{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## `A` up-regulates `B` , \n", "### by being *the limiting reagent* in the reaction `A + X <-> 2B` (mostly forward), where `X` is plentiful\n", "1st-order kinetics. \n", "If [A] is low, [B] remains low, too. Then, if [A] goes high, then so does [B]. However, at that point, A can no longer bring B down to any substantial extent.\n", "\n", "See also the experiment \"1D/reactions/up_regulation_1\"\n", "\n", "LAST REVISED: May 26, 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 ReactionData 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_1.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: 1 (at temp. 25 C)\n", "0: A + X <-> 2 B (kF = 8 / kR = 2 / Delta_G = -3,436.56 / K = 4) | 1st order in all reactants & products\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `up_regulate_1.log.htm`]\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = chem(names=[\"A\", \"X\", \"B\"])\n", "\n", "# Reaction A + X <-> 2B , with 1st-order kinetics for all species\n", "chem_data.add_reaction(reactants=[(\"A\") , (\"X\")], products=[(2, \"B\")],\n", " forward_rate=8., reverse_rate=2.)\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 (A). Conc: 5.0\n", " Species 1 (X). Conc: 100.0\n", " Species 2 (B). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(reaction_data=chem_data)\n", "dynamics.set_conc(conc={\"A\": 5., \"X\": 100., \"B\": 0.},\n", " snapshot=True) # A is scarce, X is plentiful, B is absent\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "0b46b395-3f68-4dbd-b0c5-d67a0e623726", "metadata": { "tags": [] }, "source": [ "### Take the initial system to equilibrium" ] }, { "cell_type": "code", "execution_count": 6, "id": "dde62826-d170-4b39-b027-c0d56fb21387", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "INFO: the tentative time step (0.0005) 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 0.00025) [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", "55 total step(s) taken\n" ] } ], "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=0.0005, reaction_duration=0.015,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 7, "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=A
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Changes in concentrations with time" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 0.016626464843750004 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -5.555555555555555, 105.55555555555556 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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O+Infn3RcZplREubNIgPaHWc2JEXa53Yvr4VsAwEIQAACEKgKgTkpKaIfVqPrTbRbXyHpnPRwQU6zYF24EFj89I6kePEp89EFI8Nali4eTVy4LfwAED2vOkmqxEWK2S6PMGh3sKeZap/ljWI0T6+SIs2H33Zrk/j4pI5+uGlXf7fTNLrF6LZ9L9zS9ClL3Hb7EP3g304SRF8Poh9e48/fds/1LJIirMFc5jO8Gb6/OnhYkqaAJy0oG18kMzyew3jR17RODG1JiqR9TFrYM75v8V6Fr3dpvvGPfjCNsk3Km7TGQtLfgejMg06vofHjJHxN7vTaFz9eTf7H/sO/k7/Y+7cSv8pUu/idBE6UQV6uvR5f8Z60Wwsq/vrSTkjE+xbGyyKy2j0f4v0ImR068r5s2LxT4pcgzXN1j3bHqrm/lwVws7xOMhYCEIAABCDgC4HKSgpfGkCdEIDA3CbQabr53CbD3kMAAhCAAAQgAAEIzEUCSIq52HX2GQIQKISA+Tb473/809Y6KaaIpMscF1IcSSEAAQhAAAIQgAAEIFACAkiKEjSBEiAAgblBIOlUA6Z4z43es5cQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICksAyY8BCAAAQhAAAIQgAAEIAABCEAAAukIICnScWIUBCAAAQhAAAIQgAAEIAABCEAAApYJICkUAB86NqYQhRA2CXxs8bB8cGpCzk7VbaYhdk4C/X01uWjRkBw5MZ4zEpvbJrBgeEAG+mty8sxZ26mIn5PAhRcMyemxszJxdjpnJDa3TWDFhSPCewrblPPHHx7sl/lD/XL81GT+YESwSmDxwkGZPDslH01MWc1D8PwEli8dkaMnxmS64Lfq5nWYW/EEkBQKPeANhQJEyyGQFJYBK4VHUiiBdBAGSeEAslIKJIUSSAdhkBQOICukQFIoQHQUAknhCLRCGiSFAsQKhUBSKDQTSaEA0XIIJIVlwErhkRRKIB2EQVI4gKyUAkmhBNJBGCSFA8gKKZAUChAdhUBSOAKtkAZJoQCxQiGQFArNRFIoQLQcAklhGbBSeCSFEkgHYZAUDiArpUBSKIF0EAZJ4QCyQgokhQJERyGQFI5AK6RBUihArFCIOSUp9u1/QX518LDct2HdjBaeOHlK7t7yXXntjbeD+598bIvceN1VrTFmuwe27wl+/9Kta+ShTXfJyPBg63EkRfmfEUiK8vfIVIik8KNPpkokhT+9QlL40yskhR+9QlL40SdTJZLCn14hKfzplYtK54SkePGVN+Xr33wk4PmNr6ydISnGxiflwR17ZM0N18jta2+Wt945JN/atlu+s3W9rF61Qsy2O3ftlSceuVeWLBqVR3ftDeJERQeSwsWhmi8HkiIfP1dbIylckc6fB0mRn6GrCEgKV6Tz50FS5GfoIgKSwgVlnRxICh2OLqIgKVxQ9ifHnJAUYTuSZlIYKbHj8adk2/3rAwkRlxZGSlyxcnkgMMwtLi3MfUiK8h/wSIry98hUiKTwo0+mSiSFP71CUvjTKySFH71CUvjRJ1MlksKfXiEp/OmVi0rnvKRIkg7hbIm7v/aHM2ZZmIbEZ1ogKVwcpvlzICnyM3QRAUnhgrJODiSFDkcXUZAULijr5EBS6HC0HQVJYZuwXnwkhR5L25HmuqRI+kxqm7mN+PEv/HvNgaR45U15+pnnZ6wzEZcUd9x2S2uNilmS4vFlMj14gdQXXirT81dIfcGlwb/Nz+kFlzR+jq7stT9sp0TAfKAanzgnUwVfe1lpdyobpq8mMn9oQE6Pn6vsPlZlxwYH+sT0a/zsdFV2qbL7MX+oXybPTsu5HBefr9frUqvVKsuoLDs2OjIgp8Z4/StLP9rVMdBfk3n9fTI2OVX2Uud8fUYoTU1Ny1neAJb+WFg4MiBnxs5J0W/VzeuwjVv44f1Hzx2YEf7bm+8KZuwXKSnM2QZ7n3m+tbxBnv1HUvRAL+l0j9wzKXamedNWk/rIx2TaCIwFK2R64aUiUYmxwMiNFVIfWtLDXrFJGgLzjaSYnJLpHG/S0+RhTD4C5kPQ/OH+4I8Ut3ITmGckRV9NJniTXu5GicjI0IBMnpuSqRxv0utSk1rhbx1Ljzp3gaPz58mpj87mjkMAuwQG+vtk3kBNxiaQFHZJ548eSIrpupw9h1DPT9NuhIUj8+TM+FmpF2wpzOuw9s18yb1h805Z+/mbZqxraC7esPXh3bLpnjvl+IkPZ6yDqF2Dq3hIih5IW1mT4uxpOXrwLen/6JD0nzkU/Oz76N3mz+Z940dF6t3/kNX7R2Rq/org/+n5l8iUERrm9wWN+6ZGGvfX+/SfPD3g9GoTTvfwo12c7uFHn0yVnO7hT6843cOfXnG6hx+94nQPP/pkquR0D396VdXTPcIP7csvXjrrCpPR7oRfnG/csE62btst7x05Fjwcv+pkKDzCx6MXhQivWPknf/RF+f5f/k3rypVmtsZnfvcTgShJims+Ix946fUZZxbE81x79ZXBTAtzi14V0/werQFJ0cNzLklSuLq6RyAxmiKjLxAZ5ncjM96T/jONn7Vzp1Pt1fTQRS2ZYQTG2WX/UqYWXJq47cTyz6WKWfVBSAo/Ooyk8KNPSAp/+mQqRVL40y8khR+9QlL40SckhT99MpVWVVKEH/a3bV3fWj4gqTPh1Si/dOualiyIn4YRX3YgLkBCSWHih1emDOOGksFcKCJ+JkFcUiTV/LfP/0Q+8fHLZOniUfn+U38tZu3GkeFBCXOuu+2W4LQVJEWG5130EqThZlErFcJ97Y23E42VadwD2/cEj0UPnDCW1tU9amdPtWZjNKTGe9L30W+C+/rGDkv/md9I/9jhDHvefmh93qhMDyyU+rzG/61/DyyU6XkLxDwePlYPxw0skOnBRVIfGAkenx5YIOax6eGlKjXZDIKksElXLzaSQo+l7UjMpLBNWC8+kkKPpe1ISArbhHXiIyl0OLqIwkwKF5R1clRVUpjPoWZmxK7tG2X1qhVtYSUtQRCXEvGrTppg0e3M72aWg5mNceN1VwW5ws+5ne6LS4pwfcb7NqxL1dzoRAAkRSpkbgZpSYq01c6alTF2VGpTY1I795HUpj6S2tnxxs/wvrOnpO/cGamdPS19E8fTpsk8bnpwcVNuLEiWHkZqmEVGzc+oGDFCZGC+TAc/m48NLsqcv9MGSApVnNaCISmsoVUPjKRQR2otIJLCGlr1wEgKdaRWAiIprGC1EhRJYQWrlaBIijdnrUkRlRQrll0UXHUyvvCmaUb8VIw8ksLEM3miF46INzx+Koh5PPwiP9x+zQ3XBDMrer3Nqat79Aqp23auJUW3etI83jfxgZiZG7VzZ6Tv3OmG4Jj8sCkzTknt7BmpTZ2R2sSHwWkofWdPB5LD/DvYxmxrxpjHJk+mSdnTmGDmRv+I1PvnS31gOJAZ5nfp65d6bZ5I30Dwf/jvuvm9NiDBz755Uq81Hh8ZGZbxczWZDn4/f38wTgZE+uc1tpEBqfc3f5rfzf3h47X+Zuxm3iCP+beppRk3yN+MZe43tXJLTQBJkRpV4QORFIW3IHUBSIrUqAofiKQovAWpCkBSpMJUikFIilK0IVURVZUUWU732Llr74wrbCRJik4f/tPMmjDNiI+LzqToJinCMwyiZyUkbY+kSHXY2x3ko6TQJlKbGg/khREfwayNyYbUCARIIDNOSd/ZMyKB7DD/bsiOliiJSJDGY+nW59DeD5vx6n3DDaHSZ2RHKDJiwqQpVQL50ZItRsJEJEgoUlpSpTnWjOkPxw5235W+PhExV6dpXqEmuLxgTcT8rM+8rx4+FkQ1Y5o/gx+R7ZqxgvEmRuuShbPHzNxOxFw9wFwtYnRkUE6GV/cI6gjjnK/JjA3LnvF4NF8sf2sfomOi+9X6d00aYyWyD7F9mbFdg0WjpvBqP8kcW/tsQifsV9K+hhyD8S3+0b6FPZnZyxn1tOF4Pl9zH2b0shm3xXHmMTF/ZEAG+mpy8qOp88dDrN/1/uHuxyEjrBNAUlhHrJYASaGG0mogJIVVvKrBkRSqOK0Gq6qk6LZwZrjWQ9LVPZJO9zBNaHcahoakMOtMdDrdI+mUEySF1adG78GRFL2z67Rl43QVIz+ap66Y389+JLXpSZGpSanJOZHpc1KbMpdrOye16SmR+lmpTZ8Tad3XGLNwSGR8bFympqZEpicaY8y2dfOzuU3dxGjcL8G/z0bGNB8L4wfbmsenGtsE/47GmwpmonCDAAQgAAEIQAACEIAABDwhsFH/GqjtLkFqPvDv/7sfB+tVpJEU4TqL5mod4akURkyEC1mOT0yorEkR5onOlghlyl/9zT/I4aPHW4t7hvt2/ac+GdxnbuZ0EWZSlOB4R1KUoAldSijDmhRmnZBAakT8pEAsAAAgAElEQVQFSkt6TDWlR1OOzBImTZkSSJVQmMRFipEtRtQ0JItMd7gmeN081nwRDi5IHf5vQNbFXKTazA2YOcb8Gr5wN8aEY81W58e3H3N+fF1q8Vg1k7Mmw4Pm2vPnZsQO5h1EL5w9I3ckX6zmoKbW/oX1x+6bsb/N/W+3XXicNWM2aurMMcq2Nb5tTZH8wVyLWOy2DBrbBfFr6fiHvZzFqMUw5BQ/JpKOg8iY6fHyvyBQIQQgAAEIQAACEEgiYEFSmDThjIromhKdrrhhtonPpAjvi15K1NwXSgutmRQmZvzCE2Gtw0NDM9bGMGtRfPqa1fLT199CUpTtGYWkKFtHZtdTBklRfkrFV8iaFMX3IG0FrEmRllTx4zjdo/gepK2A0z3Skip2HKd7FMs/S3ZO98hCq9ixVT3do1iq/mZn4UyF3iEpFCBaDoGksAxYKTySQgmkgzBICgeQlVIgKZRAOgiDpHAAWSEFkkIBoqMQSApHoBXSICkUIFYoBJJCoZlICgWIlkMgKSwDVgqPpFAC6SAMksIBZKUUSAolkA7CICkcQFZIgaRQgOgoBJLCEWiFNEgKBYgVCoGkUGgmkkIBouUQSArLgJXCIymUQDoIg6RwAFkpBZJCCaSDMEgKB5AVUiApFCA6CoGkcARaIQ2SQgFihUIgKRSaiaRQgGg5BJLCMmCl8EgKJZAOwiApHEBWSoGkUALpIAySwgFkhRRICgWIjkIgKRyBVkiDpFCAWKEQSAqFZiIpFCBaDoGksAxYKTySQgmkgzBICgeQlVIgKZRAOgiDpHAAWSEFkkIBoqMQSApHoBXSICkUIFYoBJJCoZlICgWIlkMgKSwDVgqPpFAC6SAMksIBZKUUSAolkA7CICkcQFZIgaRQgOgoBJLCEWiFNEgKBYgVCoGkUGgmkkIBouUQSArLgJXCIymUQDoIg6RwAFkpBZJCCaSDMEgKB5AVUiApFCA6CoGkcARaIQ2SQgFihUIgKRSaiaRQgGg5BJLCMmCl8EgKJZAOwiApHEBWSoGkUALpIAySwgFkhRRICgWIjkIgKRyBVkiDpFCAWKEQSAqFZiIpFCBaDoGksAxYKTySQgmkgzBICgeQlVIgKZRAOgiDpHAAWSEFkkIBoqMQSApHoBXSICkUIFYoBJJCoZlICgWIlkMgKSwDVgqPpFAC6SAMksIBZKUUSAolkA7CICkcQFZIgaRQgOgoBJLCEWiFNEgKBYg9hDhx8pTcveW7cvmKi+WhTXfJyPBgD1H0N0FSKDBFUihAtBwCSWEZsFJ4JIUSSAdhkBQOICulQFIogXQQBknhALJCCiSFAkRHIZAUjkArpEFSKEDsIcSLr7wpTz/zvHx4+iPZdM+dsnrVih6i6G+CpFBgiqRQgGg5BJLCMmCl8EgKJZAOwiApHEBWSoGkUALpIAySwgFkhRRICgWIjkIgKRyBVkiDpFCA2EOIR3ftlc/d9Gn5+x//VK5YuVxuX3tzD1H0N0FSKDBFUihAtBwCSWEZsFJ4JIUSSAdhkBQOICulQFIogXQQBknhALJCCiSFAkRHIZAUjkArpKm8pDhxQuTVVxVIZQyxZInIZz6TuJE51WPbn/1Atv7pV+UXv3w3mFFRllM+kBQZ+5w0HEmhANFyCCSFZcBK4ZEUSiAdhEFSOICslAJJoQTSQRgkhQPICimQFAoQHYVAUjgCrZCm8pLiuedEvvAFBVIZQ9x6q8izzyZuZE71MDMo7tuwTsK1KTZuWCc3XndVxiT6w5EUCkyRFAoQLYdAUlgGrBQeSaEE0kEYJIUDyEopkBRKIB2EQVI4gKyQAkmhANFRCCSFI9AKaSovKV5+WWTjRgVSGUNcf73Izp2zNhobn5QHd+yRO267pSUlzKkf5makRdE3JIVCB5AUChAth0BSWAasFB5JoQTSQRgkhQPISimQFEogHYRBUjiArJACSaEA0VEIJIUj0AppKi8pFBhphnjrnUOyYfNOee/IsRlhr736SnnikXtlyaJRzXSZYyEpMiObvQGSQgGi5RBICsuAlcIjKZRAOgiDpHAAWSkFkkIJpIMwSAoHkBVSICkUIDoKgaRwBFohDZJCAWKGEPv2vyAHXnp9xhoUSbMrMoRUHYqkUMCJpFCAaDkEksIyYKXwSAolkA7CICkcQFZKgaRQAukgDJLCAWSFFEgKBYiOQiApHIFWSIOkUICYMkQoI9bccM2sq3kYefGrg4cLP+UDSZGymZ2GISkUIFoOgaSwDFgpPJJCCaSDMEgKB5CVUiAplEA6CIOkcABZIQWSQgGioxBICkegFdIgKRQgVigEkkKhmUgKBYiWQyApLANWCo+kUALpIAySwgFkpRRICiWQDsIgKRxAVkiBpFCA6CgEksIRaIU0SAoFiBUKgaRQaCaSQgGi5RBICsuAlcIjKZRAOgiDpHAAWSkFkkIJpIMwSAoHkBVSICkUIDoKgaRwBFohDZJCAWKFQiApFJqJpFCAaDkEksIyYKXwSAolkA7CICkcQFZKgaRQAukgDJLCAWSFFEgKBYiOQiApHIFWSIOkUIBYoRBICoVmIikUIFoOgaSwDFgpPJJCCaSDMEgKB5CVUiAplEA6CIOkcABZIQWSQgGioxBICkegFdIgKRQgVigEkkKhmUgKBYiWQyApLANWCo+kUALpIAySwgFkpRRICiWQDsIgKRxAVkiBpFCA6CgEksIRaIU0SAoFiBUKYVVSnDh5Su7e8l157Y23ZyG79uor5YlH7pUli0a9x4mkKH8LkRTl75GpEEnhR59MlUgKf3qFpPCnV0gKP3qFpPCjT6ZKJIU/vUJS+NMrF5ValRSP7tob7MN9G9a52JfCciApCkOfOjGSIjWqQgciKQrFnyk5kiITrkIHIykKxZ8pOZIiE67CBiMpCkOfOTGSIjOywjZAUhSGvpSJrUkKM4ti68O7ZdM9d8rqVStKufNaRSEptEjai4OksMdWMzKSQpOm3VhICrt8NaMjKTRp2o2FpLDLVys6kkKLpP04SAr7jLUyICm0SFYjDpJCoY9ICgWIlkMgKSwDVgqPpFAC6SAMksIBZKUUSAolkA7CICkcQFZIgaRQgOgoBJLCEWiFNEgKBYgVCmFNUhhG5nSPK1Yul9vX3lwhZLN3BUlR/vYiKcrfI1MhksKPPpkqkRT+9ApJ4U+vkBR+9ApJ4UefTJVICn96haRw26t9+1+QAy+9Lg9tuktGhgeD5OF6kutuu6Xwz+9WJcVb7xySH+x7VjbdfWdr593id5MNSeGGc54sSIo89Nxti6RwxzpvJiRFXoLutkdSuGOdNxOSIi9BN9sjKdxw1siCpNCg6CYGksIN52iW+ISCMq0naU1SdLqyh4HD1T3cH4hzOSOSwo/uIyn86JOpEknhT6+QFP70CknhR6+QFH70yVSJpPCnV0gK972KriFpsu94/CnZdv/6Ulx905qkcI+5uIzMpCiOfdrMSIq0pIodh6Qoln+W7EiKLLSKHYukKJZ/luxIiiy0ihuLpCiOfdbMSIqsxIobX3lJMX5C5Levugc8vETkY59pm/fFV96U7/1wf/D4N76yVm687ir3NSZkRFIotAFJoQDRcggkhWXASuGRFEogHYRBUjiArJQCSaEE0kEYJIUDyAopkBQKEB2FQFI4Aq2QpvKS4tfPiTz9BQVSGUNcfqvIHc923KhMp3mEhVqXFMbOfP2bj8wA8+RjW0pjaTK2OXE4kkKDot0YSAq7fLWiIym0SNqPg6Swz1grA5JCi6T9OEgK+4w1MiApNCi6iYGkcMNZI0vlJcWRl0X+v40aqLLFuPh6kVt2tt3GfFbf+Z/+Ut4/8aFs27q+NJ/RrUqKYKd37ZUnHrm3dW6LWUxzw+adcs/Xvlz4qqHZOtx+NJJCi6S9OEgKe2w1IyMpNGnajYWksMtXMzqSQpOm3VhICrt8taIjKbRI2o+DpLDPWCtD5SWFFijFONE1KY6f+HDW53bFVJlDWZMUY+OT8uCOPXLHbbfMMjJGXjz9zPMzLnmSufISbYCkKFEz2pSCpCh/j0yFSAo/+mSqRFL40yskhT+9QlL40SskhR99MlUiKfzpFZLCfa/m7NU9tj68Wzbdc6esXrViBnUzm6JMq4fmPSSQFHkJ2t8eSWGfsUYGJIUGRTcxkBRuOGtkQVJoUHQTA0nhhnPeLEiKvATdbY+kcMc6byYkRV6C2bbft/8FOfDS6zMmDYRX51x32y2Fn/HATIps/UwcjaRQgGg5BJLCMmCl8EgKJZAOwiApHEBWSoGkUALpIAySwgFkhRRICgWIjkIgKRyBVkiDpFCAWKEQ1iSFYWQMzd5nnmdNigodML7uCpLCj84hKfzok6kSSeFPr5AU/vQKSeFHr5AUfvTJVImk8KdXSAp/euWiUquSwuwAV/dw0UZydCOApOhGqByPIynK0Yc0VSAp0lAqxxgkRTn6kKYKJEUaSsWPQVIU34O0FSAp0pIqfhySovgelKkC65KiTDtrqxZO97BFVi8ukkKPpc1ISAqbdHVjIyl0edqMhqSwSVc3NpJCl6etaEgKW2T14yIp9JnaioiksEXWz7hICoW+ISkUIFoOgaSwDFgpPJJCCaSDMEgKB5CVUiAplEA6CIOkcABZIQWSQgGioxBICkegFdIgKRQgVigEkkKhmUgKBYiWQyApLANWCo+kUALpIAySwgFkpRRICiWQDsIgKRxAVkiBpFCA6CgEksIRaIU0SAoFiBUKoS4pwkuX/MkffVG+/5d/I6+98XYirmuvvnLGgpo+M0VSlL97SIry98hUiKTwo0+mSiSFP71CUvjTKySFH71CUvjRJ1MlksKfXiEp/OmVi0rVJUVYtJEVWx/eLZvuuVNWr1oxY1/MYppPP/P8jOuyuthZWzmQFLbI6sVFUuixtBkJSWGTrm5sJIUuT5vRkBQ26erGRlLo8rQVDUlhi6x+XCSFPlNbEZEUtsj6GbcQSfHWO4dkx+NPybb718uSRaN+kotUjaQofwuRFOXvkakQSeFHn0yVSAp/eoWk8KdXSAo/eoWk8KNPpkokhT+9QlL40ysXlRYiKfbtf0EOvPQ6MylcdJgcAQEkhR8HApLCjz4hKfzpk6kUSeFPv5AUfvQKSeFHn5AU/vTJVIqk8KtftqtVlxRmlsSGzTvlvSPH2tZ+ybILZdf2jbNOA7G9s7biM5PCFlm9uEgKPZY2IyEpbNLVjc1MCl2eNqMhKWzS1Y2NpNDlaSsaksIWWf24zKTQZ2orIpLCFtnkuOE6ktH1I8u0ZqS6pAgxdFqTwm0L7GdDUthnnDcDkiIvQTfbIynccNbIgqTQoOgmBpLCDWeNLEgKDYr2YyAp7DPWyoCk0CJpPw6Swj7jaIZQUmzcsE5uvO6q4KFHd+0Nft63YZ3bYhKyWZMUhe+ZwwKQFA5h95gKSdEjOMebISkcA8+RDkmRA57jTZEUjoHnSIekyAHP4aZICoewc6ZCUuQE6HBzJIVD2CKSJCnKtCQDkkLheEBSKEC0HAJJYRmwUngkhRJIB2GQFA4gK6VAUiiBdBAGSeEAskIKJIUCREchkBSOQCukqbqkODF+Ql49/KoCqWwhlowskc8s+8ysjdrNpLhi5XK5fe3N2ZJYGG1VUnRan6JM57zk5YqkyEvQ/vZICvuMNTIgKTQouomBpHDDWSMLkkKDopsYSAo3nPNmQVLkJehueySFO9Z5M1VdUjz3y+fkC3/xhbyYMm9/68dvlWf/+Nm2kiK6JoUZ9O3Nd1VbUoyNT8qDO/bImhuukc/87ifkB/uelU133ykjw4PB+S6fu+nTrfNfMtMu2QZIipI1JKEcJEX5e2QqRFL40SdTJZLCn14hKfzpFZLCj14hKfzok6kSSeFPr6ouKV5+72XZ+H9vdN6Q6y+5Xnb+q51tJUV0TYqk2RXOC24mtDaTIrpwpsm14/GnZNv962XJolF58ZU35elnnucSpEV1fQ7mRVL40XQkhR99QlL40ydTKZLCn34hKfzoFZLCjz4hKfzpk6m06pKibN1oJyTMZIIynPLhRFIsXTwq2/7sB7L1T78aSApzGkhUWpStaVnrYSZFVmLuxyMp3DPvJSOSohdqxWzDTIpiuPeSFUnRC7VitkFSFMM9a1YkRVZixY1nJkVx7LNmRlJkJZZvfJKkmBMzKaKne5jFN6JWpkwrh+Zrb2NrJIUGRbsxkBR2+WpFR1JokbQfB0lhn7FWBiSFFkn7cZAU9hlrZEBSaFB0EwNJ4YazRhYkhQbF9DFCIRFfk+LJx7aUYkkGazMp4oiiIC5ZdqHs2r5RVq9akZ5kiUciKUrcnGZpSIry98hUiKTwo0+mSiSFP71CUvjTKySFH71CUvjRJ1MlksKfXiEp/OmVi0qdSQoXO1NUDiRFUeTT50VSpGdV5EgkRZH0s+VGUmTjVeRoJEWR9LPlRlJk41XUaCRFUeSz50VSZGdW1BZIiqLIlzOvNUkRXTizKjMm2rUQSVHOgztaFZKi/D0yFSIp/OiTqRJJ4U+vkBT+9ApJ4UevkBR+9MlUiaTwp1dICn965aJSJIUCZSSFAkTLIZAUlgErhUdSKIF0EAZJ4QCyUgokhRJIB2GQFA4gK6RAUihAdBQCSeEItEIaJIUCxAqFsCYpDCOzWObnbvp0KRbfsNkzJIVNujqxkRQ6HG1HQVLYJqwXH0mhx9J2JCSFbcJ68ZEUeixtRkJS2KSrGxtJocvTZjQkhU26/sW2KinMpUZ/sO9Z2XT3nTIyPOgfnZQVIylSgipwGJKiQPgZUiMpMsAqeCiSouAGZEiPpMgAq+ChSIqCG5AyPZIiJagSDENSlKAJKUtAUqQENUeGWZMU7S5rEnK99uor5YlH7pUli0a9R42kKH8LkRTl75GpEEnhR59MlUgKf3qFpPCnV0gKP3qFpPCjT6ZKJIU/vUJS+NMrF5VakxQuii9LDiRFWTrRvg4kRfl7hKTwo0dhlUgKf/qFpPCnV0gKP3qFpPCjT0gKf/pkKkVS+NUv29VakxSdru7x4itvytPPPC8PbbqrEqeBIClsH6b54yMp8jN0EYGZFC4o6+RAUuhwdBEFSeGCsk4OJIUOR9tRkBS2CevFZyaFHkvbkZAUtgn7Fb8QSWHWqtjx+FOy7f71nO7h1/HibbVICj9ah6Two0+mSiSFP71CUvjTKySFH71CUvjRJ2ZS+NMnZlL41SsX1RYiKfbtf0EOvPR6aWZSmKuQfO+H+2fw/vbmu+T2tTcH95l6H9i+J/j3l25dM6tuZlK4OFTz5UBS5OPnamskhSvS+fMgKfIzdBUBSeGKdP48SIr8DF1EQFK4oKyTg5kUOhxdRGEmhQvK/uRQlxRmlsSGzTvlvSPH2lK4ZNmFsmv7Rlm9akUpSBlJYW73bVg3qx5zasrOXXtbi3wmjUVSlKKNHYtAUpS/R6ZCJIUffTJVIin86RWSwp9eISn86BWSwo8+mSqRFP70CknhT69cVKouKcKiO61J4WLHsuToJCnMY1esXN6aVRGXFiYPkiIL7WLGIimK4Z41K5IiK7HixiMpimOfNTOSIiux4sYjKYpjnyUzkiILrWLHIimK5Z8lO5IiC63qj7UmKXxCFz/dIzzVY2x8Uh7csUfW3HBNS1KYmSLf2rZbvrN1fWsmCJKi/N1GUpS/R6ZCJIUffTJVIin86RWSwp9eISn86BWSwo8+mSqRFP70CknhT69cVIqkiFEOT1fZtnW9fOqqKwNJccdtt8iN110VjEySFKfGzrnoFTlyEDAfqMYnzslUPUcQNrVOoK8mMn9oQE6P85yyDjtngsGBPjH9Gj87nTMSm9smMH+oXybPTsu56d5fAOv1utRqNdulzvn4oyMDwnuK8h8GA/01mdffJ2OTU+Uvdo5XaITS1NS0nOUNYOmPhIUjA3Jm7Jz0/pdKZxfN6zC34glYlRTmlI+7t3xXXnvj7Vl7eu3VV7bWeSgew8wKwlM8/uDza1LNpDj10dmy7QL1xAjMN5Jickqmc7xJB6p9AuZD0Pzh/uCPFLdyE5hnJEVfTSZ4k17uRonIyNCATJ6bkqkcb9LrUpNa4W8dS486d4Gj8+cJ7ylyY7QeYKC/T+YN1GRsAklhHXbOBIGkmK7L2XMI9ZworW++cGSenBk/K/WCLYV5HeZWPAGrkqLTWg/F73r7CqLrULAmRZk7lb42TvdIz6rIkZzuUST9bLk53SMbryJHc7pHkfSz5eZ0j2y8ihrN6R5Fkc+el9M9sjMragtO9yiKfDnzWpMUviycaerc/9wB+ertvx90KH46B1f3KOeBm7UqJEVWYsWMR1IUw72XrEiKXqgVsw2SohjuvWRFUvRCzf02SAr3zHvNiKTolZz77ZAU7pmXOeOclxTh4pg/eu5Aq09PPraltQaFuXPf/hfkge17gse/dOsaeWjTXTIyPNgaz8KZZT7EG7UhKcrfI1MhksKPPpkqkRT+9ApJ4U+vkBR+9ApJ4UefTJVICn96haTwp1cuKrUmKUzx8VMlXOxQETmQFEVQz5YTSZGNV1GjkRRFkc+eF0mRnVlRWyApiiKfPS+SIjuzIrZAUhRBvbecSIreuBWxFZKiCOrlzWlVUphTJ36w71nZdPedM2YelBdHb5UhKXrj5nIrJIVL2r3nQlL0zs71lkgK18R7z4ek6J2d6y2RFK6J95YPSdEbtyK2QlIUQb23nEiK3rhVdStrkqLTlT0MzDJf3SNrs5EUWYm5H4+kcM+8l4xIil6oFbMNkqIY7r1kRVL0Qq2YbZAUxXDPmhVJkZVYceORFMWxz5oZSZGVWLXHW5MU1cY2c++QFOXvNpKi/D0yFSIp/OiTqRJJ4U+vkBT+9ApJ4UevkBR+9MlUiaTwp1dICn965aJSJIUCZSSFAkTLIZAUlgErhUdSKIF0EAZJ4QCyUgokhRJIB2GQFA4gK6RAUihAdBQCSeEItEIaJIUCxAqFsCopolfOuGTZhbJr+0ZZsewieXDHHllzwzVy+9qbK4ESSVH+NiIpyt8jUyGSwo8+mSqRFP70CknhT6+QFH70CknhR59MlUgKf3qFpPCnVy4qtSopwqt7/MHn18iOJ56Sr97+BVm9aoW8+Mqb8vQzz8+6lKeLHbaRA0lhg6puTCSFLk9b0ZAUtsjqx0VS6DO1FRFJYYusflwkhT5TGxGRFDao2omJpLDD1UZUJIUNqv7GtCYpzMKZWx/eLZvuuTOYPRGVFOaqHzsef0q23b9eliwa9Zdes3IkRflbiKQof49MhUgKP/pkqkRS+NMrJIU/vUJS+NErJIUffTJVIin86RWSwp9euai0EEnBTAoXrSVHlACSwo/jAUnhR5+QFP70yVSKpPCnX0gKP3qFpPCjT0gKf/pkKkVS+NUv29VakxSm8H37X5ADL70uW//0q/If9/zvwekeSxePyt1bvivrbruFNSlsd5f4LQJICj8OBiSFH31CUvjTJySFX71CUvjRLySFH31CUvjTJySFX71yUa1VSWF2wMya+Po3H5mxL08+tkVuvO4qF/vnJAenezjBnCsJkiIXPmcbIymcoc6diNM9ciN0FoCZFM5Q506EpMiN0EkAJIUTzCpJON1DBaOTIMykcILZmyTWJYU3JHIUiqTIAc/RpkgKR6BzpkFS5ATocHMkhUPYOVMhKXICdLg5ksIh7BypkBQ54DneFEnhGHiOdEiKHPAquKlVSWGu7nH46PEZV/EIL0vKJUgreDSVeJeQFCVuTqQ0JIUffTJVIin86RWSwp9eISn86BWSwo8+mSqRFP70CknhT69cVGpNUoQy4o7bbpl1agcLZ7poLTmiBJAUfhwPSAo/+oSk8KdPplIkhT/9QlL40SskhR99QlL40ydTKZLCr37ZrtaapIhegnT1qhUz9oNLkNpuK/HjBJAUfhwTSAo/+oSk8KdPSAq/eoWk8KNfSAo/+oSk8KdPSAq/euWiWmuSgpkULtpHjrQEkBRpSRU7DklRLP8s2TndIwutYscyk6JY/lmyIymy0CpuLJKiOPZZM3O6R1ZixY1nJkVx7MuY2ZqkMDtrTuvYum237Nq+UcLZFGYWxYbNO+Wer32ZS5CW8YioaE1ICj8ai6Two0+mSiSFP71CUvjTKySFH71CUvjRJ1MlksKfXiEp/OmVi0qtSgqzA6GUeO/Isdb+cAlSF60lR5QAksKP4wFJ4UefkBT+9MlUiqTwp19ICj96haTwo09ICn/6ZCpFUvjVL9vVWpcUtnegDPG5BGkZutC5BiRF+XtkKkRS+NEnJIU/fUJS+NUrJIUf/UJS+NEnJIU/fUJS+NUrF9UiKRQoIykUIFoOgaSwDFgpPJJCCaSDMJzu4QCyUgpmUiiBdBAGSeEAskIKJIUCREchON3DEWiFNMykUIBYoRBWJYW5wsfdW74rr73x9ixk1159pTzxyL2yZNGo9ziRFOVvIZKi/D0yFSIp/OiTqRJJ4U+vkBT+9ApJ4UevkBR+9MlUiaTwp1dICn965aJSq5Li0V17g324b8M6F/tSWA4kRWHoUydGUqRGVehAJEWh+DMlR1JkwlXoYCRFofgzJUdSZMJV2GAkRWHoMydGUmRGVtgGSIrC0JcysTVJYWZRbH14t2y6587WlT1KSUChKCSFAkTLIZAUlgErhUdSKIF0EAZJ4QCyUgokhRJIB2GQFA4gK6RAUihAdBQCSeEItEIaJIUCxAqFQFIoNBNJoQDRcggkhWXASuGRFEogHYRBUjiArJQCSaEE0kEYJIUDyAopkBQKEB2FQFI4Aq2QBkmhALFCIaxJCsPInO5xxcrlcvvamyuEbPauICnK314kRfl7ZCpEUvjRJ1MlksKfXiEp/OkVksKPXiEp/OiTqRJJ4U+vkBT+9MpFpVYlxVvvHJIf7HtWNt19p4wMD7rYn0JyICkKwZ4pKZIiE67CBiMpCkOfOTGSIjOywjZAUhSGPj5aYUgAACAASURBVHNiJEVmZIVsgKQoBHtPSZEUPWErZCMkRSHYS5vUmqTodGUPQ4Ore5T2mKhkYUgKP9qKpPCjT6ZKJIU/vUJS+NMrJIUfvUJS+NEnUyWSwp9eISn86ZWLSq1JChfFlyUHMynK0on2dSApyt8jUyGSwo8+ISn86ZOpFEnhT7+QFH70CknhR5+QFP70yVSKpPCrX7arRVIoEEZSKEC0HAJJYRmwUngkhRJIB2GYSeEAslIKJIUSSAdhkBQOICukQFIoQHQUgpkUjkArpEFSKECsUAjrkuLFV96Ur3/zkRnInnxsi9x43VWVwYikKH8rkRTl75GpEEnhR59MlUgKf3qFpPCnV0gKP3qFpPCjT6ZKJIU/vUJS+NMrF5ValRRGUOzctVeeeOReWbJoNNgfs5jmhs075Z6vfbkyV/1AUrg4VPPlQFLk4+dqaySFK9L58yAp8jN0FQFJ4Yp0/jxIivwMXURAUrigrJMDSaHD0UUUJIULyv7ksCYpxsYn5cEde+SO226ZNWvCyIunn3leHtp0VyWu+oGkKP8Bj6Qof49MhUgKP/pkqkRS+NMrJIU/vUJS+NErJIUffTJVIin86RWSwp9euajUmqQwV/fY+vBu2XTPnbJ61YoZ+2JmU+x4/CnZdv/61gwLFztrKweSwhZZvbhICj2WNiMhKWzS1Y2NpNDlaTMaksImXd3YSApdnraiISlskdWPi6TQZ2orIpLCFlk/41qTFMyk8POAqGrVSAo/Oouk8KNPpkokhT+9QlL40yskhR+9QlL40SdTJZLCn14hKfzplYtKrUkKU/y+/S/I3meeZ00KF50kR0cCSAo/DhAkhR99QlL40ydTKZLCn34hKfzoFZLCjz4hKfzpk6kUSeFXv2xXa1VSmOK5uoftFhI/DQEkRRpKxY9BUhTfg7QVMJMiLanixyEpiu9B2gqQFGlJFTsOSVEs/yzZmUmRhVaxY5EUxfIvW3brkqJsO2yjHtaksEFVNyaSQpenrWhICltk9eMiKfSZ2oqIpLBFVj8ukkKfqY2ISAobVO3ERFLY4WojKpLCBlV/Y1qVFI/u2iuHjx6fcRWPcK2KNTdcwyVI/T1uvKscSeFHy5AUfvTJVImk8KdXSAp/eoWk8KNXSAo/+mSqRFL40yskhT+9clGpNUnBwpku2keOtASQFGlJFTsOSVEs/yzZkRRZaBU7FklRLP8s2ZEUWWgVNxZJURz7rJmRFFmJFTceSVEc+zJmtiYpuARpGds9d2tCUvjReySFH31iJoU/fTKVIin86ReSwo9eISn86JOpEknhT6+QFP70ykWl1iQFMylctI8caQkgKdKSKnYckqJY/lmyM5MiC61ixyIpiuWfJTuSIgut4sYiKYpjnzUzkiIrseLGIymKY1/GzNYkhdlZc2WPrdt2y67tG2X1qhXB/r/1ziHZsHmn3PO1L7MmRRmPiIrWhKTwo7FICj/6ZKpEUvjTKySFP71CUvjRKySFH30yVSIp/OkVksKfXrmo1KqkiEqJ944ca+3Pk49tkRuvu8rF/jnJwdU9nGDOlQRJkQufs42RFM5Q506EpMiN0FkAJIUz1LkTISlyI3QSAEnhBLNKEiSFCkYnQZAUTjB7k8S6pPCGRI5CkRQ54DnaFEnhCHTONEiKnAAdbo6kcAg7ZyokRU6ADjdHUjiEnSMVkiIHPMebIikcA8+RDkmRA14FN0VSKDQVSaEA0XIIJIVlwErhkRRKIB2EQVI4gKyUAkmhBNJBGCSFA8gKKZAUChAdhUBSOAKtkAZJoQCxQiGQFArNRFIoQLQcAklhGbBSeCSFEkgHYZAUDiArpUBSKIF0EAZJ4QCyQgokhQJERyGQFI5AK6RBUihArFAIJIVCM5EUChAth0BSWAasFB5JoQTSQRgkhQPISimQFEogHYRBUjiArJACSaEA0VEIJIUj0AppkBQKECsUAkmh0EwkhQJEyyGQFJYBK4VHUiiBdBAGSeEAslIKJIUSSAdhkBQOICukQFIoQHQUAknhCLRCGiSFAsQKhUBSKDQTSaEA0XIIJIVlwErhkRRKIB2EQVI4gKyUAkmhBNJBGCSFA8gKKZAUChAdhUBSOAKtkAZJoQCxQiGQFArNRFIoQLQcAklhGbBSeCSFEkgHYZAUDiArpUBSKIF0EAZJ4QCyQgokhQJERyGQFI5AK6RBUihArFAIJIVCM5EUChAth0BSWAasFB5JoQTSQRgkhQPISimQFEogHYRBUjiArJACSaEA0VEIJIUj0AppkBQKECsUAkmh0EwkhQJEyyGQFJYBK4VHUiiBdBAGSeEAslIKJIUSSAdhkBQOICukQFIoQHQUAknhCLRCGiSFAsQKhUBSKDQTSaEA0XIIJIVlwErhkRRKIB2EQVI4gKyUAkmhBNJBGCSFA8gKKZAUChAdhUBSOAKtkAZJoQCxQiGQFArNRFIoQLQcAklhGbBSeCSFEkgHYZAUDiArpUBSKIF0EAZJ4QCyQgokhQJERyGQFI5AK6RBUihArFAIJIVCM5EUChAth0BSWAasFB5JoQTSQRgkhQPISimQFEogHYRBUjiArJACSaEA0VEIJIUj0AppkBQKECsUAkmh0EwkhQJEyyGQFJYBK4VHUiiBdBAGSeEAslIKJIUSSAdhkBQOICukQFIoQHQUAknhCLRCGiSFAsQKhUBSKDQTSaEA0XIIJIVlwErhkRRKIB2EQVI4gKyUAkmhBNJBGCSFA8gKKZAUChAdhUBSOAKtkAZJoQCxQiGQFArNRFIoQLQcAklhGbBSeCSFEkgHYZAUDiArpUBSKIF0EAZJ4QCyQgokhQJERyGQFI5AK6RBUihArFAIJIVCM5EUChAth0BSWAasFB5JoQTSQRgkhQPISimQFEogHYRBUjiArJACSaEA0VEIJIUj0AppkBQKECsUAkmh0EwkhQJEyyGQFJYBK4VHUiiBdBAGSeEAslIKJIUSSAdhkBQOICukQFIoQHQUAknhCLRCGiSFAsQKhUBSKDQTSaEA0XIIJMVMwFP1KanXp8X8nA5+Tjd+n56SafNf3fzffKx1X/h783GJPB4d34odxonEasacbsYM809PN8bWa1OyYLhfTpweb9bVqKdVW71+vq5WfefOj23VUQ/2JdguUqf5Pdjf5n1h3qAO85+pK8KlxaC5XbTuVqzmNiZqsG1zX87/3rj/fKzw9/N8ov2w/FQgPAQgAAEIQAACEIBAGwL1B+uwKQEBJIVCE5AUChAth3AlKcbOfSSTU5MyOTUhE1MTCT+bj50bl4lp83jj98b4SZmYGpeJs+MyaR47NxmMMfeZf5v7Js5NnP9ptmmOazw23szZiFkXXmQtH1aEhwAEIAABCEAAAhCoEAEkRTmaiaRQ6AOSQgGi5RBGUvzq/SPy2zPvy4nx43J8/JicGDsuJyaOyanJUzJ29oxMhCKgKQUaAuC8FAilQyAVpidl/Nx4UzBMipETvt6G+0ekr9Yn/X19UjM/a/3SZ/7r6w/uDx6L3ddfi4xtPh5sa7aRxvjG743tg/+lES8YE9zXHBv8Xgt+N9vNH54nE5P1Rs7m+FozZmO7WqO25n39/QMzaozmDeow45o5W3U1Ywc11Gqtuhu/N/e5r7kPrbpn8jExW7yiDML9bdbY4mfub8PH9MC3G6d7+NMxTvfwp1ec7uFHrzjdw48+mSo53cOfXnG6hz+9clEpkkKBMpJCAWKKEEYmfDjxgXw4eTL4eXLC/DwpH05G/m3ubz5uHgvGTH4gpyY+DE5tsHkzH0YH+4ZkcGBQhvqGZGhgWAb7h2Swb1CGBsxPc99Q477+IRkKfg7KUH9j3FD/YOPnwHDjvmacxvjGuDCOeczEG26Oa+QdauY1sYZt7qq12KxJYQ2temAkhTpSawGRFNbQqgdGUqgjtRIQSWEFq5WgSAorWK0ERVJYweptUCSFQuuQFOkgnpr8UE62kQxGQJiZDUYotORCc2ywzcTJdEk6jFo4b1SWjCyVJUNLZenwhc1/XyiLh5c0xEBTJIQf9gNJYCRAIBcaUiB4zMiCplAIhcPCeQtz10cAESSFP0cBksKfXiEp/OkVksKPXiEp/OiTqRJJ4U+vkBT+9MpFpUgKBcpzSVKcOXs6OF3i/P/Hgn9/MHHCumQYGZgvFwwtkkVDi+SCwcXn/z20OBAPC4cuaDzWfLz176HFctXyy+SDUxNydop1GhQOeWshkBTW0KoHRlKoI7UWEElhDa16YCSFOlIrAZEUVrBaCYqksILVSlAkhRWs3gZFUii0rkqS4siZ9+Q3p34d/P/uqd/IwQ9/Ffn9oBhJ0estj2S4cPiiXtMG27laODNXkWzMTAqPjgEkhT/NQlL40yskhR+9QlL40SdTJZLCn14hKfzplYtKkRQKlH2SFL8+9St579Rv5NcfviOHTv9Gfn3yl/Lu6YNy8MNfy69OvpWKxsXzlwenSiwdvkiWDC8N/jcSYdHwktZMhsVmZsPgaPP3xcHpFUXekBRF0k+fm5kU6VkVPRJJUXQH0udHUqRnVfRIJEXRHUiXH0mRjlMZRiEpytCFdDUgKdJxmiujkBR5O71smZwbWSDTy5bL1LLlwc/p5ZfI1PLzvwf3X5hvJkCaMs9OTcrBU+8EwuHd07+Wgyffkd+c/rW8++HB4Ofh04e6Lh65aGixrBxdJZddcLlcuvByWbnocrls4eVy6QWXB/cbIeHjDUnhR9eQFH70yVSJpPCnV0gKf3qFpPCjV0gKP/pkqkRS+NMrJIU/vXJRKZIiL+VaLVWE+rx5Mv2xi1siIxAXyy9pyY1QcEx97GKRgYG2Mc2lLn9+4p/lrRM/D2Y+/OL4P4uZHWFmRLw/9tuutXxs5OJAOBjxsGrxx2XFwsvkikVXyvKFK4KfPl4KsetOc7pHGkSlGIOkKEUbUhWBpEiFqRSDkBSlaEOqIpAUqTAVPghJUXgLUheApEiNqvCBSIrCW1CqApAUedtx+rQcfeOX0n/ksPQdOdz4efi98/8O7ztxIl2mWi2YdWGkxeHLlso/rqrJPy79SP7L/OPy32q/laNTna9ycenoSlk5eoWsGL1ULh+9Qi69oPH7paOXyZWLP5muhgqOYiaFH01FUvjRJ1MlksKfXiEp/OkVksKPXiEp/OiTqRJJ4U+vkBT+9MpFpUgKBcpp16ToP/iO9B9uioxQakSExoG+g3Jg9IT842UiL14q8psLkov75DGRTx4XueaDQVk9vViuvOx6uXTJarm8vijYoH7BBTK95EKZXrpUxv/VHyjsof8hkBR+9BBJ4UefkBT+9MlUiqTwp19ICj96haTwo09ICn/6ZCpFUvjVL9vVIilSEN63/wV5YPueYOSXbl0jD226S0aGB1tbppUU0VRvf/Bzefnwi/LqkZfkpSM/llePvjyrkqHaPLmub6XcNHGxrDm+QD51aEp+5+AZ6X/vkPQfejdF5e2H1EdHZXrBQqkvXCj1BQtlenRU6vMXNP69YIHUF45KPfzZHGN+n75gkdRHRoLHg3Fm/NLyr1OBpMh1uDjbGEnhDHXuRMykyI3QWQAkhTPUuRMhKXIjdBIASeEEs0oSZlKoYHQSBEnhBLM3SZAUXVr14itvys5de+WJR+6VJYtG5dFde4Mt7tuwLrWkODV5KhARLx/+ibz83k/kn46+KB+Mzzz9oyY1Wb3kk/LZZTfKDctvks8uv1GuvvBT0l/rb1th37H3G6eX/Pa30nf8fek7dkz6Thxv/jwmfcePS+3Uh1I7fUr6zpyR2pnTwX22btOLF7fkxgwB0kZ6tMYYITJ/vkyHYsSIj0WNWSFaNySFFkm7cZAUdvlqRkdSaNK0GwtJYZevZnQkhSZNe7GQFPbYakdGUmgTtRcPSWGPrY+RkRRdumakxBUrl8vta28ORsalhbkvOpNiqj4lbxz7WUNINP9/+4NfSF3qMzKZS3Zet+y/kxsuuSkQE9cv/z1ZOG+hm2Noelr6Tp0K5EXtzBnpO3NaaqdPBxIj+D24v/HvmhkX/Pu09M0a0xQfp0+LnDvnpvYwy8CA1AfmiQz0S90sNDowr/Fz3jyp95vf+8UsVirBvwdkYHhIztX6ZLq///wYM9Zs0z8g9XmNccG2ze0a8SL3hffHxs6KEdTVjJdUY7T2SI2N/TH71X9+f/r63HItOBuSouAGZEiPpMgAq+ChSIqCG5AhPZIiA6wChyIpCoSfMTWSIiOwAocjKQqEX8LUSIoOTRkbn5QHd+yRNTdc05IUb71zSL61bbd8Z+t6Wb1qhRw9c1T+z//6XFNIvCg//e0/ibkCR/Q22Dckn7r4M/LZi2+U6y+5Ua5fdqNcfsHHS3g49F5SbWK8ITXCWRtGaIyNSd+HJ2fcL0Z4nDIzO5oSJEGUhNKk92qqt2V9eKQhTFpSpSk0AqmScP+8QZGhQamPzBezbXCKTvi/iWVuRoCYq9OEV6gJ/x383rxqTfO++qxxZsjMMdFYwXgTo8OY1vjmGLNNX19NRucPysmxUHo1Y8TyN+pp9jladzRfLH9rHxL3t7k/0f0Nwifnn8mtse1sRrM5zmLUjn/CfjSYzqwzLDHOclY9qfYjsg9JHGP5548MyEBfTU6OTTV6kbAv9aHh6j0ZPdwjJIU/TUNS+NErJIUffTJVIin86RWSwp9euagUSZFCUtxx2y1y43VXBSPjkqL20OxLkH5i6Sfkpktvkpsuuyn4+dlLPivz+ua56OfcyXH2bGP2hvk//HfSfdHHex3b63ZZ6mmXY3p67vSUPYUABCAAAQhAAAIQgECRBOozZ78XWcpczo2kSCEpOs2k+N3Hf1dWXrCyJST+xcp/IUuGl8zlY4p9t0HgzJnzMiaNNDFjxsZEPvro/M/w3+PjIkZ+hC/C5mf4v6k9+rvNMTZjp9kP8jeOVO3+m+OLGwQgAAEIQAACEPCRAJKiFF1DUnRpQ9Y1KUrRVYqYRYCFM/04KFiTwo8+mSpZk8KfXnG6hz+94nQPP3rF6R5+9MlUyeke/vSK0z386ZWLSpEUXShrXN3DRSPJ0ZkAksKPIwRJ4UefkBT+9MlUiqTwp19ICj96haTwo09ICn/6ZCpFUvjVL9vVIilSEN63/wV5YPueYOSXbl0jD226S0aGB1tbRq/ukSIcQwoggKQoAHoPKZEUPUAraBNmUhQEvoe0SIoeoBW0CZKiIPAZ0yIpMgIrcDgzKQqEnzE1kiIjsIoPR1IoNBhJoQDRcggkhWXASuGRFEogHYRBUjiArJQCSaEE0kEYJIUDyAopkBQKEB2FQFI4Aq2QBkmhALFCIZAUCs1EUihAtBwCSWEZsFJ4JIUSSAdhkBQOICulQFIogXQQBknhALJCCiSFAkRHIZAUjkArpEFSKECsUAgkhUIzkRQKEC2HQFJYBqwUHkmhBNJBGCSFA8hKKZAUSiAdhEFSOICskAJJoQDRUQgkhSPQCmmQFAoQKxQCSaHQTCSFAkTLIZAUlgErhUdSKIF0EAZJ4QCyUgokhRJIB2GQFA4gK6RAUihAdBQCSeEItEIaJIUCxAqFQFIoNBNJoQDRcggkhWXASuGRFEogHYRBUjiArJQCSaEE0kEYJIUDyAopkBQKEB2FQFI4Aq2QBkmhALFCIZAUFWomuwIBCEAAAhCAAAQgAAEIQAACEPCZAJLC5+5ROwQgAAEIQAACEIAABCAAAQhAoEIEkBQVaia7AgEIQAACEIAABCAAAQhAAAIQ8JkAksLn7lE7BCAAAQhAAAIQgAAEIAABCECgQgSQFD02c9/+F+SB7XuCrb906xp5aNNdMjI82GM0NktDICvzTuPHxiflwR175EfPHQhSf3vzXXL72puDf7/1ziHZsHmnvHfkWPD7tVdfKU88cq8sWTSapsw5P6YT2yQ43ca/+Mqb8vVvPtK1F+G4Jx/bIjded9Wc70MaACdOnpK7t3xXXnvj7WB4N3bdxnd7jkafW5csu1B2bd8oq1etSFPqnB/TjW0cUK+vfyZOdFv6lO/Q6/aciUdPM96M2frwbtl0z508f3K0Jw3raPg0481r3I7Hn5Jt96+f8Z7h0V175Xs/3N8KF33PkWMX5symad8HhEDSjDevc786eFju27AukWP43sQ8yHv89Iea5t+qMKt5/lyxcnnrfXq0muhz6xtfWdu2n+n3gJFlIYCk6KET5sVv5669rQ+u5glibu1e6HpIwSYxAlmZdxsf7Vn4xmPjhnXBh1uz7cFDR1svhmbs4aPH+SOV8qjsxDYpRKfx5g3ft7btlu9sXR+8GTd//A689PqsXkTfkHT7oJ1yNyo/LHwDtuaGa4JjPc46DqDb+G7PuW7xKw88xw52YxsP3W18t9e/6N+3eKwcuzHnNu32nMn6HIsKXeRRvsNJuzdRgRH/YsPkeuLP/w/5kzv/IBAXoazdtnU9Qj1FG9O+DwhDdRsffb/Q7kNt9LnGF5EpmtQc0u1vT9a/VVHhkST2+PyVvjc+jkRS9NC1uNHjTVwPEDNukpV5p/EmdfxbqE4vdPQ3fbOSvuHrxLbb+Pg3HUkfdMNvrjb/L1+R+7ftllA2pa96bo6Mf+MXf9Mep9JtfKfn3PDQUDBz6Y7bbuFNeQ+Hm8vXv7gIRC710LDmJt2eM1mfY+F4ZlL03pPoB9nojIe8r3/t4iZV2i1X/r2rVoQ07wOie5x2fKeZFOFrromb9MVItQjr7Y3m36ro7OWkmRTmvfnTzzzPF4h67StdJCRFxpYk/XHhTVxGiBmHZ2XebbxJH/123vze7hv6bo9l3JXKD096LnRi2228+fbJ3MJZSvFZL9Htly4eDU5dQFKkO8yS5FtWWReOv/trfxhIiHBWhqkgqTfhaSXmcb6dStenbq9n8dNluo3v9vo3PjERPI8uX3Fx8Obvr//uQMcp0en2Ym6O0nyORWdqIinyH0+2etPudI9oxfG/Y/n3ptoR4n+XuvFLO76dpIhu3+n9S7WpZ9+7bn97sv6tio5PkhTRWRZhtcykzd63Mm+BpMjYnfBJGP1GEEmREWLG4VmZdxtv0sfPGW33h4jeZmtW0hu0bpKiUy+MpIiehxh9c/KJj186Y0ZMtzcu2fak+qOTvoXoJini31rEJUW718X4cy58ji6/eCmnyXU51Lq9nrV745e2F0ki1vT1n986KP/wk9eE0wp6fy3QfI4hKXrvQ9KWtnqTRlIwRT1bL+MfULv9rU87PklSxO9DUqTvlfbfqm6SImnWxtZtu1nrKn3LSj8SSZGxRVlNYcbwDE8gkJV5t/EmRZqZFJw3mv1w7DYzIr64bLfxnWZSLF1ywYwFTqPVYtO7907zm8RuMymSxCCnUXXvkRnR7fUs67dT3V7/4jMnTJ9445euV/FRms8xJEVvPWi3la3edJMUrHGVvY9pZ0aEkdOOT5IUZtvoAqdhTGb+de+b9t+qrJKC06i698i3EUiKHjqW9ZyrHlKwSYxAVuZ516RAUPR2CHZbYyIetdv4tOeWmrjdvl3pbY+qu5X2+fJZn3OcT5r+2HL5+pf2W8j01c/dkdrPsZAkp3vkP6Zs9aaTpEBQ9Na3LO8DTIa047td3SOMxZoU6fum+beq25oU8f4lzeRIXzkjy0gASdFDV7KuXttDCjaJEejG3LxY7X3m+dYVV7qNj5r2TusccHnE7IdiJ7Yh63W33TLj6ikmi/mmsFsvOk29RFJk61W31e3joq7b+DTPufAqOabS+BoW2aqfW6O7sdV8/UuKxUyK3o63bs+Z+Otht/FIit76kLRVN9ZZX//CHO0kBad49N67blfriL9mdRsfVoKk6L0n7bbs9rcqLuq6jQ/zJK1JEX+OMjtTv59FR0RS9NiBrNcB7jENm0UIdGIe/yMVGvAHtu8JIsSn6kUvL2Uej17aKGkxHjOGUwjSHY6d2CZJik7jTcbo5cLil3aLVoSkSNefJGbhgpbRYzxpNlH0MntJz4lOz9F4n7meebZ+uXr9M1VFpzyzJkW2PsVHd3rOJL0edhoffw4l/W3LV+3c2roT66yvf/FYhmT4Gpf0GL3Ldqx1eh+Q9P6v0/joY2EV7d7fsSZFtj51e++dNJuo29+28H28iR3/exTtJX+rsveq7FsgKcreIeqDAAQgAAEIQAACEIAABCAAAQjMEQJIijnSaHYTAhCAAAQgAAEIQAACEIAABCBQdgJIirJ3iPogAAEIQAACEIAABCAAAQhAAAJzhACSYo40mt2EAAQgAAEIQAACEIAABCAAAQiUnQCSouwdoj4IQAACEIAABCAAAQhAAAIQgMAcIYCkmCONZjchAAEIQAACEIAABCAAAQhAAAJlJ4CkKHuHqA8CEIAABCAAAQhAAAIQgAAEIDBHCCAp5kij2U0IQAACEIAABCAAAQhAAAIQgEDZCSApyt4h6oMABCAAAQhAAAIQgAAEIAABCMwRAkiKOdJodhMCEIAABCAAAQhAAAIQgAAEIFB2AkiKsneI+iAAAQhAAAIQgAAEIAABCEAAAnOEAJJijjSa3YQABCAAAQhAAAIQgAAEIAABCJSdAJKi7B2iPghAAAIQgAAEIAABCEAAAhCAwBwhgKSYI41mNyEAAQhAAAIQgAAEIAABCEAAAmUngKQoe4eoDwIQgAAEIAABCEAAAhCAAAQgMEcIICnmSKPZTQhAAAIQgAAEIAABCEAAAhCAQNkJICnK3iHqgwAEIAABCEAAAhCAAAQgAAEIzBECSIo50mh2EwIQgAAEIAABCEAAAhCAAAQgUHYCSIqyd4j6IAABCECgMgT27X9BHti+Z8b+XHv1lfLEI/fKL375rnz9m4/Ik49tkRuvu2rGmEd37ZWfvPJmMG7JolHpFOf4B6dkw+ad8t6RY225fXvzXbJyxcVBvqRbWMOLr7wZjPnSrWvkoU13ycjwYGt4p8fMoBMnT8ndW74rr73xdts6vvGVtXLFyuUzmJjabl97s7z1zqFgVIc38AAAB7RJREFUPy5auqi132GgpMfCejrtT2UOJHYEAhCAAAQgUGECSIoKN5ddgwAEIACB8hCIi4awMnP/5276dCAmjHzY+8zzMz6Umw/k39q2W76zdb2sXrVC0sSJ7rWJeeCl1xMlw9Ztu2XX9o1B3KRb+MH/kmUXzhg3Nj4pD+7YIz967kCiwGgXa+euvbOEgxlr8sRrCUWEkS1xcWMYfO+H+yUUPEbcJMUoT/epBAIQgAAEIACBtASQFGlJMQ4CEIAABCDQI4FwVsG6224JZgm0u4Uf/pdfvFTu27BOwt/X3HBNsF3aOJqSwoiFz/8Pn5XTZ8aCmkKp8PQzz8vChfPl9OmPZgkQLUlh5Mz/9Pv/vfz09bdaOYy82PH4U3L9tZ+Uv/vP/9SSHkiKHg9ONoMABCAAAQiUjACSomQNoRwIQAACEKgegbh86LSH4QyCbVvXy8FDR2fMrMgSJ8yRdyaFkRQbN6yTnf/pL2fM5jCnafzq4GE5fPS4VUmx8d/+kYQ1hLNNTF6TPzrrBElRvecNewQBCEAAAnOTAJJibvadvYYABCAAAccE4msmRE9ViJcSns5g7o+f6pAljtm+k6RIsyZFeIrG95/666DML3/xXwYzGbbdv17MfbYlhTnN5dX/+ovglJV7/80d8tCjfy6b7rkzuC8uKbrtj+OWkw4CEIAABCAAgR4IICl6gMYmEIAABCAAgV4JRNdzMDHi6z2Y+8LTOn7vuqtap1jE86WJ001SpFmTIpQUZkFOc/qFua37n//H4PQTI1NcSIqli0eDRTgXjS6Q31m9MmASX7+DmRS9HpFsBwEIQAACECgXASRFufpBNRCAAAQgMIcItDt9I74WRTcknU4D0TjdI7yqSHzRTleSwizsafbj8T//q9YCnkiKbkcFj0MAAhCAAAT8JICk8LNvVA0BCEAAAh4RMDMjzKU4b17zmVlVmw/65hYuSmn+3U5SZI1jYmlKCrNexi9++Rv517f8XlCzS0lh9n3/cwfkq7f/fpAbSeHRE4BSIQABCEAAAhkIICkywGIoBCAAAQhAoBcC4ekbl6+4eMYik+H6EvF1JzpJCnPaQ9o42pIivu8uJUU8N5KilyORbSAAAQhAAALlJ4CkKH+PqBACEIAABCpAIBQVZkZFeEtaj8I81ul0jyxxukmKbgtNGokSrkmxZNHorC5oSAojGx7YvqcV+9ub7wrWuzCzNswaGGbhTHO6RxpJ0W1/KnAYsQsQgAAEIACByhNAUlS+xewgBCAAAQhAAAIQgAAEIAABCEDADwJICj/6RJUQgAAEIAABCEAAAhCAAAQgAIHKE0BSVL7F7CAEIAABCEAAAhCAAAQgAAEIQMAPAkgKP/pElRCAAAQgAAEIQAACEIAABCAAgcoTQFJUvsXsIAQgAAEIQAACEIAABCAAAQhAwA8CSAo/+kSVEIAABCAAAQhAAAIQgAAEIACByhNAUlS+xewgBCAAAQhAAAIQgAAEIAABCEDADwJICj/6RJUQgAAEIAABCEAAAhCAAAQgAIHKE0BSVL7F7CAEIAABCEAAAhCAAAQgAAEIQMAPAkgKP/pElRCAAAQgAAEIQAACEIAABCAAgcoTQFJUvsXsIAQgAAEIQAACEIAABCAAAQhAwA8CSAo/+kSVEIAABCAAAQhAAAIQgAAEIACByhNAUlS+xewgBCAAAQhAAAIQgAAEIAABCEDADwJICj/6RJUQgAAEIAABCEAAAhCAAAQgAIHKE0BSVL7F7CAEIAABCEAAAhCAAAQgAAEIQMAPAkgKP/pElRCAAAQgAAEIQAACEIAABCAAgcoTQFJUvsXsIAQgAAEIQAACEIAABCAAAQhAwA8CSAo/+kSVEIAABCAAAQhAAAIQgAAEIACByhNAUlS+xewgBCAAAQhAAAIQgAAEIAABCEDADwJICj/6RJUQgAAEIAABCEAAAhCAAAQgAIHKE0BSVL7F7CAEIAABCEAAAhCAAAQgAAEIQMAPAkgKP/pElRCAAAQgAAEIQAACEIAABCAAgcoTQFJUvsXsIAQgAAEIQAACEIAABCAAAQhAwA8CSAo/+kSVEIAABCAAAQhAAAIQgAAEIACByhNAUlS+xewgBCAAAQhAAAIQgAAEIAABCEDADwJICj/6RJUQgAAEIAABCEAAAhCAAAQgAIHKE0BSVL7F7CAEIAABCEAAAhCAAAQgAAEIQMAPAkgKP/pElRCAAAQgAAEIQAACEIAABCAAgcoTQFJUvsXsIAQgAAEIQAACEIAABCAAAQhAwA8CSAo/+kSVEIAABCAAAQhAAAIQgAAEIACByhNAUlS+xewgBCAAAQhAAAIQgAAEIAABCEDADwJICj/6RJUQgAAEIAABCEAAAhCAAAQgAIHKE0BSVL7F7CAEIAABCEAAAhCAAAQgAAEIQMAPAkgKP/pElRCAAAQgAAEIQAACEIAABCAAgcoTQFJUvsXsIAQgAAEIQAACEIAABCAAAQhAwA8CSAo/+kSVEIAABCAAAQhAAAIQgAAEIACByhNAUlS+xewgBCAAAQhAAAIQgAAEIAABCEDADwJICj/6RJUQgAAEIAABCEAAAhCAAAQgAIHKE0BSVL7F7CAEIAABCEAAAhCAAAQgAAEIQMAPAv8/g2Z0W7rSDT0AAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'darkorange', 'green'])" ] }, { "cell_type": "markdown", "id": "7dc56592-179d-4e4c-b75a-8eb81dcafe71", "metadata": {}, "source": [ "**A, as the scarse limiting reagent, stops the reaction. \n", "As long as A is low, B also remains low.**" ] }, { "cell_type": "code", "execution_count": 8, "id": "bcf652b8-e0dc-438e-bdbe-02216c1d52a0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEAXBcaption
00.0000005.000000100.0000000.000000Initial state
10.0002504.00000099.0000002.000000
20.0005003.20900098.2090003.582000
30.0006252.89474397.8947434.210514
40.0007502.61241597.6124154.775169
50.0008752.35860597.3586055.282790
60.0010002.13029597.1302955.739410
70.0011251.92481496.9248146.150372
80.0012501.73978996.7397896.520422
90.0013751.57311296.5731126.853775
100.0015001.42290696.4229067.154189
110.0016251.28749396.2874937.425013
120.0017501.16538096.1653807.669240
130.0018751.05522896.0552287.889544
140.0020000.95584095.9558408.088319
150.0021250.86614495.8661448.267712
160.0022500.78517795.7851778.429646
170.0023750.71207695.7120768.575848
180.0025000.64606695.6460668.707868
190.0026250.58644995.5864498.827102
200.0027500.53259995.5325998.934801
210.0028750.48395295.4839529.032095
220.0030000.44000195.4400019.119998
230.0031250.40028795.4002879.199426
240.0032500.36439995.3643999.271201
250.0033750.33196795.3319679.336067
260.0035000.30265495.3026549.394693
270.0036250.27615895.2761589.447683
280.0037500.25220995.2522099.495582
290.0038750.23056095.2305609.538881
300.0040000.21098895.2109889.578024
310.0041250.19329495.1932949.613412
320.0042500.17729795.1772979.645406
330.0043750.16283495.1628349.674332
340.0045000.14975795.1497579.700487
350.0046250.13793295.1379329.724135
360.0048130.12189595.1218959.756210
370.0050000.10816195.1081619.783677
380.0051880.09640095.0964009.807201
390.0053750.08632695.0863269.827347
400.0055630.07769995.0776999.844602
410.0057500.07031095.0703109.859381
420.0059380.06398095.0639809.872039
430.0061250.05855995.0585599.882882
440.0063130.05391595.0539159.892169
450.0065940.04794995.0479499.904103
460.0068750.04326695.0432669.913469
470.0071560.03959095.0395909.920821
480.0074380.03670495.0367049.926591
490.0078590.03330795.0333079.933386
500.0082810.03100595.0310059.937989
510.0089140.02866795.0286679.942667
520.0098630.02685695.0268569.946289
530.0112870.02611095.0261109.947779
540.0134230.02620995.0262099.947582
550.0166260.02611595.0261159.947769
\n", "
" ], "text/plain": [ " SYSTEM TIME A X B caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initial state\n", "1 0.000250 4.000000 99.000000 2.000000 \n", "2 0.000500 3.209000 98.209000 3.582000 \n", "3 0.000625 2.894743 97.894743 4.210514 \n", "4 0.000750 2.612415 97.612415 4.775169 \n", "5 0.000875 2.358605 97.358605 5.282790 \n", "6 0.001000 2.130295 97.130295 5.739410 \n", "7 0.001125 1.924814 96.924814 6.150372 \n", "8 0.001250 1.739789 96.739789 6.520422 \n", "9 0.001375 1.573112 96.573112 6.853775 \n", "10 0.001500 1.422906 96.422906 7.154189 \n", "11 0.001625 1.287493 96.287493 7.425013 \n", "12 0.001750 1.165380 96.165380 7.669240 \n", "13 0.001875 1.055228 96.055228 7.889544 \n", "14 0.002000 0.955840 95.955840 8.088319 \n", "15 0.002125 0.866144 95.866144 8.267712 \n", "16 0.002250 0.785177 95.785177 8.429646 \n", "17 0.002375 0.712076 95.712076 8.575848 \n", "18 0.002500 0.646066 95.646066 8.707868 \n", "19 0.002625 0.586449 95.586449 8.827102 \n", "20 0.002750 0.532599 95.532599 8.934801 \n", "21 0.002875 0.483952 95.483952 9.032095 \n", "22 0.003000 0.440001 95.440001 9.119998 \n", "23 0.003125 0.400287 95.400287 9.199426 \n", "24 0.003250 0.364399 95.364399 9.271201 \n", "25 0.003375 0.331967 95.331967 9.336067 \n", "26 0.003500 0.302654 95.302654 9.394693 \n", "27 0.003625 0.276158 95.276158 9.447683 \n", "28 0.003750 0.252209 95.252209 9.495582 \n", "29 0.003875 0.230560 95.230560 9.538881 \n", "30 0.004000 0.210988 95.210988 9.578024 \n", "31 0.004125 0.193294 95.193294 9.613412 \n", "32 0.004250 0.177297 95.177297 9.645406 \n", "33 0.004375 0.162834 95.162834 9.674332 \n", "34 0.004500 0.149757 95.149757 9.700487 \n", "35 0.004625 0.137932 95.137932 9.724135 \n", "36 0.004813 0.121895 95.121895 9.756210 \n", "37 0.005000 0.108161 95.108161 9.783677 \n", "38 0.005188 0.096400 95.096400 9.807201 \n", "39 0.005375 0.086326 95.086326 9.827347 \n", "40 0.005563 0.077699 95.077699 9.844602 \n", "41 0.005750 0.070310 95.070310 9.859381 \n", "42 0.005938 0.063980 95.063980 9.872039 \n", "43 0.006125 0.058559 95.058559 9.882882 \n", "44 0.006313 0.053915 95.053915 9.892169 \n", "45 0.006594 0.047949 95.047949 9.904103 \n", "46 0.006875 0.043266 95.043266 9.913469 \n", "47 0.007156 0.039590 95.039590 9.920821 \n", "48 0.007438 0.036704 95.036704 9.926591 \n", "49 0.007859 0.033307 95.033307 9.933386 \n", "50 0.008281 0.031005 95.031005 9.937989 \n", "51 0.008914 0.028667 95.028667 9.942667 \n", "52 0.009863 0.026856 95.026856 9.946289 \n", "53 0.011287 0.026110 95.026110 9.947779 \n", "54 0.013423 0.026209 95.026209 9.947582 \n", "55 0.016626 0.026115 95.026115 9.947769 " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 9, "id": "b56d1612-a68c-4da3-be37-a7245b6c1a80", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.0005, in 2 steps of 0.00025\n", "From time 0.0005 to 0.004625, in 33 steps of 0.000125\n", "From time 0.004625 to 0.006313, in 9 steps of 0.000188\n", "From time 0.006313 to 0.007438, in 4 steps of 0.000281\n", "From time 0.007438 to 0.008281, in 2 steps of 0.000422\n", "From time 0.008281 to 0.008914, in 1 step of 0.000633\n", "From time 0.008914 to 0.009863, in 1 step of 0.000949\n", "From time 0.009863 to 0.01129, in 1 step of 0.00142\n", "From time 0.01129 to 0.01342, in 1 step of 0.00214\n", "From time 0.01342 to 0.01663, in 1 step of 0.0032\n", "(55 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "markdown", "id": "962acf15-3b50-40e4-9daa-3dcca7d3291a", "metadata": {}, "source": [ "### Equilibrium" ] }, { "cell_type": "code", "execution_count": 10, "id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A + X <-> 2 B\n", "Final concentrations: [B] = 9.948 ; [A] = 0.02612 ; [X] = 95.03\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.00855\n", " Formula used: [B] / ([A][X])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.2137 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 10, "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": "53fed9be-020d-4500-a68b-1638f9159fca", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "448ec7fa-6529-438b-84ba-47888c2cd080", "metadata": { "tags": [] }, "source": [ "# Now, let's suddenly increase [A]" ] }, { "cell_type": "code", "execution_count": 11, "id": "7245be7a-c9db-45f5-b033-d6c521237a9c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.016626465:\n", "3 species:\n", " Species 0 (A). Conc: 50.0\n", " Species 1 (X). Conc: 95.02611534596562\n", " Species 2 (B). Conc: 9.947769308068802\n" ] } ], "source": [ "dynamics.set_chem_conc(species_name=\"A\", conc=50., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 12, "id": "e5ce5d59", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEAXBcaption
520.0098630.02685695.0268569.946289
530.0112870.02611095.0261109.947779
540.0134230.02620995.0262099.947582
550.0166260.02611595.0261159.947769
560.01662650.00000095.0261159.947769Set concentration of `A`
\n", "
" ], "text/plain": [ " SYSTEM TIME A X B caption\n", "52 0.009863 0.026856 95.026856 9.946289 \n", "53 0.011287 0.026110 95.026110 9.947779 \n", "54 0.013423 0.026209 95.026209 9.947582 \n", "55 0.016626 0.026115 95.026115 9.947769 \n", "56 0.016626 50.000000 95.026115 9.947769 Set concentration of `A`" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=5)" ] }, { "cell_type": "markdown", "id": "24455d58-a0ea-43fa-b6ad-95c42a8b34b2", "metadata": {}, "source": [ "### Again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 13, "id": "c06fd8d8-d550-4e35-a239-7b91bee32be9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "INFO: the tentative time step (0.0005) 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 0.00025) [Step started at t=0.016626, and will rewind there]\n", "INFO: the tentative time step (0.00025) 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 0.000125) [Step started at t=0.016626, and will rewind there]\n", "INFO: the tentative time step (0.000125) 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 6.25e-05) [Step started at t=0.016626, and will rewind there]\n", "INFO: the tentative time step (6.25e-05) 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 3.125e-05) [Step started at t=0.016626, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "78 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.0005, target_end_time=0.035,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "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=A
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'darkorange', 'green'])" ] }, { "cell_type": "markdown", "id": "44beb909-5071-47e5-9499-482cf37f9ce3", "metadata": {}, "source": [ "**A**, still the limiting reagent, is again stopping the reaction. \n", "The (transiently) high value of [A] led to a high value of [B]" ] }, { "cell_type": "code", "execution_count": 15, "id": "6de58fe9-ff1e-40dd-9ac7-83eee458f818", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 16, "id": "2783a665-fca0-44e5-8d42-af2a96eae392", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A + X <-> 2 B\n", "Final concentrations: [B] = 108.8 ; [A] = 0.5945 ; [X] = 45.62\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.00995\n", " Formula used: [B] / ([A][X])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.2488 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 16, "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": "15355aeb-f702-4d10-9d13-8365f6a76772", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f6619731-c5ea-484c-af3e-cea50d685361", "metadata": { "tags": [] }, "source": [ "# Let's again suddenly increase [A]" ] }, { "cell_type": "code", "execution_count": 17, "id": "d3618eba-a673-4ff5-85d0-08f5ea592361", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.03752232:\n", "3 species:\n", " Species 0 (A). Conc: 30.0\n", " Species 1 (X). Conc: 45.62063150861952\n", " Species 2 (B). Conc: 108.75873698276109\n" ] } ], "source": [ "dynamics.set_chem_conc(species_name=\"A\", conc=30., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 18, "id": "61eead55-fcef-41cd-b29e-f2d5ad5c6078", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEAXBcaption
1310.0305730.67329545.699410108.601180
1320.0320360.63094145.657056108.685887
1330.0342310.60223045.628346108.743309
1340.0375220.59451645.620632108.758737
1350.03752230.00000045.620632108.758737Set concentration of `A`
\n", "
" ], "text/plain": [ " SYSTEM TIME A X B caption\n", "131 0.030573 0.673295 45.699410 108.601180 \n", "132 0.032036 0.630941 45.657056 108.685887 \n", "133 0.034231 0.602230 45.628346 108.743309 \n", "134 0.037522 0.594516 45.620632 108.758737 \n", "135 0.037522 30.000000 45.620632 108.758737 Set concentration of `A`" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=5)" ] }, { "cell_type": "markdown", "id": "0974480d-ca45-46fe-addd-c8d394780fdb", "metadata": {}, "source": [ "### Yet again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 19, "id": "8fe20f9c-05c4-45a4-b485-a51005440200", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "INFO: the tentative time step (0.0005) 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 0.00025) [Step started at t=0.037522, and will rewind there]\n", "INFO: the tentative time step (0.00025) 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 0.000125) [Step started at t=0.037522, and will rewind there]\n", "41 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.0005, target_end_time=0.070,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 20, "id": "ea3bc6ce-e7c3-4ba4-873a-0104286a2fe3", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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Changes in concentrations with time" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 0.07594800183881964 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -9.121065914283196, 173.30025237138074 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'darkorange', 'green'])" ] }, { "cell_type": "markdown", "id": "4cba88b2-96af-415b-85e9-efa48f862f3c", "metadata": {}, "source": [ "`A`, again the scarce limiting reagent, stops the reaction yet again. \n", "And, again, the (transiently) high value of [A] up-regulated [B]\n", "\n", "Notes: \n", "`A` can up-regulate `B`, but it cannot bring it down. \n", "`X` will soon need to be replenished, if `A` is to continue being the limiting reagent.**" ] }, { "cell_type": "code", "execution_count": 22, "id": "9556b84d-b977-4a4b-9250-bc97634d8356", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 2\n" ] }, { "data": { "text/plain": [ "(0.0004607037505267594, 3.333333333333333)" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Look up the some of the intersections of the [A] and [B] curves\n", "dynamics.curve_intersection(\"A\", \"B\", t_start=0, t_end=0.01)" ] }, { "cell_type": "code", "execution_count": 23, "id": "f044d268-7262-4154-bb29-f02b0f702242", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 73\n" ] }, { "data": { "text/plain": [ "(0.017062701624030972, 36.64925643602293)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(\"A\", \"B\", t_start=0.0151, t_end=0.02)" ] }, { "cell_type": "markdown", "id": "af3637e5-8495-4db0-b43c-194c7bdc4f67", "metadata": {}, "source": [ "Note: the _curve_intersection()_ function currently cannot location the intersection at t=0.015 (the vertical rise in the red line); this issue will get addressed in future versions..." ] }, { "cell_type": "code", "execution_count": 24, "id": "35850ec7-e78e-4b57-976c-bc0ad6c824d5", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 25, "id": "aff608b1-5c78-4070-845a-118afe7c2108", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A + X <-> 2 B\n", "Final concentrations: [B] = 164.2 ; [A] = 2.29 ; [X] = 17.91\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.00332\n", " Formula used: [B] / ([A][X])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.08288 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 25, "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": "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 }