{ "cells": [ { "cell_type": "markdown", "id": "5cbc8640", "metadata": {}, "source": [ "### Comparison of: \n", "(1) adaptive variable time steps \n", "(2) fixed time steps \n", "(3) exact solution \n", "### for the reaction `A <-> B`,\n", "with 1st-order kinetics in both directions, taken to equilibrium.\n", "\n", "This is a continuation of the experiments `react_2_a` (fixed time steps) and `react_2_b` (adaptive variable time steps)\n", "\n", "**Background**: please see experiments `react_2_a` and `react_2_b` " ] }, { "cell_type": "code", "execution_count": 1, "id": "5dd32e3b-3dfd-4f61-b9d3-32c2596af995", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"July 24, 2024\"\n", "LIFE123_VERSION = \"1.0.0.beta.37\" # Version this experiment is based on" ] }, { "cell_type": "code", "execution_count": null, "id": "bfc75f60-dd56-413b-a1e0-77e69953f0ed", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!" ] }, { "cell_type": "code", "execution_count": 2, "id": "a29db1c7", "metadata": { "tags": [] }, "outputs": [], "source": [ "#import sys\n", "#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n", "# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path \n", "\n", "from life123 import check_version, ChemData, UniformCompartment\n", "\n", "import numpy as np\n", "import plotly.graph_objects as go\n", "from life123.visualization.plotly_helper import PlotlyHelper" ] }, { "cell_type": "code", "execution_count": 3, "id": "46794745-9412-473e-90f4-9cea7fe42bb5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK\n" ] } ], "source": [ "check_version(LIFE123_VERSION)" ] }, { "cell_type": "code", "execution_count": null, "id": "a7316c65-0489-404e-96ce-b045feff89bc", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "1bc60f3e-6552-43d4-aef2-a33d95811016", "metadata": {}, "source": [ "## Common set up for the chemicals and the reaction (used by all the simulations)" ] }, { "cell_type": "code", "execution_count": 4, "id": "78077d8c", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> B (kF = 3 / kR = 2 / delta_G = -1,005.1 / K = 1.5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'A'}\n" ] } ], "source": [ "# Instantiate the simulator and specify the chemicals\n", "chem = ChemData(names=[\"A\", \"B\"])\n", "\n", "# Reaction A <-> B , with 1st-order kinetics in both directions\n", "chem.add_reaction(reactants=\"A\", products=\"B\", \n", " forward_rate=3., reverse_rate=2.)\n", "\n", "chem.describe_reactions()" ] }, { "cell_type": "code", "execution_count": null, "id": "04be6f77-eb76-4c4c-a2f9-7c80ca9bd8f0", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "b496f370-290f-4f3a-8ce4-3b0f3132e43c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "23e12ad6-03b1-4856-bc39-92130e6f1b2f", "metadata": {}, "source": [ "# PART 1 - VARIABLE TIME STEPS\n", "We'll do this part first, because the number of steps taken is unpredictable; \n", "we'll note that number, and in Part 2 we'll do exactly that same number of fixed steps" ] }, { "cell_type": "code", "execution_count": 5, "id": "d3751799-542c-4d18-a4dd-36e42b63b138", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 10.0\n", " Species 1 (B). Conc: 50.0\n", "Set of chemicals involved in reactions: {'B', 'A'}\n" ] } ], "source": [ "dynamics_variable = UniformCompartment(chem_data=chem, preset=\"mid\")\n", "\n", "# Initial concentrations of all the chemicals, in their index order\n", "dynamics_variable.set_conc([10., 50.])\n", "\n", "dynamics_variable.describe_state()" ] }, { "cell_type": "markdown", "id": "9fd83080-a135-4f3d-bbf3-a1a9e815a915", "metadata": { "tags": [] }, "source": [ "### Run the reaction (VARIABLE adaptive time steps)" ] }, { "cell_type": "code", "execution_count": 6, "id": "cab9218d-0227-4d47-b128-0394c56f92c0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "19 total step(s) taken\n", "Number of step re-do's because of elective soft aborts: 2\n", "Norm usage: {'norm_A': 17, 'norm_B': 15, 'norm_C': 15, 'norm_D': 15}\n" ] } ], "source": [ "dynamics_variable.single_compartment_react(initial_step=0.1, target_end_time=1.2,\n", " variable_steps=True, \n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"}\n", " )" ] }, { "cell_type": "markdown", "id": "01dd1821-e725-48d7-b5fc-b76b3b95edd8", "metadata": {}, "source": [ "#### The flag _variable_steps_ automatically adjusts up or down the time steps\n", "In part 2, we'll remember that it took 19 steps" ] }, { "cell_type": "code", "execution_count": 7, "id": "08985297-d0a5-4351-aef2-354ce804cde6", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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140.48957923.16016836.839832
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.000000 10.000000 50.000000 Initialized state\n", "1 0.016000 11.120000 48.880000 1st reaction step\n", "2 0.032000 12.150400 47.849600 \n", "3 0.048000 13.098368 46.901632 \n", "4 0.067200 14.144925 45.855075 \n", "5 0.086400 15.091012 44.908988 \n", "6 0.109440 16.117327 43.882673 \n", "7 0.132480 17.025411 42.974589 \n", "8 0.160128 17.989578 42.010422 \n", "9 0.193306 18.986635 41.013365 \n", "10 0.233119 19.984624 40.015376 \n", "11 0.280894 20.943812 39.056188 \n", "12 0.338225 21.819882 38.180118 \n", "13 0.407022 22.569810 37.430190 \n", "14 0.489579 23.160168 36.839832 \n", "15 0.588647 23.576169 36.423831 \n", "16 0.707528 23.828097 36.171903 \n", "17 0.850186 23.950713 36.049287 \n", "18 1.021375 23.992900 36.007100 \n", "19 1.226802 24.000193 35.999807 last reaction step" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics_variable.get_history() # The system's history, saved during the run of single_compartment_react()" ] }, { "cell_type": "code", "execution_count": 8, "id": "aa8a05ce-b039-43fa-8341-0387bc74ef08", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0009451477087572492, 1.2277468736756667 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.777777777777778, 52.22222222222222 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics_variable.plot_history(colors=['darkturquoise', 'orange'], show_intervals=True)" ] }, { "cell_type": "markdown", "id": "017a76cd-9f36-4e8c-a98e-e32e659f45cf", "metadata": { "tags": [] }, "source": [ "#### Notice how the reaction proceeds in smaller steps in the early times, when [A] and [B] are changing much more rapidly\n", "That resulted from passing the flag _variable_steps=True_ to single_compartment_react()" ] }, { "cell_type": "code", "execution_count": null, "id": "d213e19d-4910-4f11-88c3-64b7d997e493", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "123ed7bd-cb03-4f5d-88b3-bfa5bc316274", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "10c710ac", "metadata": {}, "source": [ "# PART 2 - FIXED TIME STEPS" ] }, { "cell_type": "markdown", "id": "e0529a0c", "metadata": {}, "source": [ "#### This is a re-do of the above simulation simulation, but with a fixed time step\n", "The fixed time step is chosen to attain the same total number of data points as obtained with the variable time steps of part 1" ] }, { "cell_type": "code", "execution_count": 9, "id": "f9736433", "metadata": {}, "outputs": [], "source": [ "dynamics_fixed = UniformCompartment(chem_data=chem) # Re-use same chemicals and reactions of part 1" ] }, { "cell_type": "code", "execution_count": 10, "id": "9fc3948d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 10.0\n", " Species 1 (B). Conc: 50.0\n", "Set of chemicals involved in reactions: {'B', 'A'}\n" ] } ], "source": [ "# Initial concentrations of all the chemicals, in their index order\n", "dynamics_fixed.set_conc([10., 50.])\n", "\n", "dynamics_fixed.describe_state()" ] }, { "cell_type": "markdown", "id": "6bb5d54d-e085-4467-856e-b7db5fe20d00", "metadata": {}, "source": [ "### Run the reaction (FIXED time steps)" ] }, { "cell_type": "code", "execution_count": 11, "id": "635630b3-93a2-40c5-bb4b-b7e0b153a450", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "19 total step(s) taken\n" ] } ], "source": [ "# Matching the total number of steps to the earlier, variable-step simulation\n", "dynamics_fixed.single_compartment_react(n_steps=19, target_end_time=1.2,\n", " variable_steps=False,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"})" ] }, { "cell_type": "code", "execution_count": 12, "id": "7d2144b8-7331-441a-9122-918725791627", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.00000010.00000050.000000Initialized state
10.06315814.42105345.5789471st reaction step
20.12631617.44598342.554017
30.18947419.51567340.484327
40.25263220.93177639.068224
50.31578921.90068938.099311
60.37894722.56362937.436371
70.44210523.01722036.982780
80.50526323.32757236.672428
90.56842123.53991736.460083
100.63157923.68520736.314793
110.69473723.78461536.215385
120.75789523.85263136.147369
130.82105323.89916936.100831
140.88421123.93101036.068990
150.94736823.95279636.047204
161.01052623.96770336.032297
171.07368423.97790236.022098
181.13684223.98488036.015120
191.20000023.98965536.010345last reaction step
\n", "
" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.000000 10.000000 50.000000 Initialized state\n", "1 0.063158 14.421053 45.578947 1st reaction step\n", "2 0.126316 17.445983 42.554017 \n", "3 0.189474 19.515673 40.484327 \n", "4 0.252632 20.931776 39.068224 \n", "5 0.315789 21.900689 38.099311 \n", "6 0.378947 22.563629 37.436371 \n", "7 0.442105 23.017220 36.982780 \n", "8 0.505263 23.327572 36.672428 \n", "9 0.568421 23.539917 36.460083 \n", "10 0.631579 23.685207 36.314793 \n", "11 0.694737 23.784615 36.215385 \n", "12 0.757895 23.852631 36.147369 \n", "13 0.821053 23.899169 36.100831 \n", "14 0.884211 23.931010 36.068990 \n", "15 0.947368 23.952796 36.047204 \n", "16 1.010526 23.967703 36.032297 \n", "17 1.073684 23.977902 36.022098 \n", "18 1.136842 23.984880 36.015120 \n", "19 1.200000 23.989655 36.010345 last reaction step" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics_fixed.get_history() # The system's history, saved during the run of single_compartment_react()" ] }, { "cell_type": "code", "execution_count": 13, "id": "35c15b2d-3796-4e29-b038-a003fc98154b", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics_fixed.plot_history(colors=['darkturquoise', 'orange'], show_intervals=True)" ] }, { "cell_type": "markdown", "id": "3396051b-ecff-4a08-8c71-7c96f7429da3", "metadata": {}, "source": [ "Notice how grid points are being \"wasted\" on the tail part of the simulation, where little is happening - grid points that would be best used in the early part, as was done by the variable-step simulation of Part 1" ] }, { "cell_type": "code", "execution_count": null, "id": "8f453c61-296d-4627-8d4f-85c531eb4abc", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "73229033-14a0-41cd-84fb-5d688efc2e9d", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f2d90ba4-b243-4dc0-8c83-d6e73c9cd6eb", "metadata": {}, "source": [ "# PART 3 - Exact Solution" ] }, { "cell_type": "code", "execution_count": 14, "id": "33b22e64-70f3-4bf8-bb0b-0551ab11acd0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0. , 0.03, 0.06, 0.09, 0.12, 0.15, 0.18, 0.21, 0.24, 0.27, 0.3 ,\n", " 0.33, 0.36, 0.39, 0.42, 0.45, 0.48, 0.51, 0.54, 0.57, 0.6 , 0.63,\n", " 0.66, 0.69, 0.72, 0.75, 0.78, 0.81, 0.84, 0.87, 0.9 , 0.93, 0.96,\n", " 0.99, 1.02, 1.05, 1.08, 1.11, 1.14, 1.17, 1.2 ])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t_arr = np.linspace(0., 1.2, 41) # A relatively dense uniform grid across our time range\n", "t_arr" ] }, { "cell_type": "code", "execution_count": 15, "id": "85609da5-3ce1-4252-9f30-301e6e90941c", "metadata": {}, "outputs": [], "source": [ "# The exact solution is available for a simple scenario like the one we're simulating here\n", "A_exact, B_exact = dynamics_variable.solve_exactly(rxn_index=0, A0=10., B0=50., t_arr=t_arr)" ] }, { "cell_type": "code", "execution_count": 16, "id": "00526b58-deb1-4209-b05b-f4ca927d990b", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "A (EXACT) :
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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig_exact = PlotlyHelper.plot_curves(x=t_arr, y=A_exact, title=\"EXACT solution\", xlabel=\"SYSTEM TIME\", ylabel=\"concentration\", \n", " curve_labels=\"A (EXACT)\", legend_title=\"Chemical\",\n", " colors=\"red\", show=True) # Repeat a portion of the diagram seen in Part 3" ] }, { "cell_type": "code", "execution_count": 20, "id": "c4b58649-0d8a-4a66-922f-bc0b821574c2", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "FIXED time steps
Chemical=A
SYSTEM TIME=%{x}
Concentration=%{y}", "legendgroup": "A", "line": { "color": "blue", "dash": "solid" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "FIXED time steps", "orientation": "v", "showlegend": true, "type": "scatter", "x": [ 0, 0.06315789473684211, 0.12631578947368421, 0.18947368421052632, 0.25263157894736843, 0.3157894736842105, 0.3789473684210526, 0.44210526315789467, 0.5052631578947367, 0.5684210526315788, 0.6315789473684209, 0.694736842105263, 0.7578947368421051, 0.8210526315789471, 0.8842105263157892, 0.9473684210526313, 1.0105263157894735, 1.0736842105263156, 1.1368421052631577, 1.1999999999999997 ], "xaxis": "x", "y": [ 10, 14.421052631578949, 17.445983379501385, 19.51567283860621, 20.931776152730563, 21.900688946605122, 22.563629279256137, 23.01722003317525, 23.327571601646223, 23.539917411652677, 23.685206650078147, 23.784615076369256, 23.852631368042122, 23.899168830765664, 23.931010252629136, 23.95279648864099, 23.967702860649098, 23.977901957286225, 23.98488028656426, 23.989654932912387 ], "yaxis": "y" }, { "hovertemplate": "VARIABLE time steps
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+QP1+jKVdWTFKFb8LZDnut//6j51Gol8yX9AkWKdAC7LPRyniQwwvxV6vucZeF6hO9m6Wzv568VY/UEF84tWXsD9WhYSD14pKbrFaqA73V1cx4kP9SHvlm6j63BeJhViLXe6cFvGXLDXrniZZ6Ou3kHAI4qtCdbht8PKN8xjFQ3Hw2+dHzlGfKy8esnSuey8h6xyPnCP32HB/ZgpN1fDymdd3ibvesPt8BFntStlSyGbnOPJbQcrdL78/o4r9/LoZFZpW5fSfF7uki4+g3+XuHAfp69kTRnt+vr3yIbz2u1K/le49pty+9/p8BFkq3+mbsOMh3/dUITHqFHVBxnyh70Td7/v9dks7peYh6rYV9aWLgHHiI1340Zs4CJQ6PSwOG9EGCKSdQNC8lnJzyJfzUYptYcRHKe3gXBAAARBIOgGIj6R7CPaVTADio2SEqAAESibgnnJTcoURVQDxERFYVAsCIAACWQIQHxgKqScA8ZF6F6ODBhCQf/6HDOrvuchEksz3mipU7JQZ9zS+oLlHSeIBW0AABEBANwGID91EUR8IgAAIgAAIgAAIgAAIgIAnAYgPDAwQAAEQAAEQAAEQAAEQAIFYCEB8xIIZjYAACIAACIAACIAACIAACEB8YAyAAAiAAAiAAAiAAAiAAAjEQgDiIxbMaAQEQAAEQAAEQAAEQAAEQADiA2MABEAABEAABEAABEAABEAgFgIQH7FgRiMgAAIgAAIgAAIgAAIgAAIQHxgDIAACIAACIAACIAACIAACsRCA+IgFMxoBARAAARAAARAAARAAARCA+MAYAAEQAAEQAAEQAAEQAAEQiIUAxEcsmNEICIAACIAACIAACIAACIAAxAfGAAiAAAiAAAiAAAiAAAiAQCwEID5iwYxGQAAEQAAEQAAEQAAEQAAEID4wBkAABEAABEAABEAABEAABGIhAPERC2Y0AgIgAAIgAAIgAAIgAAIgAPGBMQACIAACIAACIAACIAACIBALAYiPWDCjERAAARAAARAAARAAARAAAYgPjAEQAAEQAAEQAAEQAAEQAIFYCEB8xIIZjYAACIAACIAACIAACIAACEB8YAyAAAiAAAiAAAiAAAiAAAjEQgDiIxbMaAQEQAAEQAAEQAAEQAAEQADiA2MABEAABEAABEAABEAABEAgFgIQH7FgRiMgAAIgAAIgAAIgAAIgAAIQHxgDIAACIAACIAACIAACIAACsRCA+IgFMxoBARAAARAAARAAARAAARCA+MAYAAEQAAEQAAEQAAEQAAEQiIUAxEcsmNEICIAACIAACIAACIAACIAAxAfGAAiAAAiAAAiAAAiAAAiAQCwEID5iwYxGQAAEQAAEQAAEQAAEQAAEID4wBkAABEAABEAABEAABEAABGIhAPERC2Y0AgIgAAIgAAIgAAIgAAIgAPGBMQACIAACIAACIAACIAACIBALAYiPWDCjERAAARAAARAAARAAARAAAYgPjAEQAAEQAAEQAAEQAAEQAIFYCEB8xIIZjYAACIAACIAACIAACIAACEB8YAyAAAiAAAiAAAiAAAiAAAjEQgDiIxbMaAQEQAAEQAAEQAAEQAAEQADiA2MABEAABEAABEAABEAABEAgFgIQH7FgRiMgAAIgAAIgAAIgAAIgAAIQHxgDIAACIAACIAACIAACIAACsRCA+IgFMxoBARAAARAAARAAARAAARCA+MAYAAEQAAEQAAEQAAEQAAEQiIUAxEcsmNEICIAACIAACIAACIAACIAAxAfGAAiAAAiAAAiAAAiAAAiAQCwEID5iwYxGQAAEQAAEQAAEQAAEQAAEID4wBkAABEAABEAABEAABEAABGIhAPERC2Y0AgIgAAIgAAIgAAIgAAIgAPGhYQzsOXBCQy2owkQC3Woq6ZQeNXSgoclE82GzJgJD+/cgfA9ogmloNf37dKOjJ1qoqaXd0B7AbB0E5LsABQRAID8BiA8NIwQXHRogGloFxIehjtNsNsSHZqAGVgfxYaDTIjAZ4iMCqKgydQQgPjS4FOJDA0RDq4D4MNRxms2G+NAM1MDqID4MdFoEJkN8RAAVVaaOAMSHBpdCfGiAaGgVEB+GOk6z2RAfmoEaWB3Eh4FOi8BkiI8IoKLK1BGA+NDgUogPDRANrQLiw1DHaTYb4kMzUAOrg/gw0GkRmAzxEQFUVJk6AhAfGlwK8aEBoqFVQHwY6jjNZkN8aAZqYHUQHwY6LQKTIT4igIoqU0cA4kODSyE+NEA0tAqID0Mdp9lsiA/NQA2sDuLDQKdFYDLERwRQUWXqCEB8aHApxIcGiIZWAfFhqOM0mw3xoRmogdVBfBjotAhMNll8rN+0jebc8wN66tEHaMqE0RHQQZUgYBOA+NAwEiA+NEA0tAqID0Mdp9lsiA/NQA2sDuLDQKdFYHKx4uORXzxLjz3x3EkW3X3nDXTvXTfR/BeX0f0PPU4PfvfrNHvWjAgsJworPr727Z/QgfoG+uO8B3P2xGFnJJ1HpbESgPjQgBviQwNEQ6uA+DDUcZrNhvjQDNTA6iA+DHRaBCYXIz7kIn7l2k0nRRxEkCxauqbTxX0EJueq1CE+orQPdaeHAMSHBl9CfGiAaGgVEB+GOk6z2RAfmoEaWB3Eh4FOi8DkYsTHpEvn0g1XX0Q//v43fC1yC4OZs++lGedPoWWr1lP9oSPWeRIlGTFskBUhUcU5herGuffTxHEjO7XjjF6421CiyGnUhlfmWU+/96Of03MLlney94JpE+hb/+Xmk6ZuuY9191Xs6l/Xx6pLRJiUur69aen8R/J6yOs86e8//uQXefsplRbbZgRDpktWCfGhwe0QHxogGloFxIehjtNsNsSHZqAGVgfxYaDTIjC5GPEhQuLM0cPplw/fF0p8iOhQ4kJN23JetMsFthQ1LaoY8SFiQuV/uOvzmnblFjBKeCjRIva4xZbUu2XHbks8yRQzKUGYeJ2nhEU+kaWOKabNCIZMl6wS4kOD2yE+NEA0tAqID0Mdp9lsiA/NQA2sDuLDQKdFYHIx4kPlSShzvP7194t8qGiJ15QpufCXyIiKIIQVH248InCeeX5Jrr4g4kOEhlNUSJ1KKClBoqIQTvEltm98f2feKWde54URHxJtCdtmBEOmS1YJ8aHB7RAfGiAaWgXEh6GO02w2xIdmoAZWB/FhoNMiMLkY8eE0Q4kI9ZqaohRUfDgT0t1ioRjxIREINa1L2aREQyHxIcd7rZ7l7gvERwQDMeFVQnxocBDEhwaIhlYB8WGo4zSbDfGhGaiB1UF8GOi0CEwuVXw4TXJOWSqH+JCoheRxqOiAO2IB8RHBAOoiVUJ8aHA0xIcGiIZWAfFhqOM0mw3xoRmogdVBfBjotAhMDis+RFQ8+Z+LPJPN1cW+5HW4owgq4dw97apQ5MM91cgv4Xzrzj1W4rozVyOs+JBckXJNu8rXT2FZbLQlgiHTJauE+NDgdogPDRANrQLiw1DHaTYb4kMzUAOrg/gw0GkRmFyM+JCpSVKcF/oq0qEiDzoiH+4cEJVrMnbUMCu3wtmGEjtOMSNCwmmnW4zIe8UmnBeTf+GX81GonxAfEQz8kFVCfIQE5nU4xIcGiIZWAfFhqOM0mw3xoRmogdVBfBjotAhMDis+lAnqwt5pkjNRW4f4kLqdORwiOuSiX20U6CcclE1ij2yE6BRJasUpOabUpXbDJn/7iY9C/YT4iGDgh6wS4iMkMIgPDcBSVAXER4qcWUJXID5KgJeSUyE+UuLIErtRrPgosVmcDgJGEYD40OAuRD40QDS0CogPQx2n2WyID81ADawO4sNAp0VgMsRHBFBRZeoIQHxocCnEhwaIhlYB8WGo4zSbDfGhGaiB1UF8GOi0CEyG+IgAKqpMHQGIDw0uhfjQANHQKiA+DHWcZrMhPjQDNbA6iA8DnRaByRAfEUBFlakjAPGhwaUQHxogGloFxIehjtNsNsSHZqAGVgfxYaDTIjAZ4iMCqKgydQQgPjS4FOJDA0RDq4D4MNRxms2G+NAM1MDqID4MdJqHyY2NREePVtCxo/b9Ub4/JvdHnK93fu8Iv2cdw8e+83ZlOkCgFyAQIQGIDw1wIT40QDS0CogPQx2n2WyID81ADawO4iM5Tqs/UEH19USf7qugPXsqqKmxgj7ea9u3j19raqqghsNEhw9XUFsb0V4+Rorct7aW1o9MprTzcTYIdAUCEB8avAzxoQGioVVAfBjqOM1mQ3xoBmpgdRAf0TpNRIGIA7nV11dYwuLTffzaXn7OYkNEhbymQ0D06kVU1z9DVVVEQ4baamLQoAx160506qkZ6tMnQxXVGepxRgsdqWmligGtdKxHK53o2Uq/vnBYtCBQOwikgADEhwYnQnxogGhoFRAfhjpOs9kQH5qBGlgdxEdxTlOiof5Ah7g4eNAWFBK1sMUGcaTCjk4EKUo8DB+RyYmGESParVP71RH16pXhmy0wpMhxlsAYzPe17bSPwyG7WltoX3sb7WPVc5DDGXvbWmkvv/Zpe6v1fr2ETDxK5tyzg5iIY0CgSxOA+NDgfogPDRANrQLiw1DHaTYb4kMzUAOrg/iwndbO1/j791fQgU8r+N5+vJ8fH5DXWGDI4473ObfiWDBn9+ZoQ//+RAMGZmjAAPvWfyA/zz6W1/sPsN/vnxUVquZWFg8H2DARDp+2ttF+FhL7M22Ox/weiwx5/VMWHEFmTvWqqKQBlVU0oLqKBsp9VTXfquhno4cH6xCOioSAe5f2SBpBpSUTgPgoGSERxIcGiIZWAfFhqOM0mw3xoRmogdWlXXwcaciKCSUeLFGRFRcOgSGCQ6IWQUpNrYd4EDGRFRhKTFgCg1+r5eOdpTHDooEjEJawEOHAj/e3tdB+S2iIuGjNio4WOthmRz4KlVMrK2mgCAlLULCw4MciLvqrx3zfn58P5PueLEDcJS2rXamLeHf/xo4aRl+dcy3d/9Djubce/O7X6aPd++ixJ56jDa/M63TKzNn30ozzp9BtX7iS5tzzA0/8d995A1160Tme77vrc1aQVKGRVLsKjf0434f40EAb4kMDREOrgPgw1HGazYb40AzUwOpMFB/NzR2RCDs60RGpsKIT8lxeZzEh93J8kCLTmQZwFKK/U0jIaxypsF7LvU7Uh3Mo3OUIi4f9KkrBImK/CAkRFvzafr5XQkNExxF+L0jpiFLUsLDgqIUVsWBhwSJCRMYA9ZiFRU1FMPHk1W7axMdTjz5AUyaMPqmrXhfY3/vRz+mT/Qfplw/fZx3/tW//xLqX54UuyL3ef+QXz1qCRsTJvXfdFMiGIGMh6mMK9TXq9k2oPxbxMenSuaFZiLr+47wHQ59XjhMgPspBPRltQnwkww/ltgLio9weKH/7SRIfSixIHoWa5mRPfyJr+pOaCiVRColoBCk9e2anNOXEgx21cAoMS3BkoxZ8fX9SOWhFKDgyIQJCRIUVqVCPs5GLrOhoCjD5qZpFgiUeKlhIsJgYUMXCgqMR1mvVHL2wHvNr2alRQfrpPqby8GGqOHyIKnl5rEq+r+DnuXvXa3Js7euvFdNM4s4pdAHt975EOr5z961WfyQ6oiIXxdanBIhXBETaqj/E6xxni1w3/vC+u6wIiogmKfL4gmkTaOXaTdbzG66+yLp/bsHy3PMff/8buTpEMKlj5UU/8SXvzX9xWacIkLpu9bJLXc/61a/4iH3KNmnD2W+/9hI3eAIYFJv4yBc6c9spg23R0jUQHwEciEPKSwDio7z8k9I6xEdSPFE+O6IWH5Ib4cyVsEVFVkxkp0JZz7OPgyz5Kqs5dUQismLCkVMhkQoRGFYkg18XAeIuMpnJyqHICgvfaVCW0GilIHGKHiIaWDD0F1FhTXfKCguZEmXlWci0KHlcQ32rwu+rUdnQQJWffsK3T/m2j6pYlcm99Vju5fk+uecbHxuqBAHvU+HmzUQffxyqNS0Hjx9PdNppnasqViyoC+S6vr3plusvy0UsioOGOdkAACAASURBVK1PrJI/sGVq1+xZMzoZ6VWn8zU5WMSHXNCLwFC2uZ+r61OJ3CxbtZ6Wzn/EakeO/+ljT+eeu2G77bpx7v3WdatfX/PVr84RoeSMHB2ob8hdC/u1p2UQxFwJxIcG4Ih8aIBoaBUQH4Y6TrPZEB+agRpYXaniQ1Zz2r69gnZ9aN/v3MH32yqt/ShkCVlZFSpo4Wtza4nYgbw8bF0dr/jEqzgNGSLPKfeavC+vd+vmXWszRx4kZ8ISE5JbISs95R7bidlWfgXnUhwIOPWpdyVHKlgwdEx1yoqL6hoWGnauhS06KukUFhlhSwXvDFi17xOq2rObxQOLi0/4sYiJ7GtV+z62X5fM9xCl7fSRlGHb2obyMrrdu1HboNMow8tltdf1p/Y+p1Lm1FOpnRNU5LX+N1wToubOh371q0Tz5hV9etEn/upXRHPndj7dL+dDRQLyiQn5d9950Sw1+9Un7zlzPrwiDRJJcAoZZWlQ8eFns/t8L5EjgkJyXNzCR2yQ472mhPmxyVf/mJFDcxEbNc1NiSVlv197RTu+jCdCfGiAD/GhAaKhVUB8GOo4zWZDfGgGamB1QcSHCIgd2yroo48qaOuWytzjHSw2giRpy14TEoWQ5WJHnG4vI9uPxYWIjKE5sdGxhGwhjB+xoNjR2sy3Vl5atpW282NZUlZEhrwXtHTj6U+D+OJ8OE9xGsRRijqJVnBkYgi/NoSVkAgOeU3eC1sqmho7RyhEPHBkwhIV2ciFRCiqrEgFzysLUDI9WTiwEmsbONC6b+cQT9ugwda99Zxfb7Ne51sdww5RSsn5eOghopdeCtGYpkPv4xSNWbO8xUeYnA+pQUUL5HFSIh9hxIcXUq+oi+qrM/FeRVTyiQ+/+r3Eh7se97Qr1Z6mYRBrNbGIj1h7VIbGID7KAD0hTUJ8JMQRZTYD4qPMDkhA80p8vPd+hj7i6MWO7SwuWFTITT3Pt6ysRCDOGN1u7TlxxugMjRyVoVFn2GJDohciNsKWJo5YfMSiYgcLie0tzbSThYUtOOybLEGbr/RhASGiQhKzh4qIsESFHa0YmhUWdfyeHFdMkQhF1Yc7qZKTUyQaUbWXn/NNIhbymhXF4PeDlgzvAtg+eLAVobDEhNw4OtE24nQrWiHvWc8lghFRKUV8RGRSUdUWO00qipyPZ55f4jn1KYrIR74cj3wglS0iVLyEhJwrkYswYk6JDa+0BWd7XlGZopwe40mJER8qKT1MbkiMnPI2BfGRFE/EbwfER/zMk9gixEcSvRKNTZLMvYsjF3LbLfe77Mcf76minXydfOiQf7tDh2UscTF8eIaG8U0e2/e26OjRI7zNDZxrIRELFbnYyVOhtjeL4LCjGPmKRCKG85SnM6praRSLi5H8WESFvCbvdfNYSjawhSx6qj/aaU2BEgFR9dGH9k0e82vyHsm25QFKu0xrYvEggkKmQFnTnQZx5ELERU5osLjg48pdurL4cK5uJX5wrn5VjJgptNqVuqB3Ria8cj6CRj78potJO14rfqkcD3k/yBSufPVLHSpRXrUlQu5M3jdG5YDka6/c4z5s+2UVH2pgKaOLVZxhO637eIgP3UTNqQ/iwxxfRWkpxEeUdOOve8/urMDICosOkVFJu/m1Eye8bZJ9KDqJiuG2qOgQGRkKGyRo5uiE7La9m4WE3O/K7r69W17jlaFEdLT7RDB6c2MiJIZxtGJ4TU32sS0ulMAolq6VX/Hhhx0CQwkLiV5kBUahutt518C2ESwm5F7EBUcoctEKERoiLCRKIUkshpSuID7c03/k4n/l2o3WKk1x7vMhQ8J5Hem32lVQ8aEEk3O1KXnN79pUxMCWHbtzI9OZ/+G2S612JYLMq34lPpzD3L3qa772DPl45Mwsi/hwLzXmN5/OFJgQH6Z4Sr+dEB/6mZpYI8SHWV7jGUi5iIUVxdhVmYtk7M4KD9mp26v07s0CgyMVw1QUIxvJmDS+mvoPaqW+/YOs59S55iPttsDYxVEL654FhS0sWGDwbR8LDr8i06KGSbRCxIV6LOKC8y+G8UV7UVOiuH0rYiG3vXusW6WICvU8e0957JK8irYhQy3x0J69V89zr7PASFtJi/hIm1+S3p9CkaGk2x/WvljFh3O/D6UQ/ZZQC9uRch4P8VFO+uVtG+KjvPyT0jrER1I80WHHEV7+f/dHLCqy0QtbZPBUqezzfZ/4rx4ly8vmIhhZcaEiGDJl6tS+J+dKFEo4FwFhRSskgmGJDBXJEIHRSjJ9yqvIXhbDOK9imAgKFhjDZKpUdmqUiAsRGWE3xbOiFiIqsiKi0iUqrNWiOKE7X2nv169DWAzhCEVOYNjRChEc7X37Jm9gRGwRxEfEgFNaPcRHRI71y+mA+IgIOKqNhQDERyyYE98IxEd5XCT7XrhzL5S4EKFx+JC/wHDmX1jTonIiw54q1b17uD71611Lm4820rbGJktk2JEMjmDINKkW+7ksX+tVTuHciuEsJERgWFEMa1pUNqLBj0/j18KUyvr6bPI2Ryw6CQs7elEpkQzeEC9faTttiGfEwsqxyAqNTPciklTCdMTAYyE+DHQaTI6dQGyRDxEZsumM2rxF9RTiI3afo0GNBCA+NMI0uCqIj+icZ4kJZ+6FJHpbU6PsqVKNjd5t13D+hUQpOiIWtqjoEBkZ4qBCqHKCV4+yp0VxFIOnReVEBkcu9mRzMvwqlFWihlmRCztaYeVi8J4WltDg56eGSAap+nhvTkR0mh6VFRbymixR61cynJxiTYXqFLHgSIVDWIjACJ2gEopmOg+G+EinX9ErvQRiEx9itnPalcrzgPjQ61DUFi8BiI94eSe1NYiP4j3TLPkX2dWjRFConAvnSlJ+K8Kq/IvOIiOb4M1CQ/bBCFsOyvSobCK3ysPYzZELK4LBwsNvQz1ZbHYEi4uhaopULophRzJkulSQ1aMqGIiVX+GYFqWiFc6cC8qzTG7mlN52srYj18ItLGRPCxT9BCA+9DNFjekjEKv4UPiQcJ6+gdRVewTx0VU937nfEB/5x8GRBtfqUa5oRr7duyX/wh2xcOZf9Dk1vMD4OLdylEQvsrkXuRWlWukYRzi8Si+OTtjTomRKlJ3QrSIXk/v2pL68cmxTi0+merbCiiMNBYVF5YH9eYHKbtr5hIUIj0zvPvhwloEAxEcZoKNJ4wiURXwoSs6lyLymZJlCEwnnpnhKv50QH/qZmlgjxIfttYbDFfT2WxW04V17SpRssLd9m/0435YOIiDO4A31ZFM92UxPNtgbe2a79XgI79xdbJEN9TY0N9F7LU20NbuDt2yuV59nlSbZrfsMa+Uo3v+C526NZLExgiMXo7I3SQD3KirhvOVj3m1bRS0c06CckQwRIL6F6y+4ShRHNDK1vCshSuIIQHwkziUwKIEEyio+nDywyWACRwdMKkgA4qMgoi5xQFcUH06hsXZNJW1Yb+/o7VdkCtQo3rlbBMaoUe25xyN4epTs4l1KkUjFezxd6e3mRhYZLdb9Fl5P128FKVl+1t5Yr8YSFiNZaIxlwSGPhwTYU0JWi6revo2qt22l6g/eo+rNm6j7h9sps+sja3fuQkX2smjlzfJkjwtrepTswM3PW2XPC1kpKgGb5RXqA973JgDxgZEBAoUJxCI+RFiE2blcIiKLlq4htSlL4W6U9whEPsrLv5ytQ3yUk35y2k67+AgqNHr14ty+Ke009Zx2Om1IVmhY0Yx2kvd0lM0sMrby7t0bWFxIREMiGxLh8CoiJiZxhOCsGrnZ0QsRHUH3vpDN8qo/eN8WGDtYbGxnsbFpo5Xsna8oISH3lrCQxO7TOwSGSZvm6fBZV6oD4qMreRt9LZYAxEex5BznQXxogGhoFRAfhjpOs9lpEh8ffVhB779XSe9ttu/fz967d/WWvItxZ7XzLUNnjbfvx/F9z5564G5ngbGVE7238W1rK0+bsu5lwz1OrHAVyb0YU92NxrDAGMPiwrrnKVOSn1GoyJKzIi6qWFjUcATDupfn27b5rxjF7bWeMYZvo6n1zLOoje97Tp1MR4ePpBMDhxRqEu+nmADER3qd29X24ojSkxAfGuhCfGiAaGgVEB+GOk6z2aaKDxEaH7zfWWi8t7mS3EJDNtzLCQwWHGeNz9CZfK8jmiGrR1kCw8rLYLHBN0to8HN36nYv3g9jDEcvRFjkhAYvGyuvdef3/ErloUNUtXM7Ry+2U9WHO6iK76s5qmHf7yCvnbozLGDaTh9FbSN5OtTIM/ieH/PzVrnn5+4N9AptMqh5yKG6hBJIi/i4ce791L+uD/3y4fs6kZaZKes2fNDpdZndMnbUsE6zVdSFuttNahbM/BeX0f0PPZ57W62Aql4IU6c6N5848LNH2lObXjttTarQSKpdYT+OsYmPsIa5B3LY8+M8HuIjTtrJagviI1n+KJc1JogPSfq2IhnvVXBUw75/n++PH+9MTYSGV0SjVKHRymkdMl1qK0+Xkts2jmBYgoMfH/LY3XukJTKyQsOKZojIqKXBvGStZ+GEchESVTt2UDULjaqdHfciPPw21bOSu1lQdAgMERu2wJB8jKAF4iMoqXQflxbxocSBe8q8iJKvzrmWZs+aYTlSTZOvP9RA//7jb9GUCaOt19VFslNUfO9HP6fnFizPTcP3u5AuVOdTjz6Qa0fqXLZqvbWHXBDx4Tw330hM6kV+Uu0K+6mORXyENcq04yE+TPOYPnshPvSxNLmmpIkP2ZgvJzCyU6g+4PtjxzpTll2+JaJxpkydckQ0TjmlNG/IUraWwGBBYE+ZYsHR3EI7207OzZD8C3uqlB3BUCJDEsC9Vpaq3PcJiwsWGblIBudlqIgGJ3x7FUngtqMYHSKjVZ6PsqMZsuleqQXio1SC6Tg/LeJDvOHeh01d+DoFiYiRK2dOt6Ihgwf0ox9//xu+4sMtaPwupAvV6RQQzjp1io+Zs++l+kNHcoNS/hD/4X130Zx7fkDSvhR5fMG0CbRy7Sbr+Q1XX2Tdi8BSzxUPee7eZiKfEHJHhtQf8l52qfxov/oVF7FP2Sb2OP3o115Un8ouLz7cznI7RJ7LB2HLDjvB0CsiA/ER1fBMfr0QH8n3URwWllN8iNDwimi4hYYsWWtNneIpU+PGdUydko36ii3HeZUpe5qUiAtJBJdpU3auhtdeGaNVPoYSG7U1NJpXmhrokZtReeAAVW/9IHvbYt1XyfMtH5BsxOcuYadJFdtnv/MgPnQTNbO+UsTH5sYm+pg/O3GX8d2702k1J+dHyfWRFDX1yj3lynmxv3XnHvrpY09bEQgpXpEPqe9AfUNuepaXWAhSp/Oi3WmjTvFRyDbpo4gPuaAXgaEu3t3P1QW+M0Ij58rxTl5un7uFn1yHisjw62O++tU5IpSUL92+8GsvqrHY5cWHqEj1YRHIbge6HeQ1DxLiI6rhmfx6IT6S76M4LIxLfOzZbUc0PpCpU9kpVDJ16ujRzr0UoaESwCWioR6XIjQ+zOViyJQpW2CI6NjrkQBeV+WMZnSOangtxiurStVs3sgrSW2gmnfX8+MN1ipTXpuDZHqdwkne4+yEb7l3PJb3ylUgPspFPlntliI+vvrhLpp3oD72Dv3q9OE0t3/dSe26IxV+U67UP+9yAauEgVeOhTu3wutC2r3aaaE6xWhVbxDx4QU3aM6Hs34lPtz99XvuvriX8908nbbJ8UHtkvPy1T9m5NBcxEZNi1O+Vfb6tRfVYOzy4sMN1j14RZx85+5bc/MbvdQqxEdUwzP59UJ8JN9HcVgYhfjYuyc7dUpWm8omhcvUqSMdMwGsrsmStpIA7s7T6N2nuL0zDnP+hT1lyo5kqByNrTxlqqW9c51VvCFebnWpbFRDIhkydaqfR26GNVVqix3FsG4cxbAiGh7Tpdrr6qh1zJnUOpYFxpix1uM26/nYRG6wB/ERxyct+W2UIj4e+mQfvdTg+ichhi7fN3ggzerjHQJVF7VyAfvN7/2s05+1anrUvXfdZFkpf9aqqVfuyIccO3HcyNy0LDneSywEqTOOaVdBIx9hxIeXK92J9uoY9zQoFVHxE1hqrzx3G1K/l/hw1+PXXlTDD+LDRVZU9zPPL/FNXvJyPMRHVMMz+fVCfCTfR3FYWKr4EKGhEsCdEQ230Bh8mi00nHkaEtWQHcLDFjlDEr7tvAy1rK2dDL6fV6Byl0GVVZ3zMqxVpuyN+tylcv+nOWGhBEb1Vlt0uKMZmW7dLUGRExdZoSHPRYCYUiA+TPFUtHaWIj6itay42tW0pnMnndlplSu/1aPq+vbudP3kXonKebHtvp4KWqc7V0JFR6SHKidD/cOveh02UTsK8RE02d3tKaeQ8xIScrwzQuR3vp9oy9eeWliguNHjfxbEh4ONW6kXGnxqcB9oaNLtF9RnCIGa6krqUVtNDcdPnoNuSBdgpgYCcuEZ9HtAhMZmjmbIPhpy27zJjnA0NHQ2xIposLAYP8G+icgYP6Gdit38ejuLijcbG3n37yba1NRI7/L9gbaTRYZYcToLisk8D/xMFhdTu3ez7id063YSqYoTx6mKoxeVPEVK7u3bFuu+4vChk45vG8VL1PI0qbaxHMVw3NqHj9DghfJW0adnLZ1obqWWVvcCweW1C63HS0C+C9JU1D/iku/qtcqVezNoZ6REhIBTbMifu4898Zzvald+G0y763ReRDvrDDLtKowA8Eu4dyacB418uKfwyxgRe6W4hZK8pnI81HFOUeU1xSpf/VKHW5TJrJ4zRw/P5YDkay+K8QzxkaWqBq1zjl1Q8dHUgh+bKAanCXVW8gT2qqoKvuAI/8+zCf2DjcEISATM63tg716ijRsqaONGok28IMrGjSI2iHjbiU7lNN6XbuLEDE2YIPf24/H8uF+/YO27j2rkqVNrebOOlcdP0AoWCCv59knLyZvzncIrTZ3FkYdpPbrTRBYXU1lwTORbX48pUxUiKN7nGwuN3E2e7951kpGZwYMpwyIjc+aZ9v24jsdp3d27prqCtwvJkGtmWnEOxFnGEpDvgrQVuVCV4syPldduuf4yUlOuVJ9VpORb/+Vm64LXPa1ILfIjr7v3+ZAE7CB1uvmqpG6/yIkkWit7vHzjlVshxylhI4/9VrsKKj6kDrXUsNMGPzHkXOhIjnfa6LZLCUC/+uV88YWzuBdPytdeFOMZ4oOpuhNvnKC9cj7kA+NcogzTrqIYmmbUiWlXZvgpaitlqsW6DY0de2g48jQaDndOsR402I5iuDftO7Vv8QJ2L0+dWtvcSKv5tqrxBG3g6VStmc71yQZ900RodOtBZ3NOxnieNjWKIxruUsFRkepNG6lGkr83rLd2/655ay3J6lNeRXb4lqTvlgmTqHXSFGqR5xNYQXWxgmlXXczhPt1N27QreNV8AmGnnMXR47KID/c6xc6Ouje0iRpCoeXOsNpV1B4wu36ID7P9V6z1+z6xp0xZS9zy/fat1fTuhgwdPuQSGoNkJ3BbaKhdwWUqVd9+xQsN2RF8I4uMTbxvhoiMjTx9aiPfO0stVViRjIksMibWdKcJLDQm1XSj3hzp6FRYtMgqU7VvLGeh8Q7VrFtrPfdaZaq9f39qmTzVEhYtZ/FtytmW6CjnClPF+i+K8yA+oqBqXp0QH+b5LO0WQ3ywh72Wqi2X4/1CdGKPM1SIfT7K5aHktwvxkXwflWrhvn2yE/jJm/a5hcbAgRzRyK46Za0+JXtqjMtQv7rihYbY/r4IDM7X2MR7W2xsaaQNfP+Ja3nbodXVLDJEbPCtthtN4A36xvJjL6FhCQwWGrVvrrIiHBLp6FS4rpbJZ1viQkSGJTZYdIj4QPEnAPGB0SEEID4wDkCgMIHYIx9eiTKFzUz2EZh2lWz/RGkdxEeUdOOvWzbm2/JBJa19s9LK1Xh7XaWVDM4Bgk5Fcq8l+XvaZ9pp4qQMXXlpDdUNOVFyOkMD52psYIGxkQXGJhYcEtVwT6GSrcBEYEys5YgGRzYmidjg6VPOPI1Kzl6vln0z3ttk75/BiSbyvOqTjzv1o52TSlolisEJJq3jWWjwfQvftw8YGD98w1uE+DDcgZrMh/jQBBLVpJoAxIcG90J8aIBoaBUQH4Y6zmH2ju0VtPClKnp5YRWteoMTx12L17mFxtRzZQpVeyehUexSu9t5iVsRGhtkBapshGMX763hLIM5+VsEhpo+JdGNcSw6VKk4fowFhi0u5KbERtWe3Z3qyfTukxUZLDAkopEVHG2S7Y5SMgGIj5IRpqICiI9UuBGdiJhA7OLDvYFMxP2LpXqIj1gwJ7IRiI9EuiWvURLFWPF6Jb2yuIpe/HMVifhwlqnndEQ0vISGV+VBxMfxTLslNCQ/YwNPddrEIkMiGyf4dVVk9TSJYkhUw4poZHM2ZMdwKVYyOAsNZzSjhqMbskO4s2R69uoczciKjbZhw81zmCEWQ3wY4qiIzYT4iBgwqk8FgdjFR6EEbxOpQnyY6DU9NkN86OEYdS2bNlTSm6v5tqqSVvNt544OwXHG6Ax95vx2+3ZeuzWdKmzxEh8fibiwpk7JNCrJ22ihHRzpcJZBHNWYoHI1JEG8upu1CpUlNPh4mTZlRzNUZIPvd9hrw6uSYZGiohjW9CledarlrAnUdvrIsN3A8SUQgPgoAV6KToX4SJEz0ZXICMQuPvy2gFc9jHu1Kx1kIT50UDSzDoiPZPrt+HGyhIZ1W11l3Us+hxTZwkJEhlNw1PUvLSl8QF13WvTx4azIYLHRxKKjtYmOcA6Hs9irTtmrT8n0KREeA8UgPs4SGO/Z+Rm5yIbsCO4skgzOwkLyM5x5Gq1njEmmI7qQVRAfXcjZeboK8YFxAAKFCcQuPgqbZN4REB/m+UyXxRAfukiWXs/OnRUdgoPFxkaOdqgiu4WryMZ5HOE4Z1r46IbTwo95tSmJamyQqAbfv88Rjc2uZJH+vKytMylcPZaYS+Xhw1T7+mtU8/Y6qln/NtWuWeW5j0bb0GHUcs40apl6Lq8+NZWap5+PVadKHyqR1ADxEQlW4yqF+DDOZTC4DAQgPjRAh/jQANHQKiA+yus4O7JhRzjW8L0si6vK2VPt6MZ0iXLwbfiI4qIbcpaaPmXvq2FPpTroimqcxcvbSlK47K8xgadPSc6GTKuSIjkZtSuX820FdXt9qbVxn7vIUrYiLkRkiNho/gwLjUGDywsYrQcmAPERGFWqD4T4SLV70TlNBMoiPtSO4s4+OPfV0NS32KqB+IgNdeIagviI1yWffuqIbmRFh7JAdgi3plM5plRl0ydCGyl7aqxjgfEW39Y2nbCWvXWWfpKrwYnhk6yN/LrR5wb0oYEnWGRkD6p5195Ho5aFhoiOk1ae6nUKNV/4WWo+Z7od1eDohkQ5UMwlAPFhru90Wg7xoZMm6korgdjFxyO/eJYee+I5eurRB2jKhNEWV7XZ39133kD33nWTcawhPoxzmTaDIT60ofStKF+y+Ngz1XSqNivKcSZv6ldMOcYrTq1qbKRlTcfplcZjtJnFh7PUsdg4v1sPOpejGdN5Jaqzu3WnXhX2tK7KT/fRaTs2UcPrq6wpVDXvvE3V27d2Or+V8zSsjfvO5qiGRDamnEOyxwZKeghAfKTHl6X0BOKjFHo4t6sQiF18zJx9L91y/WUniQwRJc88v4SWzn/EOPYQH8a5TJvBEB/aUOYqksRwmULllSwu21tIZEPyNlQOh0Q8wpYjLDbWNZ7gyEZTLsKxr60tV82I6ho6hwWGiI1zWGzIfW1WbFTt3G4JDFtovGXdd9q8j4WKLTD4dvY52fupJKtSoaSXAMRHen0bpmcQH2Fo4diuSiB28eG3w7maioXVrrrqUDSz3xAfevwmS9/KErgqd8OZLD5seHY6VTZ/Q/bhKKbIFKq3OClcTafa4phK1YeTw8+t7cGCoxvfs9hg4TGg0p5EVbNxAwsMW2RYUY133ybZQVwV2byvYtq5dGzCFDu6wVGNlkmTizER5xhMAOLDYOdpNB3iQyNMVJVaArGLD0Q+UjuWumTHID6Kd7szWVweSz6HKrIalUQ3pn/GjnAMGRo+uiG7h6/jyMZbvDHfWr6J+HDWoiIaEuGYxrfRnMNRwce7oxqSv0GyM2G2tA0+jVqnZEWGFd2YSoOmTyJEQIsfC2k4E+IjDV4svQ8QH6UzRA3pJxC7+EDOR/oHVVfqIcRHcG/nSxaXfTaU0FDTqXhLi1DlQHubNY1KEsRFcEiE47BjRSoRFyIynNOpKg8e7BTVkOhG9fubO7XbOmp0p1wNERvuVaiC7HAeqjM42DgCEB/GuSwSgyE+IsGKSlNGIHbxIfyw2lXKRlEX7g7ER37ny/Qplb/h3ln8rPGdV6YaPSZcdKM1k8lFNNbxErgiOD7kXcVVkWlTMn1KplHZ06l6UL+9ezrlalj5Grs+6tQJmTJlTZ1yJIjL1Kp8BeKjC38JZLsO8YExIAQgPjAOQKAwgbKIj8JmmXUEpluY5S+d1kJ8dKYpyeLORHERHmpn8e7dOVnckSguieO9+4QTHLIK1VvNJ+zpVBzZeJfvVZGEcGeCuEQ4Rh5usJa67bZ8KdXI0rdvre00hUrObT3zLHvZ2/M/S00Xf47aTh8ZeohAfIRGlroTID5S59KiOgTxURQ2nNTFCEB8aHA4xIcGiIZWAfFB5EwWlw3/ZGlcVU4faSeLWxv9sfCYPCVcsvhe3kl8nZWvYSeKr+MpVSc44qHKeN7Iw0oU55WkpvFSuJN4mpXsr9Ft8SLq9upiqhGx4Sw8l0siGs0XXkRNF82k5gsu0rJjOMSHoR9gjWZDfGiEaXBVEB8GOw+mx0YgNvEhq1zJPh6yx0e+gtWuYvM9GtJAoKuKj3zJ4iI01K7ikjQ+aHDw6IbstyERjXWyKhULDREcnziWwB1aVW1PpZLcjewSuKds+YC6vbyQui9ZSLVvrKCKY0dzns3wcbJTePPFTiafQwAAIABJREFUIjQ4usGPM7zBn+4C8aGbqHn1QXyY57MoLIb4iIJqtHWqveac+8+FabHU88O0lZZjYxMfaQHm1Q9EPtLs3fx96yriY9++CsfeG/aSuKoMGJDd6E+mVGUjHBUdC1cVHBzrOV9DohsqwvE+P1flFJlKJZv7cc6GEhtDt26h2jWrqYZv1j3nbaiS6d6DmqefRy18U/dtpw0paEOpB0B8lErQ/PMhPsz3oY4epEV8qAtqLybyR7IU+TPZ/YexrGg64/wp9OPvfyN3qvz5PHbUMPrjvAc9Ecv77iL1er2ujnvwu1+n2bNm6HBZbqPrIOIDQkMLcopdfPjt84FNBvU4FLXESyDN4kOSxa0IR/a2c2eHopgwqUNoSHRj5Kjg0Y0mjm4s5Q3+Xmk8zvfHybnfhnhPNvib2aMHzejWky7r3ov61h/oJDZq175JFUc69tlomTiJWqZlxQbfl2OPDYiPeD93SWwN4iOJXonfprSJj3wX5N/70c/pk/0H6ZcP32eB/tq3f2Ldq+fyWK7tFi1dQ/WHGujff/wtmjJhdM4pavEhETP33nVT7nWpV4oSMFFf8IepP8yx8Y8+c1pMjPjAJoPmDBpY2kEgTeLDnSwuouP4cbuvvXplk8XPa7NyN2RalbwWtNTz1KlFJ47SSyw2lpw4Rk2OvI1eHN2Y2aMnXdq9J83kyMWoiipLbFhRDRYatWtXU9XOHbmmZJ8NZ2RDIhwZPr+cBeKjnPST0TbERzL8UG4rupL4ENYS6fjO3bda2O9/6PGTIiE3zr2frpw5ndZt+IAGD+jXKSLit++b24dBL/jdK6m6oy3SXv2hI1b1zvec9ct7c+75ATlFl/P9b37vZ7k6VD0/vO+uk84p1JY7DUFnJKfcn4Eg7SdGfIjSXbZqPS2d/0gQuxN1DKZdJcodsRpjuvjIlyw+6ozsdCqZSsU3iXaEKR/xsrcvHmfBceI4reYVqmRpXFUm1XSjWT17seDoRWdzsnj3rR90iA0RHY5E8QwnlXdENj5jTadqGz4ijCmRHwvxETnixDcA8ZF4F8ViYEniYzPvMfTxx7HY2amR8eOJTjut00thL/jr+vamW66/rFMEw1nH1p176KePPZ27xgtavxgV9Fj3zBoRPmqqlzyW4nzev66PFaUJIz4KiROJ7ARpyyl+1P53JuY8FztYYxEfXvt6eBlsqvKD+Ch2+Jl/nmniQ67/JaKx5s2O6VRqZ/FKTuNQieJqSVzJ5whaWrjylZwkvopvKzmHQx7La1L6VVXR+ZwgfgFHN+R++tFjVkTDimysWWXlb1QePpxrqnXc+M65G7yTeJILxEeSvROPbRAf8XBOeisliY+vfpVo3rz4u/irXxHNnespPryMcU+TkulWB+obTsrpUFOu1AW/iAMVUQgz2yWM+HDb5hQvzmtMZ/s6xYcSJ0HaUlPQgvYv/oERXYuxiA+n+X45H9F1MfqaIT6iZ5zUFkwQH5Isnsvd4KVwZe8NVWQlKsnZUIni0z4TLrpxqK2dRcZxWsWrUonYkKRxVSR343xOFj+fp1KdX1NLk995Jys27GTx6h3bcse2DxjYSWw0T/sMFdrYL0ljAuIjSd4ojy0QH+XhnrRWSxIfDz1E9NJL8XfpPs7ZmDXLU3wUSsKWi3iJaEhxRz7UlCuVzyEiRU29CnPBHfRY9x/dN1x9kTXNS73uN5VKCQZ53/nYSxwUel8iPDL9LEhbEB/xD/VUtQjxkSp3hupMUsVHvmRx2WvDudnfiNODRzcEzm6eTmWJDU4alyjHey3NOWbjeQqVRDbO5yVuL9m9l4a9s64jWZyjHLnCkRBrNSoWGXLfzInibSNHhWKfpIMhPpLkjfLYAvFRHu5Ja7Uk8ZGgzgS94PfL+fBbLUumZ6np9V4rY3khCGqL81x1jkQgxowcauVkBIlGFBIXQd8P0hbER4IGvImmQHyY6DU9NidFfLS2Er3zViW9sriSFi2oorf5sbOcf2E7XXpZG116RTtNPSdcdEPqkeVvV/FGf6tYcEikY5c0mC3TWWhcwBGOGY1NNOPdd6lvNkncmkp18GDuuNYxZ+YSxS3hcc40PU5IQC0QHwlwQplNgPgoswMS0nxXEh/u1a2cq1+5p1wp9zhnv/itdiXn7vlkf+jVrpw5Hm7BEiQPQ0Ur1L50zojNyrWbctEM9wyeUtoSLsWIq4QM96LNiH3aVb61o6UXJibcQHwUPf6MP7Hc4qP+QAU9+ZsqmveLatq7p2Mp3D6nZuiyy9vpiqvbrPu6/uGiG+IY2VVciQ2ZUnWQdw+X0oNXp5LIhgiOi1rbaOaCF6nHwhetHcWdeRvEu4nLpn5Nn7uMmi6/ippFbPBraSwQH2n0arg+QXyE45XWo9MmPrz8JHkVIg6eW7Dcd58PWUDIPQ1L6nILFq9rQmd0JMzFuQiMLTt250x2538UWoHKnY+iKpLpW9JX9b5KEJf3JXG8mNWu/KZlOZciTutnRPoVu/hQYbYLpk3stPKBe26gSdAhPkzyll5byyU+NrxbyYKjiv7wTDXxZuBWkelTN36BoxuXt9F5F7SHvs6X1ajs6VTH7YRxjnI0ky1aBkrCuORvSITj2HGatnABdV/4F2tn8QpHnkfb6SOpkYWGiI2mSy6LZDdxvR7UUxvEhx6OJtcC8WGy9/TZnhbxoY8IagKBkwnELj5UuErm4Ml6yWrun0pawlK7GKYmEYhTfEiUY+FL9rSqBS9VEadeEOdx09XXtNGVHOG46pp26lcXLsLR0C4rVInYkOlUJ2itQ0iMqq7NRThmHqyncS+9SN3/8ifq9vprRGraFUcymi7+HDVeP9sSG61njDHJfdpshfjQhtLYiiA+jHWdVsMhPrTiRGUpJVA28TF71gwSIaKmWYVZdi1pvkDkI2keic+eOMTHJt5pfOECvrHgWMtL5Koohy042uiSy8LlcOxta7XFRjZhfLMjYXyyJIxzdEOmVF329ls0eOUK6rZiGdWuWE4Vx49ZbUt0o/nCi6npszOo+aKLSXI5unqB+OjqI4AI4gNjQAhAfGAcgEBhArGLD5leNXHcSCuRyPkYmwwWdhaOSB6BKMXHK4urcpGOXR/Z+RyyD4cIjquubqfxE4OLjgbO11jIO4z/mXcXX8qb/h3LdJw7lsMn1/XsTZdXVtHFa9dQ7RvLqXb5Mkt0UDbPo/XMs1hwXERNF7HgYNGRtE3+yj0yID7K7YHytw/xUX4fJMECiI8keAE2JJ1A7OLDDUSiH6oUWk86qTAR+UiqZ6K3S7f40Dm1qokFxiIWGs8eP0JLWHQ0OXYYl703ruAN/25sy9CZq1dZYqP2jdep9s1VOWgtk89moXGxJTZEdMheHCjeBCA+MDIgPjAGEPnAGACBYATKLj6CmZnsoyA+ku2fKK3TJT50Ta2SpPEVnMPxLE+ReuHYkVyEo7qigj7LU6lu6NGbZh07RsNWvcFTqVhwsOio2bA+h0hWpxKxIaKjiW8mbfQXpZ8L1Q3xUYhQ+t+H+Ei/j4P0EJGPIJRwTFcnELv4wA7nXX3Ipav/pYoPmVq1KJvP4ZxaJfkcV3MCeZCpVbIi1TLO31jGUY5ljcdoQzaHo5YFxwyOcMzo3ouu3L+fJnOEQ+VvVG9533ZEZWU2d4MFB0+rEuGRqeUsdpRQBCA+QuFK5cEQH6l0a+hOQXyERoYTuiABiA8NTkfkQwNEQ6soRnzI1ColOBbyylWiFWTVqquyCeRXcj5HkH05VnDS+DJeFvd1Fh6r+bEqn+XpVBfzPhyzPtpN09etoW4ypYqjHFW7PrIOyfToaSWKWwnjnDguogOlNAIQH6XxS8PZEB9p8GLpfYD4KJ0hakg/gdjFh8n7efgNB4iP9H9Q/HoYRnxs3ljJS+TaS+WuWW2vWjV8RMZKIBfBIftzFCpv8VK4r/O0qtf5fhnncagzpvIqVRd360nXb9tGF/DO4t05aVxER+X+T60q2/v1y06nsvM3WqaeW6gpvB+CAMRHCFgpPRTiI6WODdktiI+QwHB4lyQQu/iQ3Syd+3ukgTrERxq8WFwfgoiPUqdWvd/SxNENFhs8pUpEx5F2W3KcyeGSGRzl+MKGjXTh2jep94rXqRuLjoojDdb7bUOG2pENFhsS5WgdP6G4TuKsggQgPgoiSv0BEB+pd3GgDkJ8BMKEg7o4gdjFh3N1Ky/2at8Pk/wC8WGSt/Ta6ic+Sp1atYs38bPFhkytOkH7eG8OKcOra2hmTTe6mffg+OyaNdSP9+GQKVUVLbzjIJfWUaOzK1TZokOeo0RPAOIjesZJbwHiI+keisc+iI94OKMVswnELj7MxuVtPcRHGr0arE9u8VHK1KoDHNF4nZPGRXAs5VyOnbKFOZe6qiq6gpfEvWX9evrsm6tpoAgOXq1KFYloNGUjHNYeHBzxQImXAMRHvLyT2BrERxK9Er9NEB/xM0eL5hGIXXz4rXb1yC+epWeeX0JL5z9iHEWID+Ncps1gJT6e/WOLtQO55HN89KG9IeC0z3RsCDhhkveGgCd4Lw6Vv7GMczk2NXP2OZfu1kpVPemGj/fRX/3xWTr9md9R1Z7dObvbhg6jxs9fT43X/hU1Xfw5oupqbX1CReEJQHyEZ5a2MyA+0ubR4voD8VEcN5zVtQgkRnzMf3EZ3f/Q44RpV11rAJrc24P1FbRkUTUtXlhFf3qhwlq1imdF8RK5kkDOu5DzUrl+q1a9zpGNZRzhkJWq1jhWqrqIBcdVTc1000sv0vj5f7B2G1el7fSRdPzmL1HTZVdihaqEDRyIj4Q5pAzmQHyUAXoCm4T4SKBTYFLiCCRGfHzvRz+nZavWI/KRuCECg9wEZGrVwuzeHM5Vq5Tg8Fu1qr6tjZ451kDP8uZ/GziJXJUhVdX0leZWum31ahqz7DXq9srLuShH6+ix1HTp5Xy7wrrP9OwFhySQAMRHAp0Ss0kQHzEDT2hzEB8JdQzMShSBWMSHimoU6vmD3/06zZ41o9BhiXsf064S55JIDHp1CYsO19Sqz5zXTtdfX0EXX9JMflOrVnCU44mjDfTiiaPUxDuQS5E8jlksJL755jqaykviiuCoWf+29V77qadmxQYLjksuJ4l4oCSbAMRHsv0Th3UQH3FQTn4bEB/J9xEsLD+BWMSHs5vY4bz8TocFwQnI1KqF2b05FrDwcE+tuu6viEYOr6YDDR2RDKldRTl+x5GOLdkdx+X1y3iDv7/buYsuf2MF9Xh1sSU6KCtImmZckotytJwzLbiROLLsBCA+yu6CshsA8VF2FyTCAIiPRLgBRiScQOziI+E8ijIPkY+isCX6pM2bJMphbwj45ip7Q8Bhwzs2BLzsCnuvDedqV5I8voRXq1rCS+Qu4WjHXl4uV8pkXhr3C0eO0I0rV9LEZUupG4sOtflf64SJ1ChTqi6xp1UhcTzRw8LXOIgPM/2m02qID500za0L4sNc38Hy+AhAfGhgDfGhAWJCqpCpVSI4ZHpVp1Wrsgnk7qlVIj62VbTS/P2HWXgcoxXZ5PHelVV0peRyvPkmXbT8der32itU/d4mq5ftAwflcjgkl6Nt8GkJ6T3MKJYAxEex5NJzHsRHenxZSk8gPkqhh3O7CoGyiI+Zs++l+kNHPBljtauuMvSS00+ZWrUom0AuokNWu5VVq66yBAevXMWrVvXvb+dqqHI8G+V4rfk4vXxcohz2nhxn13ajr7z3AV3L+3CMWfoa1S5fap/COR5W4rhEODiPo2XS5OQAgCUlE4D4KBmh8RVAfBjvQi0dgPjQghGVpJxA7OLjxrn3U/+6PvTLh+9LDVpEPsx0ZdCpVc7ebeD8jcWcOP7KiRP0Bu/LIeVUFha37ttPt65eRdNXLKfeMq2qocF6r2XquR1RjpmXmgkKVhckAPFREFHqD4D4SL2LA3UQ4iMQJhzUxQnELj6QcN7FR1wCuh92atVR3nn8Fd6PY7Hkchw/Rvv4uZSLWlrpb9aupStXv0GDFi+h6h3brNfbho+wBQdHOOS+vV+/BPQaJkRJAOIjSrpm1A3xYYaforYS4iNqwqg/DQQgPjR4EZEPDRAjruLQQXvVKplWlZtaxZuCy7Qqv6lV65ubcsnjq1h8SDm1qpL+dv1GunHVSpr8+lLquWa19XqGV7Gyp1WJ4LicWseOi7hHqD5JBCA+kuSN8tgC8VEe7klrFeIjaR6BPUkkELv4kGlXV86cTvfedVOieKzftI3m3PMDeurRB2jKhNE52/z2KHHmpkB8JMqVnYyRqVUqn8O5apXaEFCtWqVOOtIuK1ZxhIMTx5ccP0qfZqMcX9i9m+60kseX0yBOHq9oarROab3gQqq4+mo6eOEl1HzBZ5MLApZFSgDiI1K8RlQO8WGEmyI3EuIjcsRoIAUEYhcfcjH/08eeTtRO5s4EeC/xUcheiI/kfRJee6VjQ8APd1ZYBp47vZ2uziaQT5zU3snodyTKYYmO47Q6G+UY03CY/nbNOpq1cgWNXbaMavbssgWHY9dxuupK6tW/70n7fCSPCCyKkgDER5R0zagb4sMMP0VtJcRH1IRRfxoIxC4+JOcjXynXalf5Ih8QH2YM9dzUKlkq98XsqlXZqVVWpGNW51WrGiTKwXkci2VvDk4iP8DPpdy9Zi3dIsnjvERun3ffsV7z23Xcuc+HGZRgZRQEID6ioGpWnRAfZvkrKmshPqIii3rTRCB28ZFUeGGmXbkFEiIf5fVq2KlVIjqePHqYHj9yiPa22RsBnsKrWD3w8mK667dPUN2Gd3Mdaj3zLDo+53Y6cfOXqG3osJM6CvFRXt8npXWIj6R4onx2QHyUj32SWob4SJI3YEtSCUB8ZD3jJz7cjvvat39CB+ob6I/zHsy9degobwyBEjuBJYsr6cW/VNBLf6mkndmpVZ/5TIZmfb6druEox+Qpnffm2MYC4/HDh+jXhw7RMd6nQ8o5/Pin//ksfe7pp6h63yfWa5n+A6j5r2+m5tvupLZp0/P2q5oT0LvXVtHRE/Y+Hyhdk0DfU2oJ3wNd0/eq16f0qKHG5jZqbes8pbNrU+l6vZfvAhQQAIH8BMoiPiTpfMuO3ZZlD3736zR71gyS6VgXTJtQtv0/gooPdZwz+nG8yV56FSV6Agfrif7CguPPL9i3pibeEJCnVl37+Qx9/jr7NmBAhx1yGfAn3nPjhSNH6IVjR+lgqx3p+M7WLXT3b39DY//0PCdx2K+1T59OrX/399T6hS8Sde8eqDOsPUgESFMLLjgCAUvpQT27VRG+B1Lq3IDdkiioCA9oj4DAUnqYfBeggAAIJEx8ODcZlETv79x9qyU+HvnFs/TM80vKlogeVHyo1a+w2lW8H633NksCuaxcVUWrV/IVP5ehwzL2MrlXt9PlV3YWgPt5laqXeE+OBZzLsYgTyaVMOnCA/usbb9A1r75CIxYtsAXHoMHUeM3nqXHWddR49bVEFXZyetCCaVdBSaX7OEy7Srd/g/QO066CUEr/MZh2lX4fo4elE4g98iERDrWilFN8eF3Ul9694DX4iQ+xcen8R3IVee3QjpyP4JzDHimrVongkL05nKtWXZVNIHevWvU+T616iQXHAhYca7PL4X5hy1b6Oq9WdfEri+nUd96yTGiZMjUnOFrOzT+1Kp/NEB9hPZrO4yE+0unXML2C+AhDK73HQnyk17fomT4CsYsPuZj/9x9/y9pLIymRD+dSu4K2rm/vnOBwThGT97ymhkF86BuQUpOsWiV7cyxgwbGIb2pqlb03B0c6rmnnqVWd8zlWNB6nBbxy1YLjx2lHq52D8503VtKcZa/R2YsXUe3HH1uvNV55DTVJpINvXgnkYXsC8RGWWDqPh/hIp1/D9AriIwyt9B4L8ZFe36Jn+gjELj6+96Of07JV662LeyU+xowcam3wd8PVF9GPv/8Nfb2LqSaIDz2gw06tas1kOMohU6vs6VWyitXw+nr6hxUr6LrXXqXRLy/keVXt1M4J5Na0qqzooCp9c3IhPvT43vRaID5M92Dp9kN8lM4wDTVAfKTBi+hD1ARiFx/SIa9dw+++84bE7XoeFD7ER1BS3sfJUrnzflFFz/yu2opySBkyNENz72ql2+5oo7r+naMc+zifYwHvPv4S3xZzxEPKFVu20Ddff50u4XyO/m+ttV5rmTSZBcd1VqSjefp5pRnpczbERyRYjasU4sM4l2k3GOJDO1IjK4T4MNJtMDpmAmURHzH3MfLmID6KQ9xwuIL++z9V05NP8HJV2XL+he309W+00jWfb7NWsXKWzZzPYYkOjnS81dxovXX3ypV0B4uO6Ty1qvseewW1psuvtESHNbVq+IjijAt4FsRHQFApPwziI+UODtA9iI8AkLrAIRAfXcDJ6GLJBGIXH7JPxsq1m8i9UV+5l9othSTER3h6f/h9Ff3TP9ZQ/YEK6taN6Iu3tHKko40mTT55ydoVTSesKMcCXr1qZ1sLDTx4kL7Nq1Z9gadWjeOpVRW8VG57XV1OcDTxqlWZ2njWWof4CO/7NJ4B8ZFGr4brE8RHOF5pPRriI62eRb90EohdfEiexy3XX3bSFKtyL7VbClSIj+D0li+rpKd+W00iPqTMvqmN5tzeSjMv6Sw6WjifQ3I5LNHBieRHOHfj/K1b6e+XL6crX11Cg9eusc5vnTDRFh0sOJrPvzC4IZqOhPjQBNLwaiA+DHegBvMhPjRATEEVEB8pcCK6EDmB2MWHRDjUxoLO3pV7qd1SSEN8FKa375MKFh1V9DsWHrJk7uQp7Sw62uhLd7R22s9PksifPdZA/3bkEG3haVZSrntjBf1vy1fQTBYd3T/60Hqt6ZLLcwnkbSNHFTYgoiMgPiICa1i1EB+GOSwCcyE+IoBqYJUQHwY6DSbHTiB28YHIR+w+LnuDLzxfZQmPxYuqLKEhgkOEhwgQVZTo+H8bDllL5dYdPky3L1tK3+BIx6SXF1FFcxO1n3oqJ49nV62a9XnKdAu2C3mUACA+oqRrTt0QH+b4KipLIT6iImtWvRAfZvkL1paHQOziQ6ZXPfbEc7mNBqXbaoM/U1e8QuTDe/DK0rm/Y9EhwuNIQ4U1tUqmWMlUK1U+5nyNF3iZ3Bd4etVKzu2YxFOrvrliOV3P+Rwj3lxtHdY6bnwuytF84UXl+aT4tArxkSh3lM0YiI+yoU9MwxAfiXFFWQ2B+CgrfjRuCIHYxYdw8Vpq12sqliEMCeKjs6dYT9BTT1ZbomPdmkpr2VyJdMy5rZWGj7CXzd3dxqLj2FH604kjtIZ3Ir9i1Ur6G1616ipeKrfvhzutY5pmXmqJjqZrrqXWM8YkcjhAfCTSLbEbBfERO/LENQjxkTiXlMUgiI+yYEejhhEoi/gwjFFBcyE+OhC9scJOKP/9U3ZC+fWzOa+Dox2XXGZPsZLVqkR0vHD8CG2vP2BFOO56fRnNWLKYqhsbKdO7TzbKca11n+nZqyD/ch4A8VFO+slpG+IjOb4olyUQH+Uin6x2IT6S5Q9Yk0wCEB8a/ALxQbR/fwX97jcyxaqadmyvoImT7IRymWbVi/XDNs7j+FNWdLR+8B5d/+qrdCfndExZ86blgdax46wVqxo5l6P5opkavBJPFRAf8XBOeisQH0n3UPT2QXxEz9iEFiA+TPASbCw3gbKID0k6rz90xLPv7v0/yg0oSPtdXXz85QU7r2PRgiqS7TVEcIjwmHpOO73f0mTlc7zAy+Ye3Lub7vvVr+hv5j9LPY7bO5PLdKpjd/0NnfjSnVZCuWkF4sM0j0VjL8RHNFxNqhXiwyRvRWcrxEd0bFFzegjELj5unHs/9a/rQ798+L7UUOyq4uOD92X5XM7teLKKDh2soItm2AnlX7y5jTY1c6SD8zn+zBsDNny8m77LouOeP/yeapuaLL83XXEVi467rWiHyQXiw2Tv6bMd4kMfS1Nrgvgw1XN67Yb40MsTtaWTQOziw2+fD5PxdjXxwVtx5PbsWLO6kgYNzvDyuXZC+eEhjVY+xwssOureWUdzFi6kO3mp3EG7PqJMj5504sabqHH2F6nxymtMdnnOdoiPVLix5E5AfJSM0PgKID6Md6GWDkB8aMGISlJOAOJDg4O7kvhYvVKWz62mpznaIeW6G0R0tFHdzGPW1CoRHgPWv023LVpId7Dw6CQ6RHhcNUsD8eRUAfGRHF+U0xKIj3LST0bbEB/J8EO5rYD4KLcH0L4JBGIXHzLt6sqZ0+neu24ygU8gG7uC+Kg/wFOsWHDINKutWypo/ASeYsWi46w5R2lJhb161Wnr36E7WHTctogjHbwTeaZ7DzvSITfDp1f5DQSIj0AfkdQfBPGRehcX7CDER0FEXeIAiI8u4WZ0skQCsYsP2ePjp489TUvnP1Ki6ck5Pe3iY8GLdkL5S3+poupqTijn6VVTvnqE3h9+hP7EyeTDNqynL7Po+JKIDt6jQ3YePyFTq1IsOtTog/hIzuewnJZAfJSTfjLahvhIhh/KbQXER7k9gPZNIBC7+JCcj3wFq10lZ9hs2yrL59oJ5RL5uPCz7XTNXSdo0+f207PHGmjKpk2c07GAvsI5HYOzokMEhxXt4D06ukKB+OgKXi7cR4iPwozSfgTER9o9HKx/EB/BOOGork0gdvGRRtxpjHxITofsUr7qjUoaODBDN9zVREdv/pTmVx6iiSI6ONIxVxLJd+6gTG03K4m8K4kORD7S+Ekuvk8QH8WzS8uZEB9p8WRp/YD4KI0fzu4aBCA+NPg5TeJDVq9SuR3tvCn5575ynOruOETvDG6gPtb0qgVWTsdgJTpUpGPWdRpImlcFIh/m+SwKiyE+oqBqVp0QH2b5KyprIT6iIot600SgLOJD8j7uf+jxThwf/O7XafasGUayTYP4OHzITiiXaVayf8cZFzXR6L+tp92TGqj7pnc40rGAvsyRjiE7JNJRy/kc2UhHFxUdiHwY+VGNzGiIj8jQGlOw4VJ+AAAXYElEQVQxxIcxrorUUIiPSPGi8pQQiF18PPKLZ+mxJ56jpx59gKZMGG1hXL9pG8255wd09503GLkKluni4+WFIjqqSHYqr6hrpen3H6SjMw5St+1v0828XO5XeYrVUCvSwaLjhmxOx7V/lZKPQGndQOSjNH5pORviIy2eLL4fEB/Fs0vTmRAfafIm+hIVgdjFx8zZ99It1192ksgQUfLM80uMXAXLVPGxY3t2h3JeyerTo+10xjcPUfV1B6nnvnWW6JBE8uE7tlOmpsYWHbKCFURHp88ixEdUX01m1QvxYZa/orAW4iMKqubVCfFhns9gcfwEYhcffjucq6lYWO0qnkHwH0/be3as4ITyU754kAZwXkefxjWW6JC8jtNlepUSHbJ61eevj8cww1qB+DDMYRGZC/EREViDqoX4MMhZEZoK8REhXFSdGgKxiw9EPso7dt5aKzuU28KjdeZhOu0rB2lQjzct0XHHywtp1HaOdPBmHrlIB0RHXodBfJR3PCeldYiPpHiifHZAfJSPfZJahvhIkjdgS1IJxC4+kPNRnqFw5AjRU9k9Ozb3PUa9bzlEY4a8STe9/CLdwcLjDJlepUSHRDquu6E8hhrWKsSHYQ6LyFyIj4jAGlQtxIdBzorQVIiPCOGi6tQQiF18CDmsdhXv+Fm8SPbsqKIXdjUSXXOIpk1cTbNf+wsvmbuQxkiko6qqI5H8r26M1zjDW4P4MNyBmsyH+NAE0uBqID4Mdp5G0yE+NMJEVaklUBbxkTaaSU04/3CnLJ9bTU+sbKb68w7TOZNX0xdW/pl3JV9I47Zvo0xlZceSuRAdRQ1LiI+isKXuJIiP1Lk0dIcgPkIjS+UJEB+pdCs6pZlA7OLja9/+Ca1cu4ncieWSiH7BtAn0y4fv09zF6KtLovh49j+q6LdPVdIbZ9TTpKuX0y1LXrTyOiaw6CAWHbIb+Qlewarx+tnRA0pxCxAfKXZuiK5BfISAldJDIT5S6tiQ3YL4CAkMh3dJArGLDyScRzvO3nmbE8p5z44n9x6js65bRje/+ycWHQto4jYWHRUV1nK5EB36fADxoY+lyTVBfJjsPT22Q3zo4Wh6LRAfpnsQ9sdBIHbxgaV2o3HrsWOcUM4rWD3+7nHaN3Ef3ffRz+i/Pvkb6iuZ5lyaLv4cHf2H71v3KPoIQHzoY2lyTRAfJntPj+0QH3o4ml4LxIfpHoT9cRCIXXwg8qHfra8uqaTHlrTSaz0P01+f8jT9j5//M43as8dq6PjFM+nEP9wP0aEfu1UjxEdEYA2rFuLDMIdFYC7ERwRQDawS4sNAp8Hk2AnELj6w1K4+H+/eVUH/8z8z9NShBho5cjX97OkH6cqVb1gNHJl+HjU/8N8hOvTh9qwJ4iNiwIZUD/FhiKMiNBPiI0K4BlUN8WGQs2Bq2QjELj6kp1hqt3R/P/tsJT3y/jHq3uMN+vKOp+nLf3qeBh48SPXnTqeqL91Jx2+9jTK9Tim9IdSQlwDEBwaIEID4wDiA+MAYUN8FIAECIJCfQFnER9qcEudqV++ur6SfLj1Bb7fsoNuP/ZbufOF5Oue99+jo0KFEt95hiY7WsePShjix/YH4SKxrYjUM4iNW3IlsDOIjkW6J3ShEPmJHjgYNJADxocFpcYiPRt4f8GfPtfIUqyN05fEn6c5XnqPPL1tq7dVx6JYvUfucO6hpxiUaeoMqwhCA+AhDK73HQnyk17dBewbxEZRUuo+D+Ei3f9E7PQQgPjRwjFp8/On1DP3L+0eo7vjL9OW3/mBNsaptaaH6z11GFV+6g07c/CUNvUAVxRCA+CiGWvrOgfhIn0/D9gjiIyyxdB4P8ZFOv6JXeglAfGjgGZX42Lungh54/SjtOPwu3brtKZ5i9Sc6Y/duOjRuPFWK6LjlNmobfJqGHqCKYglAfBRLLl3nQXyky5/F9Abioxhq6TsH4iN9PkWP9BOA+NDANArx8X8vbqL5+/fRrN2/sfI6Ln7rLTpxyqnUdtvtdOLW26ll6rkaLEcVpRKA+CiVYDrOh/hIhx9L6QXERyn00nMuxEd6fImeREcA4kMDW53i48+bWuhfthyhUbufoztfnW/tTi7l0PWzqZ1FR+Os6zRYjCp0EYD40EXS7HogPsz2nw7rIT50UDS/DogP832IHkRPAOJDA2Md4qOlmej/fOkEbW5bTLcvnm/ldfRraKDDUy8guvN2e+ncHj01WIsqdBKA+NBJ09y6ID7M9Z0uyyE+dJE0ux6ID7P9B+vjIQDxoYFzqeLj+RXt9NiejXT1Rl7FivM6Jm/ZQg2DRlAFi44TsnTu6LEarEQVURCA+IiCqnl1QnyY5zPdFkN86CZqZn0QH2b6DVbHSwDiQwPvYsXHex+3039bw7uTr/8t3f76s3T1ihXUVlVNh//6Nmq//XZqvmimButQRZQEID6ipGtO3RAf5vgqKkshPqIia1a9EB9m+QvWlocAxIcG7sWIjwdfO0F73nyRbnz3GWuKVWV7O314/hXU+y5exeqLt2qwClXEQQDiIw7KyW8D4iP5PoraQoiPqAmbUT/Ehxl+gpXlJQDxoYF/GPGxYHMr/eeydXTBu7w7+cLnaMQnH9OukROoz9fu5LyO26l9wEANFqGKuAhAfMRFOtntQHwk2z9xWAfxEQfl5LcB8ZF8H8HC8hOA+NDggyDio6WVE8r//DH1X/5rmvPGH1h8rKeGU/rSpzfeRn2+fie1TJmqwRJUETcBiI+4iSezPYiPZPolTqsgPuKkndy2ID6S6xtYlhwCEB8afFFIfPxqTRN9+MLvadb6p+gLSxZbLb4zczYNv+dOarz6Wg0WoIpyEYD4KBf5ZLUL8ZEsf5TDGoiPclBPXpsQH8nzCSxKHgGIDw0+8RMfWz7N0O+efpXOfpMTypfMpz7HjtHGcefTKXPvoJqv3EGZbt01tI4qykkA4qOc9JPTNsRHcnxRLksgPspFPlntQnwkyx+wJpkEID40+MVLfDw6fyt1X/Br+uKq/6DxO7bTroEjaPfnb6Mz7r2TWkeN1tAqqkgCAYiPJHih/DZAfJTfB+W2AOKj3B5IRvsQH8nwA6xINgGIj6x/1m/aRnPu+QE99egDNGVCZ3Fw49z7acuO3daRY0cNoz/Oe7CTV53i4+X3m+iDX86jS9c8RZevW0nN1TW0/JJbafK3vkLNF16c7NEA60ITgPgIjSyVJ0B8pNKtoToF8REKV2oPhvhIrWvRMY0EID4Y5szZ91L9oSMWVrf4+Nq3f0IH6htygkOESP+6PvTLh+/LuUHERyZDNO//eYHGLP0NzXntj9Z7y6deTtW33kHDvzFHo8tQVZIIQHwkyRvlswXio3zsk9IyxEdSPFFeOyA+yssfrZtBAOIj6ye/yIcIk+/cfSvNnjXDOnL+i8vop489TUvnP5Lz8OOPv0Ft839NN6z8PQ3Zv582nD6Btl11O533D1+h9v79zRgJsLIoAhAfRWFL3UkQH6lzaegOQXyERpbKEyA+UulWdEozAYiPPOLDS5C4X/v/vvojOm/ZkzRtywY60KcfvXrxLXTW382lfhdg6VzNYzWR1UF8JNItsRsF8RE78sQ1CPGROJeUxSCIj7JgR6OGEYD4KFF8UEWFVcOKCRdSz5/+K42+5GzDhgDMLYVAVVUF1VZX0Ykm3sgFpcsS6N2zho4cb+my/UfHiXp0q6bm1jZqa+M5uChdloB8F6CAAAjkJwDxUaL4ePLab1DNuRfSrH+8E2OtCxKA+OiCTvfoMsQHxgHEB8aAEID4wDgAgcIEID7yiA95yyvn4/6HHqcNr8zL0S20yWBhN+AIUwlg2pWpntNrN6Zd6eVpYm2YdmWi1/TbjGlX+pmixvQRgPgoID6CrnaVvqGBHgUhAPERhFL6j4H4SL+PC/UQ4qMQoa7xPsRH1/AzelkaAYiPbHRDLbUrOOv69u60mlWYfT5KcwfONo0AxIdpHovGXoiPaLiaVCvEh0neis5WiI/o2KLm9BCA+NDgS0y70gDR0CogPgx1nGazIT40AzWwOogPA50WgckQHxFARZWpIwDxocGlEB8aIBpaBcSHoY7TbDbEh2agBlYH8WGg0yIwGeIjAqioMnUEID40uBTiQwNEQ6uA+DDUcZrNhvjQDNTA6iA+DHRaBCZDfEQAFVWmjgDEhwaXQnxogGhoFRAfhjpOs9kQH5qBGlgdxIeBTovAZIiPCKCiytQRgPjQ4FKIDw0QDa0C4sNQx2k2G+JDM1ADq4P4MNBpEZgM8REBVFSZOgIQH6lzKToEAiAAAiAAAiAAAiAAAskkAPGRTL/AKhAAARAAARAAARAAARBIHQGIj9S5FB0CARAAARAAARAAARAAgWQSgPhIpl9gFQiAAAiAAAiAAAiAAAikjgDER5EuLbTreZHV4rQEEijG1+s3baM59/yAnnr0AZoyYXQCewWTwhIIMw6+9u2f0Mq1mzo1seGVeWGbxPEJIxBmDHzvRz+n5xYsxxhImA9LNSfMGHC2pcYDfhNK9QDOTwMBiI8ivCgXFgfqG+iP8x60zpYvo/51feiXD99XRG04JckEivH1zNn3Uv2hI1a38EOTZO8Gty3sOJAxsHT+I7kG5MJj2ar1nV4L3jqOTAKBsGNAfhd+eN9duT8fHvnFs/TM80swBpLgzCJtCDsGVDPzX1xGv3rqL7Rlx278JhTJHqeliwDERxH+lAuL79x9K82eNcM6W75YfvrY0/hRKYJl0k8p1teIfCTds+HsK3YcqFYwHsLxTuLRGANJ9Eq8NhU7BiZdOtcSHYiGx+svtJZcAhAfIX3jdRGBC4uQEA05vBRfY0wY4uQAZpYyDlT1+Nc7AOgEH6JjDMi/5h9s24U/qRLs53ymFTsGJAL21TnX0piRQyE+DPU9zNZPAOIjJNNiv4BCNoPDE0CgFF9DfCTAgZpMKGUciAnq/Ae/+/VctFSTaagmJgKljAHnNEzk/cTksAiaKWYMyHTLT/YftKZk4zchAqegSmMJQHyEdF0xX0Ahm8DhCSFQiq/xQ5MQJ2owQ8c4uPvOG+jeu27SYA2qKAeBUsaAsleiX4898RxBgJTDg6W3GXYMuKdj4zehdB+ghvQQgPgowpde8z7vf+hx/KgUwTLppxTra/zQJN2z4ewrZhzIxYd8L2DRgXCsk3p0MWPA3Rc19x8r4CXVy/ntCjMG1Offq0b8GWGm/2G1PgIQH0WwLHbFiyKawillJlDI1zKfV4pa+UyZC/FRZsdpbj7sOMAiFJodkIDqwo4BrHiWAKdpNiHsGHA2j98Ezc5AdUYTgPgo0n3FrvVdZHM4rYwE8vnaS3w453iL2XV9eyPJtIz+09V00HGgLjK82kXehy5vlKeeoGNArHMeq6zFlKvy+E1nq2HGAMSHTvKoK00EID7S5E30BQRAAARAAARAAARAAAQSTADiI8HOgWkgAAIgAAIgAAIgAAIgkCYCEB9p8ib6AgIgAAIgAAIgAAIgAAIJJgDxkWDnwDQQAAEQAAEQAAEQAAEQSBMBiI80eRN9AQEQAAEQAAEQAAEQAIEEE4D4SLBzYBoIgAAIgAAIgAAIgAAIpIkAxEeavIm+gAAIgAAIgAAIgAAIgECCCUB8JNg5MA0EQAAEQAAEQAAEQAAE0kQA4iNN3kRfQAAEQAAEQAAEQAAEQCDBBCA+EuwcmAYCIAACIAACIAACIAACaSIA8ZEmb6IvIAACIAACIAACIAACIJBgAhAfCXYOTAMBEAABEAABEAABEACBNBGA+EiTN9EXEAABEAABEAABEAABEEgwAYiPBDsHpoEACIAACIAACIAACIBAmghAfKTJm+gLCIAACIAACIAACIAACCSYAMRHgp0D00AABEAABEAABEAABEAgTQQgPtLkTfQFBEAABEAABEAABEAABBJMAOIjwc6BaSAAAiAAAiAAAiAAAiCQJgIQH2nyJvoCAiAAAiAAAiAAAiAAAgkmAPGRYOfANBDoagQe+cWz9NgTz53U7bvvvIHuvesmmjn7Xuu9pfMfOekYea+ubx/647wHrfcK1TXp0rl58db17W2187Vv/4RWrt3keeyD3/06zZ41g26cez9t2bGb1HN18PwXl9H9Dz1OY0cNy9nlriiIHTPOn0LPLVieO/WGqy+iH3//G6HaDdKPrjbe0F8QAAEQAIH4CUB8xM8cLYIACHgQUBfHTz36AE2ZMDp3hIiIRUvX5C7e5WL9gmkT6JcP35c75ns/+jktW7U+J0qC1uUWCW7xIO9LXQfqG3zFgxyjxIfbLvV6PvHhRKHEipcdXu+FaTdIPzAwQQAEQAAEQCBqAhAfURNG/SAAAoEIiKhQ/+jnO8F9Eb5+0zaac88POkUdgtalU3z0r+tjRUiUeFJ2iSApJF6C2OEnPoK2C/ERaBjiIBAAARAAgYgJQHxEDBjVgwAIBCMg06bOHD28U0TD70y5kP5g2y4r0iH//ssFuDMSEqYuaSNfxCHIRbvYMHHcSPpk/0EaPKCfNSVKojFS5LUoxUfQdoP0I5incBQIgAAIgAAIFE8A4qN4djgTBEBAIwElAFSVKufCrwlnrsSGV+Z1OixsXYXER5CcDxEBF0ybaOV4iD1in0RBfvY/fx+5+AjSLnI+NA5WVAUCIAACIFA0AYiPotHhRBAAgagIqClLqn6v6VhKMKhkdD9bwtRVSs6HiA+VBC62qGhMmIhDMTkfQdsNY0dUfkW9IAACIAACIADxgTEAAiCQaAIyfUlWenJHN7xyPQp1xK+uQpGPQtOm1LQrER9qlS0lZMJc9JciPgq1G8aOQhzxPgiAAAiAAAgUSwDio1hyOA8EQEAbAREST/7nIity4C7qotq9Cpaf+CimLp3iQ+yXnBO1HHCYi/5SxEehdsPYoc2xqAgEQAAEQAAEXAQgPjAkQAAEyk7AOTXKGeFwrhjlTCgXg/OJD1n9SkrQunSLDyfQMBf9pYqPfO2GsaPsAwIGgAAIgAAIpJYAxEdqXYuOgYB5BLw23PPL6Sg07SpMXYXER9CEc6/ITZiLfj871HQx5VHnJoMq58PtbXe7SDg37/MAi0EABEAgjQQgPtLoVfQJBEAABEAABEAABEAABBJIAOIjgU6BSSAAAiAAAiAAAiAAAiCQRgIQH2n0KvoEAiAAAiA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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.combine_plots(fig_list=[fig_fixed, fig_variable, fig_exact],\n", " xrange=[0, 0.4], ylabel=\"concentration [A]\",\n", " title=\"Variable time steps vs. Fixed vs. Exact soln, for [A] in reaction `A<->B`\",\n", " legend_title=\"Simulation run\") # All the 3 plots put together: show only the initial part (but it's all there; you can zoom out!)" ] }, { "cell_type": "markdown", "id": "3d37253d-7510-4384-abd6-4bb5cc18ef95", "metadata": {}, "source": [ "#### Not surprisingly, the adaptive variable time steps outperform the fixed ones (for the same total number of points in the time grid), at times when there's pronounced change. \n", "If you zoom out on the plot (by hovering on it, and using the Plotly controls that appear on the right, above), you can see all 3 curves essentially converging as the reaction approaches equilibrium." ] }, { "cell_type": "code", "execution_count": null, "id": "353e5490-2cca-4f05-8f60-b6a34524a715", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "d83e4e09-853c-46af-9669-295dcff914b9", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "4375bea1-4a14-486f-906d-92b5ba588e79", "metadata": { "tags": [] }, "source": [ "# PART 5 - Repeating Part 4 with a coarser grid\n", "#### The advantage of adaptive variable step will be even more prominent" ] }, { "cell_type": "code", "execution_count": 21, "id": "71c89174-9c43-428f-bac5-af9ef17e35d3", "metadata": {}, "outputs": [], "source": [ "# A coarser version of the variable-step simulation of Part 1\n", "dynamics_variable_new = UniformCompartment(chem_data=chem, preset=\"fast\") # Re-use same chemicals and reactions of part 2\n", "\n", "dynamics_variable_new.set_conc([10., 50.])" ] }, { "cell_type": "code", "execution_count": 22, "id": "e38d2dcb-1ea1-4728-a26f-126821669d6a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "14 total step(s) taken\n", "Number of step re-do's because of elective soft aborts: 3\n", "Norm usage: {'norm_A': 13, 'norm_B': 9, 'norm_C': 9, 'norm_D': 9}\n" ] } ], "source": [ "dynamics_variable_new.single_compartment_react(initial_step=0.1, target_end_time=1.2,\n", " variable_steps=True,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"}\n", " )" ] }, { "cell_type": "markdown", "id": "aa18698d-2dea-4a83-a166-de67565e918b", "metadata": {}, "source": [ "### Note that the variable-step simulation is now taking 14 steps instead of the earlier 19" ] }, { "cell_type": "code", "execution_count": 23, "id": "6ce6eae6-0c4a-4908-9670-d096445d08b4", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "SYSTEM TIME=%{x}
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig_variable = dynamics_variable_new.plot_history(chemicals='A', colors='darkturquoise', title=\"VARIABLE time steps\",\n", " show_intervals=True, show=True)" ] }, { "cell_type": "code", "execution_count": 24, "id": "5638d0b4-77e8-425e-ad5e-f80849abf4d3", "metadata": {}, "outputs": [], "source": [ "# Now, a coarser version of the fixed-step simulation of Part 2\n", "dynamics_fixed_new = UniformCompartment(chem_data=dynamics_fixed.chem_data) # Re-using same chemicals and reactions of part 2\n", "\n", "dynamics_fixed_new.set_conc([10., 50.])" ] }, { "cell_type": "code", "execution_count": 25, "id": "e8170d78-43f1-4b2a-ba68-43605a03c374", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "14 total step(s) taken\n" ] } ], "source": [ "# Matching the NEW total number of steps\n", "dynamics_fixed_new.single_compartment_react(n_steps=14, target_end_time=1.2,\n", " variable_steps=False,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"})" ] }, { "cell_type": "code", "execution_count": 26, "id": "a2052848-23c2-4524-8052-862d2b7a9795", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "SYSTEM TIME=%{x}
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", 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A (EXACT) :
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"gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Fixed vs. Variable time steps vs. Exact soln, for [A] in reaction `A<->B`" }, "xaxis": { "range": [ 0, 0.4 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "autorange": true, "range": [ 9.222030716226515, 24.781416391696215 ], "title": { "text": "concentration [A]" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.combine_plots(fig_list=[fig_fixed, fig_variable, fig_exact],\n", " curve_labels = [\"FIXED time steps\", \"VARIABLE time steps\", \"EXACT solution\"],\n", " xrange=[0, 0.4], ylabel=\"concentration [A]\",\n", " title=\"Fixed vs. Variable time steps vs. Exact soln, for [A] in reaction `A<->B`\",\n", " legend_title=\"Simulation run\")" ] }, { "cell_type": "markdown", "id": "a4399ddd-d4c7-4342-ab47-55f04d77b755", "metadata": {}, "source": [ "### With fewer grid points, the advantage of adaptive variable timesteps is more pronounced \n", "If you zoom out the plot, and scroll to later times, you can see that the advantage later disappears when there's \"less happening\" (change-wise), closer to equilibrium" ] }, { "cell_type": "code", "execution_count": null, "id": "d53d0255-2d5d-4d9b-8830-1f94b841f68c", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }