{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## `U` (\"Up-regulator\") up-regulates `X` , by sharing a reaction product `D` (\"Drain\") across 2 separate reactions: \n", "### `U <-> 2 D` and `X <-> D` (both mostly forward)\n", "\n", "1st-order kinetics throughout. \n", "\n", "Invoking [Le Chatelier's principle](https://www.chemguide.co.uk/physical/equilibria/lechatelier.html), it can be seen that, starting from equilibrium, when [U] goes up, so does [D]; and when [D] goes up, so does [X]. \n", "Conversely, when [U] goes down, so does [D]; and when [D] goes down, so does [X]. \n", "\n", "LAST REVISED: July 14, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "838b9dfc-e3c2-4e9d-bedc-f32a2b6a6dfa", "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": "16962197", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.chemicals.chem_data import ChemData as chem\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "cc53849f-351d-49e0-bfa8-22f8d8e22f8e", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'up_regulate_2.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging\n", "log_file = get_notebook_basename() + \".log.htm\" # Use the notebook base filename for the log file\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_1\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "markdown", "id": "d6d3ca49-589d-49b7-8424-37c7b01bcacf", "metadata": {}, "source": [ "### Initialize the system" ] }, { "cell_type": "code", "execution_count": 4, "id": "23c15e66-52e4-495b-aa3d-ecddd8d16942", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: U <-> 2 D (kF = 8 / kR = 2 / Delta_G = -3,436.56 / K = 4) | 1st order in all reactants & products\n", "1: X <-> D (kF = 6 / kR = 3 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `up_regulate_2.log.htm`]\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = chem(names=[\"U\", \"X\", \"D\"])\n", "\n", "# Reaction U <-> 2D , with 1st-order kinetics for all species\n", "chem_data.add_reaction(reactants=\"U\", products=[(2, \"D\")],\n", " forward_rate=8., reverse_rate=2.)\n", "\n", "# Reaction X <-> D , with 1st-order kinetics for all species\n", "chem_data.add_reaction(reactants=\"X\", products=\"D\",\n", " forward_rate=6., reverse_rate=3.)\n", "\n", "chem_data.describe_reactions()\n", "\n", "# Send the plot of the reaction network to the HTML log file\n", "graph_data = chem_data.prepare_graph_network()\n", "GraphicLog.export_plot(graph_data, \"vue_cytoscape_1\")" ] }, { "cell_type": "markdown", "id": "d1d0eabb-b5b1-4e15-846d-5e483a5a24a7", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals" ] }, { "cell_type": "code", "execution_count": 5, "id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (U). Conc: 50.0\n", " Species 1 (X). Conc: 100.0\n", " Species 2 (D). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data)\n", "dynamics.set_conc(conc={\"U\": 50., \"X\": 100., \"D\": 0.})\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": null, "id": "e652b8fa-b7b3-4772-b602-aa15d11d9067", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "0b46b395-3f68-4dbd-b0c5-d67a0e623726", "metadata": { "tags": [] }, "source": [ "# 1. Take the initial system to equilibrium" ] }, { "cell_type": "code", "execution_count": 6, "id": "bcf652b8-e0dc-438e-bdbe-02216c1d52a0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.03) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.015) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.015) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.0075) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.0075) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.00375) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.00375) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.001875) [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", "60 total step(s) taken\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " SYSTEM TIME U X D caption\n", "0 0.000000 50.000000 100.000000 0.000000 Initial state\n", "1 0.001875 49.250000 98.875000 2.625000 \n", "2 0.002812 48.885547 98.326211 3.902695 \n", "3 0.003750 48.526223 97.784102 5.163452 \n", "4 0.004687 48.171958 97.248589 6.407496 \n", ".. ... ... ... ... ...\n", "56 0.245706 24.643947 53.475305 97.236801 \n", "57 0.282239 24.546114 52.410700 98.497071 \n", "58 0.337037 24.580376 51.371008 99.468240 \n", "59 0.419235 24.768894 50.563716 99.898495 \n", "60 0.542532 24.971820 50.109144 99.947215 \n", "\n", "[61 rows x 5 columns]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# All of these settings are currently close to the default values... but subject to change; set for repeatability\n", "dynamics.set_thresholds(norm=\"norm_A\", low=0.5, high=0.8, abort=1.44)\n", "dynamics.set_thresholds(norm=\"norm_B\", low=0.08, high=0.5, abort=1.5)\n", "dynamics.set_step_factors(upshift=1.5, downshift=0.5, abort=0.5)\n", "dynamics.set_error_step_factor(0.5)\n", "\n", "dynamics.single_compartment_react(initial_step=0.03, target_end_time=0.5,\n", " variable_steps=True, explain_variable_steps=False)\n", "\n", "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 7, "id": "b56d1612-a68c-4da3-be37-a7245b6c1a80", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.001875, in 1 step of 0.00187\n", "From time 0.001875 to 0.01219, in 11 steps of 0.000938\n", "From time 0.01219 to 0.01781, in 4 steps of 0.00141\n", "From time 0.01781 to 0.03469, in 8 steps of 0.00211\n", "From time 0.03469 to 0.03785, in 1 step of 0.00316\n", "From time 0.03785 to 0.03943, in 1 step of 0.00158\n", "From time 0.03943 to 0.04418, in 2 steps of 0.00237\n", "From time 0.04418 to 0.04774, in 1 step of 0.00356\n", "From time 0.04774 to 0.04952, in 1 step of 0.00178\n", "From time 0.04952 to 0.05219, in 1 step of 0.00267\n", "From time 0.05219 to 0.05619, in 1 step of 0.004\n", "From time 0.05619 to 0.0582, in 1 step of 0.002\n", "From time 0.0582 to 0.0612, in 1 step of 0.003\n", "From time 0.0612 to 0.0657, in 1 step of 0.00451\n", "From time 0.0657 to 0.06796, in 1 step of 0.00225\n", "From time 0.06796 to 0.07134, in 1 step of 0.00338\n", "From time 0.07134 to 0.0764, in 1 step of 0.00507\n", "From time 0.0764 to 0.07894, in 1 step of 0.00253\n", "From time 0.07894 to 0.08274, in 1 step of 0.0038\n", "From time 0.08274 to 0.08844, in 1 step of 0.0057\n", "From time 0.08844 to 0.09129, in 1 step of 0.00285\n", "From time 0.09129 to 0.09557, in 1 step of 0.00428\n", "From time 0.09557 to 0.1212, in 4 steps of 0.00641\n", "From time 0.1212 to 0.1308, in 1 step of 0.00962\n", "From time 0.1308 to 0.1357, in 1 step of 0.00481\n", "From time 0.1357 to 0.1429, in 1 step of 0.00722\n", "From time 0.1429 to 0.1645, in 2 steps of 0.0108\n", "From time 0.1645 to 0.197, in 2 steps of 0.0162\n", "From time 0.197 to 0.2457, in 2 steps of 0.0244\n", "From time 0.2457 to 0.2822, in 1 step of 0.0365\n", "From time 0.2822 to 0.337, in 1 step of 0.0548\n", "From time 0.337 to 0.4192, in 1 step of 0.0822\n", "From time 0.4192 to 0.5425, in 1 step of 0.123\n", "(60 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "markdown", "id": "cbf6c9c7-8cec-400f-9e70-49ff1a9f485c", "metadata": { "tags": [] }, "source": [ "## Plots of changes of concentration with time" ] }, { "cell_type": "code", "execution_count": 8, "id": "db4e74d0-3f9d-49dc-9553-bf3cdfe785f2", "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=U
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'green', 'gray'])" ] }, { "cell_type": "markdown", "id": "962acf15-3b50-40e4-9daa-3dcca7d3291a", "metadata": {}, "source": [ "### Equilibrium" ] }, { "cell_type": "code", "execution_count": 9, "id": "2783a665-fca0-44e5-8d42-af2a96eae392", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: U <-> 2 D\n", "Final concentrations: [D] = 99.95 ; [U] = 24.97\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.0024\n", " Formula used: [D] / [U]\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.06 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: X <-> D\n", "Final concentrations: [D] = 99.95 ; [X] = 50.11\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.99459\n", " Formula used: [D] / [X]\n", "2. Ratio of forward/reverse reaction rates: 2.0\n", "Discrepancy between the two values: 0.2705 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": null, "id": "95679484-9ebe-4765-8644-40e94c384f65", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "448ec7fa-6529-438b-84ba-47888c2cd080", "metadata": { "tags": [] }, "source": [ "# 2. Now, let's suddenly increase [U]" ] }, { "cell_type": "code", "execution_count": 10, "id": "7245be7a-c9db-45f5-b033-d6c521237a9c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.54253165:\n", "3 species:\n", " Species 0 (U). Conc: 70.0\n", " Species 1 (X). Conc: 50.10914435037049\n", " Species 2 (D). Conc: 99.94721484673187\n" ] } ], "source": [ "dynamics.set_chem_conc(species_name=\"U\", conc=70., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 11, "id": "61eead55-fcef-41cd-b29e-f2d5ad5c6078", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEUXDcaption
590.41923524.76889450.56371699.898495
600.54253224.97182050.10914499.947215
610.54253270.00000050.10914499.947215Set concentration of `U`
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" ], "text/plain": [ " SYSTEM TIME U X D caption\n", "59 0.419235 24.768894 50.563716 99.898495 \n", "60 0.542532 24.971820 50.109144 99.947215 \n", "61 0.542532 70.000000 50.109144 99.947215 Set concentration of `U`" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=3)" ] }, { "cell_type": "markdown", "id": "24455d58-a0ea-43fa-b6ad-95c42a8b34b2", "metadata": {}, "source": [ "### Again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 12, "id": "c06fd8d8-d550-4e35-a239-7b91bee32be9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.03) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.015) [Step started at t=0.54253, and will rewind there]\n", "* INFO: the tentative time step (0.015) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.0075) [Step started at t=0.54253, and will rewind there]\n", "* INFO: the tentative time step (0.0075) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.00375) [Step started at t=0.54253, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "32 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.03, target_end_time=1,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 13, "id": "35850ec7-e78e-4b57-976c-bc0ad6c824d5", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 14, "id": "5af5d869-16ff-4f1d-ab83-4865b42e6376", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=U
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U9SLGxDzd2jxSobLHexGrzaJJgARIgARIgARIgARIgARIgAQ0E6CsawY8XPaj3RO3iFVn0SRAAiRAAiRAAiRAAiRAAiRAAhoJUNY1wmXWJEACJEACJEACJEACJEACJEACJJAPAcp6PtR4DgmQAAmQAAmQAAmQAAmQAAmQAAloJEBZ1wiXWZMACZAACZAACZAACZAACZAACZBAPgQo6/lQ4zkkQAIkQAIkQAIkQAIkQAIkQAIkoJEAZV0jXGZNAiRAAiRAAiRAAiRAAiRAAiRAAvkQoKznQ43nkAAJkAAJkAAJkAAJkAAJkAAJkIBGApR1jXCZNQmQAAmQAAmQAAmQAAmQAAmQAAnkQ4Cyng81nkMCJEACJEACJEACJEACJEACJEACGglQ1jXCZdYkQAIkQAIkQAIkQAIkQAIkQAIkkA8Byno+1HgOCZAACZAACZAACZAACZAACZAACWgkQFnXCJdZkwAJkAAJkAAJkAAJkAAJkAAJkEA+BCjr+VDjOSRAAiRAAiRAAiRAAiRAAiRAAiSgkQBlXSNcZk0CJEACJEACJEACJEACJEACJEAC+RCgrOdDjeeQAAmQAAmQAAmQAAmQAAmQAAmQgEYClHWNcJk1CZAACZAACZAACZAACZAACZAACeRDgLKeDzWeQwIkQAIkQAIkQAIkQAIkQAIkQAIaCVDWNcJl1iRAAiRAAiRAAiRAAiRAAiRAAiSQDwHKej7UeA4JkAAJkAAJkAAJkAAJkAAJkAAJaCRAWdcIl1mTAAmQAAmQAAmQAAmQAAmQAAmQQD4EKOv5UOM5JEACJEACJEACJEACJEACJEACJKCRAGVdI1xmTQIkQAIkQAIkQAIkQAIkQAIkQAL5EKCs50ON55AACZAACZAACZAACZAACZAACZCARgKUdY1wmTUJkAAJkAAJkAAJkAAJkAAJkAAJ5EOAsp4PNZ5DAiRAAiRAAiRAAiRAAiRAAiRAAhoJUNY1wmXWJEACJEACJEACJEACJEACJEACJJAPAcp6PtR4DgmQAAmQAAmQAAmQAAmQAAmQAAloJEBZ1wiXWZMACZAACZAACZAACZAACZAACZBAPgQo6/lQ4zkkQAIkQAIkQAIkQAIkQAIkQAIkoJEAZV0jXGZNAiRAAiRAAiRAAiRAAiRAAiRAAvkQoKznQ43nkAAJkAAJkAAJkAAJkAAJkAAJkIBGApR1jXCZNQmQAAmQAAmQAAmQAAmQAAmQAAnkQ4Cyng81nkMCJEACJEACJEACJEACJEACJEACGglQ1jXCZdYkQAIkQAIkQAIkQAIkQAIkQAIkkA8Byno+1HgOCZAACZAACZAACZAACZAACZAACWgkQFnXCJdZkwAJkAAJkAAJkAAJkAAJkAAJkEA+BCjr+VDjOSRAAiRAAiRAAiRAAiRAAiRAAiSgkQBlXSNcZk0CJEACJEACJEACJEACJEACJEAC+RCgrOdDjeeQAAmQAAmQAAmQAAmQAAmQAAmQgEYClHWNcJk1CZAACZAACZAACZAACZAACZAACeRDgLKeDzWeQwIkQAIkQAIkQAIkQAIkQAIkQAIaCVDWNcJl1iRAAiRAAiRAAiRAAiRAAiRAAiSQDwHKej7UeA4JkAAJkAAJkAAJkAAJkAAJkAAJaCRAWdcIl1mTAAmQAAmQAAmQAAmQAAmQAAmQQD4EKOv5UOM5JEACJEACJEACJEACJEACJEACJKCRAGVdI1xmTQIkQAIkQAIkQAIkQAIkQAIkQAL5EKCs50ON55AACZAACZAACZAACZAACZAACZCARgKUdY1wmTUJkAAJkAAJkAAJkAAJkAAJkAAJ5EPAVbL+1PLV2LytBTdff2kKqx8+tBSPPL485bXv3nYNLjz7BPmaOO/b9z0qn59z6mLcfes1qCgPJNPvbO3Phz3PIYGsBJrHVID9ih3EagJV5X74fR509kaszpr5uZzAhIZy7O0MIRYbcjkJNt9KAhUBH8qDPrR3h63MlnmRAMbVBdHRG0FkMEYawxAQ30d5FJeAK2T9zXc34KvfuFeSvvaKszPKungvXeLFa+LcBx5aigfvvQkNdTUQYp+ellJV3E5ciqVT1ksxqsVvE2W9+DEo1RpQ1ks1ssVtF2W9uPxLuXTKulp0KetqnHSmcoWsGwCHG1nPJutCzqdPaUqOsqfLuziPsq6zi7ozb8q6O+Ouu9WUdd2E3Zs/Zd29sdfZcsq6TrruzpuyrhZ/yroaJ52pKOuAHC03T4M3psD3D4Rx1/2PYvGiuUlZ37hlJ+6852F8/47rMHNas4xNS9uAzhgxbxcSaGosZ79yYdx1N7my3CenwXf1Duouivm7jMC4+iD2dYUxxGnwLou83uaWB7woD/jQ0cNbd/SSdl/uY2oD6OyLYHCQt+4MF33xfZRHcQlQ1tP4Cxm//rYHcM8d12H+nIOkrF9y3kk4+vA5MmUmWY8N8Q+9uN249Er3ejxgvyq9uBa7RR54ZBWGwM+sYsei1MoXn1lDQ+xZpRbXYrdHfmZ5IPsWDxKwkkD8M4v/H47EVHDiUVwClPUM/I2p72edslhpZJ3T4IvbiUuxdE6DL8WoFr9NnAZf/BiUag04Db5UI1vcdnEafHH5l3LpnAavFl1Og1fjpDMVZX0YWRerwfOedZ3dj3lnI0BZZ9/QQYCyroMq8xQEKOvsBzoIUNZ1UGWeggBlXa0fUNbVOOlM5XpZb+/sxvIVa3DVhadLzunT3LkavM7ux7wp6+wDhSRAWS8kbXeVRVl3V7wL1VrKeqFIu68cyrpazIsh62JB8DVvrTtgq2y1GtsnlXDMG27/EW65/tLk7dT51M4Vsm7eus2A9LMf3y7BGYvIPbNiTZKf8Z7xAvdZz6dr8ZzREODI+mjo8dxsBCjr7Bu6CFDWdZEdXb5DsRiisahc+C/+GEM0GsXQkHiMJR4Trxvpku+b0sViiMWiiJkfozHEhmKIRaOmvE15yjJSyxZp4+fsP3d/nkP7yzCli9c1OjoQBTjb4/FA/Ii76+XzxBohxuvi7mgk0ojXxCFTGfcEJ96Tr5vTxTNMphPJDzhHZh1Pk8w7njBeTlp99uc3lHqOXCPAdE62/Ez1jpcpW3dAvWVd0vIzt08uSGA6L/48no+Zo7lNHq/3wHOM+iTL2s8oWQcTI5FBTWUZBsIxRBPLIWSKWQL9AYxS6pfevgSM9Fgkb/02M03Ue9j8TPGPc0iNmYxlGseMfSpDX9vf9RL9JsHIHDMdsm6sD7Zrd2vyL3PihDF46L5b5OLdxZJ1wwmbxjdm3M47148RynquxDSm5z3rGuG6NGvKuksDr7nZlHXNgF2cPWXd2uCLBdVCoQFEwiGEw2GEQ+IxFH+MJB5DAwiFQoiI92U68TyUfC0SCVtbKeZGAiTgOgJ33XWXpW02BkDTB0bFwOqTy1bJ0fRnV67hyLqJuitG1i3tZRkyo6zrJuy+/Cnr7ot5IVpMWS8EZXeWQVlXj3t/Xy96errR19sjf3p7utHbG//deF1IuVWHz+eHz+eFGJH0en3wJh898Pp88Hq8qY9eMcrmhc/nk+f4vOLRk3hMvC7f98bT+f2peRplJPP27i/DXLbMNy2/ZHnxc6oqylBRXobu/phVOAqWTzQ6GN8hQa5kH98tQS4/LsZG5c4J+5+L140V7/efk1ip3HyOTBdvQjK/xGr56efLMdhEvullxc/fv8r+/jJN9UsrN5mfqHnKe/Hx8fR6H9DetPwSJ6Wel6iTuawkL+P8mJi9YapDoj7767Cfz3CMysu8CA3GZ3mkx0P8Hs8vjdEBZR3IS0YtS8xS4mxKZ7x+QB9IVGL/66mc5XmmfmQ+P1tZ++OS2MEjUVfRXzMdVsq6ecctY5etTGUaI+vnnn6cnEYuDvPIu3FO+gj9tVecnRwRN25j/tplZ+Lmf/lpSh7vffgpvn3fo/K1BYcehAfvvQkNdTXJ2dbmLbtFGvMMa/G7UU6mGQLG9t8iHUfWC/ZxO3JBlPWRGTFFbgQo67nxYmo1ApR1NU5MlTsByjowOBhBT3c3hIxLAU9IuBBw82uqdAPBIILBcpSVBRAIliMQCKAsEJCviZ9AICh/F+nEc+NRpJfnBQKqRdk2He9Zt21oHF8x3rOuFkIrp8EL6V26bFVSjrPVwJBjs3yLBb9b9rQl72NPX2MsfQq7cQt0eh6PPL48KduifJGvOG6+/tKMsp5eZ1HOb5/5Cy4650Ts3L0PK156C3/75fNkHukXIyjran2sIKko6wXB7KpCKOuuCnfBGktZLxhq1xVUyrIuRqKSsp0YDe/p6UqOihsj5GK6+kiHEO6KympUVFahUvxUVcd/ks+r5Hvl5RUjZeWK9ynrrghzURpJWVfDbqWspwv3cLKevsBcpgW/p09pgti5yzjMaT7dtAMPPLQ05cJAeh7iPPNr5cFgypbd+ci2eRexfM7PxITT4NX66rCpKOsWQGQWKQQo6+wQOghQ1nVQZZ6CQCnIen9/Hzo72tDZ3oaO9lZ0tLehs6Md3V0dcmG1bIdYzKm8olIK9wESXpUQ8oSMiynpPNQJUNbVWTFlbgQo62q87CjrhlSbFwc3WmNMa7dC1sVI+f0/fQL3fPM6OU0+05FpEXNjNJ+yrtbHCpKKsl4QzK4qhLLuqnAXrLGU9YKhdl1BTpL19jYh4vukiLe37UNXZwfaW/ch24Js48Y3oaqmNmUkvKqqOinoYmSchx4ClHU9XJkr91lX7QNWynou0+CHG1lPHwHPJtGjHVkfSdbFKPryla8nV7EX9TBPq6esq/ayAqSjrBcAssuKoKy7LOAFai5lvUCgXViMXWU9NDCAPbt3YveuHdi7pwV7WnbI1dUzHXX1jWgYMxaNjWMxZtwENDSOgXiNR/EIUNaLx77US+bIulqErZT14RaYM98Lnmk1+EzT4EULxL3mumR9ONk27pG/5LyTUvZQp6yr9auCp6KsFxx5yRdIWS/5EBelgZT1omB3RaF2kHWxmnFcyHdhd8sO7NvTgp7urgP4l5WVYXxTM8aMHY/GMeOloI8dN8EVcXJaIynrTouYc+pLWVeLlZWyLkrMtHWbIcVTm8dn3botXdaN6efpq6//zxPP4oarv4QPNnw26nvWRX2FfL/x7oaUFePFAnNnn3oc7v2PX8K8J3v6onYcWVfrYwVJRVkvCGZXFUJZd1W4C9ZYynrBULuuoELLulj0raOtFXv27MKelp3Yu3uXnNKefm+52Jqsccw4TGhqxvgJzRg3oYmj5Q7qnZR1BwXLYVWlrKsFzGpZF6Vm2vLMvGq7sXWb2HO9ojy+q0WmxeGG2zptpMXkjHvQh1tgziAkhF2sIm8c6fekr13/mXxLvG4cYsSfsq7WxwqSirJeEMyuKoSy7qpwF6yxlPWCoXZdQYWQdXFf+c4dW7Bj2xbs3LEVkQzT2WvrGqSQT5g4CePHT5Sj50LYeTiTAGXdmXFzQq0p62pR0iHraiUzlUGAq8Fb0Bco6xZAZBYpBCjr7BA6CFDWdVBlnoKADlkXq7Dv3L41Lufbt0Cs1m4+xPZm4yZMlFPaxc+ECc0lsbc4e9R+ApR19gZdBCjramQp62qcdKairFtAl7JuAURmQVlnH9BOgLKuHbFrC7BK1ru7O/HpR+vw6cfr5DR38yHuNZ84aSomTZmGSVOmo6FxrGt5u6XhlHW3RLrw7aSsqzGnrKtx0pmKsm4BXcq6BRCZBWWdfUA7Acq6dsSuLWA0st7b041PP16Pzz5Zj317dycZiunrE5omxeV88jQ5ii72NOfhHgKUdffEutAtpayrEaesq3HSmYqybgFdyroFEJkFZZ19QDsByrp2xK4tIFdZF1PahZwLSRcLxBmHkPHmyVMx85C5OGjmbE5rd22Pijecsu7yDqCx+ZR1NbiUdTVOOlNR1i2gS1m3ACKzoKyzD2gnQFnXjti1BajIejgUwsZP1mPjJxvQsnMbxIruxtE0cTJmHnIoDjp4DsS96DxIgLLOPqCTAGVdjS5lXY0fQOJVAAAgAElEQVSTzlSUdQvoUtYtgMgsKOvsA9oJUNa1I3ZtAdlkPRwOY/NnH2PjR+vkCu7mrdXGjm/CrEMOxcyDD0VlVbVr2bHh2QlwZJ29QxcByroaWcq6GiedqSjrFtClrFsAkVlQ1tkHtBOgrGtH7NoC0mVdjJx/8N7b2LTxoxQmDWPGYtYhczHz4Dmoqa13LS82XI0AZV2NE1PlToCyrsaMsq7GSWcqyroFdCnrFkBkFpR19gHtBCjr2hG7tgBD1j9a9wHWvvsmWvftSbIQe58LOZ81ex7qGxpdy4gNz50AZT13ZjxDjQBlXY0TZV2Nk85UlHUL6FLWLYDILCjr7APaCVDWtSN2ZQHR6CC2ffoBXn755ZS90MX09vmHLZJ7oPMggXwIUNbzocZzVAhQ1lUoAZR1NU46U1HWLaBLWbcAIrOgrLMPaCdAWdeO2HUFrFv7Dt5+81X09/XKtgcCAcyZdxgWHH4070N3XW+wvsGUdeuZMsc4Acq6Wk9wg6w/tXw11ry1Dnffeg0qygMSTHtnN264/Ue45fpLcfThc9RgaUpFWbcALGXdAojMgrLOPqCdAGVdO2LXFLDhw/ekpIs90sUxdeo0zF14FCZOngq/v8w1HNhQvQQo63r5ujl3yrpa9CnrlHW1nmLzVJR1mwfIgdUTH47sVw4MnM2rTFm3eYBsXj2x1dqnH63DW2+8gu6ujvjo1ISJOHrxCThy4Wzs7QwhFtu/HZvNm8PqOYAAZd0BQXJoFSnraoGjrFPW1XqKzVNRqmweIAdWj7LuwKA5oMqUdQcEyaZVFPujv/X6y+jsaJc1HDN2PI5avARTp8+Uv6vss27TprFaNiZAWbdxcBxeNcq6WgC1yPqWLcCmTWoVsDLVtGnAjBkH5Mhp8FZCtmlelHWbBsbB1aKsOzh4Nq46Zd3GwbFp1bZ89gneXPMS2tv2yRqK1dyFpM+YOTulxpR1mwbQ4dWirDs8gDauPmVdLThaZP373we+9S21CliZ6s47ge99j7JuJVOn5EVZd0qknFNPyrpzYuWkmlLWnRSt4tZ125bP8Nc1L2Hf3t2yImJP9KOO/TxmHnIoPB7PAZWjrBc3XqVaOmW9VCNb/HZR1tVioEXWf/lL4JFH1CpgZaovfxm49lplWb/jBw/j1hsvx8xpxd3RhAvMWdAJKOsWQGQWKQQo6+wQOghQ1nVQLa08uzrb8ZcXnkXLru2yYZVV1VLSZ89dOGxDKeul1Q/s0hrKul0iUXr1oKyrxVSLrKsVXbBUb767AU8uW5WyGvzGLTtx5z0P4/t3XEdZL1gkNBZEWdcI16VZU9ZdGnjNzaasawbs8OzffWsN3nxttWxFRWUVjjjqOMxbeKRSqyjrSpiYKEcClPUcgTG5MgHKuhoqN8i6sU3bpeedhAvPPkGC+eFDS9Gypy1F4NWIWZ+KI+sWMKWsWwCRWaQQoKyzQ+ggQFnXQdX5eYpF41Y89zRa9+2RjZl/2FFyNL0sEN9vVuWgrKtQYppcCVDWcyXG9KoEKOtqpNwg64KEGEm//rYHsGt3qwRzzqmLbSHqoi6UdbW+OmwqyroFEJkFZZ19QDsByrp2xI4r4P133sTrr7wo6908eSo+f9IZqKtvzLkdlPWckfEEBQKUdQVITJIXAcq6Gja3yLoajeKkoqxbwJ2ybgFEZkFZZx/QToCyrh2xYwro7enGn5/9Pfbu3gWfz49jPneCHFHP96Cs50uO5w1HgLLO/qGLAGVdjSxlXY2TzlSUdQvoUtYtgMgsKOvsA9oJUNa1I3ZEAR+tex+vvbQSkUhY7pd+yhe+KLdkG81BWR8NPZ6bjQBlnX1DFwHKuhpZyroaJ52pKOsW0KWsWwCRWVDW2Qe0E6Csa0ds6wIGBvqx8vk/YMe2LXL7tcMXLcaRxxwPr9c76npT1keNkBlkIEBZZ7fQRYCyrkaWsq7GSWcqyroFdCnrFkBkFpR19gHtBCjr2hHbtoAtmz7FX1YsR2hgQO6ZftqZX8TY8U2W1ZeybhlKZmQiQFlnd9BFgLKuRpayrsZJZyrKugV0KesWQGQWlHX2Ae0EKOvaEduugEgkgpdefA4bP14v6zZ3wRE49viT4PeXWVpXyrqlOJlZggBlnV1BFwHKuhpZyroaJ52ptMq6sW/d2vWfHdCGBYcehAfvvQkNdTU621eQvCnrBcHsqkK4dZurwl2wxlLWC4baFgW17NqOF559Gv19vaioqMRJp5+LyVOna6kbZV0LVtdnSll3fRfQBoCyroaWsq7GSWcqrbIuNpQXx83XX6qzDUXPm7Je9BCUXAUo6yUXUls0iLJuizAUpBJiEbnVK5+TZR00aw6WnPwFBIJBbWVT1rWhdXXGlHVXh19r4ynrangp62qcdKbSJutiVP2OHzyMW2+8HDOnNetsQ9HzpqwXPQQlVwHKesmF1BYNoqzbIgxaKzE0NITXVq/Ah2vfluUcc9yJOGzRsVrLFJlT1rUjdmUBlHVXhr0gjaasq2GmrKtx0pmKsm4BXcq6BRCZRQoByjo7hA4ClHUdVO2Tp7g//c/Ln5KrvYu9008984uYNmNWQSpIWS8IZtcVQll3XcgL1mDKuhpqyroaJ52ptMm6qLSYBj99ShMuPPsEnW0oet6U9aKHoOQqQFkvuZDaokGUdVuEQUslxLZszz69FPv27kZVdQ3OPO9iNI4Zp6WsTJlS1guG2lUFUdZdFe6CNpayroa71GW9fyCMu+5/FIsXzU3x1Tff3YA77nkYD913S9FniGuV9Y1bduKxp17ArTdcjorygFqvcGAqyroDg2bzKlPWbR4gh1aPsu7QwI1Q7e7uTjzzuyfQ3dWJmto6nHPB5aipqStoYynrBcXtmsIo664JdcEbSllXQ17qsi4opN+6bSyQfsv1l+Low+eogdKYSpusD7cSvGgPV4PXGFVm7XgClHXHh9CWDaCs2zIso6pUe9s+Ker9/X1oaBwrRV2s/F7og7JeaOLuKI+y7o44F6OVlHU16m6QdUFCjKQ/uWwV7r71Gjy7cg02b2uxzQLp2mRdrQuURiqOrJdGHO3UCsq6naJROnWhrJdOLEVLdrfskFPfxb3qE5om4azzL0VZmbX7p6sSo6yrkmK6XAhQ1nOhxbS5EKCsq9HSIetbOrdgU/smtQpYmGpa/TTMqJ+RNUdx+3ZP3wB2tuzDPd+8zjbbi1PWLegElHULIDKLFAKUdXYIHQQo6zqoFifPrZs34s/Lf49YLIqp02fi9LO/BK/XV5zKcDX4onEv9YIp66Ue4eK1j7Kuxl6HrH//pe/jWyu/pVYBC1PdueROfO+U72XN0W7T342Kapd1Ma3gq9+4NwXMz358uy3uAbAq/pR1q0gyH4MAZZ19QQcByroOqoXPU+yh/tKLz0Ns03bwnHk48dSz4fF4Cl8RU4kcWS8q/pItnLJesqEtesMo62oh0CHrv3z/l3jknUfUKmBhqi8v/DKuPeLarDmKkfWPNm5DZ3cvHrz3JneMrAtRf+ChpSkNFovOXX/bA7jx6vNLZpV4yrqFf0nMShKgrLMj6CBAWddBtbB5vv3mq3jr9ZdloUccdRyOWryksBXIUhpl3RZhKLlKUNZLLqS2aRBlXS0UOmRdreTCpjLfs/7gz38vC7/5+ksLW4kspWkbWTeWwr/kvJMOGEU3AymFVeIp67boyyVVCcp6SYXTNo2hrNsmFHlVZPXK5yBG1cVxwilnYvbchXnlo+MkyroOqsyTss4+oIsAZV2NrBtk3dWrwd/xg4dx642XH7A/nRhdv/+nTxT85v2nlq/OuLpf+sr16dP0xXnfvu9R2avPOXWxXCnQfJGBsq72B89U6gQo6+qsmFKdAGVdnZWdUg7FYnjh+T9g88aP4fF6cdoXvojpMw+xUxVBWbdVOEqmMpT1kgml7RpCWVcLSanLuqv3WbfTyLr5vvlrrzg7ZVpDepDEhYQ773kY37/jOnmRIX0qv7ifQRzmqRGUdbU/eKZSJ0BZV2fFlOoEKOvqrOyUcvnTv8aObVvg95fhjHMuxKQp0+xUPVkXyrrtQlISFaKsl0QYbdkIyrpaWEpd1tUoFDeVtmnwolliRHrpslW2uWc908h6+ih/urwLOZ8+pSl5f32m+/Ap68XtxKVYOmW9FKNa/DZR1osfg1xr8Oflv8Pmzz6RW7Kde8EVGDu+KdcsCpKesl4QzK4rhLLuupAXrMGUdTXUlHU1TjpTaZV1UXE7rQafSdYzybcxen7D1V/CXfc/isWL5iZlPX3kXbSRsq6zi7ozb8q6O+Ouu9WUdd2Erc1/xXN/wGefbpAj6ud86TKMb2q2tgALc6OsWwiTWSUJUNbZGXQRoKyrkaWsq3HSmUq7rOusfK55Z5P1J5etSrkPPV3WzYvkpcv6fa/ch3NnXYQptVNzrQ7Tk0BWAjUVZejuj5CQJgKDkQgGo4MYHIwiOjgon4vHaDQqfwbFa+J303sirdjTWrwei8XktlniSH80XhMbaRnvydeQmj7TufvTe9TzHaEe5rK9YnuvoSFEh4ZS6zY0BHN9U+qdlv9wbc70nthSzJyfppCWXLahUAh79+yG3+/HBRdfhilT7Tf13QxdXAjqC0UZ65LricVtUJnXC5/fg4FwtLgVYeklR6Ay6EcoEkU0Fv+/mUdmAuL7KI/iEqCsZ9heLpeRdc/dHtQF6/HYl5bihKknFzeaLL1kCNRU+tHdN1gy7RmuIf39fQiHwwgNDCAcCUOKtJBoKdOpwixEOnKARAvJToi3lG3TeVLA4+9JOY/wAogrOlUJNfKCiy7DjINm2b5F1RV+9A4MimtBPEjAMgJ+vwdlPi/6Q5R1y6AyI0mgqtyH/kgMsSg/tIbrEuL7KI/iEnC9rI/2nvUrfnsFnvjgCRnFOz/3Pdx45M3FjShLLwkCTpkGHxGSHRpAOByK/4QSP4nfQwP9UsTjrw9I+R4Y6IMYNRTnDg4WR559Pj98fh/Eoxi59IrRG/ma+L0MPjma40+8Fk/n8/rkOeJ9cYhVueWjGK1OHMZzjxynjh9yZNmUzpQ8ea45D8jR7yz5Jk4+IH16PRLlp9ctWCba6UVfaDDnepvbmmxnamMU6m3688zQFoNber1T+WXgbdQjwc2cfn+9h7LzFvzSYpYttjI+irz31yP+ZTCdm+hXpXJwGnypRNJe7eA0eHvFo5Rqw2nwatHkNHg1TjpTWS7rxjZoX7vsTPzPr5/D2vWfZaz/gkMPSll4TmcjjbwzTYO3YjX4O/70Hfzra/8ip7meNfN8/OcZj6LcV1GIJrGMEiVQCFkXoiwlWsr0fpEWr8VlWjwOyB8h1vHR735EIvH04ncrjkAwiGCwHGVlAQSC5fD7hBRnF+X4ewmBFnLt88Pri8u2yMPj9cjXzOm8ifSBQMCKKjs2D96z7tjQ2b7ilHXbh8iRFaSsOzJsjqg0ZV0tTJR1NU46U1ku60Zl0zeYNzdCLOqWfp+4zkaOtMidFfusr9zyPP7uua+gN9KDQxoPxf+e9ztMruF97DrjWsp55yrrQrB7e7rR29stH/v6etHf14dIJC7eQq7jo+BCzgfklHMrDjHKHJftIMoCQQQCCfEOBFBRUZkQ8Ph7Io1IGyhLPEpB571QVsRBNQ/KuioppsuVAGU9V2JMr0KAsq5CiWnyIUBZV6NGWVfjpDNVUWQ9feq5zgYWIm9jNfhP2z/Gl5edj21dW1AbrMN/n/UEjp98YiGqwDJKjIBZ1sU93VLEzT8JKe/t6ZGv5zudXAq1SaTlcyHdwXIEy8shRqIDgXKUBQJy9FvKduI18T4PZxGgrDsrXk6qLWXdSdFyTl0p686JldNqSllXixhlXY2TzlRFkXUxHX3NW+tSVmDX2UjdeZu3busMdeCaZy7Dmp0vwevx4vbFd+PvF92iuwrM38EExKh4W9tedLS1orOzHb3d3RgM96GtrQPd3Z1KLRNTwKuqaxI/1fKxvLwyOZodDFbIUWwh4UK4haTzcB8Byrr7Yl6oFlPWC0XaXeVQ1t0V70K2lrKuRpuyrsZJZyrLZV2Mml9/2wPYtbs1a70nThiDh+67BTOn2XfP2Fygp++zHh2K4p9X/3/42dqHZDa8jz0XmqWbVoyQCyFvb9snH9vk4z6I14c7hGQnRbyqBtU1tSYxr0FVVY0cBedBAiMRoKyPRIjv50uAsp4vOZ43HAHKOvuHLgKUdTWybpD1TLdLn3PqYtsMKlsu60boh7tnXa17OCdVuqwbNf/1hv/FbSv/HoOxQXkf+8/OfRLTag9yTsNY07wIiGnp7W2t6Gjfh7bWfehsb5Mj52IEPdvR0DgW8mfMWCnjUyeOwUAsiOqamuTq43lVhieRgIkAZZ3dQRcByrousu7Ol7Lu7vjrbD1lXY2uW2T9gYeWpix8LrbxfuPdDQVfDD1TVLTJuloXKI1U2WRdtO6NXa/i2mcuQ9tAKyZWT8L9p/wEJ089ozQa7vJWiCnq8ZHyVrS37kV7eys621uzrpIuFmOrb2hEfeMYNDaOk48NjWNQU1ufso2WwJrrAnMuDwWbr0iAsq4IislyJkBZzxkZT1AgQFlXgMQkeRGgrKthc6usCzpC2MVx8/WXqsHSlIqybgHY4WRdZL+zZzuuXnYR1rWuRdBXjivmXo3bj/sOagI1FpTOLApBYE/LTrTs2oF9e1ukoHe0tyEaHcxYtJi2Xi9HyoWMj5OPQsxrauqUq0pZV0bFhDkQoKznAItJcyJAWc8JFxMrEqCsK4JispwJUNbVkOmQ9c7OTrS3t6tVwMJU9fX1ED/ph5gGnz6yLtJke93CKillpVXWh7t/vRj7rCsRySPRSLIusgxFB3DPq3fh4ff+Q5bQVNWMH576EE6cemoeJfIU3QRadm7Drp3bsXP7Fuxp2ZVxtXWxUFtDw9j4SPmYsahviAu6uL98tAdlfbQEeX4mApR19gtdBCjrusi6O1/Kurvjr7P1lHU1ujpk/aWXXsLKlSvVKmBhqiVLluCUU05RlnW77F6mTdb7B8K46/5HsXjRXBw2bxYee+oF3HrD5agoD8hpBUuOXYijD59jYQiKl5WKrBu1e2/P2/j757+KTZ2fypcunnMlvrvkAbnVG4/iERByvmPbFuzcsQ3iefohBHzipCkYP2EiGseMl9PZKyqrtFWYsq4Nraszpqy7OvxaG09Z14rXtZlT1l0beu0Np6yrIdYh6++//z7eeecdtQpYmGrhwoU44ogjlGW95EfWzQvMCSr3//QJ3PPN69BQVyOnFTy5bJVtVtkbbT/IRdZFWZFoGPe9/h089M6/QawcP65iPO475Sc4Y8Y5o60Kz1ck0NXZju1bN2P71k3YuX0rIpFwypniPvLmyVPR1DxZSnouU9gVqzBsMsq6FRSZxwEXncr98Ps86OyNEA4JWEqAsm4pTmaWIEBZZ1fQRYCyrkZWh6yrlVy4VNmkvOTvWTfLemN9De7598dwxz9eJWXdLtMKrOoGucq6Ue6H+97H3z9/NT5p/0i+9MVZF+N7J/0QY8rHWlU15pMgIGR857Yt2L5tM7Zt2YTuro4kG3GP+aSpM9CYWI19YvMUraPmKkGhrKtQYppcCXBkPVdiTK9KgLKuSorpciFAWc+FFtPmQoCyrkbLrbLuitXgzdPgLzz7BDn1ffqUJojnTy1fjTVvrXPtyLr5z2MwFsG/v3U//u3Nf4V43lg+Bt878Yc4/+BL1P6KmCojgaGhIezb0yLlfPuWTdizeydisVgyrZjGPnX6TEydPgtNEyfB4/XaiiRl3VbhKJnKUNZLJpS2awhl3XYhKYkKUdZLIoy2bARlXS0sbpH1r37j3hQgrthnPb0LiJH2G27/Edau/wwTJ4zBQ/fdgpnTmtV6is1T5Tuybm6WGF0Xo+xitF0cYkq8mBovpsjzUCPQ19uDbVs3STnfsX0zQgMDyRN9Pr+c1i4EfdqMWZYsAqdWq/xSUdbz48azhidAWWcP0UWAsq6LrLvzpay7O/46W09ZV6PrBllXI1G8VNoWmCtekwpfshWyLmodG4rhv975Mf7/178nV4+vC9bj7iX345I5VxW+UQ4psbenGx+tX4uNn6yXW6qZj+qaWinmU6YdJH+cdFDWnRQt59SVsu6cWDmtppR1p0XMGfWlrDsjTk6sJWVdLWqUdTVOOlNpk3XzPeulMoKeLRBWybqRv1gp/qY/X483W16TL11wyKW44cibMW/sQp19wTF5Dw5GsHnjJ9iw7j3s2pG6crtYDE5MbZ8ydQYaxjj33n/KumO6o6MqSll3VLgcVVnKuqPC5ZjKUtYdEyrHVZSyrhYyyroaJ52pKOsW0LVa1o0qPfL+T/CDV/4ZA9F++dLi5iW483PfxZFNx1hQa+dl0bJrOz5eJ0bRN6Tsey5GzWcdMhfTDpqFsrKA8xqWocaU9ZIIo+0aQVm3XUhKpkKU9ZIJpa0aQlm3VThKqjKUdbVwUtbVOOlMpU3WRaVLbT/1bIHQJeuivJbenfjW6lvw7Mank8WfPv1s3Hn893Fww2ydfcMWeUejg/j0o3V4/5030NHelqyTGEE/ePY8zJg5G4Fg0BZ1tbISlHUraTIvgwBlnX1BFwHKui6y7s6Xsu7u+OtsPWVdjS5lXY2TzlRaZV1s0fbYUy/g1hsuR0V5aYx4ZgqGTlk3yvtg33u477W7sWLLc/Ilr8eLi+dciVuP/Wc0V0/W2UeKknd3dyc+fO9tbPjwXUQi8T2hx4wdj9lzF+CgWXOKvrWabiiUdd2E3Zk/Zd2dcS9EqynrhaDsvjIo6+6LeaFaTFlXI01ZV+OkM5U2WTev/p6pAQsOPQgP3nuT3Hfd6UchZN1g9N6et3Hva/+M1dtWypcC3iD+ZsF1+MbRt6OhvNHpKLFz+1Z88N5fsXXzRojt1zweD6YddDAWHLYITc1THN8+1QZQ1lVJMV0uBCjrudBi2lwIUNZzocW0qgQo66qkmC5XApR1NWKUdTVOOlNpk3WdlbZb3oWUdaPtb+x6Ffe8+s8Qj+KoLqvG9Ud+A393xP+LSn+V3RANWx8x1f2TDR9i7Xt/Ta7oHiwvx5y5CzH/sKNQWVXtqPZYUVnKuhUUmUc6Aco6+4QuApR1XWTdnS9l3d3x19l6yroaXcq6GiedqbTJ+nCrwb/57gY8uWwV7r71mpKYHl8MWTc6xcvbV+H+Nd/BX1vWyJfGlI/FN465HV+Z93WU+ex964HYdk2Mom9Y9z7CoZCsv1jBff7CRTh4zjyIvdHdelDW3Rp5ve2mrOvl6+bcKetujr6+tlPW9bF1e86UdbUeQFlX46QzVVFkXdzLfv9Pn8A937yO0+Atiu4Lm5/FA69/D+/vfUfmOLF6Eq5ZeCPOP/hiTKqx1/Rxsd2akPQtmz5NTnWfOn2mHEVvnjzVIiLOzoay7uz42bX2lHW7Rsb59aKsOz+GdmwBZd2OUSmNOlHW1eJIWVfjpDNVUWT9qeWrseatdRxZ1xDZP216BveuuQsfta5L5n7l3K/h5mO+KQW+mMdnn27A22++ivbWfbIaZWVlmD33MMw/fBFqauqKWTXblU1Zt11ISqJClPWSCKMtG0FZt2VYHF8pyrrjQ2jbBlDW1UJDWVfjpDOV5bIuRs2vv+0B7NrdmrXeEyeMwUP33YKZ05p1tq1geRdzGny2Rv5x41N4+J3/TE6PH1cxHosnLcFFc66A2PqtkIdYLO6va15C6749stj6hkbMW7hIruzu5qnuw8WAsl7IHuqesijr7ol1oVtKWS80cXeUR1l3R5yL0UrKuhp1yroaJ52pLJd1o7LD3bOus0HFyNuOsm5w2ND2IR5970H8/uOl6I30yJeFuF8w+3JcMferOKRxjjZkYmX3N15dhb17WmQZYvT8qMVLMGv2XG1llkrGlPVSiaS92kFZt1c8Sqk2lPVSiqZ92kJZt08sSq0mlHW1iFLW1TjpTKVN1nVW2m5521nWDVYD0X4s++QpPPbBo3iz5bUkwsPGL8Llc/8GFxxyGWoCtZag7e/rxSt/eQGbNn4k8xOruR917Ocxe+5CS/J3QyaUdTdEufBtpKwXnrlbSqSsuyXShW0nZb2wvN1UGmVdLdqUdTVOOlNR1i2g6wRZNzfz0/aP8bO1/4WnPnoCnaGO5FvnzLwAV877Kk6aenreVMTCcWLKeyQSkXkce/zJWHjE0Xnn59YTKetujbzedlPW9fJ1c+6UdTdHX1/bKev62Lo9Z7fIeig6gOhQFNFYFIOxwcTzwfhz8S8mnkcRE+8PxV+PDcWfi/cuXHCG27tK0duvVdbFVPgbbv8R1q7/7ICGLjj0IDx4701cDb7IXUDc2/6/a/8bYgs442iqasbFc67EFXOvxvS6mUo13Ld3N/7ywnK0te6V6SdPmY4TTj0LVdU1SuczUSoByjp7hA4ClHUdVJmnIEBZZz/QQYCyroNq6ebZP9iH6FAsLqBDg3EBNZ4LAY3F5VTIa02lFx29AwgNRhJpYwmZTYisFNx4PkJ0pewmBFacn3we21+efD1q5GcqDwlRTpQtRVnkKcpICHJSkqUsD2EwFs9H1jel7FjynHi9Em1NtE8wsPIYumvIyuyYVx4EtMr6Dx9aKqt08/WX5lE155zitJH1TGS3dm+WU+SXrv8l9vTF7zEXx9FNx+Haw2/EebMuyhiQcDgs70vf8OF7chs2MeX9+BNOw/SZhzgngDasKWXdhkEpgSpR1p0TRG9nJ2J1ztklg7LunL7lpJpS1u0VLTFKG45GEI6FEB4MIRILIxQNy0fxeygWQiwWgxDGcDSEsHw9/n5I/B4NIRKNyHShwQH5XOYVDcfTi8dEXuL1SHQQosyIfF2ckygrGpL5ifPFbZ48hidQ7quA3+uD1+uD3+OHz+uHz+ODXz765Xs+8SOf++FNvFfmDeC161YTb5EJaJN1LjBX5MiOovjnPluGX37wCF7c+qdkLlVl1RRY6GUAACAASURBVPjawr/D6TPOxlFNi+Xrn368HmteWoH+/j54PB7MXXAkjj5uCcrKAqMonacKApR19gMdBCjrOqjqybP+xmvh7ehA9213InL4kXoKsTBXyrqFMJlVkgBlPXNnELcwikWD+yJ98rF/sBe9EfETf60v8SiEOC7O+wVbynCKYIfjMiwEWApyJP5cyHBCtvsGex3TKyv9VXHxTBdTQ1K9Ximr5f4yYMgLrxBU03uGwAqZFeni7yXyE3Ir/onXTVIrRdjjQ8AbiAtxQoZlHUQ6xB/l82S9hByb5FmWES/PyG9/2fFzhUz7PN79z03nxOsbLyfoK7csXrxn3TKUeWdEWc8b3f4TS2FkPROGlt6deHzdz/GHT36Dj9vWJ5M0+yfhcv/lqB2IT3EfO24CTjztbDSOGWcBTWZBWWcf0EWAsq6LrPX51v/911H561/JjEMnn4buf/oWwkcdY31BFuVIWbcIJLNJIeB0We8YaI8L9GBcoIU494R7Ul4Tct0f6UN3qAtCioV094mfwT70hrtTXjOvM1SsriIGb8p8ZQh4gwj6gxCjr0JSk8998d8D/qBMI9IGfUEEfPG0QX8AcqRX5CFfj+cVTx9AwBeI5+kPIpg4X6RLeZ7IK+APQMh5Podb7lnPh435HMr6aAmO/nxtsi6qJqbBT5/ShAvPPmH0NbVxDqUq62bk+/r3YvWWFfjw7bcwtq0BfvgRQggrsAJdY3pxyrQzcMq0M3HcpCU2jpRzqsaRdefEykk1paw7J1r1/3AdKp94LKXC4cXHo/uWf5LybreDsm63iJRGfYop63v7dqMj1IHOULtcjLdzQDzvQGe4Ax397egMtyde60RvpFsKthTtwV50hTq1BqAmUIPKsmopqlVl4qcaFWWV8rEy+ViFyrKqhDjHBTgpzSbZFuIsRmTFe2VStBMCbRJsUV6pHZR1tYhS1tU46UylVdY3btmJx556AbfecDkqykt3arQbZF3smf6XFcvR090l+2PDlPHY1LAFK3f9Ce/vfSfZR6vLqrFk6qlyuvwp074g93TnkTsBynruzHjGyAQo6yMzsksKY2S9894fwtvViar/+g9429pk9cKLjkbPLbdj4Iyz7FJdLjBnm0iUVkVGI+tiFFvItRDnDrNwC8kOdaK9vy0p4ulprLoPWmyJGxfouFTHBTsh1YH4Y4W/EtWBmsT7ccEWEi5eE2nl74kfkYeVU5xLq7fk1hrKuhovyroaJ52ptMn6cCvBiwZxNXidYbUu70g4jFdW/xmfbPhQZlpTU4clp5yJSVOmJQtpHdiHlZufx4rNz+Ev215IuaI8b+xCnDb9LJw8/Qy5WB0PNQKUdTVOTJUbAcp6bryKmdqQ9Y6fPoK+S6+AZ6AfVY/+H1T95N/g2x1fBDQyf6GU9v5zzwc8nmJWl7JeVPqlW3jM04/+oS5sbd0rxbpDjG6HxSh3e1LCxVTz/VLeJke79/bvGTWUxvIxqAs2oK68HvWBetSVN6A2WIeGYCNqxWvBetQF61Ff3piQ6uqkcDeUN466fGaglwBlXY0vZV2Nk85U2mRdZ6Xtlnepjqy3t7Xi+T/+Ft1d8b3Yjz/xdMxdcMSI+F/f9Qpe3PwnrNzyPD7c934yvfhPTezh/pX5X5dXjBeMO3zEvNyagLLu1sjrbTdlXS9fK3NvuPHrqFj6K7T/5GH0X3ZVMmtPOITKx36B6n9/AL5tW+Xrg7PnoPvm29F/wcWA12tlNZTz4jR4ZVSuS9gd7kqObIsRbCHaHVK449K9f9Tb9HqoHW0DraNmNbZinBTqhvIxEKPc9eVCsBtQn5BwIeB1QsSFeIv3ElIuZgnyKG0ClHW1+FLW1TjpTEVZt4BuKcr6lk2f4sU/LUMkEkFT8xR87oRTMWZs7lPaxTZwK7f8CS9sfhYvbV2BnkhPCnGxsvySKSfj+MknoaGiEXMa51kQEednQVl3fgzt2ALKuh2jkrlO2WQ9mXpwEJW/eQLVP7of/o2fxKV9xkz03HQr+i69EvD7C9pYynpBcRetsN29u+SotZhCLv5/39u3B+0DrWgfiI9odwkJD3UkRsDFSHj7qOoa9JejIRgf0a4XI9rBurhYS+FOCLYQbznCnRBvKeT1cno5DxLIRoCyrtY3KOtqnHSm0irr/QNh3HX/o3hmxRpMnDAGD913C5onjJWvLV40t2QWnis1WX/r9Zfx9puvyn43b+EiHLfkFLk1mxXHaztewivbV+HlbavwZstrB2Qp7sWaN24hDht/JOaNO0yOvs8fe5gVRTsqD8q6o8LlmMpS1h0TKhgLzHU8+Cj6Lrl82IpX/P43qP7hfShb94FMF1lwGAa+eAF6/+YaxMaMLUijKesFwWx5Id3hbuzr3w2xiGxr314p3+LWtr29u+PP+/fJ98XzfFciF/dfi1FrKdyB+LRyQ7jFRfr012sDQrzrMb6yCaO5Z91yWMywpAhQ1tXCSVlX46QzlVZZN1aDP+uUxbj/wSdw1YWnYea0Zrz57gY8uWwV7r71mpJYeK5UZH1wMII/P/M7bN+2GV6fDyeffg4OmjVHW/8Ti7+8vutVvLZ9NT7Y865cqC7btLeF446Q8j5/3GGIP19Y0ousUNa1dTtXZ0xZd0740+9ZV6l5+bN/RPW//xCBN9ckk/d+/Qb0X3YlwkcsUski7zSU9bzRWX6iWI18e9c2iNXMxUj4vv49aOtvxe6+XdjXt1dOO2/p2YmdPdtzLlvcxz22cjzGVY7H2IrxGFMxDuOqxqM2IEa8G+QMudqyWnl/txByMQ19NAdlfTT0eO5wBCjrav2Dsq7GSWcqbbIuFpi74wcP49YbL5ej6WZZF6vE3//TJ3DPN69DQ53zt4MoBVkX96U/+4cn0dnRjorKKpx53sVy//RCH2Jv97V7343/7HlHPu7q2XFANXweH2Y1zpYj7wvHH4H5iRF4sbJqKRyU9VKIov3aQFm3X0yy1SgfWTfyKvtwLSr/52FUPv5LeEID8uXolKnou/hy9F9+FQZnHmw5CMq65UgzZiju+Rb/J+7q3SEfd3Zvjz/2xh/FjxgtVz3Etl1jK8dJARdiLX8MGU8IuXy/YjyEqHs9hV0TgbKuGkmmy5UAZV2NGGVdjZPOVEWRdY6s6wxp7nmLkfQVz/4e4XAY45ua8YVzL0J5eUXuGWk6Q9wL997et/Hhnvfwzp6/4sO972Nr16aMpc2omyUF/osHX4TGijGY3ThP3sfmtIOy7rSIOaO+lHVnxEnUcjSybrTS092NyqeWouLXv0Lgjf23HUUOOwL9F1+GvsuuQqxxjCVQKOujxyj+rxMSLkbDd3Rvw67uHdjRsy0p4bt6dso9vFWOqbUzMLF6ktw+Vcj2+KomjKkYm5RxIeVjKsbD7vtnU9ZVos00+RCgrKtRo6yrcdKZSpusi0o/tXw11ry1Dnf841X4j0d/J6fBN9bX4Ibbf4RLzzuJ96zrjKxi3u++tQZ/XfMShoaGMGv2XJx46tnwFmk1YcUqy2Ri5ODDfe/i/T3vyJ91rWvxUeu6jFmILytzxy3ACVNOk/fCi9vvx1U2YWa99aNLubRhuLSUdatIMh8zAcq6c/rDiAvM5dgUsXK8WJBOrDDv/+Tj+Nk+HwZOPAUDl16J/nO/iKFRXKSlrA8fEHEfuBgFF4uybe/aKqehCxEXs8l2dG+Xv6vs7S1GwoWEN9dMQlNVMyZVT0FTdTOm1E6TQi7eG1NemHUKcuyCeSWnrOeFjScpEKCsK0ACQFlX46QzlVZZFxUXo+hf/ca9KW342Y9vx9GH67sXWiewTHk7cRp8NDqIF559Gls3b4TH68XxJ5yGQ+c7eys18UVHjLqLUfh1e9di3b64wA/3BUiMLkyrOwgTqyZhWv0MNFdPll96JldPlb+LL0bFOCjrxaBe+mVS1p0TY6tl3dzysvfeQcXSx+Wou3dvfD/qoapq9J9zHvovuRKhE0/OeQs4N8u6uDd8Z2IKujFFfacYGe/ZJe8LzzYTLL03ioXYJlY3S+EWP0LEJ9ZMwqSaKZhQNVH+P+W2/bsp6875zHJaTSnrahGjrKtx0plKu6zrrLxd8naarPd0d+HZZU+io60VwfJynHnuxXL6e6ken7Z/jHWt7+Pj1vXY0rVJjmps796qtLiOmEIvxH1y7TTMEFIvvjjJ36diSs00uYCOjoOyroMq86SsO6cP6JT1JIVoFMHVL6Li14+hYvkf4emLT7GOTmhC/4WXov/SK+TK8ipHqcq6mJIu7wnv2S6nqLf0JKaoJ14T/5eoHGLf7viI+GQp3eLCsPj/xBDz5qrJclV0HqkEKOvsEboIUNbVyFLW1TjpTKVV1sVq8C172lJWfTe2c+PWbTrDmj3v3S078Pwff4vQwIDcN13cn15V7fxF/vKhGR2Kyi9gO7q3YltC4Ld3bcG27i1yJV2xYE8kGh42a3G/3+SaaZhckxB4MSovnovXaqfmPR2Rsp5PRHnOSAQo6yMRss/7BZF1U3OFqFc8s0xOkxcCj2hUvhuZcygGLrkSfZddiWjTxKyAnCbr4vN/T29L2mJtCSlPLOAmRH0wNjhipxAXbYWAJ8W7ZnJSyuUIec1kiFFzHrkToKznzoxnqBGgrKtxoqyrcdKZSpusG1J+yXknHTDlnQvM6Qxp9rw3frIeK59fJhNMn3kITj/rS8WpiINKFSMq23u2ytF4seDP1q7N2NG1NS703dsQisZXWs52HDZ+ESr8lfB6PHKLGzmVsXpS4nGi3EdWjLSkT7enrDuokzioqpR15wQrl33WrW6VmBov72//za8hpsyLI1ZbC7EwXXjRMQiddgbCi49PKdZusi5GvMVIeHy19J3xR9PibeJecZVDzK5KjoQL8a6dkrxXXHyeT66dUrTbpVTq7/Q0lHWnR9C+9aesq8WGsq7GSWcqbbJu3rpN7K1uPrh1m86QZs77o/VrsXrFs/LNuQuOwPEnnl74SpRgiXv796TI+7auzfFp9gnB7430KLVajNCLL36Lm5dgfOUE1FSWobsvAq/Xh9pgLWoCdYl9bOtRE6yV0yXrAvXapuErVZqJHEeAsu6ckBVT1s2U/J9+Ep8m/9ST8G/ZvwvHUGUVeq+6GtGZMxFacjLGLD4ceztDiMWGtEMW94DHp6bvjI+Md2/HzoSIC0kX95CrHGIhNmM0PD4CnhBx8Vg9EWJ3ER7FJUBZLy7/Ui6dsq4WXcq6GiedqbTJOkfWdYYtt7w/2fAhVr3wjDzpyKM/h0XHfj63DJg6bwLd4S609O6S0y3FSI68/7F7B1r6dsnn4kf1nsdslRD3QtYG66XM15c3ojogfq+TIl8fbEB1oBZ1wbq45EvBr0NNQAh/vdzGh4d7CFDWnRNrK7Zus7q1Ze+/i/I/PIWK3/02RdxlORMmoP/zJyK85CQMnHI6os2T8ip+c+dGORJu7BlubF22u7dF3rK0r3+vUr5iF5CUaeniHnFxz3j1JLl6+rTag5TyYaLiEqCsF5d/KZdOWVeLLmVdjZPOVNpkXVRaTHe/456H8dB9t8AYXRej6tff9gBuvPp8bt2mM7KJvDd+vB4v/vmPcmu2+YcdheOWnFKAUllErgTaBlqluLf1t6I91AqPvw/b2lrRHepER6gdXeFOdIU65ZZ1HaE2dIe60BXqQI/iyP1w9RFT8IXIC4lvLB+LyrIqKf5C+MW+vEumHNhnxPZ3Ynp/ZVk1qsqq5P2YTtzPPtc4OT09Zd05EbSjrJvplX3wvry3PfDqywiseQXejo4UuIMHzUJoiZD3ExE64RTEGhvxWccn8uKlMSVd7iUuRsgTU9TFPuMqh7h9SKwJYqyQLhdtq26OL9pWPUku/smjNAhQ1ksjjnZsBWVdLSqUdTVOOlNplXVRcUPOd+1uTbbDblu3iYXwHnl8eQrn7952TfJigtgv/tv3PSrfP+fUxSkL5onX7Loa/KaNH2HFc3+gqOv8C9KUdy73rHeGOtAZ7ojLfKgL4ve43HfE5X5AyL54vwvd4U50DsTTdkU65XtWH0Lyq8qqUemvlI9VgRpU+CvizxNiLy4OVJQJ2Y8Lv5FWzAoo8wYQ9Jcj6CtH0B9E0BtMPhcXCHjkT4Cynj+7Qp9Z6AXm8m2f+LwRM4ew7V1sWvMi9n32LtpbPsXOsn7srgJ21ALba4E2xV0wjS3LjPU9xOJs8RHxyfF7xWum5FtVnudAApR1BwbNIVWmrKsFirKuxklnKu2yrrPyVuUtZF0cN19/6QFZitkBDzy0FA/eexMa6mqQKa0dZd0s6mL/9M+fdIZVuJhPAQjkIuujrY4YnRcj+ELgk9If3i/94gJA/2AfxP33veFe9EXiP+L3vsTr4ncx5b9QhxD/oC+YlPqAL4ByIfcJwQ8k3isXj75yyN8T75X7KxLnJl6T7wfk++WJiwTyd9MFA5F3QFw08AfljAKnHpR150SumLIuLvLt69+NPX27sa9vD/b0xh9397XI+8H39u2Rj2I3jVyOqZ3A5C5gSpcHk8ubMG7SXEyYcxzGHX4iJjbMkDLOgwTMBCjr7A+6CFDW1chS1tU46UxFWQcyCrgBXcj59ClNyVH2dHkX6ewm61s2fYo/L/+dHFGnqOv889GXdyFl3cpWiNXx+yJxsTekXgh9T7gbfYNm0e+Vr6VfBOgf7MdAtB+hwQGEoiGEoyH5fCA6UNCLAbkwEfLu83jlYoB+jx8+j08+F48+rw9exB+NND744Pf696cR6WVab/xc8dxjSpM43+vxxvNBav6+RJnifONcWbYvXhcjT7/Xh4pAAGU+H8IRpNbTVAfRhnh9EucmyhR15lE4AtX/dj+CK19Az03/hNBJ1t6+1BlqlyK+tzch5P170Nq3T96KI14Xf4Oqh7gFZlzlBEypm4TaQCPGVozH+KomjKscL19vSuyAMWlrOwKvrEbg5dUIvvoSvK37Uorou+IriE6bjsFDZsu93QdnzFStAtOVMAHKegkHt8hNo6yrBYCyrsZJZyqtsi5WhL/h9h9h7frPDmjDgkMPSo5W62ygSt7p0+CNKfCZ9oQX0/rvvOdhfP+O6+L34a9ahZaDF2Cowh6jbXFR/z1isRhmz12AE089SwUB09iMwMTGCuxqU//CbLPqa6+OGMUXAh8eDMnt80KDofjvMSH3xmtC+MMJ8Y/Lv/iJRMPyQkLqxYD4RQFxfngwLGVlf/72v2CgHTgLcBUBMctEyLZYiK2xfIzcocIs4OL3cVXjUxZpG19fjn1iNfghtdXg/R9tQPC1l1Em5P3l1RDbxZmPoepqDJx9Hganz0Bs4iQMHjoXkXnzIVah5+EeAuVlPpQHfejoCbun0WxpQQiMrQ2iszeCSDRWkPKcWoj4PsqjuAS0yvpw08uL2+zspRv32N9zx3WYP+cg3HX/ozDvFX+ArNfVAeXlwJ13Yuj/+ceiNmvjxk/x+OOPS1GfP38BLrzwwqLWh4XnT0As4Kb4nTf/QnjmqAmImQDRWBSDsUFEh6Ly+XCPMl2GNEOIJfPIliY935HKHIzG62LOLybqKF5LvGeuy0j5iXN5FJDAhg3A7t3AnDlypXUrD3EbSVN1EyZUT8DEmiZMqJogtyoTj+I1sdhkrof8zBInqbn6gdl//DE8r72KoVdehWflCuCzAy/yy5OmT8fQvPnAYYfBM38ehuYvAObPz7W6TO8QAqJfyW6Vb79ySDtZzcITGPVnVuGrXJQSjb/BohTOQiUBbbI+3D7rdmdvTH0/65TFUtYXL5qbnAZ/gKwffzzw6quySdHJU9B96zfRd9XVBW/i9q2b8PwzTyEWjWLmIYfi5NPPhYd/YQWPg1UFOnUavFXtZz56CPCedT1cdeRq99Xg09s8oaHc0n3Wvfv2IvDm6xCrzvvXfYCy9R9C7Pme7YjMW4DB2YdicN4CRMQo/KFzEZ3CVeF19M1C5slp8IWk7a6yOA1eLd6cBq/GSWcqynoGuub71FXuWW//xa9R891vJ79IiHvuur/5L+g/93ydsUvmvXP7Vjy77Ekp6jNmzsapZ36Rol4Q8voKoazrY+vmnCnrzol+MReYy4eS1bKeqQ6ecAhi+nzZug/hX/8B/Os+lBLv27UzY5WHamoQmTNPivvg3PkYnDsPkXkLERMz4ng4ggBl3RFhcmQlKetqYaOsq3HSmUqbrItKp4uuzobkm7eYAbB8xRpcdeHpMov0kfNcVoOv+tl/o+be70KMCIgjctgR6PrW3QidfFq+1RvxPCHqzy37DaLRQRw0a44UdR7OJ0BZd34M7dgCyrodo5K5TvX/cB0qn3gMHQ8+ir5LLrd9xQsh69kgeLq7EfjgPTkK7xMyv2E9yj54D56enoynRMdPkPfDx8aNl/fAR6dOxeC0GYhOm4FYQ4PtWbupgpR1N0W7sG2lrKvxpqyrcdKZSqusC/F97KkXcOsNl6OiPKCzHXnnbSwi98yKNck80veBz2WfdU9fL6r/40eo/s8fw9PfJ/MMHX8Cuu7+ASKHH5l3PTOduHf3Lvzxd09gcDCC6TMPwelnfcnS/JlZ8QhQ1ovHvpRLpqw7J7punwZvRaR8O7aj7CMh7mvhW/9BXOLXvjds1mJhO7ES/eDUaVLexQr14sJ7+KhjrKgS88iRAGU9R2BMrkyAsq6GirKuxklnKm2yPtxK8KJBdloNfrSAM23d5tuzG9X/+j1U/fyRZPbiSn7XnXdjcPac0RaJzo42PP2bXyI0MIC5C47A8SfGZwbwKA0ClPXSiKPdWkFZt1tEsteHI+v6YuX/+CP4N34C/6aN8G3dAt/mTfBv3Qzfli3whAaGl/nyCkQnNiPaPAmxpiYMTpqMoQlN8dcmTkK0aSKiU6bqq7zLcqasuyzgBWwuZV0NNmVdjZPOVNpkXWel7Zb3cPusiy8EtXd/C+XLl8lqx2pr0X/JFej7ytcQmb8wr6aIkfTf/frn6Ghvk/eon3ZWYe6Nz6uyPCkvApT1vLDxpBEIUNad00Uo68WJlW93C3xbN8O/ebN89G3+DL6tW+HbuUPeG+8ZUNtSMzZ2XFzcpcQ3IzZpcvx3IflC7puaEWtsLE4jHVQqZd1BwXJYVSnragGjrKtx0pmKsm4B3eFk3cg+8MZrqP3nOxD46xvJEiOHzkPfNX+LvkuugJh6p3r8+dnfY/PGj1Hf0IgLLrsafn+Z6qlM5xAClHWHBMph1aSsOydglHV7xsrb0SGl3duyC75dO+Br2QVvQuS9e3bDv33bAXvGZ2vJULB8v8ALkZ+UEPmJzQgtOQmxMWPtCaGAtaKsFxC2y4qirKsFnLKuxklnKu2yLhZo++o37k1pQ/o94TobWIi8VWTdqEdw1UpU/uxhVPzx6WTVxH/Y/RdejL6rvz7ifXFr33kTa155EWVlAVx4+dWoreNiOIWIcaHLoKwXmrg7yqOsOyfOlHXnxCpTTcX98kLq5U/LTniE3Aupl4/x18UaN6qHuKAfa2iM/zQ2IlafeGwcg6GGBsQaxiReb4g/it9LYLE8yrpqD2G6XAlQ1tWIUdbVOOlMpVXW01dSFw0Ri85df9sDuPHq85N7l+tsYCHyzkXWjfp4W/ehcumvUPGrX6Bs/bpkNcUWM31f+1v0X3y5nDJvPva07MQffvsYhoaG8IVzL8LU6TML0TyWUQQClPUiQHdBkZR15wSZC8w5J1b51tTb1RUfoU+K/M74KL0Yrd+7F+J7gre9Fd729ryKkCvcT5qcem6ZH7HqGoht7YaqaxETs/pq6xCTv9fEH2trEauqlmliNbVy5t9QRWVedRjtSZT10RLk+dkIUNbV+gZlXY2TzlTaZN1YZf2S807C0YenLqgmJP7JZatw963X2HaV+Fyg5yPr5vzL3n0blb/6BSqeWgoxxU4cQ+UV6D//AvRdfS3CxxyH/v4+/PZXj8rHwxctxtHHnZBLFZnWYQQo6w4LmEOqS1l3SKAAcJ9158RKe02HhuDt7IS3ow3etjZ428VPuxR5j/F78vV4Go9I29VlXdX8/v1CL2U/LvryMSH68gJArZD7hPSnp6mqie9x7/Mp14uyroyKCXMkQFlXA0ZZV+OkM5U2WRerwd/xg4dx642XY+a05pQ2iNH1+3/6BO755nVoqKvR2b6C5D1aWTdXUgh75eO/RPDFF5IvR+Yciv+58irsig1i4qSpOOdLl8Hj8RSkbSykOAQo68XhXuqlUtadE2GOrDsnVnauqZB8T3cXvN3d8PR0w9PfL6Vf7EHv7e6C2KNevC8ek2nEe12dyTTetlbLmxhrHBMftRej97V1GKqqMl0AENJfJ0f0/fX18DfWoTtYg6FAGRAIYigQwFAgCAQDGCoLYCgoXgsCgTKI2wp5kIAKAcq6CiWAsq7GSWcqbbLOkfXRhU3cz1b5+P+i4rFf4M9z5+CNY49FTVcXru7uw9D5FyG8+PjRFcCzbU2Asm7r8Di2cpR154SOsu6cWLmlpkLapeD39Oy/ACAuBMjfExcDxNR+Q/7FxYG+Png62xNpuuQMgUIcQ5VVGErIPBIyf4DsS+mPi79Ii3TxF1P//f4DLgzELxiUJS4QiIsF5RjyeQGfP57en3iUv/viv5vf8xlpfHIWJY/iEKCsq3GnrKtx0plKm6yLSj+1fDWWLluFB++9KTmCznvWcwunWPVdrP7uHRrCtT//BZo3b0pmEDnsCAyc9gWETvsCwkcfm1vGTG1rApR1W4fHsZWjrDsndFxgzjmxYk1zI+Dp74uP4ifEX8p+V+d+oe/uBvp64e3sgL+3G/6+Xgy2d8DTPwBPJAyEQvCEw6bn4vcIPL09uVXEhqnl2gAmwU8V/4T8p4t/WRkgLhaICwVe3/4LBsl0PnmxwMhr//PEhYSyQPzWBHF+4gLD/ueJ80wXGMx5yfSBAOD1JC9KpF+sGC6vYq2FIEJPWVf7A6Csq3HSmUqrrIuKczX4/MMn9lEX+6mLfdU/f9IZmDtj2nUlsAAAIABJREFUFiqfehIVv/pfBN5ck5JxrL4eA6efidAXzkbopNMgfufhXAKUdefGzs41p6zbOTqpdaOsOydWrKk+Avnesy5H+iNheKTYhwAh8+G45EM8DkbhGehPiH9C9mW6cDxdKAyICwMDA/ELA8Z5Ms9EHom0Mu/BQSA6GH9MeR6FJxp/zUgTfx7NaTcAfYTtlbO8jUHOTki7wGC6kJBxpoK42GDcHiruEk0+98Sfm3+HB0MeDwJlXgxGgZhAkJ7eeM10rjgnJS9kyDslH8hy5JF+bjLf1PcPSD/cucnbYePtGb4NiTgn0h1YTlo9jXK9XtTc9317dRIX1ka7rLuBqZX3rBu8IpEwfvv4z9Dd1YFZs+fi5NPPTUEpFo4JrnoBgb+8iPI/PSu3gTEf4aMXS3EfOPV0RBYc5oYwlFQbKeslFU7bNIaybptQjFiR+huvReXSx9Hxk/9G32VXjpi+2AkmNJRjb2cIsdhQsavC8kuIQL6y7kQEntBAQuqj2cU/cSHALP9C/OXviYsC5ufyvZSLCOaLB/H35MWFSMSUbn+aA/LKWE5U6WJFxjqLNvOwN4EhfqYXO0BaZf2HDy1Fy562lFXfjXvZFy+a6+qt20YK/HPLfoNtWz5D45hxuOCyv4FXTG0a5vB/tAHlf1mBwIsrEHzlpZQrttHxExASo+6nn4mBk0/FUFX1SMXz/SIToKwXOQAlWjxl3TmB5T3rzokVa6qPgJtkXR9F5+Ts6euVsw7kBYRY4iJAygWCA2cqyBkL4iJhTI6RA0IujR/jdwzBY0hn4r26Cj96QoOIDsbi6TOcK88x54UMeaeciwPKScnbON9UVnq9srYhrR7JupnrndKGRNwT5x1YTlqbM7EDUHPvd53TgUq0ptpknQvM5d9j3vnra/jrmpcQCAZx0eVfQ3VN6n7rKjkLYQ+sWoHgqhUIvPNWyimhJSei72vXIdo8GeGjjlHJjmkKTICyXmDgLimOsu6cQFPWnRMr1lQfAcq6PrZuz5n3rKv1AN6zrsZJZyptss6t2/IL287tW/HM75+QJ3/h3IswdfrM/DIynSX2Yw2uXongC39C+QvPw7t3T0qeYpG6yBGLMNTYiPBhRyAyfyHESqo8ikeAsl489qVcMmXdOdHlPevOiRVrqo8AZV0fW7fnTFlX6wGUdTVOOlNpk3WOrOcetoGBfvzmV4+iv68XRxx1HI5avCT3TBTOKFv3AYJiuvyfn0Xw5dUZz4hOnY7IoXMRWXg4BuctQGTefAzOGP2FA4XqMQni+1rqWAuBcN1NgLLunPhzZN05sWJN9RGgrOtj6/acKetqPYCyrsZJZyptsi4qLVaCv+Oeh/HQfbdg5rRm2Q5u3ZY9nMuf/jV2bNuCseMm4PxLvgKv16sz9jJvsdVJ8PXXUPbeO/B/sBZl69bC/8nHGcsV+4EKeRcSLwV+vvjhKLyOIFHWdVBlnpR15/QByrpzYsWa6iNAWdfH1u05U9bVegBlXY2TzlRaZd0s57t2tybb8bMf346jD5+js10FzduKEdCP1q/F6hXPwu8vw0VXfBW1dQ0FbUN6YeI+d//6D+Ff+z7K1n+AwHvvQGyFkumQo/BC3OfOR/jYzyF08qlFrXspFE5ZL4Uo2q8NlHX7xSRbjSjrzokVa6qPAGVdH1u350xZV+sBlHU1TjpTaZd1nZW3S96jlXUx7X3pY/+NcCiEz51wKuYtXGSXpqXUw7dzB8o2rEPZ++/B/+Fa+D9aDzGlfrhDyPuQ2P8yGES0eRKiU6bGHydNQXRiM6JTp0KM2PNIJUBZZ4/QQYCyroOqnjx5z7oerszVWQQo686Kl5NqS1lXixZlXY2TzlSUdQvojlbWVzz3ND779CM5/f2Cy662oEaFzaLs3bdRZozCf7we3t0t8La2wrdnt1JFYnV1cmX66KT4T2zylPjv8rHZlffKU9aVug4T5UiAsp4jsCIm58h6EeGzaNsQoKzbJhQlVxHK+v9t7+6DpKrOPI4/3QMIysiLiRKViMEkSNaoodCpNeWCZpMSYc2aMJGkNIaERc0/QQtLtCxDpQwUlsZaSwhSorHWl4xKVlmJruvqurJFYeHL4luVC6urMiPGEZwRRl56ts6duU33pXv63DvnuT19z3eqqGFmznnOPZ9zuMyv7+1uuyUlrNs5abYirDvQHUxYf///3pE/P94muVxOfjhvvowdf4yDIxo6JfKdndL0YbvkOzqkqf0DaWrfIfn2HX2fd34oTR+8bxXqC+OPkQMnTZLCcRP6Av0JE+WACfcnnhhcqRfJSX73LimMHSeFceMa/r3kCetDZw9n6UgI642zmoT1xlkrjlRPgLCuZ+t7ZcK63Q4grNs5abYirDvQTRrW9+/fJw/ff7d81t0lp3/rbDnrr//GwdE0Zglzi31TR3tfiO8w4d78/QNp+rBDzM+C7+3eHWty5op97+hm6R09WgrNR/d97v/afL8wZqzIkUdJYfToQ+3GjJXeI48sb3d0/Pe5j3WgFRoT1gcrSP9KAoT1xtkX3AbfOGvFkeoJENb1bH2vTFi32wGEdTsnzVaEdQe6ScP6xv94Wt7Y+rI0N4+R1kt/Ifl8k4OjyW6J3Oc9fcG9P8A3tbcfukr/0U7Jd/5FzHvK53ftEtPW5Yd53/liqG9ulkJzc3D1vvgAgPk6+oBA89HSc97fJjoMwnoiNjrVECCsN84W4cp646wVR6onQFjXs/W9MmHdbgcQ1u2cNFsR1h3oJgnrOzt2yGOP/FMw+pyL58mE4yc6OBJKlArkOz+WXHeX5Lu7+z53dQWfc93dku//nOv6NHiV++LXn3X3tetvG/Td81ldYHuPGCliXpyvKd/3In3mwZympr6/9//p7f9e1Tb5JukdNkwkn+vrY74u7V9WN1+5TZUxxNQtq9nXv/RYo1/3NtUao0EesOrtFan0J9gpvZIr/VnwrQrt+79f3ra3b69VbS/Va0vJGJVq9/bKiOF5acqJ7O05cGiMcLyax91/XBWPu2/ehx13WLtQqMu/oUYedOSG9TL89a2ya9Va2TP3kiE/lePGjZSPdn8uhUL/Hh7yR8wBNoIAYb0RVqkxj5GwbrduhHU7J81WhHUHunHDeqFQkEceWCu7d3XKV6f8lcz4ziwHR0EJTYEg0JtgHwb9PXsk9+nuvgcCuj4NPkv/59xnfWHfPAAg+/YHV/lz+/aJHNgvuf37RfYfkJz5e/R7ju8G0PSgNgIIpCOwa+Xdsqd1XjqDDWIUwvog8OhaVYCwzubQEiCs28kS1u2cNFsR1h3oxg3rL23eKFs2b5QjRo6UeZddIcNHjHBwFJTIkoA5Oba//7HIwYLkDh4UMX8KBw/9/eBByRX6vx+2KX7d367/69zBQl//sj5V2kTGKB+z/1jCcczVUvPgQ7FP3ziHjstujGB+xZoNdFUulzOvayhiPpuP4OuSP8EPRXoP+36Ftv01ytqa/lVrB6+pOHDtSH9Te/iwJsnlc7LvYL9ztWOTXHntw+bX/6+tv3/5cQeND/cI55LPR5xKPEr7HWZXPma5db9FpP9ha1LiedgxBz+LrmHfsfW1rb3W4XgVa5ftjUNzDtoOsNb7vz5FCl88dsif3gjrQ36JGvIACesNuWwNcdCEdbtlIqzbOWm2Iqw70I0T1s3V9EceuEcKhYMy87uz5ZSvTXVwBJTImgDPWc/aig6N+fCc9aGxDlk8CsJ6Fle1/nMirNd/DbJ6BIR1u5UlrNs5abYirDvQjRPWzfPUzfPVT/zyJLng71odjE6JLAoQ1rO4qvWfE2G9/muQ1SMgrGd1Zes7L8J6ff2zPDph3W51Cet2TpqtCOsOdG3D+puvvyovPPuUNDUNkx9dukCOGt3sYHRKZFGAsJ7FVa3/nAjr9V+DrB4BYT2rK1vfeRHW6+uf5dEJ63arS1i3c9JsRVh3oGsT1vfu3SN/vO8uMe+t3nLOTDntzOkORqZEVgUI61ld2frOi7BeX/8sj05Yz/Lq1m9uhPX62Wd9ZMK63QoT1u2cNFsR1h3o2oT1pzf8Sd7Z/rZ84YvHyfdbL5Nc+EJHDsanRPYECOvZW9OhMCPC+lBYhWweA2E9m+ta71kR1uu9Atkdn7But7aEdTsnzVaEdQe6tcL6u//7P/KvT6wLAvoP582XseOPcTAqJbIsQFjP8urWb26E9frZZ31kwnrWV7g+8yOs18fdh1EJ63arTFi3c9JsRVh3oFsrrD/4h99Ld9en8s0zp8vZ58x0MCIlsi5AWM/6CtdnfoT1+rj7MCph3YdVTn+OhPX0zX0ZkbBut9KEdTsnzVaEdQe6A4X11/97i/zX88/IkUeNDl5Ubtiw4Q5GpETWBQjrWV/h+syPsF4fdx9GJaz7sMrpz5Gwnr65LyMS1u1WmrBu56TZirDuQLdaWD9wYL88eO/vpadnr3zngovk5MlfdzAaJXwQIKz7sMrpz5Gwnr65LyMS1n1Z6XTnSVhP19un0QjrdqtNWLdz0mxFWHegWy2sv7R5o2zZvFG+cOwE+fvWyxyMRAlfBAjrvqx0uvMkrKfr7dNohHWfVju9uRLW07P2bSTCut2KE9btnDRbEdYd6FYK65/39MgD964Sc3V91kWtcsLESQ5GooQvAoR1X1Y63XkS1tP19mk0wrpPq53eXAnr6Vn7NhJh3W7FCet2TpqtCOsOdCuF9U0bn5WtL78oE750osz5wY8djEIJnwQI6z6tdnpzJaynZ+3bSIR131Y8nfkS1tNx9nEUwrrdqhPW7Zw0WxHWHehGw/revXvk/ntWSm+hENz+bm6D5wOBOAKE9ThatLUVIKzbStEurgBhPa4Y7W0ECOs2SrRJIkBYt1MjrNs5abYirDvQjYb1/3z2KXnr9Vfly5Mmy/dm/8DBCJTwTYCw7tuKpzNfwno6zj6OQlj3cdX150xY1zf2dQTCut3KE9btnDRbEdYd6JaG9a6u3fLH++6S3t5emfuTX8jYceMdjEAJ3wQI676teDrzJayn4+zjKIR1H1ddf86EdX1jX0cgrNutPGHdzkmzFWHdgW5pWH/mqcdl+9tvySlfmyozvzvbQXVK+ChAWPdx1fXnTFjXN/Z1BMK6ryuvO2/Cuq6vz9UJ63arT1i3c9JsRVh3oBuG9U86/yKPPLBWcrmc/OjSBdJ89FgH1SnhowBh3cdV158zYV3f2NcRCOu+rrzuvAnrur4+Vyes260+Yd3OSbMVYd2BbhjWn1z/iLz37nY59Runy7dnfs9BZUr4KkBY93XldedNWNf19bk6Yd3n1debO2Fdz9b3yoR1ux1AWLdz0mxFWHega8J6R/v7sv7RBySXz8tPfnaVjBp1pIPKlPBVgLDu68rrzpuwruvrc3XCus+rrzd3wrqere+VCet2O4Cwbuek2Yqw7kDXhPV/brtPPtrZIaedOV1azpnpoColfBYgrPu8+npzJ6zr2fpembDu+w7QmT9hXceVqiKEdbtdQFi3c9JsRVh3oLtpy2vy1L88KsOGDZcfX36lHDFypIOqlPBZgLDu8+rrzZ2wrmfre2XCuu87QGf+hHUdV6oS1m33AGHdVkqvHWHdwnbdhuflxhVrg5YXnt8iSxfPl1EjRxR7/uMdd4p5cblvnXWOTDvrHIuKNEFgYAHCOjtEQ4CwrqFKTSNAWGcfaAgQ1jVUqWkEuLJutw8I63ZOmq0I6zV0X3zlLbl1dZusWr5Ixo1plttWtwU9rl7YGnx+7bXX5NFHHw2uppur6ubqOh8IDFaAsD5YQfpXEiCssy+0BAjrWrJ+1yWs+73+mrMnrNvpEtbtnDRbEdZr6JpwPmniBLl41rlBy2h4v+OOO6Szs1Navj1TTjtjuuZaUdsjAcK6R4ud4lQJ6yliezYUYd2zBU9puoT1lKA9HIawbrfohHU7J81WhPUBdPf27JObblkrLdOmFsP6tnd3yA3L1sjNSxbI5JOOl6VLlwav/D7v8iukqWmY5lpR2yMBwrpHi53iVAnrKWJ7NhRh3bMFT2m6hPWUoD0chrBut+iEdTsnzVaEdYuwPnfODJl+xpSgZaWwPnv2bJk2bZrmOlEbAQQQQAABBBBAAAEEEEDAIwHCukVYH+jK+rZt22Ty5MkebRmmigACCCCAAAIIIIAAAgggoC1AWK8hXOs566a7eZ91PhBwKcBt8C41qRUKcBs8e0FLgNvgtWT9rstt8H6vv+bsuQ3eTpfb4O2cNFsR1mvo1no1eMK65vb0tzZh3d+115w5YV1T1+/ahHW/119r9oR1LVnqEtbt9gBh3c5JsxVh3UK31vusc2XdApEmsQQI67G4aGwpQFi3hKJZbAHCemwyOlgIENYtkGiSSICwbsdGWLdz0mxFWHegS1h3gEiJMgHCOhtCQ4CwrqFKTSNAWGcfaAgQ1jVUqWkECOt2+4Cwbuek2Yqw7kCXsO4AkRKEdfaAugBhXZ3Y2wEI694uverECeuqvF4XJ6zbLT9h3c5JsxVh3YEuYd0BIiUI6+wBdQHCujqxtwMQ1r1detWJE9ZVeb0uTli3W37Cup2TZivCugNdwroDREoQ1tkD6gKEdXVibwcgrHu79KoTJ6yr8npdnLBut/yEdTsnzVaEdQe6hHUHiJQgrLMH1AUI6+rE3g5AWPd26VUnTlhX5fW6OGHdbvkJ63ZOmq0I65q61EYAAQQQQAABBBBAAAEEEEAggQBhPQEaXRBAAAEEEEAAAQQQQAABBBDQFCCsa+pSGwEEEEAAAQQQQAABBBBAAIEEAoT1BGh0QQABBBBAAAEEEEAAAQQQQEBTgLCeUHfdhuflxhVrg94Xnt8iSxfPl1EjRySsRjffBD7Z3SVXXvc72frm9mDq995+nUw/Y0pFhr09++SmW9bKE89sKv58oPa+WTLfcoGk56YXX3lLLv/V8gH3Itb+CsQ5Z4VK4Z4yX5926ldk1fJFMm5Ms7+IzLyiQNxz1m2r2+TuBzcEtdhXbKqkAmbfvfNeh1y9sDVpCfohkIoAYT0Bs/kF5NbVbcVfPMx/HOaDf/AJMD3sEobvlmlT5eJZ58q2d3fIDcvWyM1LFsjkk44/TMT8knzPQ3+WK3/6/eABIbP/lixbI6tXXFOxvYekTLlfIOm5qTRU8UAQ2ykqEPe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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'green', 'gray'])" ] }, { "cell_type": "markdown", "id": "158e3787-f2d5-4a01-aaa9-6066e93e584c", "metadata": {}, "source": [ "### The (transiently) high value of [U] led to an increase in [X]" ] }, { "cell_type": "code", "execution_count": 15, "id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: U <-> 2 D\n", "Final concentrations: [D] = 145.1 ; [U] = 36.37\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.98913\n", " Formula used: [D] / [U]\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.2717 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: X <-> D\n", "Final concentrations: [D] = 145.1 ; [X] = 72.21\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.00937\n", " Formula used: [D] / [X]\n", "2. Ratio of forward/reverse reaction rates: 2.0\n", "Discrepancy between the two values: 0.4683 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": null, "id": "02d8a758-89b1-4c28-94c9-c73b11f3b8dc", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f6619731-c5ea-484c-af3e-cea50d685361", "metadata": { "tags": [] }, "source": [ "# 3. Let's again suddenly increase [U]" ] }, { "cell_type": "code", "execution_count": 16, "id": "d3618eba-a673-4ff5-85d0-08f5ea592361", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 1.0973722:\n", "3 species:\n", " Species 0 (U). Conc: 100.0\n", " Species 1 (X). Conc: 72.21103524746438\n", " Species 2 (D). Conc: 145.09842911303875\n" ] } ], "source": [ "dynamics.set_chem_conc(species_name=\"U\", conc=100., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 17, "id": "e8fe3554-d5ab-4306-b890-4e36289b5b4b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEUXDcaption
920.98191236.77151671.151097145.362231
931.09737236.37344772.211035145.098429
941.097372100.00000072.211035145.098429Set concentration of `U`
\n", "
" ], "text/plain": [ " SYSTEM TIME U X D caption\n", "92 0.981912 36.771516 71.151097 145.362231 \n", "93 1.097372 36.373447 72.211035 145.098429 \n", "94 1.097372 100.000000 72.211035 145.098429 Set concentration of `U`" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=3)" ] }, { "cell_type": "markdown", "id": "0974480d-ca45-46fe-addd-c8d394780fdb", "metadata": {}, "source": [ "### Yet again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 18, "id": "8fe20f9c-05c4-45a4-b485-a51005440200", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.03) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.015) [Step started at t=1.0974, and will rewind there]\n", "* INFO: the tentative time step (0.015) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.0075) [Step started at t=1.0974, and will rewind there]\n", "* INFO: the tentative time step (0.0075) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.00375) [Step started at t=1.0974, and will rewind there]\n", "* INFO: the tentative time step (0.00375) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.001875) [Step started at t=1.0974, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "45 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.03, target_end_time=1.6,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 19, "id": "ad01c472-3ebe-4d0d-8913-1bcd85ea7a6c", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 20, "id": "54346a72-bac9-4cc7-ba01-0533ed60371f", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=U
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mJHm6dfJIhZ17vOex22yaBEiABEiABEiABEiABEiABEhAMwHKumbA2cJ7vSduHrvOpkmABEiABEiABEiABEiABEiABDQSoKxrhMvQJEACJEACJEACJEACJEACJEACJOCGAGXdDTXWIQESIAESIAESIAESIAESIAESIAGNBCjrGuEyNAmQAAmQAAmQAAmQAAmQAAmQAAm4IUBZd0ONdUiABEiABEiABEiABEiABEiABEhAIwHKuka4DE0CJEACJEACJEACJEACJEACJEACbghQ1t1QYx0SIAESIAESIAESIAESIAESIAES0EiAsq4RLkOTAAmQAAmQAAmQAAmQAAmQAAmQgBsClHU31FiHBEiABEiABEiABEiABEiABEiABDQSoKxrhMvQJEACJEACJEACJEACJEACJEACJOCGAGXdDTXWIQESIAESIAESIAESIAESIAESIAGNBCjrGuEyNAmQAAmQAAmQAAmQAAmQAAmQAAm4IUBZd0ONdUiABEiABEiABEiABEiABEiABEhAIwHKuka4DE0CJEACJEACJEACJEACJEACJEACbghQ1t1QYx0SIAESIAESIAESIAESIAESIAES0EiAsq4RLkOTAAmQAAmQAAmQAAmQAAmQAAmQgBsClHU31FiHBEiABEiABEiABEiABEiABEiABDQSoKxrhMvQJEACJEACJEACJEACJEACJEACJOCGAGXdDTXWIQESIAESIAESIAESIAESIAESIAGNBCjrGuEyNAmQAAmQAAmQAAmQAAmQAAmQAAm4IUBZd0ONdUiABEiABEiABEiABEiABEiABEhAIwHKuka4DE0CJEACJEACJEACJEACJEACJEACbghQ1t1QYx0SIAESIAESIAESIAESIAESIAES0EiAsq4RLkOTAAmQAAmQAAmQAAmQAAmQAAmQgBsClHU31FiHBEiABEiABEiABEiABEiABEiABDQSoKxrhMvQJEACJEACJEACJEACJEACJEACJOCGAGXdDTXWIQESIAESIAESIAESIAESIAESIAGNBCjrGuEyNAmQAAmQAAmQAAmQAAmQAAmQAAm4IUBZd0ONdUiABEiABEiABEiABEiABEiABEhAIwHKuka4DE0CJEACJEACJEACJEACJEACJEACbghQ1t1QYx0SIAESIAESIAESIAESIAESIAES0EiAsq4RLkOTAAmQAAmQAAmQAAmQAAmQAAmQgBsClHU31FiHBEiABEiABEiABEiABEiABEiABDQSoKxrhMvQJEACJEACJEACJEACJEACJEACJOCGAGXdDTXWIQESIAESIAESIAESIAESIAESIAGNBCjrGuEyNAmQAAmQAAmQAAmQAAmQAAmQAAm4IUBZd0ONdUiABEiABEiABEiABEiABEiABEhAIwHKuka4DE0CJEACJEACJEACJEACJEACJEACbghQ1t1QYx0SIAESIAESIAESIAESIAESIAES0EiAsq4RLkOTAAmQAAmQAAmQAAmQAAmQAAmQgBsClHU31FiHBEiABEiABEiABEiABEiABEiABDQSoKxrhMvQJEACJEACJEACJEACJEACJEACJOCGAGXdDTXWIQESIAESIAESIAESIAESIAESIAGNBCjrGuEyNAmQAAmQAAmQAAmQAAmQAAmQAAm4IUBZd0ONdUiABEiABEiABEiABEiABEiABEhAIwHKuka4DE0CJEACJEACJEACJEACJEACJEACbghQ1t1QYx0SIAESIAESIAESIAESIAESIAES0EiAsq4RLkOTAAmQAAmQAAmQAAmQAAmQAAmQgBsClHU31FLq7D0UVhCFIVQRCBQA42tLsb+JeVHFVFWc2ooiRHp6EY72qgrJOAoIFIYCqCkvxIHWqIJoDKGSwNjqYrR29qAn1qcyLGN5JFBaHERJYRDNHd0eI7G6agIT60rR2BxGX7/qyIznhUBFaQgFBQVo7+rxEoZ1FRMoKAAm1pZiX4bvzPVjShW3yHBOCVDWnRJLU56yrgCiwhCUdYUwFYeirCsGqigcZV0RSA1hKOsaoCoISVlXAFFTCMq6JrAew1LWPQLUVJ2yrgmswrCUdQUwKesKICoMQVlXCFNxKMq6YqCKwlHWFYHUEIayrgGqgpCUdQUQNYWgrGsC6zEsZd0jQE3VKeuawCoMS1lXAJOyrgCiwhCUdYUwFYeirCsGqigcZV0RSA1hKOsaoCoISVlXAFFTCMq6JrAew1LWPQLUVJ2yrgmswrCUdQUwKesKICoMQVlXCFNxKMq6YqCKwlHWFYHUEIayrgGqgpCUdQUQNYWgrGsC6zEsZd0jQE3VKeuawCoMS1lXAJOyrgCiwhCUdYUwFYeirCsGqigcZV0RSA1hKOsaoCoISVlXAFFTCMq6JrAew1LWPQLUVJ2yrgmswrCUdQUwKesKICoMQVlXCFNxKMq6YqCKwlHWFYHUEIayrgGqgpCUdQUQNYWgrGsC6zEsZd0jQE3VKeuawCoMS1lXAJOyrgCiwhCUdYUwFYeirCsGqigcZV0RSA1hKOsaoCoISVlXAFFTCMq6JrAew1LWPQLUVN1EWX/m+Tew+oN1+MEt16C0pEjTnusP29zajutvexg3X3cFTjhmgesGKeuu0Q1WpKwrgKgwBGVdIUzFoSjrioEqCkdZVwRSQxjKugaoCkJS1hVA1BRipMl6T08PYrH4T29PbOD5wPtJ78ViMfTGYujv74f8r68P/f2IvxbPxX/iufU6Ua6vrw+wyvX3o69fvE4pm6jbJ25gb32GfsTrxsuK56KN+GvEPxtoM96GLJNoQzxa7/X2xrIeEcFgCIFAAEIuxf/EPdvlf+KNgoLEZ4nXiffjHyU+LxB1B8tbz2UMGVd8Fu+CFXugHau9RKyBdhNlkWgntU8DbSQCi3pDYw72z4op6wQCg/1I7OdgvUT/kvoy0OfU/RvgINpNqif6nehLIFCAuspiNHf0DLBK7suSxfOU/6Zu2bEX1936IPY1HBqIPWnCGKy4/2bMnl6PfMl6ONKNux54HBPH1+F7113heb8p654RqgtAWVfHUkUkyroKinpiUNb1cPUalbLulaC++pR1fWy9RKase6Gnt67Jst7d3Y1opAuRcBjhcBcikbB8HhHvdXUNe687GtULi9FJIAeBu+66SykjIeLfv/9xPPHIbUNGm99buwG/em6VHE1/4dXVHFlPos6RdQWHIGVdAUSFISjrCmEqDkVZVwxUUTjKuiKQGsJQ1jVAVRCSsq4AoqYQfsp6uKtzQLjD4c6EeAsB70K4qwvRaFg+Cinv6uxwtcdiRLmwsBAh8RMKIRQSz4sQCgYRTLxXKF6HCmW5QDA4MIIcKAgkRnITo6piBDkx2ipGqZNHqOOv4+VEPWtEWr62ysIawR4c3U4uGx/5lkPf8TiBwZHsytIiOWLcFYnFR8KHtAHZhtjXdJsYdY+P3A8d1Y+PzKcb1Y+P7Fufi5kCAzMKkuoMzDToG5xFINofnB2QNLvAqpc0O0H2NWlGghVvyKyERP9kQVF8YMaCfDE4CyJlxsNA2YGZCoP7NLDfib4kx5Uxk2dQJGYvDLSb6EdyH4tCAUS6Y/H+pOzft//+GlfHbbpK1oj6vbdfm3VauDWyfvG5J8tp5GJLHnm3YqeO0H/rq8sHRsSF/D+4YiX+7soL8L1/+smQGB99tlmeMBDbUQtn4dH7bkJtdSWskfWlSxbhsuWnD+yCdYLBesNqJ90MgR/ees1AXY6sKzt0vAeirHtnqDICZV0lTbWxKOtqeaqKRllXRVJ9HMq6eqYqIlLWVVDUE0OHrLe3teDQwQNoOnQATYnHttbmuAw62ISMlpaVoaSkNP4jn5cNvFdaWobiUvFZGUrkY6mD6GYX5TXrZubHz2vWhfSufG7VgBxnImLJcbJ8P7RiJfY3Ng1cxy5E+c57H8Pdt18rp86nTmEXsv7NG+9DaoyfPfX8sPdEP8S093SyntpnUeY3f3wdX7noDOxtOIhX3vwA3/76JXJXUk9GUNYdHPMiwSI51pZ81kO8Z8H8ZP1WWSR1akbyGZWLli0dtuABZd1BMnwoSln3AbLLJijrLsFprkZZ1wzYQ3jKugd4GqtS1jXC9Rjaq6wLCT/QuB8HGvbLx0MH9kNcH566iZHjouJiCMEWch2X7FL5Oi7kCeGWn5dK+Raj36N1o6ybmXk/ZT1VuLPJeuoCc9ZIuTUKLmLNmDpxyAh4cpnN2/bIkXWrvGgrNUbqeyXFxfKadWtk3Y1sJ/fLTf10TEb8NHhxBuTRn/8Of3fVhXKKQ+pZj9SzKKlnatIdHNYZGAsoZd2sP0CUdbPykdwbyrqZuaGsm5kX0SvKupm5oaybmRfRKyeyLkfMDzSioWEvDjTsw8HG9GIupHzsuAkYM3YC6saOQ23dWIwbP9FcCAb2jLJuYFLiVzNgYm0p9jWF03awfoy62R2qZN2S6j++snpYn61p7SpkXTjhAz95Gvfeca10yHSbNYKf/Jk1mk9Zd3nMp5Pz5ESkfp565ibdWRnKustkaKpGWdcEVkFYyroCiBpCUNY1QFUUkrKuCKTiMJR1xUAVhssk6x3tbVLGGxvjUn7wQAOikciQlsU0dSHh4ydOwoSJkzF+Yj3KyisU9m70hqKsm5l7P2XdyTT4bCPrqSPgmSTa68h6LlkXjvj8q+8MrGIv+iHeE5uYVk9Zd3nMp4JLJ98W6Ouv/tKQ6RCiydSRd/EeZd1lMjRVo6xrAqsgLGVdAUQNISjrGqAqCklZVwRScRjKumKgCsMly/runduwfesm7NqxFULWU7fKympMmFSP8ZMmY8KEeozlaLnCTAwNRVnXhtZTYD9lPdsCc8nXgqdbDd7OTOdkELmmvFsj5cnlnEyDtwZ3L7/kzCGL5VHWPR2O8crJEMXr5FsFlJYUDSljyXpyItLJulydkptRBMS1ZE4XfjFqB0ZoZ8Q/CvK3hb8yZmU4fgtWuXouN7MI8HfGrHwM9Ia/M4YmBtixYzs++eQTrF+/HpGkkXOxUnp9/WRMmTIZU6dOw+TJk1FWVmbsfoy0jln3MOe/M+ZlNtt3ZrGiv8ot3a3brIHUafXjM966LVW+rennqauv//vTL0D426cbtnq+Zt3yxnfXbhiyYrxYYG75spNx34+fHHJP9tRF7Tiy7uLISXethIqR9UzXebjoIqsoICD+royrKUVDc/rrbxQ0wRAuCdSUFyHa04twd6/LCKymg0BhMIDq8kIcbOM9fXXw9RJzTFUx2jp70NPb5yUM6yomUFoURHFhEC2d3YojM5wbAg379mDLpg3yR9xOzdomTpqCseMnYNqM2ZgybYab0KyjiEB5SUjezq0jPHyxPkVNMIwLAuIkyoSaUuzP8J15Up26a9at7qW75Vnyqu3WrdvEPdetgdR0vpbt1mkqRtat/qYuVJ56Tbq1QLl439o4Dd7FwZhpUYPU6xF4zboLuIZV4TR4wxKS1B1OgzczN5wGb2ZeRK84Dd7M3HAafP7zIm6jtvnzddi6aQPa21plh8S9umfOnIVps+Zj+qy5EPcf52YGAU6DNyMPqb3wcxq8mQTM79WIXw1epCB16ntyWrgavPkHqdMeUtadEvOvPGXdP9ZOWqKsO6Hlb1nKur+87bZGWbdLSm05cd355xs+xZbP16GluWkguBhBn7vgCMycPR/T62vR2BwGr1BUy95rNMq6V4J66lPW9XBVGXXEy3rqPdQteMn3S+d91lUeUvmPRVnPfw4y9YCybmZuKOtm5kX0irJuZm4o6/7mpWH/Hny85j1s3/L5QMPiVmqz5y3C7LkLUF4xeFslJ7du83cvRndrlHUz809ZNzMvyb0a8bLuRwq4GrwflO23QVm3z8rvkpR1v4nba4+ybo9TPkpR1vNBPXeblPXcjFSU2LdnF959+3U07t8rw4lF4hYtPg4LFi1GVXVt2iYo6yrIq49BWVfPVEVEyroKinpjUNYV8KWsK4CoMARlXSFMxaEo64qBKgpHWVdNREwWAAAgAElEQVQEUkMYyroGqApCUtYVQMwSornpIFa/9Sp279wuS1VUVuGoY47H/EWLc16HTlnXmxu30SnrbsnprUdZ18tXRXTKugKKlHUFEBWGoKwrhKk4FGVdMVBF4SjrikBqCENZ1wBVQUjKugKIaUK0tTbj3b++gW1bNspPi0tKcMySk3HE4mMRDIZsNUpZt4XJ90KUdd+R22qQsm4LU14LUdYV4KesK4CoMARlXSFMxaEo64qBKgpHWVcEUkMYyroGqApCUtYVQEwKIW639t7qN7Fpw6fo6+tDKFSII49egqOXLEVRkbMV3SnranOjKhplXRVJtXEo62p56ohGWVdAlbKuAKLCEJR1hTAVh6KsKwaqKBxlXRFIDWEo6xqgKghJWVcAEUA0EsGa99/Guk/WoLc3hoJAAAuPOBrHnXgqSkvLXDVCWXeFTXslyrp2xK4aoKy7wuZrJcq6AtyUdQUQFYagrCuEqTgUZV0xUEXhKOuKQGoIQ1nXAFVBSMq6d4hrP1iNNe+9jVisRwabM38Rjl96Giorqz0Fp6x7wqetMmVdG1pPgSnrnvD5UpmyrgAzZV0BRIUhKOsKYSoORVlXDFRROMq6IpAawlDWNUBVEJKy7h6iWNn99VeeH7hP+pRpM3HSqWeibsw490GTalLWlWBUHoSyrhypkoCUdSUYtQahrCvAS1lXAFFhCMq6QpiKQ1HWFQNVFI6yrgikhjCUdQ1QFYSkrLuDKKa8v7/6TVm5rLwCZyxbjinTZrgLlqEWZV0pTmXBKOvKUCoNRFkHnnn+Daz+YB1+cMs1KC2Jr5HR3NqO6297GDdfdwVOOGaBUuZOg1HWnRJLU56yrgCiwhCUdYUwFYeirCsGqigcZV0RSA1hKOsaoCoISVl3BrGnuxuvvPR77NqxVVact+BInHLGOTlvw+aslXhpyrobavrrUNb1M3bTAmWdsu7muDns6lDWzUoZZd2sfCT3hrJuZm4o62bmRfSKsm5mbijr9vNy6GAj/vTHZ9DR3iZXeT/1zHOlrOvaKOu6yHqLS1n3xk9Xbco6ZV3XsWVUXMq6UekAZd2sfFDWzc2H1TPKurk5oqybmRvKur28iFXe337rVfT19qK6phbnX/w38lHnRlnXSdd9bMq6e3Y6a+ZF1nfsALZt07lb6WNPnw7MnDnsM06D9z8VvrdIWfcdedYGKetm5YOybm4+KOvm54aybmaOKOvZ8yJWeF/15+exbctGWXD+osU49YxzEAyGtCeUsq4dsasGKOuusGmvlBdZv/tu4B//Ufu+DWvgzjuBH/2Isu4/+fy3SFnPfw6Se0BZNysflHVz80FZNz83lHUzc0RZz5yXluYmvPSH36CttVlOez/jnAsxa45/CzRR1s38naGsm5mXvMj6k08CP/uZ/0C+/nXgW9+yLeu33/MYbrnhKsyeXu9/X5Na5AJzCvBT1hVAVBiCsq4QpuJQvGZdMVBF4TgNXhFIDWEo6xqgKghJWU8PcevmDXj95RfkvdPFrdjOXf4lVFXrnfae2hPKuoIDXEMIyroGqApC5kXWFfRbZYj31m7Ar55bNWQ1+C079uLOex/D3bdfS1lXCTtfsSjr+SKfvl3Kuln5SO4NZd3M3FDWzcyL6BVl3czcUNaH5+XtN1/Fpx+9Lz9YdNSxOPWMc/OSPMp6XrDnbJSynhNRXgpQ1gdv03bFJWfisuWnyzw8tGIl9jc2DRH4vCQIAEfWFZCnrCuAqDAEZV0hTMWhKOuKgSoKR1lXBFJDGMq6BqgKQlLWh0IUq73v2LZZvnnWuRdjzvxFCii7C0FZd8dNdy3Kum7C7uJT1uPcxEj6dbc+iH0Nh+Tri5YtNULURV8o6+6O7SG1KOsKICoMQVlXCFNxKMq6YqCKwlHWFYHUEIayrgGqgpCU9UGIr7z4e4jp7+L69Iu+dCXGT8zv9Z2UdQUHuIYQlHUNUBWEpKwrgKg5BGVdAWDKugKICkNQ1hXCVByKsq4YqKJwlHVFIDWEoaxrgKogJGU9DvG1P/8Bmzeuk6J+8ZevwrgJkxTQ9RaCsu6Nn67alHVdZL3Fpax74+dHbcq6AsqUdQUQFYagrCuEqTgUZV0xUEXhKOuKQGoIQ1nXAFVBSMo68MarL2Ljuo/l7diWf+kKTJw0RQFZ7yEo694Z6ohAWddB1XtMyrp3hrojUNYVEKasK4CoMARlXSFMxaEo64qBKgpHWVcEUkMYyroGqApCjnZZf+cvr+HjNe8hEAziwksuR/2UaQqoqglBWVfDUXUUyrpqomriUdbVcNQZhbKugC5lXQFEhSEo6wphKg5FWVcMVFE4yroikBrCUNY1QFUQcjTL+pr3/or333lLivr5F12GKdNmKiCqLgRlXR1LlZEo6yppqotFWVfHUlckyroCspR1BRAVhqCsK4SpOBRlXTFQReEo64pAaghDWdcAVUHI0Srrn338If76xssIBAI4/+KvGCfqIrWUdQUHuIYQlHUNUBWEpKwrgKg5hFZZb25tx/W3PYxP1m8dthtHLZyFR++7CbXVlZp3UX94yrp+xk5aoKw7oeVvWcq6v7zttkZZt0vK/3KUdf+Z22lxNMq6uD5dXKdeUFCAc5d/GdNnzrGDyvcylHXfkdtqkLJuC5PvhSjrviN33KBWWRc3lBfb9667wnHHDqcKlHWzskVZNysfyb2hrJuZG8q6mXkRvaKsm5mb0Sbr4tZs4hZtQtSXXfBFzJw938zEcGTd2LxQ1s1MDWXdzLwk90qbrItR9dvveQy33HAVZk/P7z03daeBsq6bsLP4lHVnvPwsTVn3k7b9tijr9ln5XZKy7jdxe+2NJlnfs2sHnn/2lxLMWeddgjnzFtqDlKdSHFnPE/gczVLWzcwLZd3MvFDWFeeFsq4YqMdwlHWPADVWp6xrhOshNGXdAzzNVSnrmgG7DD9aZL29rQW/efoJ9HR346RTz8LiY09wScy/apR1/1g7aYmy7oSWf2Up6/6xdtuStpF10SExDX7G1Im4bPnpbvt3WNSjrJuVJsq6WflI7g1l3czcUNbNzIvoFWXdzNyMFln/7S9/joMHGuS093MuvNTMZKT0irJuZpoo62bmZbTLejjSjbseeBxLlywa4qvvrd2A2+99DCvuvznvM8S1yvqWHXvxi2dexi3XX4XSkiIzj1IFvaKsK4CoMARlXSFMxaEo64qBKgpHWVcEUkMYyroGqApCjgZZf/vNV/DpRx+gsqoal135TRQVFysgpz8EZV0/YzctUNbdUNNfZ7TLuiCceum2tUD6zdddgROOWaA/CTla0Cbr2VaCF33iavB5z/2I7QBl3dzUUtbNzA1l3cy8iF5R1s3MzUiX9V07tuLF536NgkAAl115NerGjDMzEWl6RVk3M1WUdTPzQlmP50WMpP/quVX4wS3X4IVXV2P7rv3GLJCuTdZNPCSfef6NtPDFdP2fPfX8kC7/8NZrBqZDiHrfv/9x+flFy5bKRCbPFODIulnZpqyblY/k3lDWzcwNZd3MvFDWzc3LSJb1zo52/Pqpx9EdjeKU08/BEYuPMzcRlPXDJjeUdTNTlQ9Z39G6A9uat/kOZHrNdMysmZmxXeGDHV0R7N1/EPfeca0xtxcfFbIuzpZ888b7ZHK+9dXlw86UZLvFnKj74IqVA/eET1eWsu7771vWBinrZuWDsm5uPqyeUdbNzRFH1s3MzUiV9f7+fjz76ydxoGGfvI/6eRddZmYCsvSKI+tmpoyybmZe8iHrd795N/7x1X/0Hcidp92JH539o4ztmjb93eqodllPFmWr0SceuS0v1wBkG1kXfUt3P/jURfJS5V3Uo6z7/vtGWTcLue3ecGTdNipfC1LWfcXtqDHKuiNcvhUeqbL+/uo3seb9t+V16l/56jUoLCz0jamqhijrqkiqjUNZV8tTVbR8yPqTHz+Jn635mapdsB3n64u/jm8d+62M5YXzbdyyC63tnQODtLaDayyoVdbTia1YdO66Wx/EDVdf6vsq8XanwVtT4NOtECj6f+e9j+Hu268dWB2Qsq7xCHURmiPrLqD5VIWy7hNoh81Q1h0C87E4Zd1H2A6aGomyvnf3Tvzxd08fltepJ6eOsu7gQPaxKGXdR9gOmsqHrDvonm9Fk69Zf/Tnv5PtphvE9a1DSQ1pk3VLdC+/5Mxho+jJQPxcJT6TrCeDt04m3Hv7tThywSy5nH/yPqST9ab27nzkjm1mICBkvbqiCM3Mi3HHSEVJCD29fYj29BnXt9HcoVCwAOUlIbR29oxmDEbue1V5IboiMcR6+43s32jtVHFhAIXBADoisRGBIBwO4xdPrIB4PHPZ+Tjq6MPrOvXkJNRWFqG1oxt9/JUx6tgsLQoCBQUIR0fG74xRcD10Rsi6GEjJ5DJ1lSP3bl4WtlG9Gvzt9zyGW264atj96YTwPvCTp32/eN+OrIvEWVPfLzx76bB776WT9Uh3r4dfE1bVQaC4MIhoD/Oig62XmGIEt7evH338FuUFo/K6BQUFKAwWoDvGkyjK4XoMWBQKoKe3H+JaYm7mEAgEChAMFKBnhPzOPP1fT2LHju1YsHARLv3S4XedevKRwX//zfk9Se5JMFiAAoAnHg1MT7bfmRJxkmUEb6P6PuuH68h6sqxftvz0AXEXz8XGa9bN/43lNHhzc8Rp8GbmhtPgzcyL6BWnwZuZm5E0DV5coy6uVa+qrsVXvvpNhEKH33XqyUcJp8Gb+TvDafBm5oXT4M3MS3KvtE2DF42IkeyVz60acpG+adesi6kPz7+yGl+77FzJJXXknKvBm38Qp/aQsm5uzijrZuaGsp45Lz09PejtjaGvt1c+xmK96OvrRW8sJh9j4v1YLFGmL1Em/llv4jMvWS8rCUHM3hqJs1HEPbzFrA6xiUf5n3gtnsffjr9vvSfH5Qbfs95PrS/eF/MQ4tXi9a3Y8fcT71mx41GHvB+PmchcSh/FuyXFIYhZDx3hWKKtwb4N6Xd/vD2rXeszoH/Ivid2TPZzsEy8bvJrq1PWPqWWHWxnePxgMDTsUGw6dAC/eerfIT778pXfQG3dWC+HqxF1KetGpGFYJyjrZuaFsm5mXpJ7pVXWRUMmrAafrQ/WDIA/vrJ6gEvqavW8z7r5B3JyDynr5uaLsm5mbkaDrEciYUTCYUSj8UfxOhqJIBLpGvY6Gg4jHO4yM1nsFQloILDkpC/guBNO0RDZ/5CUdf+Z22mRsm6Hkv9lKOv+M3faonZZd9qhw7E8V4M3K2uUdbPykdwbyrqZuTkcZb29rQUd7e0IhzuldEejEYS7uqR8xyV8UM67o1HX4MWU4GAoiEAgiFAohGAw/jwon4ufgHwMBIPys9DA85CsFwx4u95vJI+si+vw5Y8cdwZgve4XT+PvxR8T5ZLek+8nyovB6IFY8v2h9WULifJWTKu8iJFaf2B5gOT2En20+iXGu8W/NbHe+DoPQ/ubeC0KWX0cKFMwrGxyH5L7lxxXlkluJ6U/ov1Ec8Piixkh2bbqmlpc8fVrXf+OmFaRsm5aRuL9oaybmRfKupl5Se4VZV1BjijrCiAqDEFZVwhTcSjKumKgisKZKOs93d04dLAB7W1taGttRnt7q3wuJL2zo93xnhcVF6O4uBSlZWUoLi5BcUkJSkrKUFJaipKS0sRjmXxffF5eUem4DR0VeM26DqreY46ka9a90zArAmXdrHxYvaGsm5kXyrqZeaGsK84LZV0xUI/hKOseAWqsTlnXCNdD6HzKuhj1az50EE1NB9F86ADENbSHDh5AuKsz6x6VlVegsrI6Lt8psm3Jt5BzS8Y94MlrVcp6XvFnbJyybmZeRK8o62bmhrJuZl4o62bmRausiwXbrr/tYfzdlRfg33/5Ij5ZvzUthaMWzhqy8Jz5qDL3kLJuVvYo62blI7k3lHUzc+OXrAsRb5ZSfhCHDjaiuemQHCnPtI0ZO16uUF1VXY3KqhpUVtdIQRfTdkfLRlk3M9OUdTPzQlk3Ny+UdTNzQ1k3My9aZd0KnnqD+eRGxYJvv3puFX5wyzUoLSkyn1KOHlLWzUohZd2sfFDWzc2H1TMdst7T042G/Xuxb/dO7N+3Bwca9smV0lM3saq1EPG6MWPlStR1Y8ehbsx4KeTWStjmE9TXQ8q6PrZeIlPWvdDTW5cj63r5uo1OWXdLTm89yrpeviqia7tmPZusi9ujPfCTp3HvHdeittqM6wK9wKSse6Gnvi5lXT1TVRE5sq6KpNo4qmRdjJZv27wRu3ZsxcEDDcM6WVpWLqVcyLiU8rqxqB0zVi7Qxi09Acq6mUcGZd3MvIheUdbNzA1l3cy8UNbNzEtyr/Ii6+JWaKs/WMeRdfOPj8Oyh5R1c9NGWTczN15kff++3di2+XPs2LpJLgKXvImR8kmTp8Z/6qdCyDo3ZwQo6854+VWasu4XaeftUNadM/OjBmXdD8rO26CsO2fmdw3lsi5Gza+79UHsaziUcV8mTRiDFfffjNnT6/3eXy3tcWRdC1bXQSnrrtFpr0hZ147YVQNOZX33zm3YtuVzbN/yubxFmrWJFdenz5yDaTNmY8rUmRCvuXkjQFn3xk9Xbcq6LrLe41LWvTPUEYGyroOq95iUdUBcnv3NG+8bAvOiZUuNGVRWLuvWnmabBu/90DIrAmXdrHxQ1s3KR3JvKOtm5saOrG/bslGOoO/cvhk9PT0DOyJGz6fNmIVpM+dg4qQpZu7gYdwryrqZyaOsm5kX0SvKupm5oaybmRfKelzWH1yxcsjC5w+tWIl3124wYjF0bbJu5iGpp1eUdT1c3UalrLslp78eZV0/YzctZJL1hv17sGnDZ9i8cR3EgnHWNmXqDEybNQczZs415n7kbvb7cKhDWTczS5R1M/NCWTc3L5R1M3NDWU8v6yJbQtjF9r3rrshr8ijrCvBT1hVAVBiCsq4QpuJQlHXFQBWFS5b1WKwHn328BhvXfYzWlqaBFmbOno+5C47A5KnTEQoVKmqZYXIRoKznIpSfzynr+eFup1WOrNuh5H8Zyrr/zO20mA9Zb21tRXNzs53uKS1TU1MD8ZO6pRtZF2Uyva+0UzaCaZX1bNev8z7rNrLDIq4IUNZdYfOlEmXdF8yOGxGyXhrqw6o3/4qP17yLnu74KLq4z/n8IxZj7rwjeP25Y6pqKlDW1XBUHYWyrpqouniUdXUsVUairKukqS5WPmT9zTffxKuvvqpuJ2xGOu2003D22WfblnVT7l6mTdbDkW7c9cDjWLpkEY4+Yg5+8czLuOX6q+R91cW0gtNOWowTjllgE6/ZxTiyblZ+KOtm5SO5N5R183IjFoj7dO27cjS9OyHpM2bPw3EnnCJlnVt+CVDW88s/U+uUdTPzInpFWTczN5R1M/OSD1n/+OOPsWbNGt+BLF68GMcee6xtWR/xI+vJC8wJKsn3VRc7/6vnVhmzyp7Xo4Wy7pWg2vqUdbU8VUajrKuk6S1WuKsTaz94Bxs++whi6ntBQQHEVPfjTjwVtXVjvAVnbWUEKOvKUCoNRFlXilNpMMq6UpzKglHWlaFUGigfsq50BxQEyyTlI/6a9WRZr6upxL3/+xe4/R++htrqSpgyrUBBfmUIyroqkmriUNbVcNQRhbKug6qzmB3tbVj7wWpsXPcJ+vp6paTPnb8Iy84+E7EA74PujKb+0pR1/YzdtEBZd0PNnzqUdX84O22Fsu6UmD/lKeujeDX45Gnwly0/XU59nzF1IsTzZ55/A6s/WMeRdX9+D0ddK5R1c1NOWc9fbqKRCN5/502s+2Rw6tm8BUfiuJNORV1tLWrKC3GgNZq/DrLltAQo62YeGJR1M/MiekVZNzM3lHUz80JZH8X3WU89JMVI+/W3PYxP1m/FpAljsOL+mzF7er2ZR67DXnFk3SEwzcUp65oBewhPWfcAz0PVj9e8hw/f+8vAwnELjjgaxx5/Mioqq2RUO/dZ99A8q3ogQFn3AE9jVcq6RrgeQ1PWPQLUVJ2yrgmsx7CUdY8AfaiubYE5H/puTBOUdWNSITtCWTcrH8m9oaz7m5uWpkN49U/P4dDBRtlw/ZRpOPX0c1GTck06Zd3fvDhpjbLuhJZ/ZSnr/rF22hJl3Skxf8pT1v3h7LQVyrpTYv6X1ybrydesj5QR9Ezpoaz7f+Bma5GyblY+KOv5ycea99/G+6vflI2XlJTitLPOh1jlPd1GWc9Pjuy0Slm3Q8n/MpR1/5nbbZGybpeUv+Uo6/7yttsaZd0uqfyVo6wrYE9ZVwBRYQjKukKYikNxZF0x0DThWlua8epLv8fBAw3y0+kz5+CMZctRXFKSsXHKuv68uG2Bsu6WnN56lHW9fL1Ep6x7oaevLmVdH1svkSnrXuj5U1ebrIvuj7T7qWdKCWXdn4PVbiuUdbuk/C9HWdfHvL+/H5+sfV+Opvf2xlBUXIxTzzgPc+YtzNkoZT0norwVoKznDX3WhinrZuZF9IqybmZuKOtm5oWybmZeknulVdbFLdp+8czLuOX6q1BaUmQ+DZc9pKy7BKepGmVdE1gFYSnrCiCmCdHW2oxX//QHHGjYJz+dPHU6zjrvEpSWltlqkLJuC1NeClHW84I9Z6OU9ZyI8laAsp439FkbpqybmRfKupl58UXWk1d/T4fhqIWz8Oh9N8n7rh/uG2XdrAxS1s3KR3JvKOvqc/PZxx/g3b++gVisB4WFhTj59HMwf+FRjhqirDvC5WthyrqvuG03Rlm3jcr3gpR135HbapCybguT74Uo674jd9yg1pF1x705TCtQ1s1KHGXdrHxQ1vXko7+vD39+4XfYsW2zbGDCxMlYdsEXUV7h/AQoZV1PjlREpayroKg+BmVdPVNVESnrqkiqjUNZV8tTVTTKuiqS+uJok/Vsq8G/t3YDfvXcKvzglmtGxPR4yrq+A9RNZMq6G2r+1OHIuhrOPT09eOkPv8G+PTtlwFPOOAdHHHWc6+CUddfotFekrGtH7KoByrorbL5Uoqz7gtlxI5R1x8h8qUBZ9wWzp0byIuviWvYHfvI07r3jWk6D95Q+Vk5HgLJu7nFBWfeem3C4Cy88u1LeO10sInfuhV+W90/3slHWvdDTW5eyrpev2+iUdbfk9NejrOtn7KYFyrobavrrUNb1M/baQl5k/Znn38DqD9ZxZN1r9lg/LQHKurkHBmXdW2462tvwx9/9EmJBuXETJslp75WV1d6CAqCse0aoLQBlXRtaT4Ep657waa1MWdeK13VwyrprdForUta14lUSXLmsi1Hz6259EPsaDmXs4KQJY7Di/psxe3q9kp3IdxBOg893Boa2T1k3Kx/JvaGsu89NS3MT/vDbpxDu6pT3Tj/nwi8hEAi4D5hUk7KuBKOWIJR1LVg9B6Wse0aoLQBlXRtaT4Ep657waatMWdeGVllg5bJu9SzbNevKem9IIMq6IYlIdIOyblY+KOve8yFuyfb871eiOxrFzNnz5Yh6gfgXVtFGWVcEUkMYyroGqApCUtYVQNQUgrKuCazHsJR1jwA1VaesawKrMKw2WVfYR+NDUdbNShFl3ax8UNa95WPfnl144fe/Qm9vDLPnLcTZ513iLWCa2pR15UiVBaSsK0OpNBBlXSlOpcEo60pxKgtGWVeGUmkgyrpSnFqCjSpZF9fKb9+1H9+77oohMFPvCf/EI7fhhGMWDJQR9b5//+Py9UXLlg671p6yruXYdB2Usu4anfaKnAbvDPH2LZ/j5Zd+D3GbtoVHHoMvnHmeswA2S1PWbYLKQzHKeh6g22iSsm4DUp6KUNbzBD5Hs5R1M/NCWTczL8m90irrqRKc3PBRC2fh0ftu8mU1eHGruG/eeJ9s/ltfXT5E1sORbtz1wONYumQRLlt+OsQ193fe+xjuvv1aeU29qPvgipUDfX1oxUoZJ1n4KetmHeiUdbPykdwbyrr93Gxc9zHeePVFWeHIo4/Hyaedbb+yw5KUdYfAfCxOWfcRtoOmKOsOYPlclLLuM3CbzVHWbYLKUKyjpwM9vd3o7o2iu69bPu/p7Rl83ic+60GPfOyWj9bnok78/fjnPbFuRPui8nPxOhTqQ2u4KxE/ESMWRR/68Po1r3jrOGt7JqBV1tOJreceewiQbmQ99TZyqfIu9mHG1IlS5MWWKu/iPcq6h6RoqEpZ1wBVUUjKuj2Qmzeuw2t//oMsvOSkL+C4E06xV9FlKcq6S3A+VKOs+wDZRROUdRfQfKpCWfcJtMNmRqKsd/Z0QPx0dLejs6cTnT3xR/G6Szxar6Nt8fd7Eu93tyMai0v3MJEWQp4Q7XCsyyFl9cX77+pXH5QRHRHQJusmLjCXTtbTybd1kuH6q780ZNRdkE0deaesOzrefClMWfcFs6tGKOu5sYlr1MWq72I7fulpOPb4k3NX8liCsu4RoMbqlHWNcD2Epqx7gKe5KmVdM2CX4U2Q9ZZIs5TrQckefB6X7g509XSgXch3QsDjgt2Fju6hwi3K+7mVhcpRGCxEUaAIhcEiFAaKUCReB4vl6/j7hYn3Bz8fLBt/T5QpDhSjKFQ8EGNsZTm6IgXDYpSGyvCVxXouv/OT3eHeFmV97Qb86rlVQ65DT5X1yy85c+Aa9lRZX/6L5fjvS76D82ZdcLgfCyOm/+L6m6JQENGe3sNmn6LRKPr6ehGLxdDb2ycf+3p70TvwXi965We98ifW2ys/j5e3HpOfJ8r39Q18LuOJen19kkt/f/xsqXiUzwvSvJemnFiDfKBOujgoGB47UU7kpk+01zfYttWuiGnFHtIvQO7naNuWnnwKzjhT39T3ZJ6BQAFCwQJ098SPDW7mECgqDCDW24++xO+MOT0b3T0JBgogfm96Yof370zowX9B8P/+FLHb70TvN64eEUktLgyiO9aLxD9xI2KfRsJOiH9jxBeNWK+93xkpyD3taI92oLO7A2IauBixbo+2oyMxei3kuj3aJiVb/ogy0beXYGUAACAASURBVHaEY2G0RFvQEY2/3xTJfDtpL2xLQ6WoKKpERVG5fKwqqkJZUTkqxXuF5agoFp9VoLKoSj5WFFegorAC1SU1KBKCnZBs8SiFW4h0sHhAyEUd3Vuu78wlRUHdXWD8HAS0ybpoN3UKeb6zoWNkveAHBQgUBHDXaXfju8d/L9+7yPblPwVATWURmtu7feERi/UgGokiGo1ASHc0Eo4/ytcRRMLideIz8SjKJsp0d0d96eNobiQYCsndLxD/JW53Jh6TnwP98ddJn8s6opw8ouLPBx7TlctSNzluunZTY0+ZMh0nnXKab2kLBgtQURxCa1ePb22yIXsEqsoK0RkVJ+I4FdEeMX9KiZMoRcEAOiKH94nEuqriAWDdFyxH108eQ9/Ysf5A1NRKbWURWtq7wd8YTYAdhBWy3RJpQUu0GeFYm3xsbG9Ca7QZzeFm+bo50ozWiHjeAjHyLT5rjbYi1qf2dytYEJRCXS4kWj5WSIEuFxJdmHg/IdfitZRr67PEc1lHlE3IufX9wAESI4vWVRahKcN3ZvEZt/wS0CrrYhT6F8+8jFuuvwqlJflPto5r1n/6wU9x3R+uk1m8bP5V+PG58VXjueWPgJtp8JFIGN3RiLyPdVy0xeuo/IlEw4hG4p91d8elW5aLhCHqqdgKC4sQCAYQCAQRCoUQCAQQDIYQCIrXhXIEZ/CzIIKhoHwdDIofUS4gywXFe2k+E2WssgO3504WVydCKgbhCwrkF6FB6U3IriW1VuykuKJsdXkhumP9iCRGcAckNUWkB2PH6VrlxH5wU0+A0+DVM1UVkdPgVZFUG2ekTIOvn1glpi4NwOmrrUXLj3+KyAUXqQXmYzROg9cLW4xS7+/ci4bOfdjfsRcNXfuxt323fH4wfACt0Za4jEeaPHekrmSMlOnyUEKqiypQJoVZiHQlygrFKHaVFPByS8QL4+9bYl6eEHExpZvbcAJcDd78o0KbrGdbCV5g8XM1eCsN6WRdxWrwz3zyJ/zdH69AW7QVx0w4Hj+/+DcYWzrO/OyP0B5asr73QAe6ujrR1dkhfzrlTzvCifc6O8TnHVLEvWxCmotLSlBcXIyi4hIUFRWjpKRk4HlxSan8rFh8Jn/E82IUFcWfWyLqpQ+HS11es25mpijrZuZF9IqybmZuRoysj40LzP5Ne1B90w0o/cOz8nX4sivQ+sC/oq+62swEZOkVZd19yra3bpEivl+K+D7s69gjpVz87Ovcg11tOxwFLwmWyinf1cU1GFM6BrWlNSgPVaO6uBa1pXWoKq5GTVHtQBnxfk1JLcaVjnfUDgu7J0BZd8/Or5raZN2vHbDTTvKt26zyyfdSV3Gf9V3tO/CN5y7D503rMaF8khT2o8YdY6d7LOORQNOhA2huOoimgwdw8EADOjvaEAl3IRy2P+otBTohz0K8hVQXF8Xlu6S0VAp4XLbFe3HRjgt5sRzZ5maPAGXdHie/S1HW/SZuvz3Kun1WfpYcabK+92B81emyXz2N6lv/XxS0t6Nv3Hg0/9u/I3rGWX6i9dwWZX04QjkKLn/2xkfDE/ItHzuEnO+VA052NjGqPbGiXn7XnVhej0kVkzGhYhImldVjXPkEKeI1xTUYVzZhSDgTFpizs3+jrQxl3fyMjwpZ150G69ZtYmXI//7i3+LVHS/JJv/tgv/EJXO+orv5URNfjIALGT90sBFNhxrRfOigfJ1tKy0rR0VFJUpKy1BWXoGKyiqUlZWjvKIS4jPxXLzPzR8ClHV/ODtthbLulJh/5Snr/rF20tKIkfXENPi9+1qBwkKJILhrJ2q//U0Uvbdavu78279D2933o7+s3AmivJUdbbIuRr93d+zE7rZd2Nu+C3s7dkv5FhIel/S9tnNRXzElLuEV9VK+J1VOHpBy8V59xWS4nU5OWbedBl8LUtZ9xe2qMa2ybk0x/+MrqzFpwhisuP9m1E8YO+x2aK56blCl1Pus/+gvd+DRNY/IHv7DklvxP07+J4N6e3h0RQr5wQNSyq3n4XD6+00K2a4bMw5jxo1H3ZjxqK2txbT6sejs4Yi3admmrJuWkXh/KOtm5kX0irJuZm5GjKwnpsFbI+vJtCsfeQCVP7pLvtU7bTqafvEb9CxcZGZCkno10mR9S8sm7G7bib0du7CnfRd2tm3Hnvbd2NOx0/a0dDG1fGJZPSZaIi5GwxPPxei4eD91JFx1oinrqomqiUdZV8NRZxStsm6tBn/h2UvxwKNP42uXnYPZ0+shpqWn3i5N507qjp0q66K9336+Et/90zdl05cv+Bp+ePqDchEMbsMJiGnsjfv3Yv++3Th0QIyaH0iLSUw3r60bgzFjx6N2zFiMHTcRY8dNQGHR0MUL3Swwx7z4Q4Cy7g9np61Q1p0S8688Zd0/1k5aGg2yLk/kfbQGtX//DYS2bZF42r/3P9B+R1zgTd0OR1kXo99bWzbLSym3t2zFxqbPsLn5czlKnmurLanD9OpZUrinV83CxIpJg6Pj5fWYVjUzVwhfPqes+4LZcSOUdcfIfK+gTdbFdeC33/MYbrnhKjmanizrYpX4B37yNO6941rUVlf6vtOqG0wn66KNjxo/xN/+/ks4FDmIhWOOxPdPvRdnTFumuvnDLl7D/j3YvWOblPMDDfvR0zP8FmtiunptnRDyCRg3fiKqa8egprbO1r5S1m1hykshynpesOdslLKeE1HeClDW84Y+a8OjRdYFhIJwF6ruugPlj/9UMuk+8WR0Xv9dhC/5spHJMVnWhYxvbt4oxXxj0zpsa9mC9Qc/RaQ38xo7Ymr6lMppmFw5BVMrZ2By1VT5KK4Vn1e3wMgcpOsUZd3MVFHWzcxLcq/yIuujYWTdgixuXXHHqhvx+82/lm+dP/Ni3H3Gw/KP7GjZOjvasWPbZuzZtR17du0YJudiQbcJEydj4qQpGD+xHmPHT4C4lZnbjbLulpz+epR1/YzdtEBZd0PNnzqUdX84O21lNMm6xab4zddRfeMNCO3YJt/qWXQk2u/8J0TOX+4Un9by+Zb19u42rDv0CbY2b8Kmpo3Y0vK5HCUXK61n2sR14AvHHomZ1bMxt24B5tctwozqWZhXt1ArKz+DU9b9pG2/Lcq6fVb5KqlN1sUOiVulrf5gHW7/h6/hx4//Vk6Dr6upxPW3PYwrLjkTly0/PV/7rbTdTCPryY38ZffruPHla+WUJvFH+cYTbsN1x/wDCoPupVTpTigMFov1SCmP/2xDS/PQe20KOZ8+Yw4mTZmG8RPqbY+Y2+0iZd0uKf/LUdb9Z26nRcq6HUr5KUNZzw/3XK2OGFlPs8Bc1n2PxVD+1H+i4sH7ENy9SxbtPnYJOm7/n4icfW4ubL587oes9/X3YVf7dinhYqRcSnniubgPebqtAAWor5yCObXzMLtmPubWzcecWvEzD+PLJvrCJp+NUNbzST9z25R1M/OS3Cutsi4aynXbNPMR5e6hHVkXUaK9ETz07j34tzX/ilhfj7y26IGz/w9OnXJG7kYMLyGEfPvWz7F753bs27NzWG8nTZ6KqdNmYfK0GXJqu86Nsq6TrrfYlHVv/HTVpqzrIus9LmXdO0MdEUatrCdgFvT0oOzJJ1Dx0P9CcF98tXExPb799v+J6Gn5/U6jUtbDsS583rRBivimpg3YLEfJN8rryrv7omkPLXFv8Vk1czC7dp4U8TkJKZ9bOx/FwRIdh+NhEZOybmaaKOtm5sVXWTcfgfce2pV1qyWxsuc//PlbWNvwvnzr4tmX4Z9Pf0AuCHK4bZs3rsO6T9ZAXIeevFXX1GLy1BmYNmM2hKiHQvFbwvixUdb9oOyuDcq6O266a1HWdRN2H5+y7p6dzpqjXdYttgXdUZT//Gcof/gBBBvjt1LtPukUtP3gHnQff6LOFGSM7UbWxaxHMUpujY4LIRevs932bFzpeMxOjIxbo+RC0MX15WIUndtQApR1M48IyrqZeUnuldaRdbEa/P7GJvzglmtQWhKf7m3dzm3pkkWjahp86qHQj348ve7n+NFf70RLpBlloXLcdOId+PYx/w9CAbNvOSZG0dd98iE2bfgU3d2Di8NNnT5LyvnUGbNQWVmdt6Ofsp439DkbpqznRJSXApT1vGC31Shl3RYm3wtR1ociL4iE5QJ0Ff/6IAKHDsoPo2edg7Y7/wk9xxzna34yyXpPbze2tG6SI+Ny+roYKZeCvgldsc60fQwFCjG9aoacri5EXFxPPqdmHuaNWYSKwgpf9+twb4yybmYGKetm5sUXWbek/PJLzsQJxwxdrXI0LTCX6xAQC9Dd9eYt+M3Gp2TR2TVz5dT4k+q/kKuq759v3/I5PvvkQ+zdPTjNXSwMN2f+IsyZtwhFxcW+9yldg5R1I9KQthOUdTNzQ1k3My+iV5R1M3MzYmQ9y33W3ZAXK8eXP/4YKh65H4HmZvQXlyB69jlov+UO9Cw+xk1Ix3UCxe1Yvf0jbGoSU9cHF3jb3b4D4lrzdFtVcfXA9eNzaxckprDPl4u8BQuCjvvACsMJUNbNPCoo62bmxRdZT751m7i3evI2Wm7d5iT9b+95E7e8+h1sa90sr2kS92Y/d+ZynDPjQidhlJcVI+cb132Ezz76EO3trTK+WCDuyKOPx7wFR0LcYs20jbJuWkYG+0NZNzM3lHUz80JZNzcvlPXsuSno7EDF/12B8v/zCAJN8QXXeqdOQ9eVX0PX176B3qnTPSdXXFIoVlgXtz4TK65va96C9Yc+QUdPR8bYYor67Nq5WFB3JGbWzJa3PptVMxfjyvSupeN5Z0dAAMq6mUmkrJuZF19knSPr7pL/0Hv34MF3fjRQWfwj8p0lN+Oqhd9wF9BlrdaWZnyy9j1s2vAZxOruYquqrsXiY0/A/EVHIRAw90wzZd1l0n2oRln3AbKLJijrLqD5VIUj6z6BdtgMZd0+sLL/+g+UPflzFL379kAlsQhd+L9dja7Lr8oaSIj3hkOfyvuSb2uO35vcuhVatopHjz8OMxK3QRNyLqaxLxpzlP1Os6RyApR15UiVBKSsK8GoNYjWa9bFdPfb730MK+6/GdbouhhVv+7WB3HD1ZeO6mvWs2V1V/sO/Ms7P8SvN/zXQDGxkMk1x9yAq4/8NqqLa7QdFDu3b8GnH70vb7tmbeLe50cfeyJmzJ6nrV2VgSnrKmmqjUVZV8tTVTTKuiqS6uNQ1tUzVRFxxMi601u3eYAX2rYFpU8+gbJf/heC+/fJSH3V1QhfdgU+/PJp+HxCIba1bkW4pxNi1PytXa/hUCR+/Xu6TYyGW7c+E6uvLxxzlBwtP376fDQ2h9HX76GzrKqcAGVdOVIlASnrSjBqDaJV1kXPLTnf1zB438knHrlt2HXsWvdSc3Cnq8Hb7U5D5z785MOH8fS6JwamdYkp8lcu/Ftcv+QmTKucYTdUznLievT3Vr8x5J7o02fOweLjTsTESVNy1jepAGXdpGwM7Qtl3czcUNbNzIvoFWXdzNxQ1p3nZWvLJuxo24bNhzZgx2ersH3nB9iCg9hZld2q41PV47dBE9eTCyFfOPZIuTBvus3NavDO94Y1nBKgrDsl5k95yro/nL20ol3WvXTucKmrS9at/e/s6cDT63+On3zw8JDbiFw0+8tyiryY7uV2E4vFrX7rVRw62DgQYv6ixTj6uBNRXVPnNmxe61HW84o/a+OUdTNzQ1k3My+UdXPzMmJkXfECc2Jm4LaWLZBi3roNnzetx/bWrfLa8mzb9M5CzNvfg3mHgFnNwJwFZ2Dyxdeg/sSL0F9a5uhAoKw7wuVbYcq6b6gdNURZd4QrL4Up6wqw65b15C7+btNK/HTNj/FR4wcDbx8/cSmuP+5GXDDri7b3pjsaxVuv/wlbPl8v65SVV+D4padh/sLD/5ouyrrtw8D3gpR135HbapCybgtTXgpxZD0v2HM2OtJlXVwr3tndjvbudnR0tyEcCw9hEuuL4d29f0GkNyxvfSYWx/28aUNWbhPKJ8k73ohrycVt0MQI+czqOXKRN7EVfrQG4vr20l89hUBb20CsyLLz0HXt9YjNnIXY7Lk5c0NZz4koLwUo63nBnrNRynpORHkvoFXWxYrw19/2MD5Zv3XYjh61cBYeve8m1FZX5h2C1w74KetWX9/Z+xZ+uvbHeHHrcwPdXzLxJHzjyGvxNwv+W9Zd2rFtM9587SWEu+L3FT3h5NNx1DHHIxg0+/7udvNEWbdLyv9ylHX/mdtpkbJuh1J+ylDW88PdalXIaG9fb/ynP/7T19+LUKgfoSDQ3Bn/PNbXiz4kleuLDZbv64OQ2170os+Kk/R5b18felM+F+VFO7LNvj75PNYfk22JGKq2in+5By/NBpqOmi8vtxNiLgTd7TamZKwU8enVM+X15DNqZmF61SzMrZuPkmCp7bClz/4Gpb/4D5S8+uchdXon1SN65tnoPu0s+dg7fvgq7pR125h9LUhZ9xW37cYo67ZR5a2gVll/aMVKuWPfu+6KvO2gHw3nQ9at/RJns1es+d9Yuf5JRHsjA7t75rRzcfHcy3DhzC+ipqRWvh+NRPDWqj9h6+b42W+xcNxZ514kV3kfSRtl3dxsUtaz50bclzi4eyd6jjra1yRS1n3F7aix0Szr4VgXorGo/LdNSLN4HumNyNfdse7Ee+J1/P1IT1g+F59HYxFEYvGy8rmsF0UkJsqI9xLlRL2k5+J90e5o34RYVxZVoryoUj5WFlWhvLACFYnn4rEkWILCUBGmVs7AjOqZmFu3EBWFFUrRBRsbULryKRS/8hKK33x9WOzY3HmInrEM3V84HdHTz0JfVRUo60pToCwYZV0ZSqWBKOtKcWoJpk3Ws91nXcue5DFoPmXd2m3x5eKt3avwyvYX8fzm3w1ZQfWUyafjgqrlCG3th5j+XlRcjKWnngVxbfpI3Cjr5maVsp49N8GtWzDhxKMQPWsZOm66FdFTTvMlmZR1XzC7asQkWReSG+4JS5kV8iymRod7uuSjkGDxvvWe9XlXT6esk/x5/LklzUkSnZDrbPfJdgXRY6XSUBmCBQEEAyEEC4Lxn2AQhYFCFPQH5K1Mh30u3hPlERz4PBQIIWDVT/o8GAgiUBCA+FzElmUCQfk6ICKkix8MIVSQiBcIJPoVSpS12gzGywx8nuhTIr6IPeGKL6Ek2ovIi2+joqxWSrnOO854SUVBdxRF776DojdeQ/Gbq1C05gMgFhsMGQigZ/ExCJ13LlpO/AIiS09Bf4n90XwvfWPd3AQo67kZ5aMEZT0f1J21SVl3xittaRNkPbVj7+77K57f/Cxe2/wiTug8HvMxXxbZW7IP4xdPw8ULL8PUyukK9t68EJR183Ji9Yiynj034tZG408YXDei+/gTpbRHzl+uNamUda14PQVXJesHuhrQEm1BS7QJrZEWtESa0drdjJZws3zeLN6PtqCzuwNiUdO4kAs5Twh4nkabq4qrIe6CUhIqQXGwWD4vls/jr0tCpXKEV35mvR+Kvy/rFZYkPhf1EvVljOL4+6Hkz+NxxAhyrm2kX7Oea/9N+LygswPFb/8FRa+9guK3XkfhZ58M65Y44dl9+pmInn4muk882YRuj9o+UNbNTD1l3cy8JPdKm6yLRsQ0+BlTJ46Y+6lnSqeJsi76umnDZ/jrmy/L0fS+UB9eL3kDr3esGtiNI8YuxoWzL8XfH/1dOc1tpGyUdXMzSVm3J+v9xSWIzZk78OWzZ8FCdN54K7r+5kotyaWsa8GqJGiyrAuZFrLdEmlBW7QVzdFDcemOtqA5LGS7GS1R8boVzeFDaO2OS7nKad1i5FWMNIsfIcIDz4MlKC0U75fGPwuVorywHCWF4rUQ6vj7pfJ1/HNLluMCnpDnxHPxnskbZd287ASamlD81irUvP0Gel95FaGtm4d0MjZvPnonTkLPgiMQO3YJui6/yrydGME9oqybmVzKupl58U3WxT3Wf/HMy7jl+qtQWlJkPg2XPTRN1oWcv/bnP2Dn9vitUo5YvEQuIldYWChvo/LC1t/LqfKfHvxoYI/FSMKSiSfii/Mux6yaOThy7NG2RhdcItNajbKuFa+n4JR1e7IemzELje9/iuK330LFv9yL4tdfkxV7p81Ax43/Hzq/cY2nPKRWpqwrxZk1mBDn+Kh2C1rFiHbEEuzEKLcQbmvUO9KM9u5WNIUPyVFxL1tdyRhUF9eitrQOVUXVqC2pjb8uqUN1SQ1qiuvk9Ofq4mqUpJFx1dcie9kXE+pS1k3IQvo+WNesF+zZI69zL37lT3LafODA4C1qk2sKie+ZvxCxeQsQW7gIsbnz0XPE4X9nHNMyRFk3LSPx/lDWzcyLL7KebSV40QGuBq/n4Gjcvxcvv/gsOjvaUVlVg2XnX4JxEyalbUzcD/WFLc/ixa1/gFhdPnVbUHeEvIf7cZNOxHETT8SiMYfHP16UdT3HloqolHVnsm6VFtdmVjxwD0r+9EJc2sdPQOd3bkTn1d9Cf0XuKbu5ckdZz0Uo8+cHwwdwqOsAxOPBcKNcL+RQ5wEcEM/DB6RoN0fisi2monvZhDBXl9SipliIdg1qhGgX16CudAyqi8TrWinetcVjIKaPi9eirBgN56aWAGVdLU+V0TItMBfctRNFH69FaM37KPpoLULrP0Nw/76MTYvZTUMkft4C9Bw5Mtf6Uck/UyzKuh+UnbdBWXfOzO8aWqfB+70z+WrPlJH1DZ99JG/JJrZpM2bj7PMuQWGRvRkN7d1teHn7i/jL7lX47MBH+PjAmmE4xTTGYyeegOMmngBxb/cTJp0sR2VM2yjrpmVksD+UdXeybtUqXP8ZKv7Xj1D6h2flW/2Vlej49nfQed130Fc3xnXiKetD0e3r2APx09i1X0r4ofBBKdoHu8TzuJgLQRdi7mYbVzo+IdLxUW0p3sV1ctRbjnIX1cbFu7gGM8dNQKivClWF5v2tdbPvI6UOZd3cTDpZDb6gowPi72ro8w0IbViPwg3r5PPgnt2ZJX7WHMTmL0D0jLMQW3gk+ouL0bNgkZITp+ZS9d4zyrp3hjoiUNZ1UFUbk7KugKcJsv7uX1fhow/flXtz0ilnYvFxJ3res7UN72Nt4wf4uOFDKe/rD306LObkyqlYPP44nFR/Co6dEJf4fG+U9XxnIHP7lHVvsm7VDn2+ERUP3YeyX/8yLu3FJei4+X8getY56Jm/AP1l5Y4OgtEk62LEe2/7buzr2I29HeJxL3a37ZRyvqdjl3zPySZGsMeWjsfY0nGoKx0rH8eXTYg/LxuHcWXj5XRzORpeUoOykLPcqFpgzsk+sWxuApT13IzyVcKJrGfqo1i8rnDD+rjEb1wfF/mN6yFG5zNtfWPGyin0sVmz0TtnHrqPPlYKPbc4Acq6mUcCZd3MvCT3Srusv7d2A755431DSDzxyG044ZgF5tOx2cN8ynpvbwwvv/CsvD49EAxi2XmXYMbseTZ77rzYB/vfwUeNH+Cjxg/xaeNH2ND02bAg58y4EIvHHYtQsBBTKqfhrOnnQVwv6ddGWfeLtPN2KOvZmVmrwVvXrOciLMpXPHQ/yp76zyFFIxdchPDfXInIhRdLkc+1jRRZF9d67+3cjYbOfdjVtgP72vdgd4cQ8b3Y074LO9u25UIhPxd/r6ZWTceY0nFSuMeXTZRTzYWUi+diBFxI+cTyelvxvBSirHuhp68uZV0fW6+RVch6pj4UhLsQ2rhBinxw88a40G/bIt/LtfWNHYfeCRPRN34CeieIn4nol88T742PP4p7xY/EjbJuZlYp62bmxTdZF6L+4IqVePS+m1BbHV9tXCw6d92tD+KGqy8dMavE50vWI5EwXnh2JQ4eaJDT3S+69MqM16frOhTFvXQ/blyDjxs/xNqGD/DZwY/weVP6f7TE6r5Tq6ZhWtVM+UVYPE6rmo6pVTMwo3qWsusqKeu6su09LmVdraxb0YIN+1H25BMo/a//RGjHoJCKewyL276FL78KQuAzbYeDrIu/NTtbd2B/pxDvnVK+xQi5kHP52LHH1qrn4vrt+sopqC+fIh/F7KD6ivjjpIp6zKye4/1AVxiBsq4QpsJQlHWFMBWH0inr2boa3LkdoS1bULh5I4KbN8nV6IN79yDQ2IBAc7PtvRQnWPsSMi/WJ5ECPyD5lthPQO/kKbZjmlCQsm5CFob3gbJuZl58kfVwpBt3PfA4Lr/kzGGj6ELif/XcKvzglmtGxCrx+ZD11pYmPP/sSnS0t6GisgrLL70C1TVmXNPYFevEJ41r5Oj7Rw0fYlPzBuxo3YqOno6svxHiS/T0qpmYIkV+hvyZXj0TUyqnY1r1dHnrHzsbZd0OpfyUoazrkfXkqGIxupJnf4PS3/56yHWXYmp8+NLLEPnSVxBZdt6Qjpgg69taNw+MgIup6KkyLtbVyLWJW4LVV0weJuOTK6fJUXBxslCUOZw2yrqZ2aKsm5kX0at8yXouIuI6eHFiVch7UAj8gUYE9u8beC0/a2hAQTSSK9TA5321tUkj8xPQWz8Z3cvOH1K/v6gQ/ZXVcsS+r7oa/eXeFyW13cGkgpR1N9T016Gs62fstQVt0+DFavC33/MYbrnhKsyePnSqoBhdf+AnT+PeO64dGHH3uiP5rO+3rO/ftxsvPvdr9HR3Y+y4Cbjw0itQUmJPZPPJSUxR3dm+HbvaxM9OKfBiqqqYmrq7fReivdn/gRKLMh09YYmcYi+2YDCEMSVj5TWh48omyOmq06tmgbKezyxnb5uyrl/Wh4j7e6tR8rtnUPbrpxE4NLgYmvjCFr7ky4h8+XJ5TaVOWRcn78S09MauBuxtFwu3JUS8Q0xX3y//HjRFDtk6aMVsHGsEfErFNEyqnCxn6UwonyRHysWibCNto6ybmVHKupl5MVnW7RILtLUlBF7I+34p9gVC8MXzhoYhsm83Zmo5IfkDAl9TI9c5ERLfV14ef15ZCZSVx19XyrtiPwAAIABJREFUVKBfPFqflw9/bacflHU7lPwvQ1n3n7nTFrXJOkfWnabCXvktm9bjtT//Ef19fXLF93MuvFRK60jYxMrLO6XI74C4rdyOlq3x1+075Ht2t5PrT0NhYQDdPX0IFBTEb2EkFngqEfcUHhNfhVne0qhu4NZG4hZIvI+wXcLuy1HW/ZX15NaK//ImSn7/DEp/80sEWgbv2d1XV4fo5V9F4ZWXo3Gxs4UpxaJsYlq6XD29cw/2d+yTI+L7O/dJQRcrqHfmmFFj9VFMRbd+plSJKemT5etJ4v3KKRAn60bjRlk3M+uUdTPzMhJk3QnZISP1UugbUNB8CAWtrZDS396aeN6KQGsrCtraHI3c2+1LXPaF3A+KvHydJPqh6koUVFYiUlSaIv6JkwTJJwGqq+02zXIeCVDWPQL0obo2WRd9f+b5N7DyuVXGX7P+0IqV+NlTzw/B/cNbrxm4pl7sx/fvf1x+ftGypcOm7/s1sv7ZJx/ir6+/LPtxxFHH4ZQzzvHhEDGnCTEqv7d9lxyNE/czbuwUt1JqxIGuRjRHm7C/Y6/jlZxT904sGiWlvnhM/BZKCamXt1SS9zGuw6SKSVhaf5o5YA6jnlDW8yfrQ8T99dektJc+91sUtLcPfNR97BI5jbLn1NOw/otnYV9/y8CK6eK6cCHmQsLjQr7X9pEnpFuMfk+sqJcj4JOr4mI+uSIu5eKHW3oClHUzjwzKupl5GW2y7jYLgYMHEGiLy3ugowMF7W0IdHZCrIIvf7q65HsFifcGP4uXka9FPfHoYNq+m/7KEwGhIBAqRH8oBBSKx0IgFEJ/YQgQA1byvRD6i4qBYCD+mVUmpWx/YWG8vKwnyoUAWS+Y+BHvxZ/LMuJz8Vw+htAvysnPreeJGAHxfqKu9VyWFeXiMUS9weeD9WRs8VkeZslS1t0clf7W0SrrYlcOh9XghayL7XvXXTGMfuoieenK+iHra95/G++vflP277SzzseCI47290g5jFrrinUgWNyFTQ370BZtRVPkIMQUfPHTHDmE1kgLmqPNaI22oDl8CC3R+GdiASsVmxihF9fFip+SwlKUFZajTDwPlcrbNpUWlg58Prt2LmbVzLXdrPijGgoUojBQhMJg4jEQGvJafF4ULIRY0M+0jbKef1kXx/keId6Jk1sH167C/s3vouHgVuwr68WOauCAzbuLiVXThWiL68HF4+SqqfK5EHFx+zJxeUptiRlraZj2u2C3P5R1u6T8LUdZ95e3k9ZMvWbdyT4cbmXFKH5BlyX7nQhI6R/6ujgaBsJhxA41J04KJD7v6kKgoz3pxECHPBHALX5b1rjsx09AIJA4aTDkuTgBED95EC+bOJEgTy4kTlwkThZYJxziJx8SJydCIZSWlaAr1p90ciKQODFShMr772Yq8kxAu6znef9sNZ9N1sVnM6ZOHBhlT7fCvW5Z/+zjD/DXN16R+7Lsgi9i1pyRc9s7WwlyWMjLNeti1FCKfbQJzfIxLvKtkWZ5Xa183t2Mju4OhHu6EI6FIa7JjcS60N49OELpsMvai5cXVsTlvqAQhcEiKfxC6EMF4rFI3mZPngBIEf9CcWJAlJMnCKyTBPGTA0WhYvnesFiJOoPlB2PXVZSjvz+A3lgwcYIhcaIhEVv0YzRfjpDr1m3hWBe6xE9Ppzz+5GMs/UkmscBjW7QFjZ375TT1vZ3ievE9sLNQmzgg6zsDmNbch0ntwJS2wZ+JNdMwfv5JmLJ4GbqXnIjYfP490vkLTFnXSdd9bMq6e3a6a1LWdRN2F9/NNesFkTAQ60VBTw/QG4s/xmIoiInH3vhjTw8KYjEglnjsiaGgNxZ/f6Ce+Nyql1JWxoqXl2309iZix4A+8VzUS37eC/T2xtuQZRPtiee9ffE2+0Tf4m0OPhd1RJlEX6znIpbYl65Od2B11+rv190C4+cgoFXWhejub2waMm3cupZ96ZJFxty6LXUavDUFPl1fxeJ4d977GO6+/dr4wnmvvoqGBUejv1TPCsM7t2/FC7//dVzUz78Ec+Yv5EGdg0AAwNiaUjS2qBkpz95cwbCPxWi+kCopVj3h/7+9+w+Tq6rzPP6tH11Jp9NJdwIkBEN+MQrIj0AICYjIgOszhCery0gEwQFxshmYf0QWlujDo6yPhAmLsrqjk8nIgCho0DCOQ2ZGR+VxAEMCGgkaXKaTbhgSEqGTkKQ73fVrn3Nv3erq29VV994659bp7nfxhOquOud7Tr3Ore7+1L11S/pzbqBywpW6vRSwnLCf75eB7IDkilkZzA9KrqCus+51YVBy+dJ1ISvZfFayzvWge10YlGw+N9S33DYX+H3CY31jUkcPJNR/Cef/vmsRKd2eTCSH7nNblr/32lSvUdHO1294ezXUyDmI12fUObr1nXaJhCSPD8ikX70o/W2T5J3TF0lfKZA71zl9v8jVSdmcw8/b5si7pp0qc9rnyKKZp0p7apbz8WVqz7i6pLtelZbtz0v6hW2S2fqcpH/32xGbTKGjQ7JLl0lu2UUyuHSZZC+40NjPw7G+vUaZf2d7Ro70ZSWX5w+mKH6m+kzOJGVSOiWH+7Kmhoil7qwZ7slp9/fG8fsylockJ3ZMlrcOH5fxmDHG8k+Btskp5/fc0f5cPBvCOBgl0d9XejGg4Ab/fLb0YoL3AoF7+7AXE0ovILgvKLgvJjhtSi88uC8uFNwXJpyaeZmWSciRI/2lFx8qXlTI52Xqvf9rHEiO7YdgLKyP1RPMeZ8Dv27tajnr9IUjPn5uRFhXJ8HIZKT4P++Swl/cItKq76zsBw7sl4ce+qbkcjlZseIqOf/8JWN7a4tr9glxTixXKMTxay2OMRqDUy8UqBcCVNh3rstB331hwH0BYOi+0du6fb371QsFA/mBUWtXtvXGHVRj5VSNAckWcqUXHIaPrYIpl9EFZrTOkLbMVGlLt0lbZoq0tajrNuftFuravb1NWtOtkkgm5MQpJzoffTh76mw5pf0UmdU2a0Rx54WChNopUGd7PnJEEtu2SeKXz0niueck8fzzIocPj6hXvPxyKb7vEpGTZ0tx8XlSPOcckcn2vS1jLGxnqWRC1LIUx2PyGAsLMMocnRfnEhLT7xlzUGl1KKyov+Xz5gaJuXIqmZRCoSD2/3YODzNy90D4Gs3q4b4wzc+yxvwNbAF1/mZOpQyM2RjChOttLKyP5Y9u8w59v/Ly5U5YrzwKYERYv+QSkWefdTac/KzZcuzT/0OOrr614Q3p2NEj8uSmb0l/3zE569wlctH7r2i45kQp0Mhh8BPFqFmPU9d71tXH/BWlKIViwQkx6o8yN8wUS99XXDsth75Xu1sqv3f7j2xfvZ07jte+PF6iyrjV2lUZx6unxkvue0Omr/mkpE6aIwOPPumc60CF8NZ0m7Rn2o0tWyMf3dbyyi7JbPulswc+88Lzkn71/1Wdpzp53cAH3c//Lcw+WXKnzpf8/PmSW7DI2OMaD4U5DN7OVeQweDvXRc2Kw+DtXJsoh8Hb+UjG16w4wZz962ksrI/VPetqySrfpx7kPeu9j26SaV+8u/xHav5dc+XobXfKsRs/FWkLyOWy8uT3HpFDB3vllLnz5Mr/uqp0qGykchOuE2Hd3iXXFdbtfYSNzazee9Ybqz5670bCur+qOtGQCu0tL/1G0i/tkJadvxH1uGpd8nNPldz8BZJXAX7BIsnNmyf5eQuc2wozZpp62GOiLmHdzmUirNu5LoR1e9eFsG7n2hDW7VyXylkZC+tqEHUytrXrNsqG9be77+8WEe8w81tv/LAV71lXRwBs+elWuf7q/1KeX+V70sOcDX7Kdx6R9nvvEfW5l+qi9hgdvf0u6bv2+sBbgtrL9s//uEneeL1HZsw8UT58zQ2SVh87wSWwAGE9MFXsDQnrtcnHQ1iv9gjVR/20/HanpHd3Sap7j6R69ki6u9u5Th3YXxOl2DZVcgsXSe7UeZL3Av38BZJTYf604J+kEPvGrmlAwromSM1lCOuaQTWWY8+6RkyNpQjrGjE1liKsa8Q0VMpoWK8M5/v2v11+CA8/eJcsXWzHGYS9IwCe+unWUecX5nPW1edNtv3dBpn6lb+S5KFDbmh/93vk8P/+qgxcXP+zuZ95+sey6+Ud0jqlTf702pucay7hBAjr4bzibE1Yn5hhvdajVj8z03v2SOr1Hkl375bknj2SViFeBfqeHnFOsDPKJX/SLMmd9m7n3uK0aZI/eY4UTnmX5GfPkbxzfbLk585tymfX6npeEdZ1SeqtQ1jX66mzGmFdp6a+WoR1fZY6KxHWdWqaqWU8rJuZtl1Vq310mwrqUx9cL1P/74PlyQ4uf5/0f/Rj0v+Rj4o6g7L/snPHC7L1mZ9JKpWWj6z6hLNnnUt4AcJ6eLO4ehDWCethtzW15z3V0y3pnm5JvdYtqT1dkupxg31q7xuByhXb250gf/yyD0pRnRS0dClOaZNiZ6cUpndIoXOG83O50NHp/CtOnRqotulGhHXTwtHqE9ajucXRi7Aeh3L4MQjr4c3i6EFYj0O5sTEI6435Ob1rfc56at9eab/3CzLl8W8PG+n4ipXSd8NNcvxDVzq3v9bdJT9+arPz9YeuulpOnc9Jl6IuDWE9qpz5foR1wrrurSz1+muSenOfpPb+p6ift8k33nCuy7e91hN5yMLME6SgwnznTClMn+58XZyuvu90Q35HKeA7gd+9vXDiSZHHq9aRsK6VU1sxwro2Su2FCOvaSbUUJKxrYdRehLCunVR7QcK6BtJaYd0rr/YOTXnsW9L67UecPULeRf1h13PdDfKdEzokXyjI8ksul7MXX6BhVhO3BGHd3rUnrBPWm7F1Jt9+y9kLn3zrLUkefFuSBw9K8vAhSfT2SvLwQff7Q4ckcajXuVbfq8Pzo17UHnsnuE/vkOx5SyQ/55SRpVIpKU6ZIs7efeffFCm0udfe9+q6c3anHG5pk2yuEHU69DMgQFg3gKqpJGFdE6TmMoR1zaCayhHWNUEaLENY14AbJKxXDpPZvlVav/89mbLpMTkmIn+zZo0cmzpVzt/TLR94z3ulb9X1VQ+T1zDVCVGCsG7vMhPWCev2bp1V8vSb+9wQXw70Ktj3SsIJ9F6w75XEYTfgO8G/t9fYQyxOmiySaZFiS0aKmYxIJjP869L3w9o4bVtESn1UX5mUcd/Hn06XbndrDtWraJ+Z5N5eGtdrU22MYusUY4/dtsKEddtWZGg+hHU714awbue6ENbtXJfKWRHWNaxR2LBeOeSWjV+VNwaOy6KuLrnh0UfLd/VfvUr6bvyUZM86xzn8kktwAcJ6cKu4WxLWCetxb3PNGE99fF15L736+thRSfQdk0RfnyTV9bE+kf4+SRx1b3du6+tz2xwfkMSRd8rfp9QJ9o4cacbDiDzm6C8q+F4EUH8lqh/YznVSJJGUYvnr0m3O7Qkplu4fauv2dW8f6j/Udnh/Vb+YqGxbGtu5vdRWSteplDsf75/qp9o5t7ttWjJpSafT0pctiJTaO3Px5ulrX3586v6K+uXHVb699JhG1Bk+H6dfaug2fx3/XNz5V7RXL/yIyJwT3BdY9r41+okcI28ITepIWG8SfJ1hCet2rgth3c51IaxrXpeoYf2lX2+X55/9uUzv6JQ//eM/kY4fPCGt335Y0rv/ozxDdShl9syzJXv2uZJdtlwG3vcBKcyYofkRjK9yhHV715OwTli3d+u0c2aV71l3wvxgViQ7KInBQUlkB0UGs861+t65PZsTGRxw7x8cGH5/qY9XQwYGhtcYGCjVdmvKaGOoMZ3a7hycsY4etROQWQUSIKwHYqJRAwKE9QbwDHYlrBvE1VSaPesaIKOE9XcOH5QnHntIioWC/LeP3SgzTxg6KVHLjl9J6+YnZNLP/01adv12xAzVR8ENXHSJZJcuk8HlF0tu/kINj2L8lCCs27uWhHXCur1bp50zG4snmFMftzfiRYWBoWBfflGhUBDx/klREurrYnHotmLpNnW7lG4v3Z8oFIfaqtuKbq2Er79TX9Up3T9U3+1fHrPy/ny+Yg6lus5tQ3NLJ4uSlqIMDOTccb0+Xh11W0V7KeTdsXz/yvMq1S+3GVanIFJRf6jO0HwShYo5O2OXxvJcfPP3n5OBsG7n8388zYqwbudqEtbtXBf2rGtel7BhvVgsyg+//235w/59snjJcll60aWjzki9DzLzy2cks/U5yWx9VjIv7RDJ5Ya1V58lrD4WbvAi91/2jPe6hwVO0Ath3d6FJ6zXXpvU7i6ZdeHZkl+wUPZvfzm2hWxJJ6WjrUX+cHggtjEZKJjAWAzrwR7Z2G41Xt6zPrZXofrsOQzezlUlrNu5LoR1O9eFsK55XcKG9Zd+vU2ef/ZpmTa9U675+M2SVO9fC3hJHO+XzPNb3eCuQvz2bSPOWlyYNk0Gl10s/auuk+y550lu4WkBq4+PZoR1e9eRsF57bdJ7uuSkpWc7R8sceIGwbu+WHN/MCOvxWYcZibAeRivetoT1eL2DjkZYDyoVbzvCerzeUUbjMPgoar4+YcJ65eHvH/7oDXLirJMbnkHmxe2Sef45yTz77861OntxtYsK7bn5CyRf+pdb9EeSP3W+5BYuFOeEQOPkQli3dyEJ64R1e7dOO2dGWLdzXQjrdq6LmhVh3c61IazbuS6EdTvXpXJWhHUNaxQ0rFce/n7u+cvkwos/oGH0kSXSv39FJm19Vlp+9YKkf79L0ru7JNn7ds2x8rNmS37+QsktWCD5BYskP2+BE+xzCxZKYeYJRuZpqihh3ZRs43UJ64T1xreiiVWBsG7nehPW7VwXwrq960JYt3NtCOt2rgthXfO6BA3rjRz+3uiU1UcHpbv+Q9I9eyTV3S2pPV3O1+k9uyX1Wk/N8sW2qZI940wZ+OMPlttlz79AilPayt8Xp0xxPhu+ML2z6WerJ6w3urWY609YJ6yb27rGZ2XCup3rSli3c10I6/auC2HdzrUhrNu5LoR1zesSJKx7h78X8nn5yDWf0HL4u86Hod4rm+rpcT42LuWF+D27Jd3T7Xz2b9iLet98saNTCupfZ6cUpnW41+pj57yvvXCvbu/okKIK+tOmhR1qRHvCesOExgoQ1gnrxjaucVqYsG7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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'green', 'gray'])" ] }, { "cell_type": "markdown", "id": "ffbf3294-7a8d-4679-9c4b-5b9a975bf8fc", "metadata": {}, "source": [ "### The (transiently) high value of [U] again led to an increase in [X]" ] }, { "cell_type": "code", "execution_count": 21, "id": "aff608b1-5c78-4070-845a-118afe7c2108", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: U <-> 2 D\n", "Final concentrations: [D] = 208.9 ; [U] = 52.56\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.97443\n", " Formula used: [D] / [U]\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.6392 %\n", "Reaction IS in equilibrium (within 2% tolerance)\n", "\n", "1: X <-> D\n", "Final concentrations: [D] = 208.9 ; [X] = 103.3\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.02304\n", " Formula used: [D] / [X]\n", "2. Ratio of forward/reverse reaction rates: 2.0\n", "Discrepancy between the two values: 1.152 %\n", "Reaction IS in equilibrium (within 2% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=2)" ] }, { "cell_type": "code", "execution_count": null, "id": "7ddbe0ec-53c3-4d25-825a-cbe3bdf8e50a", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "64ebc51b-0dc7-4cff-b231-4c35843a7113", "metadata": { "tags": [] }, "source": [ "# 4. Now, instead, let's DECREASE [U]" ] }, { "cell_type": "code", "execution_count": 22, "id": "52f4843c-0671-4cd9-9c51-74a44feb4fe4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 1.6127957:\n", "3 species:\n", " Species 0 (U). Conc: 5.0\n", " Species 1 (X). Conc: 103.26703387633307\n", " Species 2 (D). Conc: 208.9136350590719\n" ] } ], "source": [ "dynamics.set_chem_conc(species_name=\"U\", conc=5., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 23, "id": "e5ce5d59", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEUXDcaption
1381.53059853.067054101.964742209.210614
1391.61279652.564398103.267034208.913635
1401.6127965.000000103.267034208.913635Set concentration of `U`
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" ], "text/plain": [ " SYSTEM TIME U X D caption\n", "138 1.530598 53.067054 101.964742 209.210614 \n", "139 1.612796 52.564398 103.267034 208.913635 \n", "140 1.612796 5.000000 103.267034 208.913635 Set concentration of `U`" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=3)" ] }, { "cell_type": "markdown", "id": "da46e3d8-58d2-4b48-8b32-887613967fce", "metadata": {}, "source": [ "### Take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 24, "id": "c392f375-c7b4-476b-809e-5cc4f5c14fa4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.03) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.015) [Step started at t=1.6128, and will rewind there]\n", "* INFO: the tentative time step (0.015) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.0075) [Step started at t=1.6128, and will rewind there]\n", "* INFO: the tentative time step (0.0075) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.00375) [Step started at t=1.6128, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "37 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.03, target_end_time=2.3,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 25, "id": "6de58fe9-ff1e-40dd-9ac7-83eee458f818", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 26, "id": "c388dae7-c4a6-4644-a390-958e3862d102", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=U
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'green', 'gray'])" ] }, { "cell_type": "markdown", "id": "a1629b91-2753-4df7-b6a0-dedf86ac3dc1", "metadata": {}, "source": [ "### The (transiently) LOW value of [U] led to an DECREASE in [X]" ] }, { "cell_type": "code", "execution_count": 27, "id": "31c9c18f-3a7f-4690-8e2f-70fdb02ef5c7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium(explain=False)" ] }, { "cell_type": "code", "execution_count": null, "id": "9382dbf7", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "formats": "ipynb,py:percent" }, "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 }