{ "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: June 4, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "d9efa3fd-e95d-4e1c-878a-81ae932b2709", "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": "01bae555-3dcf-42c1-bddc-9477a37f49f8", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.reactions.reaction_data import ChemData as chem\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "\n", "import numpy as np\n", "import plotly.express as px\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(reaction_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": "838b9dfc-e3c2-4e9d-bedc-f32a2b6a6dfa", "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": "c388dae7-c4a6-4644-a390-958e3862d102", "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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", 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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": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "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", "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": "e652b8fa-b7b3-4772-b602-aa15d11d9067", "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": "e5ce5d59", "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": "6de58fe9-ff1e-40dd-9ac7-83eee458f818", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 14, "id": "db4e74d0-3f9d-49dc-9553-bf3cdfe785f2", "metadata": {}, "outputs": [ { "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": "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": "2783a665-fca0-44e5-8d42-af2a96eae392", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "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", "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": "95679484-9ebe-4765-8644-40e94c384f65", "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": "61eead55-fcef-41cd-b29e-f2d5ad5c6078", "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`
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" ], "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": "35850ec7-e78e-4b57-976c-bc0ad6c824d5", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 20, "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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QAAmQAAmQQNIQoNwmTajZURIgARIgARIgARIwPgHKrfFjzB6SAAmQAAmQAAmQQNIQoNwmTajZURIgARIgARIgARIwPgHKrfFjzB6SAAmQAAmQAAmQQNIQoNwmTajZURIgARIgARIgARIwPgHKrfFjzB6SAAmQAAmQAAmQQNIQoNwmTajZURIgARIgARIgARIwPgHKrfFjzB6SAAmQAAmQAAmQQNIQoNwmTajZURIgARIgARIgARIwPgHKrfFjzB6SAAmQAAmQAAmQQNIQoNwmTajZURIgARIgARIgARIwPgHKrfFjzB6SAAmQAAmQAAmQQNIQoNwmTajZURIgARIgARIgARIwPgHKrfFjzB6SAAmQAAmQAAmQQNIQoNwmTajZURIgARIgARIgARIwPgHKrfFjzB6SAAmQAAmQAAmQQNIQoNwmTajZURIgARIgARIgARIwPgHKrfFjzB6SAAmQAAmQAAmQQNIQoNwmTajZURIgARIgARIgARIwPgHKrfFjzB6SAAmQAAmQAAmQQNIQoNwmTajZURIgARIgARIgARIwPgHKrfFjzB6SAAmQAAmQAAmQQNIQoNwmTajZURIgARIgARIgARIwPgHKrQoxLq1oUqEUFkECkRMo7JKG2iY7bHZX5IUwJwmoQKC4awb4magCSBYRFYFUiwldsqwor2mJqhy1M4v3Bw/tCVBuVWDMD3IVILKIqAhQbqPCx8wqEqDcqgiTRUVMgHIbMTpDZKTcqhBGyq0KEFlEVAQot1HhY2YVCVBuVYTJoiImQLmNGJ0hMlJuVQgj5VYFiCwiKgKU26jwMbOKBCi3KsJkUREToNxGjM4QGSm3KoSRcqsCRBYRFQHKbVT4mFlFApRbFWGyqIgJUG4jRmeIjJRbFcJIuVUBIouIigDlNip8zKwiAcqtijBZVMQEKLcRozNERsqtCmGk3KoAkUVERYByGxU+ZlaRAOVWRZgsKmIClNuI0RkiI+VWhTBSblWAyCKiIkC5jQofM6tIgHKrIkwWFTGBZJTblavXY9O2vVj0wHxkpKdGzC7eGatq6nDXQ3/E/QvnYuK4YRE1h3IbEbb2mSi3KkBkEVERoNxGhY+ZVSRAuVURpopFNTU1wtbSDLvNBpv439KMFlsL7LYWtDQ3o6WlBXZ7i+fW1gKnwwmnywm3ywWXywmn0wW32wWn0wmXU3nNDYfD3qGVZrMFKSkpMJlSgJQUeV/+M5k89+VrJkA8Jx+j3WPxmnheyWtKMbXe96STr8FThm86z2PAYjYj1Wr2rP3dWl/HdohiUiDKb2uX2ezTXpFEaee5dG19UfpgUtJ4ymvrt8gr2tna3gljhkQc1UNHS7HwwWdRdrqirYyePbpiydP3Y2C/YsRLbpuabXjsmaUo6l6A+xbOjbh/SkbKbdQI1SmAcqsOR5YSOQHKbeTsmFNdApRbdXn6llZXV4OmhgY0NjagqbEBzc1NaG5qkrJqs3ukVQiskFRxX7zOQz8EHnvssYgaI8T10aeXYtlzD7Ubzdy6vQRvrlorR2s/+nwTR25b6XLkNqLTjCO3KmBjESoSoNyqCJNFRUWAchsVvnaZhbyWlR5H2cnj8raqojziwtPS05GaKv6nIjUtDampaa236UgTj72eS0vLgMlsgtlklqOOZrMZJpP4L0ZLzTCJxykmmcZqbf/zt9PpgNvthtsNOeor74t/4lZ5LF9vfU2kU15rTedyucST5/LKfJ508jWvdOI5mRatr7WmM6W4kZ5qQl2jvS2fSCPSijJENnm/rR2e9snX2tK1tsGTuDWfV19a2+Ep07e9ftIBWPCLO8OOoTJiu/jhBZ3+TK+M3P74R5Plz/ri8B7ZVSr2HQH+xa0z20ZchSw/u2QF7rz5atz3+Avtytix53sp2OIYPXwAXnzqXuTn5kAZuZ00YQTmzJza1j9FyJUnlHr8jUA/8eD8trwcuQ37FNEmA0duteHKUkMnQLkNnRVTakuAchs536rKCpxqldnTp06ivq62Q2EZGZnIyMxCZlY2MrOy5P309EwpqNbUVHnfYrEgNe2cyFos1sgblaA5jTTnVkjiilVr22QyUEgUmfSW1T8sWYFTZyrb5uEKsXxk8Ut48uEFciqD75QCIbfz7nkKvmX89fXVHZ4T7RDTEPzJrW+bRZq3P1yHG2ZdhtLT5VizYRt+dfts2RVfeafchvimE8EVgVEO728I4jkF5K59h2US32F/728fs2ZM6jBZm3IbYiCYTDMClFvN0LLgMAlQbkMHVllx1jMqe/I4TpWdkNMMvA8hsj169kL3ol7o0bMY3boXQcxn5RGcgJHk1ldQO5Nb3wvKlJFYZZRVlNW/T1G7EVbvNN//cFKO3CrpRV2+Zfg+l56WJufcKiO3kcipd7siye/LxPDTEsS3hRdfeRd33nKNHD73/Ybg+43D91uNvxND+baiwKTcBv+gYQptCVButeXL0kMnQLntnNWZU6X4fv9eHD60v53MioujCrp2ayezOTm5oYNnynYEKLee6SLeDqNI6IdrNnU4W5RpBmrIrfCoZ15YjsW/XyC9y9+hjBB7v6aMFlNuI3gz+5NZ7yD4vu77LcffNxjKbQSBYBZVCVBuVcXJwqIgQLntCE+sVLB/707s27293VSD3n3PQ3Gvvp5R2R49OSobxXnnm9VIchvOtITORm59R1gDSWe0I7fB5FZ41erPN7et8iDaIZ5TBg4ptxG8EXyh+ZNVBfJdd1zfbqhdVOc7siueo9xGEAhmUZUA5VZVnCwsCgKU23PwxCjt7p3b8MOhA3L5LHEUFffB4KEjMGDQMHkRFw9tCBhJbju7oMx7Lqu/1RJC+fXZOwLBpiAoI7H+RoRDmZagDCDeNHtau4vjKLdRvg+8AYqivJfRUBY99pVb7yD4k1txlSQPEognAbG0ozwLeSrGMwxtddscLog/rsl4iCvqk/kz0eFwYPfu3di6dStOnSqTp4CYcjBixAhMmXIpunXrloynRVz6LD8XdfaZKNf+jeDwtxSYMljXt7h7wKXAfGVVmQ7guzrBy8s/ghjQ211yOOo5t6J7wqO2bC9pt6KCuKBs5ozJeOr5V9utiet7ERtHbsM8QfxNylZj5LaskusIhhkKJleZQNecNNQ12SGkikf8CYg/qHKd+SQ8ehZkIFk/E3d+txXbtnwl15kVh7j4a8TocRg97gJk53RJwrMhfl0WXy5zMq2oqG2JXyP81CzeH5Ee/pbQ8l7VwN8mDv4cp7OluNQYuVX653sxv++cWuUifvG8cojVFyi3YZwhga429J0bwjm3YUBlUt0Q4LQE3YQi6RuSjNMSSk8cw/rPP0ZdbbWMf3p6BkaOnYCRo8dDrC/LI/YEjDQtIfb0Er9Gw6+WIELkOxXBO2xcLSHxT2L2AKDc8izQC4Fkk9tNX36BXdu3Svx5+QWYOGkq+g+MfItVvcQx0dtBuU30CEbXfsPLre8atgou7/Vquc5tdCcRc8efAOU2/jFgCzwEkkVuq6sqsebj9yDWqhXHmPMn4qJLLudpoBMClFudBCJOzTC83MaCK1dLiAVl1tEZAcotzw+9EEgGud2z81ts/motxFazYtrBFVdfj+LeffUSArYDkBd0dsmyorxGX3NuxfuDh/YEKLcqMKbcqgCRRURFgHIbFT5mVpGAkeVWrFf7+SfvQ8yxlaPUvfti+lXXQuwkxkNfBCi3+opHrFtDuVWBOOVWBYgsIioClNuo8DGzigSMKrcnjv2Azz9dhZbmZphMZlx0yWUYNfYCFcmxKDUJUG7VpJl4ZVFuVYgZ5VYFiCwiKgKU26jwMbOKBIwot3t3fYev1v1DUhIXjYlpCPldC1WkxqLUJkC5VZtoYpVHuVUhXpRbFSCyiKgIUG6jwsfMKhIwmtzu37cL69d8JAmNHDNBjtiK9Wt56JsA5Vbf8dG6dZRbFQhTblWAyCKiIkC5jQofM6tIwEhy+/2Bffji01WSzvQrZ2PgkOEqkmJRWhKg3GpJV/9lU25ViBHlVgWILCIqApTbqPAxs4oEjCK3Rw4fxGcfvSvJXHHN9eg/YLCKlFiU1gQot1oT1nf5lFsV4kO5VQEii4iKAOU2KnzMrCIBI8jt8aOH8emHK+FyuTDj6msxYNAwFQmxqFgQoNxqT9nfdr9qbJ2rRssptypQpNyqAJFFREWAchsVPmZWkUCiy+3J40fx8QdvweV0Yur0qzF0xBgV6bCoWBGg3GpPmnKrPeO41kC5jSt+Vg5uv8uTQD8EElluz5wqxQfvLJebM1w89QqMHDNeP2DZkrAIUG7DwhVRYsptRNgSJxPlNnFiZdSWcuTWqJFNvH4lqtyWnz2ND1a+DrvdhvEXXoIJF16SePDZ4jYChpTbI0cA8T/WR//+gPjvc1BuYx2IGNdHuY0xcFbXgQDllieFXggkotw21NfhrdeXwtbSIjdmmHzpdL3gZDsiJGBIuX38cWDRogiJRJHtsccAUTflNgqICZiVcpuAQTNYkym3BgtoAncnEeV21dt/x6myE+h33iBcOWtOAtNn0xUChpTbZcuAV16JfZDvuAOYNy9kuX34317CA3ffgoH9imPf1tYaeUGZCugptypAZBFREaDcRoWPmVUkkGhyu3vHN/h6w+fIzcvHT+beAWtqqoo0WFS8CBhSbuMFM0C9W7eX4M1Va7HogfnISPe8bw4dLcUji1/Ckw8voNzqLF5hN4dyGzYyZlCZAOVWZaAsLmICiSS3dbXVWPHaX+F2uXD9TT9DYfeiiPvNjPoiQLnVPh7Ksl9zZ0/DnJlTZYV/WLICp85UthNe7VvSsQaO3KpAnXKrAkQWERUBym1U+JhZRQKJIrdutxvvvvk3lJ85hXETJmHiZM8fZx7GIEC5jU0cxUjtwgefRdnpClnhrBmT4i62oh2UWxXiT7lVASKLiIoA5TYqfMysIoFEkdvvvvka32zagLz8Atxwy50wmc0qUmBR8SZAuY13BOJbP+VWBf6UWxUgsoioCFBuo8LHzCoSSAS5ra6qxNuvL4UYvZ1zyzwUdO2mIgEWpQcClFs9RCF+baDcqsCecqsCRBYRFQHKbVT4mFlFAnqXW7Gl7jtvvILKirM4f+LFuOCiKSr2nkXphQDlVi+RiE87KLcqcKfcqgCRRURFgHIbFT5mVpGA3uX2m81f4rutGz3TEW6dD5PJpGLvWZReCFBu9RKJ+LSDcqsCd8qtChBZRFQEKLdR4WNmFQnoWW7FaO3K5cuQkpKCn9x8B6cjqBh3vRVFudVbRGLbHsqtCrwptypAZBFREaDcRoWPmVUkoFe5dTmdeHv5yxDzbcXWumKLXR7GJUC5NW5sQ+mZpnKrrIG2a9/hDm0ZPXwAXnzqXuTn5oTSTl2nodzqOjxJ0TjKbVKEOSE6qVe53fHtFmzZuFaO1t5w650JwZKNjJwA5TZydkbIqancisV8xXHfwrlGYBWwD5RbQ4c3ITpHuU2IMCVFI/UotzabDa8vewHidvYNP0VRz95JEYtk7iTlNpmjr+E6t2LUVg/7C8civJTbWFBmHZ0RoNzy/NALAT3KrVjPVqxrO2jIcFx+5Wy9oGI7NCRAudUQbgIUrdnILeU2AaLPJhqGAOXWMKFM+I7oTW7tdhteW/oCxO3NP1uALrn5Cc+YHQhOgHIbnJGRU2gmtwKamJbQv09R257DRgXJkVujRjZx+kW5TZxYGb2lepNbZSeyfucNwpWz5hgdP/vXSoByq+2p0NRsw2PPLMWkCSPaOd7W7SV4ePFLWPL0/RjYr1jbRnRSuqZyK/Ycfm3lZ3jgrluQkZ4at05qXTHlVmvCLD8YAcptMEJ8PVYE9CS3TqcDry79b9haWuTSX4XdesQKA+uJMwHKrfYB8P2FXllE4P6FczFx3DDtGxAPue1spQTRHq6WENe4s3KDEaDcGiygCdwdPcntzu+2YPNXa1Hcqy9m/eSWBKbKpodLgHIbLrHI0ouR2jdXrcWiB+bjo8834cjxU7pYREDTkdunalztAAAgAElEQVTIUGmXa+Xq9X7Bi+kTf319dbuKn3hwfttQu8j36NNL5euzZkySQfQeiebIrXYxY8mhEaDchsaJqbQnoBe5FevavvbyC2hubsI1196E3n3P077zrEE3BIwot0eqj0D8j/XRP68/xP9Ah3Co+sZmlJ4qx+LfL9DFEq9JIbfim8W8e56ScfnFrTM7fKvobMkykffZJSva1uT1l5ZyG+u3GuvzJUC55TmhFwJ6kds9O7/FxvWfIb9rIW68db5e8LAdMSJgRLl9fO3jWLRuUYwInqvmscsew+PTHg9Yr56mIyiN1FxuvcVSqXTZcw/FZT5GZyO3om3+1uP1vSjOV3ZFPsptzN9rrNCHAOWWp4ReCOhBbl0uF/6+7EU0NTZgxtXXYcCgoXrBw3bEiIAR5XbZ9mV4ZccrMSJ4rpo7xt6BeePmdTpyu//QcdTUNehmcy5N5dafCIqLzBY++CzuvuO6mK+iEOq0BGVKgr+rAUX7H1n8Ep58eEHblYCU25i/11gh5ZbngE4J6EFuS/bswIYvPpHLfs29/ZdISUnRKS02SysCRpRbrVhFU673nNsXX3lXFqWHjbs0k1tFDG+aPa3DKK03jFiuohBIbr0Dq8j34ocXYNSwAXKpC+8++JPbyjpbNOcG85JA1AS6ZFrRaHPA4XBHXRYLIIFoCBTkpCKen4lutxuv/OUF1NXVYsaVMzFi1NhousO8CUrAYk5BZroFtQ12XfVAvD+MciTtagmBdigTgvjMC8tjPvE4FLkVJ50yFeGa6ZM6rOPmT26bbU6jnKvsR4ISEKMUDqcbLjflVg8hdLrcMJuSc7QwPdWMeH4m7tm9Cx+seg/Z2Tm46ze/g8lk0sMpwTbEmIApJQVCcG0OV4xr7rw68f4wwpG069wm6sitt9zOmTm1w0YUnHNrhLel8frAObfGi2mi9ije0xLe+NtLqK2pwqQp0zF63AWJipHtjpIApyVECTDBs2s2LUFwESOlK1atbTfBWG9zbsWw+uo1m3DbnB/JUPqOzHK1hAQ/w5Ok+ZTbyAJtt9ngcIrpHHY4HU6IRf8D3hev2R1taZT7Mk/r8+K+0xn9SJGYIyqmicpb8c9k8tz3PClvTSme56Cka31OeV2mkaOWnvRtZYqyvJ8zmWQ68dy5vPDkVepXylLKUfKbvMpuzV+Ym46qenvrPNfWtsr2i6b4tv1cftEf7/o97T3Xb6Xv5/p9jpHFYpUnwPGjh/HxqreQlp6On867C8rzkZ0dzJXIBCi3iRy96NuuqdyK5ulhtYTO2qCMMH+4ZlMbTd/VHLjObfQnGkvQlgDltj3f+rpa1NZUo6G+Tl4xX19fh8aG+nP/GxukpPIwJoGxEy7ChZMvM2bn2KuQCFBuQ8Jk2ESay61hyXl1jKslJEOU9d3HZJXbmuoqVFdVoLqyApWVZ1FdVSnvi9HXUA6rNRVmsxlmi0WO8vm7b7VYYDZbWtN47lusnrQyj3zd674p+jl14qIo+R9uwO2GWNpKeU48Fv88z0G+rqR1e6Xr+Ny5tC53a3le6cVznrLETWuZSrrWx7ItXs95mnfuOfF6mtWEphYHZFvEP+8yvZ5T2t3Wt9a+ivrFc0o/29qitLW1TA8XT/m+X1Ruu/NuZGZlh3IKMI1BCVBuDRrYELtFuQ0RVGfJKLcqQGQRUREwutwKYS0vP4OaKiGx5aipqkRVZXlAZtbUVBQUdENWdo6UnLbbrOzWx9n8yTqqMy5w5njPudWoWyw2wQhQbhMsYCo3l3KrAlDKrQoQWURUBIwmt0Jcy04el/9LTxyVW6j6OzIys5Bf0BV5+V2RX1Ao/+flF0A8zyM+BCi38eHOWtsToNwm9xmhutwq27DdefPVePmNj7Fr32G/hEcPH6CbnSyiPQUot9ESZP5oCRhBbsU82QMlu3Fg7y7U1dW0QyJ+/i8q7oX8gm4emS3oKkdmxQgtD30RoNzqKx7J2hrKbbJG3tNv1eVWwem7uK835nht4qBVqCm3WpFluaESSFS5FXMlDx/cj/37dspRWuWQMtuzF3r16Y+evfqgsHsRd5kK9WSIczrKbZwDwOolAcptcp8IcZHbeG3ioFWoKbdakWW5oRJINLk9VXoc+/fuwg+HDsBuP7fDX1FxHwwdMRoDBg3lnNhQg6+zdJRbnQUkSZtDuU3SwLd2Oy5yK5bW2rRtLxY9MB+x3H5Xq1BTbrUiy3JDJZAIciuW5Nq3Z0eHaQfiYq/BQ0di2MgxyOmSF2qXmU6nBCi3Og1MkjWLcptkAffprupyq2zSUHa6IiDZnj26YsnT92Ngv2JD0KfcGiKMCd0JPcut3W7Hjm2bsPO7re2WbBo4eDiGjhiDXn36JTR7Nr49Acotzwg9EKDcah8Ff3sIzJoxSRcDl6rLrYKzszm32iOPbQ2U29jyZm0dCehVbg9/X4KN6z5DU1OjbHRx774YMGgYBg0ZwYvBDHoiU24NGtgE6xblVvuA+e7gKmr8w5IV2LK9JO4LBmgmt9pj1U8NlFv9xCJZW6I3uRUrH2z44hOcOPaDDEn3omJMnX61XKqLh7EJUG6NHd9E6R3lVvtI+ZNbRXDF7X0L52rfiAA1UG5VQE+5VQEii4iKgF7kVuwWteu7rfhm85dyCoLYAeyCSVMwcswErnYQVYQTJzPlNnFiZeSWGlFuq6urIf7H+sjLy4P473sEkttAz8ey3ZrKbWfzb7nObSzDzLqMTkAPcnv2dBnWrVmNqkrPfPs+/Qbg0suvkruD8UgeApTb5Im1nntqRLldu3Yt1q1bF3Psl112GaZNmxay3OphRSzN5Lap2YbHnlmKSRNGYOzIQXht5Wd44K5b5OoIYk7GpReNwcRxw2IeJC0q5MitFlRZZjgE4im3NpsNm7/6AiV7dsgmi93BLrnsCpw3cGg4XWBagxCg3BokkAneDSPK7fbt27Fjh+dzNpbH2LFjMW7cuJDl1tAjt94XlAkiz7ywHIt/vwD5uTngJg6xPC1ZVzIQiJfcnjlVik8/XNl2wdjwUeNw0cXTeLFYMpx0AfpIuU3i4Ouo60aUWx3hlU1Jyjm33nJbkJeDxX96DQ//021SbvUwZK3mScKRWzVpsqxICMRDbsVKCGs+fl82Ny+/AFNnXIMeRb0iaT7zGIgA5dZAwUzgrlButQ9eUq6W4D0tYc7MqXIqQv8+RRD3uYmD9icda0guArGW2/37dmH9mo8k5P4Dh2DaFbNgtVqTCzp765cA5ZYnhh4IUG61j0JSrnPri1WM5N710B+xa99hcBMH7U861pBcBGIptwdL9mDtZx9KwBdMuhTnXzA5uWCzt50SoNzyBNEDAcqtHqIQvzZodkFZ/LoU+5o5LSH2zFljewKxktsfDu2XUxHEkl+jxl6AyZdOZyhIoB0Byi1PCD0QoNzqIQrxa4NmcssdyuIXVNacfARiIbdHf/ge/1j9jhRbceHYlGlXJh9o9jgoAcptUERMEAMClNsYQNZxFZRbFYLDkVsVILKIqAhoLbdCbD/76F24XC4MHT5aXjzGgwT8EaDc8rzQAwHKrR6iEL82aCa3oktGW882UJgot/E7gVmzh4CWciu20P3kg7el2A4cMhzTr5xN7CQQkADllieHHghQbvUQhfi1QVO5FUt+eW/eEL9ualsz5VZbviw9OAGt5Lb0xDF8tOpNuJxOuSnDjKuv5Ta6wcOR1Ckot0kdft10nnKrm1DEpSGaya336gj+esbtd+MSb1ZqUAJayK3YoOGDd5bD6XRgwKBhUmx5kEAwApTbYIT4eiwIUG5jQVm/dWgmt/rtsvot48it+kxZYngE1JZbW0sLVrz2FzQ1NlBswwtF0qem3Cb9KaALAJRbXYQhbo3QTG47Wy2B2+/GLd6s2KAE1JbbT1e/g6OHD6J7UTGuu/F2g1Jjt7QgQLnVgirLDJcA5TZcYsZKHxe55fa7xjqJ2Jv4E1BTbg/u34O1//gQZrMFN902Hzld8uLfQbYgYQhQbhMmVIZuKOXW0OEN2rm4yC233w0aFyYggbAIqCW3YhrCildfgs1mw6WXX4VhI8eG1Q4mJgHKLc8BPRCg3OohCvFrg+pyK0ZlFz74LMpOVwTsFbffjV/AWbMxCaglt+ICsrKTx9C3/0Bc9eMbjAmLvdKUAOVWU7wsPEQClNsQQRk0mepyq3DiDmUGPWPYLV0SUENud+/Yhq83rEF6egZu/tmvkJqWpsu+slH6JkC51Xd8kqV1lNtkibT/fmomt8mElaslJFO09dnXaOW2uqoSby9/Wa5ne821c9G7b399dpSt0j0Byq3uQ5QUDaTcJkWYA3YyqeRWzPU9cvwU7ls4tx0Q3zV5lz33ECaOG9aWRuR79Oml8vGsGZOw6IH5yEhPbXudcpvcbyI99D4auRU7j73zxiuorDiLkWPG4+KpV+ihS2xDghKg3CZo4AzWbMqtwQIaZnc0ldvONnKI5SYOYumxefc8JdH84taZ7eS2qdmGx55ZikkTRmDOzKkQc4YfWfwSnnx4AQb2K4bI++ySFXjxqXuRn5sjtxQWh7cgU27DPOuYXHUC0cjtN5u/xHdbNyI3Lx833HqnXCWBBwlESoByGyk55lOTgJpyW9tSgyZHI5qdTWhyNKHZ3norHtsbPc85xHONaHY0tz3Xlkemb4TD5cAXd36qZjdZVgACmsqtPxGMZyT8jdz6LkvmK7uiD/37FEnxFYev7IrnKLfxjCrrFgQilduK8jNYuXyZhHjjrfOR37WQQEkgKgKU26jwMbNKBBS53X/6JCqbKlDZXI6qpkpUNVfIxxVN5ahq8dyva6lFo6OhnZw2O5vRYK9XqTXninE/5la9TBbYkYBmcqvHC8r8ya0/WVWk/K47rm83qivw+Y7sUm6T721lt9vgdrnhdDnhdrkgftZ3uZxwudytty75vOf12HyQ5WZZ0dDigMMRXn2bvvoC5WdOYeyEi3Dh5MuSL5jsseoEKLeqI2WBrQQqmsv9iqoQ18pWaa1prkZ501lUNZejuqVaFXbZ1mxkWDKRbs1AhkX8z0S62XNfeS7dkokMs+dxpjUL6eI1czoyrJmedJYMZFqycPO4maq0iYV0ToByu70Eb65a224era/c3jR7WtscXF+5feizh/DbifegMKMbz7UYEHA4hMDZYbfbYbPZ4bDbYRePbTbPc3YbHHZH6+viOZtcs9WTztF23+l0wuV2Qd4KOVVuhbQq992e50W5Rj6ysrKx8K7fwGq1GrmbMe2b+E5jSolplbqpLD3VjGabMy7tMb/3Lsz/+i9w/erXcCz4VVzawEpDIyAEtLyxdRS1sRwVcjS1AuWNZ1HRWIHypnJUN1XhbOMZlDdVoLq5KrSCfVLlpeeja0YBumV2R35GAQozClEgbjO7oTDTc78go6sU0ExrpkdCpcRmoktal4jq7CyTeH/w0J6AZnIrmu77k7723em8Bi1GblMWpWB80USsvuULWE2Ug3BjbLO1oKmxEU1NTRAbCDQ2NqK5uRGNDa33mxrlc01NDWioV/8nonDbK9JbLFaYTCaYzSakmEwwpZhgMpvlc57/nvvK65HUEW4ei8kEp8sN8S/cY8IFk9B/wKBwszF9JwTcbjdSUpLTbgtyUlFZZ4vL+dFl+hRYvtkq625Y+r9oufHmuLQjmSuttdWgrK4UZQ2l8vZUQylK606irL5U/hePzzScloML4RwpSEFuWp4UUY+QFqKrvN96m37usXi9e3Yheuf2QH1TfL5oBeqbeH/w0J6ApnIrRjlfW/kZHrjrlnarC2jfLf81aDHntvjZYpTVl+GmYbfhuSteilfXdF1vY0M9amuqUFNTjdrqKtRUV6Guthpi+SkxChvuIdZfFYIp/ovRRqs1FWaLufXWIm+9X7NYLbDI5yytz6fCZG4vpSkp52TUbDL7SGuK7i+yinTObbjsmZ4EghGI57SEblddBus2j9zCYkHF6++g5fIZwZrM18MkcLbxNA5UluBgVQkOVR7A/qq9OFl3AqcbyuS81VCOnNQuKEgXI6ddUZDeVY6qisdd5chqV+SnFaAgsxD5aUJgu4b966iaF5SF0p9Q04j3Bw/tCWgmt52tlCC6FcvVEhSM/uQ22tUSNp/cjEl/mSSr+Jepz+AXY36jfdR0WEN9XS3qamtQU12JGiGy1VWor62RAut0OgK2WFyZn5GZKTcOSM/IlPczMjKRnpEl72dmZSM9LR1pGRnIycnVYc/10STKrT7iwFYAupFbAO60dFS8uxq2iZ7PaB7hESirP9kqsfuwv2Ifvq/aj5LKPRCrBwQ60szpKMoqRlFWTxRlF6NXTm90zyqSz/XM7oUeWT3RJ6dfeA2JIDXlNgJoBsqimdzqiZH3UmBKu7zXso12ndvnvnoJ937mmd/1+nUfYGqf6XrqvuptEeuhnio9gbKTx1FVeRZVlYG3WhaVp6amoktuvvwvlpvqktd6m5svRZZH9AQot9EzZAnqEIin3BZePQ2p32xB+UefI+fpJ5H2xRq4s7NR/uEa2EeOVqeDBizlWN0RHBQjsZX7sb9yD76vOoD9FXsDrhYg5qMOzh+KwQXDMLRgBIZ0HY4+XfqhKLMYYo6rHg7KrR6iEL82JIXcao1XLAX2z1/8Dq/u+StyUnPw8c0b0T93oNbVxqx8MYXg8MH9KD15FKfLSuVFWr6HmB6QV1CILl3yPALbKrI5uXkU2BhEinIbA8isIiQCupDbT9bBPmo0ul4/E6lbN8FVUIDyf2yAo995IfXBqInERVy7z27H3vLd2FexSwqtENlAUwnE37NB+cMwJH8YhhaOwOD8YVJoYzHyGm0MKLfREkzs/JrKrfKT/4drNqFnj65Y8vT9KO5R2GF5rcRGeG6d29lvTcO3p7ZgUP4QrJ77JbKs2QnbtYb6Ohw6sA+Hvy/B2TOn2vUjLT0dRT17o6i4D3r0LEZuXoGcVsAjfgQot/Fjz5rbE4in3Cpzbs9+vBb2Cy5ESn09CmfNgHXPLjh79Ub5J+vgLOqZFCE7VH0Qe8p3YM/Zndh9dgf2lO+EmCvr7xCjrYPzPOI6rHAEBuUNw5CCYXIaQaIelNtEjZw67dZUbpXVEq6ZPgnPvLgct825om3XL9/lt9TpTnxKUTZxEGvw/ej1i+Sk+ml9rsBr170fnwZFWKu48Ot7RWhPl7UrpXff/ug/YAh6FvdBXkHXCGtgNq0IUG61IstywyWgJ7kVbTdVVqLwmsthOXQQjoGDUf7RF3Ik12jHd6e3YnPpRnx1Yi22lm1Ena3ObxfHdh+PEYVjMKrbWAwpGC6FtltGd6PhAOXWcCENq0Oaya33Jg5itNZbbn13BQurxTpM7L1D2fbT3+C6t2fA4bLj7vH34ZGL/1WHLT7XJLGG64GSXfh+/16cOVXarq09e/XBwMHD5X+xQgEP/RKg3Oo3NsnWsnjKbeFVlyF121aUf7wWtgsubENvLitF4czpMB8/huYrrkL1f78EVwLvxif+vnx35htsOvklvj65Ht+Ube4wP1aMxo4qHIuRhWOlyIr/A/OHwJySHOusUm6T7ZOnfX/jIrfiAi8jjtwqaF/f9wr+75q75G4kS655FdP7XaW7s0xcBLZn5zYcLNnTbjmuHkW9MHDIMAwcMoJTDXQXtcANotwmULAM3lQ9yq1Abjn8PbrOmQXzieNwdu+BqldeT6hVFDaeXI+vT6zH5rKv8NWJdR3Ooq7phbik9zRM7n0pLiy+GMMKRhr8TOu8e5TbpA4/NJNbgVUsvbVp2148/E+34fml78hpCQV5ObjroT9i7uxpmDNzqiHoe4/cKh36/9Y/gL/u/G/58PkfLcWcobfooq9Card+vQ5Hf/i+rT2Dho5A9x495bSDrOwcXbSTjQiPAOU2PF5MrR2BeMqt75xb316aamqQP+8WpG1YB7fVitonnkLDL+/SDkaEJTc7m7D55EZsLv0SG0+sx9ZTX3coqTi7Nyb1moKLe03FRcWXYEDe4AhrM2Y2yq0x4xpqrzSVW9GIYMtwhdpQPafzJ7eivY+u/79YuvMF2fR4r4FbV1eDbzZtkNMPxCGmGYweNxHDR43jagZ6PrlCbBvlNkRQTKY5AT3Lrey8y4Uujz+C7Bf+Uz5suv5GVP/XErjjeFFsvb1eiuzm0q/w9ckN8sJk36NvTn9M6XM5Lu59GSb0vBDiMY/ABCi3yX12aC63yYA3kNyKvv9p29P4968flxh+N+EBPDR5UUyRNDU1YtvmL1GydyfcLpfcaWvk2PE4f8JkzqONaSS0rYxyqy1flh46Ad3LbWtXMt59C3l3L0CKrQX2YcNR9eqbcPQfEHpHo0hZZ6uFZ5rBBmwq3YC95bvgdLffJnZg3mBM6nUpJveaiim9L0O3zB5R1Jh8WSm3yRdz7x5rKrditYRTZyqx6IH5bdvv+u4IZgT8ncmt6N+bJa/hvjUL5V7aYpveP17xZ4h9srU8bC0t+HbrRuzd9V3bDmFDR4zBxEmXIiMzS8uqWXYcCFBu4wCdVfolkChyKxovlggrmHsdzKdPwZ2Tg8qlr6Hl8itUj2xVcyU2nlwnR2WF0O6v3As33G31iL8HYiOEycWXyjmzl/Sahvx0463ooDrYTgqk3MaStv7q0kxuFYm9afY0TBw3rF3PjX5Bmb8wf3bkIyxY/VPYXC24ZuB1+J+r/hcWk1WTM2LPzm/xzeYNEIIrjkFDhuOCyVO5fa0mtPVRKOVWH3FgK+K7/W6g1RI6i4up/CwKfjYXqVs3y2S1ixaj/jf/J6pQis0SvjzxRdvIrNgowfswpZgwoutoXFQ8BRf39ozO5qblRVUnM7cnQLlN7jNCM7n1XgpsYL/idpSNvBRYZ6eT+NY+74MbIOZXTek9DW9cv1rVs6+luRmfrn4Hp0qPy3K79eiJSy+/Cl0LjbeGoargDFAY5dYAQTRIF+I5chuJ3CrYc+//HbJe+at82HzVTFS/uBSuLl1CisrxuqNyOa4Nx9bgm1ObIDZQ8D3G9bgAF/W8BJf0uUxKbXYCb/ITEpQ4J6LcxjkAca5eM7nlyK3/yO4u34GfvjsbYsMH8WH34U3rVTkFKivO4uNVb0HsLGaxWHHx1BkQ0xB4JAcBym1yxDkRepmocivYZv3tZeQ8/nuIVRXsw0eg4Tf3oPGW2ztgFyOxYn3ZLWUb5VqzpfUnOqSZWDRZrmYg/ovVDDIsmYkQPsO0kXJrmFBG1BHN5Fa0Rkw/eHjxS3LbXWX0VozaLnzwWdx9x3WGXgqss2gcqzuCO1bNwYHKEoi1CZ+c9kfMHnRDRAEUmY4cOoDPP/1Azq3N6ZKHq398A3cRi5hmYmak3CZm3IzY6kSWWxEPU2UFcp58vG0U1zF4CDY8MA9fDUrFqYYyvL5nGSqbKzqETk4xaL0A7IKeFyHNnG7E8CZMnyi3CRMqTRqqqdyKFisyW3b63IfBsuce6jAPV5PexajQYBeU+WuGmJrw0Be/wzsH3pAvX3neLDw9/b/D2gbR7XZjy9frsPNbz7IxffsPxOVXzkZqamqMes5q9EKAcquXSLAd8ZTbYOvchhIdsW3tttOb8c3O9/DdtyuxObsKTT6XRwhxndhzUutqBlMwqfjSUIpmmhgSoNzGELYOq9JcbnXYZ9WbFIncKo0QF5rd+9mv5EhAl7RcPHrJv+GnI+4M2kabzYZ/rF6J0hPHkJKSggsmXYpxEyYFzccExiRAuTVmXBOxV4kmt8dqf8DWsk3YdmoztpRuxL6K3R2wD6q14qIjdkwsBcb3m4qh9z0Px0BumqDn85Nyq+foaN82yq0KjKORW1F9dXMV/vmL3+GDQytla6b2mY7/mP4ieuX08du6muoqfPT+m6irrZZr1f7omp+guHdfFXrCIhKVAOU2USNnvHbHU279XVB2ou4YKprK0WhvkLDFElwbT6zD/sp92Fr2Nc42nm4XhIL0rji/x0RMLJ6MMd3GY3zRhchJzUHWX/4HOf/+BExVVTJ93b0PovGXv4azR5HxgmiAHlFuDRDEKLqgqdyKFRPEVru79h3u0MTRwwfgxafuRX5u4m/3Gq3cKnDeO/gmfr/uHim74uKDf7/8edww9NZ27E6fOomP3lsBu92Owm49cOWsOdwyN4o3gFGyUm6NEsnE60eToxEOlwM2lw0Opx0FuWacrKiD3eWAw2WH3WWXz9vddrhcLrQ4m9s953A65GsyjUgr8zhgF+W5HHLzmVCPzFeXYZO1FAeG90S5sxaNDo/QBjrSzRkY22MCxve4ABOKLsLo7uejd07ggQJTbS2y//1fkb3kv9qKrLvnATTdcjscgziSG2qcYpGOchsLyvqtQ1O5FZs4iOO+hXP1S0CFlqklt6IpYhTh/jV3Yc3Rj2XLxBW3f575GrpnFqGi/AxWvf132O02DB42EtOumKVC61mEEQhQbo0QRe37IOb6N9jq5HKEDfZ6NNrrIeaY1ts89+vtdWiwN6CupVa+3mDzPCdGPetb84lb+Zq9XvsGq1CD+OwszOiGwsxu6JpRiIL0buifdx4uLL4EowrHRlSD5chh5Dz2e2R8+H5bftv5E6TkNt10a8hLiEVUOTOFRIByGxImwybSTG47W+fWaDTVlFuFjdjVbNGX/wyxs404ru17Ay48MwGOZhtGj5uISVMuNxpG9icKApHKbdZfXoSprBR1jz4RRe3MqjWBZmeTFM5aWy1qW6pR21KLOnsNalvE/1rU22pR01yNGls1xNauQkA9t63CKuQ1yChmpH0QF1dZTRZYzFZYU6xIs6bC5LbAara2Pae8Jm9FWpO4tcrbVJGu9b7ynLw1W5BmSpNbhqeaUmHxquNceZa2ckSewt8/hJx9+2H506voMnG65hsjpK39HNl/+g+krV/bDl/T9Tei8bafa7LbWaRxSrZ8lNtki3j7/lJuVYi/FnIrmiX+OP3Xtv/A8p3LcIv9FhSiEKVpZRh/+ZSolhsYVxcAACAASURBVA5TocssQmcEIpHbrFeXIfeeu2VPxKhT1ct/h7O3/3neOuuuIZojvriWNZxEWf1JnKovlbfKfXGBqRDZupYauSa2Wof4GT47NRtZ1hx5m23NQaY1C9mpOXJTgazUHDm/NNOa3fZ6Vmo2clK7INOSKV8X6UR68Zy/Q29zbtVi11k55pMnkLn8VWQsfw2WHw61JXUW90Lj3FvRdPs8OPoPiEVTWEcrAcptcp8KmsmtwCqmJfTvU2SY9WwDnSpaya2oz+V04r2Vr6L89GmcNp3Bn11L4IQT/boMwMLz/wl3jP5Vcp/B7L0kEK3cynOtSxfUPP9nNM26llSjJHCqwUtWG0rl+qildcdRVl/mEdiGUjn3NJxDXOiUk5qLLmld5MoqbfdT85CXni9ltEtaHrpYuyA3PT9kGQ2nDaGkTUa59eaSunkjMl99BRnvrURK47k5v7YLJ6Ph179B07VzQsHINFESoNxGCTDBs2sqt2KN29dWfoYH7roFGenGXXtVS7kV2+kePXwQXXLz8ZO5P8eHR9/D89uexv6KvfLUE3/w5o+9G/PH3KX5T3AJfq4buvnRyK34CRVOBzJWvSsZNfzy16h56g+G5hVN547UHJJyWiZHW0tRVncCZY2lOC0F9oR8LZQjy5qNntnFKMoqRs/sXijO7o2i7GK5Skp+WoFHVNO6yBHSRNrdKtnlVol9SlMjMt5/Fxmv/y/Svmy/E6XtoovRcsWVaLjjl3AVFIRyujBNmAQot2ECM1hyzeS2s5USBEOulhD8TNr81Vrs/G4L0tMz8JOb70B2zrmfAb86sQ7/891z+PzoJ7IgMe9tWt8r5FaPPxl6S1ibQQRvCVPonUA0ctt42x2o/s8X5VJHuQ/dJ7sqth6temU5HAMG6b3rqrfvYNV+HK89AiGxx2qO4oea73Gy7riUVmUOfLBKxZdORVoVYRW3xVm90SOrp5TaQD/rBytb769TbjtGyHz8KDL//jekr3oH1pJ97RK4s7PRcvGlsE2eAtuki2GbeJHeQ5wQ7aPcJkSYNGukZnKrWYt1WLAWI7cle3ZgwxefyIsprr3xNrnsl79D/CF+4dtnsWLfq20viy19R3UfC7EdpFgzV6zZyMPYBNSQW0HIuv1bFNxxC8QcQndmFmqefg6Nt9xmKHji4qx95btxpOYwjtb+gCPVh3Cs9iiO1hwOadRVSKsYXRWSKu4X5/Ruve2FnlnF6NvlPEPxCrczlNvOiZlPHEf6mk+R+sVnSNuwFqaamvaym5YO2+SLPbJ78RS0TJ4SbgiYHgDlNrlPA8qtCvFXW26PHz2MTz54G2J73atn34g+/YJfiCCWEHtr/+t4/8Cb2Hn2u3a9yk3Lw6W9p+OqAT/G1L4z5LI4PIxFQC25FVRM1dXIWzhP/gEWR8MvFqLu94/DlZubcNDEl79DVfux68x2lFTuwb7yPTha23Hdbe+OiekB/XMHoG+X/uifN1De9utynpwyIGSWR+cEKLfhnSHWvbuRunEDUr/6EmkbN8BU0fECQiG4QnSbf3IT7MOGh1dBkqam3CZp4Fu7rbncbt1egnn3PNWO8rLnHsLEccMMQ15NuS0/exrvv/UanE4HJl86HaPGXhA2J/ET6tpj/8C6Y2uw/vhnch1L72N411G4tM90XN7vSjmyyyPxCagptwqNnOeeQc6/PiYfOoYMRcP8hXI+rh4PMWVgf8U+7K3YhX3lu3Cgch92nd0esKnn5Q7CkIJhcpS1f94Aj8Tm9MOAPC7EH218KbfREbQcPIDUrZs8wrtlMyyHv+9QoFjVxD56LOyjxsB2yVS0TJkaXaUGzE25NWBQw+iSpnIrxPbZJSva7UQmLjJb+OCzuPuO6wyzioJactvc3IS3X38ZjQ31GDl6PC6+7IowQhk4qdgzff3xz7H26D/wzalN7RKKubqTi6fg9lG/kD+ziq0meSQeAS3kVlCw7t6J3Pt+i9Rvv5FQnD2LUf/gI2j42Z1xgSQ2DhACW1K+BwcqS7Dn7A45IlvTUu23Pd0yumNY4UiM6DoGQwtHYFjBSIztPj4ubU+WSim36kbafOY0Ur/+Eqnr1yJ162aIkd5AhysvD87+A+As6imX9XP27gtnn9bbXr3l88lyUG6TJdL++6mZ3DY12/DYM0tx0+xpHUZphfS+uWotFj0w3xCrKKglt6vfewMnjx/FoCHDcfmVszU5M8XORF8e/1yO6n76w4d+5xhe2udyuTNamiUd/XLPk6NZg/KHyIvWeOiTgFZyq/Q2/ZPVyHnqCVh37fBIbp++qHvwETTe+jPNgOyr2I2Sir3YX7EHe8p3Yn/lXnlhl78j05KFoV1HYFjXkRjadThGFo7FyMIxXEFEs+gELphyqz108T4UXzwtO3fAum83LMeOwnzsaEgVO/qd5xFeIbu9+8LVpy8cffrJx0baQphyG9LpYNhEmsltZzuUidHbZ15YjsW/X4D83JyEh6uG3B4o2Y11n61GTpdc3PjT+bBYrDHh8n3VAaw/sQbbSjfju9PfdDofUcw3FJLbP3cgBhUMkdI7IG8QxE+8POJLQGu5VXqX8cF7yP73J2Dd51mKznHeQNTf/1BUF50drzuKkoo9cnm7veW7cLCyRI7OBjoG5w/FsK6jMKLbaIgpNkMLhif9RVzxPfva1065jV80zGWlEBesmU8cg/nECc/tcXH/OMwnj3e4eM1fS10FXWEfOhw2r6kO7i5d4CrsDmdhIVyF3eDqWgixQYWeD8qtnqOjfds0k1uO3IYePFtLC17/3/+BuL3murno3ad/6JlVTinm5+488y0OVpXgaM0Pcu7i4ervcaz2h05rEqIrLsIRoiHmLyriywtwVA5QgOJiJbdtkvv+SjmSazmw3yO5g4eg7p//H+SauZ0c4sLHLWUbsa1sC749tUWOyAbaFlas/SqmEQiJHVowAkMKhmN0t3GxAcpaIiZAuY0YneYZU5qbYDlyBKayk7AcPQLTyRMQy5RZFBE+4f+XkUANc+fkwFnYXb7/7WPP958sIxOuzAy5+oo7M9NzmyFuPfddWZnnHmdlq8aAcqsayoQsSDO5FTRWrl6PFavW6n7OrdhJ7a+vr24XwCcenN82J1j049Gnl8rXZ82Y1GE6RbQjt+vWfIQD+3ah33mDcOUs/e5eI648F5Ir5joeqjqAH6oP4VD1AQhhCXSI+Y0Zliz5cl56Hrpl9kD3rCL0yCyS9688b1ZCvnH01uhYy22b5K5cgZynn4Tl+4PyKbE4ffPVs3DyV3fKubAHKvbJ6QSHqw+ixWHDptINHdCJ7VzFNIIhXYfLkVhljqzYBpZH4hGg3CZezLxbLJYBNJeegPn0aZjKz8JUWQHTGXG/HKbKcpjOnoH57Fn5mhaHO12IsCK/igBnw52e7hFjIcNSkDPgGDU24AiyxZyCrHQLahrtcKemwZ2WJm+Rlgp3WnrbY7HOcCwP8f7goT0BTeVWND8RVksQciuO+xbO7UDc96I4f2mjkdszp0rx3luvyvVsb/7ZAmRlJ94f9CZHoxzh/aHmkBzlPVx1AEdaR33FBUCRHHI7UWsOxL72ual5yLBmIMua49nv3pKDzNQsuQi+2OVJ7HMvBEns6JRhyZCPlefFMmjJcMRLbqubq1BSuRs//ONvOLR1Ffan1WB3d+CM5/uM30Osvzyh6EJcWHwxRnQdLdeM5WEcApRb48QyWE9MlZWtAlwOU3293G44pbHx3P+mRqTU1yGlqcnzWoN4rQEpzc0wNfhJ39wUrEpNXxdiDasFbqsVbjE10GIBLFbPY6sFMFsAeV/8TwUsZvmc57FI35rOYvHkV8qRt2YgLV0OBvDQnoDmcqt9F6KvoTO5Fa/171PUNorrbwWISOXW5XLhrb//FTXVVbjokmkYc77xVioQ0xzONp7C2aYzcntSMcp7puE0zjSekrfiKvcGex3qbfWot9ehtqX9gubRR9eze5uQXyG8QpZ75/QN6eftVEsaUs2pSDWlIU3cN6Uh1ZIqy0szp8lbq9mKVHMa0s3pnrRmkUe85skbq4vwtJRbMW1gx+lvYXfZ5QjsocoD2CdHZfeiornjmpwiZr1qgWHlwOBKYFCtBYMGXILel89Fz1nxWWVBjfOIZYRGgHIbGiem8k8gRUpvI8T2xSZFhlsfn5PnBpgamwAhz0KIW2xIsbUgpaVF3qKlBWabDRanDfYmm0wjX2tpRorNJl/3pLdJ2Y7p4XbHtLpkrUxTuRVieOpMZbuf8ZW5uJMmjNDNUmC+0xKUKQn+2iouhntk8Ut48uEFGNivGNi0CaeGjo3o/Plu69fY8vUG5Obl4+af/RIpKSkRlWO0TGIHqXpbA+ptdWi0e27FKg/i1luE61vE8+fEuLE1z7m09aiz1RoNj27641mhYDjOyxsoLzQU86zFffFcdskhpL+9Aukr/g5z6cm2NoulippvuBktN8yVW40a9XDDjRQk5/u5R346Tlc1xyW0BT+aCuu2raj8dB3sFxhvsEALqEZVrVRzCrIzraiss4WMTcqz3QHY7Uhx2OUtHI7W+6234rF83u65tYvnHeceK897PyfSOEUaB7KfXBRye5gwcgKayW2iXlCmrMO7+OEFGDVsQIflzDrIbWEh3CNGwrXyHSA/P+RI1NRU44UX/htOpxN33jkfvXr1DjlvciRU7yO3wd6AulYRrmsRklyPZkez/N/ibEGLowU2l+dWPBbP25w2NNmbfZ7zvK6kE7fnyrDJ12zi9dYyRD2dHemWdClA4kuN+GdKMfm9L16Xr7Wm9b7vnQ+iDHRWhqeetvIqKmE6fhwoKISpf/+AdZtTzMjPKMDggsEY1FVsfjBU3i/KLgrpVEz56iukLF8O0/LXgaqqtjzu4SPg/umtcF86Fe4pxtpi1O5wwWoxhcTHaIksZhMcTldcumW+eDJStmyB86uNcF90UVzakGiVGvYrmPzcBFwu9f6WhB7bwFTNZsMSDx1PDFJqJreJvBSYMhXhmumTpNx6jzJ3kNvMTKCpCc6+/VGx4r2Q1wn84J3lKDt5DENHjMHU6VfHINSswsgEtJyWoCY3saVv+lvLkfHB+/JnR+UQW/s23PkruPMLYB8/AbbzJ0DOf+ORcAQ4LSHhQmbIBnO1BEOGNeROaSa3iTpyK8h5z7MNOud2+3Y4Z86CWF9QLItSuWw5Wi67vNMAHD5YgjWfvI/UtDTc+vNfy1seJBANgUSRW6WPYg5c2rovYN3ytdxiNPW7bZ65c16HfcQoubyQffwFsI2/IPBSQ9GAY17VCVBuVUfKAiMgQLmNAJqBsmgmt4KRuPjq4cUvYcnT93vmpwLQ2/a7YoR59ZpNuG3Oj9ra5z2nNpTVEk4dPImCn9+M1E1fAWYzap58Bg2//LXf08Rut+GNv72EpsYGXDbjGgwZPtpApxO7Ei8Ckcht5t9eRt69v0Hj7fNQ/dwL8Wq6p16nU+64lLp1E1I3b5K3YuF570Ms32MfPQb2cRPahNcxcBDAuerxjZ1P7fGU225XXSbn3J79eC3n3OrqrIh9Yyi3sWeupxo1lVtvmS07XdHW72XPPdRhS954QVFGmD9csylg+0Jd57bLow8h+8U/yXIafj4fNX/4rw7d2vL1OuzYthk9inrh2htvi1e3Wa/BCEQit1mvLkPuPXej8bY7UP2fL+qOiPlUGVK3boZ189dI3bxRju76HvbRYyGmNIhpQY7hI2AfNgKOocN1v3uS7mCr2KB4ym3hVZchddtWlH+8FjZeUKZiVBOvKMpt4sVMzRZrLrdqNlavZXkvBZbx9grkL5wnm9o0+yeoeeY5uV2hOJqbm/C3vzwv71934+3oXuQZzeZBAtESMKLc+mOS9vWXcmTXKkZ4t3wNk9cFat7pxcLszdNmwDF8pHzanZcnhdfZU/wvhpMXcEZ7ygXMT7nVDC0LDoMA5TYMWAZMSrlVIai+69yKn1cLbrsRYqcXcTTM+yXqHn0CW0t24dutG1Hcuy9mXX+LCjWzCBLwEEgWufWNt1hmTGwBbC3ZA8u+vZ77e3dDrJUZ7HD2KIKzdx84i3rC1bMYruLereLrEWDHeQODFcHX/RCg3PK00AMByq0eohC/NlBuVWDvbxMHU20tcv7l/yFr2V9kDfZu3fDsb36LFrhx1Y9vQN/+/MOpAnoW0UogWeU20AkgvlhaDn0P88nj8mJPk9hStKxUrrkrH1f433zCtzxXfj6cRcVovvJqQGzd2Xq4s7IhXnPn5sGVlw+xfq/nNh+x3s5Tb28Cyq3eIpKc7aHcJmfclV5TblWIf2c7lFn37UGXB+/FblsTPpg9GwV1dbh1xkzYLpysQs0sggQ8BCi34Z8J5mNHzglvaSlMQnyl/HoEWPnlJdyS5TzgnC7+s4mtPTMyPf/T0+HObL3NyATEc5kZra+JW6//6Z7nXZkZQHoGXCJtjj636qbchnvGML0WBCi3WlBNnDIptyrEKpTtd9/8nz+i2mHHte+/j/O//RaNN96M2n99um0+rgrNYBFJTIByq03wzadPSeEVI72m6mqkVFfBVFONlMpKmGqq5HOe5yvP3fdZ0kyblp0rVUiuWBPYI83pHgkWsmw2ASaTXMHFneK5lf9NJrjFrfKcKcXzWKQ1mc/dV9KaWl9rLc+TtrUscd9i8eSzeJ7rkpOOmha3p97W1zz3lTwWTx3er1vEc0obW19XypV1tKY3W9r6oZQtb80m2e9uV0yBdfu3vKBM65MuAcqn3CZAkDRsIuVWBbjB5PbYkUP45IO3kZGRgV/VNCLv385tvycuOmu58mo0XTcH7swsFVrDIpKRAOVWX1FPqavz7Gff1IiUpmbPrXzcBFNjo7i6FCaxiUWzeNwEyHTivyeN539rnsamc2U1NyOlsTVdY4O+Oq2j1nC1BB0FI05NodzGCbxOqqXcqhCIYHL74TvLUXryGC6YdCnOv2CyHAnqsugRiJUVlEOs4dl07fVomvtTtFx+hQqtYhHJRIBym0zRbt9XU01NO3mW8tvSDDiccv3gFLdL3sLluU0Rty7lsQspymuu1te807bL25pWeU6kczhkWbIMseWuw4Hs1BQ0NLTI+56ynUgR6cTron6nuN/atrb7rWW3Ppb5vMtW+iLaLctS6mytQylb9BvgyG3yvh3aek65Te6TgHKrQvw7k9vKirN4+/WXYTZbcPv837Tbjczy/UFkLP8bMl9/FeLnT+UQV2833XQLGm/9ORxDhqrQQhZhdAKUW6NHOHH6F885t4lDiS3VmgDlVmvC+i6fcqtCfDqT27X/+BAH9+/ByDHjcfHUwCOyaRvWSdHNWPUeUrx+brSPGYemG29G/d3/R4WWsgijEqDcGjWyidcvym3ixcyILabcGjGqofeJchs6q4ApA8ltU1Mj/v7yC3C73fjpvLuQmZUdtDbxc2L6Rx8g442/I/0fH7dLL9bltI89H/YLJ8E24ULYxk+AWJKIBwlQbnkO6IUA5VYvkUjudlBukzv+lFsV4h9IbrdsXIcd327GgMHDMOOqa8OuSey+lPHuW3JurnXHd3Jene9hHz5SbjNpn3gR7OMnwj5seNj1MEPiE6DcJn4MjdIDyq1RIpnY/aDcJnb8om095TZaggD8ya3T6ZBb7drtdtxw650o6OrZgjeaw1qyD9ZdO2DZ/i2sO7cjVQivzxXTYlkgIbtiZLd51rUQa27yMD4Byq3xY5woPaTcJkqkjN1Oyq2x4xusd5TbYIRCeN2f3O7Z+S02rv8MPXv1wY9/cmsIpUSWxLK/BGK7X+vO72D97luk7toOsQyR7yF2U7IPH+V52mKGq7A7nN17wN29h7x1dfc8drU+jqw1zBUvApTbeJFnvb4EKLc8J/RAgHKrhyjErw2UWxXY+8qtmGP7xv/+GXV1Nbhq1hz0PW+QCrWEXoTl0EE5smsR0ru/BJaDByCeC+dwFXZrJ73O4l6ANbVDEfYJE+Xi6WEfYuF4sfi6xQq31QqYLZ5bi1js3QpYredeF89xbnGniCm3YZ+BzKARAcqtRmBZbFgEKLdh4TJcYsqtCiH1ldujhw/i09XvIC+/ADfd9ksValCnCLHcmOnsGZjPnIbpjOc25cxpz+PyM3I5MpO4X1WlToUsJSEINN52B6r/88WEaCsbqX8ClFv9xygZWki5TYYoB+4j5VaF+PvK7YfvLkfpiWOYMu1KDB81ToUaYl+E3HJUEWF5ewZoXSC9Q2tsLUixOzyLtjvsnlu7uLUjRSy+Lm8dgF3cKq+L9F7Pi8Xb7T75na3liOdjvKWp6KPYWAMpKef+iyflY8+t2/s15b540ev5DmnaymifThTqt7zWupQyZRqlDK+6LBYTnG7A7fVcp+3zakfz1bNQ/9t7Yn+SsUZDEqDcGjKsCdcpym3ChUzVBlNuVcDpLbdiKsLyV5bITRt+9ovfwpra8ad8FapkESTQjkAk0xKIkAS0IEC51YIqywyXAOU2XGLGSk+5VSGe3nK7Y9tmbPl6HQYOHo7pV81WoXQWQQLBCVBugzNiitgQoNzGhjNr6ZwA5Ta5zxDKrQrx95bblW+8goqzp/GjmT9B/wGDVSidRZBAcAKU2+CMmCI2BCi3seHMWii3PAcCE6DcqnB2KHJbW1OFN/72EqxWK+5Y8H+QYjKpUDqLIIHgBCi3wRkxRWwIUG5jw5m1UG55DlBuNT0HFLn97puv8c2mDRg8dCSm/WiWpnWycBLwJkC55fmgFwKUW71EIrnbwWkJyR1/jtyqEH9Fbt9evgyV5Wdw1Y9vQN/+A1UomUWQQGgEKLehcWIq7QlQbrVnzBqCE6DcBmdk5BSUWxWiK+RWmZKQmpaGn//yn5CiLNmkQvksggSCEaDcBiPE12NFgHIbK9KspzMClNvkPj8otyrEX8jtd1s34pvNX2LYyLG49PKrVCiVRZBA6AQot6GzYkptCVButeXL0kMjQLkNjZNRU1FuVYiskNu3X38ZlRVnMfO6uejVp78KpbIIEgidAOU2dFZMqS0Byq22fFl6aAQot6FxMmoqyq0KkS05XCpXSeCUBBVgsoiICFBuI8LGTBoQoNxqAJVFhk2Achs2MkNloNyqEM4PP14jpySMGH0+LrnsRyqUyCJIIDwClNvweDG1dgQot9qxZcmhE6Dchs7KiCkptypE9fn/ekFOSZg956coKu6tQoksggTCI0C5DY8XU2tHgHKrHVuWHDoBym3orIyYknIbZVQrKyvx/PPPIyMjE7f/4rdRlsbsJBAZAcptZNyYS30ClFv1mbLE8AlQbsNnZqQclNsQorly9Xo8+vRSmXLWjElY9MB8ZKSnysfr1q3D2rVrMWrcBZg8ZXoIpTEJCahPgHKrPlOWGBkBym1k3JhLXQKUW3V5JlpplNsgEdu6vQTPLlmBF5+6F/m5OfjDkhUyx30L58rbF154AWfPnsV1N/0M3Xv0TLT4s70GIUC5NUggDdANyq0BgmiALlBuDRDEKLpAuQ0CT8hs/z5FmDNzqkzpK7uLFi1CVnYOfjrvrijCwKwkEB0Bym10/JhbPQKUW/VYsqTICVBuI2dnhJyU206i2NRsw2PPLMWkCSPa5PbQ0VI8svglPPnwAgzsVwwht2PHX4QLL77MCOcD+5CgBCi3CRo4AzabcmvAoCZglyi3CRg0FZtMuQ1Bbm+aPQ0Txw2TKf3J7a9//Wv06NFDxbCwKBIgARIgARIgARIggUgIUG5DkNvORm6rqqqQn58fCXvmIQESIAESIAESIAESUJkA5TYI0GBzbkV2sf0uDxKIJwFOS4gnfdbtTYDTEng+6IEApyXoIQrxawPlNgj7YKslUG7jd/Ky5nMEKLc8G/RCgHKrl0gkdzsot8kdf8ptCPHvbJ1bym0IAJlEcwKUW80Rs4IQCVBuQwTFZJoSoNxqilf3hVNuVQgRpyWoAJFFREWAchsVPmZWkQDlVkWYLCpiApTbiNEZIiPlVoUwUm5VgMgioiJAuY0KHzOrSIByqyJMFhUxAcptxOgMkZFyq0IYKbcqQGQRURGg3EaFj5lVJEC5VREmi4qYAOU2YnSGyEi5VSGMlFsVILKIqAhQbqPCx8wqEqDcqgiTRUVMgHIbMTpDZKTcqhBGyq0KEFlEVAQot1HhY2YVCVBuVYTJoiImQLmNGJ0hMlJuDRFGdoIESIAESIAESIAESEAQoNzyPCABEiABEiABEiABEjAMAcqtYULJjpAACZAACZAACZAACVBueQ6QAAmQAAmQAAmQAAkYhgDlNsJQBtu1LMJimY0E/BJoarbhsWeW4sM1m+TrTzw4H3NmTg1Iy/v8VBL94taZuG/hXBImAU0J/GHJCvTvU9Tp+alpA1h4UhGoqqnDw//2Eh64+xYM7FccsO8i3V0P/RG79h1uS9OzR1csefr+TvMlFUwDdZZyG0Ewt24vwbNLVuDFp+5Ffm4OxIe5OCgOEcBklpAIeJ9jyof0/QvnYuK4YX7zC7ndtG0vFj0wHxnpqSHVwUQkEA0B7y9Uwb58RVMP85KAIOD9hT8USQ3lc5NkjUOAchtBLH1HJnxlN4IimYUEOh1x8B2ZCPaFinLLEypeBDhyGy/yyVlvuCO3nQ0KJCdBY/aachtmXJVvi5MmjGj72e3Q0VI8svglPPnwAv68ESZPJg9OwN/5FUxefaclcEpCcM5MoQ4Byq06HFlKaATClVtlWkIoo72htYCp9EiAchtmVBS5vWn2tLafhCm3YUJk8rAIiPPrmReWY/HvF8hpMOIIJrfeFSg/x82dPY3zIMMiz8SREKDcRkKNeSIlEKrc+pYvPkNXrFrbNr0w0vqZT58EKLdhxoUjt2ECY/KoCUQycuvvg/zI8VOcFx51NFhAMAKU22CE+LqaBCKV20jzqdl2lqUdAcptBGw55zYCaMwSMQF/H8LB5txSbiPGzYxREqDcRgmQ2cMiEKmkRpovrMYxcdwIUG4jLuUZUQAACINJREFUQM/VEiKAxixREehstQTfaQfi14W3P1yHG2ZdJldK4FXCUaFn5jAJUG7DBMbkUREIJKm+0w7E321xKCvMhDO1K6oGMnNcCFBuI8TOdW4jBMdsERHobJ1bf3NqhWD89fXVbXVxaaaIsDNTGAR8L2LkBTthwGPSsAn4fiaKAmbNmNS2/KGv3IrpXQsffBZlpytkXaOHD+B827CpJ04Gym3ixIotJQESIAESIAESIAESCEKAcstThARIgARIgARIgARIwDAEKLeGCSU7QgIkQAIkQAIkQAIkQLnlOUACJEACJEACJEACJGAYApRbw4SSHSEBEiABEiABEiABEqDc8hwgARIgARIgARIgARIwDAHKrWFCyY6QAAmQAAmQAAmQAAlQbnkOkAAJkAAJkAAJkAAJGIYA5dYwoWRHSIAESIAESIAESIAEKLc8B0iABEiABEiABEiABAxDgHJrmFCyIyRAAiRAAiRAAiRAApRbngMkQAIkQAIkQAIkQAKGIUC5NUwo2RESIAESIAESIAESIAHKLc8BEiABEiABEiABEiABwxCg3BomlOwICZAACZAACZAACZAA5ZbnAAmQAAmQAAmQAAmQgGEIUG4NE0p2hARIgARIgARIgARIgHLLc4AESIAESIAESIAESMAwBCi3hgklO0ICxiOwcvV6PPr00nYdGz18AF586l58/8NJzLvnKSx77iFMHDesXZo/LFmBLdtLZLr83Bx0Vk5ldR0WPvgsyk5XBAT4xIPz0ae4u6zP36G0Yev2Eplm1oxJWPTAfGSkp7Yl7+y1/7+9ewmNqwrjAH7W2lKJUmuhKhRRBN9Qi49ShaIUH1AwKi4lVt1pKDS6EBcSsFR3xVJUurLWlRTrqtKNkI2IinXT+qBSSheKGK24knPxhpmbeYXMlzPJ/GaVzOP7zvndG/jnzLkz+Um///Fnemn/u+m7H37sOo7nn92dbtyyqc0kj23P7h3p3C8XqnlcM7FhYd51oU6P1ePpNZ+1d0aZEQEC4yAg3I7DUTZHAqtQoBlQ6ynk+x+89/Yq0ObQevzE6bYwl4Pc67NH0lszU2nrDZvTIHVaeXLNua/OdAynM7NH0uG3p6u6nW51YLzu2qvbnnf5n3/TGwc+SJ+dmusYfLvVOnj4+KKgmp+b+zTHUgfYHNKbgT8bvP/RyVT/Y5ADf6caq/A0MWQCBAgsEhBunRQECIycQL2KOfn4zmpVstutDo2bNk6kV/dOpvr37ffcWr1u0DrDDLc5kD58/11p/q/L1ZjqMPrJidNp3bor0vz834uC87DCbQ71j+26L3175txCjxx6Dxw6lu6+7ab0xZdfL4Rl4XbkTnsDIkBgSALC7ZAglSFAYHgCzdDaq3K9Yjk7M5XOX7jUtpK7lDp1j+Wu3OZwO713Mh187+O21eO8neDn8xfTxUu/hYbb6RefTvUY6tXt3Df3b13lFm6Hd76qRIDAaAkIt6N1PIyGAIH/BZp7QlvfUm8i1W+75/ubb8kvpU5+fa9wO8ie23orwYfHPq+G+eSjD1Qrp7OvTaV8X3S4zdsxvvn+bLW14pUXnkpvvnM07Xv5meq+ZrjtNx8nIwECBFajgHC7Go+aMRMYI4HW/ap52s39rPm+evvBtjtvWdgK0CQapE6/cDvInts63OYL1fI2gXybfOKhaptEDuErEW4nrlpfXZy2Yf2V6eatWyqT5v5kK7dj9EdkqgTGTEC4HbMDbroEVrNAt20Gzb22/ebYa7vCMLYl1J/S0LyYbaXCbb7gLc/j0NFPFy5sE277nRUeJ0BgrQgIt2vlSJoHgTUkkFdi80di7dh+x6JZ5YCYb/XFWvnnbuF2qXWGuXKbP5Eg7wc++9Ov6ZGd26oxr2S4zXM/eWouPbdnV9VbuF1DfyCmQoBATwHh1glCgMDICdTbDK7fvLHt4qt6/2xzX22vcJvfnh+0zrDDbRN2JcNts7dwO3KnuQERIBAkINwGwSpLgMDyBDp9qUGn/ba9Vm7zY0up0y/c9rsAK4fvbp9NO6yV2+YXUrR+iUPr5/sOEm77zWd5R9CrCRAgUEZAuC3jrisBAgQIECBAgECAgHAbgKokAQIECBAgQIBAGQHhtoy7rgQ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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": [ "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", "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": "02d8a758-89b1-4c28-94c9-c73b11f3b8dc", "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": "e8fe3554-d5ab-4306-b890-4e36289b5b4b", "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`
\n", "
" ], "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": "ad01c472-3ebe-4d0d-8913-1bcd85ea7a6c", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 26, "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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IgARIgASihgDlNmpSzYaSAAmQAAmQAAmQgPUJUG6tn2O2kARIgARIgARIgASihgDlNmpSzYaSAAmQAAmQAAmQgPUJUG6tn2O2kARIgARIgARIgASihgDlNmpSzYaSAAmQAAmQAAmQgPUJUG6tn2O2kARIgARIgARIgASihgDlNmpSzYaSAAmQAAmQAAmQgPUJUG6tn2O2kARIgARIgARIgASihgDlNmpSzYaSAAmQAAmQAAmQgPUJUG6tn2O2kARIgARIgARIgASihgDlNmpSzYaSAAmQAAmQAAmQgPUJUG6tn2O2kARIgARIgARIgASihgDlNmpSzYaSAAmQAAmQAAmQgPUJUG6tn2O2kARIgARIgARIgASihgDlNmpSzYaSAAmQAAmQAAmQgPUJUG6tn2O2kARIgARIgARIgASihgDlNmpSzYaSAAmQAAmQAAmQgPUJUG6tn2O2kARIgARIgARIgASihgDlNmpSzYaSAAmQAAmQAAmQgPUJUG6tn2O2kARIgARIgARIgASihgDlNmpSzYaSAAmQAAmQAAmQgPUJUG6tn2O2kARIgARIgARIgASihgDlNmpSzYaSAAmQAAmQAAmQgPUJUG4V5Ph4XoWCKAyhB4F2WYnILaqCw+nSIzxjhkkgzh6DzNR4nCmqCjMSD9eLQEZKHGodLpRV1upVBOOGSUB8zon3kJOfc2GS1Ofw+Fgb0lPi5L9FHVsl6VMIozYgQLlVcEJQbhVA1CkE5VYnsIrCUm4VgdQxDOVWR7iKQlNuFYHUKQzlViewTYSl3CpgTrlVAFGnEJRbncAqCku5VQRSxzCUWx3hKgpNuVUEUqcwlFudwFJu9QVLudWXbzjRKbfh0NP/WMqt/ozDLYFyGy5B/Y+n3OrPOJwSKLfh0AvtWPbchsatwVGUWwUQdQpBudUJrKKwlFtFIHUMQ7nVEa6i0JRbRSB1CkO51Qkse271BUu51ZdvONEpt+HQ0/9Yyq3+jMMtgXIbLkH9j6fc6s84nBIot+HQC+1Y9tyGxo09twq4GRGCcmsE5dDLoNyGzs6oIym3RpEOvRzKbejsjDiScmsE5YZlUG4VMGfPrQKIOoWg3OoEVlFYyq0ikDqGodzqCFdRaMqtIpA6hTFKbj9YtgYbvtuOpx6egaTEeJ1ao3/YgqIS3P/oX/HQzMkYMrhPSAVSbkPC1vAgyq0CiDqFoNzqBFZR2GiX26rKSlSUl6Fc/JWVytuqygo4nQ44HE5563Q44JC3TjgctXA4HO7nnS75WLyu7a891vavra2pz1RsbBxsdhtsMTbY7HbY7XbYbHav52IREwPYbDb3azYb4uPsiImxweGCPEbcl6/H2BAj94up31fE1Z632231+8r96vYXz5891r1P6zbtkJCYqOisir4wlFtz51yV3O47dBwzH3keJ07l1Te4Q7tWmPPsQ+jRtSMiJbcVldV44rlX0b5tNh6cOTnsZFBuw0aoJgDlVg1HPaJQbvWgqi5mNMhtRUU5iosKUFRYgKKCfPdtYT6KiwrhKZ/qqLa8SIMuGIqhl4xpeRU3SY0ptyZJhJ9qqJBbIa6PP/sq5v3t0Qa9mZu27MS7S1bJ3tpPVm5gz21dDthzq+A9QblVAFGnEJRbncAqCmtVuRUyu3f3DuzZ+ZMUW3+b6E1NTkl1/yWnICk5BYlJSYi1x7p7VG0Ne1jt4nFsbH1PqaI0NAjjcrnqeoadcDmdSIy3oaamFhVVtXC63M+J3mOXS/Qsu+Rj8bzWwywfOxvGcL8unnfv697HidraWpw8fkS2+44ZP9ejOVERk3Jr7jSHK7daj+3sWfc2+TO91nM74cqL5c/6YvPs2dUoefcA/+y2a+t7XIUsPz9nIe6+9Wo8+OTLDWJs/WmvFGyxDezbHa8881tkZaRB67kdfmE/TLp2VH0yNCHXntDK8dUD/fQjM+qPZc+tSc5nyq1JEuGjGpRb8+ZG1Mxqcrt313Zs++E7nDl1oh683R6LVm3aIrtVG2S3ao3WbdujVeu2EGLbEja9x9y+8++58gvA9TffgbbtO7YEJKarI+XWdClpUKFw5VZI4sIlq+pl0l9rNZn0lNW/zFmIk6fz68fhCrH8/ey5+OOse+VQBu8hBUJup//mGXjH+Nf8ZY2eE/UQwxB8ya13ncU+7y9djZvGj8bxU7lYsfY73HfHRNkUb3mn3AZ4PovkisRom+c3BPGcBvLHHfvlLt7d/p7fPsaPHd5osDblNsBERGA3ym0EoAdRpBXkVgw72LFtC7b/uFmOnxVbekYWunTrIf865XQNgoj5dtVbbrd+/w2++XqVZDVuwk3mA9ACakS5NXeSwpVbb0FtSm69LyjTemK1XlYRq1tO+wY9rJ777D1wTPbcavuLsrxjeD+XmJAgx9xqPbehyKlnvUI53puJ5YcliG8Lr7z+Ee6eco3sPvf+huD9jcP7W42vE0P7tqLBpNya94OFcmve3IiatWS5LcjPxdbvN2Lf7p3yZ3yxde7SDQMHD0HnLueYG3wQtdNbbsVFdW+++pJkOOWu+5CWnhlE7birIEC5Nfd5YBa51SR06YoNjYBpwwxUyK3wqOdeXoDZj90rvcvXpvUQe76m9RZTbkM4n33JrGcSvF/3/pbj6xsM5TaERBh0COXWINAhFtMS5VZcEPbV6uU4duRQfav79B8kpTYzKztEEuY9TG+5FS1ft2q57P0eMOgiXDzycvPCMGnNKLcmTUxdtcKV22CGJTTVc+vdw+pPOsPtuW1OboVXLVu5sX6WB1EP8ZzYxDAHym0I57M3NF+yqkG+f9oNDbraRXHePbviOcptCIkw6BDKrUGgQyympcmt9hO6aK64CGrAoAshxDYxMSlEAuY/zAi5LcjPw3tv/wvx8fG4/e4HEBfXcufojERGKbeRoB54meHKbVMXlHmOZfU1W0Igvz57tqS5IQhaT6znfsEMS9A6EG+ZOKbBxXGU28DPJ597egIUO3hOo6FNeuwtt55J8CW34spgbuYkIObsdDE95kxOXa1aQo7EVf1LlizGtm3bZK3Hjr0CQ4YMQVyc74vCqmudEP+gWWET+RGb3u+jN9/8Nw4cOICrr75GsuUWOIGW8B4KvDXW3FPLkZgXOpTN11RgWmddl45t/U4F5i2r2nAA79kJXlvwCUSH3rad+8MecyvaJzzqmy07G8yoIC4ou3bsxXjm7282mBPX+yI29twGeYb4GpStouf2RH5FkDXh7kYRaJuZiLziKjj4BcQo5EGVI3puM1LikVtcFdRxRu4sFlf4ZPF7yMs9LRcauHrCTWjXoVOTVRAiqEmhkXXVo6z05DjUOlwor6rVI3x9zMMH9+HTJe8jPT0TU6bdp2tZVgsuPufEe4gdLebMrPiim5YcJ/8t6pAd+q88vqbQ8pzVwNciDr4cp6mpuFT03GpZ8L6Y33tMrXYRv3he2zgsIchz2N/Vht5jQzjmNkiwJt+dwxLMnSCzD0vIPX0Sny55D2JGBDGe9trrb0VKqu8LJMxNOvTaGTEsQavdgjf+gZLiQowbPwldzukZeqWj7EgOSzB3wsMdlmDu1pmzdpafLUHrHhe3vpaF42wJ5jwxVdWKcquKpD5xzCy3u3duw9ovP5OLE+R07Y6xV18XlWNBjZRbMZ3aV6s/R6ecbrj2+vCX8dTnrDVfVMqt+XLiWSPKrfH5sbzces9hqyH2nK+W89waf+IZVSLl1ijSoZVjVrndtvVbrF+7UjbqvAuGYlgULw1rpNyK5Yjf/NeLqKmpwS1T77Hk7BOhvVOaPopyqwdVdTEpt+pYBhrJ8nIbKIhw9uNsCeHQ0/dYyq2+fMONbka5FUvmrvpiqWya6K3t3rNPuM1s0ccbKbcC1MavvsQPmzeh74DBGDHmqhbNzqjKU26NIh1aOZTb0LiFcxTlNhx6dcdSbhVA1CkE5VYnsIrCmk1uiwrz8f78eXA4anH5uIno0auvopa23DBGy21pSTHmv/5/yMxuhesmTZUX8XFjz21LPgcot8Znj3KrgDnlVgFEnUJQbnUCqyis2eT2/fmvIT/vDHqe2w+XXTlBUStbdhij5VbQWrPiE+za8SO6de+FK6+9sWUDNKD27Lk1AHIYRVBuw4AX4qGU2xDBeR5GuVUAUacQlFudwCoKaya5FWNsxVjbjMxsTJoyDbGxvuewVdT0FhMmEnJbUV4GMXOCGIM7bsJN6NKtR4vhFYmKUm4jQT3wMim3gbNStSflVgFJyq0CiDqFoNzqBFZRWLPIrVhKd9mid2Cz23HTrdPlT+Lc3AQiIbeiXLEcr1iWNykpGbfedV9UzlQR6DlIuQ2UVGT2o9waz51yq4A55VYBRJ1CUG51AqsorBnktrKyAu+++U+I20tHX4l+A89X1DprhImU3Ap6H77zOnLPnOLFZc2cSpRbc7/XKLfG54dyq4A55VYBRJ1CUG51AqsorBnkVvTYip7brt174SqO72yU2UjKbUFeLt5f8BpcLhduuOVOtGnXQdGZZ60wlFtz55Nya3x+KLcKmFNuFUDUKQTlViewisJGWm5/2PwNNn61Sq46JuZVjYvjOFvv1EZSbkVdNq1fgy3fbUB6RhZuuX2GHDrCrSEByq25zwiryq2v5X61dQMemjkZQwZHbhpFyq2C9wTlVgFEnUJQbnUCqyhsJOW2qLAAC9+cK1vCXkH/CY203IqaLXh9DkpKinD+RRfjouEjFZ191glDuTV3Lim3xueHcquAOeVWAUSdQlBudQKrKGwk5XbJB/Nx8vgRjudsJpdmkFvtgj9R1Ztvm4GsVq0VnYHWCEO5NXceKbfG54dyq4A55VYBRJ1CUG51AqsobKTk9vjRw1j60QLEJyTgtrv+Q95y803ADHIrarZy+RLs270DHTt3wdUTb4bdHsuU1RGg3Jr7VFAmtwcPAuLP6K1bN0D8eW0clmB0Igwuj3JrMPAgiqPcBgErArtGSm4/WbwQRw8fxOALh2PIxaMi0PKWU6RZ5LaqshIfLnwdJcVF6N13AEaPvbblQNS5ppRbnQGHGV6Z3D75JPDUU2HWJoTDn3gCEGVTbkOA14IPodyaN3mUW/PmRtQsEnIrViATK5GJ7c57fonExCRzQ4pw7cwitwJDSXEhPlz4BoTontvvPIy6/OoI0zFH8ZRbc+TBXy2Uye28ecDrrxvf2GnTgOnTA5bbWX+ai4cfmIIeXTsaX9e6EjksQQF6yq0CiDqFoNzqBFZR2EjI7crPlmDfnh1yPlsxry23pgmYSW5FTQvz87Do/TdRXVWFHr37ymWSY2JiojqNlFtzp1+Z3JqsmZu27MS7S1bhqYdnICkxXtZu36Hj+P3sufjjrHsptybLV9DVodwGjcywAyi3hqEOqSCj5ba8rBRvz3tF1lWsepWWlhFSvaPpILPJrSa4Sz54Wy680fWcnrjimhtgs9miKS0N2kq5NXfqrSq32rRfkyeOwaRr3cO7/jJnIU6ezm8gvJHIDntuFVCn3CqAqFMIyq1OYBWFNVpuv17zBX764Xv07N0Pl101QVErrB3GjHIriIup3Ba/96YU3M5dzsHVE25CTJQKLuXW3O9Bq8qt1lM785HnceJUnkzC+LHDIy62oh6UWwXvCcqtAog6haDc6gRWUVgj5VaM03zrtZfhcNRyOqkg8mdWuRVNKMjPw9IP56Oiohzt2nfCZeMmRGVvPOU2iBM6ArtaWW4jgDOgIim3AWFqeifKrQKIOoWg3OoEVlFYI+V287fr8e2GtejSrQfGTbhJUQusH8bMcivoFxbk4+MP3paCGxcfj3Hjb0KHTjnWT4xHCym35k435db4/FBuFTCn3CqAqFMIyq1OYBWFNVJu//3Pv8ufsK+7ears5eMWGAGzy61ohZhFYcWni3Hm9EnZKDFMYfiIy5CVHR2LPVBuAzuXI7UX5dZ48pRbBcwptwog6hSCcqsTWEVhjZLbHdu2YN2q5VJqhdxyC5xAS5BbrTXfbVyH7zd9Xd+4nr374sJhI5Db1WNAAAAgAElEQVSekRV4g1vgnpRbcyeNcmt8fii3CphTbhVA1CkE5VYnsIrCGiW37739Kgryc3HlNTegW4/eimofHWFaktyKjJSVluCb9auxd9f2+gRZfdo3yq2534uUW+PzQ7lVwJxyqwCiTiEotzqBVRTWCLnVFm0QS+xOu/fXimoePWFamtxqmck9cwrr16zAyRNH65MlFn44t99AZGW3QXy8e15OK2yUW3NnkXJrfH50lVttDrQfd+xv1LKBfbvjlWd+i6yMNONbrbhEyq1ioArDUW4VwtQhlBFyK36mFj9Xn3f+EAy79DIdWmHtkC1VbrWsHNi3S+ZfzKzgubXv0Bk53bojp2t3tGrdtkUnkXJr7vRRbo3Pj65yKybzFduDMycb3zIDS6TcGgg7yKIot0ECM3h3I+RWG5LAC8lCS25Ll1ut1aIHf9/uHTh0YK8couK5JSUlo3PXc9CjV18puy1to9yaO2OUW+Pzo5vcil5bM6wvbARSyq0RlEMrg3IbGjejjtJbbktKirDg9TlISk7BHTN+blSzLFWOVeTWMyliXO7hg/tw5PABHD9yCDU11Q1yFhcXh1at26F12/bo1r1Xg9dsdhvi4xIghrnExSeYYnhDoHIr5nh2Op1wuQDxfy6XC06Xs/5+48fiJRdc4hjxX90x8rG4rz3n9HhNPKe9LgqqK0M7FvIpd7nitr4edcegLqazLqZ8HS53vZ3O+oU6xJLL2rLLMXDfF81yP+9Omec+8klXw+e8X/eOVxfEZ7zGZboLbRCzrl7icy4lKQ7F5bW48DyO+TfiA5Jyq4Ay5VYBRJ1CUG51AqsorN5y+8PmTdj41ZfoO2AwRoy5SlGtoyuMFeXWO4OnTh7D0UMHcPzYETmtmJDfYDYhuvFSdIX0JgZ8qKc0Sgn0kMazj90yKMys/nUvaRRapclgbW1NwOVzR+MJPPHEE8YXGoUl6ia3gqUYltAtp339msNW5Uu5NW9mKbfmzY2omd5yu+i9N3H65HFcc91kdO7SzdwwTFq7aJBbX+iF4Iq/8vIyVFVWoLKiQi4UUVlZLu9XVVWiotz9uKa6Yc+vSVMpqxUbG+fu8RT/i4mBLcZW99jd+2mz1T2u63UUu4rnRPel1ltZ/1h7ru4YGVb2nLpj1P+J1+vjucvWyhHPi9i+H8uu0Ab1dIt+XY+y7Kutk//657UvAx7Pi05bz+M87ru7sWV/caN9xJcG9/eIxmVqPc71dfGOWVemONYm2wfU1Dpx3z0zzHx6BFy3ispqPPHcqxh+Yb8Gjrdpy07Mmj0Xc559CD26dgw4nuoddZXbfYeO460PvsDD909BUqJ1rkz1TgLlVvVpqS4e5VYdSz0i6Sm3FeVlePPVl+SqVdPv+40e1Y+KmNEqt8EmV5xvbumt0HypyRDyp3NNADXxq5fEOpEMUBrbZiUir6Ralisk0W6PDbb63F9HAlYdc+s9/FSbROChmZMxZHAfHYk2H1o3uW1qpgRRLc6W0HxyuEf4BCi34TPUM4Kecrv9x834avXn6Nm7Hy67aoKezbB0bMqt+dMb6Jhb87fEmjW0qtyKbIme2neXrMJTD8/AJys34OCRk6aYREA3uTXjKfrBsjU+wYvhE/+av6xBlZ9+ZEZ9V7s47vFnX5Wvjx87XCbRsyeaPbdmzLa7TpRb8+ZG1ExPuV360Ts4fvQQrrjmBpzDhRtCPhEotyGjM+xAyq1hqEMqSJXcHiw8CPFn9NYtsxvEn79NOFRpeSWOn8zF7MfuNcUUr1Eht+KbxfTfPCPz8rPbrm30raKpKcvEsc/PWVg/J6+vfSm3Rr/VAi+Pchs4q0jsqZfcVldX4425L8grq6ff92v+TBtGcim3YcAz6FDKrUGgQyxGldw+uepJPLX6qRBrEfphT4x+Ak+OedJvADMNR9AqqbvceoqlVui8vz0akfEYTfXcirr5mo/X+6I4b9kVx1FuQ3/T6H0k5VZvwuHF10tu9+zchlVfLEPXc3riqvGTwqtklB9NuTX/CUC5NXeOVMntvC3z8PrW1w1v7LRB0zB98PQme2537TuCopIy0yzOpavc+hJBcZHZzEeexwPTrjd8FoVAhyVoQxJ8XQ0o6v/72XPxx1n31l8JSLk1/L0WcIGU24BRRWRHveR2+dIP5GT9Y664Fr36DIhI26xSKOXW/Jmk3Jo7R6rk1oyt9Bxz+8rrH8kqmmHhLt3kVhPDWyaOadRL6wnDyFkU/Mmt5wmjyffsWfdiQJ/ucqoLzzb4ktv8kpYzDYwZ3xx61ikzNR7F5TVyDkhu5iMQaxOTm8eiqEzd3JyO2lrMeekvck7Q+37+Wzn3KLfQCaQkxsLhdKGy2hF6EB6pKwF+zumKN+zgsfYYJCfGorisBtlp1pk5KmpnS/C3QpkQxOdeXmD4wONA5FacxdpQhGsuH95oHjdfcssP/bDf+7oFSIizobpGrK7DzYwExHRIcXYbqmudyqq3c+cOLPrwfXTt1g1TbrtDWdxgAgkZtNvqlkkK5kAT7iv+YRZTTIk2cTMnAfE5V1Wj7j1kzla23FqJeW7F+0h8ziXG21tuQzxqHrXz3LbUnltPuZ107ahGC1FwzG3Lel9yWIK586XHsIQvl3+Mvbu349LRV6LfwPPNDaAF1I7DEsyfJA5LMHeOrDwswazkdRuWIBosekoXLlnVYICx2cbcim71ZSs2YOqkK2WOvHtmOVuCWU/dwOplFbmtqqyUk8O7b6s87lfC6TD+52Kb3e5e2chmg83mXpFITB4vVxkSt/I1bdUhj9fq9pMrGdlsstc2LTkeReW19asZiWPdk9s3vTKS937axPXz/vE3uWLU1LsfQHJKamAnCvfyS4Bya/6Tg3Jr7hxRbo3Pj65yK5pjhtkSmqqD1sO8dMWGevreszlwnlvjT0xVJbY0uS0vK0V+Xi7yzpxCft5p5OWdQUFeriocURMnMysbt0y9J2raq2dDKbd60lUTm3KrhqNeUSi3epH1H1d3uTW+ScaXyNkSjGceaIlmltvCgnycPnUc+blnkJd7St5WVlb4bFpcXBwSEpOQkJCIxKQkxMcnIiExEYmJSe513w3exMVaLpdTXqh39r4TLqcTTlfdrXit/r62v/sYMYhTvCZu7XVrrrvjiHGdWkxtTXftsXvtd1FG/TrwIo7T/bzDUVtPof/AC3DJ6CsMpmLN4ii35s8r5dbcOaLcGp8fyq0C5pRbBRB1CmE2uT1z6gT27dmJwwf3oagw32er27bviKzs1mjdph2yW7eRt7GxcToRimxYPcbcRrZF1iudcmv+nFJuzZ0jyq3x+aHcKmBOuVUAUacQZpHb40cPY/O3X0Pcem6du3RD6zbt0bZdB2Rmt0ZGZpZOJMwZlnJrzrx41opya/4cUW7NnSPKrfH5US632jJsd996NV5751P8uGO/z1YN7NvdNCtZhIudchsuQf2Oj7TcHjtyCN9/8xVOnjha38gevfrinJ69kdO1u2V7ZAPNKOU2UFKR249yGzn2gZZMuQ2UVGT2o9waz1253GpN8J7c17NpkVrEQS+8lFu9yIYfN1JyK6T2u43rcOrkMdkIm82O3n0HYPBFw5GWlhF+wywSgXJr/kRSbs2fI8qtuXNEuTU+PxGR20gt4qAXXsqtXmTDj2u03IoxtetWLUfumVOy8nFx8eg3cDAGnj8USUnJ4TfIYhEot+ZPKOXW/Dmi3Jo7R5Rb4/MTEbkVU2tt+G47nnp4BoxcflcvvJRbvciGH9dIud349Sr88P03stJiFoPzzh8qFxGIi7fOcovhZ6RhBMqtaqLq41Fu1TNVHZFyq5qo2niUW7U8A4mmXG61RRpOnMrzW36Hdq0w59mH0KNrx0DqaPp9KLfmTZERcisWVvhkybsQvbbx8fEYPuJy9Dy3H7RFBcxLJ/I1o9xGPgfN1YBy2xyhyL9OuY18DpqqgVXl1tcaAuPHDjdFx6VyudUS3NSYW3OfhsHXjnIbPDOjjtBbbktLirFs0TsoKixAWnomJtw4Balp6UY1r8WXQ7k1fwopt+bPEeXW3Dmystw+P2dhg8kB/jJnIb7ZsjPiEwboJrfmPtXU1o5yq5anymh6ym1e7mks++gdufCCmJd2/I1TOK42yORRboMEFoHdKbcRgB5kkZTbIIEZvHs0ya1AKwRXbA/OnGww6bPFUW4VoKfcKoCoUwi95Pbk8SP4ZPF7qK2tQbv2nXDN9ZMhVhHjFhwBym1wvCKxN+U2EtSDK5NyGxwvo/dWJbeFhYUQf0ZvmZmZEH/emxiW4N1zK/bx97yR9dZVbpsaf8t5bo1Mc/SWpYfcHti3Cys+WyKXge3WozfGjpsop/riFjwBym3wzIw+gnJrNPHgy6PcBs/MyCNUye2qVauwevVqI6suyxo9ejTGjBkTsNyaYUYs3eS2orIaTzz3KoZf2A+D+vfEWx98gYfvnyJnRxBd1iOHnYchg/sYniQ9CmTPrR5U1cRULbf79+7Eik8Xy8r1HTAYI8ZcpaaiURqFcmv+xFNuzZ8jyq25c6RKbrds2YKtW7ca3thBgwZh8ODBAcutpXtuPS8oE0See3kBZj92L7Iy0mSX9btLVpniijoVZwnlVgVFfWKolNvTJ49j0XtvyooOu2QMzrtgqD6VjqKolFvzJ5tya/4cUW7NnSNVcmu2VvqTWEuPufWU2+zMNMz+37cw61dTpdyaocta5UlCuVVJU20sVXIrxta+99arKCkpwoBBF+HikZerrWiURqPcmj/xlFvz54hya+4cRZPcWn62BM9hCZOuHSWHInTLaQ9xn4s4mPuNaKXaqZLbr1Z/ju0/bpbTfd0ydQbnsFV0klBuFYHUMQzlVke4ikJTbhWB1CmMleV2+m+eaUDN8vPcep8joif3/kf/ih937AcXcdDpHcSwjQiokNvjRw9j6UcLZOwbJ9+F1m3bk7QiApRbRSB1DEO51RGuotCUW0UgdQpjVbnVCZeSsLpdUKakdi0kCIclmDdR4cptdXU13n3rnygvK8XA84dg+KWXmbexLbBmlFvzJ41ya/4cUW7NnSPKrfH50U1uuUKZ8clkiY0JhCu3q1d8gt07fpTDESZP/Rlsdk75pfI8o9yqpKlPLMqtPlxVRqXcqqSpPhblVj3T5iJSbpsjFMDr7LkNAFKEdglHbo8ePoBPFr8ra87hCPokkHKrD1eVUSm3KmnqE4tyqw9XVVEpt6pIBh5HN7kVVbDafLb+sFJuAz/hjN4zVLmtqqyUwxEqKspx3vlDMezSxhNYG90WK5ZHuTV/Vim35s8R5dbcOaLcGp8fXeVWTPnluXiD8c0zpkTKrTGcQyklVLn9es0X+OmH75GZlY1bpt4TStE8JgAClNsAIEV4F8pthBMQQPGU2wAgRXAXyq3x8HWTW8/ZEXw1i8vvGp/saCwxFLktKy3B2/NekbgmTZmOVq3bRiM6Q9pMuTUEc1iFUG7DwmfIwZRbQzCHXAjlNmR0IR+om9yGXKMWeCB7bs2btFDkdv3aldi29Vv06tMfY64Yb97GWaBmlFvzJ5Fya/4cUW7NnSPKrfH50U1um5otgcvvGp/oaC0xWLmtrqrCm6++BIejFlOmzURaWka0ojOk3ZRbQzCHVQjlNix8hhxMuTUEc8iFUG5DRhfygRGRWy6/G3K+eGCQBIKV283frse3G9aiS7ceGDfhpiBL4+7BEqDcBkvM+P0pt8YzD7ZEym2wxIzdn3JrLG9RWkTklsvvGp/oaC0xGLl1Ohx467WXUVlZgfE3TkHHTl2iFZth7abcGoY65IIotyGjM+xAyq1hqEMqiHIbErawDlIut6JXduYjz+PEqTy/FePyu2HljAcHQSAYud3x01as+/IzZLdqg5tuuzuIUrhrqAQot6GSM+44yq1xrEMtiXIbKjljjqPcGsPZsxTlcqsF5wplxieTJTYmEKjculwuvPPvf6CkuAhjrhyPXuf2J04DCFBuDYAcZhGU2zABGnA45dYAyGEUQbkNA16Ih+omtyHWp0UextkSzJu2QOV2/95dWPHpIiQlJeP2ux+AzWYzb6MsVDPKrfmTSbk1f44ot+bOEeXW+PxEldyKsb4Hj5zEgzMnNyDtPSfvvL89iiGD+9TvI457/NlX5ePxY4fjqYdnICkxvv51yq3xJ26gJQYqtx8tfANnTp/E0EtGY9AFwwINz/3CJEC5DROgAYdTbg2AHGYRlNswAep8OOVWZ8A+wusqt00t5GDkIg5i6rHpv3lGNv9nt13bQG4rKqvxxHOvYviF/TDp2lEQY4Z/P3su/jjrXvTo2hHi2OfnLMQrz/wWWRlpcklhsXkKMuXW+BM30BIDkdvjxw5j6YcLYLfH4s57fom4uLhAw3O/MAlQbsMEaMDhwcptSXUJSqqLUFJVjJKaYpRUF6O4qqjuthgl4n7N2efKakqRnpCJ7MRWaJXYGq1T2iA7sTXaJLdD/9bnISsx24BWtuwiKLfmzh/l1vj86Cq3vkTQ+CaeLdFXz633tGTesiva0C2nvRRfsXnLrniOchvJrDZddiBy+8Uni3Bg3y70P+9CXDJqrHkbY8GaUW7Nn1Qht3nlBdidewCnyk7gYOF+HCs5jKMlR3C6/BQKq/LdIlvt/lO99co6F+e3H4KhHS/Fhe2GoXf22V/VVJfVUuNRbs2dOcqt8fnRTW7NeEGZL7n1JaualN8/7YYGvboiPd49u5Tb8E7a2toaOGodctEEh9NRf19MyyWec7nCi5+VFo+ismo4nb7jOJ1OLFv0jnxx6t0PIDklNbwCeXRQBCi3QeHSbeeTZcdxvOQojpQcwrGSozhacghHiw/jaOlhHC89KuU10C0pNhlp8elIT0hHWnyG+zYuA2nxaUhLyEBqnP/3mAsu5FfmIa88FwVVeSitLsXW0981KDozMQtD2l+MYZ1GYGiHi3Fhew4jotwGenZGZj/KrfHcKbdbduLdJasajKP1lttbJo6pH4PrLbePrXgMvxryIMQHrtW32tpaOQdsVWUVKqsqUVlRIW/l48pKVFSUy/sVlRUQK33V1NTUCWstxLG1QmKlwNbK18y09ezVGzfd3HAstpnqZ9W62GKA2Fgbqmv8fPsIsuExp0/B/tprQFEhav/kHooUic3pAkTbzLLtyd8je1oPFR3C0aLDOFh4EEeLxeODOFh0sNlqJsYmIic9B10zuqFzWmd0zTwHORk5yEnvgsyETKQnColNk0MLVG9lNWX46sharDr4Jb48tBJbTm5uVMSInJEY0WUkruw+Dpd0vlR1FUwfLyHOhupaZ9idAaZvaAutoM0Wg1h7jPycS4y3t9BWtKxq6ya3AoP3T/qRRqNHz23MUzH49ZCH8V8j/xDp5oVdvpDOoqJCFBcXobioEEWFBXX33Y+rq6vCLsM7gD02FrH2WNjsNnl79rEdsXGxYZcXa7fB4RD9QU13AQ8Zdim6dD0n7PIYIDgCdlsMUhNjUVSu5stO/JJFSJ3q/pJSuvBDVF99bXAVUrS3mFouJsZYuy2uLsKO3O3YnbcTu/N3YFee+09IbXObGNfaLaM72qd2kMIq/jrX3fZq0w2tE9qhssbRXBhDXi+qKsTaw6uw7shqrDnypWyj55Yen4GRXcZgdNfLMSrnMvTKPteQekWykMxU8QtVDcR5x818BITYJifEori8BtlpZy9GN19NrVMjXeVW9HK+9cEXePj+KQ1mF4gUPj3G3Aq5TbQnYeP0nWid1CZSTQup3KrKSpw4dhjHjx3ByeNHkJd7utk4iYlJSJB/iYiPT0BCQiLiE9y38vm6+/EJiYiNFdJqr5NWO2w2u5RXceGWURdtBTLmttlGcwfdCKgelpD48SJkT79N1tfRsRNOr98Ml0WHmmw6uR7rj63F+qNrsCN3G85U+H//dkjthM6pXdApLQdd0ruhY1pn5GR0Q8eUTuiS0U1+hvnbgr2gTLeTxU/g3Ioz+OroKqw6/Dk+2/8xhPx6bjnpXTE65wpcmjMaozqPteSvbByWYPRZF1x5HJYQHC8Ve+smt03NlCAqbuRsCRooX3Ib7mwJV/77Snyx/wvcM+gXeGrksypyoluM8rJSnDh+BCfqZLYgv/Eqcqlp6UhLz0RaWjrSM7OQLu6nZ8i/pOQU3eqmV2DKrV5k1cTVU25FDctm/hxFf3xOTWUjHGXzqU1Yf2wd1h1diW+Or0dFbXmjGomLr3pl98W52X3RK7sPemadK2ccCGczu9x6t23LqW+x7ugqrDmyAl8dXd2o6QPbDMbInMvl36icy8NBY5pjKbemSYXPilBujc+PbnJrfFP8l+g5FZi2l+dctuHMc/vt8W8xZO4QGfa7u/eifUpH0zRdXJB1YN8eHDm0DyePH0VpScOLQkQvbNv2HdG+Q2e0adcBbdq1R1yctX4yodya5nT0WRG95RYxMTjzxTrUDDrf3CB81O6HM5ux/tgarD38Jb458TXElFmem/isuaTzKFzaeYy8qEqIrR5bS5NbTwZVjkpsPP411h5ZgdWHV+Cn3B8aIRqZcxlG5VyBETljcF6blneeiAZRbvU489XFpNyqYxlopKiQ20BhhLrfuDcmYPmBpZjafwaevezFUMMoO+740cPYuX0rDu3fCzEbgba1btNOymy7Dp3Rtl17pGdY/yI4yq2y00qXQKrlNmnpYmRNm4KKCdfD2TkHKf/3Imr69sOZVRsBu7kv5DhachjLDy7FusNfYv3xtXJuWM+tTVJbXNxplJQwIbXnZPTUJSfeQVuy3Hq3pbCyAGuOrsBXR1Zj5aHP5EwQnpsYe3xppzGS8RXdroEYztESNsqtubNEuTU+P7rKrfaT/9IVG9ChXSvMefYhdGzXutH0WsY3W22JX+7+DpfPv0gGXT9tO7qkdVNbQIDRTp44io1frcLpk8flEWJsa/de56Jn7/7o0KmzfBxtG+XW3BnXU24LX5yLtkMHwn76FIqe/jPK7v+l6WCsPSJmAFiOLw4uw77CPY1Ea3inkRjZ+TIptZGa39VKcut9Ahws2geRg9VyCMOqRl8ouqZ3x5iuV2BE5zFyGIOY4syMG+XWjFk5WyfKrfH50VVutdkSrrl8OJ57ZQGmTrqiftUv7+m3jG+6uhLFIg4//2w6PtqzEDf3uR0vXPFPdcEDiFSQnyul9sih/XJvMTZ2yPCR6NG7L2Jjo3u1LcptACdQBHdRLbfaBWWV469D/usLkLjoA2T/7A64EpNw+psf5EVmkd7EcIN3t7+Jd3e91WjRg0s6jcJV3cfLoQb9Wg2MdFVl+VaWW2/AYrzu2qNfyiEMYkiI9zao7YUYnTMWI7tcDpErs2yUW7Nkwnc9KLfG50c3ufVcxEH01nrKrfeqYMY3W22JQm4PFe/HJW8MkIFXTd2s2/g3z5oXFxVg0/q12L93p3xazFpw/oUXo/+gC6Kyl9ZXVim3as911dH0lltR31Y3XI2EdWtQddkVyHt3seomBBRP/Bz+3q63MP+n17Ez/6f6Y8S8sFedMx5ju12N0V2uQEoTCxwEVJAOO0WT3Hriq3RUYMPxr7Du8Eopu9vzfmxAVwwL6ZDaEee26icv2hvY9nwMaD1Ihww0H5Jy2zyjSO5BuTWefkTkVlzgZbWeW5G63618APO3z8OEHpMw55o3dctmRXkZNm1Yiz07t0GssCWGG/Q/73ycf9ElUnC5nSVAuTX32WCE3MYeOoA2F1+AmOoq5M+bj8oJ1xsG5YuDn2DhjjexdN+HDcq8psf1uLXvnbiyW2Tm4Q0GQLTKrTejgsp8rDv6JdYcXinH64pV3Xxto7uMlcsEx8cmQExDJiS4Z1ZvXb+4UG6DOaON35dyazxz3eRWNEVMvbXhu+2Y9aup+PurH8phCdmZabj/0b9i8sQxmHSteX7WCQe96LkVm/iwu/C1nnIexReveg2XdbkqnLA+jz10YC9WfrZEXigmJonv3WcALho+ksvG+iFNuVV+CioNqFxuly1B9l23omLiDSh47e36uqb95c9I+9NTqOnbH3mLPoUzW/1KWlph+wv3YP721/HezrdxuvxkfR16Z/fFlH534eY+U9EqsbVSjnoGo9z6pis+77ed2QoxzOSHU99jW+5WnCg95jcVIufdM3uhW2Z39Mjqja4Z50CM6RVjqcWSxeFslNtw6Ol/LOVWf8beJegqt6Kw5qbhMr7J6kvU5FZE/uum2fifjU/LZShX3L4JbZPbKyvw2w1rsfnb9TJe5y7n4JJRVyAj0/ozHoQDkHIbDj39j1Utt56zJRTMm9+gAW1GDUXc9m2ovGIc8hc07EkNt6Vimq4lez/Agp9eh1hcQdvS4tNwXa9bcHu/6Rjczn3RaUvbKLeBZ0z07orpxvYV7Mb+wr0QF6wdKNzb6GJB74hiJgwpvhnd0T2rF87J7IEu6efI1dWaWmBDi0O5DTxHkdiTcms8dd3l1vgmGV+ip9yK0m98/wo5L+XwjiPx/qTPlFTo6zUr8NMP38lYIy8bhz79IzO2S0ljDAxCuTUQdghFKZfbjxcha/ptqBh/HQpeX9CgRrYzp9Fm3GjYDx9CxU2TUTBnXgg1bniIWCHsnR1vYMmeDyDGaGrbpZ1H47Z+d+PG3u6lgFvyRrlVk73DxQdwqOgg9hXuxqGiA9hbsAsHCvfhQNFevwWI2Rn6143jFb/UianKxEqYbVPao1VSa3m/dXJb9GnXGTZHJlLjzDmbgxqCLTcK5db43Okqt2K2hJOn8/HUwzPql9/1XhHM+CarL9FbbsVPU5e9faG8Evp3wx7Hb4fMCqvQlcuXYN/uHXJs7VXjJ6Fzl8hMNRZWIyJ0MOU2QuADLFa13HrPluBdjdiD+9F67KWwFRWh9JcPoviJPwRY07O7iZ+j39nxbyzY/gaEsGibWNr2tn7TMbnPHXKZW6tslFv9MykuSD5YeAD7inbjcOFBt/gW7ZM9v8FuYm5eIb1ju14NW4ytwS34i54AACAASURBVOFiCfTkuGQ5/lf8JceluG9j3c8lx7sfp8SlIMGeGGzR3N8PAcqt8aeGbnKrSewtE8dgyOA+DVpm1QvKPBv55eHluGPxDfKpD276HMM6XBp0dsXFYmJ87YF9uxAXF4fxN0yRK4lxC5wA5TZwVpHY02i5FW2M//5btJp4FWKqKlH0lxdRdteMgJq+eO97eOenN7DqyBcN9he9s6KXVvTWWnGj3EY2q7kVZ5BbcRr5FXlyDHeeeFx2BmfKT0G8JoZC5FaexKnS0z6XZA6n9qLnWJNdcdundX90Tu0STkjZSRMbEwu7LRaxNrv7Nkbcr3tOvmaXj8/uFwt7TCzibC1zastYewxSEmNRXF6DSQPVX4sTVkIserBucus5FViPrg2XpLXiVGC+zo+nv5qF/9v8ghx3u2rq98hIyAz4NHI6Hfjs4w9w9PABJCUlY/yNU5CV3XIuQgm4oTrvSLnVGXCY4SMht6LKiSs/R/ZtkwCXS154JoYx+NrEvKeil/bD3e80mJNWzHd6e//puL7XLaad2D/M1NQfTrlVRVK/OJ5jbsWvCbnlZ1BcXSSXbC6rKUN53V9pdYl8LJ4Xz3neuu+Xy+eKqgr1q2yUR3Y94YpyAsY0Xze5jfaeWy19E98bg+9PfiN/Inpj4gcBZdXhqMUni9/FiWNHkJaWgfGTpshbbsEToNwGz8zIIyIlt6KNye8uQOb9M+CKj0fe4uWovmiobHppTSnmb39NzniwK297PQ7xU++Nvafg9v53R2y1MCNzo5VFuY0E9eDK1OuCMjE/81lBLkVFbQVqnDVwuGpR66yFw1mL2vr7DnlfPlf3vLjvcDrP7ueo8XjN4Y4RQKyz5TiCA2OSvW0xYsXQGNTUurD+3saLg5ikmpaqhm5yKyiJ4QezZs+Vy+5qvbei13bmI8/jgWnXW24qMF9nxrGSIxg7f4js9Xlq5LO4Z9Avmj2BxFCEfXt2yJ5a0WMrem65hUaAchsaN6OOUi63fqYC89eetL89h7Q/PAFXairefOEXWJpyDGJu2rzK3PpDruh2DW7rNw1Xd/fdu2sUq0iVQ7mNFPnAy9VLbgOvAfdsigDH3Bp/fugqt6I5msyeOJVX37p5f3u00Thc45uurkTvC8q8I3+6fwl+tuxW+bSYPUHMouBv27b1W6xfu1IuoXvj5LuQkpqmrqJRGIlya+6kR1puNx5fh4/e+CU+ituFYo/1T8Sk+7f2nYZb+tyONsntzA1R59pRbnUGrCA85VYBRB1DUG51hOsntO5ya3yTjC+xObkVNXp8ze/w6g8vo11KB7w2fiHEmD3vrbAgH+++9U/59E233Y3sVm2Mb4zFSqTcmjuhquW2qXluNRJ7CnbhvZ1vyXG04pcVbcspAm7bBlyfcjG6/+VDONM5rZJgQ7k193tI1I5ya+4cUW6Nzw/lVgHzQORWFHPboglYc2SlnJT7pXHzcHX3ifWlu1wufLBgHvLzzuD8IZfgomEjFNSMISi35j4HVMut91RgYiqlU2Un4HS55Nj3xXvekytJaZtYGnV8zxswoeckDF+0AelPPCZnUXB0zkH+vxeiZiDnk6bcmvs9RLk1f34ot8bnSFe5FTMmiKV2f9yxv1HLBvbtjlee+S2yMlr+z+6Byq2A8NsV98m15sX25Mg/495Bv5T3N2/6Gt9uXCd7a2+8dRpstobzExp/alijRMqtOfMoFjyoqq2CA1VISHDgeEEJqh1VqKqtRJW4dVSiUt6ve6zdr61ClbMKLqfTZ8Nid+/CmVXvY0W/JBxOOLuogufOvbLOxfgeN+KantdjQN0E+drrcTt3IGv6FMTu3SMvNCv+w7Mom3GfOSEaVCvKrUGgwyiGPbdhwDPgUMqtAZC9itBVbsUiDmJ7cGbLX6WnqdQEI7cizt+/ew7PrH9Chpw+cCYeGvAYPnzndflYiC2HI6h7I1Bu1bH0F0nMs5lfmYf8ylw5F6e4X1CRj8KqfOSWnZaPxVXXck7OKvd9ozYxDV+X9G7ISe+KntluqRVy29Qmem7T/99/IuW1uXK3iok3ovClf8CVnGJUtU1VDuXWVOnwWRnKrblzRLk1Pj+6yW1T89wa30x9SwxWbkVtFu15Fw98Ng022PC7uIeRXJOEC4deiguGBr/Yg76ta9nRm5PbmMoKJM9/EzEV5Sh94Nctu7EKa3+05DByy0/jdPkpOVn8mYrTOF12Uj7OL891TyovJLYyP+RS0+LTkBCbiKTYJMTZEpBgT5CPxcpIibEJiJfPJSIh1n2bWHc/KTYZ8fI57fW6Y+wJSN28Fe2feQaZQ65Am1cWh1w3cWDip0uR+cv7YCsoQE3f/iic+wZq+vQNK2ZLPJhya/6sUW7NnSPKrfH5odwqYB6K3Ipivz25AXM+eh5Da4eg0F6Eh2Y+zeEICvLhGaI5uU196QWkP+FeHrnwlVdRfssUxTUwZzgxSfvOvG3Ymbcdu/N3yPXuj5cclRJbXFUUVKWFpGYltkab5LZyoZLspFbITmyNVkmtkZWYjezEVmiV3AaZCdnyNTFfrLYpH3Mb5FRgzTXUfvIEMv/jbiSsc89NWTHxBpTMegK1vZvu/W0ubkt6nXJr/mxRbs2dI8qt8fnRTW5FU8SwhG457S0zn62/9IQqt7mnT+Kjd/8Nh8uBV2JeQU67c/DEiGdwUfvhxp8JFi0xGLkVCPIWf4aqS/xP1dbSMGkSuyt/B/bk75JCK2RWDBFoahPTX7VJaou24jalHdqndETr5DZondwW7ZI7SGEVohruNFmq5Tbp40XImn6bXHGs4PUFytKV/NbrSH/yMdmLK7aqkaNRdv+vUHnVNcrKMGsgyq1ZM3O2XpRbc+eIcmt8fnSVWzHH7VsffIGH75+CpMR441tnUImhyq2Y9ktM/3Xe0KF48dQLWHnoM1njSedOwZMjn0WrRC63G24Kg5VbZ2YmcpevQW33nuEWbejxord1R96PEBIr5FX8idW1mpLYgW0Go2fWuejTqj/ObdUPndJypKwKqTVqUy63Sxcja9oUVEy4HgXz5itthq2oCClzX0bKnBfrJbembz+U/fy3KJ8yVWlZZgpGuTVTNnzXhXJr7hxRbo3Pj25y29RMCaKZ0Tpbgpbin374Hl+v+QIZmVmYfMe98unPDnyMx9c8JOfeTE/IwH8Of1JecMYtdALNyu3LLyD9v2ah9Oe/hvgJOun9hXB06YozK9dDiK4Zt+OlR7Hl1LfYevp7eSskVgwn8Lf1azUQ57bqi96t+qFPdn/0yj4XYgosM2yq5dZ7KjA92hhTXYXkBW8h5eUX5KwKYnN07ISymb9A2fSfwZWSqkexEYtJuY0Y+oALptwGjCoiO1Jujceum9wa35TIlRhsz63DUYu3X3sFlZUVGHv1dejes0+Dyv9102z8z8an5XNCTH4/4o8Yk3NF5BrYgktuVm7rxtyKi8mK/3s2Wt1wtRxfWT1kOHI/WRnxlospszYe+xrfn/oGW099h+9ObpQXcvna+rc+T/bEil5Y0RsrZgXontkr4m1oqgKq5TaQRRxUAklc/glS//cviN/wlQwrlvEtmzodxX98VmUxEY1FuY0o/oAKp9wGhCliO1FujUdPuVXAPFi53bFtC9atWo527Tvhupt9/5wpem//35oHsfzAUllD8ZPx/7v0j7iu580Kahw9IYKV25iSErS5coTskau4aTIK5swzHNaPZ7Zg7ZEvsfrw51h3dJXP8od2uAQD25yPIR2Ho1/r89DD5BLrD2JLl1utXXE/bkXqC88j6aP36psqhiyIMbnl0++BI6er4eeRqgIpt6pI6heHcqsfWxWRKbcqKAYXQ3e53bRlJ6b/5pkGtZr3t0cxZHDD3srgqm2uvYOV2wWvz0FJSRGunngzcrp2b7IxQnJmr39c/gQttpS4VLmi0qTet2FkzmXmAmHC2gQrt6IJ9iOH0GbsCNjy85RfmOQLkZj3de3RlVh96As5NMW7Z7Z3dh9c2H44zm93EQa3uwiih9Yqm2q5TVQ8W0KwnO1Hj8hxuWJ4ixjm4rlVXTwC1cOGo2b4pageenGLWd6XchvsWWD8/pRb45kHUyLlNhhaavbVVW6F2D4/Z2GDlcjERWYzH3keD0y73jKzKAQjtwf378Hnyz5sMNY2kFSuOvw53vhxrpQfbRMXnN3U53bc0HsyBrW9IJAwUbdPKHIrIMVt+R6tbhoPcRFRzXmDkf/mu3Jcpapt/bG1WHN4Bb48vByip9ZzS41LxYicyzAy53KMO2cCOqSqK1dV/VXFsZrcenJJWP0lkt5bgMQvPoPtTOMx0aJnt3r4pai5cCiqhwxFbQ9zDiGh3Ko62/WLQ7nVj62KyJRbFRSDi6Gb3FZUVuOJ517FLRPHNOqlFdL77pJVeOrhGZaYRSEYuV38/ls4deIYRl1+Nc7tF3wPnJhQXyzf+9ZPr+FQ8dlljQe1vRDX9rgeF3caiQvbDwvuLLDw3qHKrUAienCzb5sEsSSruLis4F9voWp0aL3lB4v2YdXhL/DloeX46uhqVNSWN6AuvpyM6XIlRne9AsM6RM9CHqrl1ugxt4G+deyHDyLhm42I+3Yj4jeuhxjG4L0527RF1bCLUXHrVLjSM+Bo09YU8+lSbgPNcuT2o9xGjn0gJVNuA6Gkdh/d5LapFcpE7+1zLy/A7MfuRVZGmtoWRSBaoHJ75tQJOa9tUlIybp9+P2x2e1i1/ebE15i/fR4W734f4sIjbRMT6U8bcB9S4lPRv8158gp5K/f+NQUxHLkVcWPKy5D56weQ9OG7spiSWf+FkoceDShvXxz8RE7v9uWhz3G4+ECDY0Sv++XdxmFst6sxsvPlyEzMCiim1XaKFrn1zltMaSniNwnR/Rrx36xH/Leb5Lnma3N06YaKcdfCJWbviIuDo0NHODrlwNGpkyG9vZRb87/rKLfmzhHl1vj86Ca37LltnMwvPl2EA3t3KV9mt6ymFJ/t/xgrDn6KVUc+hxjD6b2lxadDzGsqLkLq07o/+rUeiAGtBxl/xhlcYrhyq1U35bW5yHjYvTyvuEio4B+vyyvjtU3k4Otja/DVkdU4VnoEqw9/AfGc53Zp59Gyd3ZM1yvlLBjcgGiVW1+5j9u6GQnfrId9x3bE7t+L2H17YT9xvNnTxJndCrVdu8HZrj0cnTrD0bmLFF95X0hw55xmYzS1A+U2LHyGHEy5NQRzyIVQbkNGF/KBusmtqNEHy9Zg4ZJVph9zK1ZS+9f8ZQ0gPv3IjPoxwaIdjz/7qnx9/NjhjYZTBNJzW15WirfnvYIYmw13zvgF4hMSQk5acweKuU+3nP4O23N/xM68n7DtzFZUOSp9HiYuThJTR/VvPQiXdblS3rfSpkpuBRMxDjd72hTYjx2F6E1b9tJj+NJ2AOuOrMKmk+sbYRMsL+04GpefM04OF0m0J1kJrZK2qJbbSF9QpgSKR5CYqkrE7t4lJdd++BBsJ44h9vBh9+OjhyEuYGtuc+R0Qa2v2RrsNriSU+r+kuEU97OzUe21Ql9Koh0OJ1BZ7QBiAFdiElyJiXV/HveTU5qrCl/XiQDlViewisJSbhWBDCKMrnIr6tESZksQciu2B2dOboTO+6I4X/sGIrfr167Atq3foU//QRh52bggUqRm1/2Fe7A7fyd+OP29lN2d+T/JxSL8bULE2qa0R/uUDnLVqnYpHXBZ1yuRFJvc4JAEewJS49PkLA6id1gsPmGmTaXc7sjbhnW7l2H953/H2rQ8lMc1bKmY1WBE58sxqsvlGN5xhOTBrWkClNvwzxD78WOQf8eOyC9etiNHYD9+VM7WECuE2MfFbOGX6j+CKy0NroREuJLqxNfX/YQEKcmQopyAqtGXo+oyzuUdal4ot6GSM+Y4yq0xnD1L0V1ujW9S8CU2JbfitW457et7cX3NANGc3NbU1ODf//w7xOINYjUysSqZGbbSmlJsO7MZ2/O2YfvpH7C3YDdOlh/H6bJTfnt6A6m3EGBxxX9KfBrSpPi6b1PjU8/eT0iX+6TGp8vn5a18nIbUOPefinGowcptQWU+TpYdx6nykzhRchQ2mx1rD6+QvbPeq4C1KwXG7QMuK2mLEUOmInXG7+DMMkduA8mTGfah3BqTBTHG11ZWKsf1xpSXu28rKhFTWgKbeOzxGirK3a9VVsi/+JoquMor4BT7VVW7j5WvVSKmogKid1nMDx3Opi2iEk6MaD6Wcmvu7FNujc+PrnIrxPDk6fwGP+NrY3GHX9jPNFOBeQ9L0IYk+KqruBju97Pn4o+z7kWPrh2B4mKcdHh14Xnlcev3m7Bh3Zfo0q07rrmuZSzCUFRViFNlJ6XQnSo9Ie/nV+aitLoEpVUlEGJcWl2M0upSlIjbmlKUide8xpmGc0oLwR3YdnA4IRBnt6HW4YTLTxTR04XDB3C0UwZOxFc1KfWiJ/biziMxKudyOVVX/8I4pD30aySsdq9kJnqryu+6G+W/+A3ET8Fm22LMViEAsTYgPSUe+SXVSmqXuHQxMu68FZUTrkfRGwuUxAwliAsuxIjf8C2wpSXFotbpQkWVo9nWSEn2EGNxH3WS7Pk8Kqvc4rxmFRKWLUHZA79C6R/+3Gx87uCbQOuMBOQVV8Hl74OuCXAhHMI0NEugIdV4uw2pyXHIL6lC+ywOT2sWn4IddJPblnpBmTYP7+xZ92JAn+6NpjNrJLfnnAPnfz0J1113+U3HSy+9iIKCfNx++x3o3r3pRRsU5DTiIUqqS1BSVSKlV9wvrS5DUWWRvC+fqypBWXUZCioLpCwXV7n3K6kqlfdLa9zHF1UVGd4W0YvcMbUTOqZ1QKf0TuiU1hnZSVkY0WUkhnca7rM+MRs3IuaPf0DMsrPjtl1Tp8L18CNwDRhgeBv8FWjGf8RiYmJgiwEcTjW1s334IWy33AznDTfA+d77EWNfU+tEnDB3C2w2kSAX4AzFnJppv+1/X4DtwQfh/PVv4Hz+eQvQikwT7LYYiLeQK4QcWeMrWGS4+y/Vi2oM5Oec0wnY7SRuRLZ0k9uWPBWYNhThmsuHS7n17GVuJLcxMXDFxSFv6QpUX3BRo5zl5Z7GBwvmISExEXfd8ysjcmrZMsTcsE6Xs/7P4XLU3XffOpwOOMV/dc87nE5kp8Uit6QSteK1un1c4lbsAycS3n8Hya/+A6nX3YX03z+P5NjQL4qRS7D+z2wkLVsi/pWReagaNQalv3yQ4wn9nJXKhyV8vAjZ029D5fjrkP965HpurfQm1HO2hJRX/o6Mx/8TZf/xCxT94VkrYTO0LRyWYCjuoAvjsISgkYV9gG5y21J7bgVRz3G2zY65feAB4JVX4GjfAWdWb4SzVesGSfl24zps3vQ1evcdiNFjrwk7YQwQHIFgx9wGF9333rG7diL1heeQvHB+/Q5iJaqqocNQdc1EVA/hIhsaGNVya9ZFHFScV5GKoafcps55Eem/fwSl9/8KxU83XKY9Uu1tieVSbs2dNcqt8fnRTW5FU8TFV7Nmz8WcZx9yj08FYLbld0UP87IVGzB10pX19fMcUxvIbAlVI0Yj4as1qL5wCHI/W90gi+/Pfw35eWcwbsJN6NKth/EZjvISIyG3GvLYQweQ8tfnkPLmvAZZqD7/QrmUb80lI1A17BLUDI7epZMpt+Z/g1JuzZ8jyq25c0S5NT4/usqtp8yeOJVX37p5f3u00ZK8xjfdXaLWw7x0xQa/9WtuntuTe4+jzZhhchqe8ilTUfjiXBmrtKQY81//P9jtsZh+36/DXpEsUoxacrnNy+3fkP7EY9Dzam1bYSESP/8UCZ98jMSVyyGuXPfcXCmpqB4yFKJ3V/4NGSovTouGTbXcJnJYgvLTRk+55bAENemi3KrhqFcUyq1eZP3H1V1ujW+S8SWKqcDidmxH6ytHyiuAi/78V5T9bCZ+2PwNNn61Ct179cHYcdcZXzGWCDPIbYM0OByI37pZLrsat+FrJGxcD1vumYayGxeHmvMGo3rYJagefgmqLx5h2SnGKLfmf5NSbs2fI8qtuXNEuTU+P5RbBcy1eW4TP/kY2XdOhjM7G3kffYr3d2zFqRPHpNgKweVmPIHm5fYFpD8xS9ee2+ZaLcboJgjZ3bQB8Zs2InbvnsY9u4POl8v91vQfiNq+/VB7bl95v6VvyuV22RJk33UrKibegILX3m7peExRfz3ltn7M7QO/RvF/zzZFe1tiJSi35s4a5db4/FBuFTD3XMQh/anfI/Xvf0VFcjKefeQRORRBDEkQQxO4GU+gJcitNxVbfj4S1q9z9+yK2y3f+wVXfdHQBjMxuNLT4WzVBo42beTFjc7WbeT4XrNuquWWF5Spz7QhcssLyvwmTi6Yoc0dLBbM8JhHGHULaWTaHSjNL5aLbcjFNSorgOpq99xTTgdi5K1TzLknb2OcjrrXxHPa62efi6nbr8HxDo/XGxwv4rnjwFUXX9u37rn618V8ZZ7l1+3n+3iXu25VvpeOV3+mGxQxhOnaDKqZpYqh3CpIp/cKZUJwd329Bh9PnIjuFZUY+/B/KSiFIUIh0BLl1lc7437YgridO2Df+RPitv2IuF075BjvQDexJKqjVRs427aTvywI8XW0bQdXq1Zwtm6Lml69UTPo/EDDKdtPtdwmsudWWW60QIbIrcV7bm15ubAVFsBWVISYoiLYCvMhxuLLx4X5iKm7bysqcD9fWIiYYvctN4sRoNwaklDKrQLMvpbfXf6vl3CoogzXLVqE/rZYFLzxDhzt2isojSGCIWAVufXVZrEaVNz2n2A/eQLyH8/8PNhOn4ItNxe2vDNyLK/9jPs2nM2Zng5x0ZsrJUXe1gw4L7Te4NhYwB4r54VGXCxcsXGwx8chKTURJTVivmjP1+Pk6+79YoHYOPdx4lY8rjsecXWP5eux8sK9rJ/dyWEJ4STc61jKbdMwYw/uR+z+fYgV78W9uyEe2/LyYCuqk9TysrCzId+DiUlAYhJcSYnyvispGa7EBHnxaUJ6CirtCXAm1r2WnAzx3oDNJlYNAGJscMn7NvdzNvHYfvZ1+fjsvvJ1bd8Gx9cd43m8eD+KdT48j7fb3Y89yxdx5HMxsk7y9Zi6MmV5da/XPec+vm7fFn6BLYclhP0WCDoA5TZoZI0P8Jbb6upqvDH3BTmR/2/fWYi0HdvhbNMW+W+8wzlOFfAOJoSV5TYYDmKog5TdOul1C3AubGdOu2U4Pxe2khLI5VPLyuSt6FVqqVvFhOtRMO/sPMMttR1mqLchctsChiXEbd+G2D27ELtzB8Q4+dj9exG37YeAUuTMyIArIwvOzEz3X4b7z5Up/rIhXne/lg2XuC8fZzWaN91fYRxzG1AaIrYT5dZ49JRbBcy95Xbf7h1YuXwJOnbqgglXTkDWAz+D+LlUbCW/fghl9/9KjoXkpj8Bym34jIUYx5QL4S2DTchvhXs8X4yjFqipQUxtDVBbi5iaWqBWPPZ83oGYGvF6jXtMXnVV3eu18jiboxYJcKKyvBIxtQ738XJ/9+uoEbd1cb2fry/f83WHHG/IC8rCz7sWwRC5NdGwBLHSYOzuXYjdtQNxO7cjdvfORhd5amxqu54DR5cucHTqDEdOVzg7dUatuM1yi6wU2owMdcnwE4lyqzvisAqg3IaFL6SDKbchYWt4kLfcrvhsMfbv2YlLRl2B/ue5J+hPe+F5pD39uLwvfkYqu2cmSn/9OzizWymoAUM01aORW1QFh7iQwceW+lLkZ0uI5uypHnMbzSz1arshchvBntu4HT8h4YvlSFjxGRLWrfGJUXxO1ww8DzUDB6F2wCA5NKemT1+9kAcdl3IbNDJDD6DcGopbFka5VcDcU26dDgfm/eMFOBy1uGPGz5GUnFJfQuye3Uj965/rl2UV46bckvuwZecxVYA3rBDsuQ0Ln+4HU251Rxx2AVaUWzELScLHi5G0dBHsR480YCR6Y2vOG4TagYOkzIop98w844ioPOU27NNc1wCUW13x+gxOuVXA3FNuDx/ch88+fh9t23XA9bfc6TO6mMc07ZmnkfTRe/J1V3IKSu+ZiYq7ZqC2W3cFNWIIjQDl1tznAuXW3PkRtbOK3CasXY3ExR8gceli2E+fqgcvptOrHjIc1ZeOlAuniCEFLW2j3Jo7Y5Rb4/NDuVXA3FNu16z8FLu2/4Chl4zGoAuGNRk9dt8epD73JyS/9079fmXT74Gjew/3MqwXXKSgdtEdgnJr7vxTbs2dH8PkVqcxtwmrv0TioveR9PFHEGPHta3y8itROekWVF57HcRMBC19o9yaO4OUW+PzQ7lVwNxTbt/814uoqCjHrXfei/SMwHoAhOSm/fmPSPz8E8SUlNTXSIzNrR423L0M6yUjUT10mByvyy1wApTbwFlFYk/KbSSoB1dmS+y5Tfnn/yH1hf+B/cTxs0J7xThU3nQrKsddawmh9cwi5Ta4c9rovSm3RhPnmFslxDW5zc87g/fnv4a0tAxMmTYzpNjx321CwpovEb9qJRK+anxxQ+U1E+TFDEJ25ZyBgPyglitRdegYUplWPohya+7sUm7NnZ+W1nOb/PYbSPvzH+oXOBEdA+V33o2K8ddBLGRi1Y1ya+7MUm6Nzw97bhUw1+R2+4+b8dXqz9Fv4Pm4dPSVYUcWyw7Gr/8aCatXQPy8Jlapam6TcyW2aQtH2/bu5VfbtpVjyZzZrRscWtP7XLmf1TfKrbkzTLk1d35aitwmLXofaX/6b4hfwcQmVtsrfvJPqBo52vyAFdSQcqsAoo4hKLc6wvUTmnKrgLkmt18u/xh7d2/HmCvHo9e5/RVEbhjCVlCA+G/WQ8y6YDt2FPZcsfrUaTkRv/30ablCFbfQCJTqNOYvtNpEz1GUW/Pn2pBhCSG+/8SKdGl/fLJ+MYXanr1Q8vun5DzH0bRRbs2dbcqt8fmh3CpgrsntgjfmoKS4CLfeeR/SMzIVRA4+hLgKjMhJAgAAEy1JREFUWKxEJZZ/tJ86CduZU3Ld8pjiYthKxQpUZYgRt5Vi0vxawOWUk+vHiAn2ne77cDoQI+875XPu186+Xr+v2E++5nLHqKwIvsJBHiGWnGywNKRcorFuKcf65R3PLi1pj7PDAfE4Ru5Xv/Rk/b7u5ypuvhVld98bZG24e7gEKLfhEtT/eDPKrfiCn/HQL5Hw9VoJQCyiUPLo4yi/zfcMNfpTimwJlNvI8m+udMptc4TUv065VcBUyG1VZSXe+Of/IjExCXfe80sFURlCBYHmhiWoKIMxQidAuQ2dnVFHGiK3QSzikLzgTWT+4j7ZfDEMq/Thx1A68xdG4TBlOZRbU6alvlKUW+PzQ7lVwFzI7cH9e/D5sg/R9ZyeuGr8JAVRGUIFAcqtCor6xaDc6sdWVWQzyW3Gf/4WKf+aI5tWNfoyFL7yKhxt26lqaouNQ7k1d+oot8bnh3KrgLmQ241frcIPm7/BkItHYfCFwxVEZQgVBCi3KijqF4Nyqx9bVZH1lNuUV/6OjMf/E2X/8QsU/eFZv1W25eUie+rNiP/2G7lPqejpfepP9TPGqGprS41DuTV35ii3xueHcquAuZDbJR+8jZPHj2LCjbehQ6ccBVEZQgUByq0KivrFoNzqx1ZV5EjLrRDarGlT5DUErvgEFL48FxU33KyqeZaIQ7k1dxopt8bnh3KrgPnRM2V47f/+ApfLhbv/47ew22MVRGUIFQQotyoo6heDcqsfW1WRIym3KfP+ifTHfoeY6mo4OnZC/vwPUNN/oKqmWSYO5dbcqaTcGp8fyq0C5lu278eid/+NVm3aYdKt0xREZAhVBCi3qkjqE4dyqw9XlVH1lNvUOS8i/fePuIcZPP1Mg2qnzn0Z6bN+J58Ty5Hnv7EAzuxWKptmmViUW3OnknJrfH4otwqYL1+57v+3d/+xVVZ3HMe/i2Jgs+OHDJGM4UAjsrDhDNroxG6EbSljW0isGP+YwXRVF38ggVCNM41zZbBWky2wpgE1JhNL4n4QazDpRlyMjcaNzYgkEx1Bq2JQtCiObHE5j3tubh/vvc+Pc77POZT3/WejPed7zvM6T+/9+NxznyvP/GXI2Zc3OJgSJf4vQLgN+1Qg3Ia9PmZ2pYTbxH1uJw49KdOu/uRetcd+cqu839UdPpTHGRJuPeJnGJpwmwHJcRPCrQPQh3/7qLzyz/1qX97gYIqnbAnCbdhLT7gNe31KC7c33Czv/+wXEcaEl16U6d++Uj5z/EN5b9P98sHqT277xaO+AOE27LODcFv++hBuHZj/sqdXPjg26vXLGxwcxrgsQbgNe1kJt2Gvj3a4Td4twXzL4hdamuW0kdejL2Q4+qtPbvvFo7EA4TbsM4RwW/76EG4tzUdHR6W3t5cvb7B01OpOuNWSdVOXcOvGUbOK5raE6nD7/k/vkemtS2XC3r/Kvy+7Qo78blDEfJMgj1QBwm0qkdcGhNvy+Qm3lub79u2TnTt38uUNlo5a3Qm3WrJu6hJu3ThqVtEMt5UPlN1ws5z2+iGZtOv38p+558nbQ0/Lx01Nmoc1rmoTbsNeTsJt+etDuLU03717twwPD/PlDZaOWt0Jt1qybuoSbt04alYpI9zG8zdfp/v2n5+R/86eo3lI46424TbsJSXclr8+hFtL823btslrr/HlDZaMat0Jt2q0TgoTbp0wqhbRDLfxtgRzAB9PmCBH/viknFh8qerxjMfihNuwV5VwW/76EG4zmD82+JTctWl71HL50mbpWrdaJk08I/p3V1dX9L/myxtOP31Chmo0KVOAcFumdv6xCLf5zcruoRlu420J5piO/rpfPlx1bdmHNy7GI9yGvYyE2/LXh3CbYv7c3v3S0zcgWzeukamTm6S3byDqcXtHWyXc8uUN5Z+4WUck3GaV8tOOcOvHPc+omuH29IOvyqSHHxRp+ryM3ro2z7RoWyVAuA37dCDclr8+hNsUcxNmz509U1a2LolaJsOuuXK7YOFFcvmVy8pfPUZMFSDcphJ5bUC49cqfaXDNcJtpAjRKFSDcphJ5bUC4LZ+fcNvA/PhHJ+Tuzdul+eIFlXB74OCI3NndL/d2tsu8ObOibQkty5bL+Rd8pfzVY8RUAcJtKpHXBoRbr/yZBifcZmLy2ohw65U/dXDCbSqR8waE2wzh9qoVLbJ40fyoZa1we8stt8jUqVOdLw4FEUAAAQQQQAABBPIJEG4zhNtGV26PHj0qU6ZMyadOawQQQAABBBBAAAEVAcJtCmvanlvTfeTIcZXFoai9ANsS7A01K7AtQVPXTW22Jbhx1KzCtgRNXfvabEuwN8xbgXCbIpZ2twTCbd5Trtz2hNtyvfOORrjNK1Z+e8Jt+eZ5RyTc5hUrtz3htlxvMxrhNoN5o/vcEm4zAHpsQrj1iJ9haMJtBiTPTQi3nhcgw/CE2wxIHpsQbsvHJ9w6MGdbggNEpRKEWyVYR2UJt44gFcsQbhVxHZUm3DqCVCpDuFWCbVCWcOvAnHDrAFGpBOFWCdZRWcKtI0jFMoRbRVxHpQm3jiCVyhBulWAJt7qwhFtdX5vqhFsbPf2+hFt9Y9sRCLe2gvr9Cbf6xjYjEG5t9Ir15cptMbcxvQi3DhCVShBulWAdlSXcOoJULEO4VcR1VJpw6whSqQzhVgmWK7e6sIRbXV+b6oRbGz39voRbfWPbEQi3toL6/Qm3+sY2IxBubfSK9eXKbTE3eiGAAAIIIIAAAggEKEC4DXBRmBICCCCAAAIIIIBAMQHCbTE3eiGAAAIIIIAAAggEKEC4DXBRmBICCCCAAAIIIIBAMQHCbTE3SfvWsoJl6ZZT4N33RuXGDffJCy+9EvV88P4NsnjR/LpVevsGZNsjg2N+f8/61bKydUnOkWnuQsCsX+fP+2XdTatk3pxZLkpSo6DAgYMjsnnLDum+o12mTm6qW8W061jfI2+8daTSZuGFc2XrxjUN+xWcFt3qCBz/6ITcvXm7PD40XGmR9vwHpo5A8m8i7e8h+bplZnXO2WdJ36a1PA86WiLCbQHI5/bul56+gcqTuQlM5nF7R1uBanQpKhA/uTdfvCAKp+YJ5s7ufrm3s73uEwRrVVTbbb/qF2ae1N3a5q1W/UKb9qJsamf5O8s7B9rnFzDr9sCOJ+TGH/1QJk08Q8zrUmd3PwEpP6V1D2N/aORw5SKJeZ158/A70rVudbQ2yUf8N7e2o63hxRjriZ3CBQi3BRbfnLjnzp5ZOZGTYbdASboUEEheaUqG3VolCbcFoBW7cOVWETdn6TxXbtP+IzLn0DR3IEBgcoDoqERaJmCtHEE3KEO4zWlcK0BxJSMnoqPmtZ5A0sJrclsCWxIcLUbBMoTbgnAK3fKE2+ptCVmu9ipMl5IJAV6HwjklzLbF4ef3pV65jbfT8e6V+7Uj3OY0jcPtVStaKm8n8KSSE9FRcxNud+7aM+YJJC3cVg8d75Pq7mznrSFHa5K3DOE2r5he+6zhNjmDtLdg9WZM5Vggy7tWaJUjUCQPmDA8sGsP+9YdLhHhNicmV25zgik2L3LlttYLc/UWE8XpUrqGAOE2nNOiaLgt2i+cIz+5ZxK/Js2cMY3PfXheyqIXTHgedL9whNsCpuy5LYCm0KXInlvCrcJCWJTkSd0Cz3HXoiG1aD/H0z8lyxFsw1n2osHWHAHPg+7XkXBbwJS7JRRAU+iSdreEeNN+24qW6MN/5t+DQ8Ny7cpl0WyKvH2kcBindEme1MNZ/nohNbntYPeeZ+W8L3+xckeSPFuBwjnak38mbEUIZw3TXkuS2w5MhjCP+LaVaXt0wznSk2cmhNuCa8V9bgvCOe7W6D63yXDLfSEd41uUq7UWy5c21/0AhsVQdE0RqHXPzeuvaa28xZ0Mt+aF+brbNlaqsm5+TrFa9xs2M6leOz8zO/VGrc4D1Ucf33c4GW7z3hf31BO1P2LCrb0hFRBAAAEEEEAAAQQCESDcBrIQTAMBBBBAAAEEEEDAXoBwa29IBQQQQAABBBBAAIFABAi3gSwE00AAAQQQQAABBBCwFyDc2htSAQEEEEAAAQQQQCAQAcJtIAvBNBBAAAEEEEAAAQTsBQi39oZUQAABBBBAAAEEEAhEgHAbyEIwDQQQQAABBBBAAAF7AcKtvSEVEEAAAQQQQAABBAIRINwGshBMAwEEEEAAAQQQQMBegHBrb0gFBBBAAAEEEEAAgUAECLeBLATTQAABBBBAAAEEELAXINzaG1IBAQQQQAABBBBAIBABwm0gC8E0EEAAAQQQQAABBOwFCLf2hlRAAAEEEEAAAQQQCESAcBvIQjANBBBAAAEEEEAAAXsBwq29IRUQQAABBBBAAAEEAhEg3AayEEwDAQQQQAABBBBAwF6AcGtvSAUEEFASeGzwKblr0/Yx1RdeOFe2blwjL7/6ulx320Z58P4NsnjR/DFtevsG5Nm9+6N2Uyc3SaM67xwdlY71PfLGW0fqHsU961fL7FkzovFqPeI5PLd3f9Rm+dJm6Vq3WiZNPKPSvNHvTKN33xuVGzfcJy+89ErdeVx/TaucO3vmGBMzt5WtS+TAwZHoOKZPm1w57rhQrd/F82l0PErLSlkEEEBAVYBwq8pLcQQQKCqQDKhxHfPzKy79ahRoTWgd2LVnTJgzQe7O7n65t7Nd5s2ZJVnqVM/R1Bx+fl/NcNrZ3S99m9ZGdWs94sB4ztlnjWl3/KMTcvfm7fL40HDN4FuvVk/fwKeCqmlrxknOJQ6wJqQnA78x2PbIoMT/YWACf60aRdeKfggggEBIAoTbkFaDuSCAQCQQX8VsW9ESXZWs94hD48wZ0+T2jjaJ/9188YKoX9Y6LsOtCaTfuvwiOfbB8WhOcRjduWuPnHnmZ+XYsQ8/FZxdhVsT6r+37DL5x74DlTFM6N28ZYd8feH58qen/1YJy4Rb/tgQQGC8ChBux+vKclwInMQCydDa6FDiK5bdne1yaOTwmCu5eerEY9heuTXhdm1Hm/T85tExV4/NdoJ/HXpT3jz8jmq4XXvD1RLPIb66bcY141df5SbcnsR/IEwdAQQaChBuOUEQQCBIgeSe0Oq31JMTjt92Nz9PviWfp47p3yjcZtlzG28leGDHE9E0f/Ddb0RXTrvvaBfzM+1wa7Zj/P3Fl6OtFWt+fJV09T4k625aFf0sGW7TjifIE4NJIYAAAikChFtOEQQQCFqger+qmWhyP6v5Wbz94JJF8ytbAZIHlaVOWrjNsuc2Drfmg2pmm4B5tH3/m9E2CRPCywi306Y0RR9Om9z0Oblg3uzIJLk/mSu3QZ/2TA4BBCwECLcWeHRFAIFyBeptM0jutU2bVaPtCi62JcR3aUh+mK2scGs+8GaOY8tDf6h8sI1wm3ZW8HsEEBgvAoTb8bKSHAcC40jAXIk1t8Ra0vy1Tx2VCYjmEX9Yy/z/euE2bx2XV27NHQnMfuCXX31NvtNySTTnMsOtOfbBoWG5duWyaGzC7Tj6A+FQEECgoQDhlhMEAQSCE4i3GXxp1owxH76K988m99U2Crfm7fmsdVyH2yRsmeE2OTbhNrjTnAkhgICSAOFWCZayCCBgJ1DrSw1q7bdtdOXW/C5PnbRwm/YBLBO+692b1tWV2+QXUlR/iUP1/X2zhNu047FbQXojgAACfgQIt37cGRUBBBBAAAEEEEBAQYBwq4BKSQQQQAABBBBAAAE/AoRbP+6MigACCCCAAAIIIKAgQLhVQKUkAggggAACCCCAgB8Bwq0fd0ZFAAEEEEAAAQQQUBAg3CqgUhIBBBBAAAEEEEDAjwDh1o87oyKAAAIIIIAAAggoCBBuFVApiQACCCCAAAIIIOBHgHDrx51REUAAAQQQQAABBBQECLcKqJREAAEEEEAAAQQQ8CNAuPXjzqgIIIAAAggggAACCgKEWwVUSiKAAAIIIIAAAgj4ESDc+nFnVAQQQAABBBBAAAEFAcKtAiolEUAAAQQQQAABBPwIEG79uDMqAggggAACCCCAgIIA4VYBlZIIIIAAAggggAACfgQIt37cGRUBBBBAAAEEEEBAQYBwq4BKSQQQQAABBBBAAAE/AoRbP+6MigACCCCAAAIIIKAgQLhVQKUkAggggAACCCCAgB8Bwq0fd0ZFAAEEEEAAAQQQUBAg3CqgUhIBBBBAAAEEEEDAjwDh1o87oyKAAAIIIIAAAggoCBBuFVApiQACCCCAAAIIIOBHgHDrx51REUAAAQQQQAABBBQECLcKqJREAAEEEEAAAQQQ8CNAuPXjzqgIIIAAAggggAACCgKEWwVUSiKAAAIIIIAAAgj4ESDc+nFnVAQQQAABBBBAAAEFAcKtAiolEUAAAQQQQAABBPwIEG79uDMqAggggAACCCCAgIIA4VYBlZIIIIAAAggggAACfgQIt37cGRUBBBBAAAEEEEBAQYBwq4BKSQQQQAABBBBAAAE/AoRbP+6MigACCCCAAAIIIKAgQLhVQKUkAggggAACCCCAgB8Bwq0fd0ZFAAEEEEAAAQQQUBAg3CqgUhIBBBBAAAEEEEDAjwDh1o87oyKAAAIIIIAAAggoCPwPusq/PX1a78UAAAAASUVORK5CYII=", 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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": "7ddbe0ec-53c3-4d25-825a-cbe3bdf8e50a", "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 }