{ "cells": [ { "cell_type": "markdown", "id": "5cbc8640", "metadata": {}, "source": [ "### Comparison of 1) adaptive variable time steps, 2) fixed time steps, and 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` \n", "\n", "LAST REVISED: Dec. 6, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "3792d78d-7429-4221-a263-57b07d77b5bc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "import set_path # Importing this module will add the project's home directory to sys.path" ] }, { "cell_type": "code", "execution_count": 2, "id": "a29db1c7", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "\n", "import numpy as np\n", "import plotly.graph_objects as go\n", "from src.modules.visualization.plotly_helper import PlotlyHelper" ] }, { "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": 3, "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: {'A', 'B'}\n" ] } ], "source": [ "# Instantiate the simulator and specify the chemicals\n", "dynamics_variable = ReactionDynamics(names=[\"A\", \"B\"])\n", "\n", "# Reaction A <-> B , with 1st-order kinetics in both directions\n", "dynamics_variable.add_reaction(reactants=[\"A\"], products=[\"B\"], \n", " forward_rate=3., reverse_rate=2.)\n", "\n", "dynamics_variable.describe_reactions()" ] }, { "cell_type": "code", "execution_count": null, "id": "04be6f77-eb76-4c4c-a2f9-7c80ca9bd8f0", "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": 4, "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: {'A', 'B'}\n" ] } ], "source": [ "# 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": "code", "execution_count": 5, "id": "9853f4be-2b19-4c8e-a76e-6cef860dcf3d", "metadata": {}, "outputs": [], "source": [ "# We specify a particular group of preset parameters applicable to the adaptive time steps\n", "# Here, we're using a \"middle-of-the road\" heuristic: somewhat \"conservative\" but not overly so\n", "dynamics_variable.use_adaptive_preset(preset=\"mid\") " ] }, { "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": [ "* INFO: the tentative time step (0.1) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.04) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.04) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.016) [Step started at t=0, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "19 total step(s) taken\n" ] } ], "source": [ "dynamics_variable.single_compartment_react(initial_step=0.1, target_end_time=1.2,\n", " variable_steps=True, explain_variable_steps=False,\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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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0008877002358660705, 1.2276894262027755 ], "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=['blue', '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": "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 = ReactionDynamics(shared=dynamics_variable) # 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: {'A', 'B'}\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
00.00000010.00000050.000000Initial state
10.06315814.42105345.5789471st reaction step
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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
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.000000 10.000000 50.000000 Initial 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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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0008683068017366134, 1.2008683068017363 ], "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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MOfgAx2mP1jZ6uZGx36z46Wi6DqV7Xfcm7rQ4WVdmtYuAet7rp8txlFEtLvaLiZeLsl8GUaT3EounVvzJ2HzCbft6+8Wu2gU5jIhFcZ7ZmVnXHni9UTPTebnAu6V1il+1N0brXPxqacKc82HqtR+HTpSs1y+36Vdufcjpk26nN7Jq5TtdD+PgGqZ/Ka4mSyVfgwb2r0xvVs87rRerJhK6DzHs051013Cnm/RqN35Rjoj5aVe166Pufd1Pn/E68mW/tpgjaLq26K7xKr9aZnHStMO7JbX35Wrx97pUwK2d9g9xgvZ5r8fi9WZf12a7QJnMhg/ZS2ad88nKxmvqeft6MRO217b46Yt+rp9O5bqdI/Z+4PV92np/aq3Tnt8rD6/9zut7vtt54uV92s/9sZfZLao9fs8Dr0ycjrXHrhFzW89j/STJhOO0HbyaKqKmjKiHfVt56zCuVRScpoNVmzdun+rh1FmcRjXMdPuNGVF54/bT0XQXf93ruimYUbyZmm3wIhLVbnjVKFVQiXO6EXHqU9X6j46h7nUzniqduQWrLk+1183h82pfeWCtI8yF1mThddqM/YLn1G+qrSsw+6B9bZ5Kb90lyul4vF5ovVzg/YqY0/lsn3sexznvp94//uWNbiMw5s2/+q0Wl/u5kXC7VuimolrPN931Nq1raZj+pXhW69/Vnq8mYrobmjAiprvxi1LErHKqO7fdrofV+pa1fC99JqyIqfq83GOoD8GcHm73BCq9OVPG7SbPnCbmtDRDbcl/9exZVb8r03zv0O0M6eWa6vVYvL4HWdk67dBpP14zliqfdafEas+rdH7a4jV+fq6f1fq4U7zN56zTCd3SWd+nndrkFC8/PLz0Oz/v+W73N/YPwu3t9HN/bLZJ9z7o99rvdZSw5kXMeuJaO6H1Td4KwWk9mLkJiOrs5ncJVZsPb90wxC4E9rnjUX6PmLqwmo8opcgsU3VA+xbj9s7j5cIcVCySzletf5jt8LpJiJ92Ryliqt5qx2CXMz8XWnsfVmWp7yqav3DxHlsCe53eYV9DoM5T9emymrtvP8+c1huoY7Uek1Ma+7z3MBd4vyJmPYes30lU7fvXrGncvjvQ6zlvn7vvVK9582XlYmXm90bC6VqnNlFwu1m291e3622a19Iw/Ut3PXW6Ca4mYubz5hbxTt8j5rWPuN1Qmu9pXr5HzMuOcNWm63g5t92up7pPn732mShEzO366+WDQrMN1jWxTmuwreet/cMw+/GqNnm5B3La0CpMn/dyLH7eg9Rx2MustgmX0wfYKr/Th1TWc9Pre1eSIma9lzXrVX1CTbu0T/Xz+j7t1Efs/dNvbHT9zsrfXJfl9p7vxNjLB6Z+RMz6nm7/zl/r+6Cf8yDsyHiPGxHzc7NLWghAIPsE4lhnkf2jpoUQgEBQAnF8ABm0LT0hX9gbxZ5wjLQRAmkRCDswgYilFTnqhUAvJKA+cVOjatZtp71sNNELUXHIEICACwHdFHrgdRFAxOgNEIiHQBTXIUQsnthQKgQg4EDAPnVOJfH7VQiAhQAEIKAIVFsfC53uBBAxegQEoidgTs0M8j2m1tYgYtHHhhIhAAEIQAACEIAABCAAAQi4EkDE6CAQgAAEIAABCEAAAhCAAAQSJoCIJQyc6iAAAQhAAAIQgAAEIAABCCBi9AEIQAACEIAABCAAAQhAAAIJE0DEEgZOdRCAAAQgAAEIQAACEIAABBAx+gAEIAABCEAAAhCAAAQgAIGECSBiCQOnOghAAAIQgAAEIAABCEAAAogYfQACEIAABCAAAQhAAAIQgEDCBBCxhIFTHQQgAAEIQAACEIAABCAAAUSMPgABCEAAAhCAAAQgAAEIQCBhAohYwsCpDgIQgAAEIAABCEAAAhCAACJGH4AABCAAAQhAAAIQgAAEIJAwAUQsYeBUBwEIQAACEIAABCAAAQhAABGjD0AAAhCAAAQgAAEIQAACEEiYACKWMHCqgwAEIAABCEAAAhCAAAQggIjRByAAAQhAAAIQgAAEIAABCCRMABFLGDjVQQACEIAABCAAAQhAAAIQQMToAxCAAAQgAAEIQAACEIAABBImgIglDJzqIAABCEAAAhCAAAQgAAEIIGL0AQhAAAIQgAAEIAABCEAAAgkTQMQSBk51EIAABCAAAQhAAAIQgAAEEDH6AAQgAAEIQAACEIAABCAAgYQJIGIJA6c6CEAAAhCAAAQgAAEIQAACiBh9AAIQgAAEIAABCEAAAhCAQMIEELGEgVMdBCAAAQhAAAIQgAAEIAABRIw+AAEIQAACEIAABCAAAQhAIGECiFjCwKkOAhCAAAQgAAEIQAACEIAAIkYfgAAEIAABCEAAAhCAAAQgkDABRCxh4FQHAQhAAAIQgAAEIAABCEAAEaMPQAACEIAABCAAAQhAAAIQSJgAIpYwcKqDAAQgAAEIQAACEIAABCCAiNEHIAABCEAAAhCAAAQgAAEIJEwAEUsYONVBAAIQgAAEIAABCEAAAhBAxOgDEIAABCAAAQhAAAIQgAAEEiaAiCUMnOogAAEIQAACEIAABCAAAQggYvQBCEAAAhCAAAQgAAEIQAACCRNAxBIGTnUQgAAEIAABCEAAAhCAAAQQMfoABCAAAQhAAAIQgAAEIACBhAkgYgkDpzoIQAACEIAABCAAAQhAAAKIGH0AAhCAAAQgAAEIQAACEIBAwgQQsYSBUx0EIAABCEAAAhCAAAQgAAFEjD4AAQhAAAIQgAAEIAABCEAgYQKIWMLAqQ4CEIAABCAAAQhAAAIQgAAiRh+AAAQgAAEIQAACEIAABCCQMAFELGHgVAcBCEAAAhCAAAQgAAEIQAARow9AAAIQgAAEIAABCEAAAhBImAAiljBwqoMABCAAAQhAAAIQgAAEIICIRdAHdjR3yI7d7RGURBFpEhgxuI9s2dEqHZ3FNJtB3REQGDqwUXa3dkpLW2cEpVFEmgQG9q0XyeW4xqYZhIjq7ttYJ32a6mTrjraISqSYtAjU1+Vk6MAm+eCjlrSaQL0RExgzrG/EJVKcFwKImBdKmjRKwpSM8ejZBBCxnh0/a+sRsdqJJSJWO7FExGonlohY7cTSPBJELJ2YImIRcEfEIoCYgSIQsQwEIaImIGIRgcxAMYhYBoIQURMQsYhAZqAYRCwDQYi4CYhYxEA9FoeIeQRVLdl1110nV8+9NjMjYsufeEz23m+sTDj4kJBHFk32de+tlVdeWiFnzbggmgIjKOWeJXfIOed9XgYMGNittLRE7MXnnpKGxkaZetS0CI4ufBFbt2ySJ3/ziJz3uUvDFxZRCQ8v/ZmccMoZ8rERozyVGLeIrXztFVGcTjj5dE/tiTtRW1ur3LvkR3Lx5d+IuyrP5T+x7CGZMHGKjB03wXMep4RRidhba16XNa+vlNM+PSNUe6LMvGTRrXLRl640zv8sPJ5Z/lsZOnyETJ4yNZbm+BWxDzaul+ee+p2ce/4XYmlPkEIfuPtOOX36DBk8ZFiQ7JHneeWl56Sjo0OOmXZi5GW7FVhNxHbu2C6PPniPfPbirybaHrfKHnvoPjni2ONlzN77ZaJNb6z+i7z/3jtyymnTM9Ee1YjFt90gCxYsyEx7elNDEDERuXnRUrnz3mXd4v6day6VmdNPMp57cNlT8u0b7jL+PutT0+S6uZdK3z6lN05EzP10QcT0lxNETM8IEXNnhIjp+xAipmeEiOkZIWIlRoiYvq9US4GIBWdXizkRsbKIqeBePXvWHjF+8dXVctOipXLH9VfJkEEDDWmzpkXEELGwFwZETE8QEUPEwm6IhIjpzzNETM8IEUPE9L3EPQUiFpZgbeVHxDQipsRr7L6jKqNjdjFT3YE1YrVxUqQ1NbE26GXrKOKempito63t1kQ1NbG2KfWMo/M7NbFnHFXvbCVrxGov7qwRSyemiJjD1ERzWmJzS5ssuPEumXbU5IqIrVm7Tr61cLF8d/5lMn7/MUbUELF0Om/UtSJiURNNrzxELD32UdeMiEVNNL3yELH02EddMyIWNdH0y0tKxJwGNNI/ev8tcHIE/6WIIGI2akq0Zl9zkyycf5lMmTjOELHzzz5Fjpk60Ui5h4it/40U/nqztBzyHekcfFSQGJAnIwT696mX5tYOKfA1YhmJSPBmqBu+9s4C3wkXHGFmcjbV50VyIq3thcy0iYYEI9BQl5P6urw08/1+wQBmKFc+J9K3qV52tfDVPRkKS6imGB96RfAwBeWxJ1d0K80c5EhTxFTd8xculkU3zKkMpgQ9ZEQsKDkP+czpiJ8+dZp2REytEVsw4V+MUjs+dqq0TbpOOoce56GWeJI8vuwRGbv/OJl0yJR4KvBZ6jtr35YXnv+DnDfrcz5zxpd88Y9ukwsv+qIMHLhXt0oMEWvrlELCJvbMU8ulsalRjj3u+PgO2kfJmzdtkl8/+qBc/KXLfeSKN+k9//ETOfX0M2XUqNGeKurbVCftHUXp6Izn5v3VV16WLZs3yamn/YOn9sSdqLW1VX686Db52tfnxF2V5/IfefiXMvmQKXLghIM953FK2NiQF2Vibe3hvpz7jddXy+pVK+Xsc2eGak+UmW/71+/L5Vd8XRozsmvik0/8RoZ/bIQcPvXIKA+zUpaSsPr6nLS0eovlhvXr5PdP/lY+9/lLYmlPkEKX3PXvcs65M2XosOFBskee5/kVz0pHe4eccOLJkZftVmA+nxP1gZddxLZv3yZL7/25fGX21xJtj1tlD9x/t0z7+Cdk3/32z0SbVv71NVH3RmdOPzsT7VGNuPnG70Wya6I5mDH91OO67buwddsOmf+9xTL3ygtly9bt3fZeyAwEnw1BxHwC85Pcui5Mt0ZMidi3PvG81G98vFJF69CTZOeB35LWIcluJ6sawPb1+kizfb07I7av1/chtq/XM2L7ej0jtq93Z8T29fo+xPb1ekZsX69nFMX29aaYjBox1HHzO7MV5ojYnNmzjNGp9Rs3Gy8tuXVeZfaZ+l/J2xXzbpHXVr1pvG7dtdx87UsXnCk/uf83lTRq1O3wQw40ZrY5les0GmfKo5n+0EnjjA361MNav/r/y5+dXjk2REzfrzylUMFc9uQKuWhm6fuA7FMPve6a2PLhn2TA3/+P9N34iIiU5rYpEdt54LXSOjS5T6oQMX3YETFETN9L3FMgYnqCiJieESKGiOl7iXsKRExPEBHTM4pCxKxLe8zlPE41q/vqS755fTexUl8TtfTR5ZUdyk3RUrJmlqUGRjZ8sMX4CqmW1lZDktTD3NXcLNcUKbXTuf0e3v6/U5v/c/kLcuAB+8jQwQPlJ/c9LldcPMP4yiqzTbPOPsXYNwIR0/crTymc5rLardzte8RUJdbNOup3vSEDlZBt+KWIlKZFtQ0+XnaoEbJhn/TUJhKlQ4DNOtLhHketbNYRB9V0ymSzjnS4x1Erm3XEQTWdMtmsIx3ucdYadrMOr+uvqo1KWTfCU/fdb7+7odvImnWgREmSEjGrqDnJm/053eCKjq+1XYiYjlaCrzvtmli/e40MWHO99Ft/v0ixtJi1bdA02THhWmkddlqCraMqrwQQMa+ksp8OEct+jLy2EBHzSir76RCx7MfIawsRMa+kek66LImYGv26895le8AbPXKYsdFGFCLWp6lpjw357BXapy2q180pkupv+87qQaLNrolBqNnyuG1fX9f8blnI7pZcoa0sZMcYa8hahp8RQe0UERUBRCwqkumXg4ilH4OoWoCIRUUy/XIQsfRjEFULELGoSGannLAi5mdq4k2LllamFCoC9mVBSsTU4+rZsxwBeRn9UhndRsR0ImbOhrPOklPPrXh5pTE9EhHLSN9Vm3VcPfda2dHsvoVrXesGGfDmDdLv3SWSK7aUhGyvo4w1ZC0f+3RkR8MaMT1K1oi5M2KzDn0fYo2YnhFrxPSMWCPmzojNOvR9iDViekasEdMzimKNmG6zDnPtldOuiXYRswqPWp9lf0QhYmoNmZvw2TfrU21AxPRI4p1zAAAgAElEQVR9KfEUXkXMbFi+7QMZ8ObN0v/dH0uusNt4un2vI2TH+GulZcRZoduPiOkRImKImL6XuKdAxPQEETE9I0QMEdP3EvcUiJieICKmZxSFiKlaqm1fr6Rm2e+fN6YVehExp3KU6N3x04flSxeWBi+iWCNmbvBhHfUyhfFXv3mmsjmIkkGzTUdOmcCImL5LJZfCr4hVhKx9q/R/+xYZsPZHkuvcWRKygYfJzvHXSvPIcwIfACKmR4eIIWL6XoKIhWWEiOkJImKImL6XIGJhGSFieoJRiZiqyWkTPLedDE2Bs27WoZ6zb1+vnjO3j49qREyVacqYSclsqzl10fxiarU27LDJ4+XPK9cgYvoulWwKtzViupbkO7ZL/7d/IP3X/lDyHdtKQjZgijFlsXnkucYXmfJIhgBrxJLhnEQtrBFLgnIydbBGLBnOSdTCGrEkKCdTB2vEkuGcZC1h14gl2dZaqovNOiKIZhgRM6tXo2ID3rlD+r/1A8m3l77crn3AZNl54HxpHjkTIYsgTroiEDEdoZ7zOiLWc2KlaykipiPUc15HxHpOrHQtRcR0hHre64hYOjFDxCLgHoWIVYSs0Cz93/l36f/WrVLXttF4uqP/RNlhCNlnRHL5CFpMEU4EELHa6ReIWO3EEhGrnVgiYrUTS0SsdmJpHgkilk5MEbGQ3IOuEdNVmyu2Sr937zI29qhrfb8sZAfJzvHzZfeo86sKGWvEdGRFWCPmzohdE/V9iM069IxYI6ZnxBoxd0bsmqjvQ2zWoWfEGjE9oyjXiOlrI4WVACIWsj/EJWJdI2Tt0m/df8iANd+Xupa3S0LWb4LsHD9Pdo++YA8hQ8T0AUXEEDF9L3FPgYjpCSJiekaIGCKm7yXuKRAxPUFETM8IEdMziisFIhaSbNwiVmlesVP6rb9XBqy5Uep3v1ESsr7jZeeB/0t2j/6sSK7OeA4R0wcUEUPE9L0EEQvLCBHTE0TEEDF9L0HEwjJCxPQEETE9o7hSIGIRkI1yjZi2OcWC9N34Cxmw5v9Kw85VZSE7QHaO/1+ye8xFFSHTlkOCPQiwRqx2OgVrxGonlqwRq51YskasdmLJGrHaiaV5JKwRSyemiFgE3BMVsa4hMum78VcyYM310rDjz8aznX33l53jrpFde39BJFcfwZH1riIQsdqJNyJWO7FExGonlohY7cQSEaudWCJi6cYSEYuAfzoi1tXwPh88JgPXLJSG7X80nmwfcKi0DjtFWkb/k7QNmhbBEfaOIhCx2okzIlY7sUTEaieWiFjtxBIRq51YImLpxhIRC8k/sTViHtrZtPn3svyJX8uEuj/IYXuVR8n67Gt8D1nL6JnSNugYD6VEm2Tde2vllZdWyFkzLoi24BClsUbMHR67Juo7F5t16BmxRkzPiDVi7ozYNVHfh9isQ8+INWJ6RqwR0zOKKwUiFpJslkRMHYrarGOfMcPk8IGvSN/1v5TGj54TkaJxlJ19xkrzqH+S5tHnS/teU0MeubfsiJie04vPPSUNjY0y9ahsjF4iYvqYIWJ6RoiYnhEihojpe4l7CkRMTxAR0zPqDSK2ddsOuWLeLbLfmBFy3dxLpW+fRj2YBFIgYiEhZ1HE9t5vrEw4+BDjyNSXQvfd8Avps+6X0rjt+YqUdfQdJ82jZ0rLqPOkfeBhISlUz46I6dEiYnpGDy/9mZxwyhnysRGj9IlFJO6piYiYPgyImJ4RIoaI6XsJIhaWESKmJ9gbROzFV1fLA48ul+07d8vcKy+U8fuP0YNJIAUiFgHktNeIeT2Eutb1JSlTI2XbXuySsn4TpHmUmr54nrQPKAlcb3ywRqx2oh63iNUOqewfCWvEsh8jry1kjZhXUtlPxxqx7MfIbwtrfdfEmxctlROPO0yefv7PMnbfUTJz+kl+EcWSHhGLAGtPETHroRpStn6p9NmgpOylyksd/Q+S5lHnSfOYC6Wj34ER0Ok5RSBiPSdWupYiYjpCPed1RKznxErXUkRMR6jnvI6I9ZxYeW1pVCK2e7fICy94rTW6dP36iRx7rHN5alriwh/cLfO/fpH8/a33jZGxrExPRMQi6AM9UcS6SVnL+9J3wwPSd/0vKjsvqtfbB0wypi42j7lA1FTGWn8gYrUTYUSsdmKJiNVOLBGx2oklIlY7sTSPJCoRW7VKZPLk5PlMmiSycqVzvWpaohoJu3r2LDHXis2ZPUuOmTox+YbaakTEQoYg62vE/B5eXfO70m/DA9JHSdmOVyvZ2wdMMaYu7h5zgXT22d9zsawR06NijZieEWvE3Bm1tbXKvUt+JBdf/g09zIRSsEZMD5o1Yu6M2DVR34fYrEPPiDViekZRrhFbu1bkkkv0dUadYr/9RH760z1LbW5pkwU33iXnn31KRbzUNEX1UGKW9gMRCxmBWhMxK466lrXSb90D0meDkrLSdvjq0T7wcGOkbPfoWdLZd19XgoiYvoMhYnpGiBgipmYehHm8teZ1WfP6Sjnt0zPCFBNpXkQMEQvboRAxPUFETM8oShHT15ZsijVr18nsa26S9Rs3d6v40Enj5I7rr5IhgwYm2yBbbYhYSPy1LGJ7Stn9pZGynX/pkrK9jpTm0edJ86jzpbPP3nvQRMT0HQwR0zNCxBAxREx/noRN8czy38rQ4SNk8pR4vt7E79RERsT0EUXE9IwQMT2jWhaxB5c9JSteXtltTZjTKJmeUjwpELEIuPb0NWJ+EdQ3v1na6MOQsq4JuW2DjjamLxpS1jTab7Gpp2eNWOohiKwBrBGLDGXqBbFGLPUQRNYAvyIWWcUUFDkB1ohFjjT1AqNaI5b6gVgaYArXtKMm77FLohK0t9/dkPr0REQsgh7T20TMiqx+998NKVMbfdTvWl1+KSdtg4+VllGfMb48urNxZASU4y8CEYufcVI1IGJJkY6/HkQsfsZJ1YCIJUU6/noQsfgZJ11DLYpY0gyD1IeIBaFmy9ObRcyKQk1Z7LP+Qem74ZdSv/uNykvNI2dIx16HS/teU6Vt8MelUL9XBNSjLwIRi55pWiUiYmmRj75eRCx6pmmViIilRT76ehGx6JmmXSIilk4EELGQ3HvLGjG/mBp2/En6rH9INv79GfnD+gPli/v8rFJE+4DJ0jboOGkfcpy0DZ4m6rvLknzcs+QOOee8z8uAAd0XaKYlYqwR00efNWLujNg1Ud+H2KxDz4g1YnpGD9x9p5w+fYYMHjJMnziBFKwR00NmjZieUS2vEdMffbopELGQ/BExd4Bqs45XX1gu5328jzRseVYaP/qDNOxcJSLFSsZCw1BDyNoHf1zalJwNOlqK+T4hI1M9OyLmjnbrlk3y5G8ekfM+d2lsMfBbMCKGiLFZh9+zxn96REzPDBErMao2IrZzx3Z59MF75LMXf1UPM6EUiJgeNCKmZxRXCkQsJFlETC9ir7y0Qs6acUElYa5jhzQpIdv6rDRuXSGNH70kuWJL5fVirkHaBx5WkrOh06Rt8PGRbv6BiCFiIU97WfnaK6KE9YSTTw9bVCT5GRHTY2RETM8IEdMzQsQQMX0vcU/xxuq/yPvvvSOnnDY9bFGR5UfEIkPpuyBEzDeyPTOwRiwcxFyhXRq2/1EaP1ohjYacPSf59u7f99DZZx9pGzRN2oZ+vCRoAw8TydWFq9iWO62piZEeBIUZBFgjVjsdgTVitRNL1ojVTixZI1Y7sTSPhDVi6cQ0VRHbum2HXDHvFnlt1Zt7HH1WvmjNS1gQMS+U/KWp3/WGMY3RELMtz0l985puBRTz/YwpjG2D1VqzkpwVGgb7qwQRC8Ury5kRsSxHx1/bEDF/vLKcGhHLcnT8tQ0R88erJ6RGxNKJUqoidvOipcZRXz17VjpHH1GtiFhEIF2KybdvkqYtz0rD1j9I40fPSeP2V0WKHZYcOenoP6HbqFlH/4N9NYwRMV+4Mp0YEct0eHw1DhHzhSvTiRGxTIfHV+MQMV+4ekRiRCydMKUmYmo0bP73FsvcKy+U8fuPSefobbWaX/ymnr5u7qXSt0+jkUJ96du3b7jL+PusT03r9hprxNxDpzbrsK8RiyLYuUKLNH70QknKjE1Anpdc545uRRcahpR2Z1TTGdW0xsFqE5C+whox9wiwWYe+h7JGTM/oiWUPyYSJU2TsuAn6xC4pohIx1ojpw8AaMT0j1oiVGLFZh76vVEvBGrHg7GoxJyJWjqopYY89uaKbbL346mq5adFSueP6q2TIoIFiH8VDxNIRMadaG3b82Vhf1rjlaWnc+gepa9uwR7L2gVPl31aeK5858yjpP2CgdPSfKIWGQUa6tEbE2L5ef2ll10R3RmzWoe9DiJieESKmZ4SIIWL6XuKeAhELS7C28qcmYgqjkpqx+46SmdNPSp2q2RbVkBUvr6yMetnbaBczRCw7ImZvSV3zO9K47fmSnG1+Whp2/dVIcstbV8uX9/mx7NWw3fi/0PAxaR9wsDQMmSy7myZIa/+DpaPfQdLZd79E+iUipseMiCFibF+vP0/CpkDE9AQRMURM30sQsbCMoszvtB9FlvahSFXE1qxdJ3c/+DuZe8WFlWmAUcL3WpZ1lEtNQzRFTOVfcONdMu2oyRVZVG3+1sLF8t35l1WmVLJGzCvpdNN1bZv/gtTvWiUNO1dL/a7VVRulNgRR687UWrOOgZOML55Wf6svpOaRbQKsEct2fPy0LqqpiX7qJG08BFgjFg/XNEpljVga1OOts1bXiJkiNmf2LDlm6kQDYpb2qEhNxNx2TFSQkrJVJV5vv7uhsmGIk4idf/YpleA5iVi8pwalx0qg2Cmy802R7atLP9tWdf1u/8i5arVt/oBxIntNEtlrosigiaW/B00SKU9zjLXNFA4BCEAAAhCAAAQgoCXgJGLWe31zPwhtQTElSE3EYjoe38UqK77z3mV75FObcsz7/z4v1//bzxkR8021Z2awrxHLt30gDTv/JvW7/iZ1O/8mDbvUCNrrUtfynogUHQ+ys3FkaQRtwMHSOeBgae8/0RhJU9+DxiM5AoyIJcc67poYEYubcHLlMyKWHOu4a2JELG7CyZcf2YhY526RTS8kfwD1/USGHbtHvdVGxLKyNKrXi5g9YnZLZo1YuHMprl0Tw7Qq7K6Juc5dor7nrMEQNCVnJVmr371GcoU2x6YV6wYY0xzb+ytBU3KmJO1g6ew3Xl54/jlpaGyUqUdNC3NYkeVl10Q9SnZN1DNi10Q9oyWLbpWLvnSlcf5n4cEaMX0UWCNWYsSuifq+Ui1FzW/WsX2VyK9TWMKhZib948qqImb/zuLvXHNpJvaoSF3E1OYXl3zz+m7gltw6rzIVMHhXD5bTLmLsmhiMo5mrFkXMjUj97jdKkrZztdQZI2hvSP3OVZLvKG0M4vR4Ytv5kh90oBw7PidS1ySdTaOls8++pd999zW23E/ygYjpaSNiekaImJ4RIubO6ION6+W5p34n557/BT3MhFIgYohY2K5W8yK2a63Ic5eExeQ/f//9RD7+06oiZl0j5jRK5r/CaHKkKmJ2yVGHpNZgzb7mJrny4nNTMVWneaN8j1jwztbbRKwaqbq2jVJfmeb4ujTsWmX8X9f6vjy56TRpyrfIJ4Y+45i9UD9IOvvsLZ1Nexu/C/32K0la0z6l55Ws1fUPHiRbTkRMjxIR0zNCxPSMEDFETN9L3FO88tJz0tHRIcdMOzFsUb7yMyLmC1e3xDUvYsHRxJKzmnRlZef21ETM/N4u60YYZgSUoD3w6PJuX5wcS3QiKpRdEyMCmXIxaXyPWGma4+tS37zWkLJ88zqpa35X6lrel7q290Vtwe/loaY+GlLWZ5+SsPXdRwrG/+Wfpr2l0DDYS1E1kYY1YjURRuMgWCNWO7FkjVjtxJI1YrUTS/NIIlsjljE0TiLGiJiIKAjzv7dY5l55YWUbeDN2alTsxtvvk4XXXmZ8iXLWH4hY1iPkrX1piJi+ZUXJt31YErPyT76lLGot68rPrZNcsUVbVEnWxnSXs75qVK08smbI2hBtOT0hASLWE6LkrY2ImDdOPSEVItYTouStjYiYN049KVWti5h9jViay6Cs/YIRsQjOEkQsAogZKCKbIuYNTL59U0nKWjdI3e61kleS1qqEzZS19yVXaNYWVsz1MUStbegnjN/mo9gwSAoNw6TQMFQKjeXfxv/ZHGVDxLSh7jEJELEeEyptQxExLaIekwAR6zGh8tzQWhUxzwBSSpiaiKnjVWuvlj66XO64/qrKyFfaa8T8xuG6666Tq+deKzuaO/xmjSX98icek733GysTDj4klvL9FsoaMT2xF597KpFdE/PtW43pj3Wt640pj8Y0SEPWzNG2dZLr3Ckfto2QB9afJ1fuf7u+8SJSaBheljP1e4ghbJ1NH5Ni/ZAuaWscWk5X+u338fDSn8kJp5whHxsxylPWuEWMNWL6MLBGTM+INWLujNisQ9+HWCOmZ/TYQ/fJEcceL2P23k+fOIEUrBFLAHIPqiJVEVOcsrZrot/YIWLuxBAxfY9KSsT0LRHJt2+TbRtXy2//6wX5/OkjJd+2RfLtWyTftqn892bJt22WfMcWybdullxhl5di90ijRtIK9cOk0PgxY1StUBa1YpN1tE29Xvr/l7/6LSLmQrqtrVXuXfIjufjybwSKRxyZEDE9VUQMEdP3EvcUiJieICKmZ7T4thtkwYIF+oSkiJxA6iIW+RElXCAihoiF7XJZEjF1LH53TVQjbPl2JWhbRU2RNEStfYvkjN9lgev4SPKtH5bSdWzzjWzxu1+V08e/I6P779gzb75RinX9pFDXT4r5fsYOkn36D5J2aZJ26Ws8V6jrL8W6vlKsGyjFuiYjjcpj/OT7S6FhkK82MSKmx4WI6RkhYoiYvpcgYmEZIWJ6goiYnlFcKRCxCMiyRiwCiBkooievEcsAPu9NKBZKI2rGaFt5hE2NuqkfQ9bMUTglcuYI3FaRYqf3OgKkLOYayrKmJK2/8f1txu/68m9D6MryVt9PpG5AV3pDAPtJod6Uu5IQVmRPPZ9rCtAqsrBGrHb6AGvEaieWrBGrnViaR8IasXRiiohFwB0RiwBiBopAxDIQBJcmqM1Gch3Norb8N/5Wvzt3S76wW3Idu42/S6/tln51rdLeslMKbTuN/0uvlV+v/F16Ll8uT4oxr/PM1ZXlzjpC131kzhi1qy9LYL0SvbLYVUb0SiN7xghfWf6M9Cpfvl+2AxiwdYhYQHAZzIaIZTAoAZuEiAUEl+FsiFg6wUlcxMy9+790wZnyk/t/I/btJE0Mh04a120Tj3TweKsVEfPGKeupELGsR8h7+4Ju1pFv/6gieCWB22XInylrpvwpgZPOnRUxzCu5qwhfi7HpiVX8gkzH9H603VOqkTzJ1UtRTdnMNYjkG6SYaxTJ13f9b7zWKKLk0EjTKMV8g4gaFTR/q+eN/9Vr9cbfUtdUfs4sq1yHNZ/Kb9TZRyQnUszViUhdua7Sb6Pe8nOSy3elyVvSFfNGugH9VTvrZXtrQ1Ak5MsIAUQsI4GIoBmIWAQQM1YEIpZOQBIXMfMw3b5HrCd9oTNrxNw7Lpt16E/snr5GTH+E4VPUxK6JxYIhdsYInjGap0b4SqN6FelTz6k0nc0iHUrmzBFAS/pCWQwtI3tt7Z1y65qvyrzx14eHHVEJ96+/UA4f+KpMHLA6ohKtxVjkzRC7vBSVxJnCJyWJk3yX8K3etr/89aOxMvOA57tkcA9JVPnyFklUotpVbqWe8nPGa93EspzfmseQ2FIZpfSltqm/b1+2U75y5hBpbKiXomqz2f58uf2VPBZBdRJYU2a9Sm5FjEvtNcX4mf/+vQwdPkImT5kaQ8xE/IoYuybqw8BmHXpGrBHTM2KNmJ5RXCkyKWI96QudETFELOzJiYjpCdaEiOkPM3AK666JxmhcoUOk2C65YrtIoc34XXquTXKF9tJr6v/ya2barte68qkpm0Y5na0iBbNMy29pl1xnm1TSGWna5MG/TZJDh70nBw3ZIKIkVK3xM3+ks/x/wXguJ50ihdLrRjr1f+XvYum5gv5Ly90Arto5WV7bMUVmjV4amHPUGReuuVbmHPB9acy3RV10oPIe++AfZWTjBjl68Evd8pdGN8vSJjkp5nKl/w15VD/qOfN19bv8elEJc+l1lT6Xz0sul5fOoogYI55dZZZGRruXuW73EHli7cHyxUNUe3KlNhm/yn9XnrP+3/21opHGzGt5TbWxq0BbmtJrpbzqpa4y7nx5osyY+LYM62/GrEr55dINVmY9bnUW9zymSv0ux7li7V7S0SnyifE7y+208CmXWWqDEzP7c3uydWx/MSf5fE76NtbLrlZz7W6prO3NeVn6QoN85ZT2ch+xlFmtHQ7HXuG/BzMzHtX6gS12kpNf/GG3TDuoSfYZXh5Vt7bDKSbl57rxt6cz21zlmLr6jnkqdcVg1dqd8t4HzXL6sSMtfXDP/tiNvbWv6uJpb79qq8txqr5x2z0r2DUx0FUzfKZMipj6frEVL6+U6+ZeKn37NIY/yhhLQMTc4TIipu98iJieESLmzqjXbV9vil1Z2CqiZxW4stCZAvjm2+/LG2velTM/eURFCCvSV1ACWJLCihiaf6vndfWYMmnkKUhOSWWuXJ4hwCW5NJ4v16Pq/sF/j5CvHv++NNYp2bUKaLErj0VgrWkq9XST1oIhtIbYmm2xlLun6JrHXDDyPLbxTEcR05+h8aR4v2UfefzDM+Ur+/44ngoClPrDtf9DLhh9nwxv3BQgd/RZnt5ykrQX6uXU4b+PvvAAJW7rGCw/efcS+eYBtwbIHU+Wn753iZw8dLmM7fd2PBX4LPVP26fKW7vHyoxRD/vMGV/y6974F0QsPryuJScuYuYXNq/fuLlqw0aPHCaLbpgj4/cfkxIWf9WyRswfr6ymZo1YViPjv11B14j5r4kccRNgs464CbuXrzbGUWNDJYFUo5NKTMv/G7KpJM58vfS/8bqo58v/F40hMOlTL9LUmJPtu1qNslSakkTvWaZRl/G6al8pfymP+b/lt3o+V3rNaIvxUjlP5W9bPoeyco7lu9Rp1lWp015/lTrLbXU6phJLD3V2S9M9fYVBtbIqec3Yd9XZnV+5/WZ7LXXmc0Xp21Qvu5rbu8ek3E/2iJP9mFSZtue68zfjaGljt9h2Z1vJ68K2e33WflIqy+uxV46tavttfbPSZ211Gm3t/lypDXu2rVqd1n7eLe7V6uxWfhfb5n0ulsGHfjndi00vrT1xETM5u60R62mxQMR6WsSc24uI1UYc1VEgYrUTS0SsdmLpd41Y7Rx57R0Jm3XUXkzZrCOdmKYmYukcbjy1ImLxcE26VEQsaeLx1YeIxcc26ZIRsaSJx1cfIhYf26RLRsSSJh5/fYhY/IydakDEQnJnjZg7QNaI6TsYa8T0jFgj5s6o160R03eZPVK8teZ1WfP6Sjnt0zMC5I4ny5JFt8pFX7pSGhqzsRb6meW/ZddETagfuPtOOX36DBk8ZFg8ncJnqeyaqAfGrol6RuyaqGcUV4pURcxtvVhP+R4xRAwRC3tyImJ6gogYIqZmHoR5IGJ6eoiYnhEiVmJUbURs547t8uiD98hnL/6qHmZCKRAxPWhETM8orhSpiVhzS5ssuPEumXbUZDn8kAPl7gd/J3OvuNDYJfHmRUvlxOMOk2OmTozruCMrFxFDxMJ2JkRMTxARQ8QQMf15EjYFIqYniIghYvpe4p7ijdV/kfffe0dOOW162KIiy4+IRYbSd0GpiZh1sw7V6htvv08WXnuZDBk0UHrSFzqrtrNGzHe/y2QG1ohlMiyBGsUasUDYMpmJNWKZDEugRrFGLBC2TGZijVgmwxKqUawRC4UvcOZMiNjQwQNl4Q/ulvlfv8gQsZ70hc6IWOC+l7mMiFjmQhK4QYhYYHSZy4iIZS4kgRuEiAVGl7mMiFjmQhK6QYhYaISBCkhNxKxTE2dOP8mYjjh231Gi/u5JX+iMiAXqd5nMhIhlMiyBGoWIBcKWyUyIWCbDEqhRiFggbJnMhIhlMiyhGoWIhcIXOHNqImZvsZqqeMW8W+S1VW9KT/pCZ9aIufc9dk3Un5usEdMzYo2YOyN2TdT3ITbr0DNijZieEWvESozYrEPfV6qlYI1YcHa1mDMzItZT4SJiiFjYvouI6QkiYogYm3Xoz5OwKRAxPUFEDBHT9xL3FIhYWIK1lT81EbNu1jF+/zE9lioihoiF7byImJ4gIoaIIWL68yRsCkRMTxARQ8T0vQQRC8uoN+VHxCKINrsmRgAxA0WwRiwDQYioCawRiwhkBophjVgGghBRE1gjFhHIDBTDGrEMBCHiJrBGLGKgHotLTcRU+3rS94W58UTEPPa2jCdDxDIeIB/NQ8R8wMp4UkQs4wHy0TxEzAesjCdFxDIeoADNQ8QCQIsgS6oiprapt36RcwTHk0oRiFgq2COvFBGLHGlqBSJiqaGPvGJELHKkqRWIiKWGPvKKEbHIkaZeICKWTghSEzHrLolOh37opHFyx/VXGd8rluUHa8Tco8OuifreyxoxPSPWiLkzYtdEfR9i10Q9I9aI6RmxRqzEiF0T9X2lWgo26wjOrhZzpiZitQITEUPEwvZlRExPEBFDxNisQ3+ehE2BiOkJImKImL6XuKdAxMISrK38qYmY266JL766Wh54dLlcN/dS6dunMdPEETFELGwHRcT0BBExRAwR058nYVMgYnqCiBgipu8liFhYRr0pfyZFTK0du/H2+2ThtZdlfmqi6iysEauNU4Y1YrURR3UUrBGrnViyRqx2YskasdqJJWvEaieW5pGwRiydmGZSxB5c9pSseHllYiNiavfGO+9dVonAklvnyTFTJ1b+V+359g13Gf+f9alpe7QLEUun80ZdKyIWNdH0ykPE0mMfdc2IWNRE0ysPEUuPfdQ1I2JRE02/PEQsnSxnTu4AACAASURBVBgkLmJqtGv2NTfJ+o2bqx7x6JHDZNENcySJL3pWUyR/ct/jcsXFM4xpkKp931q4WL47/zKjfjVN8qZFSysbhyhpU4+rZ8+qtB8RS6fzRl0rIhY10fTKQ8TSYx91zYhY1ETTKw8RS4991DUjYlETTb88RCydGCQuYuZhuq0RSwdFqVZzN8c5s2cZo2JKvMbuO0pmTj/JeN0uZqwRc48WuybqezNrxPSMWCPmzohdE/V9iF0T9YxYI6ZnxBqxEiN2TdT3lWop2KwjOLtazJmaiGUVphKt+QsXGyNyY0YOlwU33iXTjppcETH7iBkihoiF7cuImJ4gIoaIsVmH/jwJmwIR0xNExBAxfS9xT4GIhSVYW/kRsXI8rVMmzTVizS1thoidf/YplTVjTiI279pvS1tHIRM94/HHHpGxYw+QSYccmon2vLP2bXlhxbNy3gUXZaI9qhGL7/g3ufDzF8vAgXt1a1P/PvXS3NohhWKyTX3mqf+SxsYmOXba8clWXKW2zZs+lF8/8pBcfOnlmWiPasQ9P7tLTj3j0zJq1GhPbVJToNo7C9LRGU8wX33lZdmy6UM59fQzPbUn7kStra3y4x/9m3ztG/8z7qo8l//IQ7+QyVMOlQMnHOw5j1PCpvq8SE6ktT3cNfaN11fL6pV/lbNnfCZUe6LMfNutN8rlV35DGhuzsTvwk799XIaPGCmHTz0yysOslNVQl5P6urw0t3V6Kn/D+nXy+9/9p3zuC1/ylD6JREvuXCTnzPiMDB02PInqtHU8/9yz0tHRLieceIo2bZQJ8jmRvk31squlo1ux27dvk6X3/Id85av/I8rqQpX1wH0/l2nHnyj77rd/qHKiyrzyL3+Wd95ZK2dOPzuqIkOXc/MN35UFCxaELocC/BNIVcTcvtQ5rS90tk5NnDJxnHZETCFvbe+UtpA3Cf5DR46oCRgi1tYphaRNLOoDoTzp21Qn7R1F6egMd/MOyvQJNDbkRZlYW7u3m/f0W0wLqhFQElZfn5OWVmLZ03tJPp8T9YGXXcR6+nH15vYP7NfQmw8/tWNPVcScNr5IjYSlYuu6MN0aMZWNzTqyELXwbWCzjvAMs1ICm3VkJRLh28FmHeEZZqUENuvISiTCt4PNOsIzzFoJbNaRTkRSE7GsbNahpho++fTLcvnnS0PE5hTFhfMvM6YjsmtiOh0zjVoRsTSox1MnIhYP1zRKRcTSoB5PnYhYPFzTKBURS4N6vHUiYvHyrVZ6rxcxcx3YY0+uqDDy8z1ibNbh3nHZNVF/YrNZh54Rm3W4M2LXRH0fYtdEPSM269AzYrOOEiN2TdT3lWop2KwjOLtazJmaiCmY9ml/PREwIoaIhe23iJieICKGiLFrov48CZsCEdMTRMQQMX0vcU+BiIUlWFv5UxUxNQ3w7gd/J3OvuND4MuWe+EDEELGw/RYR0xNExBAxREx/noRNgYjpCSJiiJi+lyBiYRn1pvypiZjbjokqAGntmhgk+GzWEYRa9vKwRix7MQnaItaIBSWXvXysEcteTIK2iDViQcllLx9rxLIXk7AtYo1YWILB8qcmYsGam81ciFg24+K3VYiYX2LZTY+IZTc2fluGiPkllt30iFh2Y+O3ZYiYX2LZT4+IpRMjRCwC7ohYBBAzUAQiloEgRNQERCwikBkoBhHLQBAiagIiFhHIDBSDiGUgCBE3ARGLGKjH4lIVMeuOhaNHDpNFN8yRMSOH7/Elyh6PJZVkrBFzx86uifpuyRoxPSPWiLkzYtdEfR9i10Q9I9aI6RmxRqzEiF0T9X2lWgo26wjOrhZzpipi5q6Jnz51mtx4x31y0czTZPz+Y4zv7nrg0eVy3dxLM7+JByKGiIW9MCBieoKIGCLGZh368yRsCkRMTxARQ8T0vcQ9BSIWlmBt5U9NxKxf6KxGwawipnZTvPH2+2ThtZfJkEEDM00cEUPEwnZQRExPEBFDxBAx/XkSNgUipieIiCFi+l6CiIVl1JvyZ1LEetKImOosrBGrjVOGNWK1EUd1FKwRq51YskasdmLJGrHaiSVrxGonluaRsEYsnZimJmLqcB9c9pSseHmlzP/6RfJvdz1kTE0cOnigXDHvFpl19ikyc/pJ6VDxWSsi5hNYRpMjYhkNTIBmIWIBoGU0CyKW0cAEaBYiFgBaRrMgYhkNTIhmIWIh4IXImqqIqXar0a9Lvnl9t0NYcus8OWbqxBCHlWxWRCxZ3nHVhojFRTb5chGx5JnHVSMiFhfZ5MtFxJJnHleNiFhcZNMrFxFLh33qIpbOYUdXK2vE3Fmya6K+r7FGTM+INWLujNg1Ud+H2DVRz4g1YnpGrBErMWLXRH1fqZaCzTqCs6vFnKmKmNo1ccMHW7rtjmhuaT/tqMk9YmoiIoaIhb0wIGJ6gogYIsZmHfrzJGwKRExPEBFDxPS9xD0FIhaWYG3lT03ETOE6/+xT9piG2JM260DEELGwlwRETE8QEUPEEDH9eRI2BSKmJ4iIIWL6XoKIhWXUm/KnJmLW7evVd4dZHz1p+3rVbtaI1cYpwxqx2oijOgrWiNVOLFkjVjuxZI1Y7cSSNWK1E0vzSFgjlk5MUxOxWhkRQ8TS6bhx1IqIxUE1nTIRsXS4x1ErIhYH1XTKRMTS4R5HrYhYHFTTLRMRS4d/aiKmDldNQZy/cLEsumGOmKNiajRs9jU3yZUXn9sj1oghYul03DhqRcTioJpOmYhYOtzjqBURi4NqOmUiYulwj6NWRCwOqumWiYilwz9VEVOHbIrX+o2bKwR60vb1rBFz77jsmqg/sVkjpmfEGjF3RuyaqO9D7JqoZ8QaMT0j1oiVGLFror6vVEvBZh3B2dViztRFrKdDRcQQsbB9GBHTE0TEEDE269CfJ2FTIGJ6gogYIqbvJe4pELGwBGsrPyIWMp6IGCIWsgsJIqYniIghYoiY/jwJm8JJxFpaRIpFkUJB/eSkWLD8X35eKq+X0hnpi2KkreQrijTW5aWhvk4+2tluKbOUrlJHuSz1/64d62Tdu7+TcQddbLyuftTD6Xf5JVFtMdO4pncqy+E5s1yzrA/X/7sMHvYZqasf5tCOXLf67W2ttKccKKdjUu330+7O9melUOiQuoaTzUPXMugqP7cHKyu/CkdLe83nVM6+TfWys7mjW0xyxY+kX5+fy47dX+t2HHsckwMD59jt2UZHPmbsHModNeLnsvWjE6W5ZX/3vuEh/ta67e0oxa6rvdXiP2zon2XggLflzbXn7BFrv/G39qEKP5f+1b3PdbX1zDO+IwsWLAh7CSF/AAKpipjaOfGKebfIa6ve3KPph04aJ3dcf5UMGTQwwGElm4VdE5PlHVdtrBGLi2zy5bJGLHnmcdXotEbMuLnvFOksiHSq3525bv8br5VfN/9WEtE9T/cyCp25clkleSiVW5IEbT2d1jylepSIGGV0FG1tKdVTrS2lYyu3xTzOclt0x2y2u6v93o65JEvl460YTVwRpVwIQCBrBOZc0y7f/78NWWtWr2hPqiKmvtBZPa6ePatHw0bEenT4Ko1HxGojjuooerOI7dol0tGek/YO9Vukrb30Wz1n/l16LSdtbSIdHSLt6nX1u82Sr/JarpKmrbVY/jtn5OnKp/7uSld6LSedHV0SYwjNHoJUlhLLa1bZKAlNSSbUyAyPdAg0NYnk8+ZPUSRn+T8nklM/lddL/xvpy8+b/9fViaifQrFovGaWab5eKaNcpnpdPaceKk3pd9Hyt/01SzoTVbms7mVYy6tehjpOM1+l/nK5Xe1xLku1s5TZoQzLc5XyHcq15vXSfmubKlU71LXHMbmwrcYgn89Jv6Y62d1aGhFz5KGCXO01Kxdfx+4cf/uxV9ptq7/6se8ZR9fYVSm3crwWpp7q9Mhgjxi79C/V/vLLzvGx5N1v/4IcO7WPedbwO0ECqYmY2/eIJXj8kVSFiEWCMfVCELHUQxBZA7IoYmrEYdeunLQ0i+zeLdLcnJPdu9TfOWm2PrdbpGV3TnbtKpbS7O6eXj3XbOQv5zVez/UqUTFu4NVNfb50Y19XV6z8X3mtfNOv/renMYXAWoa64VflqNe68lSpp1y3kb+cvmo99blS/WabzTpUvpzZtu715MtpuvKU6zHLKbfV2n6zLd3b38Wl0k4Lt1KermOur4/sFHQsiF0T4+WbZOnsmpgk7WTqYtfEZDjba0HEQnJnjZg7QHZN1Hcw1ojpGSW1RmzbR6b4WORIiZIpTmUBamv5o3R2figfbjrTEKWSXJXytDQriSr9XxIuke3bzM8l9ccaJEWfPq3yzW/eItdfP0/69BFpaChKQ4NIfYP62/wpirrRNv5vlPLfpeca1f/qefV6Y9H43fW/+rsoTUaaXPm1ovF6o1mHPV+DyMZ1v5TBQ6fIkGEHVYTJiywoYTCkqCxQgwbUSV1dTjqkPQiaSh52TdTjY7MOPSM26ygxYtdEfV+ploLNOoKzq8WcqYmYgqmmJo7dd1SP+b4wpw6AiCFiYS8MiJieoBKxYz5+hvTrP7prNKksOc1KeHaVR5jKzxU76mXb9oLs2KFGlbqPOhnCVB5FUq+ZkqWm5nl9HHvsizJ8+IeybNl0r1mMUZG+fYvSt69I337qpyj9+on061d6Tv2tXu/X3/ydKz9fSmemN8ow0pbz9lMC1SIP3f8jufjyb3huT9wJn1j2kEyYOEXGjpsQqqqovkcMEdOHARHTM0LEEDF9L3FPgYiFJVhb+VMVMfUdYnc/+DuZe8WF0rdPY48ki4ghYmE7bm8TMTVFb+vWnGzdkpOtW0W2bFa/S/9v2VwsP6/+Lr2unp8588fy61+fJevWjQmLu2p+NcJjiJAhR11/dwlQSYaUAA0d+pL0adwk9U3/UE5bkqI+NrGqSFb/ojHqFNeD7xHTk0XE9IwQMT0jRAwR0/cSRCwso96UPzURc9sxUQWAXRN7UzfMxrGyRsx/HNQmEFuUQCmpMn5K/yux2rJZ/V0SqdL/JbFS0/TMbX/91KhEpl//8uhQWZjMUSG7AA0bkpeGpqI0NhXKI1CWUSeHkShVrhqx4pE9AlGNiGXvyHpfi1gjVjsxZ41Y7cTSPBLWiKUT09RELJ3DjadWNuuIh2vSpSJiIju252Td+zn54IOcbN5slSjz764RLCVWag1UkMegwUUZMkRk+PCiGH8PLcrQoSJDh4kMGaL+LsrQYUUZPESNPhVlxEh/e2pncbOOIJzII4KI1U4vQMRqJ5aIWO3EEhFLN5aIWAT8EbEIIGagiFoXsY+25mT9+pxs3JCT995VwiXG/xvWl+Rr/bq8scmE38ewYSVpUiI1uCxRSqyGDM0ZzxtiZfwWQ7hU+rgfiFjchJMrHxFLjnXcNSFicRNOrnxELDnWSdXEiFhSpLvXk7qIvfjqarnkm9d3a9WSW+fJMVMnpkPEZ62sEXMHxq6J+g4VxRqxzZuVSOXkg405efcdJVci779vSlbeeM3L9zCp7wuaNPkD+dSnfiGr/za7Ik5DhqqRqpJIqREqQ7SGiDGalcQjqV0TvR7Lytdeka1bNskJJ5/uNUus6VgjpsfLGjE9I9aI6RmxRqzEiF0T9X2lWgo26wjOrhZzpipiSsJuWrRU7rj+KhkyaKDBV23gMfuam+TKi8/tEbspImKIWNgLg5uIqbVUmzaVJKs0apWTdevE+K1GsNRvNaLV2qpvhdqAYszeBRk9plj6GV2UMXtL5f8xY9RUQLVZxiZ58jePyHmfu1RfaEIpEDF30IiYviMiYnpGiJieESKGiOl7iXsKRCwswdrKn5qINbe0yYIb75Lzzz5lj9EvJWgPPLpcrpt7aeZ3U0TEELEwlwS1ffrvf/u07NjRJDt3HV+RLWO64LrSFEIvjwEDSnI1Zu+ijBpV+q0ka8w+pf+VdHkdvULE9MQZEdMzYvt6PaMli26Vi750pTTEuaWmvhmVFIiYHhYihojpewkiFpZRb8qfmoipXRPnf2+xzL3yQhm/f/ctqdWo2I233ycLr72sMlIWV1BMIXzsyRWVKuxTIx9c9pR8+4a7jNfP+tS0PQSRNWJxRSfZcuNcI/bhBzlZ8/ecvP63vLzxek7eVH+/njfES/fYa1DXCFZJtkqjWPvsU5SRo4qyz74FYwt1Hl0EWCNWO72BNWK1E0vWiNVOLFkjVjuxNI+ENWLpxDQ1EcvKiJgSwp/c97hccfEMY/RNjcbNX7hYFt0wxxBE+/RJ9SXU6nH17FmViCFi6XTeqGuNQsTeXKOEKy9/fyMvr/9NjL9f/1vO2I2w2uOAcUUZN740ZXDvfURGjS7K3nt3SVafPlEfae2Xh4jVTowRsdqJJSJWO7FExGonlohYurFMTcTUYauRpqWPLs/UGjHz+83mzJ5lTJlU4jV231GV9WpO69oQsXQ7cVS1exUxNZ1QiZb6eeNvpb/feCMnb72Zl/Y259b07y8y/sCCHHhQQSYcJDJhQkHGTyjKuHEFUV8kzCNaAohYtDzTLA0RS5N+tHUjYtHyTLM0RCxN+vHUzYhYPFx1paYqYqpxWds1UU2L/NbCxfLd+ZfJmJHDjXVs046aXBEx6+tqxIw1Yu5drCfvmvjhhzn5++tKuHLGdEL1W0mXmk5Y7QuJPzaiKAdOKMoEQ7hKfx84oWCs2ar2iGLXRN2J7ud11ojpabFGTM+INWJ6RqwRc2f0wcb18txTv5Nzz/+CHmZCKVgjVgLNronBOxybdQRnV4s5UxexLEE1p0ua4uU0fdJJxBYsWJCZw3jooYdk/Pjxcthhh2WiTW+99ZY8/fTT8sUvfjET7VGNuOWWW+TLX/6y7LXXXtLZKfLmmyKrV5d+Vq3q+v3RR85NrqsTGTdOZOJEkUmTun6rvwcN8n+YTz75pDQ1NcknPvEJ/5ljyPHhhx/KAw88IFdeeWUMpQcrcvHixXLWWWfJmDHd15MGKy18rhdffFEUp+nTp4cvLIISWltbjX49b968CEqLpoj7779fDj/8cJmoTpQMPFatWiWvvfaazJrVNa087WYtXLhQ5syZI40Z2azjsccek5EjR8rRRx+dNhqj/vfff18ef/xx+cpXvpKJ9qhG/PCHP5QLLrhAhg8fnok2qffX9vZ2OfXUUzPRnm3btslPfvIT+eY3v5mJ9qhG/PSnP5WTTz5Zxo4dm4k2/elPfxJ1bzRjxoxMtEc1Qg0qZOleNjNgEmhIqiKmpv1t+GBLt80v7DKUAAOjCrPeUSOGVtZ/ObWFETF/EcnSiNiOHTl58fm8vLHqh/Kn1y6RVX8dZGyeUe3Rt29pOqEa3TrwIDFGtiZMKMrBkwr+IGhSMyKmx8n29e6M2L5e34fYvl7PiF0T9YwYESsxYkRM31eqpWBELDi7WsyZmohlZbOOahJmBps1Yj2326ut3198vk5efiknzz2bl9WrnKVr+PCisV7rsCk52e+AThk3oSAHHliQffZN5suKey7h7LacNWLZjY3flrFGzC+x7KZnjVh2Y+O3ZawR80ss++lZI5ZOjFITsaxtX29dB2YNBbsmptMxg9T617/kjREvJV0vPJ+XDzbuuVPhlEMLcuy0gkyeUlq7dfDBRVHbw6uH1806grSNPMkSQMSS5R1nbYhYnHSTLRsRS5Z3nLUhYnHSTadsRCwd7qmJWFZGxNRUw9nX3CTrN27uFoEvf3Z6ZYoi3yOWTud0q7W1VeTlF+vkxRfy8sJzOXn5pbyoqYfWh/oC46OOLsgxxxXl6GMKcsRRnaKmG1Z7IGLZi3PQFiFiQcllLx8ilr2YBG0RIhaUXPbyIWLZi0nYFiFiYQkGy5+aiKnm2r+zSz1nitGVF59b2akw2KElk4tdE905R7VGbPPmnLzwXF6eX5E35Osvf85LR0dX3blcaT2XEq6jy+KlRrzU8/bHPUvukHPO+7wMGDCw20tpiRhrxPTnKmvE3BmxRkzfh1gjpmfEGjE9I9aIlRixRkzfV6qlYI1YcHa1mDNVEbOKl3VEasmt84zv8OoJD0QsHhFTX4Ssphe+sCInL6yok7ff6m5UamTr8CMKcvSxnXLMsUU55tiCqBEwLw9EzJ0S29frexHb1+sZsX29nhHb17szYvt6fR965aXnpKOjQ46ZdqI+cYQpELHgMBGx4OxqMWfqItbToSJi4UWso13kT6+qka46Q7zUOq8tW7qLl/oeLjXadcxxBTnqmIKotV5qG/kgD0QMEQvSb6x5EDE9QURMzwgRQ8T0vcQ9BSKmJ/jYQ/fJEcceL2P23k+fOIEUiFgCkHtQFYhYBMHasbtddjRb5slFUGYtF2FuI/+8IV118uof86LWfJmP+gaRQ6aUphkq8Tr2uIKMHOVttCsMt7SmJoZpM3mdCbBGrHZ6BmvEaieWrBGrnViyRqx2YmkeCWvE0okpIhYBd0TMHaK5jbwSLzXd8PXVeSlavGrI0PKmGmqK4XGdMvXIgjQ1RRAYn0UgYj6BZTg5Ipbh4PhsGiLmE1iGkyNiGQ6Oz6YhYj6B9YDkiFg6QULEIuCOiO0JcdXKvDz6cF5+/UidqPVe1of6QuQjjyxtqnHkUQU56OBovyA5aEgRsaDkspcPEcteTIK2CBELSi57+RCx7MUkaIsQsaDkspsPEUsnNohYSO6sEesC+Pc38vLQL0rypf5Wj3Hj3pLp05+WfMNnjW3k1aYaA/eKf5qhW1hZI+be6dmsQ39RYI2YnhFrxPSMWCPmzojNOvR9iDViekasEdMzWnzbDbJgwQJ9QlJETgARC4m0t4vY2rdz8uAv6uWRh0tTDtVDbRl/xFEFOWdGpxx//Jvy9pvPyVkzLghJOrrsiBgiFrY3IWJ6goiYnhEihojpe4l7CkRMTxAR0zNCxPSM4kqBiIUk2xtFTMnXww/WyyMP5WX1qq5ph2o7+XNmFOTcf+qQ0WNKo15RfY9YyDB1y46IIWJh+xMipieIiOkZIWKImL6XIGJhGSFieoKImJ5RXCkQsQjI9oY1Yu++m5OHf1mSr5V/7ZKvQw8ryDn/VJKvvfdJd8ph2FCyRiwswezkZ41YdmIRtiWsEQtLMDv5WSOWnViEbQlrxMISzF5+1oilExNELALutSpi779Xlq+H8/KX17rkS20tb4x8faZD9t23Z8uXNfyIWAQnQ0aKQMQyEogImoGIRQAxI0UgYhkJRATNQMQigJixIhCxdAKCiEXAvZZETMnXrx6qN3Y8/POfuuRr4qTSyNeMmR2y/9jakS9ELIITIINFIGIZDErAJiFiAcFlMBsilsGgBGwSIhYQXIazIWLpBAcRC8m9FtaIrV9Xki+14cafXumSL7WtvClfB4wLJl+sEdN3sBefe0oaGhtl6lHT9IkTSMGuiXrIrBHTM2KNmJ4Ra8TcGbFror4PsVmHnhFrxPSMWCOmZxRXCkQsJNmeKmIbNyj5qpNHHq6TV17ukq8DJxTk7HM7jamHB00M//1eiJi+gyFiekYPL/2ZnHDKGfKxEaP0iUUk7hExREwfBkRMzwgRQ8T0vcQ9BSKmJ4iI6RkhYnpGcaVAxEKS7UkipuTr0V+V5OuPL+WlWB7kUqNdZ5/bYYx+TZocXr6sSBExfQdDxPSMEDF3Rm1trXLvkh/JxZd/Qw8zoRSImB40IoaI6XsJIhaWESKmJ4iI6RnFlQIRi4BslteIffhBzhCvRx+uk5de7JIvtc7r7BkdxsiX2nyDhwibddROL4h7RKx2SGX/SFgjlv0YeW0ha8S8ksp+OtaIZT9GflvIGjG/xKJJj4hFwDFrIrZpU1m+HqqTF1/okq999yuNfJ09oyCHHY582UOPiEVwMmSkCEQsI4GIoBmIWAQQM1IEIpaRQETQDEQsAogZKwIRSycgiFgE3LMiYst/Xye3/1udPPt0XeWoRowsyszzOuQfzynIEUchX27hRsQiOBkyUgQilpFARNAMRCwCiBkpAhHLSCAiaAYiFgHEjBWBiKUTEEQsJPcsrBF78ok6ueX79camGzNnPiSbNo2TgyYdIuf+U6cceXS68sUaMX0HY42YnhFrxNwZsUZM34feWvO6rHl9pZz26Rn6xAmlYI2YO2h2TdR3RDbr0DNijZieEWvE9IziSoGIhSSbloipjTZ+81id3HpTfeXLltXUw9mzH5TjT9xfDp58SMgjiyY7IqbniIjpGSFiiJiaeRDmgYjp6T2z/LcydPgImTxlqj5xgBR+R8QQMT1kREzPCBHTM0LE9IziSoGIhSSbtIgVCmJsvvGvN9fL66tL287vt39Rvn51h5x/QYc881+Pyd77jZUJByNi1UJ7z5I75JzzPi8DBgzsliStqYmImP4kRMQQMURMf56ETYGI6Qk+cPedcvr0GTJ4yDB94gRSIGJ6yIiYnhEipmcUVwpELAKySawR6+wUefCBevnBLfXy5pqc0Wq18+E35nTIebM6pK5rWVgER9Q7i0hLxHon7XiPmjVi8fJNsnTWiCVJO966/I6IxdsaSg9DgDViYehlMy9rxNKJCyIWAfc4RayjXeT+e+vltlvr5Z13SgI2bnxRvnF1h8w8v0PyXd/FHMGR9O4iELHaiT8iVjuxRMRqJ5aIWO3EEhGrnViaR4KIpRNTRCwC7nGIWFubyN0/q5cf/qBe1q8rCdiBEwryzTmdcu5MBCyCsO1RBCIWB9V0ykTE0uEeR62IWBxU0ykTEUuHexy1ImJxUE23TEQsHf6IWEjuUa8Ra2kR+eld9XLHbfWivoxZPQ46uGBMQTxnRqd2BGz5E6wR04WUNWLuhLZu2SRP/uYROe9zl+pQJvY6a8TcUbNror4rslmHnhFrxPSMWCNWYlRNxHbu2C6PPniPfPbir+phJpSCNWJ60KwR0zOKKwUiFpJsVCK2c2dOlvy4XhbdXidbtpQE7OBJBbnqf6rvAOuUXOkp7QMR0yISRAwR0/cS9xQrX3tFlLCecPLpYYuKJD8ipseIiOkZIWJ6RogYmnU3vgAAFIBJREFUIqbvJe4p3lj9F3n/vXfklNOmhy0qsvyIWGQofReEiPlG1j1DWBHbsT0n/35Hndy5uF62fVSyrUmTC3L13A759D96FzCzVYiYPqCIGCKm7yWIWFhGTyx7SCZMnCJjx00IVVRUUxMRMX0YEDE9I0QMEdP3EkQsLKPelB8RiyDaQdaIfbQ1J7ffVic/vbNe1GiYehwypSRgZ57VGUGrKMIvAdaI+SWW3fSsEctubPy2LCoR81sv6aMnwBqx6JmmVSJrxNIiH1+9rBGLj61byYhYBNz9iNiHH+bk9h/Uy38sqZfm5lLlhx1ekKvmdsgZZyJgEYQjcBGIWGB0mcuIiGUuJIEbhIgFRpe5jIhY5kISuEGIWGB0mc2IiKUTGkQsAu5eREztfHjbv9bLvT+vl9bWUqWHH1EaATvtDAQsgjCELgIRC40wMwUgYpkJReiGIGKhEWamAEQsM6EI3RBELDTCzBWAiKUTEkQsJHfdGrH338vJrTfVywP310t7W6myI48uCdgnPxW9gLFGTB9Q1oi5M2LXRH0fYrMOPSPWiOkZLVl0q1z0pSulobFRnziBFKwR00NmjViJEbsm6vtKtRRs1hGcXS3mRMQsUb150VIZu+8omTn9pG6xfnDZU/LtG+4ynjvrU9PkurmXSt8+pTfOaiL29ls5ueX79fLwL+ulo6NU3NHHFOTqazrk5E9GL2BmgxEx/WmKiCFi+l7ingIR0xNExPSMEDF3Rh9sXC/PPfU7Off8L+hhJpQCEUPEwnY1RCwswdrKj4iJiFW0vnPNpd1E7MVXV8tNi5bKHddfJUMGDRQla+px9exZjiL2+t/ycsuN9fLrR+qkUCh1luOmldaAnXhyfAKGiHk/MRExRMx7b3FOiYjpCSJiekaIGCKm7yXuKV556Tnp6OiQY6adGLYoX/kZEfOFq1tiRCw4u1rMiYhZouo0ImZ/zi5mKrtaI/biHwty4/X18p/L6qRYLBU67fiCzLmmQ47/RPwCVoudM+ljYo1Y0sTjq481YvGxTbpk1oglTTy++lgjFh/bpEtmjVjSxOOvjzVi8TN2qgERcxGx5pY2WXDjXTLtqMmVUbI1a9fJtxYulu/Ov0zG7z9GXnpJ5Fv/uyC//c98paQTTuyUed/qMNaC8eg5BBCxnhMrXUsRMR2hnvM6ItZzYqVrKSKmI9RzXkfEek6svLYUEfNKKtp0iJgHETv/7FPkmKkTjZR2ETvjDJEnnigV8slTi/K//7kgxxxbHhKLNlaUFjOB/n3qpbm1QwqEL2bS8RevbvjaOwvS0Ukw46cdbw1N9XmRnEhrOx9sxUs6/tIb6nJSX5eX5jZmicRPO94a8jmRvk31squlvAg+3uooPQECxodePBIngIh5EDG3ETG1Wcezz/6z/O9/7pQjjkz/pu/xZY/I2P3HyaRDpiTemZwqfGft2/LC83+Q82Z9LhPtUY1Y/KPb5MKLvigDB+7VrU2GiLV1SiFhE3vmqeXS2NQoxx53fCYYbd60SX796INy8Zcuz0R7VCPu+Y+fyKmnnymjRo321Ka+TXXS3lGUjs54bt5ffeVl2bJ5k5x62j94ak/ciVpbW+XHi26Tr319TtxVeS7/kYd/KZMPmSIHTjjYcx6nhI0NarZBTtraw928v/H6alm9aqWcfe7MUO2JMvNt//p9ufyKr0tjRnZNfPKJ38jwj42Qw6ceGeVhVspSElZfn5OWVm+x3LB+nfz+yd/K5z5/SSztCVLokrv+Xc45d6YMHTY8SPbI8zy/4lnpaO+QE048OfKy3QrM53OiPvCyi9j27dtk6b0/l6/M/lqi7XGr7IH775ZpH/+E7Lvf/plo08q/vibq3ujM6Wdnoj2qETff+D1ZsGBBZtrTmxqCiFmiHWSNmG77+qQ7E7sm6omzWYc7I7av1/chNuvQM2KzDj0jNutwZ8Suifo+xGYdekaPPXSfHHHs8TJm7/30iRNIwWYdCUDuQVUgYhoR87trYtqxR8T0EUDEEDF9L3FPgYjpCSJiekaIGCKm7yXuKRAxPUFETM9o8W03MCKmxxRLCkTMtn29ojx65DBZdMMcYzMO9XD7HjH1uto1cUcz86Rj6aEJFspmHQnCjrkqNuuIGXCCxbNZR4KwY66KzTpiBpxg8WzWkSDshKpis46EQNuqQcQi4I6IRQAxA0UgYhkIQkRNQMQiApmBYhCxDAQhoiYgYhGBzEAxiFgGghBxExCxiIF6LA4R8wjKLRkiFgHEDBSBiGUgCBE1ARGLCGQGikHEMhCEiJqAiEUEMgPFIGIZCELETUDEIgbqsThEzCOoasnYrMMd4Lr31sorL62Qs2ZcEJJ0dNlZI+bOks069H2NNWJ6RqwR0zNijZg7Izbr0Pch1ojpGbFGTM+INWJ6RnGlQMRCkkXEELGQXUhefO4paWhslKlHTQtbVCT5ETE9RkRMzwgR0zNCxBAxfS9xT4GI6QkiYnpGiJieUVwpELGQZA0Ru+ZbxoYdWXiwa6I+CoyIMSKm7yXuKRAxPUFETM8IEUPE9L0EEQvLCBHTE0TE9IziSoGIxUWWciEAAQhAAAIQgAAEIAABCFQhgIjRNSAAAQhAAAIQgAAEIAABCCRMABFLGDjVQQACEIAABCAAAQhAAAIQQMToAxCAAAQgAAEIQAACEIAABBImgIgFBL512w65Yt4t8tqqN40Sltw6T46ZOjFgaWRLgoCfmDW3tMmCG++Sx55cUWkaMU4iSt7qsMfnO9dcKjOnn+Qp882LlsoLr66WO66/SoYMGugpD4niJfDgsqfk2zfcZVRy1qemyXVzL5W+fRqrVhom/vEeCaX7jaU6H++8d5kB7tBJ4zgve0gXUu+n87+3WOZeeaGM339MD2k1zVTn29h9R7m+X3L/k2w/QcQC8DY76bSjJhudec3adfKthYvlu/Mv44IUgGcSWfzGTL3J/OS+x+WKi2cYN4Qvvrpa5i9cLItumEOMkwiYpg71ZqIeV8+eJaZgz5k9S/thiHnTxw1fBoJYboI6t25atLRyA26NrVMr7edydo6ElviNpZK2FS+vrIi3/X+IZo+A9SZ99MhhvCdmL0SOLbJ+QKL74JL7n2SDiogF4K3E68bb75OF115mfKLOjUEAiAlnCRszPzf7CR9ar6vO6ZNY3c27gqTeiN5+d4OceNxh3W78ex3AjB2w/RNa+828vblmHJWE88gWAb+xtJ+3uthn62h7d2sYEeuZ8fcyImY/Mu5/4o01IhaAr9ObhZcbwQBVkSUiAmFjxqhnRIGIoBinWOg+Sbe+/pfVbyJiEcQhiiKcPsTSnWvWqWyqDXwqH0UkwpcRJJYq1rOvuUmmn3qcMbod5CYxfMspIQgBRCwItfTzBDnHdNfk9I+qZ7cAEQsQP3VT/8Cjy7utY0DEAoBMMEuYmDHimWCgPFRlH91UWdxEzB57PnX3ADmhJOa5df7Zp1Smlbq96TulV7Ff+uhy1hYlFLNq1fiNpSrHzLNtxy555oXXWCOWcgz9VI+I+aGVnbR+RYz7n/hjh4gFYBx2dCVAlWQJSSBozMyL0KgRQ41PbHmkT8DviJh1bry19awTSz+WfkdRnG72mTaTfhytUmWunVbP6T5Jt98UItXZiKWXViBiXihlL40fEeP+J5n4IWIBOIddbxSgSrKEJBAkZlyEQkKPKXvQNWJmcxgRiykwAYsNsq7IuusXN4QBwceQzU8sg4ygxdBkigxIgPMuILiUs3kVMe5/kgsUIhaAtd8d+AJUQZaICehiZn6qPuvsU4ydMBmOjzgAERen2zVRvb7hgy2O26AjYhEHI2Rxup327LG072CqWx8Ysnlk90FAF0v7iJc9toyI+YCdclJELOUABKzeScTMtZoL519mTBHn/icg3IDZELGA4Px8J1XAKsgWMQG3mNlFzLwwrd+4uVsrvvzZ6UxRjDguQYrTfY8UIhaEanp53L57yimW1vRMMU0vbk41u8XSLlr285hYZiuWTq1x+o4pL9/9l/0jq+0W2qfoWzc5sosY9z/J9gVELFne1AYBCEAAAhCAAAQgAAEIQEAQMToBBCAAAQhAAAIQgAAEIACBhAkgYgkDpzoIQAACEIAABCAAAQhAAAKIGH0AAhCAAAQgAAEIQAACEIBAwgQQsYSBUx0EIAABCEAAAhCAAAQgAAFEjD4AAQhAAAIQgAAEIAABCEAgYQKIWMLAqQ4CEIAABCAAAQhAAAIQgAAiRh+AAAQgAAEIQAACEIAABCCQMAFELGHgVAcBCEAAAhCAAAQgAAEIQAARow9AAAIQgAAEIAABCEAAAhBImAAiljBwqoMABCAAAQhAAAIQgAAEIICI0QcgAAEIQAACEIAABCAAAQgkTAARSxg41UEAAhCAAAQgAAEIQAACEEDE6AMQgAAEIAABCEAAAhCAAAQSJoCIJQyc6iAAAQhAAAIQgAAEIAABCCBi9AEIQAACEIAABCAAAQhAAAIJE0DEEgZOdRCAAAQgAAEIQAACEIAABBAx+gAEIAABCEAAAhCAAAQgAIGECSBiCQOnOghAAAJpENi6bYdcMe8WeW3Vm92q/841l8qnT50mC268y3j+urmXSt8+jZU0a9auk9nX3CRXXnyuzJx+kriVo16/+f+1dzehcVVhGIDPVjS0VtD6h9ZmUStqQZQsC11Z6bIh7hSJ9WdjLQWjFLrRlIjSTSsxCHVRKhEKVSwV/0pRKBWtIqjgRihoLVgEQ01dyblyh8ntzCQHvknC8NxdZr5855znzixe7rl3pmfTO8dOdl3i/ffek97c/3w6+Pb76aPPzl5T99i2kWoO+chzyjVHDr6UHt6yqVX7z/y/Xd+ri46fPJP2Tf2/pk7HrbfclKb2PZOmDh1rmeS5vXVgd7pxzVBrHdknr6v9qNdYv9c+n+ZY9XraTVfi/BuTAAECBFafgCC2+s6JGREgQCBUoBmm6ub59aPHP017nx1L81evVkFtdMfWBcEjh458vLhrNC2lT3vgqEPbnl2jHYPU+pvXVX07He3h5qnHty+o+/q7n9MTLxyo/q0Z0nr1Gnlo8zWhqh6nOZc6bDWDVG3w+x9/pmYQ67We0BOqGQECBAgMhIAgNhCn0SIIECDQXSBfHZr98HTrak+3yhxwJiZn0vTUnrTxrttS/vuN6dnW/y21T90/IogNb7g9ffvDL2nvc2PVnOrg9MDmjenI7Kk0OTG+IORFBrG5K/Npbu5K2rlja2uMHNBuuP669PlX51uhtVuY85kkQIAAAQK9BAQxnw8CBAgMuEAzYPVabg4aFy9dTruf3pl27z+04ApZSZ88RkQQy1exfr1wsZpyfVXu9cPvpXyVLIfGfgaxPObdd65PZ7/5sdouma8aTrw2U42dA2p99VAQG/AvkOURIECgTwKCWJ9gtSVAgMBqEeh0D1One5/yfNu33jW35ZX0WUoQW8o9YjmIPXjfcHplcia9OjGeTpz6sgpH+bV871q/g9iTY49WWzbz9soLv12qQmH9WjOI9VqPe8RWy7fBPAgQILB6BASx1XMuzIQAAQJ9F2i/vyoP1rz/Kr+WtyAefvdEa4tip0ktpU/UFbH6ISDnzv+U1q4ZSpMvj6fLf/29LEEsX4WrtmR+8EXFkMPgurVDC+6nc0Ws7x9bAxAgQGAgBQSxgTytFkWAAIHFBbptNWzeG7ZYp259IoNY80Eh9d/9viKWg1i9jke2bKq2R9Z/25q42CfD+wQIECDQS0AQ8/kgQIDAgAucOft9yo9mz49lbz9ymKm3/OUHYdRHtyBW2icyiOW5HT3+Sdq+baRax3IGsTz2x6fPpeENd1QPDBHEBvwLY3kECBBYJgFBbJmgDUOAAIGVEqh/U6v9Ue/1dro8p+Zvh3ULYqV9ooNYM0Quxz1inR6vL4it1CfZuAQIEBgsAUFssM6n1RAgQKCjQKcfOO50f1j+515bE0v6LBbElvqwjuYPKuc5RlwRa/44dfMHnfM4JUHMwzp8+QgQIECgREAQK9FSS4AAAQIECBAgQIAAgQABQSwAUQsCBAgQIECAAAECBAiUCAhiJVpqCRAgQIAAAQIECBAgECAgiAUgakGAAAECBAgQIECAAIESAUGsREstAQIECBAgQIAAAQIEAgQEsQBELQgQIECAAAECBAgQIFAiIIiVaKklQIAAAQIECBAgQIBAgIAgFoCoBQECBAgQIECAAAECBEoEBLESLbUECBAgQIAAAQIECBAIEBDEAhC1IECAAAECBAgQIECAQImAIFaipZYAAQIECBAgQIAAAQIBAoJYAKIWBAgQIECAAAECBAgQKBEQxEq01BIgQIAAAQIECBAgQCBAQBALQNSCAAECBAgQIECAAAECJQKCWImWWgIECBAgQIAAAQIECAQICGIBiFoQIECAAAECBAgQIECgREAQK9FSS4AAAQIECBAgQIAAgQABQSwAUQsCBAgQIECAAAECBAiUCAhiJVpqCRAgQIAAAQIECBAgECAgiAUgakGAAAECBAgQIECAAIESAUGsREstAQIECBAgQIAAAQIEAgQEsQBELQgQIECAAAECBAgQIFAiIIiVaKklQIAAAQIECBAgQIBAgIAgFoCoBQECBAgQIECAAAECBEoEBLESLbUECBAgQIAAAQIECBAIEBDEAhC1IECAAAECBAgQIECAQImAIFaipZYAAQIECBAgQIAAAQIBAoJYAKIWBAgQIECAAAECBAgQKBEQxEq01BIgQIAAAQIECBAgQCBAQBALQNSCAAECBAgQIECAAAECJQKCWImWWgIECBAgQIAAAQIECAQICGIBiFoQIECAAAECBAgQIECgREAQK9FSS4AAAQIECBAgQIAAgQABQSwAUQsCBAgQIECAAAECBAiUCAhiJVpqCRAgQIAAAQIECBAgECAgiAUgakGAAAECBAgQIECAAIESAUGsREstAQIECBAgQIAAAQIEAgQEsQBELQgQIECAAAECBAgQIFAiIIiVaKklQIAAAQIECBAgQIBAgMB/H6MVHYe1NLQAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics_fixed.plot_history(colors=['blue', '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": "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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szFnQqP1emjjcili1e7m8cdWz+uXMbys2s6v2qCfvjuNeH66wnP2J80qPjapcBEGIBT1bEtrPu2tiKtcvo17/uoza+g+Syh2SfLpTDp60UA5+4EbJpzsSSig+h80AFp9c1BMJk8R6KMWrDTUWr3zUioYaq0Uoft9TY/HLSa2IGt2+frjNOtx7r6rtmljt0sTKnb/DEGLDCSkV74MPP1G28QhCrNYZxPfDEqi2fX3LkZ0y+uUl0rmz8ADogc4TZP/vLJOeif8NmhESYACLEH4A10wSA0CLuAs1FnECfLqnxnwCi0FzaiwGSfAZQqNCbKjt690rttSVXPUIMVeYvbl916BdCqdOmVDaLdz72KZ6VskqV8TcVS+1g+Oc2ec7tFzBqN57nznm2vduEMKKmM8TLOnNh3uOWNu+Z6T7hb+Q1oMvOZj6uj8qe89cLdmRH0w6tkiOnwEsEuyBnTJJDIwuso7UWGToAzmmxgJhi7QTNRYp/kDOGxVirtPKbd+991VVe6BzNRGlbA21fXxHe/ug3cKDCDHlwxVjO9553wm/8h6wW1asK32+aMEX5J71j5ae0YsQC3SaJbdTzQc653My8u17pOs3t0q6f7ez3f2hqfPkwCl/L7nM6OSCi+DIGcAigN6ASyaJDcCLqCs1FhH4gG6psYDgIuxGjUUIP6BrXUIsoHu6xZhA4ndN1JGbmkKs6CTdv1e6fvN3MvKt/+N8kmsdJ/tO/4azqQcvMwQYwMxw1uWFSaIukubsUGPmWOvwRI3poGjWBjVmlrcObwgxHRSb0wZCTENe6xVirqvWgy/K6BdvlPY9TzofZUecIgdOuVl6Js3VEA0mhiPAAGbX+cEk0a58qWipMbtyRo3ZlS9qzL58uTmzM3KiDpsAQkwDYb9CzHXZuWODdP32K6Xt7guC7BbpmfR/aYgKE9UIMEm067xgkmhXvpgk2pcvasy+nDGO2Zkz+6ImYhMEEGIaKAcVYo7r/ICM2LFBRr3yNcn0bHU+6h95uhw85W+lZ+LnRCSlIUJMuAQYwOw6F5gk2pUvhJh9+aLG7MsZ45idObMvaiI2QQAhpoFyQ0LM9e8Isgdk1CvLJNPzWkGQdZ0lB07+W+mdcImGKDHBJNG+c4BJon05Y5JoV86oMbvyxThmX77cnNkZOVGHTQAhpoGwFiFWEmRZGbH9funaulxaet4oCLLRH5IDJ98ivcdepCHaZJtgkmhX/pkk2pUvJon25Ysasy9njGN25sy+qInYBAGEmAbKWoVYMZ5Url9GbP8nGbX1H6Sld5vzaV/378rBU26R3vGf0hB1Mk0wgNmVdyaJduULIWZfvqgx+3LGOGZnzuyLmohNEECIaaAchhBzw3IE2dv3FQTZkbcLgmzMeXLg5L+TI+P/UEP0yTLBAGZXvpkk2pUvhJh9+aLG7MsZ45idObMvaiI2QQAhpoFymELsqCDrkxFv3SOjXl0pLUe2FwXZx5xdFo+MO1/DUSTDBAOYXXlmkmhXvhBi9uWLGrMvZ4xjdubMvqjDi/iONRvk6c0vy+rlN8jY7q7wHGmwvPWN7TJ/8Sq57urLZM5s/fNthJiGJJkQYt4wR765WkZtXSktfTudj3uPuUgOT/0z6Z1wqYajaW4TDGB25ZdJol35QojZly9qzL6cMY7ZmTP7oq4v4p7ePrl15Tp5c/uuuoTVM5tflgcffkJuW3StdHa0idv/kcc3lTk889ST5I6//5Lc9Y8PyqxzTisTQcrG0mVrZc2KhTJ92hSn3559B2TBkjvlhCkTSra9Bl1BteOd90sf33vXEvnpL5+Xbz2wserBXnzhLMfW9nfek5V3r5dlN83TLhwRYvWdZ8O2Mi3E3GBGvfFNGfnqnSVBlu08SQ6deL0cPv5PJJ8eoeHIms8EA5hdOWWSaFe+EGL25Ysasy9njGN25sy+qOuLWAmcNd/+vuw/eFi+eOVsOXfmjCE7uqLr8ksvKLVzP6sUW64RJbCWfm2tLLruCkd0uYJr4fy5Zb5cgaficNu6NtR313x5uSjh5can7Nyz/lFZcPXnHUGoXmqlTr1unD930DE8tPFJ5zPdq2IIsfrOs1gKMRWUuoesc+e/yMjXvy6tB37lxJlrHSOHjv+iHD7xL2WgbaKGI2weEwxgduWSSaJd+UKI2Zcvasy+nDGO2Zkz+6KuL2JXoKjWr2/bWVXEuJaUaKtcWaolxFRf7yraoz/ZVNWPElEfP+8sZ4XrxKmTSoKpHvtufMMJMRX7/Q89JosWXFESbvURGr4VQkwDxahWxCpDb9/9Uxn5+jek491HlRyTfKpVeib9kRw6aaH0jzpdw5Hab4IBzK4cMkm0K18IMfvyRY3ZlzPGMTtzpiPqjRtFcjkdlvzZuGSIx9kqkbNy9Xq5as4nHYO1Lt9TgkoJJe+KU71CSYmkg4d7ZfvO9wZdIqhWt5Z9435Zev1V8sprb5dd+qgE1M3L1spXl84rXcY41NEPJ8QqV+b8ERy6NUJMA8m4CDH3UNQDoUe+9nUZ8fb9ksodcj4+MvZ8OfSB66X32M+qdTQNR22nCQYwu/LGJNGufCHE7MsXNWZfzhjH7MyZjqhTEU3f8vnq0XtXiVQLda/YUJcYqu+rXd433D1i3s08hrokUdn1CrzKdtVW4YIIMa/odO9L05LTfH4ovDrMJ8NG3ISYSz2d3S8j31wrI95cXdppMTviFDl04l/K4ePUfWSdyUiQ5ygZwOxKOZNEu/KFELMvX9SYfTljHLMzZzqinjNHJJvVYcmfje9/v3p7tYLkvQxQCa1Nz75YdbOMWkJsOAGn+ipfv966TfYdOFS2KUi1+868K1u6VsQQYv7OGaOt4yrEShDyWRmh7iN7Td1Httn5ONc6rngf2XWJuo+MAcxoaTTsjEliwwiNG6DGjCNvyCE11hC+SDpTY5Fgb8ipylmzvdyVpy0vvVp2aJMnji/bzdD7ZdBLE733iK2+718dk+7ljdV2Q1Tfq10X1YpaR3t7zZU6N8bhLk1EiMX4DI69EPOwa9/zMxn5+jelY9fDpU8PTvsrOXLspxPxgGgGsBgXUpXQmCTalS8VLTVmV86oMbvyRY3Zly83Z3ZGPnTUShytWrNh0Jb1latkXgtBNuuotWtitVW4ylUyHbsmsllHjM9gm4SYi9G5j+z1b8iIt75Tuo9soP04OXzcldJz3NWSHTE9xsSDh8YkMTi7KHoySYyCemM+qbHG+JnuTY2ZJt64P2qscYamLTTjithQq0eVzwnzsh5u+/ogzxH7+u3Xy33//GjV+9KUQPPu4jjUc8S82+2zfb3pytDkz0Yh5h56auCgjNixQTrfuk/a9j1TItLX/bvSM+Uq6Zn8BWc7/GZ5MYDZlUkmiXbli7/W25cvasy+nDGO2Zkz+6IOJ+LhhFo4Hhu36mfDD7/e2DXRL7Eq7W0WYt7DyRx8WUa8dZ+M2P5dSfe/63yVT7dJ7zEXSc9xV8mRYy6SfLpVA7HoTDCARcc+iGcmiUGoRduHGouWv1/v1JhfYtG3p8aiz4HfCJpxRcwvA297tfL09OaXB13W2IjNsPq6K2nXXX2Z9oc5q5gRYhoy1yxCrIQin3WeRaZEWcd7PxLJF7boybWOl57Jlzs7LvaP/rAGcuZNMICZZ96IRyaJjdCLpi81Fg33oF6psaDkoutHjUXHPqhnhFhQcs3fDyGmIcdNJ8Q8TNJ978qIt78jI966VzKHf1v6Jjvyd6TnuD+Vw8ddZdWuiwxgGk54gyaYJBqErckVNaYJpCEz1Jgh0BrdUGMaYRoyhRAzBNpCNwgxDUlrZiHmxdO29xcyYtu3pXPnv5Q2+FDfH55ypfR3f0R6J35OBtonayAangkGsPDYhmGZSWIYVMO1SY2Fy1e3dWpMN9Hw7VFj4TPW7QEhppto89hDiGnIZVKEmIsqlTssnTsfkhHb7hUlzryvvtHnyJGJl0rvhNnSP+oMDXT1mmAA08szbGtMEsMmrN8+NaafaZgWqbEw6YZjmxoLh2uYVhFiYdK12zZCTEP+kibEvMgyh7dK587vSfuuR6Vt31NlNAc6p0nPhM/JkQmz5ci4P9BAunETDGCNMzRpgUmiSdp6fFFjejiaskKNmSKtzw81po+lKUsIMVOk7fODENOQsyQLMS++dP9e6Xj3B9K+6xFpf//Hks7uL32ttsDvPeYzhdWyYz4j+ZaRGsj7N8EA5p9ZlD2YJEZJP5hvaiwYt6h6UWNRkQ/ulxoLzi6qngixqMjH3y9CTEOOEGJVIOaz0r7n59L+ziPODoyZnq2lRmpL/L6x50uvcwnjpTLQPklDFuozwQBWH6e4tGKSGJdM1B8HNVY/qzi0pMbikAV/MVBj/njFoTVCLA5ZiGcMCDENeUGI1YaYOfQbR5A5q2V7nxLJD5Q69Y/+UEGUHXux9HedWdtYAy0YwBqAF0FXJokRQG/QJTXWIEDD3akxw8A1uKPGNEA0bAIhVg6c54gd5YEQ01CMCDF/ENUli+3v/kA6lCh770eSzu4rGRjoPEF6jr1Ejky4RI6M+32RVMaf8RqtGcC04gzdGJPE0BFrd0CNaUcaqkFqLFS8oRinxkLBGqrRZhRiPb19cuvKdfLI45tK7CZPHC9rViyU6dOmDMnzmc0vy4MPPyG3LbpWOjvapJod1fnMU0+SO/7+S3LXPz4os845rexhysrG0mVry3zt2XdAFiy5U06YMqFk2xuE+2DmHe+8X/r43ruWyE9/+bx864GNVeO9+MJZjq3t77wnK+9eL8tumidju7u0nisIMQ04EWINQMwPSPueX0j7ro3S8e7GsmeV5TLdcuSYz0jvxEuk99iLJN8yqgFHha4MYA0jNGqASaJR3FqcUWNaMBozQo0ZQ63NETWmDaUxQ80sxLwi6aGNT8qmZ1+sKoQUbFd0XX7pBXLuzBkOf/ezSrHlJkcJrKVfWyuLrrvCEXiu4Fo4f27JhmrrCrz9Bw+X2ro21HfXfHm5KOHl+lV27ln/qCy4+vOOIFQvtVKnXjfOnzvo3FDHpl5zZp+v9bxBiGnAiRDTALFooqXndenc9X1HmCmBJvms803hvrKPS++ES6R34mWB7ytjANOXKxOWmCSaoKzXBzWml2fY1qixsAnrt0+N6WcatsWkCDEleFat2SCrl99QdeVIrUpVrizVEmJekaVWpx79ySZ5fdvOQWJJiaiPn3eWs8J14tRJJcFUj303/8MJMRX7/Q89JosWXFESbjrOG4SYBooIMQ0Qq5hIZQ9Ix3s/dO4r61CXMPbvKbXq75pZWCmbcIn0d51VdwAMYHWjikVDJomxSIOvIKgxX7gib0yNRZ4C3wFQY76RRd5BmxDbvlEknzN/PMddMshnNYGjVo2qiSS3sxJqSih5V5zqFUpKJB083Cvbd7436BJBtbq17Bv3y9Lrr5JXXnu77NJHJaBuXrZWvrp03rCXTKoYhxNilStzupKAENNAEiGmAWIdJtr3/KywUvbeD6X14EulHtkRp0jP5MtlYMQ06es+T7IjPzikNQawOkDHqAmTxBglo85QqLE6QcWkGTUWk0T4CIMa8wErJk21CbHvpqI5oj/ODynEvPeIqUZfvHJ21Uv71HfVLu8b7h4x78raUJckKrtegVfZrtoq3FAQhxNiKs6Vq9fLVXM+WVPQ+UkSQswPrSHaIsQ0QPRpoqXnTel892Fne/y2PT+XVL6/ZCHXeoz0jf2o9I39PekbM0vUrozq0kb1YgDzCTri5kwSI05AAPfUWABoEXahxiKEH9A1NRYQXITdtAmxJ+eUbtkwejh/8P0hhZj33q5aq1vDCbGh7hFzHSuR9Out22TfgUNllz5Wu+/MK6h0rYghxIyecf6cIcT88dLdOpXrkbY9T0nb+0+KWjVr3f8fksr1ldzkU+3S332OHBk7S7pOuEB2tpwjudaxusPAXggEmCSGADVkk0wSQwas2Tw1phmoAXPUmAHIml1oE2Ka42rE3FCia7jLE4NemujdaXH1ff/PRaZsAAAgAElEQVTqhO1e3lhtN0T1vdp1Ua2odbS3O7s71hJ6qg8rYo2cERH2RYhFCL+K61T+iLTteVra9vxU2nY/KW17nxEl1rwvdTlj35iPSt84tWr2UcmOPCVeB0E0DgEmifadCEwS7coZNWZXvlS01JidObMv6uEjribEaq2IBdmso9auidV2aqxcJdOxayKbdcT4DEaIxTg5xdDa9v5C2nf/VLoO/ELyu342SJj1dZ8r+cxo6e86w7mUUW0Akh1V2FqVV3QEmCRGxz6oZyaJQclF048ai4Z7I16psUboRdO3mVfEKu8Ru33xtUNu8T7c9vWVdup5jtjXb79e7vvnR6uudlWuzA31HDF3O3t1ZrB9fTT1UfLqniDqA/dBc+q9SuYtK9Y57dyHu7nPHFCfIcQiTpwP984A9t5Badv/nLTt+Zm07f6ptO35RdlDpV1z+fRI6R99hvR3nS393UqcnS3ZUaeV7jfz4ZamAQkwSQwILsJuTBIjhB/ANTUWAFrEXaixiBMQwH0zCrEAGJwulQ90DmrHZD8/G374jYvNOorEvLu2eMVW5TMRqqllhJjf0y669tUHsLxkDr8irft/JZn9m6Vt/6+c9+n+9wYFmk+1SnbkDOnvPluyo2dK3+iZzuqZjodNR0clvp6ZJMY3N0NFxiTRrpxRY3blS0VLjdmZM/uiDi9iNZd+evPLQz5vLDzP/i27K2nXXX2Z9oc5q2gQYsWcqJNCPQBOvbxPBXc/d5+kXe1hdQgx/yd2VD38DGAtvW9L64GCKGvdv9l5r3ZrHPxKSXbE9MKKmRJn3WdL/+iZonZv5NUYASaJjfGLorefGosiPnyWE6DG7DsjqDE7c2Zf1ERsggBCrOKaUO9NfyoBlTutVNsGEyFm4lTV46PRASzdv7cozjaXVs8yh38rkh8YFOBA+xTpH312mUAb6Jim50ASYoVJon2JbrTG7DtiuyOmxuzLHzVmZ87si5qITRBIvBCrvJmvmhC7/NILxL2Zz8/zCEwkEB8xIDDQI7LnVyJ7nhPZ/Vzh594XRHK9g4NrGysy9kOFf+OKP0fPEEmlY3AghAABCEAAAhCAAAQgYIpA4oWYuvTwWw9sHMRb3Se25L//iSz/5nfKdmNhRczUqRmOH5N/SWw9+IK07lP3nf1KWg+oe882S2rg4KADy6c65Mgxf+js1ijpTunvOs251DE78oPhQLDIKn+ttyhZxVBN1ph9dOIXMTUWv5zUiogaq0Uoft+zWUf8chKXiBIvxCoTUfk8Au4Ri8upqieOqAewTM+r0rr/ecnse86576ztwK8k3bdryINTzzvLjjhJ+rtOl4GRpzjPO1MCLSn3nzFJ1HPem7QSdY2ZPNZm8EWN2ZdFaszOnNkXNRGbIBCpEFMPaVuw5E7Z8tKrg47VfSL22O4uExxKPiqFGLsmGsUfurM4DmDpvncdcdZ6+GVpOfBrZwfHzKFfS8uRHUPyyLd0Sf+oMyQ7aroMjJwhfaM/JEfG/2Ho/Ew7YJJomnjj/uJYY40fVfNaoMbsyy01ZmfO7IuaiE0QiFSIDffgNBMHX81HtSd08xyxqLKh369NA1gq1yOtB/5LMoe3Ssuh30rmoBJpW53LHId75VrHSLZzuuQ6pjirabmO4yTbOU0GOk+QgY4TJNc6Vj/YkCwySQwJbIhmbaqxEDFYY5oasyZVpUCpMTtzZl/URGyCQGRCTK2GLf3aWll03RUyfdoUE8camg92TQwNrXbDzTKAqW30HVF26CVpOfgbZxWt5fDroi59rPVSzzzLKlHmirPOE2Wgc6qoHR3V57m2Y2uZMPY9k0RjqLU5apYa0wYk5oaosZgnqEp41JidObMvaiI2QQAhpoEyQkwDREMmmn8Ay0vLkZ3S0vuG88yzzOE3Jd3zhmR63pCW3jelpWebqJW24V759AhHmGU7Cqtouc5pkh1RWE1zxFv7RPUIQiMZY5JoBLNWJ81fY1pxRW6MGos8Bb4DoMZ8I4u8A5t1RJ6C2AYQmRBTRCo3wogtpRqBIcTsyRwDmDibg2R63iyKtW3OSpoSbUqoqc+r7exYmWF16eOAK85GTHNW046M/wNRz07T+WKSqJOmGVvUmBnOurxQY7pImrNDjZljrcsTQkwXyeazE6kQU1vB3//QY7JowRXS2dFmLV2EmD2pYwCrnat0/x5pcVbRCmItffhNyfS+Kene7ZLp2Srqoda1XrnW8Y4oG+g4TgY6pkiu8/jC+/bjZaB9snP/Wi4zupYZYZJYE1HsGlBjsUvJsAFRY3blS0VLjdmZM/uiJmITBCITYsPtmKgOPKpdE4NAR4gFoRZNHwawxrmrSxszh191xJpaSUv3viWZQ69Jy5G3paV327C7PXq9q3vVlChzxVq2+0PSP+qsUpN8S6t0jjpW8u3jZX92TOOBY8EIAWrMCGZtThBi2lAaM0SNGUOtzRErYtpQNp2hyIRYM5FEiNmTTQYwM7lq6X1bWo5sF/dnqneHZHq2Sdr5rPAvle/1FYxaQctnxkmubazkWscV/6n34yU/6DPVTrUZ78sHjRsnQI01ztCkBYSYSdp6fFFjejiatIIQM0nbLl8IMQ35QohpgGjIBAOYIdB1uEn37ZaWvqJY690u6SM7JN33nqjP0/27JdW/RzLZPZLq2y2pbO3LIYdymct0O6It3+oRcEq4ZcZJvn2c89MRbZmxBZGXGe/8zisYAWosGLeoeiHEoiIf3C81FpxdVD0RYlGRj7/fyIWYemDyNV9eXkbq3ruWyLkzZ8SfXjFChJg1qeLaentS5URamiQeOiLp7D5J978v6h42JdTSfXsknd0tqSPvSzq7p0zAFdqoz/eLSD7AUacl19pdFGkF0aZEmrMi1z7eeRZbXq3KuQLOEXnq825jO0oGOCgjXZgkGsGszQlCTBtKY4aoMWOotTlCiGlD2XSGIhViSoStWrNBVi+/QcZ2dzlw1QYe8xevkuuuvkzmzD7fCuAIMSvS5ATJAGZPrsqE2OH+YIHnc87mIuns+0XhVhRsjoDb7Qg5R9AVBZ5ahSsIuAPBBVymS/JKxLWolbgxhfeZ0ZLLjJF8plvybWNErdKp9+p7533raMm1jHF+l1Q62LHGpBc1FpNE1BkGQqxOUDFqRo3FKBl1hoIQqxNUAptFJsR6evvk1pXr5PJLLxi0+qUE2oMPPyG3LbrWit0UEWL2VA4DmD250iLEgh5ufkDS2b2lVbbSKpy6ZLJ46aT3MyXmUkrUOStwjb3y6TbJpzskn+4USXdKvqVD8i2dkk91SD5T+Nz5pz533hc+l5YRR39X7Vs6RJw+xTZOH/d9sW/Rns7nwlFjjeXfdG+EmGnijfujxhpnaNoCQsw0cXv8RSbE1K6JS7+2VhZdd4VMn1b+7CG1Krby7vWy7KZ5pZWyOCNFiMU5O+WxMYDZk6tIhVhgTPniCtxeSWX3S7pfXU65V1ID6uc+San36rPS7/uKl1zuk9SAWrk7IJIfCOw9aMd8qv2osGtRAlD9Xin4lJBrL4rAgqCTjBJ/RVHnCMYOGdvdLe8fbhHxfq7el9nrSPwlnEFzpbsfQkw30fDtMY6Fz1i3B4SYbqLNYy8yIcaKWPOcRDYdCQOYTdny3CMW9NJEuw7XiTaV65XUQK+oxwQ4/wZ6RZzPCu9Ln6vPsj3O7pNOm+zhQt9SvyPF/j0iuSOSHjgsUrRXapft9b17pU6kzmWZStB5V/7SIyTfUlwVVCt6Le1FYdhRWBVMt4uUVvnaRZQAdISkEonqe2WvVfKpjEgqU/pZep9ukbxkRNLq+5bC95KRfLql0F71T9ALIWZfshnH7MyZfVETsQkCkQkxdXAPbXxSNjz8BPeImcg0PhwCDGB2nQhMEs3kq1z8FYWdI9q84k+JvKIgdAViSfy5n/dKZ6ZPjvQcPCogS+KvKCwd8Xck4D14ZngUFHGmJNjyqaJIK4o7JeLyoj5rkbwSdEVhd1TUFUTeUfFXFISqXSpd6uP0LROLRWGo/LS0FgWia+uogCwTmUpAKiGp+jhxeURmMTY3/mpidGSnEq4ZOdgr4rRzbaj3vGJJgHEslmkZNihWxOzLmamIIxVi6iDZNdFUqvGDELPvHECI2ZezeieJ7mpf4acSaUfFnAyo1bzCal3KfZ/rFedzJeLUSmCu2MZZJVQq4khxxfCIc3lnKt8nkstKKp8t/JRs4fNcVkS9d7+TbOGzfE5SucP2ATcQcT49sm4B6QrTfLq1sPGMI2iLAs8Vss7KY7mALKxKFlcpnZ9thSNzNq9JiaRSxctZi+/zynZK8mXfqSYV7aTYRrVz2la359jx2sqX+8w7x+IENDge9zPlq4p/r0/HT4XtQszFTXrU1+q9a0f9VO09sR3T3SHv7u8bHIt7bMV4ytmo4xkcf+G4K5hUHMOwbNQfFkqxFe17+idthXmockSIGfiPylIXkQsxS7mVhc09YvZksd5Joj1H1NyRIsTsy28z1ZgSiV7xVhBshX+OwHMEX+Gn81lR5KVyxd+Lgu9oe9VG3QN4VCA6NkrCsNDP+ZfrP+ond7SNY6vUPlceT0lwHvUztBgt+Eq78Tv+lFBFjNpXdc0ZsboU+aggdXeT9Yhdr2D0iOGSQK8mvN0++SFEs6MlC+K0JKq9wnkooV8WS7mwVSK+/bNPNmeSOKqGCSDEGkYoghDTANGQiWaaJBpCFqkbhFik+AM5p8YCYYusU60aGyRGlegsCU6vGC0K1GHFaFGgem14VyydVUqvGFWiVT0HMO+sWEpK/Sz8nir+LHyn8Lntij/dNiklVgd/V7Lj9C9+77Hv+Cv5Kdov85kvxFPsr9bd3Pcig32Wvq8Spxt/quizajweP62ZlPT3V7BRsRXjKWfjPkfRc5xB2Lhxu7koy4E69KPc1Xu1ms3LQ+CPgzzPEoJJIIAQ05BlhJgGiIZMMEk0BFqTm1qTRE1uMKORADWmEaYBU9SYAciaXTR7jTmXGnsFuKOD1QWQ5WLSEX8eMewI51KbKgK8KLTLRbMroF2xnSvYKBOe5SLT/W6Q4K0Q/Uf9iIw/5dOazwLMNQsB40JMbVu/YMmd8mdfuEju+ecfyJaXXq3K8sxTTyrbxCPOwBFicc5OeWzNPoDZk4n6ImWSWB+nOLWixuKUjdqxUGO1GcWtBTUWt4zUjod7xGozSmoL40LMBT3cc8R4oHNST8fwj5sBLHzGOj0wSdRJ04wtaswMZ11eqDFdJM3ZocbMsdblCSGmi2Tz2YmlEOOBzs13osXliBjA4pKJ+uJgklgfpzi1osbilI3asVBjtRnFrQU1FreM1I4HIVabUVJbxFKIqeeLbXr2Rblt0bXS2VHcwjbGGeLSxBgnpyI0BjB7cqUiZZJoV75UtNSYXTmjxuzKFzVmX77cnNkZOVGHTcC4EFOrXfMXr5Id77w/5LFNnjhe1qxYKNOnTQn7+LXYR4hpwWjECJNEI5i1OWGSqA2lMUPUmDHUWhxRY1owGjVCjRnFrcUZK2JaMDalEeNCzKU43D1itpFGiNmTMQYwe3LFiphduXKjpcbsyhtCzK58sSJmX75YEbMzZ6aijkyImTpAE34QYiYo6/HBJFEPR1NWmCSaIq3PDzWmj6UJS9SYCcp6fVBjenmasMaKmAnKdvpAiGnIG0JMA0RDJhjADIHW5IZJoiaQBs1QYwZha3BFjWmAaNgENWYYuAZ3CDENEJvURKRCbLj7xXiOWJOecREfFgNYxAnw6Z5Jok9gMWhOjcUgCT5CoMZ8wIpJU2osJonwEQZCzAeshDWNTIj19PbJrSvXyaxzTpOzTz9Z7n/oMVm04Apnl8Q71myQj593lpw7c4YV6WBFzIo0OUEygNmTKxUpk0S78kWN2Zcvasy+nDGO2Zkz+6ImYhMEIhNi3s061IGuvHu9LLtpnozt7hIe6Gwi9cn0wQBmV96ZJNqVL4SYffmixuzLGeOYnTmzL2oiNkEgFkJs3JguWfaN+2Xp9Vc5QowHOptIfTJ9MIDZlXcmiXblCyFmX76oMftyxjhmZ87si5qITRCITIh5L02cM/t853LEE6dOEvWeBzqbSH0yfTCA2ZV3Jol25QshZl++qDH7csY4ZmfO7IuaiE0QiEyIVR6culRxwZI7ZctLrwoPdDaR+mT6YACzK+9MEu3KF0LMvnxRY/bljHHMzpzZFzURmyAQGyFm4mDD8sFmHWGR1W+XAUw/0zAtMkkMk244tqmxcLiGZZUaC4tseHapsfDYhmWZXRPDImu/3ciEmHezjunTplhNEiFmT/oYwOzJlYqUSaJd+WJFzL58UWP25YxxzM6c2Rc1EZsggBDTQBkhpgGiIRMMYIZAa3LDJFETSINmqDGDsDW4osY0QDRsghozDFyDO1bENEBsUhORCTHF07bnhQ11DiDE7KkOBjB7csWKmF25cqOlxuzKG0LMrnyx6mxfvtyc2Rk5UYdNIFIhprap9z7IOeyDDcs+QiwssvrtMknUzzRMi0wSw6Qbjm1qLByuYVmlxsIiG55daiw8tmFZZkUsLLL2241MiHl3SayG8cxTT5LVy29wnisW9xdCLO4ZOhofA5g9uVKRMkm0K1/8td6+fFFj9uWMcczOnNkXNRGbIBCZEDNxcKZ8IMRMkW7cDwNY4wxNWmCSaJK2Hl/UmB6OpqxQY6ZI6/NDjeljacoSK2KmSNvnJzIhNtyuic9sflkefPgJuW3RtdLZ0RZ7qgix2KeoFCADmD25YkXMrly50VJjduUNIWZXvlh1ti9fbs7sjJyowyYQSyGm7h1befd6WXbTPC5NDPsMSJh9Jol2JZxJol35YpJoX76oMftyxjhmZ87si5qITRCIpRB7aOOTsunZF42tiKndG7/1wMYS73vvWiLnzpxR+l3Fc8uKdc7vF184a1BcrIiZOFX1+GAA08PRlBUmiaZI6/NDjeljacISNWaCsl4f1JheniascWmiCcp2+jAuxNRq1/zFq2THO+8PSWzyxPGyZsVCMfGgZ3WJ5D3rH5UFV3/euQxSxXfzsrXy1aXzHP/qMslVazaUNg5Rok29bpw/txQ/Qsyek58BzJ5cqUiZJNqVLxUtNWZXzqgxu/JFjdmXLzdndkZO1GETMC7E3AMa7h6xsA96OPvubo4L5891VsWU8Dpx6iSZM/t8p1ulMFOfIcSizJg/30wS/fGKujWTxKgz4N8/NeafWZQ9qLEo6QfzTY0F4xZlL1bEoqQfb9+RCbG4YlFCa+mytc6K3JSJx8itK9fJrHNOKwmxyhUzhFhcM1k9LgYwu/LFJNGufPHXevvyRY3ZlzPGMTtzZl/URGyCAEKsSNl7yaR7j1hPb58jxC6/9ILSPWPVhNiBnqyJXOFDAwE16SBfGkAaMtGeSYukRI705wx5xE2jBKixRgma7U+NmeWtwxs1poOiWRvOHzx4QaAKgUiF2HAPdY7qgc7eSxPPmHFSXStiBw73c3JZQqBrRKuQL0uSJSJtrWlRSqyvf8CeoBMeKTVm1wlAjdmVLxUtNWZnzuyLmohNEIhUiFXb+MLEQdfy4b0vjHvEatGy63su6bArX1w2ZVe+VLTUmF05o8bsyhc1Zl++3JzZGTlRh00gMiEWl8061KWGj//0WfnzP7nUYe1eorhs6TznckR2TQz7FDRrn0miWd6NemOS2ChB8/2pMfPMG/FIjTVCL5q+1Fg03BvxymYdjdBr7r6JF2LufWCPPL6plGmeI9a8Jz0DmF25ZZJoV774a719+aLG7MsZ45idObMvaiI2QSAyIaYOrvKyPxMHHIYPtq8Pg2o4NhnAwuEallUmiWGRDc8uNRYe2zAsU2NhUA3XJjUWLt8wrLMiFgbV5rAZqRBTlwHe/9BjsmjBFc7DlG19IcTsyRwDmD25UpEySbQrX6yI2Zcvasy+nDGO2Zkz+6ImYhMEIhNiw+2YqA48ql0Tg0BHiAWhFk0fBrBouAf1yiQxKLno+lFj0bEP4pkaC0It2j7UWLT8g3hnRSwItWT0iUyINRNehJg92WQAsydXrIjZlSs3WmrMrrwhxOzKF6vO9uXLzZmdkRN12AQQYhoII8Q0QDRkgkmiIdCa3DBJ1ATSoBlqzCBsDa6oMQ0QDZugxgwD1+COFTENEJvURKRCzLtj4eSJ42XNioUyZeIxgx6iHHf2CLG4Z+hofAxg9uSKFTG7csWKmJ35QojZlzfGMTtzZl/URGyCQKRCzN018bOfmCUrV6+Xq+Z8UqZPm+I8u+vBh5+Q2xZda8UmHggxE6eqHh8MYHo4mrLCJNEUaX1+qDF9LE1YosZMUNbrgxrTy9OENVbETFC200dkQsz7QGe1CuYVYmo3xZV3r5dlN82Tsd1dsSeLEIt9ikoBMoDZkytWxOzKFStiduYLIWZf3hjH7MyZfVETsQkCsRRirIiZSH0yfTCA2ZV3Jol25UtFS43ZlTNqzK58UWP25cvNmZ2RE3XYBCITYurAHtr4pGx69kVZev1V8s1133MuTRw3pksWLLlT5l56gcyZfX7Yx6/FPitiWjAaMcIk0QhmbU6YJGpDacwQNWYMtRZH1JgWjEaNUGNGcWtxxqWJWjA2pZFIhZgiqla/rvny8jK49961RM6dOcMa4Agxa1LFX+vtSZUTKZNEyxLGiph1CaPGrEsZ45h9KXNyxgsC1QhELsSaIS0IMXuyyF8S7ckVQsyuXLnRUmN25Q0hZle+VLTUmJ05sy9qIjZBIFIhpnZN3Llrd9nuiO6W9rPOOY1LE02cAQnzwQBmV8KZJNqVLyaJ9uWLGrMvZ4xjdubMvqiJ2ASByISYK7guv/SCQZchslmHidQn0wcDmF15Z5JoV74QYvblixqzL2eMY3bmzL6oidgEgciEmHf7evXsMO+L7etNpD6ZPhjA7Mo7k0S78oUQsy9f1Jh9OWMcszNn9kVNxCYIRCbEWBEzkV58VBJgALPrnGCSaFe+EGL25Ysasy9njGN25sy+qInYBIHIhJg6OHUJ4tJla2XNioXiroqp1bD5i1fJdVdfxj1iJs6AhPlgALMr4UwS7coXQsy+fFFj9uWMcczOnNkXNRGbIBCpEFMH6AqvHe+8Xzpetq83kfpk+mAAsyvvTBLtyhdCzL58UWP25YxxzM6c2Rc1EZsgELkQM3GQYftg+/qwCeuzzwCmj6UJS0wSTVDW64Ma08szbGvUWNiE9dunxvQzDdsizxELm7C99hFiGnKHENMA0ZAJBjBDoDW5YZKoCaRBM9SYQdgaXFFjGiAaNkGNGQauwR1CTAPEJjURqRBTOycuWHKnbHnp1UF4zzz1JFm9/AYZ290Ve/QIsdinqBQgA5g9uVKRMkm0K18qWmrMrpxRY3blixqzL19uzuyMnKjDJhCpEFMPdFavG+fPDfs4Q7WPEAsVr1bjTBK14gzdGJPE0BFrd0CNaUcaqkFqLFS8oRinxkLBGqpRVsRCxWu18ciE2HDPEbONKELMnowxgNmTK1bE7MqVGy01ZlfeEGJ25YsVMfvyxYqYnTkzFTVCTANphJgGiIZMMEk0BFqTGyaJmkAaNEONGYStwRU1pgGiYRPUmGHgGtyxIqYBYpOaiEyIKZ7q0sQTp06y5nlhQ50DCDF7qoMBzJ5csSJmV65YEbMzXwgx+/LW7OPYkSMi+XzhXy6nfqac91L8zP3O+ak+9nzutin0q/hXbFvVTtGH08ftW2G70l6lnVyFv6Pfp+SPPtdm34lGxEYIRCrE1DPE7n/oMVm04Arp7LD3JEWIGTlXtThp9gFMC6QYGWGSGKNk1BkKNVYnqJg0q1Vjvb0i2WxKBrIi2QGR3ID6vfDe+czznfrcbTeQTTntBtz22WJfp1/hu6M2jrZzviv2yQ3kyyfknolx+SS4MFGvNlGunBwPO5n22Hcn8gU/1e17RYA3nmoiwPl+yIl90X6leKjSXhnJtKSlrz9XIVaO2h8sNAbHr9r4YuOJv5xNdT5KTPE6SsARkrwgUIVAZEJsuB0TVZzsmsj5GgYBJolhUA3PZq1JYniesRyUQDPVWKUIKQiPChFSFA1KcAwnQlxB4gqNki0lUHIFu14Rku3Pl4sdj6BxbeUGhhY0uVxK+vtdu8Wfjo2CqBoo+iwIK2Un7/zs6QmaefpBQC+B9naRVKrwL51WP/POeyl+5n7n/FQfez532xT6VfmnQq32edGH08ftW2G70l6lnXSl3bTIUz9P64WDtaYhEJkQaxqCIsKKmD3ZbKZJoj3Ug0eKEAvOLqqe9daYEjm9PSlxfjr/UtLbI6L+kq7eq5/OP8979Xlfn+qXlyNHim16i33U773ifK8ExXAixF1xOSqcCn1UHLwGExgxQqSlJS8tGbUaI4WfGfVZ4Wcmky+9d9tkWgt91PdqMuy0L/YvvM+X2Tpqt+CnrbUQRyqdqjqRdie75ZPgwkS96kS5OJkeamI+aFJeOfn2CIFBPjxtq03uvT6d76tM7FUb53iVEKgUDxXtjx3TLu/tPzLoOEt+iu0HxzKYj2ozSDhUMByOjRN3qf1g+0pM8So81oMXBKoRQIhpOC8QYhogGjJR7yTRUDi4qUEAIWbmFHHET1EUue97XIHk/bwollzh1HO4IIgKoqogoCTXInv3DxTsOaKqQnD1FMRU3C/V8QqNQaKhJC6OihOv0CgIlXKhURIxdQqaTGvKI1QKQscVPuWCqMKPVxwVhU/a/awkoo4Kp+5RGVGiqbcvWxBHRYGlfPGKJwHGsXjmZbioEGL25cxUxJELsWc2vyzXfHl52fHee9cSOXfmDFMMGvaDEGsYoTEDDGDGUGtxlEQh5hVFZSLGI5aqrSApUeSsKnkEVGF16ehqkyOuegorSa7tKO/l6Bqdl44Okc4OkY7O4vtOkbb2vKi/pDv/OvLS3qZ+Fn9vz0tHZ6r4fUW7Yp+2tsGrN2UrLkVh4oib0ipPQYQk7S/4SawxLf85RWiEcSxC+JxPrHgAACAASURBVAFdI8QCgktAt0iFmBJhq9ZskNXLb5Cx3V0ObrWBx/zFq+S6qy+zZjdFhJg9lcIAZk+uVKS2TRLVKs++vSnZv19k376UHNifkv37RPbtV+/Vd8XPD4js35cqtim+3y9y8EDK2dzA9Kut7agQUsKoo6Mgipx/RYGk3itRVPq8Iy+dI1KltkooqX5Tjm2Tw9k+6Sy2dT/32nPv/TB9nPgbTMC2GiOHhcvcmHfYdSYgxOzKl8loIxNiPb19cuvKdXL5pRcMWv1SAu3Bh5+Q2xZda8VuivyHaPKUbcwXA1hj/Ez3jmqSqMSQElJ7dqdk7x6RvXuL7/eK7NktsmeP+jwle53fC+/37BVHeDX6alWiqChivCtFSrx4RVGlQOrsVKKo2Lez+NPp4xFWnvdee84N8Jpe1JgmkIbMRFVjhg6vKd1QY/alFSFmX85MRRyZEFO7Ji792lpZdN0VMn3alLLjVatiK+9eL8tumldaKTMFJIgfhFgQatH0YQCLhntQr41OEtVudGqFao8SU45wqi6o3O+VwFLv1cpUkHuY1I3ro7ry0t0t0tWVl9HdIt3deVGX4I0eXXjfPUakS71Xn3WLjO5W3xW/H5N3Njaw+UWN2ZW9RmvMrqNtjmipMfvyiBCzL2emIo5MiLEiZirF+PESYACz63xwJ4n7DvY7gkqtQDmrT54Vqd3vF1as1MqVWp3a47wvCCq1QhVUUCnxNHasyJixeRkzJi9jx+Vl7BiRseMLnznvxxW+c34fWxBVOleX7MpWIVpqzK6sIcTsyhc1Zl++3JzZGTlRh00gMiGmDuyhjU/Khoef4B6xsLOM/RIBJonxORmUaNq5MyU7tqdk547CeyWq3MsBlaByVrN2q3upgsetxNEYJZocsaREU1FIqd/HSeG7CkGlfucVjAA1FoxbVL0QYlGRD+6XGgvOLqqerIhFRT7+fiMVYgoPuybG/yRppggZwMxk0xVXzs+d6p/I9rdSsmNHuiS8/O7W56xQjSmKKEc4Fd6PU++VuCoTVAVxpb7jZZYANWaWd6PeEGKNEjTfnxozz7xRjwixRgk2b//IhVgzoOUeMXuyyADWeK7Utuevv5aWbW+m5K1tKdm+XeSN19KyY0dK3n4rJe/srG/nh5EjRSZNzsnkKXmZNDkvU6bkZdx4tXJVvBxwbF6On9zirFq1j+hvPHAsGCFAjRnBrM0JQkwbSmOGqDFjqLU5QohpQ9l0hiIVYnes2SA7d+0u2x3RvXds1jmnsX19051u0R8QA1jtHKj7q7ZtS8nb2wo/d+4oCC8ltF5/rXC5YK2XWolS4soVWccdr0RXQWxNnJSXyZMLG1jUejFJrEUoft9TY/HLyXARUWN25UtFS43ZmTP7oiZiEwQiE2Js1mEivfioJMAAJvLuu0dF1lvb1MqWOCtbb72VkrfeTMuhQ7XPmxM/kJfjp+Zk6tS8TJ0mcvzx6mdOJk3KywnTagus2h4KLZgk1ksqPu2osfjkop5IqLF6KMWrDTUWr3zUEw0rYvVQSmabyIQY29cn84SL+qibfQBTOwTueqewkuWIqzfTsm2byFvqMkIltLalRV1aONyrs1MckXX8VCW28jJ1qsjxJ+QKYuuEvBw7wdzOgEwSo64Y//6bvcb8E4l3D2os3vmpFh01ZmfO7IuaiE0QiEyIsSJmIr34qCTQLAOYElmvvJKWV19JySu/Tclrr6bkjdfT8sbrtS8bHDWqILBKQuuEgvBSq1vHTc3LMcfoW9Fq9AxkktgoQfP9m6XGzJOLxiM1Fg33RrxSY43Qi6YvK2LRcLfBa2RCTMFROyYuXbZW1qxYWHqos3qY8/zFq+S6qy8zco+YKwgfeXxTKV/33rVEzp05o/S72mb/lhXrnN8vvnBW2T1t6jM267DhVC/EaNMAplauXn4xLa+9mpZXt4r85tcFobXl+eGf+Kt2ElSXDqrLBD9wUk4mTZbC75PV6pZ6oHB8hFatM4dJYi1C8fvephqLHz3zEVFj5pk36pEaa5Sg+f4IMfPMbfEYqRBTkFzhteOd94cUQmHCVJdI3rP+UVlw9eels6NtkDhUYnHVmg2lZ52pDUbU68b5c0thIcTCzJBe23EcwN57LyX/tSUtv/1NYXXr1a3qZ3rY3Qe7uvIy49S8fGB6Tk4+WeR3Ti2saE37QE46OvQyi9Iak8Qo6QfzHccaC3YkyehFjdmXZ2rMzpzZFzURmyAQuRAzcZB+fChhtmDJnbJw/lxnVUwJrxOnTiqtzlUKM2UbIeaHcLRtox7A1IrWiy+kZfPmws8tv0o7m2cM9Tppel6mn5xz/p38QZGTT8mJ+mz8eHtWtRrJOJPERuhF0zfqGovmqO31So3ZlztqzM6c2Rc1EZsggBCroKxW6G5etla+unSeTJl4jNy6cp14t9L3fj992hSnN0LMxKmqx4fJAeylF9PywvNpeWFL4XLC/9qSkoMHB4uu9naR087IyQc/mJOTTxH54IyccymhEl1JfzFJtO8MMFlj9tGJX8TUWPxyUisiaqwWofh9z6WJ8ctJXCJCiHkyUfkMs2obilQTYnFJJnFEQ6CnR+T550X+8z9Fnnuu8O+FF6Tq7oTqYcUf+lD5vxkzRNLD3/YVzYHhFQIQgAAEIAABCEAgNAIIsSJaV3RNmjCudP9XtYdLsyIW2rloxHCjf0lUDzN+YYu7ylW4t2vrK2kZGBgcvtoc44wzc86/M8/Ky+lnFe7j4lU/Af5aXz+ruLRstMbichxJiYMasy/T1JidObMvaiI2QQAhJiLVRJgLn3vETJyG5nz4GcB27ihcUugIr+cLAkxtG1/5SqUKuxJ6BdeZZ+UScx9XmNljkhgm3XBs+6mxcCLAqh8C1JgfWvFoS43FIw9+ouDSRD+0ktU28UKs2qqX9xRg18TmKohqA5h6CLJ6DpcSWlueL6xyqXu73n9/sOjKtIpzL9cZZ+XkzLML4uv0M3IycmRzcYrL0TBJjEsm6o+DSWL9rOLQkhqLQxb8xUCN+eMVh9YIsThkIZ4xJF6IVds+X6Xqi1fOLl2iyHPE4nnyBolK/We4bVePs1vhU79okU2/SMnTv0zL/n2DRdeIESKnnV4QXWecVRBdM2bkpLUtiGf6BCHAJDEItWj7MEmMlr9f79SYX2LRt6fGos+B3wgQYn6JJad94oWYjlSza6IOiuHZyParDTTSsukXLfLcMxn52c9EDh0q9zd23NH7uQqiKy8nTc+xiUZ4aanLMpPEujDFqhGTxFilo2Yw1FhNRLFrQI3FLiU1A0KI1USU2AYIMQ2pR4hpgKjRRF+fyLPPtMhTv0jLUz9PyX/+R8ugHQzVc7nO/UhOzp2Vd36q33nFjwCTxPjlpFZETBJrEYrX99RYvPJRTzTUWD2U4tUGIRavfMQpGoSYhmwgxDRAbMBEb6/I05taHNHlrHo9l5b+vqMG29pEZn4oJ7973oBc9MlWmX5qr4wZy+6FDSA31pVJojHU2hwxSdSG0oghaswIZq1OqDGtOI0YQ4gZwWylE4SYhrQhxDRA9GlC7V74w0db5Ec/SMump1pEXX7ovsaPz8u55+Xk3PPUateAnHX20fu6GMB8go64OZPEiBMQwD01FgBahF2osQjhB3RNjQUEF2E3hFiE8GPuGiGmIUEIMQ0Q6zChNtX40aNpefyxFvnNy0efgHzc8Xn5wwsH5MO/m5dzfjcnJ58y9GWGDGB1gI5REyaJMUpGnaFQY3WCikkzaiwmifARBjXmA1ZMmiLEYpKIGIaBENOQFISYBohVTBw4kJJ/fzztrHr9++MtsnfP0Z0N1Q6Gn5mdk09fNODsZljviwGsXlLxaMckMR558BMFNeaHVvRtqbHoc+A3AmrML7Ho2yPEos9BXCNAiGnIDEJMA8SiiTffTMkPHmmRH/8w7dz3lc0WvlDP7/q9jw3IZz6bk9mXDMiEicHu8WIA05crE5aYJJqgrNcHNaaXZ9jWqLGwCeu3T43pZxq2RYRY2ITttY8Q05A7hFhwiAMDIs+oSw5/0CKP/SgtW185esnh6O68fOJCtfI1IBd+akDLQ5MZwILnKoqeTBKjoN6YT2qsMX6me1Njpok37o8aa5yhaQsIMdPE7fGHENOQK4SYP4gH9qfksR+3yGM/TMtPHi9/mPLxU/PO5YZq5WvW7w1IJuPPdq3WDGC1CMXreyaJ8cpHPdFQY/VQik8baiw+uag3EmqsXlLxaYcQi08u4hYJQkxDRhBitSG+8tu0PPajwi6H//F0WtRKmPtSuxq693uddnr993vV9jq4BQNYEGrR9WGSGB37oJ6psaDkoulHjUXDvRGv1Fgj9KLpixCLhrsNXhFiGrKEEBsMUd3b9cunCvd6/fiHLfL6a0c32mhtE/mYut9rdk4+e8mAHHtssPu9gqSOASwItej6MEmMjn1Qz9RYUHLR9KPGouHeiFdqrBF60fRFiEXD3QavCDENWUKIFSDu25uSx39cWPV64t/Toi5BdF/dY/LyiU8OyEWzc87PESM0gA9gggEsALQIuzBJjBB+QNfUWEBwEXWjxiIC34BbaqwBeBF1RYhFBN4CtwgxDUlKshBTK12PfD/jbLShnvPlfZ1wQl4++ZmC+PrYxz3XImpgHtQEA1hQctH0Y5IYDfdGvFJjjdAz35caM8+8UY/UWKMEzfdHiJlnbotHhJiGTCVNiPX0iCO+vvtPLfLLTeXia+aH1bO9cvLJTw/I6WeEe79XkNQxgAWhFl0fJonRsQ/qmRoLSi6aftRYNNwb8UqNNUIvmr4IsWi42+AVIaYhS0kRYmrFa8N3W+TfvpeRw4ePgvv98wurXur5XhMnmbvfK0jqGMCCUIuuD5PE6NgH9UyNBSUXTT9qLBrujXilxhqhF01fhFg03G3wihDTkKVmFmLvvZeSDQ9kZP395c/4OuWDObn8CzmZe2VWjp0Qb/HlTTEDmIYT3qAJJokGYWtyRY1pAmnIDDVmCLRGN9SYRpiGTCHEDIG20A1CTEPSmk2IqR0P1Vbz6+9vkX9/vEXU7+o1blxeLpszIJdfMSBnz4zfZYf1pJIBrB5K8WnDJDE+uag3EmqsXlLxaEeNxSMPfqKgxvzQikdbhFg88hDHKBBiGrLSLEJs6ytpuf/bLfIvG1pErYSpl9pq/sJPDcjlXxiQT35qQDKtGoBFaIIBLEL4AVwzSQwALeIu1FjECfDpnhrzCSwGzamxGCTBZwgIMZ/AEtQcIaYh2TYLsYMHU/JvD7XIA/e3yHPPHt14Q226ocTXf/ujAVFbzzfLiwHMrkwySbQrXypaasyunFFjduWLGrMvX27O7IycqMMmgBDTQNhGIfbmGylZc3fGuf/L3XhjynF5mXN5Vq68akBO/EDziC9vipkkajjhDZpgkmgQtiZX1JgmkIbMUGOGQGt0Q41phGnIFCtihkBb6AYhpiFpNgmxXz6Vln9cnZEfbGwpHfkfzc3KF66Mz7O+NKRkSBMMYGHS1W+bSaJ+pmFbpMbCJqzXPjWml6cJa9SYCcp6fSDE9PJsJmsIMQ3ZjLsQU5ttPPyvGVlzd4tseb5w+eGYsXn506uz8sU/H7Bq18NG08UA1ihBs/2ZJJrlrcMbNaaDojkb1Jg51ro8UWO6SJqzgxAzx9o2TwgxDRmLqxA7sD8l374nI+v+T4vs3FHYfOOk6XmZ9xdZZ9v5jg4NB2+ZCQYwuxLGJNGufKloqTG7ckaN2ZUvasy+fLk5szNyog6bAEJMA+G4CTF1/9f//l8ZeXD90fu/PvqxnMy/Liuf/PSApAqaLJEvJol2pZ1Jol35YpJoX76oMftyxjhmZ87si5qITRBAiGmgHBch9tTPW+QfV7c4zwDL5cTZav5zn8/Kl64fkBmn2vncLw3pKTPBAKabaLj2mCSGyzcM69RYGFTDs0mNhcc2LMvUWFhkw7PLpYnhsbXdMkJMQwajFGLZfpHvF+//emFL4f4vtd38n1ydlXnzk3X/Vz2pZACrh1J82jBJjE8u6o2EGquXVDzaUWPxyIOfKKgxP7Ti0RYhFo88xDEKhJiGrEQlxNatzcg378rIrncK1xqecEJe5n8pK1/446x0dmo4sCY0wQBmV1KZJNqVLxUtNWZXzqgxu/JFjdmXLzdndkZO1GETQIhpIGxSiPX1iXzn2xn5n3dl5J2dBQF23kcL9399+qJk3/9VTyqZJNZDKT5tmCTGJxf1RkKN1UsqHu2osXjkwU8U1JgfWvFoy4pYPPIQxygQYhqyYkKI9feJfPc7GfnGnZnSDogfOS8ni5Zm5fd+f0DDUSTDBAOYXXlmkmhXvvhrvX35osbsyxnjmJ05sy9qIjZBACGmgXKYQkzdA/bA/QUBtv3twgrYOefmZNGSrHz8DxBgftPHAOaXWLTtmSRGyz+Id2osCLXo+lBj0bEP6pkaC0ouun6siEXHPu6eEWIaMhSGEFMCbMP6jHz9joy8ta0gwGZ+uCDALvgEAixo2hjAgpKLph+TxGi4N+KVGmuEnvm+1Jh55o16pMYaJWi+P0LMPHNbPCLENGRKpxDLZkUe/OeMfH1VRra9WRBgZ52dk79ekpULP4UAazRdDGCNEjTbn0miWd46vFFjOiias0GNmWOtyxM1poukOTsIMXOsbfOEENOQMR1CbGBA5F8ezMidKzOiHsisXqefkZOFf5OVz3wWAaYhTY4JBjBdJM3YYZJohrNOL9SYTprh26LGwmes2wM1ppto+PYQYuEzttUDQkxD5hoRYkqAfe//zcid/yMjr79WEGDq4ct//TdZuehidkHUkJ4yEwxguomGa49JYrh8w7BOjYVBNTyb1Fh4bMOyTI2FRTY8uwix8NjabhkhpiGDQYXYv32vRf7hq63yxusFAXbS9LwsWtovn/s8K2Aa0lLVBANYWGTDscskMRyuYVqlxsKkq982NaafadgWqbGwCeu3jxDTz7RZLCLENGTSrxD79UtpuXlJqzz187TjffrJOblxcVY+PwcBpiEdw5pgAAubsF77TBL18jRhjRozQVmfD2pMH0tTlqgxU6T1+UGI6WPZbJYQYhoyWq8QO7A/Jcu/mpF7v5VxvHaPycvSv83Kn16T1RAFJuohwABWD6X4tGGSGJ9c1BsJNVYvqXi0o8bikQc/UVBjfmjFoy1CLB55iGMUCDENWaklxHI5ke/+U8YRYXt2p6SlRRzxteTmrHSNzmuIABP1EmAAq5dUPNoxSYxHHvxEQY35oRV9W2os+hz4jYAa80ss+vYIsehzENcIEGIaMjOcEHvu2bTc+Fet8puXC5chnvuRnPyPr/fLyafkNHjGhF8CDGB+iUXbnklitPyDeKfGglCLrg81Fh37oJ6psaDkouuHEIuOfdw9I8Q0ZKiaENv1Tkq+8ncZ+d6/FC5DPH5qXv7uK/1y8aXcB6YBeWATDGCB0UXSkUliJNgbckqNNYTPeGdqzDjyhh1SYw0jNG4AIWYcuTUOEWKeVN2xZoOcOHWSzJl9flkCH9r4pNyyYp3z2cUXzpLbFl0rnR1tpTZeIdbXJ7Lm7lb5xh0ZOXxYpKND5Et/lZUvXd8v7e3WnBdNGygDmF2pZZJoV75UtNSYXTmjxuzKFzVmX77cnNkZOVGHTQAhJiJeoXX74mvLhNgzm1+WVWs2yOrlN8jY7i5RYk29bpw/d5AQ+9EPWuTv//bodvSXXjYgt97eL5OncB9Y2CdyvfaZJNZLKh7tmCTGIw9+oqDG/NCKvi01Fn0O/EZAjfklFn17VsSiz0FcI0CIeTJTbUWs8rNKYaa6//yZXlny163ysydbHGsfnJGTFXf0O/eD8YoXAQaweOWjVjRMEmsRit/31Fj8cjJcRNSYXflS0VJjdubMvqiJ2AQBhNgwQqynt09uXblOZp1zWmmVbOsb2+XmZWvlq0vnyfRpU2TxYpGVKwtGxozNy9/clJX/+8/Yjt7EyRvEBwNYEGrR9WGSGB37oJ6psaDkoulHjUXDvRGv1Fgj9KLpy4pYNNxt8IoQq0OIXX7pBXLuzBlOy0ohlkoVDMybn5O//bucjB1rQ9qTG6OadBzoQSjbcga0Z9IiKZEj/awu25IzasyWTBXipMbsypeKlhqzM2f2RU3EJgggxOoQYsOtiN1+u8inP5uV007jPjATJ2yjPrpGtMqBw/2NmqG/IQJtreqxDynp62e3UUPIG3ZDjTWM0KgBaswobi3OqDEtGI0aUTnjBYFqBBBiwwgx9VU994jVeqAzp158CHBJR3xyUU8kXDZVD6V4taHG4pWPWtFQY7UIxe97aix+OakVEZcm1iKU3O8RYjWEmJ9dE5N7Gtlz5Axg9uRKRcok0a58qWipMbtyRo3ZlS9qzL58uTmzM3KiDpsAQqxi+3oFfPLE8bJmxUJnMw718vMcsbAThv3GCDBJbIyf6d5MEk0Tb9wfNdY4Q5MWqDGTtPX4osb0cDRphRUxk7Tt8oUQ05AvLk3UANGQCQYwQ6A1uWGSqAmkQTPUmEHYGlxRYxogGjZBjRkGrsEdQkwDxCY1gRDTkFiEmAaIhkwwgBkCrckNk0RNIA2aocYMwtbgihrTANGwCWrMMHAN7hBiGiA2qQmEmIbEIsQ0QDRkggHMEGhNbpgkagJp0Aw1ZhC2BlfUmAaIhk1QY4aBa3CHENMAsUlNIMQ0JBYhpgGiIRMMYIZAa3LDJFETSINmqDGDsDW4osY0QDRsghozDFyDO4SYBohNagIhpiGxCDENEA2ZYAAzBFqTGyaJmkAaNEONGYStwRU1pgGiYRPUmGHgGtwhxDRAbFITCDENiUWIaYBoyAQDmCHQmtwwSdQE0qAZaswgbA2uqDENEA2boMYMA9fgDiGmAWKTmkCIaUgsQkwDREMmGMAMgdbkhkmiJpAGzVBjBmFrcEWNaYBo2AQ1Zhi4BncIMQ0Qm9QEQqxJE8thQQACEIAABCAAAQhAAALxJYAQi29uiAwCEIAABCAAAQhAAAIQaFICCLEmTSyHBQEIQAACEIAABCAAAQjElwBCLL65ITIIQAACEIAABCAAAQhAoEkJIMQCJvahjU/KLSvWOb0vvnCW3LboWunsaAtojW66COzZd0AWLLlTtrz0qmPy3ruWyLkzZ1Q139PbJ7euXCePPL6p9P1w7XXFiJ1yAkFr6ZnNL8s1X14+bI5hrZ+Anxpzvbu5Ur+feepJsnr5DTK2u0t/cFisSsBvjd2xZoN864GNji3yFb+TSuXnxKmTZM7s8+MXXIIj2vrGdll593pZdtO8Yf9/8/5/yBwywSdM8dARYgHOAVVEq9ZsKE0m1H+K6nXj/LkBrNFFFwFXWM065zRngFL/Kd68bK18dek8mT5tyiA3akJ5z/pHZcHVn3dEtMrr0mVrZc2KhVXb64oTO0cJBK0l70CGeDZ3RvmtMRVZZY7NRYunavxrjVdKtG169sXSHxcrf4dqdAS8gvr2xdcixKJLRZln7x+n6vnDhcrj1CkTnD8Su/+nTpowjjlkTPJpOgyEWADilX+NYqIRAGIIXSr/GlU5aazl0v3PdOH8uUOuotWywff+CASpJTfPi790pdy0bK2QL3/MG2ntt8ZUTS392lpZdN0V/HGjEfAN9PVbY5VCjfGtAfghdWVFLCSwDZqtd0Ws0g1/7GgQvOXdEWI+E1htcl9r5cWnC5oHJFBtwlDrr79eV+QxIPiA3YLUkjdH48Z0OZehIsQCJiBAN781pvI1f/Eq2fHO+yVvX7xyNn/5DcA+SJegNaZyNvsT5zl5YtIfhHy4fchJuHyDWg8qxPzMU4LGRr/4EkCI+cyNO7BdfukFpVUTJvA+IYbUXE0SH3z4ibL79er9D87v6llIh5Aos35rqXJ1hRVM86eL3xqrbO/mbO6lF3BZlYH0+a0xFZLbZ9+BQ/Kzp7dwj5iBPPl1gRDzS8xM+yBCjBVnM7mJsxeEmM/sBPkLo08XNA9IwO9f6103XKMdEHiD3fzWUrXVFTcE7hNrMBl1dvdbY9WEG5fh1AlbQzO/NaZcVk7yVb42PPwEG6xoyIcuEwgxXST12vErxLgvXS9/W60hxAJkzu819wFc0CUAAb/3r3j/+suNsgGAa+jSSC2xIqYhAT5N+K2xahMTNbF/fdtOLk/0yT5ocz81FmQFLWhc9AtOACEWnF2YPf0IMURYmJmwyzZCLEC+gu70FsAVXXwQqLWjm7uismzpvLLditxdFn24oqkmArVqSU04du7aXfXxEAgxTUnwYSZojbl/6CBnPmBrauq3xiprjhUxTYnQaAYhphGmRlNDCbHKmuJyRI3Qm8AUQixgEv0+lyWgG7r5JDDcM44qhdhQl7qxmYBP6A02H66WEGINwg2hu58aU+4r27PtdghJqWHST41VPl+xnu24zR9RMj1686gITJ44nsetxOBUqPw/ToXknUdUjmPe5/S54ZPLGCQyohAQYhGBxy0EIAABCEAAAhCAAAQgkFwCCLHk5p4jhwAEIAABCEAAAhCAAAQiIoAQiwg8biEAAQhAAAIQgAAEIACB5BJAiCU39xw5BCAAAQhAAAIQgAAEIBARAYRYROBxCwEIQAACEIAABCAAAQgklwBCLLm558ghAAEIQAACEIAABCAAgYgIIMQiAo9bCEAAAhCAAAQgAAEIQCC5BBBiyc09Rw4BCEAAAhCAAAQgAAEIREQAIRYReNxCAAIQgAAEIAABCEAAAsklgBBLbu45cghAAAIQgAAEIAABCEAgIgIIsYjA4xYCEIAABCAAAQhAAAIQSC4BhFhyc8+RQwACEIAABCAAAQhAAAIREUCIRQQetxCAAAQgAAEIQAACEIBAcgkgxJKbe44cAhCAAAQgAAEIQAACEIiIAEIsIvC4hQAEIAABCEAAAhCAAASSSwAhltzcc+QQgAAEIAABCEAAAhCAQEQEEGIRgcctBCAAAQhAAAIQgAAEIJBcAgix5OaeI4cAEEjwzAAAB1tJREFUBCAAAQhAAAIQgAAEIiKAEIsIPG4hAAEIDEfgoY1Pyi0r1pU1OfPUk2T18hvkldfelmu+vFzuvWuJnDtzRlmbO9ZskKc3v+y0G9vdJcPZ2b33gMxfvEp2vPP+kKHcvvhamTplguOv2suN4ZnNLzttLr5wlty26Frp7GgrNR/uO9Voz74DsmDJnbLlpVeHjOOLV86WE6dOKmOiYpsz+3zZ+sZ25ziOGdddOm7XULXv3HiGOx7OTghAAAIQgEDYBBBiYRPGPgQgAAGfBCrFlNtdff7x885yxJcSWBsefqJMeCjRcfOytfLVpfNk+rQpUo8db2jK5qZnX6wqpJYuWytrVix07FZ7ueJm8sTxZe16evvk1pXr5JHHN1UVaUPZWrVmwyBRpdoqP5WxuGJLCcpKcaoYfOuBjeKKWCVOq9nwmSKaQwACEIAABBomgBBrGCEGIAABCOgj4K4Ozb30Ame1Z6iXK3AmTRgnN86fK+7vs845zelXrx2dQkyJp0987ENy8FCPE5MrnB58+AkZNWqEHDx4eJDI0yXElAC95FO/J8+/uLXkQwm0lXevlw+feYr85OfPlYQdQkzf+YolCEAAAhAITgAhFpwdPSEAAQhoJ1ApsIZz4K4ELVs6T7Zt31W2QubHjuuj0RUxJcQWzp8rq/73P5etyqlLCl/ftlN27todqhBb+BdfEDcGd9VQ+VX+vauHCDHtpy0GIQABCEAgAAGEWABodIEABCAQJoHKe5i8l9VV+nUvvVOfV16W58eO6j+cEKvnHjH3csJ71j/qhHnZRb/vrEgtu2meqM/CFmLqksxf/dcrzuWVN/z55XLbHffJouuucD6rFGK1jifM/GIbAhCAAAQgoAggxDgPIAABCMSUgPf+KhVi5f1X6jP3EsSPzJxRuhyw8nDqsVNLiNVzj5grxNQmIOpSQfWa+7k/dC6VVILRhBAbN6bL2fiju2uk/M70qQ6TyvvpWBGL6QlPWBCAAAQSRgAhlrCEc7gQgICdBIa61LDy3rBaRzfcJYs6Lk10d2us3CjElBBTm4mo47j7vn8rbRqCEKt1VvA9BCAAAQhEQQAhFgV1fEIAAhAYgoBa4VLbuJ8/6+xBLZSYUS93Iwz1figh5teOzhUxtTOhun/tldfeks9c8BEnZpNCTB37xsc3yVVzPuX4RohRbhCAAAQgEEcCCLE4ZoWYIACBxBJwLzU8YcqEso0t3Pu9Ku8DG06IqUv06rWjW4hVJtCkEKv0jRBLbDlx4BCAAARiTQAhFuv0EBwEIJBEAtUecFzt/rDhVsTUd37s1BJitTa3UEJxqGd/6VoRq3w4tfeBzt7np9UjxGodTxLPO44ZAhCAAATMEkCImeWNNwhAAAIQgAAEIAABCEAAAuyayDkAAQhAAAIQgAAEIAABCEDANAFWxEwTxx8EIAABCEAAAhCAAAQgkHgCCLHEnwIAgAAEIAABCEAAAhCAAARME0CImSaOPwhAAAIQgAAEIAABCEAg8QQQYok/BQAAAQhAAAIQgAAEIAABCJgmgBAzTRx/EIAABCAAAQhAAAIQgEDiCSDEEn8KAAACEIAABCAAAQhAAAIQME0AIWaaOP4gAAEIQAACEIAABCAAgcQTQIgl/hQAAAQgAAEIQAACEIAABCBgmgBCzDRx/EEAAhCAAAQgAAEIQAACiSeAEEv8KQAACEAAAhCAAAQgAAEIQMA0AYSYaeL4gwAEIAABCEAAAhCAAAQSTwAhlvhTAAAQgAAEIAABCEAAAhCAgGkCCDHTxPEHAQhAAAIQgAAEIAABCCSeAEIs8acAACAAAQhAAAIQgAAEIAAB0wQQYqaJ4w8CEIAABCAAAQhAAAIQSDwBhFjiTwEAQAACEIAABCAAAQhAAAKmCSDETBPHHwQgAAEIQAACEIAABCCQeAIIscSfAgCAAAQgAAEIQAACEIAABEwTQIiZJo4/CEAAAhCAAAQgAAEIQCDxBBBiiT8FAAABCEAAAhCAAAQgAAEImCaAEDNNHH8QgAAEIAABCEAAAhCAQOIJIMQSfwoAAAIQgAAEIAABCEAAAhAwTQAhZpo4/iAAAQhAAAIQgAAEIACBxBNAiCX+FAAABCAAAQhAAAIQgAAEIGCaAELMNHH8QQACEIAABCAAAQhAAAKJJ4AQS/wpAAAIQAACEIAABCAAAQhAwDQBhJhp4viDAAQgAAEIQAACEIAABBJPACGW+FMAABCAAAQgAAEIQAACEICAaQIIMdPE8QcBCEAAAhCAAAQgAAEIJJ4AQizxpwAAIAABCEAAAhCAAAQgAAHTBBBiponjDwIQgAAEIAABCEAAAhBIPAGEWOJPAQBAAAIQgAAEIAABCEAAAqYJIMRME8cfBCAAAQhAAAIQgAAEIJB4AgixxJ8CAIAABCAAAQhAAAIQgAAETBNAiJkmjj8IQAACEIAABCAAAQhAIPEEEGKJPwUAAAEIQAACEIAABCAAAQiYJoAQM00cfxCAAAQgAAEIQAACEIBA4gn8/1kNoi908Cg4AAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig_fixed = dynamics_fixed.plot_history(chemicals=['A'], colors='blue', title=\"FIXED time steps\", show=True) # Repeat a portion of the diagram seen in Part 2" ] }, { "cell_type": "code", "execution_count": 19, "id": "1dfe1166-2bb3-4472-9b4e-a167c1a7d54d", "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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" ] }, "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
Chemical=A
SYSTEM TIME=%{x}
concentration=%{y}", "legendgroup": "A", "line": { "color": "aqua", "dash": "solid" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "VARIABLE time steps", "orientation": "v", "showlegend": true, "type": "scatter", "x": [ 0, 0.016000000000000004, 0.03200000000000001, 0.048000000000000015, 0.06720000000000002, 0.08640000000000003, 0.10944000000000004, 0.13248000000000004, 0.16012800000000005, 0.19330560000000005, 0.23311872000000006, 0.28089446400000007, 0.3382253568000001, 0.4070224281600001, 0.48957891379200014, 0.5886466965504001, 0.7075280358604801, 0.850185643032576, 1.0213747716390913, 1.2268017259669095 ], "xaxis": "x", "y": [ 10, 11.120000000000001, 12.150400000000001, 13.098368, 14.144924672, 15.091011903488, 16.117327332206184, 17.025411223536032, 17.989578375994412, 18.98663519835745, 19.984623670615306, 20.94381162849702, 21.819881668013238, 22.569810450307923, 23.160167565358876, 23.576169251301298, 23.828097086531773, 23.950713378038216, 23.992900047366195, 24.000192655593363 ], "yaxis": "y" }, { "hovertemplate": "EXACT solution
A (EXACT) :
SYSTEM TIME=%{x}
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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 (hover and use the Plotly controls 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": "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 = ReactionDynamics(shared=dynamics_variable) # 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": "41393ff8-a6e7-48ed-b45e-34e2398b734d", "metadata": {}, "outputs": [], "source": [ "# We specify a particular group of preset parameters applicable to the adaptive time steps\n", "# This time, we're using a \"fast\" heuristic: advance quickly thru time\n", "dynamics_variable_new.use_adaptive_preset(preset=\"fast\") " ] }, { "cell_type": "code", "execution_count": 23, "id": "e38d2dcb-1ea1-4728-a26f-126821669d6a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.1) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.06) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.06) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.036) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.036) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.0216) [Step started at t=0, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "14 total step(s) taken\n" ] } ], "source": [ "dynamics_variable_new.single_compartment_react(initial_step=0.1, target_end_time=1.2,\n", " variable_steps=True, explain_variable_steps=False,\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": 24, "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": [ "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\", 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 }