF1q3cuMGhQzg4YGbGvXtYWNCuHePHs3071tbUrcuCBVSrxh9/YGdHxYo8eECtWiQlySPZ2eHhwdSp1KyJoyPu7lhaMmUK6emSvlNC4RIdDTBuHNOmoaibB6qpyWbPzpowgRcvmDdPMW0KQtFWvz5GRsyZQ3o6Z8/KB1S9w9CQ0NCPtGNjQ6VKeHjw/DmZmYSEcOnSu9smJaGpSbVqAIcOvT7r16nT6wHv73eXlsalS2Isb1EiK2Hc3d0/Z7PkZFl09OuHp0/LunaV1a4t69BBtm2b7P59WcWKslGjZKdOyU6elI0cKdPXl7Vq9VYLe/fKVFRknTvLTExkFhay4cNlx4/Lfv1VpqYm8/eXrxMbK+vUSTZ27OfuXBGQmJh45coVqVMUGbGxsooVZYcPy2rUkKWlKazZM2fOpKent2wpW7ZMZmKisGaFvLt582ZsbKzUKUq06OjoW7duvfXU7duy1q1lOjqy6tVl3t45bOPrKzMzk+nqytavl8lkMiMj2d9/y1+aNUs2bJh8OSZG1ru3zMhIpqsra9JEdvx4DtuOHy+rUUPWoYNs8mRZ7dqyP/6QyWSy+HhZhQqyZ89y7s7XV+boqND3oEDNmDFD6ggFTUmWfWSyxBgzZsyyZcsU325iIosWcfYsMhktWzJ6NO3bY2+Ppyd6ety/z+DBnD/PixcoKXH7tvzykD//RFOTjRvp2JEyZQD5hBGnTrF5M6GhmJrSq1f28PziISkpKTQ0tH79+lIHKRqiomjUCD09Fi2SDw5UiKCgoKZNm169qtqli7wXoYCFhIQYGBiIydwlFBMTk5CQUKNGDamDvG3mTEqVYvLkHF5q1gwvr8+8wqUQ8PT0LGmzTJeYU4T5TUeH2bM5eZJTp5g9G0NDAgJIS8PSEl1dmjWjXTtq1WL7doDq1Zk4kcBA1NVp2pSNGzExwcWF//0PXV20tGjbFiMjRo7E1pYhQ5g4UerdEySTnEyFCoqsroCUFJUHD5QMDKhdm6Qk+WRw9++/nsdHEARpTJ+ec3UFnD9fdKurkqlkDHKXRLlyeHnh5UViIjo6AN98Q6dOnDpFmzYkJLB+PWXKMGwYzs4kJODry6xZDB1KVBQ7d+LqKm+nd29sbfnuO8SNNUqMXbvw9QV49oykJFRU5D8OEyfSqJEC2j982OjgQWUlJVJTSU6mTRuUlVFVZe1avvpKAe0LgiAIosDKf9nVFVC3LiEhrFvHoUPo6DBzJpGReHnh5ISuLoMGMWgQ/fuzcycjR7J5M4MH06ULZcvSty9HjhAdzfnzAM2b06XL5083KRR6jRvLrx/y8UFNTT5/lYpKbnd0/iRdu0YtXlxRVVU1KoqqVZk8mWHDFNOyIAiCkE0UWAWrbNm3zvelp3P0KM2aMWwYenr4+3PwIO3b4+PD3r0sW8aPPzJlCurqrFpFQADffQeweDHLl3PwoJjTobiqVIlKlcjKYuJEypalW7d87EtTEy8vUWAJgiAomBiDJSk1NQ4cwMODCxfYvh0TE3x9uXOHUqXo1Us+BZevL9OnU6oUJ04wYQITJhAURNWqTJ8udXohfx04gKEhpUrlYxdKSqirk5LChQv52IsgCEIJJAqsQsDFhQ0b8PXlp59o3Rpzc0aNIjkZoHlz2rcnM1M+TfyKFbx8iZISU6eyZ4/UuYX8tXw5P/xAmzb52IWxMbt3M2wYXl752IsgCEIJJAqswsfHh9RUzMxo1IgKFThwABUV/Pw4cICTJ6lZk/37MTHhyROOH6dfP9q0Yfhw/v5b6tyCIt24QWgoPXqwdWs+9qKkRPPmDBzIoUP8+28+diQIglDSiAKr8NHT49dfCQvDy4vr1/H3p2pVrl+nfn327eO335g2DTs71NUZO5avvmLqVKys6NCBX3+VOrqgML/8wg8/FNDdwHV1cXLK30pOEAShpBEFVmGlo0PDhvL7tI8cyejR8num2Ntz5AgPH/LsGQ4OdOtG69aMG8fp00yezNOn0qYWFOLffzlwgMGDC67H77/Hy4usrILrURCEj5o5k/nzc36pWTOCgws2jfCJRIFVFIwYQefO1KtHx4507EjDhlSvztixPH1K3bocPgxQpQrNmnH6tNRZBQVYu5auXRV258G8aNIEXV0CAgquR0EQcpeYyNq1jBwpf2hmxuXLr18dP55p0yTJJeSVKLCKAiUlfvqJGzdwd8fdnRs3sLGhYkV27WLDBsaMYcQIUlLQ1eX5c4C0NKkTC58vPZ3161//VS0wYqi7UAJt2MDy5VKH+ABvb9q0QVs751cdHQkK4tGjgs0kfApRYBUd5cvToQMdOmBoSJ06nDkD0KYN166RlESDBpw6xePH1K2Lnh46OnTvTni41KGFT7Z7N9bW1K1b0P326kVgIJGRBd2vIEjo6dOPXN4RGkq7dujpYW3N7t3yJ42NWbMGKyu0tBg/nogI7O3R0sLRUX79NxAbi6srhoZYWrJ0qfzJGzdo3BgdHTp3ZvDg1zfFmT4dCwu0tbG1JTBQ/uSRI9jby5dHjCAmBicnLC3lwyVLl6ZxY44fV9Q7ISieKLCKpp49uXKFRYvIyEBbm9Wr0dcnOpqFC1mxgsREHj6kfn2aNxc38i1Cbt7k5k1WrMDdXYLey5ShRw82bpSga0EonDIzcXKiWTNiY1m/nkGDuHZN/tLevZw7R3AwmzbRvTsrVxITQ1yc/DdIJsPZmYoVefiQwEDWruXIETIzcXame3fi4pgwAW/v1x1ZW3PpEgkJjBiBqysvXwIEB1O9unyFNWswNubgQcLC6Nfv9VbXrxfQWyF8BlFgFU1aWgQEEBgoP5plZkbNmmhpoafH6tUkJ6Ojg4cHvXu//uokFHp79rB0KXFxCr61c96NHMn69fTpI8byCcWciws1axo2a1Zt1ix++QUDAwwM6NDh3dWuXiUmRj7Ts50d3buzfbv8pcmTMTCgcmXs7Gjdmrp10dLCxUVegQUHc/MmCxagro6FBaNG4ePDlSskJTF2LCoqODjQvv3rjnr2xMgIFRWGDEFDgzt3AOLjP3h+MJu2NgkJCntPBIUTt8opsiwtOXyYhAQePaJyZR4+5NQprl3D3Z3Gjdm7l1q1+OYbMeF7ESKTceECo0fLb0RY8KytqVKFO3dITJQmgCAUjHXriIh4mpiY6OdXNTlZfgOz0qXfXS0qClNTVP/7P2lpyc2b8uXsK7wBTc23lrPHwYaHk5pKrVry59PSqFePqChMTF7/dpubv+5o61b5MTAVFaKiePIEQE+PZ89y24tnz9DV/bQdFwqSKLCKOF1d+W+Yigrp6WhosH49v/9Omzbs2UN6+uu/DUKh9+wZ9+/Tv7+UGYYPZ8wYKQMIQgEwMCAjI1NDI6NsWZSVMTPLeTUTEyIjyciQ/x0NC8PUNE/tm5ujq8utWygpvX7y4kWiosjKktdYERHUqAFw9y7u7pw+TZ06AJUrI5MB1K3LnTvY2ck3f/97161bdO2atx0WpCD++xYXVaqQlsalSzRuTN++mJry3XfUqUOrVqSnExJCUhK1alGunNRBhXfVri0fKffsGTIZlpYAJibcuFFwGZ49Y9Ei0tLIzCQujtWrOXsWoF49evQouBiCUKjUr4+REXPmMGUKly6xezenTuVpQxsbKlXCw4Pp09HQ4PZtnj+nQQO0tVm6lDFjOHMGPz95gZWUhO+IPM4AACAASURBVKYm1aoBHDrEgwfyRjp1IjCQQYPkDw0NCQ2lYUP5w+y/9+vXK3B3BQUTY7CKC2VlVqzA2ZnffiMiAn19HBw4fZrISKpXp18/pkyhWjXGjxeTOBQ2ly5x7x537qChQf/+3LvHvXtcuVKgGZSU0NZGTw8DA3R0iIlBTw89vfy91bQgFHIqKhw4wOnTlC/PoEGsW0f9+nnaUFmZ/fuJiqJqVQwMcHMjIQFVVXx92bkTPT0WL8bVVX5SskEDevbE1paOHTl3jtq15Y306oW/v/ycIzBlChMnoqfHhg0Ahw/TosVb5xmFwkZJln0sssQYM2bMsmXLpE6Rb65cYdYsrl1DV5eOHbG1pU8fundn2zaAuDjc3DA3Z+VKqQImJSWFhobWz+NfqZLk2DEGDWLIEDw9872voKCgpk2bqn7g9HGrVty9S1TUW2c3BMUKCQkxMDAwNDSUOkjJFRMTk5CQUCP7IJIUnJxwdGTIkNzWmTmTUqVez+bwpmbN8PKiXr18Sqd4np6engXw160wEacIi5cGDdi///VDNzd+/plDh3BzY/16ypVj82YqVWLePLS0pEsp5GDzZmxtpQ4BgK4uKipcufL6ZIQgCAoRFISVFeXLc+wYAQGsWfOR9XO5SOn8ecVGExRPnCIs1m7fxsEBPz8ePaJ3bzIz0dPDzIywMKmTCW+Ji8PPj3Hj+OYbqaOAri7t2rFjh9Q5hELm5ElOnnzrmdRUFi2SKE3R9M8/1K1LuXJMnIi39wcH1wvFgyiwijVdXR4/RltbPqHDiBHIZDx5gp6e1MmEt2zfTqdOtG5No0ZSR4GtW/HwYOdOMjOljiIUJoGBrycZz/b0KcV4wEV+GDyYmBji47lxAycnqdMI+UwUWMValy6sWEFGBqVKsW8fN27IZxfO46XGQkHZvJmBA6UO8YYaNTAykt+NSRAEQfgMYgxWsTZwIH5+NGrEkCHo6lKpErt2yac5eviQ0FBMTalWTbJ5LQUArl/n6VNat5Y6x9t69mTHDhwcpM4hSC06Wn7nln//JTmZwEBSU3n2DAMDnjwhLY379wFUVTEzE39LBOE1UWAVa6qq+Phw5AhHjpCYiK0tP/1E+/acPElkJDVrEh5OuXJs3CjBvYWF/2zeTP/+he4/U48e1K/PypVipoYSys+Ptm1RVqZrV2JiePmS2FgAb2+yssjKQlUVmYyMDBo1QkcHJSXWr6dNG+7dw9QUdXWpd0AQpFbI/qgL+eGbb1izhu3bmTCB6tUxMODOHdav58QJQkP54Qc6diQuTuqUJVRaGjt2SDx7e47MzbG2xs9P6hyCRAYOJCYG4OhROndGWRlXV6ZNIy2NjAyyskhLIzwcIyOaN6d8eQ4fpk0bgPHjOXFC2uyCUCiIAquEuXiRtDT8/Rk8mKAggL59adtWXDMmlYMHqVWLKlWkzpGT7LOEQknm50edOkRH8/ffVK+ewwoqKhw8yKBB2NuzYAGZmfLjW4IgiAKrhLl9mwYNaNyYrVvp1o3QUICGDbl9W+pkJVRhG97+pm7dOHLk9UTSQokik+HhwcCBrFrF7t3o6aGk9O7cs9kPlZQYOpRLlzh+HDs7kpMlySsIhY4osEoYPT0ePwb4+mt++olu3UhJ4fFjMXGDJKKiuHABFxepc3yAgQHNm3P4sNQ5hIJy4gT6+pQrh54e0dHs3s2LF/Tvz9KlAG5uuLm9tb6RkfwYZ0wMPXqQlMSjR5w8yfDhNGxIw4ZMmiTBXghCISEGuZcwDg4MGcK1a9jaMnIkFy4wbBgnT741/7tQIObOJSsLFxc0NaWO8mHZZwnF/Z5LiK++IjSUzEy6duXyZf78E2NjQH7fh/dve6esTKtWAEZGeHnJzwy6ufHgAevWUaEC5csXZHxBKFyKyRGstLS0UaNGValSRVNT08bG5uDBg1InKqzKlmXdOjp0wMODHTuoWhVvbxo3zustTAXFWb2aLVsK7/nBbF26EBjI06dS5xAKhLIyenosWoSqKjo66OjI7/mtpvaRDZWUsLWlQQMaNMDCQj4cvmZNKlYskNyCUCgVkwIrNTVVSUlp165dYWFhI0aMcHV1Dc0eXSS8r0sXrlxBXZ1Dh0hOxtub06e5eVPqWCVOWhpZWTRtKnWOXGlr074969axbp3UUYQCceAAu3axc+cXNfLtt1hZ4e6uoEyCUDQVk1OE2traK1euzF4eNmzYkiVLrl69WrVqVWlTFV5mZvz88+uH6ek4OeHgwOXLAM2bM306FSpIla4YS08nIkK+nJxM9+48eABgZESZMhLmyk3Pnnh6YmHBsGFSRxHyR2oqT55gasqdOwwdypEjGBgwfjz6+p/T2tdfU60av/5K06b8+iuDBgGkpYkJ1YQSp5gcwXpTTExMWFhYnTp1pA5SdNjaEh3NxYv8/ju//46hIfXr888/UscqhoKCaNeOdu1o25aXLzlwQP5wyxapk31Yx448eEBKitQ5hHxz4gQjR/LsGV26MG8eDRsCjBtH6dKf09rIkdSogZYWe/bw449cvcqJE/Trp9jIglAEKMlkMqkzKFJqamqHDh1q1aq1atWq91/dunVr/7endKxbt+7y5csLKl0hVXvatAQbGyM/v+jOnaOcnADTvXv1rl27MWuW1NGKrYAAwwULanh7X9TXT5U6ywc9fVrq6dPSwLJlVomJqjNmhABqalmVKokL8YuVc+f0Dx82KV06S1s7fdy4Owps+exZg5Urqw4e/ODkScM5c/5WYMtC4ffDDz/cuHHjzWe2bt3at29fqfIUvGJVYKWnp3ft2rV06dI7duxQUVHJcZ0xY8YsE/d/f4euLvfvExdHixb87380aMDTp1StSny8wrtKSkoKDQ2tX+LH1Ds6cvYsN25gYiJB70FBQU2bNlVV/cgIgdGjOXcOIDqa2Fjq1QNQVubAAXEC+UuFhIQYGBgYGhpKHQTg0CEmT0ZLi9OnP/OoVS4mTODUKSpU4NAhBbf8hWJiYhISEmrUqCF1kJLC09PT09NT6hQFqpiMwQIyMjJ69Oghk8m2b9/+oepKyFl6OqVLU7Uqy5czYIB8CHx6utSxiq0nTzh7Fg2Nd6dtLGxWrJAv7N9P9+7s34+ZmaSBBIWaOpVLlwDCw7l3j+bN5bfE2boVIyMFtL9+PVeukJXFgwfcuycfw1e6NDNnoqurgPYFoZArJgVWZmZmnz594uPj9+3bl5mZmZmZqaamJsqsvGrYkKNH6dqVHj3YtYv586lZUz4QQ8gHu3bxzTeMGCGfZKjwU1HByIi9exk9WuooguL0789XXyGTMXAglSszYwaAurrCJq+qVEm+kJHB779jaYm+PsrKij9IJgiFUzEpsCIiInbt2gXo/vfNaOnSpWPGjJE0VNExcyY9e6KsjJMTy5dTty6lSuHjI3WsYmvbNjw9adZM6hx5pqSEiQm+vqLAKlasrLCy4vffKVOG6tVp21bB7bdrJ1+oUIHz5wkOFre2FEqWYlJgWVpaFqfBZAXN3h4fHyZOpF8/ZDKMjVFXx85O6ljF0717PHhAmzZS5/gUX32FiQlt2hAdLUZfFSsvXzJtGt9/z9mz+dtRlSqcO0dQEC1b5m9HglB4FMNpGoTP0aIF584RF0d8PHfvoq+Pl5fUmYqn33+nVy8+Nr68cClThvr16dSJAwekjiIo1JIlNGmCo6P8jjf5pHx5LCyYOZMJExBfhIWSQxRYwhtKlaJUKZSV2biRn39+PSemoDg7dtC7t9QhPouLC76+UocQFOfxY5YvZ84catZkwoR87KhpU9asoW9fMjPZtSsfOxKEQkUUWEJOrKwYOZKvv6ZRI0xMsLdn716pMxUHFy6grEyDBlLn+CwdOvDnnzx5InUOQUGmTmXgQArshhfKyixezKRJvHhRQD0KgrREgSXkRCbj3DkiI3Fy4soVJk/m55/56SepYxV527fTp4/UIT6XpiZt2xa62YyEzxMSwsGDTJ5coJ3a29OwIf/d1UwQijlRYAk5OXyYhAT8/Fi9GlVVOnbk5EnWrxcnDb9ERgZ79tCrl9Q5voA4S1gMTJvG1auMHcu0aZQrV9C9L17M4sXExDBtGi9fFnTvglCQRIEl5CQwEBcXmjShd2/56Ixy5bC3l0/sLXyWY8ewsno9OVBR1LkzQUEkJkqdQ/gC169z4ADh4dLcvbtyZfr0YeZMNm3Kj1tFCEIhIgosISeZmfLr3GbO5ORJLl4EUFMjM1PaXEXatm1FdXj7K9ra2Nlx5IjUOYQvIJOxZQuLF6OmJk2A6dPx9SUjQ5reBaHAiAJLyEmTJhw+DFCmDDNnMnYsz59z6hSNG0udrEi6epVJkzh+nG7dpI7yxcRZwqIoLQ1fX3x88PEhOBjg5Ut8fOS3yinIGFevcv8+ffuSkEBwMFeucOUKz54VaAxBEv/8Y71vn9QhCpYosIScdO1KcjKDBhERIf9b2KwZjo4Fd8VR8RIZyR9/8NVX6OlJHeWLOTlx4gTJyVLnED7Fs2fyAmvXLiIj0dWVF1v5Pb/oO86fZ+hQhg3j5EnS0xk1imHDGDaMbdsKNIYgiZgYo+vXpQ5RsIrUdIdCgVFVxd+fmTNp0oSnTzEwICODZcukjlWEPXrEtGlSh1CEcuVo0kR+70qhqNDXx9sb4LffOH2aWbNwdJQghr09ly/Ll3V1qVSJP/6QIIZQABIT0dGROoTUxBEs4QO0tVm0iKgonj8nMpJ69di0SepMRcylS/LjBMeOkZBASgo+Pvj6kpYmdbIvI84SFlEyGUuWUKWK1DkA0NQkOJgbN6TOIeQPW1v+/Rfg0iX8/fH35/Fjw/v35csFfG5aKuIIlvAx2UNhFy2ifXv69BHfSvLu1Cn59/U//6RUKfbvB1BXx8EBfX1po32RLl3w8KBFC44c4b+7q+dZWhp371K2LObm+RJO+LCjR1FTw8SEUqWkjgLKygwcyKJFbNkidRQhH6Smkp4OsHgxoaE8esSTJ9apqURHA5QrVyLm9BcFlpA3devSqRMLFzJnjtRRioxJk+QLVapgY8Pu3ZKmURxDQ2xs+PtvXrzItcDKHtIcGUnVqtjYkJnJvHksWYKpKYmJ6Onh5UWLFgAvXvDsGUZGBbUHJdTChUyaRMeOlC0rdRTYtw8rK6pWJTwcCwup0wj5ICmJw4e5eRN1dWbPZtu2oNat7Tw9pY5VgESBJeTZ7NnUrcu33xIXh54edeqgqSl1piLg1i0SE6lZU+ocCuXiwp9/5rrGuXO4uaGtjYUFwcGYmVGjBrdv8/ffmJkBHDqEiwtr17J8OZcvU6YMwM8/M3QoSkoFsAslzaVLhIfTtWthudF4o0YAbm4sXSqGdxYT16+zZg1ARgaPH2Njg6UlNWsycCBOTnh7l7hZfgrHr5pQJOjpYWGBvT0ODsTHExnJihU4O0sdq7Dz9sbBAZlM6hyKEB7Ozp0ASUm8fMnKlfIjWA4ONGnyxnqxsTg78+uvdO4MkJXF3Ll4ehIRQYUK8nUcHenfn169WLWKEydQViYkhAEDiIvjxx8LdrdKhEWLGDeusFRXr4wZQ+3aTJtWtE+aC9kqVKBRI+LjWb0aZWV+/BETE4Bq1QCUlWUqKtIGLGiF7LdNKMzc3bG0JDKS+fOxseHKFZycMDF5+1+r8BaZjB072LWrmExwkZLyevbt7IrI2hrg+XM4c0Y+0X/z5ly5wrffyqsrID0dW1tUVFi0CCUlHjxAX5+aNTl/nnLlcHOTr1azJr6+2NgwbhzA/fuYmhaKs1lFX2gop0/z229S53hPhQq4uLBqFTNmSB1F+Fzh4QQF0bs3hoY0bUrnzgwZwpo1DB0qL7CyNW588YcfvpIupgREgSXkzbNn7N7Nw4ds28bEifj50aABU6bg5SUKrFxcuICaGg0aSJ1DQapXZ/58+bKXF7q6zJ8PL1/Spw8hIXz7LcDQoaSnM3IkUVGsXo23N9HRVKhAZibXr9OxI82aERfHzZtcvUpaGuXKUbMmLVowahTm5hgaMnAgBw9SsSKRkdjbs3KlGKTzhRYv5vvv5adhCxsPD5o3Z/x4tLSkjiJ8luBgdu2id2/8/endm19+oXdv+bnCN6mrp3zyNTFFnJimQcib8HDMzSlblqFDefhQPn2NrS1370qdrFDbsaNo3905F+rqHDtGVhbMmoWKCsHBzJ/P/PkEByOTMW8ederIh7kmJ/PgARoaNG/OhAl07crQoSxdioYGgwdz9y5z5iCTYWtL//6EhZGezqNHhITw5AktW9K6tZjY9Es8foyPDyNHSp3jA6pUwc5OTAJT5G3eTJ8+7N4tvyFYo0aiYhZHsIQ8KleOx4/JykJVlenT8fSkXTtiYsTQiVxkZODjw+nTUufIHwYGyGRcvEiz7dv54w/U1MjK4sgRVqwgPl5+J5TateVrnzmDujrr15OSQps2JCTg5YWeHv/+i74+9vbY2zNtGoMHk5ZGVBRnzuDoiJoakyZx6RI7djB4sKS7WyQlJNClCy1b0rMn5ctLnebDPDxwcUFZGRUVvv9e6jRC3iQl8eQJQEwMN25w/Tq///56LET2rDQlnDiCJeSNiQlVqsi/Znbvzr//4u/PL7/w3XdSJyu8TpzAwkI+wLP4uXmTrl3Ztw9iYrC05OFDWrZkzhyGDOHRI5SVaduWSZPkYzFcXdmxg7//Rk2N5cvZv59Bg7h6lfBwXFzw9+fyZdas4dgxWrdm0CAmT6ZJE7LvrGFnx99/S727RdKLF9y5w/r1jB0rdZRcNWpEtWoEBBAbK3UUIc/GjaNdO9q1Y9w4wsNRUmL4cOzt5TNdCYgjWMIn2LSJjh0JCKBNG2xt6dIFFxf69ZM6VuHl7V1Mzw+GhrJuHXfuOJdu6np+7MKKFVm/ntmzmTCB8eNRUuL6dSpX5sgR9uzh5k1q1mTePPnBzrlz32oqKIjVq1mwgPh4bG2ZOxc/P9zcGDiQbdto3x5PTxIT0dLi9m3Onwdo1ozq1SXY66LpxQu+/rqwzN6eCw8PevemTh2pcwh5tnEjwMGDDBlCixYcOyZ1oMJHFFhCntWowc2bbN7M+fOYmaGtzbBhKIuDoDl7+ZJDh1i4UOocCuftzdixfP89gwbZhoVl7vv3b8MqdSZO5MAB2rcHSEpi3DgGDaJatY9PuFCqFGPHvj7A8uQJnp7cu0eVKvTti50d3bsTEoK9Pa1b064dwNSpODuzfDkl7ZrvPLt8mRMnABISePYMQ0MWLEBFhe7dC+P8+Rs2EBcHkJrKwYPyyfWyL3UQCrk7dxgyhMmTOXlS6iiFkiiwhE+hqfl6rGyVKsyfz8GDkgYqvA4dolGjYjc5eUIC7u4EBsonTn30qMv8oH3/tqzTSZ2BA2nbFpkMf3+6dWPChM9p38CAefNo1YqJE6lfnwcPePYMLS1OnODQIdq2BXj2DBcXFi4U02V9SEKCfDaN4GCUlChTRv7w+XNpc+Xs339JSgKoUIGwMHnUzBI3J2XR8/w5zs7Mm4ehoSiwciYKLOFzubkxdy5//UW9elJHKYyK5/nBU6do0kReXR09ipub87eLRx8YPL1OKosXc/48MhnTpn3RuLPBg2ncmFWr2LcPMzOWLGH0aDw86NMHDw/GjEFbm8WLcXERBdaHtG0rr0Xt7Slb9vXMGoXTlCnyBTU1li1jwABq1JA0kJArPz/q1aN8eQYNolUr3NxISCjUl1BISBRYwudSV2f8eObMwcdH6iiFTnw8p04Vx7vYJiXJh1Lt28fIkfj4tGjeMnZH8v2HqpWrVlXYbKp167J+/euHDx8yYgTOzvTowZUrbNlC9eo8fKiYvoqve/fkt4ErKlRUqF+fNWtYsULqKMKHrVrFkCGEhBAeztatALq6YjLEnIkBNMIXGDaMM2e4cUPqHIXLqlWsXEn79ujoSB1F4aytuXgRf3+GD+fQIVq2VFamc/mL+5Pb5WOnFSrw4AEWFpw6RUICvXpx795bU0QLOVm7ll69itIPoZYW9vZs3y4/YygUWsHBrFjBnj2ULi11lMJNFFjCF9DUZPRoFi4kJYV//5U6TWHh54ePT3E8Pwg0bEiZMjg5sX07DRqQlcXatc5JW/ZF5ecX2D59mDKF9HRKl8bXl2fP+PprevbMxx6LvtRUfv+dH34gOFjqKHk2YQIzZ/LVV2zfLnUU4cNevmTJEry95TdtF3IhCizhy7Rpw86dlCtHrVqYmrJxYzG5rfEXSEkhPJyOHaXOoRCJiUycSN26VKyIoyM7dxIRQbNmdO9OixaYm7NjR2v/KTf/UcnHGYymTUNVldq18fBg+nRCQ0lP584dfvqJKlVQV6dOHTZuJCsr3xIUPXv2YGNDtWqoqUkd5RONHMnq1VKHEN4WHU3p0igpoaSEvz/x8Tg4oKRE165SJyvcRIElfIEHD/j2Wzp0oHdvHj/m2DHWri2OMxN8nEzGtWtcucKVK4SGUrs2N25w5UoRHykUH0+jRiQns307Z89iZ0ffvvTrx4kT3LnDokWcP09gYOm61Tt04MCBfItRujS7dvHbb+jro6/Pb78RGoq/Pzt2cOQIiYls3MjmzYwZk28Jip61axk+XOoQn+Wrr1BW5tQpqXMIb6hQgdRUZDLWrEFPjwMHkMmQydizR+pkhZsosIQvsHQpw4fz22/s3Ut4OHXqsHcvCxaQmip1soIWG8uIEQwbxrBhPHzIw4fy5VWrpE72JZYvx8GBNWvk8z96efHjj+zaRVYW+vo0b07FitkrOjvn/50xmjVj0iQmTaJ5c44do3ZtLC1ZuBA1NZo04dgxdu/m/v18DlE03LjBgwc4Okqd43MNHy4OYhVGMTHMmIGNDUpKUkcpIkSBJXyBa9do04Zy5RgyhCVLACpWxMioBP6fMzbm/HkuX2bbNtTUWL2ay5e5fLmIH847fRpXV4DYWFq3ZsIEZs1CTe39z7djR86eJSGhoIKdO4ezM4cO8eCB/ECNtjYODly8WFAJCrW1axk8GNUie414v36cPMmjR1LnEN42ZgxDhqCtLXWOokMUWMIXKF2aFy8Axoxh+3b5FIEvXhSlS8MVzdsbU9PiMr99Rob8Fs59+tCjh3yOWTW192eBzL7+a8YMdu8ukGBKSmRloanJ4cNcvSov7mUy8c0aePGCnTtxc5M6xxfQ0qJXr7dm6shNejohIZw/X4AFfkl0/DgXLzJlCiNH0qiR1GmKiOLxf0CQSLt2/PYbgLExjo5s2EBAAGpqWFpKm0tCO3dibl5cCqwmTTh8mHnzSEvD0xPg9m3i43O8s52zM/7+hIQUSLCWLdm3j6wsypTh4EGWLWPPHk6dolmzAum+UNu+HTu7Vydvi6offmD9+g+MNUhPf73s54e1Nd26MX48Varg4UF6OseP06kTVlZ89RUbNoirH77cy5eMGMGqVZQpw9dfY2wsdaAionj8HxAkMmoUd+/SrRsnT/LNN8ydS8+eeHmV2AMJFy+iosLGjbRpI3UUhRg3ji1bmD+f1auRyQgIwMmJ2bNzPPnk5MT9+2RkFEiwb79FQ4OuXbl+HS0tPDzo1QsnJywsCqT7QioxkcRE1q1j2DCpo3yxatWoU4cdO5g06Y1n9+2jXj10dNDVpUcPjh6lf382buTmTc6d4/Zt+W0rR4/GzY0jR5g6FW9vunYVlzZ/tvBwgJ9/pkkTvvlG6jRFTZE9Sy8UBmXKcPYsK1YwezZxcWho4OEhvyNvibRjBz175nh8p2hSV6d0aaytsbMjLY1q1ViwgC5d3lnr5EmePAHQ1ubUKfnE/gYGfPVVvgVTVuZ//+OXX+jdm4gIqlenVy8uXSI5mTJlyMwsmfeBXrmSyEji4+U33S7qRo5kzhyiov4byOjlxfLleHlhZ8fz56xdS9eueHjg4CDfwMCABQuoXZv79+UH0atVw96eJk349Vf8/Dh7FqBFC+bM+aK7OZUYsbHY2fG///Hrr1y/LnWaIkgUWMKXKV2aiROZOBHgwAHmzSuxV8tnZrJ7N4GBUuf4QsnJ/PMPurpYWuLmhqurfIRTWhqlSuW4hbc3iYkAKircvCkvsHR08rPAAkqX5scf37odoZsbHTrw4gUhIWhq0qEDCxaUqMkQMzK4eJGhQ4vJGWpHR34YkZmeIiMxGU1NZswgKAgrKwBdXSZPZsUKAgNZuJBr14iKomxZEhJQU2POHKpWxcAAOzusrGjRAnd35s5l6VIAX19atuTYMSpUkHYHC7/MTDIzGTaM2bPFrRM+hyiwBMVxdGT8eM6fL5lDYQICMDcvyl+MMzL4+WdWraJyZRISSE5GT49du+SvfqC6AjZskC+MH8/atXh7S3T9WoMG7NhBr16cP8/z53h50bQply+XnAEjqancusXAgVLn+GJPnhAeFMG8eW3jW+1Mc75i9i2NG6PRsqa5lUZ8PJs2ERjIX3/x+DFJSdjY0KkTZmY8f87//sfFixgYEB/PzZvMmEGZMjx5Qs2ajBwp/7kcPRotLaZOZdMmqXe0CEhOJjOTIUOkzlE0iQJLUBxlZdzdWbasZBZYO3fSo4fUIb7E5MncuMGtWxgbc+0arVvz5Am3b8snwcoDbW10dTl9mtat8zVoTrKrw+PH6dWLgAA6dGDqVOLj+eWXIj5Vxsf16MHTpwDXrqGqSu/eAMbG/P67tLk+374dKesmJGDk+bJy+ZQQpcGVA1T+CldJeLqk15KWp+fi5MSAAdSrx4oVbN3KokWvzwjfvg0wY4b8Qubs+X8bNeLffzEy4uuvGTiQdu347jvGjFF5+LDcnj2kp2NlRc+e6OpKtsOFzJYtbNsG8Pw5SUkoKfH11wAzZ5bMP+2fTxRYgkINGMDPP/PwYZG/iukTpaSwfz8zZ0qd47MlJ7NxI6GhGBjw/Dk9erB2LRERrFjx+gjVx6iqUqsW+/ZJUWCFhqKnR6tW7NqFiwvnzlG5Mp07M2NGgUcpaGPH8uwZQPfu8tlYoWhPVjSk1JYhqqZeFwAAIABJREFUzifZuTMqiqpVGdTq7qh7Yzl6FLoQEoKRkXy9Z88wNqZJE4YORU8Pf38OH6ZDB777Tn4gNi6OzZsBLl8mLY3Dh3F3x8iIqVNJS9P/5pvETp2wteX8eWbPZtu2fD6rXWS0bYupKcCSJZQuzaxZ8udr15YwVJEkCixBobS1GTCAlStZtEjqKAXqyBHq15f/VSqSwsIwM8PAAGD0aFq1ont3zp79pAna3d3p3JnOnVmxosAvJFVRkV/B2KIFP/5I376cPl1CRrs3aQLw999kZtKsGW3bSh3oy928SYsWAJcuaaZZrd+oPGqVC8+fc+oUx47RujUJCaxZQ1AQFy8SGMj//kd8PLa23LyJpiZLl9KihXyKvt69adWKo0fp25ehQxk0iK1bcXUlPT1h1arHNjZ6NWoAnDpF797cvYumppQ7XjiYmmJqSlgYFy+iq1ssfqIkIgosQdFGjaJRI2bMQEtL6igFJ/v6wSJMW5u4OGQyAgMJCODmTYC4OMqW/aQ2si+iv3RJ/l+/4FSpQmoqly/TsCGjR3P4MAsWEBZGq1YFm0Myv/5KvXpFdoKUJ0+YN4+gIICWLVFR4fFjJk1S/v0PDd1zqfrVLtSq1lRnP1Onsncv06ahq0vHjvz5J2XL8u23fPvtW615eODhQVKS/Kf3zz9xdCQ1VX5r4owM0tJo0ED3hx9UmjVj6VIqV8bBgRo1CAwsLjdpV4CffsLNjR07pM5RlIkCS1A0S0tatGDoUMzNMTWlS5dif7owKYkTJ/7P3nlHNZV9bfgJXZCmoCLFhthBRWyAjgoqjl0BHRV7r2PvfRy7Yi9jL4go9t5QsY4F7B0LqGBBQKRzvz+4n/qbcRQ0yU0wz5q1JonJ2W8Qk33P2fvd/PWX1Dp+BDs7ChRgyxYmT8bfHyMjMjNZtOifX13ZoGVLduxQeoKlpcX8+TRvzvTp1K3L6NH8+iuWlj9Jc3laGgEBTJigngX9Dx5QuzZt27JwIcDWraxdS2Iiv/5a6PqRg9F59u9nxay46ufPs349Q4dmd9mP1wYuLhw9yqhRYrOzqytNm1Kz5isvL21/f6pXZ9IkevfG1paYGAW8PbXk+nWOHiU8XNwH1PB95Ip2Xg0qxalTnD3L3r3ky8fdu7i4sGqV1JoUy/bt1K2r/jWyf/1Fz54kJQGsW4erKzo639E+1KIF27fLX923ad2a4GC2bKFqVfr1o04d0cfrJ2DvXsqUoU8fWraUWsp3MGoUQ4YwezZVq1K5MpaWpKeTLx83b7JtW7lnBzvH++/cSeyURZibf2eI8uXZs4fYWGJj2buXKlW4fl0wMnrdpw8XL7J+PS1acPUqGRl4e1OyJC4ujBtHYqJc36c6MWIEY8dSsCBLlkgtRZ3RJFga5EpSEm3bsnkzZcpQtiyLF3PuHGPGcOeO1MoUQno6mzer//lgFvnyoadHixasWcOJEwwcyN696OrmdJnKlcnI4MYNRUj8FlWrsncvkZHcvMm+fVSqxJgxUuhQNmvX0qmT1CK+m6NH8fMDuHePGjUICeHsWVJTWb6cy5fx97eIe9igoWxzhq/cIv72Gzt36md51hUtyokTvH3LrVsMG4aHB/v3s3Qpz5/j4kJ8vNyCqg+nTnHnjsaaQQ5ojgg1yJWQEEqXxsODV6+YN48mTSheHD8/tm1j7FipxcmfmBiGDCE1NVcMkejXjxEjxGOUH6N5c4KDVaDnaMkSnJwQBCIiePcOJyeGDct91qMxMZw6JfbVqyUpKRgacv48LVowfjy9epGUREoKdep8bOvrfpxBg8Rp43KgUCG2bTPp2NHA3JyyZblyBXNzTEyQyXj9mhIl0NJi1Sq6dMHfn3Hj5BRVbRg5kj/++Ek2fxWLZgdLg1yJjsbWFqB1a+7f5/p1ADs7oqOl1aU4kpJo2pQ8eaTW8YMEBREZKS8X/hYt2LFDLiv9GHnyYGrK8uX4+jJpEmZmODtz+rTUsuTMhg20aKGGvgwf51ZWrsyMGTRrxurV9O6NTMaRI1Sq9Plz69QhJYXz5+UX3d39dUjIq0GDaNCAtWtZswZTU8LDOXYMT0/x86ptW0JC5BdS1YmOJjqa7dtJTMRXftuFPzOaBEuDXClWjFu3AHR16dGDpUsBbt6kWDFpdSmOrENR9UMQ2LCBBg0oX56mTenbl6VLv+NA8Iu4uhIdzaNHclnsB1i6FAcHOnfm4EFq12bSJNaupUcPqWXJmfXr1ep8MD2dhQuxt8fQkMKFGTYMFxf++INRo8QOvgMH6NuXiRM/f5FMRrdu2XdkyxaCnt4HFxfat8fFhfR09PSwtubIEWrWxNWVhw/R11fW9HKVYPlyli5l3Dhmzswl05YkR/NT1CBXXF1JTGTRIgSBbt0IDGTvXrZvV3OP838ybRoyGTIZ1takptKggXj38GGplWUb7fbtWbqUAQMIDCQ1leRkzp2T1+JaWjRpkiMLLcVw8CDdujFrFufPi4X3Xl4kJPD4scTC5MelSyQm4u4utY7s06cPwcFs305yMufPc+oUS5eyfDlr12Jqiqkpo0axbt2/zZc6dWLHDnHqpfyxt+f1ax48QFubKVMYPpxatVizhipVANLSFBZYhcjM5MoVChUSfds1/DiaBEuDXNHRYdcuNm6kcmVGj0Zbm06dCAzMZZNCR49GEBAEhg/HyEi8LQjUry+1suxhdvEit28TEsKvv5KSQng4584xYwYvX8orRIsWBAfLa7Hv5cMHTEwwNGT9evr35+1bAFPT3NR6vnYtHTuqj/3V/fvs3cu+fTg5IZOxaBHv3+PsTN68hIXx7BnPnhEWRr16/36ppSX16yus1ExXl4kTadaMs2cRBNq3p3591q/HxgYvL8zMKFKEYsVYu1Yx4VWC9HROnmTaNKl15CI0CZYGeWNvz7lzLF5M7dqMHEmBArl4AMWuXWpZfWV2+bLg44OeHpmZ9O7Nn39Srhzu7nKsT6pbl1u35JiwfReOjmR1ilWrhrc3w4fz/DnPn1O8uKSy5EZKCoGBYgeeenDxIr/8gqEhmZl06cKZM5w+TcuWXLgAYGLydWPbHj1YsYIlS7h3TwHa+vVjwgS6dcPYmIIFiYvD35+hQ7G2JjaWd+/Ytg1/f+bMUUBsKWnQgCpVqFKFhQtJTaVfP6pU0WxiyQdNF6EGBSCTUbMmNWsCrF7NyZPUri21JvkTHs779+jpSa0j52ilpYkjQTZuRFeXjh0BDA1JSZFXCD09GjVi50569ZLXkjln0CDc3bG3x9eXqVMpXZoLFxg0SJwErObcucO1a1SsSJEiUkvJPh8nGg0aREQER45gaJj9iUZ16pCcTEAAtrY4OChAno8PPj4kJaGvL46u79aN/ftZsYJ+/XB2ZscOnJ3p318t/9n/BwsXkpBAaioeHjRuzMiRoOazLFUHzQ6WBgXTu3du9aoLCKB9e2bPllpHznnv4CA7epTkZMaPZ9YsZDJSUjh1isqV5RilRQu2baN/fzkumUMcHNi/n3nzsLCgUiXi47MGsEgnSJ54erJ8uVqVtwOuroSEMHYsp06xa5eYXW3bls2JRjIZXbvy9KmCRebJI9Z4X7lC+/acPs2iRWLRfdGiFCjAw4cKVqBUHBxwdubCBYoWpVw5nJ1xdlZM/vrzoUmwNCiYDh04epQXL6TWIWcEgcBA2rVTyxbC1/Xq8eQJDRtSsSI1ahAZia8vrq6ULSvHKF5eXLzItm1yXDLnODtz/jz37nHoEHFxuLszY4akguRGWhpXrtCihdQ6coStLVWrMmsWw4eTlMT58zRpgoUFjRt//XWCQFgYly/j7Mzz59y4weXLXL5MZKQi1errk5RE0aKcPs327fzxByDub+UuUlKYPRs3N6l15Do0R4QaFIyJCb6+rFzJ+PFSS5En585hZESFClLr+C4ydXUztm/XqVQJLS0KFSIlhYEDxbMB+WFoiKurWF0jMfnykS8fwMKFVKyIj498U0lJSEqiSRPxpFd1efWKCRM4eJB376hYkfr1uXyZOXNYvpwhQ7C2pl07+vX7ZpV+dDQ9e5KRASCTMW+e2BXq5sb8+QoTX68e69dTvz6Wlhw7xi+/8OwZWlq5z3Rm1SoqV1bPOUuqjSbB0qB4+vXD05NRo+Rls6QKBASot/WE1vLldO2Kvz+vX1OwoHwXf/lSHJVTvDjHj3P0KIC2NlWrYmQk31A5xMqK8ePp0oUWLXjwAGtr9Uq2zp5lwgTxdkICN27g6QnQrp1KnhW+fk3Vqnh7c/Qo5uYsX86YMYwbR79+9OuXo5UKFfqUqdeoQUwMly7JX+8/6d8fNzd++40+fTAzw9eXKVPo3ZuMDEJCuHcPa2vq1lX3eqXUVGbOZOtWqlaVWkquQ5NgaVA8ZctSogR79uSaS6SMDIKCOHNGah3fi8HLl1obNnDjBtracs+ugIMH2bQJIDGR1FSmTROLmCdNEjsfpKRoUa5cwdCQ337jyRM8PBg6lMGDpZaVLZycGDkSQeDePU6cYNQo8ucHcHSUWtkXmT+fxo2ZORPg5k3mz2fxYiZPZty4bFa1fxFLSx4/5tIl0aNKgeTNy/nzzJ3LqFHiDtyRI3TowM6d2NpSqRL79tGvHytWiBap6sn69ZQurcmuFIPwkzFw4ECpJfyUBAQIHh7C27fxT55cvnxZajU/ysGDQrVqUov4AaLr18+YMEEJgaKiBH19IShICaGyR0KCULCgsGmTUKCA8PKlIAjCixeCtbUQHq5kITdv3oyOjv7ulw8aJBgbC1FRclSkAGrXFo4dEwRBePpUsLUVNm8WBEEoUUK4e/dHVm3aVPDzE3r2/FF1L168uH37ds5ek5oqFCkimJkJW7aIj5w7J1haCk+f/qgaiUhPF0qWFE6dUkasCUr5zFEpNEXuGpRC3ryEhFC0aF4np7Le3hw6JLWgHyIgQC1r24mPJz6eq1fNrlzJ/P135cTMk0csl1EJQkJwcuK33+jaVRy8WKgQfn6qMToxu6SnExioDgZsgoBMRnIyLVvSv7/4b+aHh7DMns3EiWzdSkKCHDTmjNOnsbLi9GkGDWLXLoDq1fH1ZcsWpUuRD5s2YWOjVpMA1ApNgqVB8Rw4QJ8++PrSuXPCkyfPhg2je3cOHpRa1neSnMyePXh7S60jRxw5gqMjtrbY2lKr1us6dZRTDKWlhaEhBw+SnKyEaNngzRusrADGjePvv8XZRlZWvHkjra4cceQIxYrh64uZmdRSvo6rKzt30rs39vYMGwZw/ToJCZQo8SOrlixJsWLUqkVQkHxk5oCnTylVivLl2buXHj04cQKgVCnFW0fIn+fPychg2jTGjZNaSu5Fk2BpUDxTprBkCX/+ycaNsg8fEqpWZckSpkyRWtZ3sm8flSqp1eyfQ4fo0oVZs4iLIzAQMzOLkBDZkSNKiFyoEMePU7GiykxptLfn6lWAPHlYvJi+fUlJISwMe3upleWATZto144FC1S+hfD339mwgf37mTyZxER276ZpU2bM+JECrI907y7n2c/ZwspKHGTp7ExQEG3aEBZGRIRafRyI1KjBqlXky5eLB21IjybB0qB4wsKoWxdbW9zddbKuOuvWFb/n1BD1Ox+cPJklS2jQgMxMRo5k4cIHgwdrTZ2qnOClStGqlcqcEtaogZ4ekyeTkUGDBpQrR+fO7N/Pb79JrSy7JCayfz8+PlLryA5376KjQ5061KlDwYLMnMnKlfKa7OPlxfPnhIfLZbFsU7s2ERHs3g1QqxYLFuDlxbp16rahDZCezrx5n5pSNSgCTRehBsVjYEBiIoaG9O6tN2IErq4kJqpDCck/SUoiIYGjR1mxQmopOeLqVXF67qZNGBvTvPm7o0dlkycrLX7r1kyYQGqqCswX0dJi5066dcPeHkdH7t3jwQOCg7GwkFpZdgkOxt1dVfVevMjkyYSHY2aGmxu7drF+PQ0bKiKUlhadOrF6Nf7+ilj+PzAwICgIX19Wr6ZSJSIieP8eMzMsLEhLE0ckOjiohR9NcjL586vNfHo1RbODpUHxeHqyZk3WDVl8vNHNm6xeLRr4qBVz59KnD7Vri6aVakNWgpuWxqRJTJsGaCcnKzPBLVSI0qU5flxpAb+KtTUHDnDgAF27smkT48axerXUmnJA1vmgKrJtGy1a4OPDuXOsW8fOnaSmUr264gJ26cLmzUov76talVu38PVFEHBz48EDvL2pXh1bW3GUoZ0d69YpV1N2+ftvUaOPD+/eYWCAry8+Pupbo6/qaHawNCie6dOpVYvnz/H2Tq9bt8jEiaSmcuqU1LJyTFoaYWHiwAx1wsODdeswM6N48ax+oQIHDgh1637DPFuutGxJcLCC9jK+i9KlKV0aoHx5HB3Zt49ff5Va07eJjubvv1Wy5TEzk99/Z9cu0Zxq8mSqV8fSkvnzxSl+CqBIEZydCQ5W+gFvnjz/UyVQpQqrVlG9OgcOoKXFjRt4e6Ovr4JOxCVL4utLZibh4eJgx6xrRY0JloLQ7GBpUDzFinHtGgYGjBihffWqflQUp06p47iJDx+IjPzm2DTVY/p05s1jyBB8fDh/nsGDrYOCMqdNU6aEVq3YsYP0dGXGzB56esyfz6BBKtPo+DU2baJFC5U8XX/4ED09Mbv66y/OnGH9enx8FH0dJU2p+z+YPZugIFJSGDoUoHx5lixh1iypZX0BMzNatcLbm3PnMDGhSRO8vfH2pkgRqZXlUjQJlgalYG7O9OmEhiYePx5br55YJaom9Owpbqpv3IiBAZ074+NDz55Sy8o+xYszZAj587NqFYMGoa19Zc0aQbkJbtGiFCnC6dPKjJltGjakSBEcHTEzw8yMRo24dk1qTV9Gdc8HMzLQ0QG4do3Ro9mxA2NjdHXF8YEKo2lT7tzhwgWOHVNonK9y6xa1arFzJ4cPi5MRa9Tg1i3pBH2Dy5d58AADA6l1/ARojgg1KJvXrVvnmzWLAQO+OeFVRWjVirg4gBMnqFBBbBgyNZVWVE5IScHfn6CgjycB6aGhyleR1Uuoij3h588THk5yMmfOUKQI27dTvz67dlGtmtTK/ofbt4mOplYtqXV8EXt7YmMJC6NtW+bNw8EBYM8eRf8MdXXx82PmTNLSxEYOCTAx4e1bChdm/35cXSlalKpVMTGRSM23mTGDwYO5ckWVNeYSNAmWBmXz3skJfX1OnuSXX6TWki2yGm2ePycxkV9+UcOO7JUrcXKSvM6idWuxsf2HrbzlzbhxzJ/PkyeMG8euXXTpgr4+Y8eiFKuw7LNxI+3by8VDSgHo6DB1KrVrU7MmPj7ExrJ0KVu2KGEmc48euLhIOuOySRMWLuTPP7GzY9cuGjakYUOVrSR49IiQEFavZuBAqaX8BGgSLA1S0L07y5apS4KVxZYtlCmjql9vXyE5menTVeFMtmRJLC05dw5XV6ml/INz5wgORl8fR0f27qVxY5o0oVcvqWV94tUrwsIICBCns6goefJgYsKLF5iZoaeHlxfnzlGokKLDliiBjQ3R0YqO899Mm0adOjx6ROvWAA4OBARw7px0gr7GrFn06kXevFLr+DlQtWvJ7ychIaFNmzZGRkY2NjbLli374nNiY0lJUXHz45+D9u05coSXL6XWkQO2bqVBA0qVklpHTlm+HBcXKleWWgegSo6jn6OlRWYmenosXMjAgSQlkZmpUvts588zcSImJlSoILWUzxEEIiIIDSU6mnv3GDKE/fsJC+PdO2Jj2bwZW1uFxm/Xjnz5yJeP+/e5fFm8bWnJixcKDfsvChbk6lVcXQkKIigIb29mzqRjR9aupWVLqlWjXTsuXFCupi8TE8PWrfTrJ7WOn4bcs4M1ePDgmJiYx48f37lzp1GjRuXKlXP/1wTLRYsID9eMtVQBTExo3ZrVqxk9Wmop2SIigogIJk8WC3lVnaQkdu3i3j0KFGDmTPbvl1qQSKtWNGrEnDkqVn3n7k5QEN264emJszMzZmBjg5ub1LL+h8hI+veXWsTn3LpFjx48e4adHbdvk5nJ2LFiAqgsm821a3n/HmDPHrp358gRihdHV1eK7Rl9fQYMYMCAT4+sXEn//qxYQYkShIfj48PQoZL/FS5YQNu2FCggrYqfCBW6SvsR0tLSAgICJk6caGlp6e7u7uvru+5LVm8ZGWRm/s9HuyCobMNQbqdPH5YvV3STkbzYsgVvbzXJri5epGxZNm0iI4O//uLtW27fllqTSPnyGBnRsKE4JFdVmDaNMWOYN4/ISIYOZfZsRo5EuTYWXyc9nZcvVclW6d076tenUyceP+b0aby9sbBg504EQZkqdHUxNxf/s7Fh+3bMzVXj8Ov4cWQy6tThyBGqVqV7d0JDmTyZmBgJRSUmsnIlgwZJKOGnI5ckWI8fP05MTKxYsWLW3YoVK968eTM7L4yOplEjRSrT8F84OVGggPjFtmcPaWlSC/oaW7eqyfS3lBS8vfH3Z88ehg8nKoqtWxkwgAcPpFYm0rIljx6JGw+qgpMTZ89y8SI1a9KqFSVLUr48Tk5Sy6J1a2QyZDJatiQ1FVtbZDKMjJR+BPZvNm/ml1/o1g2ZjB07OHyYCxd4/Zq//5ZKUZEirFmjMp8ihw/z228EBHD9OllDP21tcXWVyqckPp6wMFaupE4d9RprrvaoxSX5t3n//j1gbGycddfU1DQhIeHjn2Y1tQA3bnyIiXE3MnqgoxOno/OuZMkxlpZOqamLwsP/x7Pk6VP9AgXSDAwylfcGfhrS09OTkpLCw8NNQ0Js797NfPz4XcOGebZs0R048PGMGclZ3d0qxuPH+s+flzA2vqXsybI5x/jcuYKWlg+KFCE8vMCaNXkqVnxiZ1e4YcP0BQtiunb9+LSMjIwbN27IpDioq1Ahz7x59hERT8LD45Uf/WuMHJn1f1l6uoOPz8t58+Lq1lVctMTExMTExBdfzZXGjWPcOICOHUsmJcm2br2X9XhMjLRbIViHhqbY2b0OD9d78aJk9+4RCxZ8ePrUzt4+4fDhWH195evJk0e3WTPDhAQLf//Xnp5x2XxVampqWlpauAL+VVs/e5Zibf36wQPd6dPt/fxeymSxjRvbpacn3L0bK8WHyKlTJtu25b93z2Du3Mfh4UlKi/vHH388ffr0492oqChnZ+cmTZooTYDk5JIEK2/evEBCQoKJiQkQFxf3MdkChg/n3TuAlSu1jx+PMjW1iIwsZm39rlKlZTVqaF+6pG1nZ/f5aqNG5e3YMaV+fRW5GspVfPjwISoqqiiYTJ36ftu2vO3a6Q0blmZrK9u+veTw4XHnz6vAQOB/EhBg0KpVZtGidt9+qtTohYbqOjjY2dnJ3r833bw5Ye9eOzs7/fLltR88MPjslzw+Pt7GxkZbiS2R8fEyf3+DzEyAtDSt4GCbR48yAAeHjLZtU5UmI5ukzZ9v17dvvK+voDDT9CdPnpiampqZmX3zmQkJsvv389Sokf6PjykJyWNtnVcQDK2tjXv1ShswwMLLC8ibnKxbvLixFCLt7HB2xshItnGjddeu2XWoe/v2bWJioq0CKvH1atQw3b/f0M4OO7vk4GCbJk3MS5c2unZNe9QoSX4+Fha6sbF5SpXKbNjQUplxBw4c+OrVq493AwMD/10YnbvJJQlW0aJFDQ0Nr1275ubmBoSHh5crV+7jn2bNbwBCQ/WfPLl3/nzD+fNZuDD/1q35//qLjAzKlzc3MyNPHubOpVYtdHQwNNQ1N/+0fmYm8fFk48NQwzfQ1tbW0dExPXiQdu2M69enQwfTrVuZOpVu3VizxvzGDensAv+T3btZswZzcwkuzXNMmTJs3Khnbs6yZXh6mmR5Xz17RsmS+p/9QstkMjMzMx0l1pTp62NtLY7KMTXl3TtdKytdoGhRzM2NlCYjuzRpwpYtZvPnU7cuUVHY2+PuLt++whcvXhgZGZl//inzH+zahZNT1ifSt5+sJHx88PY2kMkwMNAZOzaPlhbXrxMWpvvrrxI68HbowJgxvH1rXqJEtp6fkpKSlpamkJ9q164sWmQ+fz6jRlGtGqtWGXt74+ZmIpFDiZERjx8zZ462kn+FXD++3zdvmD7dOTTUrFEjXF0ZOZL8+ZWpRCpySYKlq6vbtm3byZMnBwYG3r17d+vWrXv37v3K8/38sobeEh1Nu3b88gshIcTHExyMltYXKjUPH2bFCoKDFfYGfjYiI0XDg169qF2bcePQ16dkSSIjpVb2T65dIzlZcpPObOPuzps3LF+Ov79YSX7+PIGBXL4srS5DQ4YMEW/v20dEBCNGSCromzRtym+/ERpK2bIsW4YgsGmTJC4dAQF06oTK7F4B4OJCnTrMni1as165wooVLF4s7XwDfX38/Fi5kunTJVQBQJ48nDjB4MFYWGBhwZs3NGjAlStERHDpEmFhmJrSoIGi6/y6d+f4cYDYWBITRWc3bW1OnsTKSqGR/5eHD6ldGx+fww0adO3alW3bcHLi5EmymQirM7kkwQLmzZvXrVs3GxsbU1PTGTNmfHErslIlrlyJAtExBXj+HENDNm3i5Us8PQkKYuVKkpI4dYqCBTE2xt2d+fNJS1PJObXqS+HCPHwI4OBAhQoEBdG+PQ8f0r691Mr+SWAgPj4qZivwFXR12bkTDw8yMli6lIgIrl5l7VpFOxLlCDMz0tK4fl3FXJ0+JyqK/v3p04c7d/jrL4Dly2nenOvXldxKGh3N33+zc6eKDXiOi+PkSaZP59kzNmygVCnOn1eF8e3du1OrFpMnq0ChgZUVAQGkpvLiBTY2aGszdixlylC9OvXr8/o1jRvj68usWYr7cJk5Uyw+btSIwoVFs2FtbeVmV8CoUfz+O0OGPJs4kRo1qFEDKytGjWLrVuXqkIDck2AZGxsHBgZ+/TnNmnHixPUv/lHBgmzYIJoG9OmDlRUPH/L4MWXLcuwYmV+qd+/ZkzlzVKMrWO1o04Zq1ejcGUdH+vXjzz/R0yNZWhFSAAAgAElEQVQqChU7oRcEAgPZtk1qHTmiSBEyM/nzT5KSqFMHDw8+q0dUBQoXxsODoCAVTrACAvD2Zt48nJ3FDtKePVm9mtBQJY8f2LqVJk1UI7uKihKbBF1cGDKEX39l6FCpNf0TBwfKlWPnTpXp+dXTo0gR8fb587i4oKXF0KHo6TFuHLVrExSkOK1ZBhaXLhEbS9WqFC+uoDjf4uhRFi8GzLJKoYGOHVXKBkVx5BKbhu/G3JyOHQFkMipWxNkZZ2cKFqRrV65fp3t3rl3Lqjfg+HHq1cPHh7Ztef0aYO9e4lWsEUptKFaMZcto0IC2bTl7lvBwhg5l+3akaEH6CpcuoaPD/7t/qAlLllC7Nt260b8/LVqoWnYFLFvGwIEEBUmt4ys8eUKZMujosHgxQ4aI/87LlOHJEyULCQigbVslx/wXgsCYMVSqxLp1rFtHmTKcOMHMmVLL+jI9erBihdQi/k10NGFhHD9Ovnx07owgYGzMiBEEBCg68uzZNGki6R58cjJGRoSHd121SnzEyIiUFOkEKY+fPcHKk+drmXSrVowdy7JldO2KmRl37nD2LNra/+nik5GhLsaZKkDLlty4QePGmJnh7U3t2lSqJLWm/yEwkIAAfH2l1pEjEhOZO1ds7ldhqlQhJYXrX95NVgEKFhRzKTc3vLwYNQrgyRMlTNb7nEePePgQDw9lxvwS/v6cPMnNm+zYwcyZ6Olhbc3y5VLL+jItWnDjBvfvS63jH8TEYGWFri4bNvD0KYMHA9jZKXqGYkQEx47x+++SjqivVIklS2jQ4MBHz8mjR1Xt015B5J4jQjni5SUWs7q44OICYGBAVBS7d3PkCAsW4OSEvT3x8Rw/Ln7kliqFrS1z5wIMGyaddPUif37atQOIjaVECWJiVGqIQ9Zn4NGjUuvIEUuX4u5O+fJS6/gGMhmtW7Ntm6qeEvr44O5Ojx6ULMmsWZQvT/HiPHxIrVrKVKEq8wOWL2fjRiwtSUujQwcmT6ZaNdq3V01TcD09OnZk5UqcnPD1VYGfXha2tjx7xocPGBqydy/16jFxIjY2ii5cmz+frl0pV47PuuoVz82bLFnC/ftYW9OuHS1bMnw448ffymofO3SIvn35uJuVq1GR3z7Vonfv//wjU1OSk6lShVev+PCBLl2wtsbGhj59aNuWxEQlqsxNmJvTogWrV380e1QFUlOxtKRMGal1ZJ8PH5gzh8OHpdaRLby96diRSZOk1vFFHByYNQs3N5o1o2hRbG0ZNYojR5RcDBUQwH+MrVcujx6JKfuYMRQsSO/epKYSESG1rP+ke3dcXdHWpk4dCheWWk0WZmY0asTvv7NwIaamHDhA9erExip0+Pnbt2zcqPR94jVrGD2awYNp3pzHj+ncmbdvmTmT9etH3r3L/PnY2bF6NZ6eypUlDZoEK1vY2oqFOFWrcuSI+KC1Ndu2sWsXq1axeTOWlgiC+rSbqRr9+9OsGUOHqswlJ0lJNGsmtYjsEBLCgQPExfH6NTVqqOqm0D9xcSE1lRs3VHW7zc+PevXYvZvISHr0IF8+Tp2idm2lxQ8PJz6emjWVFvC/KVCAyEju32fLFq5cQSYjMlKlNpv/gb09FSpw5YrUOv7BsmV06ULp0ri5ERdHfDw6Oty+ze3bHDzIu3c4OTF8uBwbfpcupVkz5aaYb98yfDhnz1KyJMDu3aSlkS8f1aszZMj8UaNGjhwprZeHklGVLzMVp2LFL1c6FynC9Ono63P+PG3akJxM4cJ8+ICWFsbGjBlDfDwdO7Jjh9IVqx0VK2Jry549tGghoYojR6hf/9Pd6dNFT52ZM1Xy5Dczky5dOHeOLl2wtWXYMPLn584dSpeWWlm2aNmSoCBVTbAAa+tPu9keHlSujLe30n62W7bw22+qccHm68vIkZw5Q2AgFhZkZjJxosr06X2Znj3p0EFqEf/AxIRt27IcWTE1ZdUqYmKoVIkyZZgyBTMzjh+nShW2bpVLHp+SwuLFSt/ODgmhRg0xu1q/nlGjOHSInTvZvx9X12R9/Z8qu0JT5P4jaGuTNWvEzo66dRk6lFKleP2aNWuIiKBgQYD377l4UVqZ6kO/fixaJK0ET08EAUHgxAl0dYmKEu+qYnYFrF/Pgwdcu8aIEaSn06gR48fz2cxBFcfbW7V7CT/HxoYJE+jRg4cP2bGD48f5bNqp3BEE1egfzGLCBNGwMjSUP//ExYWYGNU83D18WByP7eNDSgrW1shkaGkxa5bUyj5SoQIdOtC0KRYWHDhArVrExJCZibs7Eyawbp3oB/rDbNxIxYpKv3p5/54ss/iZMxk/nuPHcXLC3FzFprsrD80O1vdz9qyYRX38RktOBvD0ZPp0/viDzEwaNpRMnvrRsiVDhnDrFmXLSi2FoCDVMB/6Otu3M3gw+vokJTFrFvv24ejI2LG8eKF0M8HvwcWFlBQVPiX8B35+TJqEszN16/LuHXfuMHs2v/0m9zgvXnD3LkZGODrKfe3vYv58KlZkyBBCQwGmTOFjO5iKUb/+pzkcJib4+Ig2sSrKoUMMHkyBAjRqhJERHh40bEj37jx+TNGi373qgwcULszcuSxcKD+pXycjg5QUDA0pV44pU+jXj9OnOXMGa2uA0FAVaIWVBk2C9f3Y2Hz5cVdXZs8mMJAFCxg3jsREtm4Vt/pr16ZAAdLS0NVVplI1QU+P7t2ZMQNfX8zMcHLCSJopdZmZ7NiBgYEkwXPCmzdiF+vy5VSrJh5jFyzImzdqkWABrVqp9inh5/TvT40anD3LokUULszNmzRsiJ0dbm7yjdOnD+npYn+tNEREsGKF2AVWpgxLl3L5MlZWKptXfRFDQ4KDmT9fhb2gP3zA2BhnZ4KDadmSv/6iSRNMTPjw4UdWHTKESpUwMKBuXXkJ/W/u32foULHX2tqa0aNJSGDHDi5eFIePLljA33+zerXipagimiNCeWJlJX6v3brFjRuULYu9PUlJ9O7NihVs387z5wB+fuKOu4b/ISmJBw/YuJH588UDV0W22HyF0FCsrJgzB0ulzp7POfb2hIWRlMTs2UyYABAfz7Nnn8yjVR61OSWMi2PnTjZtolcvBgwAKFeOMWMUYQeVns7p07RpI/eFs0dgINWro6ND27YUKED//tSqpS75+udoa1OzJhs2SK3jKzg6EhIC4OrK/v306MG8eTx//oOe64JAcPCn0Z8K5NkzatWibl3evCExkcWL6dcPS0saNaJsWZycKFiQI0c4dkyFk1wFI/xkDBw4UJnhoqKEwoWFdesEKyuhQwchOloQBKFJE2H3bmWqUCHi4uIuX7785T/r1k3w9RVatxb8/QVBEC5fFgoXFs6dU6a8LPr2Ff78U/lhc865c0LhwsKgQYK3tyAIQny84OsrdO/+zdedPn06LS1N4fKyR/HiwvXrUov4JtevC+XLC4IgJCcLpUoJQUGCIAhnzgg1a37fejdv3ozO+jj4F9WqCaVLf6fMH+XdO8HSUvz7yMwUGjcW+vcXihQRLl6USND3s2WLcOSIULaskJn55Se8ePHi9u3byhX1v9y7JxQoIGzeLEo8eFDQ1xcaNRJCQwUfH6FSJaFxYyEg4D/fwH/g7i5YWAipqQqR/D8MGiSMHi3ejogQSpcWevQQ8ucXUlOFhAQhLEx4/frzp0+YMEHxmlQLzQ6WMvDz4/Zt8uenQgWWLv1UJaDhE/HxBAWxYgWDBrFkCYJA5cqMHs3SpUoWknU+2Lq1ksN+F9WrM3MmCxbw4AG//oq9Paam+PtLLStntGzJwoUqbz5vYcHLl2Rmoq/PunX060dUFM+fy2uTMyaGhg3x9MTTk7AwEhLE28r+sYSE4OIiHtn6+/PqFXPm4OfHnj3K1SEHfH2pVw/g5EmppfwXJUty4AALF5I/P8WL064dI0bw9980bkyDBqxaRdeuzJuHn983V3r5kmrVqFKFKlU4fx6gRg2qVFGwF+zlyzRoAHDxIm5u9O3L8uVYWPDgAXnz4uRE/vyKDK8GaGqwFIuu7qfxenny0Lgx06cTHU1SEmfOAJQpIw5D/Nl5+hRbW0xMcHXF0JBDh2jYkEqV2LxZyULOnKFAAeztlRz2e3n6lNatGTCAd+9wdJSjiY7S8PamdWuVH/hYqBBly7J4Mf37U60affrg50dCAgMHymX5/PkZMUKsFQ4JoX17sSw4q0pYebx7h4UFwJkzTJ/OuXPo6mJpqXqjZ7KFTEbfvixerOQJ3TmhcmXOniU2lnfvKFKEV69YuBBra27coHNnKlXCywtnZ44dE7PF/6BgQZYvJyODqChat2boUPH3RyFuZR8+oK+Ptja6uiQns2IF48axciVNmwKkpKCnp4CoaokmwVIslpZcvQqgq4uFBaamODiwYAFnzqCvj7u7eAEcE0N4+E/ibfsf5MtHdDSZmWhpMXgwc+bQsCEvXyr/GigoSNK5XTkiPp758zl9GgcHqaV8P1m9hIo0PZATq1fTqBHHjlG3LpmZnD1L5cry6iLMsh0HgoIwN8fVVaK+qzJlmDGDyEh8fVmzRhzkcuECrq5SqJEDHTowbhxRUUpPVXOEubnobnDqFL/8wurVNG5Mly6sWIG+Pm3bcuTI1xMsmUy8RFm9mqJFKVsWZ2cF6Ny0iUmTiIoC8PCgfHn69sXA4NNHUFaf6Y/VkOUmNEeECifLWc3QkMGDGTGCESNwdmbJEhITOXIEJyeACxeU2FKrmhQuTMmSYlO1ry/37nHhAnPm0KqVMlVkZrJ9u5Jj/gDz5+Plpb7Z1cWLBAWxbRtFi3L3LkFBBAWxfTtpaVIr+yIlSnD9Os2b8+gRmZls3Mj9+9y4Id8gAQGSpgIuLlhYUK0a3bvj5YUg8NdfnDypMpZcOcbYmHbtVHYy9b9ITsbICDMzDh8mNpY6dYiKIm9e0QHoW8TEEBCgsPGG8+czfTrr15OYyJs3VKzI0qXExODoSGwsd++yeDGtW7NokWrY46oEmh0sabCw4Ngxpk+nShWWLhUNS392Vq/Gy4vjx6lXjwoV8PSkVSsl+zGfPYulpTjqW9V5947Fizl7Vmod309ICJcuAaSk8OqV2E6YJw+//KKqxRt6enTq9OluQgJt23LmDI8eER9PuXLi+dr3EhfH8eMMGqToEcD/jUxG8eJERLB4MceO8eQJtrYcOoSZmUSC5ECfPtSty9ix6nByVakSY8eSmoqhITt2sGABLi7Y2eHjQ5cu4v6QmxuTJn2xGGDRItq0oXx5BXyCpaYydSoXL4q7UydOsGwZbm6UL4+FBQMGEBdHpUocPaomnitKQpNgSYC1NRYWaGszZgz169OuHTY26mBrqWhKleLmTdat4++/KVmS0FAmTEBLqZusQUEqPgIE+P8aiDlzaNqUEiWkVvP9DB8u3tizh7ZtGTWKSpUkFZRTOnXir7+ws6N4cUxNuX4dPz9mzPjub/LgYOrVY+JEuYr8JseOceiQOAtPW5uLF7l1i8RE7t/HxoaiRdV9Q6J0acqVY9s2RZjCypvy5alalXbtWLSIggXp3p2//2bLFm7cYORIRo4ECArCxYVjxyhX7vOXJiayfDlnziimfvThQywtKV6c1FSmTGHtWrZvJzOTsWM5dYrx4xUQMjegOSKUgKVLqVEDoHVrqlbl/n1OnGD/fnHIg5ERL15ILVEq8uShVy9WrGDePPr0Yd48ZQbPzCQ4WLXPBzdtwsEBS0uMjZk5k/btpRYkNwoXZssWqUXklEuXuH8fAwNmzSIkhAcPePyYwYO/e70tW5Rrf5WRgZ8ffftiaYmLC7t20a8fs2djbEyhQri7U6yYumdXWWSVusfEEBMjtZRvsn49pUrh4ICNDZaWyGS4uWFlxfnzWFjg4MCYMUycyOjR/3jdypX88ov8sqsPHxg/Hnt78uTB0ZGdO0lOFusOr13j779xcyM5WR12BSVFap8IZaNkH6xssnu34Ogo2Nioo91MzviaD9Y/eP5cyJdPePNGwYo+ERoqODkpLVrOmTdPKF9eNAYbMkRwcxOsrISnT79jJZXywRIE4cABoV49wc4up44/UtOpk+DvLxw5ItjYiJY/sbGCqamQkPDNl/7bBys6WjA3Fz58UJDWL7F6teDmJqSkiOHt7IS+fYUaNZSoQEmkpwtFiwo9ewqTJn16UHofrK+QmSlERopmViYmQkyMMHSoUKyYEBoqCILw5o1gaioIghATI1y9KsTFpaYKRYoIly7JKXp6uuDmJrRpI9y+LSQlCWfPClWrCnp6goWF6ACXhZ+fMHVq9lfV+GBpkIwiRcRG1127xEfc3Hj3TlJN0mJlRcuWLFmitIBBQSpsf5VVA7FrF9WrExPD2rUEBNC5s5I3+RRE/fps346xsWjhozbcu0eVKnh44OND165kZmJmho0Njx9/x2KBgTRpotxSgeBgfv8dPT3S0/HxoWNH0VMt122ha2vTowcXL5KZKbWUbCKTYW0tjlRLTydPHmbNYu5c2rShQwdevyY1lfr1KVuWzp2xtQ3wXF2yWLrcOgd37EAmY/NmSpfGwIBXr8QhJIJATAx373LhAh07cuWKONVAw3+gSbBUiIYNOXiQ/v3FIoyIiB+cSaX+DBnC4sXZ7KD5ETIyiI1lxw4VPh/8WAMBTJ8uFu41aCBWias5WlqYmuLrq26nhGZm4pnTn3/y5g0TJiAIvHpFvnzfsVhAgNJ79bJmWQoCPXtibMzEiWhpibMscx3du3P7NklJUuv4DqpVY98+gObNuXOHIkVwdiYtjfr1efmSq1eFyKhZ1xuOSBj7/SHCw2nUCDMzzMxo1Ijdu2naFJmMe/fw9mbYMDZupEULhg8nNJRmzRgwgBIluHABY2N5vctciabIXSVwcRGvVZycCA3l119z5UdczildmqpVWbeOnj0VGufIEaZPx9SUMmUUGucHyPL0Ax4/ZsMGrl8HclkNRJs21K7N3Lnq01TbogX+/jRujJ4ewcFUq8abNxQtSuHCOV3p8WMePPi61ZECKFmSq1fZt48bNzh+HC0t4uLUa5ZldvDy4tUrAJmMZcs4dgzAyoqVK6XVlW0mT8bbm8xMWrZER4eyZQHy5WPx4nTbYttplTdvXl07I4/4YHZUY9cuwsMxM6NhQwYN+uRz/Q+eP+fBA6ytKV6cCxdo3pxp0wgIANi+nf79SUmhdWtOn6Z/fzZswMCAJUuws/vUmaIhG2gSLJWgUCEaNgR48oQtW2jdmk2biInB31+8GK5dm+rVpdUoEcOG0akTRYuKXU6lSysiSFoaz56ptqV+iRIIAmfOsHQp/fpRqBDApk2iPWWuoGRJChfm5Enq1pVaSjbp3JmjR3F2pkcPTExwdGT5cjZt+o6Vsv7VZ11lKY8+fWjQADMzLl3CyIj4eLp3x9c3l21LzJtHYiLAtGkcPszixejoYGQktazs4+bG7t0MH0737gAuLjRqhKsrjo4xff8Y/KC2ffHM4SNN2WBHp05MmMCgQcTGsmwZNWpw+DDLlnHgAPHxODkxejQWFvTrx8mTlC7N06cUKoRMxpw5tGsnhrOxIX9+tm1j7lzWrRN/Uu/eERLCzJmS/RDUE02CpVokJxMbC9C8OfPmERiItzfa2j/xWeHDhzx9yogRlC7NsGG4ubFihdxnswsCL16otoG7TMbixTRtSkYGISFcuMCSJVy5wqJFUiuTJ23aEBioPgmWtjZbtnDgAPv2ER9PrVq0acOwYVSuzOnT3L+PtTXNm2dnflFAgFKshtPT2bGDsDBMTWnQgCdP0NEhJYWmTTEz4/JlWrbMHVV9n/PxoqxCBcLCuH9f7L59+VJCUTnExYUTJ0hPB9DRYcwYYmP55RcOuqeWT498Gus92Jb4WDp25PffxcbPOnXw8aFCBerVY+ZMTE05cYK6dcmfn0aNePoUfX0EgbVr6dqVwEAePuTIEVasID2dsWPp04dTp6hbl6JFuXKFoUPp0CGXbW0qAU2CpVqUKsX06eLtTZsoX56HD9m6FZ2f8y/q5EnGjWPuXDZtYssWkpPp25c+fVi/Xi7LT5/OlSsAd++SlsaECQBaWixa9IOGkYrh118pWZLMTNq0wdSUX39l6VIMDaWWJU98fHB2ZtEipe/l/AheXnh5fbp74gQVKtCsGc7O3L7N1Kn8+SddunxlgZs3iY3FzU3BOp88oUkTChSgbl1ev8bTk8REzp7FwYHwcGJjcXRU7YEycqBmTWbPpl079XSf+Pg18Ouv+PkxeDDaxu9TtSfOLqRdYDG+vly4QIkSdOhArVo4OGBoiEzGxo3iq8qXR0+P/v2ZMUP0F4yLw9QUmYxKldDTw9OTqVPx8iIujmHDcHamTRuePaNUKQYO/LTFpSHb/Jzf22rD4sX07UvHjqxfj7a2WFCrkPmdqsmKFYwdS7duLFzI6dO4u7NgAdbW4ufCD+PhIfp0zpmDpaW4g2VgIJe1FcD+/SQkEB6ei9NtOztKleLIERo1klrK95GUxL59uLmhrc3w4chkDB1KzZq4un7FXXvLFnx9FW+p27Ur7duLNTRhYaxdi7U1d+/i5PST1B9Uq0bVqly7xtGj6j34dVpIzTEPH2Ai3u3Xj35469Bi/1wdzwLhbNjA1KncuUNMDPr6/PYbpUphZUVsLKdPAzRrRno6MTHcv0/NmhQoQJEi/9PBu20bbm6MHv1vty0NOULTRai6mJtjbExwMLGxYg/4smUsWya1LGUSEUGFCmhpMXSouLNnZIStLc+eyWX5KlXw9sbbm8hIHBzE202aqOT2SUYGI0YwfXouzq6yyDolVFdCQihVin37iIjgjz8AihfHz08cA/Qv4uNp3pwtWxRvMh4dTVgYQ4YAPHpE48YsXcqUKWJd88+BlxeNGjFkCLNmSS3lxxg9GkFAOHa8RZGrJjofhH79hfBraeYFPB2e4OTE7NmcOMGLFxQuTI0aeHmRmsrly7x9i7k5WlrUrs2AAeIkwYMHadqUGzeYN4/ISJ49Y948xoxh2jSp32VuQJNgqS43bpAvH3p6bNtGRAQDB5KZqT4+LnLB0pLISICOHbl9m7NnycjgxQssLeUY5No10tIwMfn2M6Vk3Try56dJE6l1KBxfX/bsUc92eiA6GltbDAzYsYO//hKvh+zsiI7+4tPfv+fMGXR0FD8jKCYGKyu0tbl3Dw8Pxo6lVauvCMvFtG3L3btcvSq1jh/mgV3d04mVjCwNWbgQR0dGjaJlS8LDAdLTWbGCt28pW5YOHfjjD5YvZ8YMhg0jNZU6dfDyompVDAx4+5aDB9m4kYsXqVmTmjW5eJEzZ3Bykvr95QZy+dVw7sDQkD178PBAW5sGDaRWo0zatGHGDBo1wsiI8eMZOZLmzXF0pGBBOQbZsYMGDaQbr/sVPnwgNJSoKGxtmThRnTd2coClJc7O7N+vwp5kX6FoUW7dArCy4uRJPDxITOThw69MMElKUor9Vda+b2goPj5MmiT2o928qZK/94pFV5f+/Zk7V+33saZMoUuXTxVWDBsmXoMlJ5OYiKsru3fTvj2lS9O9O3p6/P033brRsSONGtGtG5UqERHBwoV07Urz5jRvLuWbyaVoEiw1oGFDXr8mPZ1bt7h5k717ASwsOHhQamWKpk0bzp+nXDk6dMDUlKtXefKEkBD5Btm5kwULcHeX76o/zLFjdO1KiRIUKcLBg6SkqGThvULw9SUwkMqV1fDb382NxEQWLaJfP4oU4dQpatYUi10ePODCBYBq1W6n2QcFmefNmyctjaQkZDJWrEBLi6ZN5VphGRLC5s1ERWFvT58+ODvj6cnatfj6Ajx4wNSprFkjv3hqQ48eFC/O779rq2+LyMOH7N/PnTs4On72aJcudOnC69cYG4sOWCdPMngwI0ago0P+/EyYgJ8fT5+yYgWBgdjYsH07Li4SvYncjybBUgP8/Xn/HmD+fHbsoFMnatSQu1OBSiKT4e9Phw4cPMiLF3TuzNmzFC0qxwgREbx4Qc2aclxSHkRF0bYtQUHUrs2rV+zZw8CBNGvGtWu5vgYLaNmSoUM5e5bLl+W7Wal4dHTYtYt27Vi9mooViYggI4NChWjalOfPRf+JYcPuV5l8U7+lQR6drJk0kZHiSbiLi/wSrKFD2bWLwYNp3pywMKpXJzOTatUYNYp9+4iL4/x5/vgjN/moZR8TEzp3ZsUKw0GD1NXQedo0+vYlf/4v9fZ9fiXm4MDevaSl8eHDp+YdOzumTlWOzp+c3P9hnQv42H5UogRt2jB1KmfOiO1vPwVVqlClCoAgUL06O3fSooW81g4Oplkz1bMODwjA25vatQEmTsTPj/Hj2buXM2fEB3M1+fLh7s6ZM2RkSC3lO7C359w5zp3j3j3atsXNjRkzmDcPb29xnyourmmrVtVL3mbEiP798+TNy/Ll8tZw7hw7dnD1qlhaGBGBvj4pKezYQWSk6IO1atXPsyf6bwYNokKFPF27akdEqN9G6dOn7N7NvXvZfoGurqq2RudyNEXuaoaNDePG0bKl6E38cyGTMWkS48bJ8Yt3xw45Zmvy48kTcWrPrVsEBYnN0mXLft8UYXXE11dt69wBLS1cXencGU9P8uRh82YOHOD2bXr2JDMTU1PmzDHbvj0lRXb4sGKmO+/di58fJiYIAmPGsHAhFy7g6srJk1SoQIcONG36M2dXgLU1Hh4pa9fmU8cLlj/+oFcvzM2l1qHhW2gSLHWiWjWqVaNvXypXFqtU4ef5zgWgYUPy5WPzZrksFh3NrVsqeUhSsCBPnyII9OnDxInkzw+Icy1yNWfP4umJpyerV5OcTOvW4t21a6VW9iM8eUKVKhw6xKNHNG1KdDSlS+s+f374sJ6jo/ycYiMjCQ4mOJjISBISyJePJ0/w9OTkSUJDKVKE/PmJj5dTsNxAr16JQUGmWe7oasTTp2zfzqBBUuvQkA00R4TqxEe/6KVLqVWLuXNp145atXj6VFJZSmbaNIlGcgYAACAASURBVDp0wNubN28oUOBHTKt27sTL6z/HoUqJtze1amFhQWKiOOj64EHu36dWLamVKRZHR0aMEG+fOUP58vj4iI+rMYUK8fgxDg4cOsScOTg6Mnx4uoXFzj+edH63tkXCehzyMXAgvXp951l1ZiZjxrB6tWgG37s3lStz+TJTp9K7N+PGoa1NZibnzzNggHzfmVpTtmx6sWKp9+6pzZfgtWsAy5fTvbt4zaVBxVGb3y0Nn2NgwLZtVK+Ora161qn8CM7OaGtjbk7+/MTG0qIFs2d/39bOzp1fH2EiHaVKMX48AwbQsiWzZ3PlCmfPsmWLYs6TVIi8efHw+HT72jVWrJBUkFxo146xY9m0CV1dRozA3Z2GDRNSjU5n2m+6MsikzCyuX2fQIK5f/04fYX9/QkO5dUv81r1zB1dX4uIYMoTx49HSIjGRoUOxs8PZWb7vTE1Zt46NG0lNzffunRAXh4eHODln8mRq1JBa3H8THExCAlu2cOeO1FI0ZA9NgqWu2NmxdSutWqnnUK0foUMHihXjwwfu3UMmEzuhrl7FwCBHy8TFcfYsW7cqSOUPExZGly5UrMizZzRowKpVP0fj6CcMDIiIQB1rkP/J+PG0a0fFijRrBrBzJw4OgffreKYeM3miRXk7KlZk3z7s7Rk6lLg4sQjd3f0/WyifP2fNGu7dw9qaNm1YvpzNm8XsKiiI/v1p2pSTJ7l8GSsr7Oy4f5+WLVX4d13ZeHpibc3bt++jopKHDy9crRp16qCjQ4UKUiv7FmfO0KWLfI2WNSgQTYKllmRdgQF58xIRoTZXYHLgxg0uXeL+fX77jSVLGDqUqVO5do0tW+jUKUcr7dtH7doYGytG5w9y9iwHD3LzpsobzCuQFi3IyGDTJsaOlVrKD2JgwPbtnDrFmTMAy5axY8eGmN792r6kT1u8vBg6FHt7atbEx4f376lVi3fv6NuXCRPo04cjRzh0iNhYKlaka1eOHqV7d9q2pV49Hj/Gy4voaMqWZc8e/P158YK9e6lQAVNTHj3i5UsiI7G3x8xM6p+CClG4MIUL8/Jl6r17H0xNCQpi0iQ18D95/55r19i5U2odGrKNyv9OafgSHh7i2Ps3b/Dzw8aG9u0BypeXVpfiuXoVd3d0dZkyhV9+oVs3zMyoW5ewsJyupIr9g4IAkJ5Or17MnfszZ1fAokVcvEjHjuqfYGVRq9bHErqnG0/deVWw9gBjRoXz55+4ulKxIpcv4+zMxYviV/2TJ9Sty/btvHhB166ULcuxY8yaRWIihw6JxiVA27aULk2xYtjZ0b8/Pj7o6fHwoWioVahQrm+M+EH09bG1Zd06unaVWsp/UKzY/3QyWVkBlCyZE5sGDRKh6SJUS6yt8fDAwwN3d8zN2b+ffPnw8FDV/Rg58n/t3Xtczvf/x/HHVXSOcqiQShFzXjmNyJk5jwmTw5rTMOY0MfazDLMxzPk4x1HOEubYnM0ph+WwkCI5RonO1++Pri3fja10dX3qul73m9tu11Wf6/N+Nul69f68P6+3mZmmQUWlSnTpgr8/QGJiThcnJSWxf39+2tnv7FlatKBIEYoUoUoVihSha1elMymvTh3Uas6cUTqHtq1P7tzZYldhozRsbJg+nago3n+fx48JCyMgQHPTirMz3t5cuqTZpNnPj3Xr6NSJjAxq1SI1lXPnGDSIunUpVgwrK06cwNcXExMyMvi//9O0axf/yto644MP+PZbJk8mOVnpNG9w6xZqNTduYGHB6NGo1ajVUl0VDFJgFXjGxnz7LZ98Qmqq0lF0oFEjDh/W9L2eOpWdOwkNZf36rKXR2bN3Lx4e+aYT0PHjtG1Lr17ExnL6NLGxXL/OiRNKx8oXPvrold3W9MW685V9yoTa9OnDb7/x4AGhoSxahJ0dBw/y9CnvvkuFCjRvTkgIajXr1xMayvHjrFrFzZskJFC+PEWL0rMnpUtz5Qr+/qSm4unJlClMmYKnJ48fM2mS0l9lAWBunjFvHrVrU61afr+dYswY6tfH0lLpHCIn5BJhwVa0KJ064efHpk1Mn64vF1P+hb09EyfSsCETJ+LhQffutGlD5840a5b9c/TsyZMn+en64MSJzJ5N9+4A/v6MHYurKxMnsn+/0smU17s39erx/fe5aceRv4SH8+wZZbYPTNmxzeTTT7lzhwoVGDOGL76gYkV+/JEZM4iM5PZtevXC0pIDB7h9m+Rk3N1xdMTIiBkzaNMGExPNGS9fZtQo3N05cgRg2jRat1bwCyyIpk6ldWv8/PJpBXPyJKdP06uX0jlEDkmBVbBZWjJ/PsCyZXh40LFjAbgRJreGD6d2bX78kblzcXSkYsWcLj2Lj+fEifz0C+upU5qVq9u2ce0aQUEkJ2d1kjVsLi64ubFvH23aKB1FS1av5qOPUJkUejFokNVXX2V9IiiIadOYOBETE9zdKVmSlBTat2fp0qxj4uJYtowTJ2jXTvORDRv45RdmzKB4cVq10ulXokeqVaNBA+bNy2rDln+o1YwezbRpVKmidBSRQ1Jg6YnSpZk8mT59OHWKjRvx8sLJSelMead+/az9mW/dok4dfHxwdc3mqx8/xt6esmXzKl2OGRmRns69ewwezMaNmJiQmJj/9kdUjK8v69bpSYGlVhMYyI4dr/vcihV07Mi+fTRtytOnBAXRsSMhIZw+Te3aAPHxDBhAz55cuUK5clSvzq1bmJkREiJ9J3Pvm29o0ICBA/PdDZdBQbx4QY8eGMmKnoJGCiz90a8fmzYxYwYnTmBtrdcF1qvKlWP0aAYPZs+efzkqPp7p0zVNWcPDKVtWsz6+SpV8MPHu7U1gIJs3M2gQDRoABAXpfdP27OvWjfHjSUgo8PdwrFrFtWtYW1OtGuHh//h0mTL89hvBwYSF4eLC/v1Ursz27XTpQqlS2Npy7hxduzJzJmZm3LzJ1as4OlK1qrzxaoW7O+3aMWsW8fF0707dukoHAiAlhfHjWb5c/pILJCmw9IdKxdKl1KpleDPJo0axZg3Nm3P/PkCDBnz1FaVLv3pIZu/3zALrxQvKl9dslZov3rOnTqV+fUqWZMECbt1i40ZmzuTAAaVj5RfFitG4MVu20KeP0lFy59Yt9u6lZ883H2FkRMeOmn6kmTp2pFUrLl4kLo7q1TX36AOurtmfshXZ9H//R61a1KrFgwdKR/nTvHlUqULjxkrnEG9FCiz98ewZ1taMG8ekSTx7RlwcgJmZ3m+vAn/8QWwsUVHs3k2RImzejKcnhw5RqdJfh1haMno0QFgYkyfj55efejQkJWFqyrvv0rIlQIMGnDqFi4vCqfITX18WLSrwBVZ6Oleu5Lx/gpkZderkSSDxv1xc8PFh716lcwDg7c2qVUyfzqFDSkcRb0sKLD1x7x7vvktKCkBCAv36YWEB0L49q1YpGy3vjR/PpEmEh7N2LQsXUq0aJUowbhxbt/7z2ODgN25AolNPnxIRgaMjVlb4+rJsGZ06KZ0p/2rXjoED2b2bkiWzWmwWFJs38/gxwJ49mJtr3r+TkqwzbxsV+cHLl6xbR0YGLi5ERrJlC/fuAbi65rQDjNZERDBtGl26ULmyMgFE7kmBpSdKlSI2VvO4SRPCwrh5M9+t1swrhw6xfDnGxlSpgq8vDRrQo8ebWlbs2EHlyhQrpuOIr4iLY+RItm3DzY3oaFQqmjWT6urfmZrSuTOzZlG/fsErsE6eJD4eICKCokU5exYgNdWie3dD26c9/0pOJixM00rQyoo9ezRNMBTc6TU9nU2buHJFsQAi96TA0kPW1tSty5QpfP+90lF0IzUVU1MsLVmwAF9fTp/GzIy0tH8eGBNDZCQnTii679iHH1KpEnfuYGnJTz/x5ZccOUJ8vIFvjPOffH3x8cm6ebQAyfxn+OgRq1czaBDTpgGEh9+HfNLoVmBjw7x5msd37hAWRvv2Wa0wdCY6mp9/1jx+8oQGDfjpJ4AWLfDw0HUYkXtyZ4J+6tmTlSu5dUvpHLpRqxa7dwN06ECPHnTrRkjIayc6goNp3VrR6urMGe7cYe5cLC2JiGDsWPbsoUED1q9XLlPB0LAhycn5aPVxTv38M+7umJoqnUP8F2NjhgxhyBASEnQ9dGIicXHExXH6NOnpVKyoefrkia6TCK2QGSw9NH48lSoRFYW/P4GBSqfRgYAATZeYDh346ivq1aNfP0JC/nngjh307avzeK8KD6dePYyMeP6crl0JCKB6dd57j99/VzRWvubmxs2bmscLF7JwoeaDEREKhsqxlSupXVsKrALA3Jy6dblxgy+/5McfdTp0pUp8+y2PHlGjBsWK/fNmaFHAyAyWHqpXDxsbRo7k1CmOHlU6jQ54e7NpEzNnYmND8eKYmGBtzcOHfzsqMZFjx5TeRMTamidPSE3lww+pXZtBgwCePKFoUUVj5Ws3bmg2uB02DAsLkpJQqwtYdXXpEk+eMHcuI0cqHUX8l9WradaMH35g61aOH1cgwJAhmm27RUEnM1h6y9ycyZMZPZoTJ5Rcqqkj9etz7JjmLkoTEy5coGVLHj7kyBHu3sXdnaFDf4mo/t57Sje+atyYAQPw8cHEhAULAJ49Y80a1q1TNFbBYGuLnR3BwXz4odJRcmj5cvr0MYCGKXohc5axaFFmzGDQIM6e1ek+mOvXc+kSq1YRHCzznQWezGDpM19f0tMJCkKt5tkzpdPogImJ5ve+GjWoVo3hw2nYkK+/5p13eP/94JnXFet99fw5MTEAtrbUqUNICJ6e7N3LggV4etKlC/XqKZSsgPHwYPlypUPkUEoK69fTu7fSOUQOdetGuXJ8/z1nzzJmjC5GvHePESNYtQozM8LDZQOkAk9msPSZSsWMGXz8MRYWrFzJ5s1KB9KZI0eIjqZ3b3bvZuBAvL0z2nfcXdF60vw4sNVpkrAwhg/n/HmsrUlNxcuL27c5dox165g/nzJlWL4cb2+dRiqwPvyQ9u1p3Zrbt3F2VjpNtu3cSeXKuLkpnUPk3Ny5eHpiY8O1a3k4yr17XLhA69b078+gQZqdJ4UekBksPeftTY0abNmiafFiKHbvxteX+fN5+DDztvjjsa5lrOOdb+q2KXJEBK1b4+fHs2fcvcuYMezaRdu21K7N7NmEhLBkiVRX2Ve1Kp6e9OihuXe9oFi5UulbK8TbcnJi4kTNfRV558wZFixg+XJiYvjyy7wdS+iSzGDpv+nTqVPHwK5BJSbi4ICJCRs34uWFuXlw7Ih2zpdITNRpjNmzGTxYs8PLnj388AO7d9O5MwEBsrzirfXrR/v2fPVVwdj+9v59jh7Nam4kCpDDh7l6FVNTHj7k6VOWLAEwNaV7d+3/8335knHjOHhQp+u9RF4rCD+ixNv67jt8fJgwAQsLjh7FxwcfH3r31mzcoc+qVuXwYYAyZTh8mMWLg1c87PBkJdWq6TRGWBhNmwKEhtKnD1u20KQJpUpx44ZOY+iX6tWxt88vG8b9p7Vr6dQJKyulc4icu3CBs2c5d47y5bl3j5AQzp7l5Ent/5qmVhMWxqhRVK2q5TMLZckMlj5r3Jhy5QAcHFi4kObNsbXFyEjpO+l04KOP+PZbvvuOESMoW/aPeb8ktEr1cLqInR1ffEFYGDY2tG5N3755Ow1ibs7z5yxZwldfsX49770H8Py5Zp9I8bb69WP5cqU7bmTPypXMn690CPFWPvtM8yA4mKlTOXWKQ4d45x2tnb9rVzZtynrq74+/P+bm3LhBqVJaG0UoSGaw9FmdOnTtSteutGiBkxN//EHXrnTpYgAdViwtOXiQY8coWZKqVbe3XdKh0nWVlSVubqhUjBlD166sW0fz5iQna3PcP/7Azw9PT5o14/vvadKEESOYMYPQUM1U1r59mJvj4qLNQQ3PRx9x8GAB6Op++jSJiTRsqHQOkWslSzJrFq1aER2ttXNu3IhazYwZlClDy5aaZm8vXkh1pT+kwDIUbm789BOPHimdQ2ecndm+ndu3CQwMrjO5/czGpKVRuTJXr9KwIV27sn8/VlYsWqS1EffuxcuLypVZupTx4zl2jOnTiYmhQgVu3+bUKaZMoWdPbY5oqKys6NiR1auVzvGvWrdmyRL8/AygC52+MzXFxIQePRg8mDZtePoUYMIEXr7M7ZnnzGHxYqZOlTWZ+kkKLINQpgx169KlC3PnKh1Ft+IyilbrXuXiZaPGrlEkJHDiBIUL07EjCQmoVAwYoNnEMPfUagYPZsMGRo/GwwNHR65coVQpxoyhVSt++IHhw7lzh1OnaNJEOyMatk8+Ydky1Gqlc7zZxYts3Srtr/RBixaaG1f9/WnalA8+IDmZn34iLu5tzjZ6NKdPAyxfzqxZ7NuHrW5bxwidkTVYBsHDAw8Pbt6kTh1GjjSgfVlevuTOHZo3xyw1ARsbTEwIDGTYMKpWZfZs7OxISGD+fHbv5tkzatZkzBicnLJ79tRUwsK4e5fy5bGwIDVVUzyFhODnx9SplCnDzJns28ewYXn3NRqmBg0wNubYMapWxcZG6TSvk5REtWo5+G4S+ZZKlbVuddYsfHxy1Xfj+nViY1m1ioAADh3C2RkLC+nyr5+kwDIgrq60acPChfj7Kx1Fh5KTadcOXF25c4fYWBwcmD+fbt0YNAi1mkeP2LWLTz+laFEOHaJ2bYKCstWb6uRJ/PwwM8PZmUuXsLPDxIRLlxg7logINm2iYUOOHNHyGi/xik8+Yd48Tp3i1i2lo/zp7t2sTcafP6d0ac29/XXqULOmgrmEdqSkcOkSI0cyeDBPn3LxIvfuAbi75+zOocOHWb+egwdxdQUoWZLmzfMksFCWFFiGxd+fZs0YPlzPf2H69VfNpb9nz0hK4tw5rlwxN666/eOOo8pvnIaTE40a8fXX9OqFWk3t2rRsiYkJDRtSty4DB7J+PfPmcf06Zcrg60u7dmRkEBio2Trby4smTejUicWL6dgRICODsWOZOZMmTRgzhq1bNUsq9u+X99W806sXAQH56zv52TPOngWIjyctDZVK81TuatAPJ04wapTm8cuX+Pjg7IypKZ98wqefEhgI0K1b1vGpqfz0EwMGkJzMunWkpQGEhXHgAGPGEBrKgwd4een8yxC6IgWWYalcmQYNWLpUz69ZFS6sWdYQFYWREaVLA9CukXHcFWrWxMGBp0+xt6dGDQYNIiiI2rWZMYOmTWnVigcPaNOGceP4+GMiIxk/ns2bNQ0HfXwAlixh3DhattRUV8+eMX06K1diaUmxYrRpg6kp6emsWMHixZw8qdj/BX1XsiSNGmn6neUTlSuzeDHA6NFYWjJjxp/fe0IveHtz5ozmcenS9O/PggUMGqS5Ynjlyt+Pf/iQr79mwAASEzl9mjt3OH2aJ0+oXZt797h3T7N7ltBXUmAZnPHj6dSJQYP0uVlD/frUrw/wySdYWjJ2bOaHVTCIKf2IiKBoUUqVwsuLChXYvZugIMaNIyqKFi149ozt22nXDsDLi86dKVMGb2+2bdOcffBgqlXj+nVWreLAAfbsoUMHLlxg/HiMjHj/fVJTSUykXj0OHJC5i7ywebNmtuDBAxISNHWvsTFffMG77yobDSAxkVWrsLRUOofISyoVAwcyYACjRlGlCrNn/9vBERFERBAZycyZbNjAgAEotvG80CEpsAyOhwdVq7J6NQcPsnixnjcd3b8fM7P//VChQlSqpHlcvTqhoXh5aZrcR0UxdixqNb6+tGhBhw6ajjQpKZiYcPYshQoRGcn+/cTEEBeHkxPNmxMQoKmiYmIYPpwVK3jwAGvr/HXtSr9Uq0ZGBsCTJ5w5Q7Vqmr9SR0dlc2msXYuXF+Hhcu+9PlOpUKkoXZp+/XB3Z/BgMjJwcyMjA3NzrK1p0IAXL0hOpm1bLlxg7FgGDaJwYc3vBsIQ6EmBlZKSMnLkyN27d9+7d69ChQqTJ0/u0KGD0qHyr/Hj+fhjXrwgIUGfC6zffwc0y0hfb8QIGjbE1ZUePVCpSE7mzBmqV+fAAYKDCQ7W3If98iWhody8SVoa9vY0b86PP9KrF7NnZ10BOn6cS5c0q+Pt7PL4KzN07u64uwPExDB2LOfOMXGi0pn+pFYzbx5z5uDlpc+TxCIkBAcHgMBAnj2jXj2OHiUsjOvXSUggKQmVStM7NDQUExP+7/+oVIkWLTA1lcrbUOhJgZWcnKxSqQIDA52cnLZu3erj43P58uXy5csrnSuf8vKidGkuXVI6Rx4LDqZjR3788c1HZF4fHDqUIUOwsSEhAT8/Nm+maFH69s26FbtoUfr1Y+rUrBeeOIGDA56e9O1LuXKcO8e2baxaJXvO6Z6FBcePc/Vq1ryksg4eRK2mSRPpL6rnatTQPFi6VPNg0qSs/2aKiaF2be7e/Z8Xrl0rlbeh0JNGo9bW1nPnzq1Vq5adnd3AgQOdnJzOnTundKj86PFjNm5k40YaNSI+nuBgzdOICKWT5YFdu2jT5r8Oevddjh3j1i0OHeLhQ777jsqV+eQTzdxVaipTp2Jmxu7dWXtkREUxZAhff01oKJaWnD1LhQpcvkyrVnn65Yh/sramUSMGDGDePKWj/GnePD77TKor8UampvLtYSj0ZAbrVbGxsZGRkdWqVVM6SH4UGcnGjZrHajUrVuDsrHmqZ/N9jx9z8SKNG2fvaBubrG6V69fz5Zc4OeHoyN27NGvG6dMEBeHhQeY3VWazq/79ASZMyIvwIpusrdmwgdhYqlQhIIBixRTOExnJ0aOsXatwDKGIQnr4dipyRaXOz5tN5FxycnLr1q2rVKky73W/0p45c2bixInOf9UUUKpUqV69eukwYD7y7rsuVaokr117T5eDJicnP3361N7ePq8H2rbN6pdfLBcuvP92L1elphaKikp3cMj482Ywo/h40/BwILly5YwiRbQWVAl37twpXbq0kZGeTGAD/v4lnZxSBw9+qmyMb78tBip//8f/eeSjR48sLCwsLCx0kEq8VmJiYlJSUvHixbV1wpcvVYC5edZbano6v/5q0bTpC20NUbCsWbPm3r2s95czZ84sWrSoVq1aCkbSsQJcci9atOjTTz8FvL29Q0NDgdTUVB8fn5IlS86ZM+e1LzE3Nzc1NbV9ZecnW1vbQob6e4eZmfraNZOoKDNX1zSdDZqeng7o4P95aKhV8+ZJbz9QoULqihWNXr2IXqxYqpcXYKQXV9YLFSqkTwVW//7Pe/a0Gzgw0dRUsd8Yk5JUW7YU2bYtNjvfdUZGRkZGRgb7wyc/0PpfwT9vGCpUiJYtUwr0+2xu2NraJiUl/fXU3Nzc3MDurdafGay0tLRu3bqlpqZu3ry5cOHCbzrs888/n/3vHUsMhosLHTtibMwPP+hu0Pj4+IiICA8PjzwdJS0NOzsuX5Y2j6939OjRevXq6dm7e+vW9OhBnz6KBVi6lJ072b49WweHh4eXKFHCTm44VU5sbOzTp08r5ZObIwzApEmTJr16C4AB0JOfsOnp6b6+vnFxcVu3bk1PT09PTy9cuLCxsbHSufK1c+d4/hwPDwIC9O3utyNHKF9eqivDMmoUI0fSu7cCK4hPnmTNGo4eZeZMXQ8thMi39OQaQXR0dGBg4KFDh2xsbDLnIefOnat0qPyuWDHNpnz6tyY3JIS2bZUOIXSrRQuMjdm/X4GhHz4kLIzUVJo1U2B0IUT+pCczWC4uLnpzrVPHPvuMoUMZOFCv7hzeuZOff1Y6hNC5zz/nhx/Yt49u3fD01OnQt24xcaJe/SMSQuSSnhRY4q01boxKRWgoTZooHUVLIiJISMgXe9IJHevRgy+/JCmJhg11UWDt38/NmwDHjvHgAWlpLFmCkRE9e8o+SUIIfblEKN6aSsXQofmoT2Pu7dxJmzYyl2CITE0ZMkRT9OjAjRucPcvZsxw6hKUlly9z9iwXL5KcrKMAQoj8TGawBL6+TJhAVBROTkpH0YaQEIYOVTqE0K2UFIKDycjAwYGYGPbuJfP28LJlqVcvrwYdOBDg+nUCA6lfn8WL82ogIURBJAWWwMqKXr1YuJBp05SOkmvx8fz2G82bK51D6FZCAlu3kpICYGbG5s3cvw9Qr14eFliZJkygY0fN1kpCCPEXKbAEwNCh1K+PhwcmJnTsqHSat3XxInv34uXFn93XhaEoXjzrZtj33+fkSSZORAfbZZ05w/HjLFnCqlV5PpYQomCRNVgCwM0NT0/WreP8eaWj5MKWLaxdKw0aDF3hwvj4MGKELsby92fSJNq0Yc0aXQwnhChApMASGp99xqlTSofIHbWaiAjatFE6h1BU5izs/fuEhOTtQHv3Eh1N376aQYUQ4lVyiVBw5gxPn1KoEC9ecOqUplVj8eIFr9PBnTtYWeHionQOoagVK7C2xsSEoUNp2ZI375uVK2o148czbRr6teGQEEJr5GeD4LvvNEt0Cxfm2DHS0gBsbQkKUjZXdpUrR2Rk1tPMBg0VKnD9ukKBhKKKFAFo3pxy5Vi4kGHD8mSUoCCMjfnggzw5uRBCD0iBJbIKqbFj+fFHgoKwtVU0UA7duqV5YG9Phw4sXapoGpFvzJqFtzc9e1K8uDZPO2AAPXsyYQKLF0u7NSHEG8kaLJHF3Bw3N9avVzrHW7l9m8RE2eBZZKlUCR8fAgK4eZPVq7V22thYNmygfHmaNtXaOYUQ+kcKLJHF2JhatQpqv8Tt26lYUWYUxP8ICCAwkN272bRJa+dMTycoiClTtHZCIYRekkuEIsvQoWRkULs2587h4aF0mhzauZNevWjcWOkcIj+xtcXfn5UrKVUqV+dJTGThQtLTAU6fpmhR9u1j3z4qVqRTJ60kFULoGymwRJbMpVd+fixfXsAKrMwG7lu3SotRkeXJE54+pU0bpk8nNVWzR6GxMc7OOT5VejpxcaSnEx3NkyfUqqW5LyQhQcuZhRB6Qwos8Xd9+1KzJt9/j4WF0lGybc8eaeAu/m7sWA4eBEhOUoCe1wAAETxJREFU5uJFmjShUCGMjfn11xxPaBUpwpQpREZSvz516vDpp7RvnxeRhRD6Q9Zgib9zdKRePW2uWdGBHTsK8A4/Io8sXcqNG9y4wapVvPMO1tacOcP16295ufDlSz78kPHjKVFC20GFEPpICizxGp98wvLlSofItvR0fvlFGriLf+PmRqtWdOpEUlLOXvjsGYBaTd++VK3K0KFYW2NtnRcZhRB6RQos8Rrt2xMRwZUrSufIniNHKFeOMmWUziHyq8x7S2fMwNmZ7t01a9UDAzU9df/Fw4ea/QwCArhzR3OD7bp1ci+FEOK/SYElXqNQIXr1YuVKpXNkT3CwLIgR/8bbm8mTUalYvpwXL/jsM4CRI3nw4D9emJpKcjLbtrF0KRs3Ymqqg7BCCD0hBZZ4vf79Wb2a1FSlc2RDcDAdOigdQuRj1tbUqAFQuDCbNnHyJNOnv+aw+Hji4//+wbQ0Bg5k61bpYSuEyBm5i1C8npsbFSuyYwf29nh5KZ3mza5eJTmZ6tWVziEKiCJF2LkTLy9evvz7p378EWDCBHbsICQE4MYNHj6kaVOWLWPZMgYP1hRqQgjxn6TAEm/Urx8LFnDtGnfuKB3lzTKvD0oDd5Ed+/bRsmXW07/W7X33HWPGZC3JKleOtDT27SMtDQsLfHwAjIxy261UCGFQ5BKheKMuXTh//r8XAitrxw65Piiyq0UL1GrNn1KlWLyYdu0oUoTTpwkOJiODlBTmzKFdO65dY/58TdP2AQMYMIB+/bCzU/oLEEIUHDKDJd7I3JyOHdm8Wekcb/boEZcv4+2tdA5RAKlUtGvHgAF07syFC/zyC4mJACVL4uxMuXK0b09MjNIphRAFlhRY4jXmzNGsR3n5koQE3Nw0H1+6lKZNFcz1d7t20by53NslcuWLL3j+HGD+fFQqBg8GsLLS/Ld2bSWzCSEKLimwxGv066dpfPDgAQ0bMmkSDRoAODkpm+t/7N/P9u2y1a54S9OnU7IkQL16mo8cPQrQvHnWMUWKsG2bzpMJIfSCFFjiNSwtcXUFMDPD0pLdu+nVS+lM/9C7N4mJmt6PQuSUr6/SCYQQek0KLPEfzM3Zs4e4OGxtlY7yv1JSqFxZNoYTWiPNPoQQWiQFlvg3xYvz+edcvMjPPzNkiNJp/ldSEi1aKB1C6JHOnZVOIITQI9KmQfwbU1PGjs1Hez8fOICbm+ZPYiLLl2sez56tdDIhhBDiFTKDJf5bkybEx3P+vGbjW2WT7N+PWs25c/TowebNmtZEjo4KBxNCCCFeJTNY4r+pVPTuzYoVSucAIyPKlcPVlWPHMDfHyQlXV1xdMTFROpkQQgjxCimwRLb4+bF+/Wu2b1OEWs2WLZibK51DCCGEeAMpsES2ODpSqxbbtyudA4Bjx7CxYcwYihdXOooQQgjxOlJgiezy88sXVwmBjRvp2pXRo6WHuxBCiHxKCiyRXZ06ceECN28qHCMjg82b+fBDhWMIIYQQ/0IKLJFdJiZ0787q1QrHOHaMkiWpVEnhGEIIIcS/kDYNIgf69aNtWywtadeOd95RJkPm9UEhhBAiP5MZLJED1aphZ8eWLUREKBMg8/qgFFhCCCHyOSmwRM74+REdrdjoR45gb0+FCooFEEIIIbJDLhGKbMnI4OhRUlIoU4b79zlxQtOGysWF8uV1F0OuDwohhCgQpMAS2fLwIVOmkJEBYGzM6tWcPg1QuzZTp+ooQ0YGW7Zw+LCOhhNCCCHemhRYIlvs7fnlF83jhg2JiOCXXzDS7RXmw4cpXVqnE2ZCCCHE25E1WCLHbG2xsmLvXl2PK9cHhRBCFBRSYIkcMzKibVvmz9fdiC9fcv06W7dKf1EhhBAFg1wiFDk2axa2tri7c/Mmrq66GPHgQaZOpUwZ3Nx0MZwQQgiRSzKDJXKsXDlsbOjbl0WLdDRiRgZ378r1QSGEEAWGFFjiLQ0Zwk8/8eKFLsbKyCA2li5ddDGWEEIIkXtyiVC8JWdn6tVjwwb8/PJqiM8/5+hRgHv3SEujWzcAY2O2b8fBIa8GFUIIIXJPCizx9oYMYdy4PCywRo2iVy+Avn2xtGTxYgBjY+zt82pEIYQQQivkEqF4e61a8eIFJ07k1fnLlsXTkxIliIqiQgU8PfH0pGZNVKq8GlEIIYTQCimwxNtTqRg0KM/7NcyfT7NmGBvn7ShCCCGEFkmBJXLl44/ZtYvLl/Oq7+jLl6xcyeDBtG6dJ+cXQggh8oKswRK5YmPDhx8yfTrPntGypfbPv3Yt771H8+Y0b679kwshhBB5RGawRG4NG8bu3Zp9oLVu3jw++yxPziyEEELkHSmwRG5VrYq9Pffva//Mv/5KairNmmn/zEIIIUSekgJLvL0uXVCpUKkID+fMGc1jU1Pu3dPO+efNY8gQuWdQCCFEwSMFlnh7mzejVqNWs307RYuyZQtqNcnJlCqlhZPfvcvBg5o+WEIIIUTBIgWW0AKVisqV8fcnNVVr55w/n969KVJEaycUQgghdEYKLKEdJUrg4sKSJVo4VUQET5/y0098+qkWziaEEELonrRpEFpQpw6mpjg40KoVvXrldtpp1ChcXfHwwN1dS/mEEEII3ZIZLKEF9va0bEn16rRuzXff5fZsajU7d0p3BiGEEAWYFFhCm775hkWLiI7O1UmePOHFizxpWyqEEELohhRYQpvKlGHAACZNyvELY2OpW5datahVi99+IyWFOnWoVYsRI7QfUgghhMhrsgZLaNm4cVSsyPnzTJ/O0qVYW2frVfb2LF5MejrbtnH1Kl98QdOmAHZ2eRpWCCGEyBNSYAkts7Zm3Di+/JILF0hIyG6BpVJRsyYRESxeTK1aVKqEp2ceBxVCCCHyjFwiFNo3aBARESQn5+xVycn4+DBlivS+EkIIUeDJDJbQpkePOHQIoH175sxhxw6KFweoUeO/ey74++PqSv/+pKRIgwYhhBAFm2HNYK1YseL3339XOoU+i45m40Y2btTcSPj112zYwMaNhIdrDrhx48akV9bAp6cTEgKwezdbtmj6lA4ZQsWKOg5uWD7//PPknE4wCq2aM2fOiRMnlE5h0EJDQxcuXKh0CqHPDGsGKyoqKiEhQekU+uzddwkK0jwuU4ZGjYiJYccOihbVfPDJkyeRkZF/HX//PgMGcP48/fqxdi3Fiuk6sGG6evVqUlKSpaWl0kEMV3R09IMHD5ROYdBiY2Pv3LmjdAqhzwxrBkvo2IwZ1KmDlxd37wLMns3mzWX/eZifH/360aSJruMJIYQQecSwZrCELhUujIkJ33+PoyONGrFnD0+fkphY+G+HPX/Ow4dMmKBIRiGEECJPyAyWyCthYZQsCTB8OOPG0aQJsbGaT02ahLU15uY4OxMfz7Vr2NtTrBj79imYVwghhNAag5vBio+Pnz59utIpDMuJE++mpJja2xdftuwdM7PiSUmhV66k2drGV678R/HicXv3Nvz882WZR549m3TunLJhDcXChQsLF/77bKLQmfj4+DNnzjx58kTpIIbr2rVrcXFx8nagM8eOHVM6gq6p1Gq10hl058KFC0CNGjWUDmJYZs7k4UOAo0dJT08vXfpmhQoVSpZk1ChiYqhdW7NCS+jM2rVre/bsqVKplA5iuA4ePOju7u7o6Kh0EMMVGRkZHR3dsGFDpYMIvWVYBZZQVmZ/hld3KpQCSwghhF6SNVhCSSVKMHGi0iGEEEIIbTO4NVhCQTY2f/+IiQmDBikRRQghhMhLcolQCCGEEELL5BKhEEIIIYSWSYElhBBCCKFlBlRgJSQkdO/e3dLS0tHRcdGiRUrHMTgpKSlDhw51c3OzsLCoUaPGjh07lE5kuCIjIy0sLFq3bq10EAO1evXqihUrmpqaVqxY8fTp00rHMUTh4eFNmza1trYuVarU6NGjMzIylE4k9JABLXIfOXLkgwcPIiMjr1692qZNmypVqkgHFF1KTk5WqVSBgYFOTk5bt2718fG5fPly+fLllc5liD777DNPT0+lUxionTt3fvHFF0uXLq1bt25UVFSJEiWUTmSIfH19PTw8du7ceffu3RYtWlSsWLF///5KhxL6xlAWuaemptra2u7atatRo0ZAv379gGXLlimdy3C5u7t/8803Pj4+SgcxONu2bVuxYkX9+vVDQ0P37NmjdByD4+HhMWzYsL59+yodxKDZ2tpu37498+2gf//+lpaWs2fPVjqU0DeGcokwMjIyMTGxZs2amU9r1qz5+++/KxvJkMXGxkZGRlarVk3pIAYnMTFx7Nix8l6ilOTk5LCwsNjY2DJlypQqVWrYsGFJSUlKhzJEI0aMWLNmzYsXLyIiIg4cOCCXy0VeMJQC6/nz54C1tXXm06JFiyYkJCiayHAlJyf36NFjwIAB77zzjtJZDE5AQMBHH33k6uqqdBADdffuXbVaHRIScu7cud9+++3XX3+dNm2a0qEMUZs2bY4cOWJpaVmhQoW2bdtKgSXygqEUWFZWVsBfRdWzZ8/+KraELqWmpvr4+JQsWXLOnDlKZzE44eHh27ZtGzt2rNJBDJe5uTkwevRoe3v7smXLDhs2bNeuXUqHMjgvXrxo3bp17969X758GRUVdfbs2W+++UbpUEIPGUqB5eLiYmFhcfHixcynFy5cqFKlirKRDFBaWlr37t3VavW6deuMjY2VjmNwDh8+fOfOHRcXFwcHhylTphw6dMjFxUXpUIalVKlSJUqUkG22lRUTE/P48eNhw4aZmZmVLVv2o48+ksWIIi8YSoFVuHDhHj16BAQExMXFnTx5MigoqE+fPkqHMizp6em+vr5xcXFr1qxJT09PSkpKT09XOpRh6dOnz40bN8LCwsLCwoYPH96gQYNTp04pHcrgfPzxxzNmzHj06FFMTMy8efPatWundCKD4+LiYmdnN3/+/NTU1Hv37m3YsKFGjRpKhxJ6yFAKLGDWrFm2traOjo6dO3eePn269GjQsejo6MDAwEOHDtnY2Jibm5ubm8+dO1fpUIbF3Nzc4U9WVlYmJib29vZKhzI4kydPrlixopubm4eHh7e3t7+/v9KJDE6hQoV27NixY8eO4sWL16hRw8XFZcqUKUqHEnrIUNo0CCGEEELojAHNYAkhhBBC6IYUWEIIIYQQWiYFlhBCCCGElkmBJYQQQgihZVJgCSGEEEJomRRYQoh8xMXF5cyZM0qnEEKI3JICSwiha0lJSarXWbt2bUBAgLOzs7YGcnR0lHJNCKGIQkoHEEIYHDMzs5cvX2Y+dnR0XLNmTZMmTQATExMjI/mtTwihD+RnmRBCAWZ/AgoXLpz52MjI6K9LhA4ODgsWLHB3d7eysho1alR0dLS3t7eVlVX79u0TExMzT3L//n0fHx87OzsXF5dZs2b9bYjBgwfHxsZ26NDBxcVl9erVOv4ChRAGTgosIUQ+tWXLluPHj1+8eHHFihXdunWbO3dubGzskydPli1bBqjV6g8++MDJySkqKurXX39dtGhRSEjIqy9fsGCBg4PDjh07IiMje/furdAXIYQwUHKJUAiRT/n7+5coUaJEiRINGzasXr169erVgS5dupw/fx64ePHi77//fuTIEWNjY2dn56FDh27cuLFt27ZKpxZCCJACSwiRbzk4OGQ+sLCwePXx8+fPgdu3bycnJ1epUiXz4ykpKTVr1lQkpxBC/JMUWEKIAqls2bI2NjZXrlxRqVRvOkaWzAshlCI/fYQQBVKNGjXKlSs3duzY58+fp6enh4eH//bbb387xs7OLiIiQpF4QggDJwWWEKJAMjIy2rZtW0xMTPny5UuUKOHn5/f06dO/HTN+/PgxY8bY2touXbpUkZBCCIOlUqvVSmcQQgghhNArMoMlhBBCCKFlUmAJIYQQQmiZFFhCCCGEEFr2/wPWr5e/c9zFAAAAAElFTkSuQmCC" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 153, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let vp = A.init ~w:800. ~h:360. [\"jupyter\"] in\n", "A.Axes.box vp ;\n", "A.Viewport.xlabel vp \"Time t\";\n", "A.Viewport.title vp \"Solution to the pendulum ODE with Runge-Kutta 1\";\n", "A.set_color vp A.Color.red ;\n", "A.Viewport.text vp 8.5 3. \"o theta(t)\" ;\n", "A.Array.xy ~style:(`Linesmarkers \"o\") vp t (column sol 0);\n", "A.set_color vp A.Color.blue ;\n", "A.Viewport.text vp 8.5 2.5 \"+ omega(t)\" ;\n", "A.Array.xy vp ~style:(`Linesmarkers \"+\") t (column sol 1);\n", "A.close vp;;" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val t : float array =\n", " [|0.; 0.000999900009999; 0.001999800019998; 0.00299970002999700022;\n", " 0.003999600039996; 0.004999500049995; 0.00599940005999400044;\n", " 0.00699930006999300094; 0.007999200079992; 0.008999100089991;\n", " 0.00999900009999; 0.0109989001099890012; 0.0119988001199880009;\n", " 0.012998700129987; 0.0139986001399860019; 0.0149985001499850015;\n", " 0.015998400159984; 0.016998300169983; 0.017998200179982;\n", " 0.018998100189981; 0.01999800019998; 0.0209979002099790028;\n", " 0.0219978002199780025; 0.0229977002299770021; 0.0239976002399760018;\n", " 0.024997500249975; 0.025997400259974; 0.026997300269973;\n", " 0.0279972002799720038; 0.0289971002899710034; 0.0299970002999700031;\n", " 0.0309969003099690027; 0.031996800319968; 0.032996700329967;\n", " 0.033996600339966; 0.034996500349965; 0.035996400359964;\n", " 0.036996300369963; 0.037996200379962; 0.038996100389961;\n", " 0.03999600039996; 0.040995900409959006; 0.0419958004199580057;\n", " 0.0429957004299570053; 0.0439956004399560049; 0.0449955004499550046;\n", " 0.0459954004599540042; 0.0469953004699530039; 0.0479952004799520035;\n", " 0.048995100489951; 0.04999500049995; 0.050994900509949;\n", " 0.051994800519948; 0.052994700529947; 0.053994600539946;\n", " 0.054994500549945; 0.0559944005599440076; 0.0569943005699430072;\n", " 0.0579942005799420068; 0.0589941005899410065; 0.0599940005999400061;\n", " 0.0609939006099390058; 0.0619938006199380054; 0.062993700629937;\n", " 0.063993600639936; 0.064993500649935; 0.065993400659934;\n", " 0.066993300669933; 0.067993200679932; 0.068993100689931;\n", " 0.06999300069993; 0.070992900709929; 0.071992800719928;\n", " 0.072992700729927; 0.073992600739926; 0.074992500749925;\n", " 0.075992400759924; 0.076992300769923; 0.077992200779922;\n", " 0.078992100789921; 0.07999200079992; 0.0809919008099190124;\n", " 0.0819918008199180121; 0.0829917008299170117; 0.0839916008399160113;\n", " 0.084991500849915011; 0.0859914008599140106; 0.0869913008699130103;\n", " 0.0879912008799120099; 0.0889911008899110095; 0.0899910008999100092;\n", " 0.0909909009099090088; 0.0919908009199080084; 0.0929907009299070081;\n", " 0.0939906009399060077; 0.0949905009499050074; 0.095990400959904007;\n", " 0.096990300969903; 0.097990200979902; 0.098990100989901; 0.0999900009999;\n", " 0.100989901009899; 0.101989801019898; 0.102989701029897;\n", " 0.103989601039896; 0.104989501049895; 0.105989401059894;\n", " 0.106989301069893; 0.107989201079892; 0.108989101089891;\n", " 0.10998900109989; 0.110988901109889; 0.111988801119888015;\n", " 0.112988701129887015; 0.113988601139886014; 0.114988501149885014;\n", " 0.115988401159884014; 0.116988301169883013; 0.117988201179882013;\n", " 0.118988101189881013; 0.119988001199880012; 0.120987901209879012;\n", " 0.121987801219878012; 0.122987701229877011; 0.123987601239876011;\n", " 0.12498750124987501; 0.125987401259874; 0.126987301269873;\n", " 0.127987201279872; 0.128987101289871; 0.12998700129987;\n", " 0.130986901309869; 0.131986801319868; 0.132986701329867;\n", " 0.133986601339866; 0.134986501349865; 0.135986401359864;\n", " 0.136986301369863; 0.137986201379862; 0.138986101389861;\n", " 0.13998600139986; 0.140985901409859; 0.141985801419858;\n", " 0.142985701429857; 0.143985601439856; 0.144985501449855;\n", " 0.145985401459854; 0.146985301469853; 0.147985201479852;\n", " 0.148985101489851; 0.14998500149985; 0.150984901509849;\n", " 0.151984801519848; 0.152984701529847; 0.153984601539846;\n", " 0.154984501549845; 0.155984401559844; 0.156984301569843;\n", " 0.157984201579842; 0.158984101589841; 0.15998400159984;\n", " 0.160983901609839025; 0.161983801619838025; 0.162983701629837024;\n", " 0.163983601639836024; 0.164983501649835024; 0.165983401659834023;\n", " 0.166983301669833023; 0.167983201679832023; 0.168983101689831022;\n", " 0.169983001699830022; 0.170982901709829022; 0.171982801719828021;\n", " 0.172982701729827021; 0.173982601739826021; 0.17498250174982502;\n", " 0.17598240175982402; 0.176982301769823019; 0.177982201779822019;\n", " 0.178982101789821019; 0.179982001799820018; 0.180981901809819018;\n", " 0.181981801819818018; 0.182981701829817017; 0.183981601839816017;\n", " 0.184981501849815017; 0.185981401859814016; 0.186981301869813016;\n", " 0.187981201879812015; 0.188981101889811015; 0.189981001899810015;\n", " 0.190980901909809014; 0.191980801919808014; 0.192980701929807;\n", " 0.193980601939806; 0.194980501949805; 0.195980401959804;\n", " 0.196980301969803; 0.197980201979802; 0.198980101989801; 0.1999800019998;\n", " 0.200979902009799; 0.201979802019798; 0.202979702029797;\n", " 0.203979602039796; 0.204979502049795; 0.205979402059794;\n", " 0.206979302069793; 0.207979202079792; 0.208979102089791;\n", " 0.20997900209979; 0.210978902109789; 0.211978802119788;\n", " 0.212978702129787; 0.213978602139786; 0.214978502149785;\n", " 0.215978402159784; 0.216978302169783; 0.217978202179782;\n", " 0.218978102189781; 0.21997800219978; 0.220977902209779;\n", " 0.221977802219778; 0.222977702229777; 0.22397760223977603;\n", " 0.22497750224977503; 0.22597740225977403; 0.226977302269773029;\n", " 0.227977202279772029; 0.228977102289771028; 0.229977002299770028;\n", " 0.230976902309769028; 0.231976802319768027; 0.232976702329767027;\n", " 0.233976602339766027; 0.234976502349765026; 0.235976402359764026;\n", " 0.236976302369763026; 0.237976202379762025; 0.238976102389761025;\n", " 0.239976002399760024; 0.240975902409759024; 0.241975802419758024;\n", " 0.242975702429757023; 0.243975602439756023; 0.244975502449755023;\n", " 0.245975402459754022; 0.246975302469753022; 0.247975202479752022;\n", " 0.248975102489751021; 0.249975002499750021; 0.250974902509749;\n", " 0.251974802519748; 0.252974702529747; 0.253974602539746;\n", " 0.254974502549745; 0.255974402559744; 0.256974302569743;\n", " 0.257974202579742; 0.258974102589741; 0.25997400259974;\n", " 0.260973902609739; 0.261973802619738; 0.262973702629737;\n", " 0.263973602639736; 0.264973502649735; 0.265973402659734;\n", " 0.266973302669733; 0.267973202679732; 0.268973102689731;\n", " 0.26997300269973; 0.270972902709729; 0.271972802719728;\n", " 0.272972702729727; 0.273972602739726; 0.274972502749725;\n", " 0.275972402759724; 0.276972302769723; 0.277972202779722;\n", " 0.278972102789721; 0.27997200279972; 0.280971902809719;\n", " 0.281971802819718; 0.282971702829717; 0.283971602839716;\n", " 0.284971502849715; 0.285971402859714; 0.286971302869713;\n", " 0.287971202879712; 0.288971102889711; 0.28997100289971;\n", " 0.290970902909709; 0.291970802919708; 0.292970702929707;\n", " 0.293970602939706; 0.294970502949705; 0.295970402959704;\n", " 0.296970302969703; 0.297970202979702; ...|]\n" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val sol : float array array =\n", " [|[|3.04156; 0.|]; [|3.04156; -0.000499279607296539596|];\n", " [|3.04155950077031578; -0.000998434407171997374|];\n", " [|3.04155850243574211; -0.00149746691424664175|];\n", " [|3.04155700511855942; -0.00199637964189098346|];\n", " [|3.04155500893853548; -0.00249517510223822188|];\n", " [|3.04155251401292581; -0.00299385580619668289|];\n", " [|3.04154952045647509; -0.00349242426346224686|];\n", " [|3.0415460283814193; -0.00399088298253077144|];\n", " [|3.04154203789748534; -0.0044892344707105|];\n", " [|3.04153754911189322; -0.00498748123413446723|];\n", " [|3.04153256212935741; -0.00548562577777289128|];\n", " [|3.04152707705208725; -0.00598367060544555563|];\n", " [|3.0415210939797892; -0.00648161821983419227|];\n", " [|3.04151461300966641; -0.00697947112249484164|];\n", " [|3.04150763423642134; -0.00747723181387021513|];\n", " [|3.0415001577522558; -0.00797490279330204457|];\n", " [|3.04149218364687313; -0.00847248655904342569|];\n", " [|3.0414837120074778; -0.00896998560827114676|];\n", " [|3.04147474291877851; -0.009467402437098019|];\n", " [|3.04146527646298681; -0.00996473954058518796|];\n", " [|3.04145531271982072; -0.0104619994127544448|];\n", " [|3.04144485176650337; -0.0109591845466005186|];\n", " [|3.04143389367776562; -0.0114562974341033807|];\n", " [|3.04142243852584659; -0.0119533405662405161|];\n", " [|3.04141048638049494; -0.0124503164329992054|];\n", " [|3.04139803730896929; -0.0129472275233887858|];\n", " [|3.04138509137603918; -0.0134440763254529139|];\n", " [|3.04137164864398679; -0.0139408653262818177|];\n", " [|3.04135770917260784; -0.0144375970120245306|];\n", " [|3.04134327301921115; -0.0149342738679011343|];\n", " [|3.04132834023862131; -0.0154308983782149838|];\n", " [|3.04131291088317868; -0.0159274730263649252|];\n", " [|3.04129698500274026; -0.0164240002948575076|];\n", " [|3.04128056264468105; -0.0169204826653191823|];\n", " [|3.04126364385389492; -0.0174169226185085027|];\n", " [|3.04124622867279459; -0.017913322634328311|];\n", " [|3.04122831714131348; -0.0184096851918379191|];\n", " [|3.04120990929690604; -0.0189060127692652763|];\n", " [|3.04119100517454921; -0.0194023078440191399|];\n", " [|3.04117160480674187; -0.0198985728927012287|];\n", " [|3.04115170822350755; -0.0203948103911183801|];\n", " [|3.04113131545239357; -0.0208910228142946755|];\n", " [|3.04111042651847274; -0.0213872126364835977|];\n", " [|3.04108904144434389; -0.0218833823311801422|];\n", " [|3.04106716025013224; -0.0223795343711329434|];\n", " [|3.04104478295349079; -0.0228756712283563896|];\n", " [|3.04102190956960072; -0.0233717953741427245|];\n", " [|3.04099854011117232; -0.0238679092790741523|];\n", " [|3.04097467458844539; -0.0243640154130349181|];\n", " [|3.04095031300919; -0.0248601162452234056|];\n", " [|3.04092545537870818; -0.0253562142441642047|];\n", " [|3.04090010169983183; -0.0258523118777201875|];\n", " [|3.0408742519729266; -0.0263484116131045693|];\n", " [|3.04084790619589107; -0.0268445159168929672|];\n", " [|3.04082106436415733; -0.0273406272550354504|];\n", " [|3.04079372647069146; -0.0278367480928685788|];\n", " [|3.04076589250599527; -0.0283328808951274387|];\n", " [|3.040737562458105; -0.0288290281259576779|];\n", " [|3.04070873631259353; -0.0293251922489275313|];\n", " [|3.04067941405257081; -0.0298213757270398248|];\n", " [|3.04064959565868298; -0.0303175810227439939|];\n", " [|3.04061928110911506; -0.0308138105979480874|];\n", " [|3.04058847037959; -0.0313100669140307583|];\n", " [|3.04055716344336968; -0.0318063524318532506|];\n", " [|3.0405253602712552; -0.0323026696117714|];\n", " [|3.04049306083158744; -0.0327990209136475863|];\n", " [|3.04046026509024792; -0.0332954087968627271|];\n", " [|3.04042697301065923; -0.0337918357203282269|];\n", " [|3.0403931845537846; -0.0342883041424979496|];\n", " [|3.04035889967812967; -0.0347848165213801436|];\n", " [|3.04032411833974203; -0.0352813753145494249|];\n", " [|3.04028884049221215; -0.0357779829791586845|];\n", " [|3.04025306608667334; -0.0362746419719510368|];\n", " [|3.04021679507180309; -0.0367713547492717549|];\n", " [|3.04018002739382176; -0.0372681237670801635|];\n", " [|3.04014276299649433; -0.037764951480961588|];\n", " [|3.04010500182113086; -0.0382618403461392406|];\n", " [|3.04006674380658604; -0.0387587928174861415|];\n", " [|3.04002798888926; -0.039255811349537|];\n", " [|3.03998873700309913; -0.0397528983965001123|];\n", " [|3.0399489880795949; -0.0402500564122692667|];\n", " [|3.03990874204778594; -0.0407472878504355693|];\n", " [|3.03986799883425673; -0.0412445951642993955|];\n", " [|3.03982675836313954; -0.0417419808068822|];\n", " [|3.03978502055611344; -0.0422394472309384067|];\n", " [|3.03974278533240483; -0.0427369968889672602|];\n", " [|3.03970005260878828; -0.0432346322332246707|];\n", " [|3.03965682229958611; -0.0437323557157350828|];\n", " [|3.03961309431666882; -0.0442301697883033|];\n", " [|3.03956886856945507; -0.0447280769025263092|];\n", " [|3.03952414496491308; -0.0452260795098051518|];\n", " [|3.03947892340755921; -0.0457241800613567|];\n", " [|3.03943320379945847; -0.0462223810082255174|];\n", " [|3.03938698604022628; -0.0467206848012956533|];\n", " [|3.03934027002702623; -0.0472190938913024591|];\n", " [|3.03929305565457231; -0.0477176107288443882|];\n", " [|3.03924534281512759; -0.0482162377643948|];\n", " [|3.03919713139850467; -0.0487149774483137538|];\n", " [|3.03914842129206697; ...|]; ...|]\n" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let t = linspace 0. 10. 10001 ;;\n", "let sol = rungekutta1 f_pend y0 t ;;" ] }, { "cell_type": "code", "execution_count": 154, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 154, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let vp = A.init ~w:800. ~h:360. [\"jupyter\"] in\n", "A.Axes.box vp ;\n", "A.Viewport.xlabel vp \"Time t\";\n", "A.Viewport.title vp \"Solution to the pendulum ODE with Runge-Kutta 1\";\n", "A.set_color vp A.Color.red ;\n", "A.Viewport.text vp 8.5 3. \"o theta(t)\" ;\n", "A.Array.xy ~style:(`Linesmarkers \"o\") vp t (column sol 0);\n", "A.set_color vp A.Color.blue ;\n", "A.Viewport.text vp 8.5 2.5 \"+ omega(t)\" ;\n", "A.Array.xy vp ~style:(`Linesmarkers \"+\") t (column sol 1);\n", "A.close vp;;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "## Runge-Kutta method of order 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The order 2 Runge-Method uses this update:\n", "$$ y_{n+1} = y_n + h f(t + \\frac{h}{2}, y_n + \\frac{h}{2} f(t, y_n)),$$\n", "if $h = t_{n+1} - t_n$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we need some basic functions as OCaml `Array` are quite poor.\n", "With Julia arrays or NumPy Python arrays, we can write `h * f(y, t)` to multiply each entry of `f(y, t)` by a number h." ] }, { "cell_type": "code", "execution_count": 92, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "val aplus : float array -> float -> float array = \n" ] }, "execution_count": 92, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val ( ++. ) : float array -> float -> float array = \n" ] }, "execution_count": 92, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let aplus a k =\n", " Array.map ( ( +. ) k) a\n", ";;\n", "\n", "let ( ++. ) = aplus ;;" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "val aaplus : float array -> float array -> float array = \n" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val ( +++. ) : float array -> float array -> float array = \n" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let aaplus a b =\n", " Array.map2 ( +. ) a b\n", ";;\n", "\n", "let ( +++. ) = aaplus ;;" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val amul : float array -> float -> float array = \n" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val ( **. ) : float array -> float -> float array = \n" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let amul a k =\n", " Array.map ( ( *. ) k ) a\n", ";;\n", "\n", "let ( **. ) = amul ;;" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val rungekutta2 :\n", " (float array -> float -> float array) ->\n", " float array -> float array -> float array array = \n" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let rungekutta2 (f : float array -> float -> float array) (y0 : float array) (t : float array) =\n", " let d = Array.length y0 in\n", " let n = Array.length t in\n", " let y = Array.make_matrix n d 0. in\n", " for j = 0 to d-1 do\n", " y.(0).(j) <- y0.(j);\n", " done;\n", " for i = 0 to n-2 do\n", " let h = t.(i+1) -. t.(i) in\n", " let fyt = f y.(i) t.(i) in\n", " let fyt2 = f (y.(i) +++. (fyt **. (h /. 2.))) (t.(i) +. (h /. 2.)) in\n", " for j = 0 to d-1 do\n", " y.(i+1).(j) <- y.(i).(j) +. h *. fyt2.(j);\n", " done;\n", " done;\n", " y\n", ";;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For our simple ODE example, this method is already quite efficient." ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val t : float array =\n", " [|0.; 0.0990099009900990146; 0.198019801980198029; 0.297029702970297071;\n", " 0.396039603960396058; 0.495049504950495045; 0.594059405940594143;\n", " 0.69306930693069313; 0.792079207920792117; 0.891089108910891103;\n", " 0.99009900990099009; 1.08910891089108919; 1.18811881188118829;\n", " 1.28712871287128716; 1.38613861386138626; 1.48514851485148514;\n", " 1.58415841584158423; 1.68316831683168333; 1.78217821782178221;\n", " 1.8811881188118813; 1.98019801980198018; 2.07920792079207928;\n", " 2.17821782178217838; 2.27722772277227747; 2.37623762376237657;\n", " 2.47524752475247523; 2.57425742574257432; 2.67326732673267342;\n", " 2.77227722772277252; 2.87128712871287162; 2.97029702970297027;\n", " 3.06930693069306937; 3.16831683168316847; 3.26732673267326756;\n", " 3.36633663366336666; 3.46534653465346532; 3.56435643564356441;\n", " 3.66336633663366351; 3.76237623762376261; 3.86138613861386171;\n", " 3.96039603960396036; 4.05940594059405946; 4.15841584158415856;\n", " 4.25742574257425765; 4.35643564356435675; 4.45544554455445585;\n", " 4.55445544554455495; 4.65346534653465405; 4.75247524752475314;\n", " 4.85148514851485135; 4.95049504950495045; 5.04950495049504955;\n", " 5.14851485148514865; 5.24752475247524774; 5.34653465346534684;\n", " 5.44554455445544594; 5.54455445544554504; 5.64356435643564414;\n", " 5.74257425742574323; 5.84158415841584144; 5.94059405940594054;\n", " 6.03960396039604; 6.13861386138613874; 6.23762376237623783;\n", " 6.33663366336633693; 6.43564356435643603; 6.53465346534653513;\n", " 6.63366336633663423; 6.73267326732673332; 6.83168316831683242;\n", " 6.93069306930693063; 7.02970297029703; 7.12871287128712883;\n", " 7.22772277227722793; 7.32673267326732702; 7.42574257425742612;\n", " 7.52475247524752522; 7.62376237623762432; 7.72277227722772341;\n", " 7.82178217821782251; 7.92079207920792072; 8.01980198019802;\n", " 8.11881188118811892; 8.21782178217821802; 8.31683168316831711;\n", " 8.41584158415841621; 8.51485148514851531; 8.61386138613861441;\n", " 8.7128712871287135; 8.8118811881188126; 8.9108910891089117;\n", " 9.00990099009901; 9.10891089108911; 9.20792079207920899;\n", " 9.30693069306930809; 9.40594059405940719; 9.50495049504950629;\n", " 9.60396039603960361; 9.70297029702970271; 9.8019801980198018;\n", " 9.9009900990099009|]\n" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val sol : float array array =\n", " [|[|3.04156; 0.|]; [|3.03911254614617565; -0.0488267043837982695|];\n", " [|3.03183092241293961; -0.0988404593793910102|];\n", " [|3.01948127772376; -0.152388585215509798|];\n", " [|3.00159483065725174; -0.211923116134953959|];\n", " [|2.97745224188518653; -0.280106126962090252|];\n", " [|2.9460575795158439; -0.359915119550046958|];\n", " [|2.90610187009085497; -0.454746846467090182|];\n", " [|2.85591658999954312; -0.568512488459194332|];\n", " [|2.79341852588212358; -0.705707056702320923|];\n", " [|2.71604980667654772; -0.871417812472915942|];\n", " [|2.62072159504783; -1.07120512144372437|];\n", " [|2.50377854277070533; -1.31073777557490101|];\n", " [|2.3610159594913549; -1.59498872770536404|];\n", " [|2.18780513934095255; -1.92670587301033902|];\n", " [|1.97941455921401221; -2.30382082261406795|];\n", " [|1.73164679588694903; -2.71560548610054786|];\n", " [|1.44191154148313938; -3.13804848237782785|];\n", " [|1.11075480950422323; -3.53044584205407341|];\n", " [|0.743572352514064394; -3.83725457909199763|];\n", " [|0.351758622387601194; -3.99957876824615033|];\n", " [|-0.0477823187833688046; -3.97551260420907848|];\n", " [|-0.435355379078979254; -3.75873893055921959|];\n", " [|-0.792566330837187083; -3.38121852743959517|];\n", " [|-1.10574407550246878; -2.8973969458654607|];\n", " [|-1.36716000728090981; -2.3623768246026|];\n", " [|-1.57416289561318345; -1.81743549025345841|];\n", " [|-1.72737271016564775; -1.2862384265376352|];\n", " [|-1.82893933061530634; -0.777756413931331325|];\n", " [|-1.88129651085227101; -0.291240213889777222|];\n", " [|-1.886439820040684; 0.179192594251308|];\n", " [|-1.84562089865235701; 0.640925073236255471|];\n", " [|-1.75936063343311178; 1.09985381280031236|];\n", " [|-1.62773895223768394; 1.55755230771725195|];\n", " [|-1.45096675062721703; 2.00830812610837084|];\n", " [|-1.23025362332544352; 2.43632820045757681|];\n", " [|-0.968918385066261267; 2.81433103704307896|];\n", " [|-0.67351953612175719; 3.1056585677510693|];\n", " [|-0.354547903212739823; 3.27179885370290968|];\n", " [|-0.0261084401934915111; 3.28443628530758902|];\n", " [|0.295698398658890971; 3.13662613817199531|];\n", " [|0.595270261290242297; 2.84596832523174781|];\n", " [|0.859819841409028673; 2.44743139225582418|];\n", " [|1.0805709012737108; 1.98083632592742709|];\n", " [|1.25264496742762099; 1.48035044177632|];\n", " [|1.37412283593078266; 0.969698968223488889|];\n", " [|1.44490944640484531; 0.462413620202401954|];\n", " [|1.46581287840047891; -0.0352383219593074282|];\n", " [|1.43799464484600303; -0.520516426851603708|];\n", " [|1.3628045813203864; -0.990557587736249801|];\n", " [|1.24196416474831528; -1.43913433247567824|];\n", " [|1.07804479128885755; -1.85411054146652865|];\n", " [|0.875149593837422; -2.216241424541467|];\n", " [|0.639622619355808553; -2.50035497682177432|];\n", " [|0.380498291815628276; -2.67976599575457408|];\n", " [|0.109356994580230626; -2.73341990183247763|];\n", " [|-0.160603905511440936; -2.65307922813173436|];\n", " [|-0.416114927732840034; -2.44671882330057|];\n", " [|-0.6454600443102817; -2.13603282352703161|];\n", " [|-0.839588192768512376; -1.74961989675213392|];\n", " [|-0.992431423756186204; -1.31569413075129171|];\n", " [|-1.10056449840736703; -0.857392350245871682|];\n", " [|-1.16255675909603573; -0.391455573074287411|];\n", " [|-1.17834164809000641; 0.0705805769255422|];\n", " [|-1.14879578161057139; 0.519942157737366184|];\n", " [|-1.07559608109481819; 0.947893575800511368|];\n", " [|-0.961343337819828614; 1.34339665772494898|];\n", " [|-0.809884806196925711; 1.69172414498315193|];\n", " [|-0.626711904469132; 1.9746365504195329|];\n", " [|-0.419249779616737039; 2.17258967945957693|];\n", " [|-0.196827758700094557; 2.26880258893402331|];\n", " [|0.02981868916202704; 2.25392822334985476|];\n", " [|0.249487332939835216; 2.12924443807099406|];\n", " [|0.451643447796762743; 1.90667949135001069|];\n", " [|0.627391080054349626; 1.60566258030707587|];\n", " [|0.770013347948908; 1.24849018107622145|];\n", " [|0.875035674223142; 0.856314657708687643|];\n", " [|0.939958944379134076; 0.446994478711824961|];\n", " [|0.963877532861861286; 0.034882683497337641|];\n", " [|0.947157913711899502; -0.36806262007216034|];\n", " [|0.891272978842545; -0.750618111970555835|];\n", " [|0.798810509166694938; -1.10076437142558659|];\n", " [|0.673612570255083; -1.40484595188823835|];\n", " [|0.520952319112750306; -1.64786573966020122|];\n", " [|0.347619051432104809; -1.81511348099665915|];\n", " [|0.161780333936247855; -1.89485037549946722|];\n", " [|-0.0274542642815124305; -1.88116723211021308|];\n", " [|-0.210730571520729909; -1.7757989665522389|];\n", " [|-0.379249920380139605; -1.58801466145910841|];\n", " [|-0.525459966123299704; -1.33263364367163462|];\n", " [|-0.643477740530508768; -1.02711420011423016|];\n", " [|-0.729209638217741; -0.688915462994294514|];\n", " [|-0.780246110816953; -0.333918707582131769|];\n", " [|-0.79565835672033125; 0.023947572411301854|];\n", " [|-0.775810417760952831; 0.372200606965266079|];\n", " [|-0.722252549738436445; 0.698921727954476935|];\n", " [|-0.637707549933894224; 0.992005726665617704|];\n", " [|-0.52611412873334; 1.23895677403037396|];\n", " [|-0.392656274012012751; 1.42748628240091024|];\n", " [|-0.243692590313146967; ...|]; ...|]\n" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let t = linspace 0. 10. 101 ;;\n", "let sol = rungekutta2 f_pend y0 t ;;" ] }, { "cell_type": "code", "execution_count": 156, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 156, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let vp = A.init ~w:800. ~h:360. [\"jupyter\"] in\n", "A.Axes.box vp ;\n", "A.Viewport.xlabel vp \"Time t\";\n", "A.Viewport.title vp \"Solution to the pendulum ODE with Runge-Kutta 2\";\n", "A.set_color vp A.Color.red ;\n", "A.Viewport.text vp 8.5 3. \"o theta(t)\" ;\n", "A.Array.xy ~style:(`Linesmarkers \"o\") vp t (column sol 0);\n", "A.set_color vp A.Color.blue ;\n", "A.Viewport.text vp 8.5 2.5 \"+ omega(t)\" ;\n", "A.Array.xy vp ~style:(`Linesmarkers \"+\") t (column sol 1);\n", "A.close vp;;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "## Runge-Kutta method of order 4, *\"RK4\"*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The order 4 Runge-Method uses this update:\n", "$$ y_{n+1} = y_n + \\frac{h}{6} (k_1 + 2 k_2 + 2 k_3 + k_4),$$\n", "if $h = t_{n+1} - t_n$, and\n", "$$\\begin{cases}\n", "k_1 &= f(y_n, t_n), \\\\\n", "k_2 &= f(y_n + \\frac{h}{2} k_1, t_n + \\frac{h}{2}), \\\\\n", "k_3 &= f(y_n + \\frac{h}{2} k_2, t_n + \\frac{h}{2}), \\\\\n", "k_4 &= f(y_n + h k_3, t_n + h).\n", "\\end{cases}$$" ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val rungekutta4 :\n", " (float array -> float -> float array) ->\n", " float array -> float array -> float array array = \n" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let rungekutta4 (f : float array -> float -> float array) (y0 : float array) (t : float array) =\n", " let d = Array.length y0 in\n", " let n = Array.length t in\n", " let y = Array.make_matrix n d 0. in\n", " for j = 0 to d-1 do\n", " y.(0).(j) <- y0.(j);\n", " done;\n", " for i = 0 to n-2 do\n", " let h = t.(i+1) -. t.(i) in\n", " let k1 = f y.(i) t.(i) in\n", " let k2 = f (y.(i) +++. (k1 **. (h /. 2.))) (t.(i) +. (h /. 2.)) in\n", " let k3 = f (y.(i) +++. (k2 **. (h /. 2.))) (t.(i) +. (h /. 2.)) in\n", " let k4 = f (y.(i) +++. (k3 **. h)) (t.(i) +. h) in\n", " for j = 0 to d-1 do\n", " y.(i+1).(j) <- y.(i).(j) +. (h/.6.) *. (k1.(j) +. 2.*.k2.(j) +. 2.*.k3.(j) +. k4.(j));\n", " done;\n", " done;\n", " y\n", ";;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For our simple ODE example, this method is even more efficient." ] }, { "cell_type": "code", "execution_count": 107, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val t : float array =\n", " [|0.; 0.322580645161290314; 0.645161290322580627; 0.967741935483871;\n", " 1.29032258064516125; 1.61290322580645151; 1.93548387096774199;\n", " 2.25806451612903203; 2.58064516129032251; 2.90322580645161299;\n", " 3.22580645161290303; 3.54838709677419351; 3.87096774193548399;\n", " 4.19354838709677402; 4.51612903225806406; 4.83870967741935498;\n", " 5.16129032258064502; 5.48387096774193505; 5.80645161290322598;\n", " 6.12903225806451601; 6.45161290322580605; 6.77419354838709697;\n", " 7.09677419354838701; 7.41935483870967705; 7.74193548387096797;\n", " 8.06451612903225801; 8.38709677419354804; 8.70967741935483808;\n", " 9.03225806451612812; 9.35483870967742; 9.67741935483871|]\n" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val sol : float array array =\n", " [|[|3.04156; 0.|]; [|3.01514459001706; -0.168073982292008067|];\n", " [|2.92524068186212505; -0.40997602608111805|];\n", " [|2.73082595162226482; -0.83986111238677208|];\n", " [|2.34558387188495843; -1.62374367239927175|];\n", " [|1.63147992840831235; -2.86279243145111817|];\n", " [|0.508849624613306517; -3.94638176996873646|];\n", " [|-0.729938057166801491; -3.4423574128899137|];\n", " [|-1.58130089343988933; -1.76934614226155151|];\n", " [|-1.88100723824819749; -0.124998397630503355|];\n", " [|-1.67675988248597196; 1.38189318693121943|];\n", " [|-0.998660995093421544; 2.76245745655193087|];\n", " [|0.00990026972481095; 3.26207897518789913|];\n", " [|0.9349425506047504; 2.28077702467475563|];\n", " [|1.41418850276070662; 0.663566385977470086|];\n", " [|1.36910538191439057; -0.919824478454474903|];\n", " [|0.846941901653241791; -2.23857035893071554|];\n", " [|0.0178465256173153675; -2.70513906586802078|];\n", " [|-0.754166736888580491; -1.91125086669990418|];\n", " [|-1.14564076405576865; -0.47621471666032722|];\n", " [|-1.06175338137134245; 0.966682274531973|];\n", " [|-0.561766705543892408; 2.02888883753261595|];\n", " [|0.146152092751127172; 2.18268237193314318|];\n", " [|0.731805215477561388; 1.32587845081367828|];\n", " [|0.954379467760988254; 0.0337641526393033242|];\n", " [|0.763316350305066615; -1.16858571345420392|];\n", " [|0.257276461206502716; -1.84530056233370932|];\n", " [|-0.327139986143612616; -1.63299256455690345|];\n", " [|-0.715665389025514687; -0.703045696222519889|];\n", " [|-0.759083554196956722; 0.425753036314224231|];\n", " [|-0.467540082468857643; 1.30687972996076196|]|]\n" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let t = linspace 0. 10. 31 ;;\n", "let sol = rungekutta4 f_pend y0 t ;;" ] }, { "cell_type": "code", "execution_count": 157, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 157, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let vp = A.init ~w:800. ~h:360. [\"jupyter\"] in\n", "A.Axes.box vp ;\n", "A.Viewport.xlabel vp \"Time t\";\n", "A.Viewport.title vp \"Solution to the pendulum ODE with Runge-Kutta 4 (31 points)\";\n", "A.set_color vp A.Color.red ;\n", "A.Viewport.text vp 8.5 3. \"o theta(t)\" ;\n", "A.Array.xy ~style:(`Linesmarkers \"o\") vp t (column sol 0);\n", "A.set_color vp A.Color.blue ;\n", "A.Viewport.text vp 8.5 2.5 \"+ omega(t)\" ;\n", "A.Array.xy vp ~style:(`Linesmarkers \"+\") t (column sol 1);\n", "A.close vp;;" ] }, { "cell_type": "code", "execution_count": 109, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val t : float array =\n", " [|0.; 0.0990099009900990146; 0.198019801980198029; 0.297029702970297071;\n", " 0.396039603960396058; 0.495049504950495045; 0.594059405940594143;\n", " 0.69306930693069313; 0.792079207920792117; 0.891089108910891103;\n", " 0.99009900990099009; 1.08910891089108919; 1.18811881188118829;\n", " 1.28712871287128716; 1.38613861386138626; 1.48514851485148514;\n", " 1.58415841584158423; 1.68316831683168333; 1.78217821782178221;\n", " 1.8811881188118813; 1.98019801980198018; 2.07920792079207928;\n", " 2.17821782178217838; 2.27722772277227747; 2.37623762376237657;\n", " 2.47524752475247523; 2.57425742574257432; 2.67326732673267342;\n", " 2.77227722772277252; 2.87128712871287162; 2.97029702970297027;\n", " 3.06930693069306937; 3.16831683168316847; 3.26732673267326756;\n", " 3.36633663366336666; 3.46534653465346532; 3.56435643564356441;\n", " 3.66336633663366351; 3.76237623762376261; 3.86138613861386171;\n", " 3.96039603960396036; 4.05940594059405946; 4.15841584158415856;\n", " 4.25742574257425765; 4.35643564356435675; 4.45544554455445585;\n", " 4.55445544554455495; 4.65346534653465405; 4.75247524752475314;\n", " 4.85148514851485135; 4.95049504950495045; 5.04950495049504955;\n", " 5.14851485148514865; 5.24752475247524774; 5.34653465346534684;\n", " 5.44554455445544594; 5.54455445544554504; 5.64356435643564414;\n", " 5.74257425742574323; 5.84158415841584144; 5.94059405940594054;\n", " 6.03960396039604; 6.13861386138613874; 6.23762376237623783;\n", " 6.33663366336633693; 6.43564356435643603; 6.53465346534653513;\n", " 6.63366336633663423; 6.73267326732673332; 6.83168316831683242;\n", " 6.93069306930693063; 7.02970297029703; 7.12871287128712883;\n", " 7.22772277227722793; 7.32673267326732702; 7.42574257425742612;\n", " 7.52475247524752522; 7.62376237623762432; 7.72277227722772341;\n", " 7.82178217821782251; 7.92079207920792072; 8.01980198019802;\n", " 8.11881188118811892; 8.21782178217821802; 8.31683168316831711;\n", " 8.41584158415841621; 8.51485148514851531; 8.61386138613861441;\n", " 8.7128712871287135; 8.8118811881188126; 8.9108910891089117;\n", " 9.00990099009901; 9.10891089108911; 9.20792079207920899;\n", " 9.30693069306930809; 9.40594059405940719; 9.50495049504950629;\n", " 9.60396039603960361; 9.70297029702970271; 9.8019801980198018;\n", " 9.9009900990099009|]\n" ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val sol : float array array =\n", " [|[|3.04156; 0.|]; [|3.0391226684992545; -0.0492285629019174747|];\n", " [|3.03177276128229733; -0.0996338062721686679|];\n", " [|3.01927516015746411; -0.153620003759229684|];\n", " [|3.00115241209564187; -0.213696393492316|];\n", " [|2.9766689247853475; -0.282586378652772197|];\n", " [|2.94480437110224091; -0.363336300206605733|];\n", " [|2.90421640674631698; -0.459421802365044596|];\n", " [|2.85319326842347198; -0.574843794764229199|];\n", " [|2.78959810389226659; -0.714194965104298696|];\n", " [|2.71080965865368428; -0.882657987552806|];\n", " [|2.61366933385879374; -1.0858624704672728|];\n", " [|2.49445437940516; -1.32947272354123558|];\n", " [|2.34891337747415152; -1.61829970140246937|];\n", " [|2.17242504413163218; -1.95464379348485062|];\n", " [|1.96037272241410943; -2.33555053709422911|];\n", " [|1.70885073221755923; -2.74888146198779859|];\n", " [|1.41579566533549261; -3.16888687934279778|];\n", " [|1.08249517159997977; -3.55354957515189|];\n", " [|0.715109711947466087; -3.84770377368949612|];\n", " [|0.325441250106985047; -3.99536686046597067|];\n", " [|-0.0699190864919839727; -3.95904774800841208|];\n", " [|-0.452287687444798803; -3.73554535387515418|];\n", " [|-0.804467169392459214; -3.35673269485760128|];\n", " [|-1.11357474679483404; -2.87467196041220285|];\n", " [|-1.37205587780615756; -2.34200178397280734|];\n", " [|-1.57700879364184265; -1.79866877944456216|];\n", " [|-1.72866651635680224; -1.26803574155739063|];\n", " [|-1.82883871793355479; -0.759255125090063|];\n", " [|-1.87972614160690199; -0.27186408672986262|];\n", " [|-1.88319494772193252; 0.199754224892532639|];\n", " [|-1.84045392115182849; 0.662711676307255804|];\n", " [|-1.75206143877875142; 1.12254614316519419|];\n", " [|-1.6182252493199738; 1.58031278585125734|];\n", " [|-1.43939291209877784; 2.02962670364174791|];\n", " [|-1.21712505674593463; 2.4540415503089843|];\n", " [|-0.955162531422122152; 2.82604474993697741|];\n", " [|-0.660430305711281362; 3.10967848132059599|];\n", " [|-0.34353383787510211; 3.26823308268441926|];\n", " [|-0.0182828421951334308; 3.27563108435625772|];\n", " [|0.29988995231147525; 3.12629814733551825|];\n", " [|0.596151233707482575; 2.8375005425207136|];\n", " [|0.858257214380308; 2.44260762434597423|];\n", " [|1.07759690578971656; 1.97974392787833819|];\n", " [|1.24915018030287173; 1.48208982599572381|];\n", " [|1.37072155712265542; 0.973166564272889056|];\n", " [|1.44194967693485165; 0.466767478570425|];\n", " [|1.46345948781373059; -0.0304287144576129154|];\n", " [|1.43633119759964156; -0.515294348898755583|];\n", " [|1.36192787952049943; -0.984670590846349447|];\n", " [|1.24206138750156536; -1.4321665633009637|];\n", " [|1.07944285254233874; -1.84568988317779|];\n", " [|0.878316056391732269; -2.20636299151447624|];\n", " [|0.645090032944561353; -2.48978191303466367|];\n", " [|0.388698736892993613; -2.67030320443958669|];\n", " [|0.120403804144515847; -2.72774383108151941|];\n", " [|-0.14708801964373408; -2.65398358815839597|];\n", " [|-0.401014093611074762; -2.45610407390851693|];\n", " [|-0.629997905437077121; -2.15426998471919617|];\n", " [|-0.825063506953729098; -1.77565126645040539|];\n", " [|-0.979986860814240912; -1.34767078914604421|];\n", " [|-1.0910679227066189; -0.89337466666507992|];\n", " [|-1.1565949674863385; -0.429847881471155435|];\n", " [|-1.17628143989641787; 0.0309220266056009496|];\n", " [|-1.15086377377149418; 0.479837337099708772|];\n", " [|-1.08194373033462554; 0.908093424482677825|];\n", " [|-0.972077812548367781; 1.30488663625732659|];\n", " [|-0.82505430457777329; 1.65601407508140652|];\n", " [|-0.646240433036617379; 1.94394948589238603|];\n", " [|-0.442829622786570176; 2.14981996365949968|];\n", " [|-0.223801781785368276; 2.2571237113826963|];\n", " [|0.000528489775196344658; 2.25607234986715977|];\n", " [|0.219348908747622; 2.14671521943166699|];\n", " [|0.422366789921064; 1.93929511007784194|];\n", " [|0.600710760394784216; 1.65167055463977475|];\n", " [|0.74748362573778071; 1.30514678495061487|];\n", " [|0.857902204805326196; 0.920583984378085307|];\n", " [|0.929122154365651; 0.516052437651637552|];\n", " [|0.959921681840344321; 0.106299134247129612|];\n", " [|0.950405114828223; -0.296423506018091476|];\n", " [|0.901827225513500808; -0.68086468247841|];\n", " [|0.816570279638364926; -1.03528621433651136|];\n", " [|0.698244496501420175; -1.34654412027003123|];\n", " [|0.551832059877745085; -1.60018721507722805|];\n", " [|0.383760349982204596; -1.78179552755520376|];\n", " [|0.201787149120740694; -1.87936224564236398|];\n", " [|0.0146267505409670706; -1.88598419251135474|];\n", " [|-0.168661078918962176; -1.80178276010032268|];\n", " [|-0.339395470111264641; -1.63417945592763658|];\n", " [|-0.489935641633520325; -1.39639794156977781|];\n", " [|-0.614132507559556617; -1.10489127599143466|];\n", " [|-0.7075165529098707; -0.776757359358784427|];\n", " [|-0.767265518869675645; -0.427970848742863064|];\n", " [|-0.79205159527398461; -0.0727208064874359|];\n", " [|-0.781871429406644447; 0.276331513203226298|];\n", " [|-0.737929788874430503; 0.607306508710532156|];\n", " [|-0.662601233432069781; 0.908353861544634|];\n", " [|-0.559448723938056669; 1.16731564334651239|];\n", " [|-0.433242417624848775; 1.37209070227011587|];\n", " [|-0.289903982741078; ...|]; ...|]\n" ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let t = linspace 0. 10. 101 ;;\n", "let sol = rungekutta4 f_pend y0 t ;;" ] }, { "cell_type": "code", "execution_count": 158, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 158, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let vp = A.init ~w:800. ~h:360. [\"jupyter\"] in\n", "A.Axes.box vp ;\n", "A.Viewport.xlabel vp \"Time t\";\n", "A.Viewport.title vp \"Solution to the pendulum ODE with Runge-Kutta 4 (101 points)\";\n", "A.set_color vp A.Color.red ;\n", "A.Viewport.text vp 8.5 3. \"o theta(t)\" ;\n", "A.Array.xy ~style:(`Linesmarkers \"o\") vp t (column sol 0);\n", "A.set_color vp A.Color.blue ;\n", "A.Viewport.text vp 8.5 2.5 \"+ omega(t)\" ;\n", "A.Array.xy vp ~style:(`Linesmarkers \"+\") t (column sol 1);\n", "A.close vp;;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "## Comparisons" ] }, { "cell_type": "code", "execution_count": 120, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val methods :\n", " ((float array -> float -> float array) ->\n", " float array -> float array -> float array array)\n", " array = [|; ; |]\n" ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val names : string array =\n", " [|\"Runge-Kutta 1\"; \"Runge-Kutta 2\"; \"Runge-Kutta 4\"|]\n" ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val markers : string array = [|\"o\"; \"s\"; \">\"|]\n" ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val colors : A.Color.t array = [|; ; |]\n" ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let methods = [|rungekutta1; rungekutta2; rungekutta4|] ;;\n", "let names = [|\"Runge-Kutta 1\"; \"Runge-Kutta 2\"; \"Runge-Kutta 4\"|] ;;\n", "let markers = [|\"o\"; \"s\"; \">\"|] ;;\n", "let colors = [|A.Color.red; A.Color.blue; A.Color.green|] ;;" ] }, { "cell_type": "code", "execution_count": 159, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val test_1 : ?n:int -> unit -> unit = \n" ] }, "execution_count": 159, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let test_1 ?(n=101) () =\n", " let t = linspace 0. 10. n in\n", " let vp = A.init ~w:800. ~h:360. [\"jupyter\"] in\n", " A.Axes.box vp ;\n", " A.Viewport.xlabel vp \"Time t\";\n", " A.Viewport.title vp (Format.sprintf \"Solution to the pendulum ODE with different methods (%i points)\" n);\n", " for i = 0 to (Array.length methods) - 1 do\n", " let sol = methods.(i) f_pend y0 t in\n", " A.set_color vp colors.(i);\n", " A.Viewport.text vp 6.5 (2. -. 2.*.(float_of_int i)) (Format.sprintf \"%s %s\" markers.(i) names.(i)) ;\n", " A.Array.xy ~style:(`Linesmarkers markers.(i)) vp t (column sol 0);\n", " done;\n", " A.close vp;\n", ";;" ] }, { "cell_type": "code", "execution_count": 160, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 160, "metadata": {}, "output_type": "execute_result" } ], "source": [ "test_1 ~n:10 ();;" ] }, { "cell_type": "code", "execution_count": 161, "metadata": {}, "outputs": [ { "data": { "image/png": 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nK79np/6J5p+9r3+212pRRo5QWNcK8vORvXFvtk377NW/Zx+9lN3r6+wB32Yn5otE9eoKwzAMwzAf3JeRYAEYMEAHOiOiRxyOPawM5RZDFmH1tFSk1nVzkQienh7wuIZry7F8JVa27rNA0OcElZbUsQKFy9b7Y38/oLA/Qudod/OmJ5v9arRlmlxRLgSCOtbgsG6V0TlZS0Gs5a2Dlud/syyItgzdqNtE6c6dunaizIMHWLkSM2dixw6U1DX+BicWi/fu3dtYrTOVnD9/Pjk5ubGjYAAgKyvrr7/+auwomDKHDh0qLi5u7CiYT9KXcYmQA8rJhbp6UFDQdr3zRR2Sc5q9Et93tI7hiyAr5krKS4rlxaWKFc4IyVCpajHAyRepqsjmczgQqRRLZCUi7WyRYRo4BLEs5ITI1uCUKMgUK8jmqsqWyMkWySvmKXJLuIqFsor58orFUCnA7dzOnUqi9PMLVQqRb5514+u4LOMi4cJFe0+fNOGlCOXkShQUSuXkBHJyAjm5EkVFoZycgMstUVAQyMsL5eRK5eQ2v3AW/jJHqMZxPefa9GFTEOREon9WD2897LKmWXodh8IjMrLt3bt37OwKlZTMkpL0Xr/eOXhwmrZ2ww54XeTn52/fvn3q1Kkfv2nmbQcPHrSxsWnRokVjB8IgPj7+6tWr3t7ejR0IAwCbN28eOHCgnp5eYwfyyYuIiIiIiGjsKD6qLybB+v2P12N6D4wYeM3xmq+qb+ABG6PhP9S961oKBfHzd2rO849EZDCCYxAzO9pzdrvF8UmaGpqUIcrJKCzOKSl5LcrOKiopouLUkpxiKskTFeVQbglK8sSFV+9mNjHPk+hSCTevmJuXp50g0EoDcZBkxE1sovRaTyVHQyNbQydX2TBX0SRD1ixHbJVToitM0hEkaQtT5ItyXBIObJSdktv12pwVsiU8zvw/TIbcb9b2zNKN3Y87uylCVxfa2tDRgbY29PSgplZFN86dg78/rl6FllbZmh07sHo1oqMbZqDrIykpqXnz5llZWR+/aeZtPXr0GDZsmI+PT2MHwuD48ePLli27fv16YwfCAIC5ufnRo0dbtmzZ2IF88oKCgoKCgho7io/qi/gWIXRez8qfGFLq30zOupOXXUif5li8GPihHjXweNevrfj16YaYJgWzS344erAfd/b82fJrAXDA0eFq6KhrQL2mCqz65f9lMMYy/I8I1eiFWPgUvFkHv1o+Y0NIBBXbp8cVJr0sTX8pTk6hJ9e5qad5KYXK6aVK2dwsXSQbipOMuBlOksTjAwWDjRRn6p/QkG36cNbUjQu4T0TjL5GOIbKf4vFjZGQgIwPp6UhPh1AIbe2yZEuadWlr/70v95X+AqzIhooQfD4UFYHRSIn3vBhv3LVpPUYjLQ2nTyMtDc2aoVcvyMnVY1uGYRiG+QJ8GQlWWOcVoePRZOb1VH0AnNMAJtWrgoJdwwa3lLf46RvL7R0OCTiH1NVhGZ9/uz6jp6p6c5jWd3d1ntopzAp39VmuwVUUrpRpaimQteTbgl/FFkII03TTknWT01qmPStKXb45oanZwaKvdGPlMlNVnogkEpFMqWTfbI/d/u1uT2hjaGXvwbG1ha0teDygpAQZGXj9GmlpZYlXRsYi3SZKmUpNdz1AcTGKiiArCzW1v7Mmmi3fa5ykB0tLWFlBR6eWjuzciRkz0K0bDA3xzz+YPRuHD8PWth5DwTAMwzCfuy8iwSLbB7AFfkBQUFBoaOi1a9fqW8Nmg0DDOFvZflz0e7MyAPWYBCv951HfNI/SXLdJZUj/FSKZFQoK4PFeJtW0iRzkjGFsDGMAUMKe/VjZdI3zvNWJE/v+3E12d9Pr3S7zIuLnNh0Y/2jogMvyr9QTm0vu2+ftt1ONc3IUtnGwMra3N7azg6NrWZwFAYsfzp/dVGXEHMwxgxmysxEf37PjQ2hoIDwcO3bg2TMkJ8PQEHZ2sLeHhUXZT5MmkJEBgJgYzJyJy5fRrFlZlNu3Y8gQ3L9fVoBhmHfj4IDYWAC91NSU5OSQlYU6zgHTgAHMmoVvvgGAM2cwdCh+/x0DB1Zb3tgYx46hTZuqX9Zq7Vr88QdiYuDri82b3y90hvkv+iISrHKmpqaq9ZsYtMy3bZq/Z9OhLot0ik1lp8hiyr/Wm5jUo5KnEwdtW3njsMaOb660vHH0N42eI93nyq1sD2cT5CL3ftP7t5reujXo1nXRbxEyzx7kWKjGOYmuO6UuclJ40Mq+iXLuk1lef+hKTjx1cnb2lOm5QG2u1aFDUB8OHx/0+P/NN9nZePas7OfWLRw69CbrsrBARgYcHBAXBzk5mJlBVhY+Pli7FjdvwsWlXgPC4/Gsra3rtQnz4ZiYmOjq6jZ2FF+8HTvw9df3jx1rMn485sxptLTj1Cl88w327EHv3h+wFWNjLFqEAwc+YBMNwcLCQq3KW1oZplb0hZk6dWpjh/COzH9fyMnQVlyxgG+epaFB5T+3b1dRuJRKYyhmB+2YQlNcyVVJrKJfaKF8oY/lph+tB65RafpAY/583mtVj78dOo58EBpaW9v5+XTnDh0+TK1bU5cu1LUrmZqSigp16ULz51OHDrRnT327U1paGhkZWd+tmA8kJiYmPT29saP4rMXHk4cH8flkY0MHDlRRwN6edu0ioqysrOSpU8nFpWy9rCylpJQtT51Kc+eWLevpUXAwOTuTlRWNHk1CYdn6+/fJ2ZnU1Kh3b/L1pYCAsvWpqeTlRTo6ZGZGq1dXG8CRI8Tn09mzb9ZXGcCECSQrSwYGZGZGO3ZUfklE8+eX/ZVo2ZIuXap2WCZOpPHjax65xnX9+vXCwsLGjuJzEBgY2NghfGzsss4n4+AYz0ytuOKZC7OfaWRlofynVasqCstD3h723vBei7URiMiRyQpV+tP89mCHXgK9Qwc5D5z4U393uTvqiiU3YnvLqTFbDh1Cfn71bauooGVLDB6Mnj3h5oYLF/DiBVJSMHcuZGRw7x7GjYO9PcaPx86dePGi9s5IJJyHD/lRUUhIeOcBYZhPhliMfv3Qvj3S0vDbb/D1RfXz18kkJ6tfvAgrq9qrjYpCZCQePMDDhzh4sKyhgQMxbBiysvDjjyifao4IAwfC1BSJiQgLw+bNqHKqrSNH4OuL48fh4VFL07/+Cn19nDiB58/h7V35JQBbW0RFIScH/v4YOhRsKinmy8MSrE9GG7TRgMa7bSsHOUc4Gp0dM+HR2suykdnc/O+0Jsd6HBRaxyqnWhhbCHaHZpiYoGNHrF2LpBruDBs5EiEhePAAAFRU4OEBfX2YmyM7Gzt3ws4Op06hTRsYGmLoUKxdi1u3qnji4717aNuWO2SI4b59cHND375gU1wyn7fbt5GaigULIC8PNzcMG4Y9e6ooNmoUOBx1BwdIJPj559qrnTIFcnKQk4OHB27fBoBbt5CXhx9+gKwsunRB9+5lJe/dQ2wsVqyAoiLMzDBpEg4dqqLC8+dhb4+2bd+5o2+MGAE9PcjKYtw48HiIi2uAOhnmk/Jl3YPF/BNKJ3HqlNNCMUc06M6vrRIGrbh8VWH5rssD57X+rY3jvVHRvw9a1lpFWxteXujbF05O/9p86xW7Gw6RaHMVhilQVkZ6OgTa8Lg8Nlre2dkJTk6QThz67BkiIhAZid9+w6tXcHGBqys6doSbG4qK0KsXgoOFw4Y9uHmzg4sLFi9G//64fp3dJv8FIqr6JCaHA3Pzjx7Nh5OcDCMjcP//97ZJE+n97JXt2oWRI/PPn1f85hukpEBfv4oyFZVPaMfjITOzrCFDwzcfpfJ7PF+8QGnpm6eXCgRo2RKbN2PCBADo3BmXLgHAihXYsQODB+Po0fedfmXnTqxfj9RUyMoiORkZGe9VG8N8gliC9QWx8ruwy+UHrkix9b5FpjGeAO4A3ZU6Ts3raIG1J2VP7my183Kryd3X9mjzcFTm7l5ff80VCtG3L/r2RZcu4HJx/jxULKyce+vj4UPk5qKzBezstm6XefoUzs4VWpJ+91B6pSA1FTduIDISQUGIiYG2Nvh88PnIzgYALhcLF+L4cVy5go4dG2NUmMZUUgIrq8q5FBFSU1FU1EgxfQiGhkhKgkhUlmM9fw4jo6pLcjgiJ6fXo0YZTpmC8HAAUFZGaWnZu5mZUFGpqSEDAyQnQyIpy7FevoSNDQCYmIDPx8OH4HD+Vf677/71UlUVoaFwd8fw4ThwoCza6gKo9D+iii/j4zF1Ki5fRvPmAGBhUcWZbIb53LEE6wvSdlCSJ5Z7whOT335T0QteXvDKQtZhzuGddisSln03ZNmQNgleyQc7BgXh8WP06oUY7UsDeir69W4HvMmnLobV2Kq+flmOBiAvD6NHo7AQP/8sf+tWCxMTTJiAkSPh5IS4OJZgfZnkPS4/PtOBW+FvUXHxm1MzdeHq+iYBqCgyEgoK7x1fg2jdGnp6WLoUc+YgKgoHD5adMapG5uDBhtu34/x5uLujZUucPg0/Pzx9ipMnManGOfycnKCqil9+wfffIzwcZ86UJViOjjA3R0AAFiwAj4fHj1FQUPU3f/l8nDmDrl0xahR274asbLUB6OriyZM38zJUfJmXByUlNG0KACdPVn2WUiSCSASxGGIxSkrA5b45w8cwnwV2UeYLMgqjPOFZcxlNaPrBLwIRV3DFEIaLzX12BNh5RAQdufu0TRu8yipa6jBC/7bngr+vSa9I1I+aGlq3hpMTLl0SpKS8+O47REXB0hKhoXj5EhJJ7TUwnxcCCWcutYPdDuwQQVT7BlW5cwfr1iEk5F8/MTH/pQNKVhbHj+PyZejowNcXISFo3bqG4hIeD/7+WLQIANaswaZNcHFBQEDt8yZwuThyBPv3Q0MDq1Zh6NCyHFNGBseOITkZVlbQ1oaPD3Jyqq1ESwvnziE6Gj4+kEiqDWDOHMyYAQ0NbNlS+aWTE0aMQKtW6NULV67AwaGKVoKCwONh82Zs3QoeD/Pm1dI1hvnUfBHPIqzo+++/X7NmTWNH8Sm5hVs7sXM/9pvAhHaOGsH1etLk3B6LxSUv9AbfXrpxaOdJk9C/P4YPr1t19+6hVy/cvi3Q0Lh582aHDh0QEQFPT9jZISkJI0di/PjP6+6bT0NsbKyurq5OrfP4NzTpyaotDyJ/lgt+yotpfmp2m3s+qjzuihXYsgXq6uDzy35Lfypd4JJSUkJmJni82ld+ErKzsxMTEx0dHRugrn790Lcvxo1rgKq+VFFRUQ4ODkpKSo0dyCePPYuQYSpzgpMTnFZj9UVcHGe+c2HbRV3kO6zDnCyeeLHFWIOneia8pT1KOte1uhYt8P33aN1a1s9PhwhHj2LnTuzYgYED8eABdu5Eu3Zo0QKjRsHL65P85/FLkppT4pD+lcXZ8WYRIzniN39MNDQQElLtVkSIj8fNm7h1C1FRKC5GUDfXNm1OdugXGd4leNeA5W0vzCZZnwsXuLm5yMlB+e/sbKir/yvrkv4W9DyxYlMXI1U1Ph82NmW3/Xy5IiJgbQ0dHYSG4sIF/PprYwf0sd25gzNnqljfqtWbb1XWLDoa+/aVLaekmGhry0nv+Hd0xIgRDRQl8wVgCRZTJ7KQ9YBHu189uqfncQb/uRu7Y9RjFmDmEZW/rmzvMmHBypw1MyZMqNstLzNmoEcP7N7Nj45Ghw64dQvGxgBgZ4fgYCxciBMnsHMnpk3D4MH47ruqZ/pi/gMkRYqC71cW/xEYMXrJ4IfzOr4YKUvc7GwsXFi55JMnuHWrLKm6fRuauiJ791TTjokdv3l1bV9Sn5WJr/DqFl6pQrY1rC4MmCJ+saCb7qqu6GoIQw7enLaqmG+V/yb70z99M872/CTjI1NjZqsJBPD0hFiMwsIvMkV/9AhDhqC0FEZG2Lu37MP1Jbl6FQcOVM6l7txBYmJdE6yHDxEaWpZLFRSINDQgJ4foaLx4wRIsph5YgsXUz55NapZnxlhwvAvd1wT0W0BcscaG+XPUf7xyBatXY948+PjU4V7VFi3ESyqV7bMAACAASURBVJbE37yp06FD5bcUFODlBS8vJCVh924MHgxNTYwahW+++dedz+Hh2L4dCQmwtMS4cWjXrmG7ydSRanTH+7rnr+DKcuflfzkHzcbsnsk+Cxdyk5Nx47b4clzq9ZTE+1lJMH6l3TpRccwryewkJf6LJJnXAuhkwlRfbIRIY+VM086iDtoS3XNKJ46o7tAXmb68Y7Wpx6YZmJGDHHOYm8O87LmYfAtzvrmlmYUK3nyZLkBp460xM37pv/xwf/NxGDf8+ayoM/ytW2FpCRcXeHigX78v6XHkY8di7NjGDqIxCeQKHbsXBAfrVVz5669Vz4xRHVtbBAQAQFRUioODlpKS3P79OH68QQNlPncswWLqYexYPHkmuW1+5ITzPJVincnnjnNI5siwmbvVTq+dvnL69c5z5mD1aixejCFDqr5dph6MjBAQgBkzcOECdu7EwoXw8ICfH9zdsXAhdu5EQADGjEFsLIYPx4QJZX8OmcbQDu18c6ZvzTw6Q3upv8Z08SUDU5RQzzTlztqGYpNOPGNLBWNTmBqhrTGMTWFqAAPp1wZLhLD/BXvXCwv67suZ4suNMdf8+W/ZaBcbRUTGAkAxiv//aMxnCUi4iIvSZVWoWsBCmniJR1u84FjMwZyZmLkSK92bWI7zGycXOCs+mh8ejr//hrs71NXRuzc8PeHmVsUET6dOVT3TeJ8+X+Q5sE/cC52b+78erIIRszDLCNVMh1EjCUcsVCoA1Bs8NuaLwhIsph7E7mdWuU80hekhbHVTd0NvAFiFqAM44AMfu7Z2684Hp5yznzMHwcFYuhQ9e753kzIy8PCAhwdycnDwIGbORFYWMjMRHo6WLQGgc2cMHgxHR3h5wcLivdtj6kfY/PZ3hXv2iA4UJ+qaJLfVI/vn5pdkkyzCugQ5wUlOtZbJKhUVMfvp1sVY7ILmgdjnbOoM138V4IFnD3t72FfaMBWp5VmXuEP4kNgdAqMEoUa6UryjSvTonz23iWK2Plb5e/Bgl8GDQYTbt/H335gzB48fw90dnp7w9Hwzkef48WjdunIudeoUnjxhCdanp2ly5z4/Pkrw3WBh3ZJ7YpBc8HyZZOPSUojF2LcPQiEKCmqrwvk2/unF+ckHq37kvHZp1kzSsSO43BqfJ8Ywb2EJFlMPXHC3Y7sb3Cqu5IAzHMMHYdAmbHKHe1+PvkfdF14/ajh9OpYvx/LlePsy4Lvg8+HnBz8/TJuGs2fh7o4OHTBuHPr2hZ4e+vTBmTOVZ01kPpineLoXe7dr7s3YJNi5+euBOGEzLnxTixXO6Lg1/faIkTbtanjgUgUEikb0YRx2hnPtpSvQh74+9DugA4A+DpBIgFfIS8neZDTv1PDfOByhRalVpPxFI2hbwILDgZMTnJwwfz7S0xEair/+wo8/wtISnp5lMw+EhMDQ8F9NVDcVKPPflJ6O8+dx7hyOHYNAoD2kJGht70lx/TbsHNmqj2CQyR/zU24Y//QTuFyoqtZS1f79zgfmPGgWsnrbDPuvUt1HJQU/v9pk/37cvQsdHbRvD1dXdOiANm2qzb8TEsoeDlmJuTmGDn3fnjKfCpZgMfXwFb6q7i15yE/F1DEYswIrWnIcxw8aHzlg5tkjat7eMDfHihU1z/tTH5qa6N8fc+bg8GEsXIhVq7B+Pfh8FBY2UANMtdKQdgAH9mLvM8lz02tDM4N+V4puPjNu62b1PkJ0vIALNrBJrs9sVhxw1mP9e0bVqhWKULQFW37CT63QKhLhLdAiTDHsEA51QAcjGA3BEC94WcEKgK4uvL3h7Q2xGHfv4uRJ+PsjNRXjx8PLC/36gc9/z3CY9zL7zsE98r+3+mue/tN/ncz09ET//pULFxXhyhWcO4dz5xAXh7Zt4d5NMnRmYpJSfJvJcQ/w+CmetkPbqwqXdvlt0+7ZykSjjypUVaDCB18ZykpQUoOaGtSUoKQMZT7e7HvFPN1gBE/DtBk0Y0zrNiOdRn5jMstkv8Evv5Q9mWL2bNy9CzMzdOwIV1d06oQmTd4EFheHkJDKuVRCAi5eZAnWF4QlWExDUof6Mizzh38gAm1krOd6zb3bf/zvIfJ9+qBrVyxciF9+Kf/auDzw5tTWxo3w969bG82b4+efsWQJvL0xahR27ULPnhCJvsCvo78/AQTykK+1WD7yj+LoXuy9jutfFfbV/j0ofrGH+xjupp9L2upYbL/n7njkIpKbLQCAqm9m+qA2YuMSLOmMzqdxuvxi4lf46it8tQEbwhF+CIfc4KYPfWmmZQ1rALKyZae1goKg16S4QwfegQOYNAmdO2PGDHTq9LF7wUjx/hmkoVR49bvR2vnmfW8FWaa6Avj7b9y8WZZgicW4caMsqbr5LMu6T1yTno/sJ8c1MYyP58QtRJxigbbkkXX63abaWdbq+a4PrI+9sEzhJ7gYvewoNBO+xMsiFGUjuxCFhSgsQEEucgtRWISiXOSqQEUJSuijkteCb5KgLCdUoixF80ej/zKI29ijaVMZf3X9hX378qRPpiguxs2buHIFhw9j+nQoK8PVtez8lkQCa2sEB/+ra6dP45dfPv6IMo2GJVhMwzOG8TZsi0FMAALWya9bOnlpnI/XurWcDh2gq1v2vBCBQFA20SgwcWJ9au/dG4GBmD0bgYFQVMSQIbh+HUeOYOJEJCdj0iTIyn6gfn1mMpBhD/tv8e2P+LHKAgIIQhG6B3tO43RndO79eoxh0NETB3h+fvgjFtraKC5W3H76gbKQX+nGqfHjP0b85YpRfA7n3r5PC4AsZLugSxd0WY/1EYg4hENd0VUb2tJMywY20mK5+zxPt5ZfPjuoZXH73bsxdix0dFBSwh6g1whkJNx+md8uVBt9RO3IPCMfHegswqI26V+9TC+duz/uXGLcvZI4Xot4xW8eFQbEyXJFXI41D02tYGONIdawboqmMTEqx45BIF9wu/3GCx6TzJ519V53UzPDul07DKit9XzkF6LwXmrRqRvZArlCgVzhy+LHia6hiWaXSUaY6XFgPFJd4NIWbVuiJY8n5+YGt//fMfH4Ma5eRWQkNm1CQk421+PS/KB+HdrKtm/PTot+qegLM3Xq1MYO4ctygS44k7MLuVyiS1lZZDPiNq/z9R9/pOTk0sjISGkZf3/auLE+laam0ogRpKZG9vakqkqjRlF6Ot29Sx07UuvW9P9qmVqlUVoABWiT9siMkTEZMdKVYhJfokt+5KdFWp2o02bafCsh09eXtLRo7lzKyGjckN+XmMThFD6FphiTsQM5BFFQDMUYmArWZu9oSk1dyfUCXRCL6dAhkpOjZs1oxw4SCD5qhFlZWXfv3v2oTf6XLF5M8+YRET2hJ8tzN9qnuHNLlTjFPJTKqyfbOL3s718wYwttCaOwVEqtsoYCKlhEi3RIZwyNeUJP3jkSAQl20A6TYpP24vYX6IKIRPfp/lbaOo7GOZKjMim3o3ZTaMoe2hNP8ZW23XoqRfVmF83X1rbLdqryRR4etGsXnThBPXq8czifvMDAwMYO4WNjCRbzwUlIso/2WZBFH+rTdfcWjZwmpjG9+D2vjhv3oqSE6B0SLKn8fIqJofz8f608cYLMzGjUKEqt+o8v87Y0SvN97asp1vyavvYnfxMyaUEtVtCKF/QiPp7GjCFtbVqwgLKyGjvQBiUmcSRF/kA/mJAJ97Fdn1sLVpy5PfH6DoP8ps1euwZeuqChQfv3k7s7mZrS2rVUUPBh47G3J4AA0tKS9OyZnZn5YZurMoBdu8qWT58mdXX688+ayhsZ0Y0b1b6sWWkpTZxIFhbE41GLFnT8eNl6EYnG/hHe4XKAWYGdYra+/O5vLU9ONXndSiXbyPP4ZjGJ61J5GIWNo3Hvk1qJSLSNtlmQRTfqtiV2S2Fh4dtlCqggjMJ+op+G0BATMtEiLU/yDKKgv+nvDMoIDaUePSicwj3Io4nEfNyNkF59haqqZGz85f4HkCVYnz+WYDWWUipdQ2uU8vTaP/BZQ2tMSy3V77c1874UEfGuCVZ1CgooMJD09GjNGhIKG67ez82TJ+TkRE5O1NItT++nZQrPm8oWqMqUKJpf8MmkzMePadQo0tGhhQspO7uxY/2QJCQZEHzV+sR0pXQz1Vc2dofnt9i1kpdlqHe3+4Xcm0R04wYNHky6urRwIX24vMfennbsIKGQ7tzJad68cPz4D9VQDQFIE6yTJ0ldnU6dqqX8+yRYeXk0aRLduEFpabR5Mylo561POeRN3loSbfVnLZV+nmcx/PrMo5G9RH3MyGwNrQlcViI9rfVxRFFUX+obSZFEdP369SoTrEqSKfkYHZtDc9zJXY3UjAqbGpwfuZbWXqWrF+iCB3mYk7nv9ZCmtkJbW2rWjJYto5cvP3xP/ktYgvUJy8vLGzZsmJKSkpGR0aZNm6orxhKsxjV2ek6PW7O1SXumaOaMJzMMCqwUbrg2GX3p558buqXHj6lXL7KxoTNnGrrqz8T9+9TEKWNs8ny+UNv1Rd9pD9Z2zOmtXWiqu2DTWP9SXV0KDPzMU6tKJCS5TtdH0SgFUpAn+eE0/DW9Ln/36VOaMoW0tWnKFEpMfJf6AwNJX5/U1cnamq5fr/xueX6TlZU1dWqyi0vZellZSkkpW546lebOLVvW06PgYHJ2JisrGj36zX8l7t8nZ2dSU6PevcnXlwICytanppKXF+nokJkZrV5dRXjSAI4cIT6fzp59s77KACZMIFlZMjAgMzPasePNS+M2KesOpBLR/PlkakoqKtSyJV26VPWAJFDCOlrXjbrJFKjaJfbwPLVRq9ULS0vymHe1D5WlViVUQhWuG358dUywKhKT+LeIWP1Zv7e7PcEotbW8QNniRRf7uAEgDj+2Qw7l3LxJU6aQri65ulJIyAc/Ofof8QUmWDKNfQ9Yg5k2bVp6evrz58/37ds3Y8aM8PDwxo6IqYJ8sXq/a8vu4m46J32b6baZyhO7Oeo8/6PLXMw9dqxBW7K2xt9/Y+VK+Pmhb18kJjZo7Z+8ZCT/pD/95XlrjkHqbu4fKnzBwWY/dSzu1tb7cday74x05B8/RlDQl3Vz7gu82IZtf+GvSZi0ARtSkeoAh5mY+RiPAVhYYO1axMRAQwNOTvD2xoMH9aj81i388Qfu3UNODkJDK8+5VVFysszFi+pWVrXXGRWFyEg8eICHD8tmXRKLMXAghg1DVhZ+/BF795aVJMLAgTA1RWIiwsKweTP++quKCo8cga8vjh+Hh0ctTf/6K/T1ceIEnj+Ht/eblz/fuLxwqP00TDNolRoVhZwc+Ptj6NA33y2VQHIN1+ZgTgu0aIu2d3DH6cZ3MExOah5qdcb/xhHT1j/tuzxhRN7uft384x+MnzplvML48ThxovbR+O+QgUxnHbvRNKbzgV+/+eXWqPVRKObFNTmjVKgjtHg8HuPvOm37ce3LxERMnYqTJ2FmBm9vnDv3ry9VFBbi1q0qfh49aryOMfXV2BlewxAIBMrKymFhYdKXvr6+vr6+VZZkZ7Aal79/2Y0mAMFnGzI1IZDDholTvhdbWtLIkfT6de2V1E9REQUGkpYWBQaS9J6vL1sCJUyhKdqkPTJjipn/qd7U25RMv7u7qO/gPD09+uEHsrNr7BA/uif0ZAyN0SGdRbQoh3LK18dRXCAFmpKpEzmFUEgBlZ1qyMqiJUtIT48GDKBr14iIHBwqHNgVfu7fL6vq7l3S0aGzZ6m0tOoYyu/BAsjBobD8pFENZ7DKzwzNmUPTpxMRXb9Ourok/v+tSv37l53BunuX1NRIJCpbv24djR5dRQCqquTqWvlTUl0A1V0iTKf0AArgE9+P/JIoiYjMzOj6vaITdMKP/AzJ0IIsptCUk8Vnf/1NaGdHysrUpQuVnyS6eUe0aYswJIQq/URFVT1uH9o7nMEq94ye+ZGfHukFUqD0uEqjtIN00I/8jMjIgiz8yO8gHXyQlLN0KVlbk60trVhByclERJdvFiqMONK6rUB6HV/6Y2NDzs4N2LmP6gs8g/WZTNPw/PnzwsLCltJnpwAtW7bcs2fP28UePnz4/Pnz2bNnl68xNTXtLZ3ImfkoAgIQEIAIxYgV6isKRAU/Fi9Rz1ZfPm75ZTgF/TD38pLudnbK8+fn9O/foLOG+vhwPTz4wcHytrbZgYHFXbsC4D5/rnLgADcxUWRoWDRokOALeBrwY7nHm9U2n+edH1Q4KDQvNCFe8dC0IUOejJGdvevQRRUfn6yVS3JevuT+/bd2YmJKYwf7UU3SnmQvtL+Yf1FVopqL3FzkStcrQMEHPqMx+qri1b0qe2cpzupV1Ovrgq+bC5qPGgUvL87BgypeXqpGRqKcHO6ZM6+bNRNWrLZ7d4OUlAw1NSEADQ3MnKkyfbrKs2dcD4/iBQuytbQkFQsLhQZr1uQNGFB4/TpNnmxw506qvb0AAGCalJQkEIgB5OdrSCSUmJgDQCw2EgjSExOFAAQC9dRU2cTErOhonra2+qtXqdI6+XyNvDxKTMy5eZNXUqJtbS36f1scOzvBsmUlc+dqAmjXrvTAgTSh0CAgIP/IERVPT/GWLRlcbvnplGoDSE19nZgoDbLsZXS0KD9fpg+mCMLH7tT5bcswW7n7rYXbuJ1srzQvtfMo9thTvEfumfXOnSreh1ScnUt5PHGXLuL16zMyMsoa09GEZ/eqd1OjnIYWCoUpKSlybz/Aska5MrmBGoHhiuE++T4XCy4qS5TLj6u2aNsWbedibiI38Rzv3DreutsGYyx/tHSf1FH3Xtfbm7sts1Vzcipt0TldbvKvGc4/TM6dPKhoEJe4AKKj5efP10xMTP0gXW1ox48fT05OLn8ZGRk5fPhwGxubRgzpI/tMEqyCggIAqv9/AoK6unp+VU+Nys/PLy0tzc7OLl+joKAgEtVn5mnm/UQrRC/QXiCBZFLmJPun9sZGxgCOFhw9rnI8wHBqi19aLBkxZ/0UlyNHeEuWZBgaNtiuERkapq5bx7tyRXvhQuWdO4tdXPhbtuSNGFHcvbvcixfao0fnfvtt7rhxDdXcf81dhbub+JuiFaO/zf028HWgikQFwMNXPKWBMduAYcPyDx26p6OjIC+vJBZziOhL+1BsTN0oXRCh6o63K2jXrqBdKjf1sOrh77S/UxerD8sf1k/S7+uvhcOHZ1+8qDTxfKTPUofv+2r261cgK1uWmhCRWCwuH8xBg3IGDcrJzpadOVNn7VrVBQsyKzYhLSwWixwcSkaMSFmwQO/AgWQAPJ6kqKiskqwsDo/3psLyyiUSiUTCEYlEWlqCtDRZgUAkIwMASUkylpZCkUikpydQU5OcOfOy0iPYhw/PKeu4CETE44m2b0/+5hsDf3/N9evTpR2pLgAO51+9k77csEH18GEVrvOdzI6nuO3PcMRcidkz0k6z/GvigeYTb95U/GmH+pUrvP798//8Myk4WJPPp9Wr04jov3zEiUQiTj2fXV8kW+RQ4rDw9UJliTKqOa4MRYbeJd7e2d7FnOIbvBsRvIh9LvPS2/u1L3TVvOl+4Zc+xYvOWs85v++7FWsN1k7ImTAkf4hYLPsJfTwzMzOzs7MLNApUslUAFBUV5eXlNXZQH1djnj5rOHFxcQByc3OlL9evX9+uXbsqS7JLhI3rAl04RsckJCktfTMPllQxFQdTsA7p+IsnzV6drqNDGza8udjRYAQCWrKEZGTIz+/NzaWpqWRgQA8eNHRjje88nXcndzMy20AbiqhIujI9nX74gfh80tEpm3whJiYmPT2diO7fJweHRoz3EyAm8Rk6M5SG8ok/mkaHUzgRGS7ZqFKko/f3GNOuTzZupLw8IiIHhzeXCGNiKDKShEIqLaXhw8uu6FVU8Sb3q1fvaWrSuXNERJ06UUgIEdGTJ6Su/q9LhOWVL15M0m8dCoVkaUmrVpFIRBcvEo9XdolQLKZ27WjGDMrPJ5GIYmNruss+I4OaN6fhw8suKVYXgJMT7dv3ZvPWLsJ55y+0vjxVM7eJSYmVyqYf9wgOjaWxaqXaWLigvWeWvT01b06//UaFhSQS0bBh1LUr5eRQcTEVF7+5fPlf8z6XCN9BEiX9QX+MpJEaAl2FZzbtoiYbjDtp7nveJr6PkaDJ7ISQNu0/7rRs760VtepEnS7QhS/wEuFncpN7kyZNlJSU7t27J30ZHR1tb1/FtM5Mo+uKrv3Rn4Mq/juoCMUABDzAA66MzJYf7L6JXb73aHGnTnj4sEEjkJODmRl690ZODpo3x/HjAKCnh2HDcOpUg7b0YWUicx3WFaCgyncJdAIn2qHdREwchVHxiJ+IiTzwcnOxYAFsbSEW49gxFBSgWze0aYOhQy26ddNo0wbDhn3kfnx6ZCDTDd0O4EA84h3hOB7jbWErUSw6/PL6D71sck+3C2491MQ9bsIElJS82aqgABMnQlMTRkYQiTB3bk1N8HgSf38sWgQAa9Zg0ya4uCAgALXezsDl4sgR7N8PDQ2sWoWhQ6GgAAAyMjh2DMnJsLKCtjZ8fJCTU20lWlo4dw7R0fDxgURSbQBz5mDGDPCNCiec/XM0Rj8JN1ipFXDvnK7zwlMRCuetHQTeBRNO79Wy6v2YE7Qw5YHG+vW4dw/jxkFJCS9f4sABXLwIPh88Hng8rH/fJ1J+JgxhOBqjd2N36N1Uq/n7Bjob2/+2Ni1kQJZCSsYN8+Um/nf32IfGvqxjbeUXuxvRTdychEn+8N/us/0kTjZ2OB9XY2d4DcbX17dbt25ZWVlXr15VU1O7fPlylcXYGaz/iLfPYFUUT/Fe5GVCJqPO/66jJ168uEFn016/niZOJCK6cIFsbMjXl4qKaOlSmjOn4dr44HIpdySN1CO95bQ8n97Mtioi0R7a05yat6bWh+lw+dyMhYUUHEy6uuTrSy9eEBEVFdHNm2U/Bw8+PXs2S7ocG9soHfqERVKkxtFv1UQaQ2jIn/TnclquKdZ2eODFtXvs6Eg7d1JxcT1qa8CZ3Pv2pd9+q0f5O3TnIT2sS8l0St9KW/tSXzVS607df6VfX9ErIhq/MKlt9DgtifaQ2AU9R2Tp6NDMmTRuHK1a9W49aHwf+QxWuaioN/ezx1HcUBqqQipG2fZyD5pzinnyjx3sbnhPefbLRXFYLuVWWUMu5eqR3rf07VN6+s5hhFJoKVXzvYy6OXuWzp6lM+fEndZPNCmwsc92XXz3RMV5QD5jn0+ClZeXN3ToUCUlJQMDAzYP1n9fzQmW1FW62pE62gkcXeadbtGi4b5GdPYslc8yVFREY8eSrS117Uo7dzZQAx9Pxa8ppVFaCIVYkqUbuf1D/5SXKS2l9evJ0JCGD6fHj6uup/wSIfNuHBzoamzuZtrsTM56pDeQBhqQAUco5/fXMU9P0tGh6dMpLq5OVb1nghUeTmlpJJHQ33+TsnL9ZrM8TIf1SG8kjawuzXpCT1bRKjdy4xN/KA3dS3srfumyqIjaBB/SD1mgZpbVsyf9/nvZdwOnT2cJVr1FRZGdHf11L3F42hS+UHt42pQz0ak7d5KzMwlIcDD+dr/jW7X2+8vdbCdXqmxU2HSoZFgwBZ+lsxlU9jQrsZgSs/MCi4K1JNr9S71u5MRlZVFWFuXk1NzyG0ISSickC6GQd0izhCR8Rs/Q9YLdqm3mu+ar/DnQvbvIYfluuVwthHW6R/fqW+En5/NJsOqIJVj/EXVJsKT+pD+tydoxtbvWV3f9/GjFzuSOI597eFCln92769y2SEStWlFgYNlpMbGYRo0iWVnatu0dO9PYYiimPbWXIRkrsgql0PL1YjEdPEiWluThQbdu1VgDS7Dez5tpGpQKsXABsjSQZIhMTbMSa3/y35J5JHBNlrExubrSwYO1nI59zwRryxbS0yM+n+zt3zyCpu4KqGANrTEkQy/ykqZZEpLcoBtzaa4DORiQwXga/w/9I53/U6qkhE6coFGjiM8nIyPq37/yc6pYgvUObj0s1Dk0gZujpb9tjuNXGeUzNYwa9a9iCQm0eq2o1TcxKhN22v7zg116Z1WJmhmZDaSB32cu4vQ5pW6TzDfJ4wUFczK05Y95qbaOs7SsXyR36a4XeZmS6RpaU0xVnIyVkOQVvQqn8J20cxEt+pa+7Updm1ATBVIwIzNc6jyGxgRR0IA/B1ygC52oUzNqhpG7RfRfve2u4XDoC3te/Pfff79mzZrGjoKBQCC4efNmhw4d6lJYCOEWbFkoWcy/1jNpd1fh8h/dC/t9nTBXv9hcWuCPP2Bjg3nz6tx8cjImTMCNG7C2RkICzM0REICZM9GqFTZvhpLSO/Xpo8rJwc2beKQWddrw9zC9g62y3M0Lmu+yWNisuGWE0hkN0jx1CvPmQVUVS5eic+daaouNjdXV1dXR0fkosX+eilC0BVt+wk+t0GoRFrVCKwLdw71zOHce5yMRaU3NTB57vNjmkXy4w+hhihMmwMzszea/4Td96PdF35zsnMTEREdHx8brCgpRGIKQZVjGB78QhXzwB2DAAAxwhrMMyu7cFYtx9Sp27cKhQ7Czg5cXhg3DqlVQUICv779qW7YMtraYPr0ROvL+oqKiHBwclD7634RsZG/FVh/4aEGrLuVfv8Y//+DQIVwOJ6ehT+2+uV1kc3t/3G3ljne44LZGa13oPsCDO3SX88juR1tPbWgrQ1kBCkpQUoQiDzzp7/IFRSgqSpRSnitI638oH/2rxtLbClc8C4c5CFsJtJMSkPAczxOQ8AIvNKFpDvMmaGIO8/IFE5jIQY7DAREiEOH9zBsWmIVZPvCR43C/hNSDJVhM46hXgiWVj/wVWLGqYDNnxxhbY7VX/Tb25PSYj/lN0XT+fCgo1CfBknr5Es+ewcQEFhYAUFCA777DnTs4eBD/7S9JpCN90bPdmwXbFdRKDU6PUY9zTuq1Ndfmus6uaWah42d9rzhvHhQUsGRJ7VNyS7EE6z1tx/a5mNsJnRZggT2qOHgEPOIFUwAAIABJREFUEFzF1fM4fw7n7kliNOPaZR50d8nzmNWjVTd3GRkZOH5/8Z73jwCwMBAn+4LKvggSFoZOneoUw27s5oI7FEPLc6B6yULWkmMxYRmxuab384wf5JhFq6ZYi3h5+QbxPi8WbjUvuy1fKMS5czh4ECdPwt4eQ4diyBDo6ZVVsmwZtm2rovI5cypnXZ+Kxkqw3tnr1zh+HEePIjwcEgk2bEDrAYnP+LfDEX4CJ7LEuYJzbv49rAQQFKGoBCXFKJb+Ll8oQUkRikpRKv3NKVLmCOVlipXFatkcMVeiXMApVvRVHtEaraWJVBM0UYTi25EIhUhIQLNxly33zs/kpsmv8EtePVUWsgCkWdfnr7FPoX1s7BLhf0TdLxFWMnXlK8db3yrl6aktWjXi3lJd0h1Fo/x/iVu8uIEi27GD9PRoz54Gqq4hCUl4nI73p/584vdMHe04OewO3al49n7tWlJTo+bN631tiF0ifE/7aX8MxdSxcC7lHqfjEwRTDLPtuDlaKv8MGXR6cyuv+LAwOktnWwlbNS1uepAOSkjSqRP9//kUtbtG11zJ1Y7s9tG+8i831BDDVbq6hbZ8T997kIcBGaiTum58B7twv2/vrJ1/6dz0K4dtXnc0yrW1W7x32+9ioZBOnyZfX9LWJldXWruWkpLqGtgnrbEuEb6/O3dIT48GDyblHuGat93VM82Hngv56RehoSHFxJTdqFezzEzS1KQCKsiirEf0KIiC9EjPq3SkusujSiWFQnryhP75h9ato8mTqWdPsrQkRUWytCQcHdB9x+61G0QjR+4qL/+FpB6fyUSjzJdDNc9oyN/b+827N35ywJ+FcYohY6K6PoyfbN8h6vu5WFHlBBD14+0tnbcAoaH/ncuFD/Dgd/y+G7stYekDn13YFfZMMPpr7wGInYM5u7E7+oZ8v7l4+BCGhrh7FzKfyQQsn4xhqMf8FmpQ64d+/eT6/cpHMpK3WJ/fnXruyZpFPWXlPdI8/FX8X2S/WGq8dDmWC1yDCH1Rt6O6LdpGICICEQuwYBEWzcKskRgpPWFQjOKHeBiDmFjExiDmAR68xmtb2DrAwR72PdDDHvYmMPFZBjc3NP02IhCBKUiZjVnDxSP7R8ruKsGsmbC0xNChCAqCsfE7jhLzMamqQtb9UsaeICNK9bw9T3friPQU2YgEZGdj+HCkpyM7G9ra0NWFgQF0dSsv6OiA+/8EYSd2rsRKV7hewiXtPJumcTh7Fk+eID4ecXGIj0diIvT10bQprKzQtCl69EDTpjA3h5wcOJyjpwkAgl4/acTRaBQswWI+SS3Q4ir/nz/5f84YPT9O/jGyNB88wNqSe5PcHLnvf1Db2eHqVXz3HZydy24waWgEyke+GtRqLpaL3AM48Dt+T0SiN7wv4VIzNJO+JSvJ07004kLToaEn5PsfRGws5s+HlRWCglh29SkxhGGgxahAi1GurjD3fHgO5y61P8lxvCsW5RZx82hZ/55iZW1o8MBTg5oKVHjgqUJVFao88FSgogY1HnjKUFaD2prlvOsXlJGrjuJ16HBl9LRlo7WmI8HcwC47RznJGtZ2sGuO5n7wc4CDOczfvpKY2eTWcs/vucj8Pn++1a1h/2vvzsOqKhc2Dv+24ACCgAKKIuKEAyIoammg5pCmOQcOGaaVQ5mUZWin0yGtU5RDpJlmWmJpSplDmeWc5owDCs6IEzgjIsrM9wd+amYnLWWx2c99cXXtNbD3syHw4V1rveu76BKvf0duLm3a8OWXvztjTIq+KyUuXxw15jle7Gvqa+VvhT/AkSN06MCePQA5OZw7x7lzJCVx9ixnz3LqFDt3cvYsycmcO8f58+S++oHjhYkuu9s1Xb4662CdXoc4coTsbN57j9q1qV2bVq2oXZuaNa/PuHZHK1cCJCTUKHhgOVSwxCwlkvge733Lt8+XeT6MDa8sOLSpyrdj6vYYdcK6aWLQ6FpPdq3a6B+9gL09X39NVBRt2jBpEn373qfg18US25a2gxk8kpHOON+2NZ/8taydxawf+KEtbd/kzY50LBiKKHDqFL98W+70l/3rfsBjjxESQo8elCnDr7/e35hSeKytGRxYb05gva9/eeL9TZMOtZxXfulLKW+MKmNVtqLvlSq1rlWsleZcPa18lWvlKl+xcrp8jWvppKeSeo5zV7l6iUvH2l3zfe5aSZdL17iWT35NvGKJPe60K/Dw6K/rvGX9h9/2+fkkJ5OYyLFjHD/OsWP8lnkyf9wLmVG9x5Qs4eVF9+5s2sS4cQQGql2ZH7u8cm49N3WO4dbb06TeMvOotTVubri50bDhnZ/h9Pmc6l+lLLiwrnROnbMNsXmI2rVxdsbHh9Wr7zZGu3ZERAAkJAQkJ99caQlUsMTMXC538ouab4679FPVRS81/P5ozNVywXDkSLNBg5q92e2DHxPj3suN7pnZ1yo5I+BCtzG1gtqWeeTvHzcsOFwYFMRPP93fw4W++O5k53jG16NeP/qNYUwlKgGnOPUVX81gRmlKhxAygQmuuN74rMREFi8mOpp9+2jYkIoV2b4dO7v7FUoMdqnkuTGmCZ8/9nmHCx1WlIt1e8qt1We8/jqVKjklJJCQQMJ3bEsgIYGkJCpXpkaN331cHctzz9GtGxe4MJnJn/BJT3omDv53787uZ+1JTub6kySQlERyMvv3U6rU9c91c6NaNRr+3C0wkFeO4+ho9NdC/rESJbh0iZo1b19fvfrdPkOpEta2497r8jJ43Vx58eK9xVix4vqD8PCo8PDwe/tkM6eCJWbGr//eJ6/W7r7rY1v3crx0c33B75HOnt6dPb2zssI/WRv3ydnojqWft3W+2jWv+9AKQY9wvWl9k/3dWyXefC3jzZ5ZfW4dFipTBhubP7xe/fps3syQIQQEsGABtWrdl3dx6RJnj1QNIbJDqdfmVBxfr3wD7/RmOaacA2V3BFv1+pIvAwi4sfOePSxcyMKFnD1L9+785z+0bs2mTQwfzubNv3vagpF/MUcngyc+3eS/z/PMxssbr5265ubsVrDe3h5/f/z9f7fzlSskJHDkyPX/rllz/fGmgxdevjT5dK9P6sT1DPx6Z/xO95gY1syhShU8PPD0pFo1mjWjWjWqVcPD4/bDOgcO4OmpdlVMVK9+z2Xoj/LySEj43Zr/cZMluY0KlpiZgW4dB9KRP/xZdqtSpXjlMe9X8D52LPy9b3bPy/72u27Pla2Q8VTpJ/uWfPLkxz2PLav44lvhw6q9VSYyrPTXg8ixzsjghRcYP/5OT2dvz9y5REUREMBHH9Gnz3GOb2NbD3r8vevhgXXrCBmdVPHR+IyacVe9Ll9pnbctY2+24/laS16a0OPfdtjl57N16/VelZNDz5588gktWtw8v8rJiYoVr4+93+q2f4nFXDjEBiYkOE+oM2GCwwSqOPNNO178hIvl77iznR0NG95+ZMfvkxmHnx0TeL5v88W78k5UqdIUzyDeeYehQ+nR464yfD+uwbrPRv8U3B844/vLpleCm079ImlNj8DAO+/vjvsiFjWhyR0X71IiifWp35KWy1l+T58oD1qJEpQvT/v2t6/39DQgjDlSwZLirFo1pg3znZrnu3r1uA8n75nu8u2XTz2bNyjNp1mvjwPH5pAzdtLYo5MiwghLnTTozKn/+eMQEoKPD8HBLFuW/VnYxDIT/8N//s2/gy61L+HghOkvjkKe5GQ88XHE7WNfHHG7O8XntCpd1dG7HvW8aQbNptpPzb7o7rS7zS4Xu+hoFi6kVCmeeIIvvuCRR+7w9D4+N8fepSg7w5mKVPzL3XZMb9oA69eZ/XjK49vObRvbZ6xfnzemMe3uX8jpULOP1+0e1KEKT91caWNzDxc9lC9P584ENiDG7YcfH+r/6pavG1frzAc0bXr3Ke7ZS7zkj/4sKIocHTlyxOgQ5kyXG0nxV6IE7drx83ifY8+8Pfa7uDI9forf6Njz3JA+ef288GpHuwlMePd5z986vrmb3ac4dZWrd36iRo3YsYPs7J3eUac91qZ0Hj9wbaRN0sOuAyfVdDpd0zM3LOz6jsc49jM/T2DCczzXnOaOODaj2Yd8mEiiP/7v8/70lUc6PnN6JSs70GEGM77Mi+q9+7+1B2zc+X6HIUNwcuLnnzlyhMhIAgL+srxJkfYczzWl6Sd8kkLKX+5cghLWWFfJqtKDHjvZWbDSGuvTnC54/DIvv8n1GXUrUSmCiGY0q03tZ3im3AnvChlVgL3sbUYzBxye4Ildw5+Lqj+6YP8znAkm2BVXTzwnMemPr25jQ7NmWAUtnB7w9OKS374X0DkoiKAganneIcALvHCa013p6olnFFG3LQJv8VY1qtlj34hG61h3x/e7iEUmTJ3pfNdfThGzoREssSAVKxIaSna297Zt3iX3/GfJwf2bXvoxo+mGpOoXskrk7q+3qE/O4svWFy9yEShP+ds+nHAqb1++/Lwe2yaerjF38ltZyxytZ8Y7no+Y+tqZieNcfvX83tl3Lfv2sa8c5epTvz71m9FsIAPrU98Jp4IM165x6hS/7szfU29B5fPjTFfsq3353v7IDisaXr/m+eefDf0ayf32Pd8vY9lsZo9hzOM8PpCB7Wl/68l/f3Sm5JlFLKrFX5/wt5Wtv/EbEEBA7iMLunfvh1Uu+3swbSgfvfxj4HqWdfI/OQLIJ78HPVrQ4jjHz3DmMR7zwuuPzeY7vlvL2sUsbslfzB8/lalLWHLjmGAIIbcuAvWot5WtzjjPYlYwwYkk2vC7kxzTSQ8j7Cd+WsCCv3ynImZHBUssjslE1aqMH8+iKydHZsxPz81o9sWnyZOfPH/OlFKClBRcXalS+6pTjZTytS7aul+0qXLR2vVivvPFcw4Xj5U5dpGLcb1On2l3or/zqYsVfK+Uzq5KVRvbCru773I6cu1zPmtIw5zzjklJnDhBUhIrTvHFSZKTOX6c5GTS06lShfyGsadGffrE9+MDr3ao7E2rA7i6sngxX3xh9FdH7jdrrLvStStdL3JxHvP+zb+f47lXefUVXvnjzk/zNE7gRDOaTWDCXz75CEaUpCTQjnaZI3dsH9lvKzFduJw8/pUS40tA6+48Vrs2QCyxccStZ70VVtWoNpzh0UT/sWCtYlVDGj7EQ//8jffl+uQmz/P8u7x7kIO+/O4Gi2MZ249+Najxz19LpAhSwRJLdKz2yma8kWGXEWH37yd50jTUNCGd5GTGjycrizNnOHnS9vRp25Mnq5zex6mVJCdz6hTJyVy9SuXKWF274nD5atenHdx/m3+59vqF7xw7Uemg5+SxVz8aNqi886lTlC1L5cpUrUrlylSpwsMP4+aGhwdubjg7Ayxe7PtFxJpvFxn9hZBC5IRTQxr64XeAA0e487ktc5jTKaXTsvPLxtQek0xyweQd/8ONOwHbYHOBC0ASSZWpfOPyi6pULXhwjGOZZN64T2IWWX74TWPaMIYBrWi1lrVABBGzmd2LXt/zfUF1+9uiiJrM5NOctsIqiaTznL91azzxi1i0m93/5CVEijIVLLE4e2t//6vvexOv/Ovx7K4mTAUXHV+7dn1rqVJUrUrVqnf+3GvXSEpi5utJm9ZlmlonTBsRfdppR5OJgf13Tjqa6nnS8Vzkcmd3d8rc4c6nt7t0iZiY363R+aTF1WEOz2HOHOaUpewABhzi0P847d2Eyeeqz0hGjmDEetYDZSmbSWbB1gtcsON/TX3mhlsSSXnkFXSsE5yoS12gKlUdcdzHvtumhRvK0FsX7bFfzvK2tO1Dn/nML5ie9M8C3HYV7a2LhzgUSuiv/OqDD1CDGvn87u6+v/LrSU564gmkk55FlieeiST+j7cmYl50krtYnCYnemQ32vqSR7daNU01a1LwMXHinSbB+gMbG2rWpHznnENzn170ZHBYva4plRLXjp46uu7qh3d+WtE2rVatu2pXjo5cucKQIb/7mDv3DrMCirkbzOCHeOg85+czfw97XuO1u7mocDCD44lfxSrAD7+f+Rk4wpGlLP3fn+iPvz32k5iUS+5a1v7CLwXrffGtTvUwwq5wJZfceOK3svWOz+CI4y/8cohDT/N0Lrn/I4Arroc5fMfFy1y2xbY2tYGlLD3K0dteZQADjnBkF7t2sSuU0Ed4ZAtb/vLLImJGVLDE4rz4Ihcv3uFj3Li7fYbccqWrb3nyoHfJ5+fZlTyQwPbt7NlDjRokJdG2Lfv3/+UztGrF9u13+Jjw12fdiJl5nueTSPqET5pyD7MdlKXsC7wwlrHAR3z0KZ82o1kYYX95wZ011t/x3Td844TTeMYHE1ya0kAJSixiURJJtajljPMgBl3iT6eMrECFlazcze5BDMoj788CvMEboxjlhNMMZty26I9/X/o2otHjPL6RjQ1ocNtL2GBTiUoFH3bYlaLU3fROETNiys/P/+u9ipGXX375o48+MjqFkJWVtX379hYtWhgd5O/44gtCQ3Gxu0ZqKtnZWFtjZ5eG/ROd8mY1msy4cTz3HOHhdzWWVTTExcW5urq6uLgYHURISUk5fvy4r6/vX+96F7rStQtdnuf5+/JsFmjr1q0NGjSwvX+3ybJY4eHhulWOiPyFJ5+kVSvAht9fdm5vXwKXUIKCGD2aBg34+GM6dTIoo1iuDWzwwssFl+UsX83qqUw1OpGIJVLBErln9vbY2//55sqViYpizRpeeIFPP2XKFKpVK7xwYvH2s/9JnswkswpV5jLXHXejE4lYIp2DJfJgPPoosbEEBNC4MeHhZGUZHUgsxXM8d5rTKaTsZW9XuhodR8RCqWCJPDAlSxIWxrZtbNuGjw8rVxodSERECokKlsgDVqMGP/7I+PE89xzBwZw5Y3QgERF54FSwRApFly7Ex1O/Pg0bEhlJbi7AxYt8+CEDBzJ6NFs0CZCISPGhgiVSWGxtCQ9n/Xp++IGmTZk+HW9vDh+mVSscHOjdm1GjjI4oIiL3h64iFClcXl6sWMH8+Tz1FK1b89//UqECwPDhNGvGY4/Rvr3REUVE5J/SCJaIEapXp359vLzw8SEqitxc7O0ZNoyFC41OJiIi94EKlogRLl6kShWmTmXxYmbMoEoVXnyRCxe4cMHoZCIich+oYIkYoXZtYmPJzqZpU9avZ+tWvLyYNYsffyQkhKVLyckxOqKIiPx9KlgiRqhZk0aNePllMjIAPDyoW5fMTFaswN+fiAjc3NS0RETMlwqWiEHmzCElhRo16NyZRo0YMYLoaFq0IDSUDRuIibm9aWVn3/l5kpNZtYodOzRZvIhI0aGrCEUM4uTE3LkcP05cHBUr4uNDyZI3t3p4EBpKaCjHj/P990REMGgQjz9OUBAdO17f8+pVXnmFhQvx9eXCBS5f5tNPeewxo96QiIjcoIIlYigPDzw8/mKHP2ta8+cDJCRcv/X0r78SHMzKlTRoUBjJRUTkz+kQoYiZKGhaN44evvMOc+eSl8fatdePHrZsycsvM22a0UFFREQFS8TsFDStjz/G15dGjRg3jqpVGTGCLVvw9+fgQaPziYiICpaImXJy4tIlRo1i61Y2bcLVlQEDCAkhOZmEBKPDiYhYOhUsEfPk5YWdHQsWAFSvzptvsmsXzs7UqEGLFjRpQmQk584ZnVJExELpJHcRszV7Nl278ssvtGrF+fNMn05AADNmkJfHmjVERTF2LC1aEBTEk09ia2t0XBERC6IRLBGz1bgx8fHUq8fKlRw/ztSpfP45JhNWVrRrR1QUJ08SEkJ0NB4ehISwciX5+Xd4nqQkuw0bSm7bRnp6ob8HEZHiSSNYIuasXDleffVPt9rYEBREUBBJSURHExbGuXP06MGgQfj6AmRmMnIk335bwcurdGYmp04xcSK9exdafBGR4koFS8QCVK58fTKtuDiio+neHVtbQkI4cIDUVA4ePHbypKurq0tSEk88QeXKBAYanVhExLzpEKGIJfH2JjycI0eYPp2DB/nySy5cYPHiElevAvj68p//MHWq0SlFRMyeCpaI5SlRgoAARo+mZk0GD+abb7zatSsbHs7FizRqxKFDRucTETF7KlgilsrJiQsX6N2bZcuOLFpkSk+nTh0mT8bR0ehkIiJmTwVLxFI5O+Pry6efAtmurlc+/JBNm1i+nK1biYwkJ8fofCIiZkwFS8SCzZjBRx8RFOT03Xe2U6fSrRtt2rByJUuX0qAB0dF3ntZBRET+igqWiAWrVYu9e2nXzmbPHtPZs3z0EXPn0qwZK1cyZQrvv89DD7F6tdEpRUTMj6ZpELFsZcowZEhSQICrq6uti8vN9e3asX07337LkCF4ehIRQePGxqUUETEzGsESkT9hMhEURHw8QUF06UJwMEeOGJ1JRMQ8qGCJyP9UsiSDB3PwIP7+PPwwQ4Zw+rTRmUREijoVLBG5C2XLEhbG/v04OdGgAaNHc/nyza2bNzNlCjNmcOCAcRFFRIoQFSwRuWsVKvD+++zYQUoKtWsTEcGFC3TrxjPPcOAA27bRpg2jRunaQxERFSwRuUceHkyfzurVxMTg6cn58+zaxeTJfPYZ8fFs2MDMmUZHFBExmAqWiPwt3t7MnUt+Pnl5NGlCdDSAgwNjxzJ7ttHhREQMpoIlIn/XpUvY2LBxI2+/zb//TXAwly5RuzYnTxqdTETEYCpYIvJ3OTqSlcXFi/Tqxe7duLnh58fixbi7G51MRMRgKlgi8ndZW9OnD6NGkZND6dJERvL++4wahZMTeXlGhxMRMZIKloj8AxMmcOECPj68/DJDh/LqqwwcSGoqjz1GcrLR4UREDKOCJSL/gJ0dixczaxbVq9OoEatWXb/AMCAAf3+WLzc6n4iIMXQvQhH5x5o3p3nzm4tWVoSH07o1Tz9Nz56MH0/JksaFExExgEawROTBaN2anTs5coSAABISjE4jIlKoVLBE5IFxdmbpUvr14+GHmT/f6DQiIoVHBUtEHiSTidBQli3jzTcJCeHqVaMDiYgUBhUsEXnwmjQhJobcXJo2Ze9eo9OIiDxwKlgiUijKlePrrwkL49FHiYw0Oo2IyIOlgiUihSgkhPXrmTWLoCAuXTI6jYjIg6KCJSKFq25dtmyhcmUaNWLz5usrr11j50527yYz09BwIiL3h+bBEpFCV6YMkZG0bk23bgwbhrMzY8fi7k5uLmfPEhFBSIjREUVE/hEVLBExSI8e+PvTpg3nzrFyJU2bAuzdS8+elC1Lr15G5xMR+ft0iFBEjOPhgZUVwcE8+SS//grQoAEff8yECUYnExH5R1SwRMQ4ubkcPcr06UyfTp8+vP02ubk89BD79xudTETkH1HBEhHjWFlRpgyXLtGxIzExbNxIq1bs3o2Dg9HJRET+ERUsETFU167Xp8Vyc2P5coKC6NSJ2rWNjiUi8o/oJHcRMdQHH9CmDfv20asXOTmsWIGnJ0lJBAczfTpOTkbnExH5OzSCJSKGqlyZ3btp2ZJFi/jpJ7p2JTaW7dtxc6NxYzZsMDqfiMjfoREsETFa6dIMH87w4TfXWFsTGUmnTvTty1NPMW4cJUsal09E5J5pBEtEiqoOHYiJYc8eAgM5csToNCIi90AFS0SKMFdXfviBvn1p3pyvvjI6jYjI3VLBEpGizWQiNJQ1a/jwQ4KDdYtoETELKlgiYg68vdmyBTc3GjXSme8iUvSpYImImSi4RfS0afTty+jRZGcbHUhE5E+pYImIWdGZ7yJiDlSwRMTc3PHM9z17mD6dqVOJiTE0nIgIaB4sETFLBWe+t2tH374sXoy9PStX0qkTVlZMmEDz5sycSenSRqcUEculESwRMVve3mzdSnIy33zDrFlMm8YnnxAfT0YG4eFGhxMRi6aCJSLmrEwZUlL44AMGDiQ8nNxcSpfmgw+YPdvoZCJi0VSwRMTMnTrF00+zZQsbN9KgAZGRODpy7hy5uUYnExHLpYIlImauShUOH6ZyZX75ha++Ij6eGjWwtmbNGqOTiYjlMr+CFRkZ2ahRo5IlSw4dOvTW9WlpaX369Clbtqy7u/u0adOMiicihW3AAMaM4epVAH9/Pv6Yli1p3ZrQULy9iYzkyhWjI4qIxTG/guXu7j527NjevXvftn7kyJFnz55NTEycN2/eqFGj1q9fb0g8ESlsr75KjRrUq8cLLzBiBPXrY2fHokXs3UtkJL/9RrVqDBnCrl1GBxURC2J+0zT06tUL+Pnnn3Nycm6szM7Onjdv3rJly1xcXFxcXHr37j179uzAwEDjYopIYbGyYto09uxhwwZycpg/nyZNrm9q14527UhOJiqK7t1xdmbwYPr3x9bW0MQiUvyZ3wjWHSUmJqanp/v5+RUs+vn5xcXFGRtJRAqVjw/DhvHSSzfb1Q1uboSFkZDA+++zciUeHgwZwh9/Rezbx/TpfPwxGzcWTmQRKcbMbwTrjq5cuQLY29sXLDo4OKSlpf1xtzVr1mzevLljx4431lSvXn348OGFE1JulZeXl5OTox5cRFy+fDkzM/Ps2bNGB3nA3Nz4z39KDh3q9N13Ti1bZlWrdqF//7S2bfOtrCqNH+/w009prVvnlSxpFxmZ5eFxMiIir2zZws+YlZV19epV/WgUEZmZmYcPH7aysjI6iPmJjIw8fvz4jcUjR460bt26devWxiUqbGZQsKZNmzZs2DCgVatWa9euveM+dnZ2QFpaWrly5YDU1NQbZetWtWrVql279q3fYGdnZ1dX1weQWv5CTk5OamqqvvhFRGZmpoODQ8GPT/Hn6oqPT8obb5RevrxiVFSVDz7IqV+/xIULlzZuzC9XDrick2P/2mvVP/kkbfz4wk+Xnp6em5urH40i4vLly+XLly+tuwLcu86dO58/f/7G4pIlS2rWrGlgnsJnBgVr6NCht10w+Eeenp62traxsbEBAQHA7t27vb29/7hb1apVK1So8Oyzzz6QoHIvsrKyjh496uLiYnQQATh79myR88DXAAAgAElEQVS5cuUs7tvx7LM8+ywHDpRq1460NOehQxk8mJ49sbLi44+pUaPMzJlYF/YvSWtr69TUVIv7XhRVR48eLV++vK1O2rt33bp1u3XxxIkTVatWNSqMIczvHKycnJyMjIzc3Nzc3NyMjIyCU91LlizZt2/fsWPHpqSkbN68ecGCBQMGDDA6qYiYgzp1sLZm40b69OGDD6hendGjSUqiVCkuXTI6nIiYK/MrWOHh4TY2NtOmTfv8889tbGzefPPNgvWTJk1ycnJyd3fv2bNnRESELiEUkbtVpQpJSTz7LNu2sXw5ZcrQpQsXLzJ5MgkJRocTEbNkBocIb/POO++88847f1xvb28/f/78ws8jImbvmWd4802aNsXBgfr1+de/OHqUy5e5dIkWLahVi6AgnnoKZ2ejg4qI2TC/ESwRkfvs2Wdp2ZL69Rk8mJdewseH1FS++orISI4dIyyMmBi8vOjShaio61PGi4j8T+Y3giUicp+ZTHzwAc89x7p1ZGby1FM8/PD1TaVL06ULXbqQmsrixURHM3IknToRFESnTtx29f769SxfTno6fn7060epUoX/VkSkiNAIlogIAF5ePP88w4ffbFe3cnAgJISlS9m9G39/IiKoVo3QUDZsAMjNZeBAnn0WW1uqV2fhQho25OjRQn4HIlJ0aARLROReVKlCaCihocTHs2ABzzxD6dLUrMnp0+zZQ8GESaGhTJzI4MGsWGF0XBExhkawRET+lvr1CQ/n0CGmTWPnTvbvp0MHZsy4PrnDiBFs387Fi0anFBFjqGCJiPwDJhOBgbi6smIFr7zCihXUrk14OOnpuLhw4YLR+UTEGCpYIiL/WM2axMfTrRsLFhATQ3Iynp4cP86d7tklIpZABUtE5B8bNozwcPbtA/DwYMIEHnmEmjXx8yMiQjM7iFggFSwRkX/s0Ud55x3atKFtW7p3p3Zt3NyIiWHNGuLiqFmTiAgyMoxOKSKFRwVLROR+ePppDh7kX//imWfYvJkZMyhThnr1iIpi5crrU5VGRpKZaXRQESkMKlgiIveJvT1t2tC9O9Wq/W69tzcLFvDDD/z2G3Xq8Nln5OQYFFFECokKlohIoWjYkAULmDeP6Gi8vPjsM3Jzjc4kIg+KCpaISCFq3pwVK4iK4ptvaNiQqCjy8m5uzc62io2127qV06eNiygi94EKlohIoQsIYPVqIiOZMgVfX6Kjyc/nl1+oW7fs8OEVP/8cHx+GDtXlhyLmSwVLRMQg7dqxdSuTJvH++/j6EhzMrFmXf/31yGefkZBAWhovvGB0RBH5m1SwREQM1a4d27fj4YGtLWPGWK9bB2Bvz2efsWSJ5oIXMVO62bOIiNFMJrKy+PJLzp4t+9prNdzcmD+fypWpXZvDh6lQweh8InLPNIIlIlIEODpy7hz9+6du2pTu44O/P0uWcPYs5csbnUxE/g4VLBGRIqBnTz7+mMxMrK3PDBnC4sUMGcKlS1SubHQyEfk7dIhQRKQI6N2bFSvw8yv99NNO+fkcPYrJRIsWNG3K3Ln4+RmdT0TujUawRESKAJOJmTOZMsXq5En7zZupW5d9+/jxR95+m8cfJyLid9NliUiRpxEsEZEio23bq40bHz9+3MnX9/qaoCCaNeOpp1i1itmzcXMzNJ+I3C2NYImIFG3VqrF2LS1a4O/Pjz8anUZE7ooKlohIkWdtTXg4333HiBGEhpKZaXQgEfkLKlgiImaieXN27ODcOfz92bPH6DQi8r+oYImImA8HB+bO5fXXadOGyEij04jIn1LBEhExNyEhbNhAVBQ9euheOiJFkwqWiIgZqlOHzZvx9aVhQ5YvNzqNiNxO0zSIiJinkiUJDycwkGeeoWdPPvyQUqW4cIE1azh3jnr1aNUKk8nolCIWSiNYIiLmrG1bdu7k6FEeeYSJE/H2Zu5c9uzh1Vd55BGOHzc6n4iFUsESETFzzs4sWUL37owaxcCBLFzI1Kls30737gQHGx1OxEKpYImIFAsXL/Lii/z0E08+SUoKJhOjRnHuHHFxRicTsUQqWCIixcKJEwQGsmkTlSrh78/WrZhMeHlx4oTRyUQskU5yFxEpFtzcOHoUGxumTGHJErp0Ydgwjh6lcmWjk4lYIo1giYgUC089xeTJ189q79qV7dv5+muSk1WwRAyhESwRkWKhWTPGjKFpU7p1w82NjRuxtubpp/H35+uvCQgwOp+IZdEIlohIcfHCC2zfTpMmlCjB0KHExjJlCjNn0qcP4eHk5RmdT8SCaARLRKQYqVqVwYN/t6ZdOzZvpl8/Nmzgq6+oVMmgZCKWRSNYIiLFnbs7a9YQEEDjxqxYYXQaEYuggiUiYgGsrAgP56uvGDSI8HByc40OJFLMqWCJiFiMNm2IiWHTJtq3JznZ6DQixZkKloiIJXF1ZflyOnSgcWN+/tnoNCLFlgqWiIiFMZkIC2PePJ59ltBQsrONDiRSDKlgiYhYpNat2bmTgwdp355Tp4xOI1LcqGCJiFgqFxeWLaNHD5o2Zdkyo9OIFCsqWCIiFsxkIjSUb75hyBBCQ0lJYcwYatSgdGl8fJg1S9OTivw9KlgiIhavZUt27uTwYapW5cABfvmFtDRmzGDGDF57zehwImZJBUtERMDZmX79qFKFzZvZv59SpXj4YZYv56uvrt9AWkTuhQqWiIgAsHkzL77Id98xfDihoZw5g4MDgYFs2WJ0MhHzo4IlIiIAmEzk5dG8OTt2kJND/fo8+yypqZTQvxQi90w/NiIiAkBgIAsXkp9P+fJ88gkJCdSsyZo1RESwdCn5+UbnEzEnKlgiIgJAz56YTAQHExvLpUts3050NKNGMWoU48ZRty6RkVy7ZnRKEfOggiUiIgBYWfHzzzRqRL9+VK/Ov/7F6NG8/z5BQWzdysyZrFxJ9eqEh3P+vNFZRYo6FSwREfl/Zcrwxhvs3UtKCps307v3zU0BASxdyvr1pKTg5UVICPHxxgUVKepUsERE5K7Vrk1kJAcO4O3NY4/Rvj1Ll95ht+xsTp4kN7fQ84kUFSpYIiJyj1xcCAvjyBGefpoxY2jUiKio6zeNPneOQYNwdKR5cxwdGTmStDSj44oYQAVLRET+ltKlCQlhzx4+/JDoaKpV4623aNsWR0fOnuXECY4d48IFnnzS6KAiBlDBEhGRf8Bkol07li7lp5/YtIn9+0lP5+RJgPLl+eILTpxg0yajU4oUNhUsERG5H3x9eeghXnmF8uUJCKBXLxYvJieH1q3ZtcvocCKFTQVLRETuExsbTCbee4/ERDp2ZOJEKldm5UqOHycvz+hwIoVKBUtERO6T9u2JjiY9nbJlef551q1j1SqSk1m5Eg8PQkPZsMHoiCKFRAVLRETuk2bNePxxWrRgwQJ27mT2bHr1YswYtm3jl19wcmLgQOrXJzycQ4eMziryYFkbHUBERIqRKVNYvJgvvyQxkdq1+fxzWrcGrveq8HBiYoiKIjCQChUICWHAACpVuv1J8vPZvZtjx/DwwNdXd5sWc6SCJSIi91W3bnTr9qdb/f3x92fiRDZtYs4c6tXD25uQEPr2xd4e4MABnnmGS5eoU4dDhyhbli++wNu70OKL3Bf6s0BERAqdlRUBAUyfTnIyYWGsXIm7O126MHcujz/OgAHEx7NoEXFxDBtGp06kpxudWOTeqGCJiIhxypShSxcWLCAxkaAgIiI4eZKNG/nhh+t32hk4EF9fliwxOqjIvVHBEhGRIsDJiZAQ+vdn0CC8vfnXv6hZkylTyMjAz4/Dh43OJ3JvVLBERKTIqFCBK1cICyM2luhofvmFWrVYsQIHB6OTidwbFSwRESkyOnXi55+Jjwdo2pQlS5g2jZ07GTeOiAiuXjU6n8jdUsESEZEio1Ilpkzh0Ud55RU+/5xXX+XZZ/nsM1avJiaG6tVVs8RcqGCJiEhR0rs3MTFUrMiWLTg7s3UrISH4+LBgAatWERdHjRqqWVL0aR4sEREpYtzdGT36DusbNCAqir17+eADatRg6FBGjqRcuULPJ/LXNIIlIiJmpaBmrVpFQgJeXoSHc/my0ZlEbqeCJSIiZsjbm6goVq++WbNSU29uzc8nJoZvvmHDBrKyjEsplksFS0REzFb9+jdrVp0612vWkSMEBvL00yxezGuv4ePDpk1GBxWLo3OwRETEzBXUrH37eO89vLzIz+eVVxg9GpMJ4Mcf6dGDPXtwcTE6qFgQjWCJiEixUK8eUVFMnIjJxEcf8fbbXLoE0LkznTvzzTdG5xPLooIlIiLFSEYGXbrw66/Xz82aOxfAx4eEBKOTiWXRIUIRESlGXFw4dYo6dYiKYscO+vfnhx+oUIHKlY1OJpZFI1giIlKMtGnDrl1s2ADQuDE7duDgwKef4u5udDKxLBrBEhGRYsTOjjlzCAqiUyf8/EhIYOFCXnqJN95g+3Y++IDSpY2OKBZBI1giIlK8tGtHXBx+fhw6hJsbmzczaRI7dnD8OE2aEBtrdD6xCBrBEhGRYqd8eV566XdrXFz4/nuiomjbltdeY9QoSmiIQR4g/e8lIiIWIySErVtZupSOHUlKMjqNFGcqWCIiYkmqV2ftWtq2pUkTFi0yOo0UWypYIiJiYaytCQtj0SJef52QEK5cMTqQFEMqWCIiYpGaNSMmBhsbGja8Pq2DyP2jgiUiIpbK3p7p0xk/niefZPRosrONDiTFhwqWiIhYtp492b2bvXsJCODQIaPTSDFhZgUrKytr+PDhNWvWtLW19fX1XbJkyY1NaWlpffr0KVu2rLu7+7Rp0wwMKSIiZqZiRZYu5dlnadGCyEiAmBieesp7wIDSPXsyezb5+UZHFDNjZvNgZWZmmkym+fPne3h4fP/998HBwXv37q1VqxYwcuTIs2fPJiYm7t+/v1OnTt7e3oGBgUbnFRERM2EyMXgwAQH0709UFMnJvPVWYocOtWxsrD7+mEWLWLgQk8nolGI2zGwEy97efvLkyU2aNHF1dR0yZIiHh8eOHTuA7OzsefPmhYeHu7i4BAYG9u7de/bs2UaHFRERc1O/PitWsG8fOTlUrZpet25u586sWUNSkuZ0kHtiZgXrVqdPn05MTPTx8QESExPT09P9/PwKNvn5+cXFxRmaTkREzNP27bRowTff8MIL1SZOJDMTa2v692fFCqOTiTkxs0OEN2RmZvbt23fw4MH16tUDrly5Atjb2xdsdXBwSEtL++NnLViwYP78+d9+++2NNV5eXu+9916hRJbfyc/Pz87O3rJli9FBBCArKys1NTUhIcHoIEJeXl5OTo5+NAzkFBvrkpV1sGxZ65kzPd59N79Fi13vvlvu7Fn7EycS9H25a6NHjz50yxUDaWlp3t7eQUFBBkYqZGZQsKZNmzZs2DCgVatWa9euBbKzs4ODg11cXCILTkUEOzs7IC0trVy5ckBqauqNsnWrLl26rF27dvjw4TfW2NnZubi4PPg3IbfLzs7es2dPw4YNjQ4iAIcOHapQoUL58uWNDiKkpqYmJSUV/OkohjA5OJT+8MOGtWpha7v7vfd8Nm3yHTw4v27d3B499Cvr7s2ePfvKLTO4Tp069YknnjAwT+Ezg4I1dOjQoUOH3ljMycnp06dPfn7+119/bWVlVbDS09PT1tY2NjY2ICAA2L17t7e39x+fysbGplSpUvXr1y+c5PI/WFlZmUwmGxsbo4MIgJWVValSpfTtKAoyMjKsrKz0vTBS3bp06WIzYADTp5coUcL0zDOmw4dNM2aU8PEpaWVFqVJG5zMPHh4ety46Oztb2v/VZnYOVm5ubv/+/VNSUubMmZObm5uRkZGbmwuULFmyb9++Y8eOTUlJ2bx584IFCwYMGGB0WBERMU+ffspDD+Ht7deli627O2fOsHs3588TEMDRo0aHE/NgZgXrxIkT8+fPX7NmjaOjo42NjY2NzeTJkws2TZo0ycnJyd3dvWfPnhEREZqjQURE/qZSpfj3v0lJiZ858+qpU3z7LfXqsWABTz3FI4/w009G5xMzYAaHCG/l6emZ/yezvdnb28+fP7+Q84iISLFlMmW5ut48JmgyERpK8+b06UOXLowfT8mShuaTIs3MRrBERESM1KwZW7dy8CDt25OUZHQaKbpUsERERO6FszPLlvH44/j7a3Is+TMqWCIiIvfIZCIsjHnzGDSI8HDy8owOJEWOCpaIiMjf0ro1MTH89hvt23PmjNFppGhRwRIREfm7XF1ZvpzAQJo147ffjE4jRYgKloiIyD9gZUV4OFOn0rMn4eH8yaXuYmlUsERERP6xzp3Zvp0VK+jenZSUm+uvXNEZWpZJBUtEROR+qFqVdeuoV49Gjdi0iWnTqFYNNzfKlaNPH06cMDqfFCozm2hURESk6LK25v33ad6c9u1xcWHpUho2JD2dyEgCAti5E91S3WJoBEtEROS+atUKKyvKl+ftt0lNpWxZ3niDjh359FOjk0nhUcESERG5r/bsoWFDfvsNZ2cefpjlywE6dCAmxuhkUnhUsERERO6rUqXIyKBMGaZP5913ef11Gjdm7Vrdu9CiqGCJiIjcV35+HDtGXBxAz57ExhIRwVdfsXo1kZFkZBidTwqDCpaIiMh9Vbo0EyfSoQOzZnHgAOvXM3UqdeuyYAErV1K9OuHhXL5sdEp5sFSwRERE7rf+/fn+e5Yto1s3xozhkUdYu5ZHH2XpUpYvJyEBLy/Cw7l40eig8qBomgYREZEHoGlTvv32Dut9fYmKIiGByEjq1KFfP0aNwt290PPJg6URLBERkUJXowaRkezZg40NDRsSEsKBA0ZnkvtJBUtERMQglSrx/vscPEiNGgQE0KUL27ff3HrtGp99xosv8sYbbNhgXEr5O1SwREREDOXsTHg4R4/Srh3du9O+PRs3sn8/3t788gv162Nnx8CBDB6s2xqaERUsERGRIsDOjtBQEhJ4+mkGDqRZMzp1Ijr6+gjWnj3ExjJ3rtEp5W6pYImIiBQZpUoREsIvv2AysW4dTZrw7bfk5lKmDK++euez5qVIUsESEREpYlJT8fQkNpb//IePPsLdndBQLl7kwgWjk8ndUsESEREpYqpV49gx0tPp2pUNG9i8mRo1eOcddu4kNJQdO4zOJ39NBUtERKSIcXCgZ0+GDiU9HaBaNVq2JC+PGTNwciIoCG9vwsM5fNjooPKnVLBERESKnilTKF2aWrXo2pWWLXniCSIj6duX8HCOHCEqipQUAgJo0oTISE6fNjqu3E4zuYuIiBQ9trbMnMmxY8TG4uCAvz9ly97c6u+Pvz8TJ7JpE3PmUK8e3t6EhNCnD+XK3dxt3z7GjmX7duztaduWf/0LR8fCfyuWSSNYIiIiRVW1anTpQsuWv2tXN1hZERDA9OkkJxMWxoYNeHrSpQtRUaSns2oVrVvTogXLljFzJpmZNG7M2bOF/h4slEawREREzFyZMnTpQpcuXLrEkiVERzNyJLm5vPwyQ4dSsiRAo0ZYWxMRwYQJRse1CBrBEhERKS4cHQkJYelS1q0jK4tly6halREjiIsD6NuXtWsNTmgxVLBERESKnfLlsbdnyxY2bMDZmXbt6NWLhARycoxOZilUsERERIqdSpUoVYodO6hVi7feIjGRDh0YMoQzZ1i92uhwFkEFS0REpNgxmfjvfwkOZtUqcnPJyyM3l9KlefVVhg0jIIClS42OWMypYImIiBRH/fsTGcmrr+LggIsLP/zAunWMGsW+fYSGEhZG48ZER5Ofb3TQ4kkFS0REpJjq3Jldu7hwgdRUfvyRunUBSpQgKIi9e3n7bT78EF9foqLIzTU6a3GjgiUiIlKslS6NldXtK0uUoEsXtm5l4kSmTaNOHT77TKfA30cqWCIiIhasXTs2buTLL1m6lNq1iYwkI+N3O2Rmsns3+/erft0TFSwRERGLV3Da+9dfs3Il1asTEcHVqwAff4y7OwMG0KMHNWrw7bdGBzUbmsldREREAGjRgqVLiY1l/Hhq1qRxY06dYtMmatUC2L6doCDs7OjY0eigZkAjWCIiInKLhg2JimLlStatIzGRzz/n4kWAJk0YP57x443OZx5UsEREROQPPD3Jz2f7ds6dw8uLDz8kL4/mzdm3z+hk5kEFS0RERP6gTBny83FzY+ZMtm3jp59o3ZrYWMqVMzqZeVDBEhERkT+wsqJDBz75BKB6dVaton9/evSgcmXNTXo3dJK7iIiI3MmkSbRtS1wcXbuSlcXixdSsycWLdOrEzJlUrmx0viJNI1giIiJyJ56e7NmDjw/z5rFkCd26sWsX27bRujVNm/L990bnK9I0giUiIiJ/wtaW1167fWVYGI8+SkgI8+YxfTpOTkYkK+o0giUiIiL3qFkzdu7EzY1GjVizxug0RZEKloiIiNw7GxsiI5kxgwEDGDLk+szv8v9UsEREROTvat+e2FiuXqVpU2JijE5ThKhgiYiIyD/g6MicOYSH07kzo0eTnW10oCLBsgrWrFmz4uLijE4hAFeuXBk5cqTRKeS6SZMmbdmyxegUAhAfH//uu+8anUKuGzNmzOnTp41OYSaCgti1i717CQzk4EGj0xjPsgrW8ePH09LSjE4hANeuXTuon8Ai48SJE2fPnjU6hQCcP3/+2LFjRqeQ6xISEi5fvmx0CvNRqRJLlzJoEI88QmSkhc9HalkFS0RERB4gk4nBg9myhehoOnbk1Cni4+ne/fUPP8TFhe7diY83OmIhUcESERGR+6pGDdaupU0bfHxo3pwOHaa8+CL79tGhA48+yvbtRucrDCpYIiIicr9ZWxMWhpcXZcuyZk2+yYSzM8OG8cEHvPmm0eEKg8XN5H758uWIiAijUwgZGRn5+fn6XhQRaWlpW7duPXfunNFBhOTk5IyMDP1oFBG5ubnR0dE///yz0UHM1Ss7d05//fUWq1cPXLqUgv+ru3dn+HCjcxUGU74lnYO2e/duwNfX1+ggQm5u7vz58/v162d0EAFYtWpVvXr1KuvWrUXAxYsXN23a1LlzZ6ODCEB0dPQTTzxhY2NjdBCzZW/PyZM4ONxck5pK1apYwKUDllWwREREpPB07EifPjzzzM01X3zBggX89JNhkQqLxR0iFBERkULy3//y+OOkpxMcTH4+CxYwbpwltCt0kruIiIg8KI0b8+uvrF5NgwY0aMCaNaxbR+PGRscqDDpEKCIiInKfaQRLRERE5D5TwRIRERG5zyyoYKWlpfXp06ds2bLu7u7Tpk0zOo7lysrKGj58eM2aNW1tbX19fZcsWWJ0IiExMdHW1rZjx45GBxGioqLq1KlTunTpOnXqbNu2zeg4lis+Pr5Nmzb29vZubm6vvfZaXl6e0YnEzFjQVYQjR448e/ZsYmLi/v37O3Xq5O3tHRgYaHQoS5SZmWkymebPn+/h4fH9998HBwfv3bu3Vq1aRueyaC+99JK/v7/RKYQffvjh9ddfnzFjxkMPPXT8+HFnZ2ejE1mu/v37N27c+Icffjh16lT79u3r1Knz/PPPGx1KzImlnOSenZ3t5OS0bNmyli1bAs899xzw+eefG51L8PLyeuedd4KDg40OYrkWLVo0a9asFi1arF27dvny5UbHsWiNGzceMWLEM7dOGiQGcXJyWrx4ccE/Gc8//3zZsmU/+ugjo0OJObGUQ4SJiYnp6el+fn4Fi35+fnFxccZGEuD06dOJiYk+Pj5GB7Fc6enpYWFh+pejKMjMzNy1a9fp06erVKni5uY2YsSIjIwMo0NZrldeeWXOnDlXr149fPjwqlWrdABd7pWlFKwrV64A9vb2BYsODg5paWmGJhIyMzP79u07ePDgevXqGZ3Fco0dO7Zfv341atQwOohw6tSp/Pz8H3/8cceOHVu3bl23bt17771ndCjL1alTp/Xr15ctW7Z27dqdO3dWwZJ7ZSkFy87ODrhRqlJTU2+ULTFEdnZ2cHCwi4tLZGSk0VksV3x8/KJFi8LCwowOIgAFN7x77bXXKlasWLVq1REjRixbtszoUBbq6tWrHTt2DAkJuXbt2vHjx2NiYt555x2jQ4mZsZSC5enpaWtrGxsbW7C4e/dub29vYyNZspycnD59+uTn53/99ddWVlZGx7Fcv/7668mTJz09PStVqvTuu++uWbPG09PT6FCWy83NzdnZ2WQyGR1ESEpKunDhwogRI8qUKVO1atV+/frp9ES5V5ZSsEqWLNm3b9+xY8empKRs3rx5wYIFAwYMMDqUhcrNze3fv39KSsqcOXNyc3MzMjJyc3ONDmWhBgwYcOTIkV27du3atSs0NPSRRx7ZsmWL0aEs2sCBA8ePH3/+/PmkpKQpU6Y88cQTRieyUJ6enq6urp988kl2dnZycvI333zj6+trdCgxM5ZSsIBJkyY5OTm5u7v37NkzIiJCczQY5cSJE/Pnz1+zZo2jo6ONjY2Njc3kyZONDmWhbGxsKv0/Ozu7UqVKVaxY0ehQFm3cuHF16tSpWbNm48aNW7VqNXr0aKMTWShra+slS5YsWbKkQoUKvr6+np6e7777rtGhxMxYyjQNIiIiIoXGgkawRERERAqHCpaIiIjIfaaCJSIiInKfqWCJiIiI3GcqWCIiIiL3mQqWiBQhnp6e27dvNzqFiMg/pYIlIoUtIyPDdCdfffXV2LFjq1Wrdr9eyN3dXXVNRAxhbXQAEbE4ZcqUuXbtWsFjd3f3OXPmPProo0CpUqVKlNBffSJSHOh3mYgYoMz/A0qWLFnwuESJEjcOEVaqVGnq1KleXl52dnavvvrqiRMnWrVqZWdn16VLl/T09IInOXPmTHBwsKurq6en56RJk257iRdeeOH06dNdu3b19PSMiooq5DcoIhZOBUtEiqiFCxdu3LgxNjZ21qxZvXv3njx58unTpy9evPj5558D+fn5PXr08PDwOH78+Lp166ZNm/bjjz/e+ulTp06tVKnSkiVLEhMTQ0JCDOr0NAYAAAEPSURBVHoTImKhdIhQRIqo0aNHOzs7Ozs7BwYGNmzYsGHDhkCvXr127twJxMbGxsXFrV+/3srKqlq1asOHD4+Oju7cubPRqUVEQAVLRIqsSpUqFTywtbW99fGVK1eAY8eOZWZment7F6zPysry8/MzJKeIyB+pYImIWapataqjo+O+fftMJtOf7aNT5kXEKPrtIyJmydfXt3r16mFhYVeuXMnNzY2Pj9+6dett+7i6uh4+fNiQeCJi4VSwRMQslShRYtGiRUlJSbVq1XJ2dh40aNClS5du2+eNN94YNWqUk5PTjBkzDAkpIhbLlJ+fb3QGERERkWJFI1giIiIi95kKloiIiMh9poIlIiIicp/9H4zEY/+QyZ5rAAAAAElFTkSuQmCC" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 161, "metadata": {}, "output_type": "execute_result" } ], "source": [ "test_1 ~n:30 ();;" ] }, { "cell_type": "code", "execution_count": 162, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 162, "metadata": {}, "output_type": "execute_result" } ], "source": [ "test_1 ~n:100 ();;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "\n", "> *That's it for today, folks!* See my other notebooks, [available on GitHub](https://github.com/Naereen/notebooks/)." ] } ], "metadata": { "kernelspec": { "display_name": "OCaml 4.04.2", "language": "OCaml", "name": "ocaml-jupyter" }, "language_info": { "codemirror_mode": "text/x-ocaml", "file_extension": ".ml", "mimetype": "text/x-ocaml", "name": "OCaml", "nbconverter_exporter": null, "pygments_lexer": "OCaml", "version": "4.04.2" }, "toc": { "colors": { "hover_highlight": "#DAA520", "running_highlight": "#FF0000", "selected_highlight": "#FFD700" }, "moveMenuLeft": true, "nav_menu": { "height": "193px", "width": "251px" }, "navigate_menu": true, "number_sections": true, "sideBar": true, 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