{ "cells": [ { "cell_type": "markdown", "id": "76d0cfef-8918-4004-ba88-d27425d05675", "metadata": {}, "source": [ "### One-bin `A <-> 3B` reaction, with 1st-order kinetics in both directions,\n", "### taken to equilibrium\n", "\n", "Diffusion not applicable (just 1 bin)\n", "\n", "LAST REVISED: May 6, 2024\n", "\n", "* [First Step](#reaction_2_sec_2_first_step)\n", "* [Numerous more steps](#reaction_2_sec_2)\n", "* [Equilibrium](#reaction_2_sec_2_equilibrium)" ] }, { "cell_type": "code", "execution_count": 1, "id": "6e80c184-9e85-4f2a-8426-35aaba9f2628", "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": "decd55ad", "metadata": {}, "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.life_1D.bio_sim_1d import BioSim1D\n", "\n", "import plotly.express as px\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "cdc446c6-4b9f-4938-b119-8855f4c530fe", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'reaction_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_2\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "code", "execution_count": 4, "id": "55ae0052-2f52-4d9b-8f13-cb65adb9d04b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "1 bins and 2 species:\n", " Species 0 (A). Diff rate: None. Conc: [10.]\n", " Species 1 (B). Diff rate: None. Conc: [50.]\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = chem(names=[\"A\", \"B\"]) # NOTE: Diffusion not applicable (just 1 bin)\n", "\n", "# Reaction A <-> 3B , with 1st-order kinetics in both directions\n", "chem_data.add_reaction(reactants=[\"A\"], products=[(3,\"B\",1)], forward_rate=5., reverse_rate=2.)\n", "\n", "bio = BioSim1D(n_bins=1, chem_data=chem_data)\n", "\n", "bio.set_uniform_concentration(species_index=0, conc=10.)\n", "bio.set_uniform_concentration(species_index=1, conc=50.)\n", "\n", "bio.describe_state()" ] }, { "cell_type": "code", "execution_count": 5, "id": "025dc8d4-cc77-48fe-90f6-eab7f3383310", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> 3 B (kF = 5 / kR = 2 / delta_G = -2,271.4 / K = 2.5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'A'}\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 6, "id": "fd1b6f4c-1327-4f5c-8ac0-ad0a61cc728e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
0010.050.0Initial state
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0 10.0 50.0 Initial state" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Save the state of the concentrations of all species at bin 0\n", "bio.add_snapshot(bio.bin_snapshot(bin_address = 0), caption=\"Initial state\")\n", "bio.get_history()" ] }, { "cell_type": "code", "execution_count": 7, "id": "6aa601cb-5f4a-4a16-bde8-abb514bb25c2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `reaction_2.log.htm`]\n" ] } ], "source": [ "# Send the plot to the HTML log file\n", "chem_data.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "markdown", "id": "c505025d-9bfd-485f-8465-2204353575a7", "metadata": { "tags": [] }, "source": [ "### First step" ] }, { "cell_type": "code", "execution_count": 8, "id": "1ec91d5e-717e-45f5-a88c-f8e8df328e48", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.1:\n", "1 bins and 2 species:\n", " Species 0 (A). Diff rate: None. Conc: [15.]\n", " Species 1 (B). Diff rate: None. Conc: [35.]\n" ] } ], "source": [ "# First step\n", "bio.react(time_step=0.1, n_steps=1, snapshots={\"sample_bin\": 0})\n", "bio.describe_state()" ] }, { "cell_type": "markdown", "id": "7a9b3abf-86e7-4ef3-9ddc-23e4a2698c7c", "metadata": {}, "source": [ "_Early in the reaction :_ \n", "[A] = 15. [B] = 35." ] }, { "cell_type": "code", "execution_count": 9, "id": "23c2fb5d-c5ea-4873-a4fa-cd28a55865b0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SYSTEM TIMEABcaption
00.010.050.0Initial state
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.0 50.0 Initial state\n", "1 0.1 15.0 35.0 " ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bio.get_history()" ] }, { "cell_type": "markdown", "id": "8eaf0873-53fd-4928-804c-2a2385fc4931", "metadata": {}, "source": [ "### Numerous more steps" ] }, { "cell_type": "code", "execution_count": 10, "id": "6c178528-e88b-4be4-ab61-a5f1f6d57c36", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 1.1:\n", "1 bins and 2 species:\n", " Species 0 (A). Diff rate: None. Conc: [14.54545455]\n", " Species 1 (B). Diff rate: None. Conc: [36.36363636]\n" ] } ], "source": [ "# Numerous more steps\n", "bio.react(time_step=0.1, n_steps=10, snapshots={\"sample_bin\": 0})\n", "\n", "bio.describe_state()" ] }, { "cell_type": "markdown", "id": "260cfdf1-a424-44cb-af29-7cdc693d16f6", "metadata": { "tags": [] }, "source": [ "### Equilibrium" ] }, { "cell_type": "markdown", "id": "17457676-5007-41b3-b8c2-a83a3d72ee47", "metadata": {}, "source": [ "Consistent with the 5/2 ratio of forward/reverse rates (and the 1st order reactions),\n", "the systems settles in the equilibrium: [A] = 14.54545455 , [B] = 36.36363636" ] }, { "cell_type": "code", "execution_count": 11, "id": "bb44d88c-bb34-41d7-b8c2-ca15938495d6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> 3 B\n", "Final concentrations: [A] = 14.55 ; [B] = 36.36\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.5\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 2.5\n", "Discrepancy between the two values: 6.875e-10 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "bio.reaction_dynamics.is_in_equilibrium(conc=bio.bin_snapshot(bin_address = 0))" ] }, { "cell_type": "code", "execution_count": 12, "id": "0f7ccafe-3fa4-4934-8f6f-8f6b774d1cf6", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.000000 50.000000 Initial state\n", "1 0.1 15.000000 35.000000 \n", "2 0.2 14.500000 36.500000 \n", "3 0.3 14.550000 36.350000 \n", "4 0.4 14.545000 36.365000 \n", "5 0.5 14.545500 36.363500 \n", "6 0.6 14.545450 36.363650 \n", "7 0.7 14.545455 36.363635 \n", "8 0.8 14.545454 36.363637 \n", "9 0.9 14.545455 36.363636 \n", "10 1.0 14.545455 36.363636 \n", "11 1.1 14.545455 36.363636 " ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bio.get_history()" ] }, { "cell_type": "markdown", "id": "7fbc0ddf-9903-48c2-af88-5fa2d2048371", "metadata": {}, "source": [ "Note how the simulation initially **OVERSHOT** the equilibrium values; the first step was too large!" ] }, { "cell_type": "markdown", "id": "715af433-0129-4fdf-a172-77f9d3d127a2", "metadata": { "tags": [] }, "source": [ "# Plots of changes of concentration with time" ] }, { "cell_type": "code", "execution_count": 13, "id": "9ee92b39-26ee-4fa0-a93b-a0ee5048293d", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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VyNphWHbdTjXZ4Ye9VqcQpJR+lTuvel52faUEsk73iR2oFgoEne6DJ/7iT+QHW3865AWu1Pi5Z7jaQVMhm2z74brmnsuZex5psb+C8x0r4hTKqbHyBXPlOLjZEV1qD4cbyLr93C7kWigUd3ohwtxzab0IZJ0+3/IFmbk15buHvOqx07nHTnPm/h2kQuMPPjoqTkdKlLIzvNjnBI8jgAACCCCAAAIIIIAAAgiYIUAga0afyqqy2Iv0lDUoT0IAgcgKFNrVG9lFh7wwtzuuQy6T6RFAAAEEEEAAAQQQQAABBDwUIJD1EDPModTuuq/ccHXmFeVVLYXOLAyzVuZGAAF9BUp9cS99V6J/ZVjr3yMqRAABBBBAAAEEEEAAAQT8ECCQ9UM1hDFzf/xblZD748QhlMWUCCBgoID9I/f8HeJf8/KdUe7fjIyMAAIIIIAAAggggAACCCCgiwCBrC6doA4EEEAAAQQQQAABBBBAAAEEEEAAAQQQiLwAgWzkW8wCEUAAAQQQQAABBBBAAAEEEEAAAQQQQEAXAQJZXTpBHQgggAACCCCAAAIIIIAAAggggAACCCAQeQEC2ci3mAUigAACCCCAAAIIIIAAAggggAACCCCAgC4CBLK6dII6EEAAAQQQQAABBBBAAAEEEEAAAQQQQCDyAgSykW8xC0QAAQQQQAABBBBAAAEEEEAAAQQQQAABXQQIZHXpBHUggAACCCCAAAIIIIAAAggggAACCCCAQOQFCGQj32IWiAACCCCAAAIIIIAAAggggAACCCCAAAK6CBDI6tIJ6kAAAQQQQAABBBBAAAEEEEAAAQQQQACByAsQyEa+xSwQAQQQQAABBBBAAAEEEEAAAQQQQAABBHQRIJDVpRPUgQACCCCAAAIIIIAAAggggAACCCCAAAKRFyCQjXyLWSACCCCAAAIIIIAAAggggAACCCCAAAII6CJAIKtLJ6gDAQQQQAABBBBAAAEEEEAAAQQQQAABBCIvQCAb+RazQAQQQAABBBBAAAEEEEAAAQQQQAABBBDQRYBAVpdOUAcCCCCAAAIIIIAAAggggAACCCCAAAIIRF6AQDbyLWaBCCCAAAIIIIAAAggggAACCCCAAAIIIKCLAIGsLp2gDgQQQAABBBBAAAEEEEAAAQQQQAABBBCIvACBbORbzAIRQAABBBBAAAEEEEAAAQQQQAABBBBAQBcBAlldOkEdCCCAAAIIIIAAAggggAACCCCAAAIIIBB5AQLZyLeYBSKAAAIIIIAAAggggAACCCCAAAIIIICALgIEsrp0gjoQQAABBBBAAAEEEEAAAQQQQAABBBBAIPICBLKRbzELRAABBBBAAAEEEEAAAQQQQAABBBBAAAFdBAhkdekEdSCAAAIIIIAAAggggAACCCCAAAIIIIBA5AUIZCPfYhaIAAIIIIAAAggggAACCCCAAAIIIIAAAroIEMjq0gnqQAABBBBAAAEEEEAAAQQQQAABBBBAAIHICxDIRr7FLBABBBBAAAEEEEAAAQQQQAABBBBAAAEEdBEgkNWlE9SBAAIIIIAAAggggAACCCCAAAIIIIAAApEXIJCNfItZIAIIIIAAAggggAACCCCAAAIIIIAAAgjoIkAgq0snqAMBBBBAAAEEEEAAAQQQQAABBBBAAAEEIi9AIBv5FrNABBBAAAEEEEAAAQQQQAABBBBAAAEEENBFgEBWl05QBwIIIIAAAggggAACCCCAAAIIIIAAAghEXoBANvItZoEIIIAAAggggAACCCCAAAIIIIAAAgggoIsAgawunaAOBBBAAAEEEEAAAQQQQAABBBBAAAEEEIi8AIFs5FvMAhFAAAEEEEAAAQQQQAABBBBAAAEEEEBAFwECWV06QR0IIIAAAggggAACCCCAAAIIIIAAAgggEHkBAtnIt5gFIoAAAggggAACCCCAAAIIIIAAAggggIAuAgSyunSCOhBAAAEEEEAAAQQQQAABBBBAAAEEEEAg8gIEspFvMQtEAAEEEEAAAQQQQAABBBBAAAEEEEAAAV0ECGR16QR1IIAAAggggAACCCCAAAIIIIAAAggggEDkBQhkI99iFogAAggggAACCCCAAAIIIIAAAggggAACuggQyOrSCepAAAEEEEAAAQQQQAABBBBAAAEEEEAAgcgLEMhGvsUsEAEEEEAAAQQQQAABBBBAAAEEEEAAAQR0ESCQ1aUT1IEAAggggAACCCCAAAIIIIAAAggggAACkRcgkI18i1kgAggggAACCCCAAAIIIIAAAggggAACCOgiQCCrSyeoAwEEEEAAAQQQQAABBBBAAAEEEEAAAQQiL0AgG/kWs0AEEEAAAQQQQAABBBBAAAEEEEAAAQQQ0EWAQFaXTlAHAggggAACCCCAAAIIIIAAAggggAACCERegEDWgxYfPtHhwSgMgQACuQKJhMi4plo5cpLPMe4OBPwSaKyrlJ6+tLR39vo1BeMiEGuBVDIhFzZWy7FTnbF2YPEI+ClwQUOVtHf1SWd3n5/TMDYCsRWoqkjKyLpK+exMV2wNTFz4hNG1JpYdm5oJZD1oNYGsB4gMgYCDAIEstwUC/gsQyPpvzAzxFiCQjXf/WX0wAgSywTgzS3wFCGTN7D2BrN59I5D1oD8Esh4gMgQCBLLcAwiEIkAgGwo7k8ZIgEA2Rs1mqaEJEMiGRs/EMREgkDWz0QSyeveNQNaD/hDIeoDIEAgQyHIPIBCKAIFsKOxMGiMBAtkYNZulhiZAIBsaPRPHRIBA1sxGE8jq3TcCWRF5vGWrPPXc9iGd+u79i2XB/Jusj23bvlMeWrfF+v2tt8yTR1Ytltqaqsz1BLJ63+RUZ64ARxaY2zsqN0eAQNacXlGpmQIEsmb2jarNEiCQNatfVGueAIGseT1TFRPI6t03AtnBQFa16b6lC8/r1u49+2VDy1bZtHaFNDU2WOFt7rUEsnrf5FRnrgCBrLm9o3JzBAhkzekVlZopQCBrZt+o2iwBAlmz+kW15gkQyJrXMwJZ/XtGIFskkFUB7JRJ4zK7ZXMDWtViAln9b3QqNFOAQNbMvlG1WQIEsmb1i2rNEyCQNa9nVGyeAIGseT2jYrMECGTN6pddLTtk9e4bgazDkQX2cQUdnd3y8PotMm/OzEwge+DQYXlwzWZ5tHmJTJs8weougazeNznVmStAIGtu76jcHAECWXN6RaVmChDImtk3qjZLgEDWrH5RrXkCBLLm9UxVrFsge+pMqyxbvVFWLl0oc2dPNxNVRJyywnIWQyCbo6YC16X3b5A1zUvkqulTrUD29ttuztws5wWyr6yVc5cskP7GqeX48xwEECggkBCR+toKae3oxQkBBHwSqKlMSl9apKe336cZGBaBeAskEyIjqiukrZN/y+J9J7B6PwVqq1LS09cvveofNN4QQMBzAfXNxerKpLR39Xk+NgP6J9BQW+Hf4HlGdnqNpnvumG8dERpmIKt+2r15zWZpWbcys7myXBwC2XLlXDzPPqbgG1+dV3yH7IaEpCvqpOvLG6RnxmIXo3MJAgi4FkiI1NdUSltHj+uncCECCJQmUF2Vkv7+NIFsaWxcjYBrgUQiISNqUnKOby66NuNCBEoVqK1OSU9vWnr7+OZiqXZcj4AbASuQrUpJO99cdMOlzTUNIyoDq8UOWy+ZMEYeWbVYamuqrLnt8FJtdLzs0ovZIZvVEXbIOtye2efGFj1D9mfLRN74+4EbbfK35MyXnpT+6lGB3fRMhECUBTiyIMrdZW26CHBkgS6doI6oCnBkQVQ7y7p0EuDIAp26QS1RFODIAjO7GuSRBSo7O3r85JAwNlfNDm2X3/VN+dE//5u89PIu6xJ7B619vX3d3n0HrQ/desu8zLh2wHv1zGny5tsHhozxnUXfsAJf+3n2caRqDKfXg7J/Qv7IsRPWPLNmTJVNa1dIU2OD5O70zX6MHbIefT6oRm9/eZd8e8HXrBFzjyTIbZpqinpT263tt5Ovb5VRv1wqye7T0lc7Tk793jPSPeZLHlXIMAjEV4BANr69Z+XBCRDIBmfNTPEUIJCNZ99ZdbACBLLBejNb/AQIZM3seVCBrB2gLrzt5szrLzmJ2dd9dvJM5uiA7GND1bmyTscaZIe9alx1tOhrb7173hjqMftIgmLZXu686rk/3fGKXHbpROtIg+8986Lc8pU5meMNnGrIfr2pcu6Q2O+QtZNtO5lXiE8/sXrIAcPbtu+Uh9ZtsXyzk3kbXL2oV6rjqIz6X3dL9dGdIpKU1ln3Seu1fy6SDP7MjnJuBJ6DgI4CBLI6doWaoiZAIBu1jrIe3QQIZHXrCPVEUYBANopdZU06CRDI6tQN97UEFcg6hZuFAtnsF/XK3W2q8rcPPjo6ZBNkdrg6YeyF5x0t6rRjNfdjbjZbFpJVNax/8nlZ88ASqamuPq8G9135/MrYB7LloOU+RwWyA29pqX/rr6XhtYcl0d8tPaOvlVM3/3fpbeAFv7xwZoz4CRDIxq/nrDh4AQLZ4M2ZMV4CBLLx6jerDUeAQDYcd2aNjwCBrJm9NjGQdXpRMKU/fuxoa/erF4GsHaiqc23VrlynN6fNm4VqKOcOIZAtRy3nOZ8HsgMPVJ7aK03/cqdUnH1X0qk6OXPj49J+2X/wYCaGQCBeAgSy8eo3qw1HgEA2HHdmjY8AgWx8es1KwxMgkA3PnpnjIUAga2afgwpkSz2yoNAOWadjQrP13eyGVdcX2iFbLJC1d/zO/+oNmZ26xXbplnOHEMiWo1YkkFUPJ/o6ZeSvVkndb5+yru685DY5/TstvOCXB94MER8BAtn49JqVhidAIBuePTPHQ4BANh59ZpXhChDIhuvP7NEXIJA1s8dBBbJKp9CLeqnjAtTbZZdebL3oVrEjC3a9+nbeFwfzIpC1X7RL1ZT9+lB2l1W9L7y4Y0gNBLKafg7k7pDNLrPm45/IqJ2LecEvTXtHWXoLEMjq3R+qi4YAgWw0+sgq9BUgkNW3N1QWHQEC2ej0kpXoKUAgq2dfilUVZCBr75K9ZMKYIUGm/ZpM6rWa3ASyTrtTVQi76R//X/nOom84nt/qJqTNPUNW/fnue9cOeQ0p+0W9Tp46K81rNmdeIMwe334hMadjE4r1wulxdsiWo5bznEKBrLqUF/zyAJkhYilAIBvLtrPogAUIZAMGZ7rYCRDIxq7lLDgEAQLZENCZMlYCBLJmtjvIQNYWyj0D1j53ddrkCWKHtoV2yKpx7Ov27juYgb/njvnWblY34at6UrEX9VLX2KGsPcmsGVNl09oVonbQ2kGyekytYdWyfy/ff/7H8mjzEsdzbMu5Qwhky1ErMZAduDwt9W//rTT8+iFe8MsDc4aIhwCBbDz6zCrDFSCQDdef2aMvQCAb/R6zwvAFCGTD7wEVRFuAQNbM/oYRyJopFU7VBLIeuBfbIZs9BS/45QE4Q8RGgEA2Nq1moSEKEMiGiM/UsRAgkI1Fm1lkyAIEsiE3gOkjL0Aga2aLCWT17huBrAf9KSWQVdNZL/i1e7XU7f+eNTsv+OVBExgikgIEspFsK4vSTIBAVrOGUE7kBAhkI9dSFqShAIGshk2hpEgJEMia2U4CWb37RiDrQX9KDWTtKa0X/PrFEkl2nZD+mjFy6qbvS9eE3/OgIoZAIBoCBLLR6COr0FuAQFbv/lCd+QIEsub3kBXoL0Agq3+PqNBsAQJZM/tHIKt33whkPehPuYGsmjrZeVyadt4j1Ydftio5d/l35OwN6yRdUedBZQyBgNkCBLJm94/qzRAgkDWjT1RprgCBrLm9o3JzBAhkzekVlZopQCBrZt8IZPXuG4GsB/0ZTiBrT1+3f7OM3P2AJPrOSV/dRDn9laeka9xXPKiOIRAwV4BA1tzeUbk5AgSy5vSKSs0UIJA1s29UbZYAgaxZ/aJa8wQIZM3rmaqYQFbvvhHIetAfLwJZVUbq3CFp2rFYqj79N3XSrJybvlTOzn1U0qlaD6pkCATMEyCQNa9nVGyeAIGseT0pq+YRAAAgAElEQVSjYrMECGTN6hfVmilAIGtm36jaHAECWXN6lV0pgazefSOQ9aA/XgWyA6Wkpf7tv5OGVx+WRF+H9NVPllO/+wPpvmiuB5UyBAJmCRDImtUvqjVTgEDWzL5RtTkCBLLm9IpKzRUgkDW3d1RuhgCBrBl9yq2SQFbvvhHIetAfbwPZgYIqWg9I044/lMoTr6uTZqXtyv8srdc9IulUlQcVMwQCZggQyJrRJ6o0W4BA1uz+Ub3+AgSy+veICs0XIJA1v4esQG8BAlm9+5OvOgJZvftGIOtBf/wIZK2y0v1S/5u/kobX/kIS/V3SO/JyOfW7T0vP6Gs9qJohENBfgEBW/x5RofkCBLLm95AV6C1AIKt3f6guGgIEstHoI6vQV4BAVt/eFKqMQFbvvhHIetAf3wLZwdoqzrwrTTvulMpTe0USKWm9aqW0XfugpJOVHlTPEAjoK0Agq29vqCw6AgSy0eklK9FTgEBWz75QVbQECGSj1U9Wo58Agax+PXFTEYHsgFJHZ7c8vH6LfHj4uGxau0KaGhvc8Pl+DYGsB8R+B7JWif290rD3v0n9G2sk0d8jPaNmyOmbn7He84ZAVAUIZKPaWdalkwCBrE7doJYoChDIRrGrrEk3AQJZ3TpCPVETIJA1s6MEsgN9O3DosLT84J/kbFu73HPHfJk7e7oWDSWQ9aANgQSyg3VWnt4no9Ru2dP7rB2ybbMfsHbMSrLCg5UwBAJ6CRDI6tUPqommAIFsNPvKqvQRIJDVpxdUEl0BAtno9paV6SFAIKtHH0qtgkB2QGzb9p0Zug8+Oir3LV1YKqUv1xPIesAaZCCrylU7ZOv3PGbtmJV0n/Q0zZJTNz8jvY2Xe7AahkBAHwECWX16QSXRFSCQjW5vWZkeAgSyevSBKqItQCAb7f6yuvAFCGTD70E5FYQRyP7oR78tp9RhPaeqKiVf//o0xzHUcQXrNz0v317w+9bj6598XtY8sESLYwsIZIfV9oEnBx3I2iVXnnhdmv7X3VJx9l1JJ6ul7Zr7pe2qlZJOVXmwKoZAIHwBAtnwe0AF0RcgkI1+j1lhuAIEsuH6M3s8BAhk49FnVhmeAIFsePbDmTnoQPazz9rloovWD6fksp570UUj5PjxVY7PVccVPLvtZ7Jq2SLrcXWW7Lw5M2XB/JvKmsvLJxHIeqAZViCrSk/0dUv9G2ul/q0N1s7Z3obL5PRN/yDdF33Rg5UxBALhChDIhuvP7PEQIJCNR59ZZXgCBLLh2TNzfAQIZOPTa1YajgCBbDjuw5016ED27NkuufPObcMtu+TnjxxZLc88s8DxeY+3bJUpk8ZlAlh1fMGuV9+WR1YtltqacDczEsiW3OrznxBmIGtXU3H6HWn6xT1SeeI1FdPKuS98R1qvf0z6q0Z6sEKGQCAcAQLZcNyZNV4CBLLx6jerDV6AQDZ4c2aMnwCBbPx6zoqDFSCQDdbbq9mCDmS9qturcU6daZVlqzfK3n0Hhww5fuxoaVm3UqZNnuDVVGWNQyBbFtvQJ+kQyA5UlJa6/f8gI1/9vyTR0yp9NWPl7I0bpGOy83cKPFg6QyDgqwCBrK+8DI6AJUAgy42AgL8CBLL++jI6AkqAQJb7AAF/BQhk/fX1a/S4B7K79+yXDS1bZdPaFUPOjM3dNeuXf7FxCWSLCbl4XJ9AdqDYVMdRafzlcqn55CfWnzsv/gM586W/kb66i12shksQ0EeAQFafXlBJdAUIZKPbW1amhwCBrB59oIpoCxDIRru/rC58AQLZ8HtQTgVxD2RV8Kre7lu6cAifCmpfeHFH6McWEMiWc1fnPEe3QNYur/bQP8nIXSsk1XFE0hX10jrnYWmbvkwkkfRg1QyBgP8CBLL+GzMDAgSy3AMI+CtAIOuvL6MjoAQIZLkPEPBXgEDWX1+/Ro97IOuXq1fjEsh6IKlrIKuWluhpk5G/flDq3vkH60iDnqar5fTvPiU9o670YOUMgYC/AgSy/voyOgJKgECW+wABfwUIZP31ZXQECGS5BxDwX4BA1n9jP2YgkPVD1bsxCWQ9sNQ5kLWXV/XpKzJq53+Uitb3RBIV0nbln0jrtQ9JOlXrgQBDIOCPAIGsP66MikC2AIEs9wMC/goQyPrry+gIEMhyDyDgvwCBrP/GfsxAIOuHqndjEsh6YGlCIKuWmejrlvq3Nkj9G38pif5u6au/RE5/+XvSNe4mDxQYAgHvBQhkvTdlRARyBQhkuScQ8FeAQNZfX0ZHgECWewAB/wUIZP039mMGAlk/VL0bk0DWA0tTAll7qRVn35NRv/iPonbNqreOyf+7nP3iOl70y4N7gSG8FSCQ9daT0RBwEiCQ5b5AwF8BAll/fRkdAQJZ7gEE/BcgkPXf2I8ZCGT9UPVuTAJZDyxNC2QHlpyWut8+LQ27myXZc9Y6uqDt6j+TtqtWSDpV44EKQyAwfAEC2eEbMgICxQQIZIsJ8TgCwxMgkB2eH89GwI0AL+rlRolrEChfgEC2fLswn0kgG6Z+8blDDWRPnWmVZas3yt59B8+rdNaMqbJp7QppamwovoqQrzAzkB1AS3adkJGvPCAjDjxjhbR99ZPl7Ny10jH5myGrMj0CIgSy3AUI+C9AIOu/MTPEW4BANt79Z/XBCBDIBuPMLPEVIJA1s/cEsnr3LdRA9vGWrZbOfUsX6q1UpDqTA1l7aZUnXpdR/9+fiHqv3rrGfkXOfOlvpLfxC0b3huLNFiCQNbt/VG+GAIGsGX2iSnMFCGTN7R2VmyNAIGtOr6jUTAECWTP7RiCrd99CC2TV7tjmxzbLquWLZNrkCVoodXR2y8Prt1i1PLJqsdTWVFm/37Z9pzy0buDjt94yb8hj6mNRCGQHGpCWEe89Jw2/flBSncdEEhXSNv2PpfW6P5d0Zb0WPaKIeAkQyMar36w2HAEC2XDcmTU+AgSy8ek1Kw1PgEA2PHtmjocAgayZfSaQ1btvBLKD/bHD2Jde3jUkdN29Z79saNmaOT7BaVdvdALZAYxE7zlp2POo1L39pCT6u6W/+iI5e/1fSPvlf6ge1fuOprpICRDIRqqdLEZTAQJZTRtDWZERIJCNTCtZiMYCBLIaN4fSIiFAIGtmGwlk9e5baIGsYlHh5pRJ42TB/JtCV7JrUYXsevXtzC7Y3BpzA1p1fdQCWbsZFW3vS+O//iepPrLD+lBP0yw5/eW/l57R14beLwqIhwCBbDz6zCrDFSCQDdef2aMvQCAb/R6zwvAFCGTD7wEVRFuAQNbM/sY9kM3eeGl3cPzY0dKybqUWP6kfaiB74NBheXbbz2TVskWZ4wHCuM2zd72q4wnsQFbVoo4wmDdnZiY0VjU/uGazPNq8JNPAqAaydi9qPvmpjNy1Sipa37N2yLZf9n/I2esfk/6ai8JoF3PGSIBANkbNZqmhCRDIhkbPxDERIJCNSaNZZqgCBLKh8jN5DAQIZM1sMoHswLGk2ZleduZnH1MaVndDC2TVGbLLVm+UvfsOOq591oypmWMC/MRRzfjgo6OZFxZzCmRvv+1mmTt7ulWGUyDrZ33ajN3fI/LqRpF/+65IT5uIOlP2+vtErv8zkaoGbcqkEAQQQAABBBBAAAEEEEAAAQQQQACBeAvYO2SzA1mnn3oPSym0QDasBefOq3bHPvXc9vPKUS/etfo/3ylr/+aZ2O+QzcZJdn4qI3c3y4gDz1kvAtZfPVrarvk/5dwVfyTp1MCLoPGGgFcC7JD1SpJxEMgvwA5Z7g4E/BVgh6y/voyOgBJghyz3AQL+CrBD1l9fv0YPZYfswR/5tZz84yarRKZ8/bzHnQLZ3E2ZwRf7+YyxD2Rz8XO3L8f5DNlCN2blyTdl5K8fkOrDP7cu66u/RFpnPyTt0+4QSSTDvKeZO0ICBLIRaiZL0VaAQFbb1lBYRAQIZCPSSJahtQCBrNbtobgICBDImtnEwAPZjs9EngzhaMvai0SWH88byL708q4hj91zx/zMT8mH2dnQA1m1Xfjue9cOMXj6idWZIwKCxskNZHO3M2efN2vXFvUzZAv1oPrYL2TkK81SeeI167KeUTOkdc5fSOekW4NuHfNFUIBANoJNZUnaCRDIatcSCoqYAIFsxBrKcrQUIJDVsi0UFSEBAlkzmxl4INt9VuSlO4PHqh4pMv+ZvIFs9pEFTrtmgy94YMZQA1mnsxvUGa1L798gy+/6ZuaFtILEcTrgV33soXVbrDLUUQaPrFo85EXI4hzI2r2p+fBFGfnaw1Jxer/1oe4L58rZL66V7jE3Btk+5oqYAIFsxBrKcrQUIJDVsi0UFSEBAtkINZOlaCtAIKttaygsIgIEsmY2MvBAVjOmfOGrLscWhBbI2jDZL5hl904FtS+8uOO84FOz3mbKIZAdpEj3y4iD/7c0vPZdSZ37yPpg58V/IK3X/1fpaZqpa/uoS2MBAlmNm0NpkREgkI1MK1mIpgIEspo2hrIiJUAgG6l2shgNBQhkNWyKi5IIZLvl4fVbhrwuFDtkReTUmVZpfmyzrFq+SKZNnjDkVlK7ZNc/+byseWCJNDU2uLjNwr2EQHaof6KvW+p+u1nq9/ylJLs+E5GktE9dKK1zHpa+usnhNovZjRIgkDWqXRRrqACBrKGNo2xjBAhkjWkVhRosQCBrcPMo3QgBAlkj2nRekQSyA4Fs7hmy371/cSg/kZ/bIHbIevB5RSDrjJjoaZP6t/9a6vc+IYneNkknK6Vj6kJpm3W/9DZe7oE8Q0RdgEA26h1mfToIEMjq0AVqiLIAgWyUu8vadBEgkNWlE9QRVQECWTM7G/dAVveuhRbIKhh1bsPWF3fIprUrMjthwz5DtpyGEcgWVkt2npT6N/9S6vZ/TxL9XeroYumc+A1pu+bPpPuieeWQ85yYCBDIxqTRLDNUAQLZUPmZPAYCBLIxaDJLDF2AQDb0FlBAxAUIZM1sMIGs3n0LNZBVNOq82LvvXTtE6eknVsvc2dP1lsuqjkDWXatSHcek7jd/JXXvPCWJnlbrSd0X3WgFsyqg5Q2BXAECWe4JBPwXIJD135gZ4i1AIBvv/rP6YAQIZINxZpb4ChDImtl7Alm9+xZ6IKs3j7vqCGTdOdlXqTC2fv9mGfH230qq46j14Z5RM+TcVSuts2YlWVHagFwdWQEC2ci2loVpJEAgq1EzKCWSAgSykWwri9JMgEBWs4ZQTuQECGTNbCmBrN59I5D1oD8EsuUhqhf/qj34nNTvfVwqzr5rDdJXN1HOXfmncu6KxZJOjShvYJ4VGQEC2ci0koVoLEAgq3FzKC0SAgSykWgji9BcgEBW8wZRnvECBLJmtpBAVu++Ech60B8C2eEipqXmwx9J/d4NUvXpK9Zg/VWj5Nz0P5ZzM/9E+msuGO4EPN9QAQJZQxtH2UYJEMga1S6KNVCAQNbAplGycQIEssa1jIINEyCQNaxhg+USyOrdt8AD2VNnWmXZ6o3ynX//B/L9//ET2bvvoKPQrBlTh7zYl86MBLLedaf62C+l7q2/kpqPXsoM2jHldum4/E7pvPhr3k3ESFoLJLvPSqLnlKS6T8vo6i45eVa9GFzOW7pPpL9PEqLe94qk+yTR36f2WQ98XD0u6mO91p/V45//uT/zuPVc9XgyJZJIDvySpKQH34tKhQc/npbBx+3rEoPXqT+nBx6znpf1nMxYWc+xPpY7VokdSVv1Vko6WSmSqpR0Iut9cuDP6VSliPp9qqbE0bk8TgIEsnHqNmsNQ4BANgx15oybAIFs3DrOeoMWIJANWtyb+QhkvXH0a5TAA1l7ISqYbX5ss6xavkimTZ4wZH3qhb5eeHGHPLJqsdTWVPm1ds/GJZD1jDIzUMXp/VL/1hMy4r0fZD7WN2KCtE+7UzquuEt66y/1flJG9EUg2XVKkp2fSbLrU0l2npCU9fvPJNH+qfWxVOcJSXadlETXaUn2nBJ1PW/+CljHgajw2Ap11a8KSav3g39OJyoGQuhkStKiPq7+nBq4Rr1XITBvkRGoSCUknRbp609HZk0sBAGdBNT36CpTSenu7depLGpBIFIClamE9KXT0s+nWaT6ymL0EUgmRFKphPT08vWiPl0pXkn1nTuLX8QVoQloGcgeOHRY1j/5vKx5YIk0NTaEhuN2YgJZt1KlX5fs/FRGvPeMjHjvv4sKae237jFfkvYr7paOKQs4a7Z0Vs+eocLTVPvHkmo/IqnWQ5I894mkzh2S1LlPpOLcR5JqO1TWXOmKeumvHmUdXVFZd4F09Tj8w2/tQh0MCK0wcTBUtAPGpNqpmhIRFSBWfB422gFjUu1mHQgjrevUDtq0+ipe7Z7tH/i9SqkGf5+QgcfsP6v31nVZHxt43uBzBq//fKzPn2uNZc8h6vrSv7BJ9PeIpHsk0ff5+0S6R6Q/52N958rqAU9CAAEEEEAAAQQQQAABBBAwWGBl6f/PNHi1xpWuZSC7bftO2fXq2+yQNe528rfgqs9+LbUqnD3wnCR6Wq3J0qk6K5Tt+MJ/kK6xX/a3gJiOroLwitYDUtF6UFJnD0jq7PtSoULXtk8k4SLsGwhXL5S+2gut9/216vdjJV092vq99bHqC6S/qmkghK25KCPNGbLe33SJvo7B4x1UKKxC6N6B4xsGj3VIpAeOf1BbTOxjH9SxDplrrGMg1PEPvEVFoK4mJWrjXlc3fY1KT1mHXgLq+4ONdVVyqrVbr8KoBoEICTSMqJCunn7p7mGLbITaylI0ElA/UVVXUyFnzvVoVBWlFBMYfeXXi13C4yEKBB7Iqt2vS+/fIEeOnci77PFjR0vLupXnHWUQolPBqdkhG2xnEv1dUnPon2TEuz+Q6sP/MrBDUZ0OOmKCdE34fema9HXpGv/70l81MtjCDJ0t0dsmFWcHAteKswclaf9eBbDnPlGxd96VqR9976u7WPrqJ0nfiInS13CJ9NVNlL4RkwbeN1wi6WR12TIEsmXT8UQEXAtwhqxrKi5EoCwBzpAti40nIVCSAGfIlsTFxQiULMAZsiWTafEEzpDVog15iwg8kLUrKXSGrN5k51dHIBtex1RgOOLAMzLinX+U1LkPhhTSfdE86Zr4NSuk7b5obnhFajCzOvrB2uV69n1Jtb0vqTPvSkXrB1Jx9j1JduX/5ogVdNdfIr0NU61ffSOnSe/IywcC2LqJ0l892tfVEcj6ysvgCFgCBLLcCAj4K0Ag668voyOgBAhkuQ8Q8FeAQNZfX79GJ5D1S9abcUMLZL0pX49RCGT16EPlqbek5uP/KdUf/Viqjv/rkKL6q5uka/wt0jXx30n3uC9F8kXBKlTQ2nrI2umabH1/YNfr2YPWn9Uu2EJvKmTtrZ8ivY1XSP/IKYMB7DTpbbw81OYSyIbKz+QxESCQjUmjWWZoAgSyodEzcYwECGRj1GyWGooAgWwo7MOelEB22IS+DkAg6wEvgawHiB4Poc6YrfnkZan+eLtUf/zPkuo8lhPQjpbuMfOkZ8wXpfuiG6T7wutEnXWq81uq7SNrHalzH0rF2Q8kqY4YaPtg4EzXtvcLlq6OFlDham/9ZOkbOVX6GtRO12nS2zBF+uqnaLtsAlltW0NhERIgkI1QM1mKlgIEslq2haIiJkAgG7GGshztBAhktWuJq4IIZF0xhXZRqIFsofNkZ82YKpvWrpCmxobQcNxOTCDrViq86+zds1Wf/E+p+nS3WC9slPPWVztO+lRgWad+RP9S6a+fNPC+ZrT1o/nqR/S9fEt2nrSOC0h2n5Bkx2cDv+86KcmO45JqPyLJjmNWAJtsPyrJ7tNFp+6rGSt91tECk6331u9HXmoFr/01Y4o+X8cLCGR17Ao1RU2AQDZqHWU9ugkQyOrWEeqJogCBbBS7ypp0EiCQ1akb7mshkHVvFcaVoQWyHZ3d8vD6LTJvzky55srL5NltP5NVyxZJbU2VPN6yVb5yw9Uyd/b0MExKnpNAtmSy0J9QefINqfrsNak8/opUnnhdKk+96aqmdKpO+msHAtr+EnbUqleoT3aflER3qyR7zorawVvqmwpc+2vHWi+i1Vt/qfQ3Xjpwrqs6aqBhiqRTtaUOqf31BLLat4gCIyBAIBuBJrIErQUIZLVuD8VFRIBANiKNZBnaChDIatuagoURyOrdt9AC2ewX9VJE6598XtY8sMTaEbt7z3554cUd8siqxVZAq/sbgazuHXJXn3qBK+tYgHMfSqpN/fpA1IuGpTqPi7WbtfO4u4FcXtVfOXIg2K0dI/1VozI7cdO1Y6RvxFjpVzteawdD2NqxLkeN1mUEstHqJ6vRU4BAVs++UFV0BAhko9NLVqKvAIGsvr2hsmgIEMia2UcCWb37pkUge8GoBlnz189K859+2wpk1VEG2QGt3oQiBLK6d8i7+pLdZyTZ9ZkkO09Ioq/L9cDpZIWkq0ZKf0WDpK0gdpTr58b5QgLZOHeftQclQCAblDTzxFWAQDaunWfdQQoQyAapzVxxFCCQNbPrBLJ69y20QDb7yIIF82+yjimYMmmcqN9v275Tdr36Njtk9b53qA4B3wUIZH0nZgIEhECWmwABfwUIZP31ZXQElACBLPcBAv4KEMj66+vX6ASyfsl6M25ogWxu+eoIg2WrN8refQdl/NjR0rJupUybPMGbVfo8CjtkfQZm+NgKEMjGtvUsPEABAtkAsZkqlgIEsrFsO4sOWIBANmBwpoudAIGsmS0nkNW7b9oEsnozFa6OQNbk7lG7zgIEsjp3h9qiIkAgG5VOsg5dBQhkde0MdUVJgEA2St1kLToKEMjq2JXiNRHIFjcK84rQAtnsF/UyZSdsvkYRyIZ5CzN3lAUIZKPcXdamiwCBrC6doI6oChDIRrWzrEsnAQJZnbpBLVEUIJA1s6sEsnr3jUDWg/4QyHqAyBAIOAgQyHJbIOC/AIGs/8bMEG8BAtl495/VByNAIBuMM7PEV4BA1szeE8jq3bfQAlnFol7I6ys3XC1zZ0/XW6lIdQSyRreP4jUWIJDVuDmUFhkBAtnItJKFaCpAIKtpYygrUgIEspFqJ4vRUIBAVsOmuCiJQNYFUoiXhBrIHjh0WJ7d9jNZtWyR1NZUhcgwvKkJZIfnx7MRyCdAIMu9gYD/AgSy/hszQ7wFCGTj3X9WH4wAgWwwzswSXwECWTN7TyCrd99CC2TVGbLLVm+UvfsOOgrNmjFVNq1dIU2NDXoLigiBrPYtokBDBQhkDW0cZRslQCBrVLso1kABAlkDm0bJxgkQyBrXMgo2TIBA1rCGDZZLIKt330ILZPVmKa06AtnSvLgaAbcCBLJupbgOgfIFCGTLt+OZCLgRIJB1o8Q1CAxPgEB2eH48G4FiAgSyxYT0fJxAVs++2FWFFsiqHbLNj22WVcsXybTJE4Yo7d6zX154cYc8smqxEUcZEMjqfZNTnbkCBLLm9o7KzREgkDWnV1RqpgCBrJl9o2qzBAhkzeoX1ZonQCBrXs9UxQSyevdNy0BWnS27/snnZc0DSziyQO/7h+oQ8FWAQNZXXgZHwBIgkOVGQMBfAQJZf30ZHQElQCDLfYCAvwIEsv76+jU6gaxfst6Mq2Ugu237Ttn16tuB7ZB9vGWrPPXc9ozo00+slrmzp2f+rOp5aN0W68+33jLvvLrYIevNzcgoCOQKEMhyTyDgvwCBrP/GzBBvAQLZePef1QcjQCAbjDOzxFeAQNbM3hPI6t23wANZtft16f0b5MixE3llxo8dLS3rVp53lIEflOrohO8//2NZdte3rOMRVH0PrtksjzYvseZXxydsaNmaeYExFd6qt/uWLsyUQyDrR2cYEwERAlnuAgT8FyCQ9d+YGeItQCAb7/6z+mAECGSDcWaW+AoQyJrZewJZvfsWeCBrcxQ6QzZMMlXXstUbZeXShdYuWRXATpk0ThbMv8kqKzegVR8jkA2zY8wdZQEC2Sh3l7XpIkAgq0snqCOqAgSyUe0s69JJgEBWp25QSxQFCGTN7CqBrN59Cy2Q1ZVFBa7NazZbO3QnjL1QHl6/RebNmZkJZHN30BLI6tpJ6oqCAIFsFLrIGnQXIJDVvUPUZ7oAgazpHaR+EwQIZE3oEjWaLEAga2b3CGT17huB7GB/so9SsM+Q7ejstgLZ22+7OXOmrFMg29rRq3eXqQ4BQwUSIlJfWyF8jhnaQMo2QqCmMil9aZGe3n4j6qVIBEwTSCZERlRXSFsnXy+a1jvqNUegtiolPX390qv+QeMNAQQ8F1DfXKyuTEp7V5/nYzOgfwINtRX+Dc7IwxYINZC1jwfYu+/geQuZNWNq5tzWYa+yhAGyjyy4avpUVztkW9t7SpiBSxFAwLVAQqS+plLaOvgcc23GhQiUKFBdlZL+/jSBbIluXI6AW4FEIiEjalJyjm/guyXjOgRKFqitTklPb1p6+/jmYsl4PAEBFwJWIFuVkna+uehCS59LGkZU6lMMlZwnEGog6/QCWTr0KPvcWM6Q1aEj1BBXAY4siGvnWXeQAhxZEKQ2c8VRgCML4th11hy0AEcWBC3OfHET4MgCMzvOkQV69y20QFaXF/VSRxC8/ItX5Y/uvM3qlH10wZrmJdYxBbkv4uUUIvOiXnrf5FRnrgCBrLm9o3JzBAhkzekVlZopQCBrZt+o2iwBAlmz+kW15gkQyJrXM1UxgazefYt9IGufE/vSy7synbLPkLU/sG37Tnlo3Rbrj7feMk8eWbVYamuqMtcTyOp9k1OduQIEsub2jsrNESCQNadXVGqmAIGsmX2jarMECGTN6hfVmidAIGtezwhk9e9ZaIGsosk9DkB/LucKCWRN7Rx16y5AIKt7h6gvCgIEslHoImvQWYBAVufuUFtUBAhko9JJ1qGrAIGsrp0pXBc7ZPXuW6iBrDoe4NltP5NVyxYN2XGqN9n51RHImtYx6jVFgEDWlE5Rp8kCBLImd4/aTRAgkDWhS9RougCBrOkdpH7dBXNXJOgAACAASURBVAhkde+Qc30Esnr3LbRAVp0hu2z1Rtm776Cj0KwZU2XT2hXS1Nigt6CIEMhq3yIKNFSAQNbQxlG2UQIEska1i2INFCCQNbBplGycAIGscS2jYMMECGQNa9hguQSyevcttEBWb5bSqiOQLc2LqxFwK0Ag61aK6xAoX4BAtnw7nomAGwECWTdKXIPA8AQIZIfnx7MRKCZAIFtMSM/HCWT17ItdFYGsB/0hkPUAkSEQcBAgkOW2QMB/AQJZ/42ZId4CBLLx7j+rD0aAQDYYZ2aJrwCBrJm9J5DVu2+hBrIdnd3y8Pot8tLLu2T82NHSsm6lTBh7ofWxeXNmyoL5N+mtN1gdgawRbaJIAwUIZA1sGiUbJ0Aga1zLKNgwAQJZwxpGuUYKEMga2TaKNkiAQNagZmWVSiCrd99CDWQfb9kqUyaNk298dZ6s3/S8fHvB78u0yRNk95798sKLO+SRVYuNeLEvAlm9b3KqM1eAQNbc3lG5OQIEsub0ikrNFCCQNbNvVG2WAIGsWf2iWvMECGTN65mqmEBW776FFsiqF/VqfmyzrFq+yNoVmx3IHjh0WNY/+byseWAJL+ql9/1DdQj4KkAg6ysvgyNgCRDIciMg4K8Agay/voyOgBIgkOU+QMBfAQJZf339Gp1A1i9Zb8bVMpBlh6w3zWUUBEwXIJA1vYPUb4IAgawJXaJGkwUIZE3uHrWbIkAga0qnqNNUAQJZMztHIKt330ILZBXLtu07Zderb0vzn35b/mbL/2MdWXDBqAZZtnqjLLztZs6Q1fveoToEfBcgkPWdmAkQYIcs9wACPgsQyPoMzPAIsEOWewAB3wUIZH0n9mUCAllfWD0bNNRAVq1C7Ya9+961Qxb09BOrZe7s6Z4t0u+BOEPWb2HGj6sAgWxcO8+6gxRgh2yQ2swVRwEC2Th2nTUHLcAO2aDFmS9uAgSyZnacQFbvvoUeyOrN4646All3TlyFQKkCBLKlinE9AqULEMiWbsYzEChFgEC2FC2uRaA8AQLZ8tx4FgJuBQhk3UrpdR2BrF79yK0m1ED28ZatcvT4SXlk1WKpramyauvo7JaH12+ReXNmcmSB3vcO1SHguwCBrO/ETIAARxZwDyDgswCBrM/ADI8ARxZwDyDguwCBrO/EvkxAIOsLq2eDhhbI2sHr7bfdfN7xBLyol2f9ZSAEjBYgkDW6fRRviAA7ZA1pFGUaK0Aga2zrKNwgAXbIGtQsSjVSgEDWyLYJgazefQstkD11plWaH9ssq5YvkmmTJwxROnDosKx/8nlZ88ASaWps0FtQRDiyQPsWUaChAgSyhjaOso0SIJA1ql0Ua6AAgayBTaNk4wQIZI1rGQUbJkAga1jDBsslkNW7b6EFsuyQ1fvGoDoEdBAgkNWhC9QQdQEC2ah3mPWFLUAgG3YHmD8OAgSycegyawxTgEA2TP3y5yaQLd8uiGeGFsiqxamjCZrXbJaWdSszu2TV7til92+Q5Xd9kzNkg7gDmAMBjQUIZDVuDqVFRoBANjKtZCGaChDIatoYyoqUAIFspNrJYjQUIJDVsCkuSiKQdYEU4iWhBrJq3XYAe+TYiQzD00+sPu9c2RCNik7NkQVFibgAgbIECGTLYuNJCJQkQCBbEhcXI1CyAIFsyWQ8AYGSBQhkSybjCQiUJEAgWxKXNhcTyGrTCsdCQg9k9eZxVx2BrDsnrkKgVAEC2VLFuB6B0gUIZEs34xkIlCJAIFuKFtciUJ4AgWx5bjwLAbcCBLJupfS6jkBWr37kVkMg60F/CGQ9QGQIBBwECGS5LRDwX4BA1n9jZoi3AIFsvPvP6oMRIJANxplZ4itAIGtm7wlk9e5bqIHsqTOtsmz1Rtm77+B5SrNmTJVNa1dIU2OD3oIiQiCrfYso0FABAllDG0fZRgkQyBrVLoo1UIBA1sCmUbJxAgSyxrWMgg0TIJA1rGGD5RLI6t23UAPZx1u2Wjr3LV2ot1KR6ghkjW4fxWssQCCrcXMoLTICBLKRaSUL0VSAQFbTxlBWpAQIZCPVThajoQCBrIZNcVESgawLpBAvCS2QVbtjmx/bLKuWL5JpkyeESDD8qQlkh2/ICAg4CRDIcl8g4L8Agaz/xswQbwEC2Xj3n9UHI0AgG4wzs8RXgEDWzN4TyOrdNwJZD/pDIOsBIkMg4CBAIMttgYD/AgSy/hszQ7wFCGTj3X9WH4wAgWwwzswSXwECWTN7TyCrd99CC2QVizqyYMqkcbJg/k16KxWpjkDW6PZRvMYCBLIaN4fSIiNAIBuZVrIQTQUIZDVtDGVFSoBANlLtZDEaChDIatgUFyURyLpACvGSUAPZA4cOy7Pbfiarli2S2pqqEBmGNzWB7PD8eDYC+QQIZLk3EPBfgEDWf2NmiLcAgWy8+8/qgxEgkA3GmVniK0Aga2bvCWT17ltogaw6Q3bZ6o2yd99BR6FZM6bKprUrpKmxQW9BESGQ1b5FFGioAIGsoY2jbKMECGSNahfFGihAIGtg0yjZOAECWeNaRsGGCRDIGtawwXIJZPXuW2iBrN4spVVHIFuaF1cj4FaAQNatFNchUL4AgWz5djwTATcCBLJulLgGgeEJEMgOz49nI1BMgEC2mJCejxPI6tkXuyoCWQ/6QyDrASJDIOAgQCDLbYGA/wIEsv4bM0O8BQhk491/Vh+MAIFsMM7MEl8BAlkze08gq3ffQg9kd+/ZL3ffu3aI0tNPrJa5s6frLZdVHYGsMa2iUMMECGQNaxjlGilAIGtk2yjaIAECWYOaRanGChDIGts6CjdEgEDWkEbllEkgq3ffQg1kVRi7oWXrkLNi1Qt9Lb1/gyy/65uyYP5NeusNVkcga0SbKNJAAQJZA5tGycYJEMga1zIKNkyAQNawhlGukQIEska2jaINEiCQNahZWaUSyOrdt9AC2Y7Obnl4/Ra5/babz9sNq4LaF17cIY+sWiy1NVV6C/KiXtr3hwLNFSCQNbd3VG6OAIGsOb2iUjMFCGTN7BtVmyVAIGtWv6jWPAECWfN6piomkNW7b6EFsqfOtErzY5tl1fJFMm3yhCFKapfs+ieflzUPLJGmxgZfBe1g+KWXd2XmyT0yYdv2nfLQui3W47feMu+8oJgdsr62iMFjLEAgG+Pms/TABAhkA6NmopgKEMjGtPEsO1ABAtlAuZkshgIEsmY2nUBW776FFsjqskNWBcPff/7Hsuyub1m7cdXu3OY1m6Vl3UorKM49VuHxlq1WR+9bujDTWQJZvW9yqjNXgEDW3N5RuTkCBLLm9IpKzRQgkDWzb1RtlgCBrFn9olrzBAhkzeuZqphAVu++hRbIKha183Trizu0OkNWBbTLVm+UlUsXWkcpqAB2yqRxmfNsnc69JZDV+yanOnMFCGTN7R2VmyNAIGtOr6jUTAECWTP7RtVmCRDImtUvqjVPgEDWvJ4RyOrfs1ADWcWjAs677107RCr3yIAgGdVxCQ+u2SyPNi+RCWMvtM65nTdnZiaQzX7cPmqBQDbIDjFXnAQIZOPUbdYalgCBbFjyzBsXAQLZuHSadYYpQCAbpj5zx0GAQNbMLrNDVu++hR7I6sRjH6NgB7BOxyo4BbI6rYFaEEAAAQQQQAABBBBAAAEEEEAAAQQQQEBfgVADWXUcwNHjJ4e8SFZuKBoUnT3vuDEXZM6HdaqFHbJBdYR5EBBhhyx3AQL+C7BD1n9jZoi3ADtk491/Vh+MADtkg3FmlvgKsEPWzN6zQ1bvvoUWyOryol6qPU5hrN02zpDV+wamumgLEMhGu7+sTg8BAlk9+kAV0RUgkI1ub1mZPgIEsvr0gkqiKUAga2ZfCWT17ltogax68azmxzbLquWLxD6L1aZSu1DXP/m8rHlgiTQ1NvgqWGxHbu6LeKmAVr3dt3Rhpi7OkPW1RQweYwEC2Rg3n6UHJkAgGxg1E8VUgEA2po1n2YEKEMgGys1kMRQgkDWz6QSyevcttEBWlx2yKvxdev8GOXLsxJBO3XPH/Ezoum37Tnlo3Rbr8VtvmTfkiAX1MQJZvW9yqjNXgEDW3N5RuTkCBLLm9IpKzRQgkDWzb1RtlgCBrFn9olrzBAhkzeuZqphAVu++hRbIKha1+7R5zWZpWbcys0vWDkiX3/VNWTD/Jr31BqsjkDWiTRRpoACBrIFNo2TjBAhkjWsZBRsmQCBrWMMo10gBAlkj20bRBgkQyBrUrKxSCWT17luogayicdqh+vQTq2Xu7Ol6y2VVRyBrTKso1DABAlnDGka5RgoQyBrZNoo2SIBA1qBmUaqxAgSyxraOwg0RIJA1pFE5ZRLI6t230ANZvXncVUcg686JqxAoVYBAtlQxrkegdAEC2dLNeAYCpQgQyJaixbUIlCdAIFueG89CwK0AgaxbKb2uI5DVqx+51RDIetAfAlkPEBkCAQcBAlluCwT8FyCQ9d+YGeItQCAb7/6z+mAECGSDcWaW+AoQyJrZewJZvftGIOtBfwhkPUBkCAQIZLkHEAhFgEA2FHYmjZEAgWyMms1SQxMgkA2NnoljIkAga2ajCWT17huBrAf9IZD1AJEhECCQ5R5AIBQBAtlQ2Jk0RgIEsjFqNksNTYBANjR6Jo6JAIGsmY0mkNW7bwSyHvSHQNYDRIZAgECWewCBUAQIZENhZ9IYCRDIxqjZLDU0AQLZ0OiZOCYCBLJmNppAVu++Ech60B8CWQ8QGQIBAlnuAQRCESCQDYWdSWMkQCAbo2az1NAECGRDo2fimAgQyJrZaAJZvftGIOtBfwhkPUBkCAQIZLkHEAhFgEA2FHYmjZEAgWyMms1SQxMgkA2NnoljIkAga2ajCWT17huBrAf9IZD1AJEhECCQ5R5AIBQBAtlQ2Jk0RgIEsjFqNksNTYBANjR6Jo6JAIGsmY0mkNW7bwSyHvSHQNYDRIZAgECWewCBUAQIZENhZ9IYCRDIxqjZLDU0AQLZ0OiZOCYCBLJmNppAVu++Ech60B8CWQ8QGQIBAlnuAQRCESCQDYWdSWMkQCAbo2az1NAECGRDo2fimAgQyJrZaAJZvftGIOtBfwhkPUBkCAQIZLkHEAhFgEA2FHYmjZEAgWyMms1SQxMgkA2NnoljIkAga2ajCWT17huBrAf9IZD1AJEhECCQ5R5AIBQBAtlQ2Jk0RgIEsjFqNksNTYBANjR6Jo6JAIGsmY0mkNW7bwSyHvSHQNYDxACG+PDQaTl27JycPdMl5851y7lzPdI++P7cuS5pP9crHe3d0t7eK+3t3dLR0SPdXf3S09snvT390tPTJ3196n1aenv7pKenX/p67cfT1pi5b9XVFVJRkZRkSiSVSor6T1lSvU8lMn9OVQz8Oak+lvz8MfXnCnVtRVJqqlNSW1clI0ZUyIgR6n2l1NVVSu3g70fUVVofsz9eU6MeU78qpLa2UmprK6SurioAZW+nSCRExjXVypGTHd4OzGgIIJARIJDlZkDAXwECWX99GR0BJUAgy32AgL8CBLL++vo1OoGsX7LejEsg64EjgawHiMMYQgWnB947JYc/OStHj7TJ0SOt1q9jR9vkyNE26/3pU53DmCE6T1UBsR3SqnBXhbUqqK2uSVlBrwpua2oHgl11nR3+DoS66uPq+QNhr3qeCoXV+xF1VVJfX+k5FIGs56QMiMB5AgSy3BQI+CtAIOuvL6MjQCDLPYCA/wIEsv4b+zEDgawfqt6NSSDrgSWBrAeIRYY4dbJTDn1wSt5//7Sona4HD5yUDz84I+8fPCmfftruqoDxExpE/RrZUCUj6rPDxEqpr6/O7DC1gskRFdbHKisTUlGRkorKpLXTtdL6fUIqKlNSWTHwMfvxysqk1NRUDKlFhcW9vWnp70tLX3+/9PWp3w+8t/7cq34v1s7b/v609d6+pjfz+7R0dg7s2h3Y1dsj7e091m5e68/t6tfAzt6Oc2pnr7p24GPq96qGjvZeawy/39T6Pw9pK2XkyBqprEpKVVVKVBisflVVqz9XSHVVSqqqU9ZjKgRWj6nnV9cMvK8d/P3FY0bIibPn7z72ey26j6/uF/tXWkTS/WlJp7M+ls762ODH02mxnqPeq+vt3/cPPq4eyHws8/jAuPZzsx+XwfHU8+25B8bu152P+rIE1Oei6mtPL33jxkDAD4FEIiEjalJyrsP/f4f9qJ8xETBBoLY6JT29aVFfP/OGAALeC6hvLqqvGdsD+D+l99XHd8QN674W38UbsHICWQ+aRCDrAaKItLX1yLvvfCYfvH9aDrx3Qg4eOCWHDp2WA++ekNbWwoHctMuaZNIlo2TcuHoZN179apAJF4+Ui8bUyfjx9dZ73mQgyFUhrRXYqt/3SKcKbFWIe27wsY7Pw1wr6FVHOQxeZz+nq7NPzp5VRz8MHPswEAD3QIwAAggggAACCCCAAAIIIIAAAhoIpNMPa1AFJeQTIJD14N4gkC0N8a29xwd2ux44LQcOnJAPDg4EsCdO5D8nVO2YnHbZBTJpcqNMndokk6c0yaXW+1EycdLI0grgat8E1Dm6Kti1z+hV7zs7+qS7u1e6u/qkq1v9vk+6u3qt911dA39WobDawdvVNbCTVwW+nZ091p/TfWnp6mG3Q27T1I6rZFJEHeuQVGcTq99YHxv4ZX9cXZcYfDz7Y9Zzc65TY5z3MXs8sa+35xiYe+D6gfmz5/XtJmNgzwXYIes5KQMiMESAHbLcEAj4L8AOWf+NmSHeAuyQNbP/7JDVu28Esh70h0DWGVGd67p/33HZ//anokLY/fs+s44byPemfmR9ytRRMnXaBaJ2vF469QKZOq1JpkxpkjFj2eHqwa1q3BCcIWtcyyjYQAHOkDWwaZRslABnyBrVLoo1VIAX9TK0cZRtjABnyBrTqiGFcoas3n0jkPWgP3EPZNULZg0Ersfl7bcGgtd39n/meGapOnN10iWNVtCqAle161UFsJdOHWUdMaACON4QsAUIZLkXEPBfgEDWf2NmiLcAgWy8+8/qgxEgkA3GmVniK0Aga2bvCWT17huBrAf9iVMg++GHZ+Q3bx6TvW8ek7f2ql/H5djRNkdF9QJa02dcKDOuvEhmzhxrvb/ssgusF8jiDQE3AgSybpS4BoHhCRDIDs+PZyNQTIBAtpgQjyMwfAEC2eEbMgIChQQIZM28Pwhk9e4bgawH/YliIKtecfu9d0/Kb/YelzffOCpv7T0qv3nruJw53XWeWF1dlVyhgteZF1m/ZqoA9sqx0jCyygNdhoizAIFsnLvP2oMSIJANSpp54ipAIBvXzrPuIAUIZIPUZq44ChDImtl1Alm9+0Yg60F/TA9ke7r75O23P7XC171vqvD1uOz7zafS0dFzns7o0bVy1dVj5cpZY2TW1eNk1tVjZcqlTRw14MF9xBDnCxDIclcg4L8Agaz/xswQbwEC2Xj3n9UHI0AgG4wzs8RXgEDWzN4TyOrdNwJZD/pjUiCrdr7+9p0Tsuf1I/L6q4fljdePyr59n0qvw6vYXzxxpFw1a4xcNRi8qt+rYwh4QyAoAQLZoKSZJ84CBLJx7j5rD0KAQDYIZeaIuwCBbNzvANbvtwCBrN/C/oxPIOuPq1ejEsh6IKlzIPvhodOy5/Wj8vqrR+SN149YZ7+2tw/d+ZpMJqwX1bpq1jiZdc04K4RVO19HNdV4oMMQCJQvQCBbvh3PRMCtAIGsWymuQ6A8AQLZ8tx4FgKlCBDIlqLFtQiULkAgW7qZDs8gkNWhC/lrIJD1oD+6BLKnTnbKq7/+RPa8dkRef+2IvLHniKiP5b5NuqRRrpk9TmZfN0FmXztOrrl2nIwYUemBBEMg4K0Agay3noyGgJMAgSz3BQL+ChDI+uvL6AgoAQJZ7gME/BUgkPXX16/RCWT9kvVmXAJZDxzDCGTVEQNv7T0mr716WH79ymHr/UcfnjlvNerM12uuHW8Fr9fOmSDXzZnAzlcPes4QwQgQyAbjzCzxFiCQjXf/Wb3/AgSy/hszAwIEstwDCPgrQCDrr69foxPI+iXrzbgEsh44BhHIfnr8nOz+1Sfy692fyGu/PixvvnFMurp6h1RfX19pnfd67XUDu1/VztdJkxo9WCFDIBCOAIFsOO7MGi8BAtl49ZvVBi9AIBu8OTPGT4BANn49Z8XBChDIBuvt1WwEsl5J+jMOgawHrl4Hsj3dfdZZr9m7Xz/5+OyQSlVQNe2yC2TO9RNkztyLrV9fuGK0qPNgeUMgKgIEslHpJOvQWYBAVufuUFsUBAhko9BF1qC7AIGs7h2iPtMFCGTN7CCBrN59I5D1oD/DDWQPf9I6GL5+Yr3f+8Yx6e7uG1JZw8gqufa68TLn+oHw9fq5F4v6GG8IRFmAQDbK3WVtuggQyOrSCeqIqgCBbFQ7y7p0EiCQ1akb1BJFAQJZM7tKIKt33whks/rzeMtWmTJpnCyYf9OQrm3bvlMeWrfF+titt8yTR1Ytltqaz8PQUgLZdFrknf2fySu7PpZXdn0kv9r1sahANvtNhVCXf2H057tfr79YLr9itKiP84ZAnAQIZOPUbdYalgCBbFjyzBsXAQLZuHSadYYpQCAbpj5zx0GAQNbMLhPI6t03AlkRyQ5cv3v/4iGB7O49+2VDy1bZtHaFNDU2iApt1dt9SxdmOlsokFU7Xfe8fkR27/pEfrXrI9n9yidy9kzXkLtiZGO1XKd2v35xolynjiC4foI0NLD7Ve9PHaoLQoBANghl5oi7AIFs3O8A1u+3AIGs38KMj4AIgSx3AQL+ChDI+uvr1+gEsn7JejMugWyWo9MO2dyP5Qa06unZgWzr2W555VcfD4Svuz6xwtjc4wcmThopc2+4WObdeIl88YaJ7H715l5mlAgKEMhGsKksSTsBAlntWkJBERMgkI1YQ1mOlgIEslq2haIiJEAga2YzCWT17huBbIFAtqOzWx5ev0XmzZmZ2TV74NBheXDNZnm0eYlMmzxBPv74rPxw+3uZ4wfe2ffZeR2fMfMi+eK8iXLDjRNl3o2TZOy4er3vCqpDQBMBAllNGkEZkRYgkI10e1mcBgIEsho0gRIiL0AgG/kWs8CQBQhkQ25AmdMTyJYJF9DTCGRdBLK333azzJ093boyN5BNJB4Z0qqamgq5bs54K3j9nS9fIvNunCgNDdUBtZNpEIiWgDo2ub62Qlo7eqO1MFaDgEYCNZVJ6UuL9PT2a1QVpSAQHYFkQmREdYW0dfJvWXS6ykp0E6itSklPX7/0qn/QeEMAAc8F1DcXqyuT0t419MXHPZ+IAT0VaKit8HQ8BvNWgEDWRSBbaIfs1VdvkosnjpQvfekSufFLE+Xa68ZLVVXK2y4xGgJxFUiI1NdUSltHT1wFWDcCvgtUV6Wkvz9NIOu7NBPEVSCRSMiImpSc45uLcb0FWHcAArXVKenpTUtvH99cDICbKWIoYAWyVSlp55uLRnW/YUSlUfXGrVgC2QKBrHqo1DNk43YDsV4E/BTgyAI/dRkbgQEBjizgTkDAXwGOLPDXl9ERUAIcWcB9gIC/AhxZ4K+vX6NzZIFfst6MSyBbJJDNfREvFdCqt/uWLsw8M/tFvbxpC6MggIASIJDlPkDAfwECWf+NmSHeAgSy8e4/qw9GgEA2GGdmia8AgayZvSeQ1btvBLIism37Tnlo3ZZMp8aPHS0t61ZaL9ql3rIfv/WWefLIqsVSW1NFIKv3vU11ERAgkI1AE1mC9gIEstq3iAINFyCQNbyBlG+EAIGsEW2iSIMFCGTNbB6BrN59I5D1oD/skPUAkSEQcBAgkOW2QMB/AQJZ/42ZId4CBLLx7j+rD0aAQDYYZ2aJrwCBrJm9J5DVu28Esh70h0DWA0SGQIBAlnsAgVAECGRDYWfSGAkQyMao2Sw1NAEC2dDomTgmAgSyZjaaQFbvvhHIetAfAlkPEBkCAQJZ7gEEQhEgkA2FnUljJEAgG6Nms9TQBAhkQ6Nn4pgIEMia2WgCWb37RiDrQX8IZD1AZAgECGS5BxAIRYBANhR2Jo2RAIFsjJrNUkMTIJANjZ6JYyJAIGtmowlk9e4bgawH/SGQ9QCRIRAgkOUeQCAUAQLZUNiZNEYCBLIxajZLDU2AQDY0eiaOiQCBrJmNJpDVu28Esnr3h+oQQAABBBBAAAEEEEAAAQQQQAABBBBAIEICBLIRaiZLQQABBBBAAAEEEEAAAQQQQAABBBBAAAG9BQhk9e4P1SGAAAIIIIAAAggggAACCCCAAAIIIIBAhAQIZCPUTJaCAAIIIIAAAggggAACCCCAAAIIIIAAAnoLEMiW2Z9t23fKQ+u2WM++9ZZ58siqxVJbU1XmaDwNgfgKnDrTKstWb5S9+w5aCE8/sVrmzp7uCNLR2S0Pr98iL728K/N4oevjq8rKEfhcIPfz5rv3L5YF829yRfR4y1Z5Zc9+2bR2hTQ1Nrh6DhchEEeB3Xv2y933rrWWPmvGVFefM+rz66nntlvPueeO+XLf0oVxpGPNCLgSKPXfstyvL/kcc8XMRQjkFVCfU82PbZZVyxfJtMkTkEIAAQ8ECGTLQFRfdG9o2Zr5Ylt9Qa3e+EK6DEyeEmsB+4vreXNmWgHRgUOH5cE1m+XR5iWO/9CrLwS+//yPZdld37K+AaI+F5vXbJaWdSv5wiDWdxKLLySQ/W+U/R/UlUsX5v3Ghz2WHRa5DZfoAgJxFcj9t0t9037Xq28X/GY9XzvG9W5h3eUKlPJvWe7Xl7l/LrcGnodAHAWyvxkyfuxo/t8Vx5uANfsmQCBbBq36gmDKpHGZHUa5AW0ZQ/IUBGIpoP4Tu/7J52XNA0us3XelfsFcSrgUS2AWHXsBp90MboIgFSh98NFR+coNVw/5BmTsQQFAwEHA/nyxvzFf7JuL6uvGF17cwU9XcTch4FKg1H/LnL4+dPNvn8tyuAyBWAqwQzaWbWfRPgsQyJYI7BQYFfvCu8QpuByB2Ag4fTOjlC+YIF9ctwAADXJJREFU+dyLza3CQssUcPocKbZ7L/vxt/YfJJAt056nxUcg99+tYt8szD72ylbi+J343C+stHSBcv8tU8fLqc+tyy69mB+1Lp2dZyAwRIBAlhsCAe8FCGRLNLUD2dtvuznz456EQiUicjkCgwJOu4TcBrKl7qYFHYE4CuTuQlcGhQLZ3M9JfgIkjncNay5VIPcnp4oFsk4/acXxO6Wqc32cBEr9t0zZ2P8/U7/fu/99zmmO0w3DWn0RIJD1hZVBYy5AIFviDcAO2RLBuByBAgLl7pC1Pw/HjbmAs5u5wxAoIFDqriKnnXtqeM6R5TZDIL9AqTtkcwNZvsHI3YVAYYFS/y3LDY74upE7DIHhCxDIDt+QERDIFSCQLeOe4AzZMtB4CgIOAuWcIcsX1dxKCLgXKPXcvdyR2SHr3por4ytQ6hmyudc7/fRVfDVZOQLnC5T6b1k5O2pxRwCBwgIEstwhCHgvQCBbhmnuf1Dd/oh1GVPxFAQiLZC7Kyh3B4T689L7N8ia5iXWESHsIor07cDifBIo9srU6vGjx086vsAQgaxPTWHYSAnk/tuVeyxI7r9luX/m8yxStwOL8UmglH/LOru6ZNnqjbLwtputF2Hmm/k+NYVhYyVAIBurdrPYgAQIZMuEzv6xzltvmccr5ZbpyNMQsM/a27vvoIWR/cIm+f4Te+TYiSFw99wxn6MLuJUQyCNg/0f0pZd3WVd89/7F1n9Q7TcCWW4dBIYvoELVu+9daw2Ue8RH7r9l6prs68ePHS0t61bKtMkThl8IIyAQUYFS/y2zP+/srxn5WjGiNwbL8l0g93NPTUj+4Ts7E8REgEA2Jo1mmQgggAACCCCAAAIIIIAAAggggAACCCAQvgCBbPg9oAIEEEAAAQQQQAABBBBAAAEEEEAAAQQQiIkAgWxMGs0yEUAAAQQQQAABBBBAAAEEEEAAAQQQQCB8AQLZ8HtABQgggAACCCCAAAIIIIAAAggggAACCCAQEwEC2Zg0mmUigAACCCCAAAIIIIAAAggggAACCCCAQPgCBLLh94AKEEAAAQQQQAABBBBAAAEEEEAAAQQQQCAmAgSyMWk0y0QAAQQQQAABBBBAAAEEEEAAAQQQQACB8AUIZMPvARUggAACCCCAAAIIIIAAAggggAACCCCAQEwECGRj0miWiQACCCCAAAIIIIAAAggggAACCCCAAALhCxDIht8DKkAAAQQQQAABBBBAAAEEEEAAAQQQQACBmAgQyMak0SwTAQQQQAABBBBAAAEEEEAAAQQQQAABBMIXIJANvwdUgAACCCCAAAIIIIAAAggggAACCCCAAAIxESCQjUmjWSYCCCCAAAIIIIAAAggggAACCCCAAAIIhC9AIBt+D6gAAQQQQAABBBBAAAEEEEAAAQQQQAABBGIiQCAbk0azTAQQQAABBBBAAAEEEEAAAQQQQAABBBAIX4BANvweUAECCCCAAAIIIIAAAggggAACCCCAAAIIxESAQDYmjWaZCCCAAAIIIIAAAggggAACCCCAAAIIIBC+AIFs+D2gAgQQQAABBBBAAAEEEEAAAQQQQAABBBCIiQCBbEwazTIRQAABBBBAIB4Cp860yrLVG2XvvoNDFvzd+xfLN746Tx5ev8X6+COrFkttTVXmmgOHDsvS+zfI8ru+KQvm3ySFxlGPP96yVZ56bnte1Fkzpsrj/+U/yRPfe0FeennXedfdess8qwb1pmpS1zz9xGqZO3t65tqOzu68j9kXbdu+Ux5aN7Amp7fxY0fLuof+WNb93XMZE1XbprUrpKmxIbMO5aPWlf1mr9F+LLue3Lns9WSbxuOOY5UIIIAAAggggAACpQoQyJYqxvUIIIAAAggggICmArmhql2m+viz234mq5Ytks6uLiuwXXjbzUMCSBU+qrf7li4UN+NkB492eLty6ULHQHXcmAuscZ3eskPOe+6YP+S63Xv2y933rrWelhvWFhpr3pyZ54Wr9jy5tdiha26gahscOXZCcgPZQuvR9NagLAQQQAABBBBAAAGNBAhkNWoGpSCAAAIIIIAAAsMRULtFt764I7P7M99YKuhsXrNZWtatlGmTJ4j684aWrZnnuR3HHt+LQPaySy+W1/a+K6uWL7JqsgPUq2dOk6e3/kTWNC8ZEvZ6Gci2tXdKW1u73H7bzZk5VFBbX1crP//X1zPhdb5Qdzg947kIIIAAAggggAAC8RMgkI1fz1kxAggggAACCERUIDdoLbRMFTgePX5SVvzR7bLiv/zdkB2zpYyj5vAikFW7Wj/46KhVsr1Ld/2Tz4vaNavCYz8DWTXnlEnjZNerb1vHKKhdxM2PbbbmVkG1vZuYQDainzgsCwEEEEAAAQQQCFiAQDZgcKZDAAEEEEAAAQT8EnA649TpbFQ1f/aP5Of+uH4p47gJZN2cIasC2WuuvEweXLNZHm1eIj/8yS+tkFR9TJ1t63cg+51F37COclDHLnx0+LgVDtsfyw1kC62HM2T9ursZFwEEEEAAAQQQiI4AgWx0eslKEEAAAQQQQACBjED2+avqg7nns6qPqaMJnvzHH2aOLnDiczOOVztk7RcLe+X1fTKqsUHWPLBETp5uDSSQVbtyraMa/ulfLAYVCl8wqmHIebvskOUTDAEEEEAAAQQQQMALAQJZLxQZAwEEEEAAAQQQ0Fgg3xEEuWfHFltCvnG8DGRzX1DM/rPfO2RVIGuv44uzp1vHJth/5siCYncGjyOAAAIIIIAAAgiUIkAgW4oW1yKAAAIIIIAAAhoL7Nz1hsyaMVWaGhuGVKlCTfsoAPWCWfZbvkC21HG8DGRVbc9u+2eZf8s8ax1BBrJq7p/ueEUuu3Si9cJiBLIa3+yUhgACCCCAAAIIGCxAIGtw8ygdAQQQQAABBBDIFlA/cv/Qui3y9BOrZe7s6dZD9o/Zq9+rF6zKPuM0XyBb6jheB7LZawo6kM2em0CWzy8EEEAAAQQQQAABPwQIZP1QZUwEEEAAAQQQQCAkATtMzZ7e6fxY9XihIwtKGadYIOv2Rb3UGbK5b14EsnZ9e/cdtIZXu4g3rV1h7cB9vGWr9TF1REHuW75Alhf1CunmZloEEEAAAQQQQCAiAgSyEWkky0AAAQQQQAABBBBAAAEEEEAAAQQQQAAB/QUIZPXvERUigAACCCCAAAIIIIAAAggggAACCCCAQEQECGQj0kiWgQACCCCAAAIIIIAAAggggAACCCCAAAL6CxDI6t8jKkQAAQQQQAABBBBAAAEEEEAAAQQQQACBiAgQyEakkSwDAQQQQAABBBBAAAEEEEAAAQQQQAABBPQXIJDVv0dUiAACCCCAAAII/P/t2DENAAAAwjD/rrFBljqA8kGAAAECBAgQIECAAIGIgEM2MqQaBAgQIECAAAECBAgQIECAAAECBAj8Czhk/zeSkAABAgQIECBAgAABAgQIECBAgACBiIBDNjKkGgQIECBAgAABAgQIECBAgAABAgQI/As4ZP83kpAAAQIECBAgQIAAAQIECBAgQIAAgYiAQzYypBoECBAgQIAAAQIECBAgQIAAAQIECPwLOGT/N5KQAAECBAgQIECAAAECBAgQIECAAIGIgEM2MqQaBAgQIECAAAECBAgQIECAAAECBAj8Czhk/zeSkAABAgQIECBAgAABAgQIECBAgACBiIBDNjKkGgQIECBAgAABAgQIECBAgAABAgQI/As4ZP83kpAAAQIECBAgQIAAAQIECBAgQIAAgYiAQzYypBoECBAgQIAAAQIECBAgQIAAAQIECPwLOGT/N5KQAAECBAgQIECAAAECBAgQIECAAIGIgEM2MqQaBAgQIECAAAECBAgQIECAAAECBAj8Czhk/zeSkAABAgQIECBAgAABAgQIECBAgACBiIBDNjKkGgQIECBAgAABAgQIECBAgAABAgQI/As4ZP83kpAAAQIECBAgQIAAAQIECBAgQIAAgYiAQzYypBoECBAgQIAAAQIECBAgQIAAAQIECPwLOGT/N5KQAAECBAgQIECAAAECBAgQIECAAIGIgEM2MqQaBAgQIECAAAECBAgQIECAAAECBAj8Czhk/zeSkAABAgQIECBAgAABAgQIECBAgACBiIBDNjKkGgQIECBAgAABAgQIECBAgAABAgQI/As4ZP83kpAAAQIECBAgQIAAAQIECBAgQIAAgYiAQzYypBoECBAgQIAAAQIECBAgQIAAAQIECPwLOGT/N5KQAAECBAgQIECAAAECBAgQIECAAIGIgEM2MqQaBAgQIECAAAECBAgQIECAAAECBAj8Czhk/zeSkAABAgQIECBAgAABAgQIECBAgACBiIBDNjKkGgQIECBAgAABAgQIECBAgAABAgQI/As4ZP83kpAAAQIECBAgQIAAAQIECBAgQIAAgYiAQzYypBoECBAgQIAAAQIECBAgQIAAAQIECPwLOGT/N5KQAAECBAgQIECAAAECBAgQIECAAIGIgEM2MqQaBAgQIECAAAECBAgQIECAAAECBAj8Czhk/zeSkAABAgQIECBAgAABAgQIECBAgACBiIBDNjKkGgQIECBAgAABAgQIECBAgAABAgQI/AsMp8wwTbsLR5QAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Same plot, but with smooth line\n", "fig = px.line(data_frame=bio.get_history(), x=\"SYSTEM TIME\", y=[\"A\", \"B\"], \n", " title=\"Changes in concentrations with time (smoothed)\",\n", " color_discrete_sequence = ['navy', 'darkorange'],\n", " labels={\"value\":\"concentration\", \"variable\":\"Chemical\"},\n", " line_shape=\"spline\")\n", "fig.show()" ] }, { "cell_type": "markdown", "id": "8d1fb634-3575-44fb-aa0c-0a9110fe54bc", "metadata": {}, "source": [ "The early **OVERSHOOTING** of the equilibrium values shows prominently in the last plot!" ] }, { "cell_type": "code", "execution_count": null, "id": "a84d9709", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }