{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## Comparing the reaction `A <-> B` , with and without an enzyme\n", "\n", "LAST REVISED: Nov. 3, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "cbb1af2e-3564-460e-a4ae-41e4ec4f719f", "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": "087c0d08", "metadata": { "tags": [] }, "outputs": [], "source": [ "from src.modules.chemicals.chem_data import ChemData\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics" ] }, { "cell_type": "markdown", "id": "d6d3ca49-589d-49b7-8424-37c7b01bcacf", "metadata": {}, "source": [ "# 1. WITHOUT ENZYME\n", "### `A` <-> `B`" ] }, { "cell_type": "code", "execution_count": 3, "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 <-> B (kF = 1 / kR = 0.2 / delta_G = -3,989.7 / K = 5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'A'}\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = ChemData(names=[\"A\", \"B\"])\n", "\n", "# Reaction A <-> B , with 1st-order kinetics, favorable thermodynamics in the forward direction, \n", "# and a forward rate that is much slower than it would be with the enzyme - as seen in part 2, below\n", "chem_data.add_reaction(reactants=\"A\", products=\"B\",\n", " forward_rate=1., delta_G=-3989.73)\n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "markdown", "id": "0e771dda-1c0f-4fc0-ab21-049740643897", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals" ] }, { "cell_type": "code", "execution_count": 4, "id": "5563e467-a637-44fa-9ba1-d35ddd82c887", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 20.0\n", " Species 1 (B). Conc: 0.0\n", "Set of chemicals involved in reactions: {'B', 'A'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data)\n", "dynamics.set_conc(conc={\"A\": 20., \"B\": 0.},\n", " snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "651941bb-7098-4065-a598-e50c0b641ab3", "metadata": { "tags": [] }, "source": [ "### Take the initial system to equilibrium" ] }, { "cell_type": "code", "execution_count": 5, "id": "76f24d9a-a788-41d8-90a4-db87386f91aa", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.1) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.05) [Step started at t=0, and will rewind there]\n", "30 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(reaction_duration=3.0,\n", " initial_step=0.1, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 6, "id": "e58db01b-b932-4f60-91c2-a578353a3702", "metadata": {}, "outputs": [], "source": [ "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 7, "id": "4a19ad2a-fbd2-420a-b958-2daf88bcc841", "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 (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.002003206525530134, 3.5917493002755303 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['darkorange', 'green'], show_intervals=True, title_prefix=\"WITHOUT enzyme\")" ] }, { "cell_type": "markdown", "id": "ef7ed670-39dd-4e44-afec-82dbd6e6a431", "metadata": {}, "source": [ "#### Note how the time steps get automatically adjusted, as needed by the amount of change - including a complete step abort/redo at time=0" ] }, { "cell_type": "code", "execution_count": 8, "id": "550dc065-6f3a-4961-b1ea-d52e0aa0baff", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 18\n" ] }, { "data": { "text/plain": [ "(0.7406363152021436, 10.0)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(\"A\", \"B\", t_start=0, t_end=1.0)" ] }, { "cell_type": "code", "execution_count": 9, "id": "19e66cfc-8e1c-4332-b85d-2b8ced01d4b3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [B] = 16.6 ; [A] = 3.398\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.88533\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 5.00000519021548\n", "Discrepancy between the two values: 2.293 %\n", "Reaction IS in equilibrium (within 3% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=3)" ] }, { "cell_type": "code", "execution_count": null, "id": "6517c7bd-3243-4326-9c7e-0ca04da6d812", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "27401e5d-8f3e-4c27-8438-129d3e3408a2", "metadata": {}, "source": [ "# 2. WITH ENZYME `E`\n", "### `A` + `E` <-> `B` + `E`" ] }, { "cell_type": "markdown", "id": "878edb65-e2f9-46d0-b3ba-3a82c064243b", "metadata": {}, "source": [ "### Note: for the sake of the demo, we'll completely ignore the concomitant (much slower) direct reaction A <-> B\n", "This in an approximation that we'll drop in later experiments" ] }, { "cell_type": "code", "execution_count": 10, "id": "ffaef48b-e95b-4cb9-ab9f-c526a159222e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A + E <-> B + E (kF = 10 / kR = 2 / delta_G = -3,989.7 / K = 5) | Enzyme: E | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions (not counting enzymes): {'B', 'A'}\n", "Set of enzymes involved in the above reactions: {'E'}\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = ChemData(names=[\"A\", \"B\", \"E\"])\n", "\n", "# Reaction A + E <-> B + E , with 1st-order kinetics, and a forward rate that is faster than it was without the enzyme\n", "# Thermodynamically, there's no change from the reaction without the enzyme\n", "chem_data.add_reaction(reactants=[\"A\", \"E\"], products=[\"B\", \"E\"],\n", " forward_rate=10., delta_G=-3989.73)\n", "\n", "chem_data.describe_reactions() # Notice how the enzyme `E` is noted in the printout below" ] }, { "cell_type": "markdown", "id": "12a8ca3f-a25c-4902-baef-586805338279", "metadata": {}, "source": [ "### Notice how, while the ratio kF/kR is the same as it was without the enzyme (since it's dictated by the energy difference), the individual values of kF and kR now are each 10 times bigger than before" ] }, { "cell_type": "markdown", "id": "d1d0eabb-b5b1-4e15-846d-5e483a5a24a7", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals (to what they originally were)" ] }, { "cell_type": "code", "execution_count": 11, "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: 20.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (E). Conc: 30.0\n", "Set of chemicals involved in reactions (not counting enzymes): {'B', 'A'}\n", "Set of enzymes involved in reactions: {'E'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data)\n", "dynamics.set_conc(conc={\"A\": 20., \"B\": 0., \"E\": 30.},\n", " snapshot=True) # Plenty of enzyme `E`\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": 12, "id": "dde62826-d170-4b39-b027-c0d56fb21387", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "*** CAUTION: negative concentration in chemical `A` in step starting at t=0. It will be AUTOMATICALLY CORRECTED with a reduction in time step size, as follows:\n", " INFO: the tentative time step (0.1) leads to a NEGATIVE concentration of `A` from reaction A + E <-> B + E (rxn # 0): \n", " Baseline value: 20 ; delta conc: -600\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.25 (set to 0.025) [Step started at t=0, and will rewind there]\n", "\n", "*** CAUTION: negative concentration in chemical `A` in step starting at t=0. It will be AUTOMATICALLY CORRECTED with a reduction in time step size, as follows:\n", " INFO: the tentative time step (0.025) leads to a NEGATIVE concentration of `A` from reaction A + E <-> B + E (rxn # 0): \n", " Baseline value: 20 ; delta conc: -150\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.25 (set to 0.00625) [Step started at t=0, and will rewind there]\n", "\n", "*** CAUTION: negative concentration in chemical `A` in step starting at t=0. It will be AUTOMATICALLY CORRECTED with a reduction in time step size, as follows:\n", " INFO: the tentative time step (0.00625) leads to a NEGATIVE concentration of `A` from reaction A + E <-> B + E (rxn # 0): \n", " Baseline value: 20 ; delta conc: -37.5\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.25 (set to 0.0015625) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.0015625) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.000625) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.000625) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.00025) [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", "43 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=1.2, downshift=0.5, abort=0.4)\n", "dynamics.set_error_step_factor(0.25)\n", "\n", "dynamics.single_compartment_react(reaction_duration=0.1,\n", " initial_step=0.1, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "markdown", "id": "33d9466e-c41e-4e92-a8fd-3b594aa201b0", "metadata": {}, "source": [ "#### Note how the (proposed) initial step - kept the same as the previous run - is now _extravagantly large_, given the much-faster reaction dynamics. However, the variable-step engine intercepts and automatically corrects the problem!" ] }, { "cell_type": "code", "execution_count": 13, "id": "b0543cac-f3cd-453c-ae9b-c00f01e61fa8", "metadata": {}, "outputs": [], "source": [ "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 14, "id": "8cc14786-cc9f-4399-9203-290526d3a326", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -5.907847895959514e-05, 0.1059277127745541 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.6666666666666665, 31.666666666666668 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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Pdem/sM7knb5kx7b+umZ8P18ioZroXtTq/WC8+0rV94n6J76MxVziCSUr74m1utNn5gOr51QrfTNqp69BtG3fjb0HDjc60LXPCgubYcnyNY0+00B6SfRZySFIRfRpJ9Rk39TqdwTEDaJZ0Ns9mFXuvFg5mcXb5TA7CVjdEYl3gMnk9Im2Wv5CotwW44U83s29WexYvcmwwjFZm0R+1eaWygubvSj6VIo/vdiz8vhlPD9YEX2piK9MFH1WrwmiwEL/vudY3pVTcd4w+jlZzpX+CyerX76Ia6XYddEqQIu4sXptckL0JRpby9Fp1aIoVrnSbk6f/nFTK+PuP3A4VkHTyq681fNxonNeshgyO8aNwjTRMW08jyeLL2MenZVHIsUazHJDEz3Foj/vaXMqLirAodLyhl1N/VyN4sVsHTIcrHy5pp+jrA/jfXlg9e9Wj+1E13Er13Cze0Kzfm7fJy5c/CH69+0J/aOlxmMnnv+t3gcKlvGYGb8ssXNOtdLXqugLRE6fBl7sYpk9HqBt8cZ7dMDqBV5cUOIp/2QHnIzQiSfQRIDqK3NZ/SZY9oY72fPDdg9mjffHn37Z6H2Jmh/Ff/VljJPtTiYTI4kOYI3N3v2HGuaiHTzGQjfCzqzH52HCmMHo0PaEJlUp9SLS7JFP/S6L8YKQ6JtXswuh8fGzeDFs9SYjGcNkn1s5ScocA1YvnsnmleikbKWv1TayjwPqv7ixG99Wbka0bxSt3Jga1+wn0Zfo3GLVl1o7s3NDPL9ZPRebHSfxzhtWbcaLce26Z9w5iRcL4ryvVSM2GzvZNc7ITS++ZNaS7EsN/Rcjxi/LzHZoNQ762JeZj5lN47hWmIp1yZyP47WV2aWLd2+U6HydyPfGqoDi3JUKV7M1WP1SwfiFm/GLbM0XZpVNjV8KyHIQY1s9DhL524nHO7XxxOPbxvO8/thOdB5MFFuyrNJ5n2i2JrPjxxjbidZk5T5QFIMxO17M7rntnFOt9LUq+gQr0dbXj3fqD0SzRwMSPTZg9oyt2bftyW58kp0IZG94zZ53F+tMVorV7KSkXfTMDgyz3KRka7V7MBtvnPTzMgpzbe52dkCSCRL989vayVJ/I6afn5mY0/ITBUvtnT5mjxEbn7k3xqoxFlW+p89YtEc2HpPdMFt5HC7RBSWRfRU7fXardyZbvxc+NzuXafOymitjto5k5wMrvktX9U6Voi/Recp43pQREcZzS7zzhoxN/c29Nm9xzhTpDmaPlpvFinFNxvOV1TxWJ3b6tDWZ5doYb3CNbczmLcvWyrhWmZo9Pmc2H2OcaNcL/Xv6tC9H9ceg8Xov4kD8GIuEGO8xtGtbsp0L7T1xdrlavfeKd34xE/P6+x/jPUM8USnLIdm9nn6+Mj60uqOnPy+ZFX6xEofxmCa7V5Jhlc77RLP1mN3DmV0H461J2LRyHxjv/trsqbpUz6l6Qa+t1Xj8yYg+YcP3os8LN11BmYNqQRAULlwHCZAACfiFgN0vS/yyTs6TBEhAHQEZUatuVP9a8uv9MkWff2NO6cxlH7FQOjiNkQAJkAAJSBMwe3wrUZ6w9ADsQAIkkDEErOZWZgyQBAul6GMU+JqAXwPY19A5eRIgARKwQcDskS47j/TamAq7kgAJ+JxAonxmny9N+fT9es/MnT7loUCDJEACJEACJEACJEACJEACJOAdAhR93vEFZ0ICJEACJEACJEACJEACJEACyglQ9ClHSoMkQAIkQAIkQAIkQAIkQAIk4B0CFH3e8QVnQgIkQAIkQAIkQAIkQAIkQALKCVD0KUdKgyRAAiRAAiRAAiRAAiRAAiTgHQIUfd7xBWdCAiRAAiRAAiRAAiRAAiRAAsoJUPQpR0qDJEACJEACJEACJEACJEACJOAdAhR93vEFZ0ICJEACJEACJEACJEACJEACyglQ9ClHSoMkQAIkQAIkQAIkQAIkQAIk4B0CFH3e8QVnQgIkQAIkQAIkQAIkQAIkQALKCVD0KUdKgyRAAiRAAiRAAiRAAiRAAiTgHQIUfd7xBWdCAiRAAiRAAiRAAiRAAiRAAsoJUPQpR0qDJEACJEACJEACJEACJEACJOAdAhR93vEFZ0ICJEACJEACJEACJEACJEACyglQ9ClHSoMkQAIkQAIkQAIkQAIkQAIk4B0CFH3e8QVnQgIkQAIkQAIkQAIkQAIkQALKCVD0KUdKgyRAAiRAAiRAAiRAAiRAAiTgHQIUfd7xBWdCAiRAAiRAAiRAAiRAAiRAAsoJUPQpR0qDJEACJEACJEACJEACJEACJOAdAhR93vEFZ0ICJEACJEACJEACJEACJEACyglQ9ClHSoMkQAIkQAIkQAIkQAIkQAIk4B0CFH3e8QVnQgIkQAIkQAIkQAIkQAIkQALKCVD0KUdKgyRAAiRAAiRAAiRAAiRAAiTgHQIUfd7xBWdCAiRAAiRAAiRAAiRAAiRAAsoJUPQpR0qDJEACJEACJEACJEACJEACJOAdAhR93vEFZ0ICJEACJEACJEACJEACJEACyglQ9ClHSoMkQAIkQAIkQAIkQAIkQAIk4B0CFH3e8QVnQgIkQAIkQAIkQAIkQAIkQALKCVD0KUdKgyRAAiRAAiRAAiRAAiRAAiTgHQIUfd7xBWdCAiRAAiRAAiRAAiRAAiRAAsoJUPQpR0qDJEACJEACJEACJEACJEACJOAdAhR93vEFZ0ICJEACJEACJEACJEACJEACyglQ9ClHSoMkQAIkQAIkQAIkQAIkQAIk4B0CFH3e8QVnQgIkQAIkQAIkQAIkQAIkQALKCVD0KUdKgyRAAiRAAiRAAiRAAiRAAiTgHQIUfd7xBWdCAiRAAiRAAiRAAiRAAiRAAsoJUPQpR0qDJEACJEACJEACJEACJEACJOAdAhR93vEFZ0ICJEACJEACJEACJEACJEACyglQ9ClHSoMkQAIkQAIkQAIkQAIkQAIk4B0CFH3e8QVnQgIkQAIkQAIkQAIkQAIkQALKCVD0KUdKgyRAAiRAAiRAAiRAAiRAAiTgHQIUfd7xBWdCAiRAAiRAAiRAAiRAAiRAAsoJUPQpR0qDJEACJEACJEACJEACJEACJOAdAhR93vEFZ0ICJEACJEACJEACJEACJEACyglQ9ClHSoMkQAIkQAIkQAIkQAIkQAIk4B0CFH3e8QVnQgIkQAIkQAIkQAIkQAIkQALKCVD0KUdKgyRAAiRAAiRAAiRAAiRAAiTgHQIUfQp8UVpZi9KKGgWWaCJIBJrlRpCTHcHBsuogLYtrUUSgdfNclFXW4EhNvSKLNBMUAuEQ0KZlPnbtrwzKkrgOhQQK87IQDodwmPcdCqkGx9SJLfJwsPQIauqinl1Uh9b5np1bkCdG0afAu0LwCeHHHxLQE6DoYzwkIkDRx/iIR4Cij7GRiABFH+MjEQGKPsZHPAIUfQpig6JPAcQAmqDoC6BTFS6Jok8hzICZougLmEMVL4eiTzHQgJmj6AuYQxUuh6LPJsx7770Xl48eiyXvvoNQKIy6ulpUVpQjGgXyCwoQiWQhBCArOxvhcARFzYuRnZ2NLzeux9ARY/HB0kXoftoZKC8vQ5u27bFl8xcYNGQkFrz4NC4cOBSVlRVYt3olLh15JXbv3I4V7y/GyCsmYO+eXVj6zkKMvuo6HDq4HwtfW4BxE2+KrWblimWIhMP4Qe8fx36f90wJho8aHxtb/Hz84XsQm/69+pzfsPqd27dh1YfLcNnoq5sQmVvyKCbcMBXZOTlNPvt8w1rs3rUD/QcOjUty65ZNEO0uGT4mKe1P16xC6eGDOK/foKRttQZfbvwU27/9BgMGD7PcR99w4Wsv4/Qzz0Hnrt1T6q/v9Ne5j2Pk2IkoLCyCStEnw9DuIvRxZtdWqv1f/8d8nHNuH5zUqUuqJhzrp2puboi+Z2b/HlddezNyc/Mc4+Om4X/87Tn0vWAg2rbr4OY0bI+tQvTZPS/aXkQADJhdK72wrEwSfWs+XoEjVVXo8+MLvYDeF3Pwuuib/ccHMWPGDF+wDNokKfoAPFwyH0++8HqDb+c+ehd69+zR8PuC15fgngfnxH4fPqgv7p02Cfl5RwUQRR9FH0Wf+tOiKmGlfmaAqrlR9Kn3DkXfcaYUffbji6LPPkO7Fij65AlS9Mkzy5QeGS/6DhwqxVPz/o1brhsVE3Jfbd2BX82cjfumT0a3kzvgo9Ub8VDJfDz+wG1oWVwUE4ji5/Yp4yj6gNgOHnf6jp8uuNOn5tSpSlipmU1jK6rmRtGn3jsUfRR9KqOKok8lzdRsUfTJc6Pok2eWKT0yXvQZHS1E4C13PYI7poyL7fYJkdelUzuMGdY/1tQoAsXfmNOXKYeL3DpVPt4pNzJb+4GAG6LPD1w4R0DF453kGFwCmfR4Z3C96NzKvC76xMpZvdM5/yeyTNFnoCNE3fSZs1Hy4B3o0PYEzJg1B317ndEg+ow7gRR97gSuH0al6PODl9ybI0Wfe+y9PjJFn9c95O78KPrc5e/10Sn6GntIpGgtX7WhUWqW131oNj+zTSfZdVD0HSMmxNyUOx/Czt37oOX0VVZVx0TflSMGNOT4GUVf5buVqFpSJcud7UmABEiABEiABEiABEggowiEf5yD4kEFytasv3/XjLZv2zq2eSPStNwSfZqGaNemVUNKmJ1FU/TZoRenr/7xzrN6nJJ0p08UcrksdBnej76PEEKoQx0qUIEooihAASKIxEbKRnbs381DzZEdzcZGbMSI0AgsjS7F90LfQ1m0DO1C7bApugmXhi/FC/UvYHBocMzWJ9FPMCo8CjuxE8vql+HK8JXYgz14u/5tjA+PxwEcwGv1r+En4Z/ExloeXY4wwugT6hP7fW79XIwJjYmNLX5WRFfE/vuj0I8aKGzHdiyvX44rwlc0IfNE/ROYFJqEnFDT6p3ro+uxM7oTg8OD43pjc3QzNkQ34LLwZUk9tjq6Goejh9E/fPRxWis/n0U/w7fRb3Fx+GIrzZu0eTX6Ks7CWega6ppSf32nOfVzcGXoShSFimzb0huQYWh3YH2c2bWVav+/R/+Oc3EuOoc6p2rCsX5enluyRZfUl+D60PXIDeUma+rLz+fXz0e/UD+0D7X35fxVTtrueVHlXPxqy+xa6de1+HXeq6KrUBWtwvnh49XG/boWzvsogd/X/15Z9U6t0KKxAKMQSC+9uji2u/fvt5dzp+9Y8HGnz+Qo1OfxJcvpY/VOFnLRhxALuai5rKkqlqJmNo2tqJqbG4938pUNTkSEepsqHu9k9U77fmEhF/sM7VpgIRd5gl5/vFPVKxu0Hb6Z0yc3qrhvJKbt9F128Xmxmh3iR78TqLXXV+oXf9MLSc3G98/ohpl/eD7W5ezTT4kVeRTFILU3AOgr/Gs7ffoUMdHP+MaAX985KZZCZhzfOEfu9MkfC016iKBZtHQVbp44IvaZMYhYvRPge/qsBxpFn3VWiVqqElZqZkPR5wRHJ2yyeudxqhR99iOMos8+Q7sWKPrkCWaK6BMiaf6rixuq68cjpYmpG68e1vCYpRBeu/bsb8jzMz4CatQCmg1NoGmC7l+LlsP4N03kmYk+47ji6cLXFy3HhDEXx0Rfpw5tGgSscX0UffLHQpMeesdpH8q8p0/0YfVOBY4IoAkWcgmgUxUuyY2dPoXTpykHCajY6XNwejTtMgEWcnHZAR4f3uuiT+BTUb3TKKASiT5jIRe9gBL9pt8/G9Omjo/lAGo/+le0meUFJvubsKMvBmlWCDJRKAlBqJ8XRZ9HDjyKPo84wmPToOjzmEM8Nh2KPo85xEPToejzkDM8OBWKPg86xUNTouhr7AwzcaYXUPsPljYUcjS6UdsdTCbwxHu+xY++nVH06fMMtfbG8YyPforPtY0oij6PHGQUfR5xhMemQdHnMYd4bDoUfR5ziIemQ9HnIWd4cCoUfR50ioemlCmiT+bxzkQ7fUL0/WrmbNw3fXKjnT69S50WfVoRyc4d2jQ8cmp8bzhFnwcOMhZyYSHZ6CIWAAAgAElEQVQXfRgyp0/NQcmcPjUcjVZYyMUZrqqtqhB9zOmz7xXm9NlnaNcCc/rkCXpd9KWjkItI3Xr5X+/iiuEXmlbvND7eKQq83DFlXNyCMCpEX6LHO8Vnsx6bh5l3T0bL4qPV3yn65GPf8R4UfRR9FH3qDzOKPvVMhUWKPme4qrZK0aeaaGr2KPpS46ayF0WfPM1MEX2CjNkrG4y7ZmavbDAr0vj62ysa3u0nbIs223bsaaisadwtTCYEhQ19Tp9WQ0T8XbxKQjziqRVy6dvrzNgjpvpKpNqjnny8U/4YcKwHRR9FH0Wf+sOLok89U4o+Z5g6YZWizwmq8jYp+uSZqe5B0SdPNJNEn6Bj9nJ2faXOZDl92s5aolcmJBN4VnL6xFzNikdq1T+FyLz+1gcaHP7wf0/FUy++0bADycc75Y8FR3owp88RrL43ypw+37vQ0QUwp89RvL42rkL0+RoAJ5+QAHP6GCCJCHhd9Im5q6jeySiQJ8CXs8sza9KDok8BxACaoOgLoFMVLomiTyHMgJmi6AuYQxUvh6JPMdCAmaPoC5hDFS6Hok8BTIo+BRADaIKiL4BOVbgkij6FMANmiqIvYA5VvByKPsVAA2aOoi9gDlW4HIo+mzCZ08ecPn0IsXqnzQPqWHfm9KnhaLTCQi7OcFVtVYXoY/VO+15hTp99hnYtMKdPnqDXRZ+q6p3yZNiDos9mDFD0UfRR9Nk8iEy6U/SpZyosUvQ5w1W1VYo+1URTs0fRlxo3lb0o+uRpUvTJM8uUHhR9Nj1N0UfRR9Fn8yCi6FMPMI5Fir60obY1EEWfLXzKOlP0KUOZsiGKPnl0FH3yzDKlB0WfAk8zp08BxACaYE5fAJ2qcEnM6VMIM2CmVIi+gCHhcnQEmNPHcEhEwOuiT8yd1TvdiWGKPgXcKfoUQAygCYq+ADpV4ZIo+hTCDJgpir6AOVTxcij6FAMNmDmKvoA5VOFyKPoUwKToUwAxgCYo+gLoVIVLouhTCDNgpij6AuZQxcuh6FMMNGDmKPoC5lCFy6HoswmTOX3M6dOHEKt32jygjnVnIRc1HI1WmNPnDFfVVlWIPlbvtO8V5vTZZ2jXAnP65Al6XfSxeqe8T1X1oOizSZKij6KPos/mQWTSnaJPPVNhkaLPGa6qrVL0qSaamj2KvtS4qexF0SdPk6JPnpkTPT5avRHX3/oAfn3nJIwZ1t+JIaRtUvRJI2vcgaKPoo+iz+ZBRNGnHmAcixR9aUNtayCKPlv4lHWm6FOGMmVDFH3y6Cj65Jk50ePhkvkxs7v27Me90yYhPy/HiWGkbFL0SeEyb8ycPgUQA2iCOX0BdKrCJTGnTyHMgJlSIfoChoTL0RFgTh/DIREBr4s+MfegV+88cKgUM3//PH563eV48E8vYNrU8eh2cgfXA5eiT4ELKPoUQAygCYq+ADpV4ZIo+hTCDJgpir6AOVTxcij6FAMNmLmME337NwLlu9LvxVY9gIJ2puOKRzuXrliL26eMg9jx69KpnSce8aToUxAmFH0KIAbQBEVfAJ2qcEkUfQphBswURV/AHKp4ORR9ioEGzFzGib43JgHrn0q/F4fMAc66wXRcIfT6/ej76N2zB4QAfKhkPh5/4Da0LC5K/zx1I1L02cTPnD7m9OlDiNU7bR5Qx7qzkIsajkYrzOlzhqtqqypEH6t32vcKc/rsM7RrgTl98gS9LvqUV+/88DfA12/Ig7Lbo/cvga5Dm1j5ausOzHpsHmbePTkm8sSjnrfc9QjumDIuJgLd/KHos0mfoo+ij6LP5kFk0p2iTz1TYZGizxmuqq1S9Kkmmpo9ir7UuKnsRdEnTzPjRJ88Ikd7LHh9Ce55cE6TMW68eljscU83fyj6bNKn6KPoo+izeRBR9KkHGMciRV/aUNsaiKLPFj5lnSn6lKFM2RBFnzw6ij55Zqp6VFZVY8asOejb64xGOXzG3T9V48naoeiTJWbSnjl9CiAG0ARz+gLoVIVLYk6fQpgBM6VC9AUMCZejI8CcPoZDIgJeF31i7kGt3inE3a9mzsZ90yc3qtapicErRwxw9RFPij4F5w6KPgUQA2iCoi+ATlW4JIo+hTADZoqiL2AOVbwcij7FQANmjqIvYA5VuByKPgUwKfoUQAygCYq+ADpV4ZIo+hTCDJgpir6AOVTxcij6FAMNmDmKvoA5VOFyKPpswmROH3P69CHE6p02D6hj3VnIRQ1HoxXm9DnDVbVVFaKP1Tvte4U5ffYZ2rXAnD55gl4Xfcqrd8ojytgeFH02XU/RR9FH0WfzIDLpTtGnnqmwSNHnDFfVVin6VBNNzR5FX2rcVPai6JOnSdEnzyxTelD02fQ0RR9FH0WfzYOIok89wDgWKfrShtrWQBR9tvAp60zRpwxlyoYo+uTRUfTJM8uUHhR9CjzNnD4FEANogjl9AXSqwiUxp08hzICZUiH6AoaEy9ERYE4fwyERAa+LPjH3oFbv9Hpkuir6tLfUr/tscxNOZ59+Ch5/4LbY2+y9/kPR53UPuTM/ij53uPtlVIo+v3gq/fOk6Es/cz+NSNHnJ2+lf64Ufeln7pcRXRV9D5fMj3Fy+w31dp1F0WeXYDD7U/QF06+qVkXRp4pk8OxQ9AXPpypXRNGnkmbwbFH0Bc+nqlbkmugTu3zT75+NaVPHN3qBoaqFpcsOc/qY06ePNVbvVHPksZCLGo5GK8zpc4araqsqRB+rd9r3CnP67DO0a4E5ffIEvS76WL1T3qeqelD02SRJ0UfRR9Fn8yAy6U7Rp56psEjR5wxX1VYp+lQTTc0eRV9q3FT2ouiTp0nRJ88sU3q4JvoEYPF4Z5dO7TBmWH/f8qboo+ij6FN/+FL0qWdK0ecMUyesUvQ5QVXeJkWfPDPVPSj65IlS9MkzU9njo9Ubcf2tDzQyeePVwzyRyuaq6Ptq6w48v+AtTLtlPPLzclQyT6st5vSlFbdvBmNOn29c5cpEmdPnCnZfDKpC9PlioZxkSgSY05cStozp5HXRJxwR5OqdQvQ9VDK/oRilVrTyjinj0LtnD1fj0DXRl6hypyDC6p2uxgUHV0CAok8BxACboOgLsHNtLo2izybAgHen6Au4g20uj6LPJkCb3Y2ir7KqGjNmzUHfXme4/mSja6LPJlNPdedOn6fc4ZnJUPR5xhWenAhFnyfd4olJUfR5wg2enQRFn2dd44mJZZro27h3I3aV7Uo7+x4n9EC7wnZNxjXb6fNK4UqKPpthwpw+5vTpQ4jVO20eUMe6M6dPDUejFRZycYaraqsqRB+rd9r3CnP67DO0a4E5ffIEvS76VFfvnPSPSXhq9VPyoGz2mHP5HNzQ8wZT0WfM6WvftjVKHrzD9bcVuC76zBIe5z56l+vPvVqNBYo+ij6KPqtHi/V2FH3WWcm0pOiToeVeW4o+99jrR6boc98PFH3yPsg00feb936DNza9IQ/KZo9fnv9LDO0+NOlOn2hg3P2zOXTK3V0VfWYQRHGXKXc+hKnXXe76s69WqFL0UfRR9Fk5UuTaUPTJ8bLamqLPKil321H0uctfG52iz30/UPTJ+yDTRJ88IWd7mGkbr7yb3DXRpyU2XjliQJNdPQHspVcX495pk3xR1ZM5fc4eQH61zpw+v3ouPfNmTl96OPtxFBWiz4/r5pytEWBOnzVOmdrK66JP+CWTqndypw9AItUrdvtmPTYPM++ejJbFRZ4/bin6PO8iVyZI0ecKdt8MStHnG1elfaIUfWlH7qsBKfp85a60T5aiL+3IGw1olrbmlTcScKdPQWxQ9CmAGEATFH0BdKrCJVH0KYQZMFMUfQFzqOLlUPQpBhowcxR9AXOowuW4JvrEGha8vgTzX13c8AJD8Tfm9H2BQUNGYsGLT+PCgUNRWVmBdatX4tKRV2L3zu1Y8f5ijLxiAvbu2YWl7yzE6Kuuw6GD+7HwtQUYN/GmWGisXLEMkXAYP+j949jv854pwfBR41HUvDj2u1mews7t27Dqw2W4bPTVTcJrbsmjmHDDVGTn5DT57PMNzOnTQ2H1TjVnJ+b0qeFotMKcPme4qraqQvSxeqd9rzCnzz5DuxaY0ydP0OuiT3X1TnlCmdvDVdEnsLtdvVPLLfzXouUNUWCsHirE6T0Pzol9PnxQ30a5hizkQtFH0af+BErRp56psEjR5wxX1VYp+lQTTc0eRV9q3FT2ouiTp0nRJ88sU3q4LvrcBi1yC5+a92/cct2oWNEYIUKnz5zd8D4NYxWeh0vmx6Z8+5Rxsf9S9FH0UfSpP4op+tQzpehzhqkTVin6nKAqb5OiT56Z6h4UffJEKfrkmWVKj4wXfUZHCxF4y12P4I4p42JVRYXI69KpXcPrI8xKsTKnL1MOF7l1MqdPjlemtWZOX6Z53Pp6VYg+66Oxpd8IMKfPbx5L73y9LvoEjSBX70yvt+VGo+gz8BI5hb+aORv3TZ+MDm1PwIxZc9C31xkNok//ebeTO8R6U/TJBV2mtKboyxRPp7ZOir7UuGVCL4q+TPBy6muk6EudXSb0pOjLBC+ntsa0iz5tJ+2Gq4biqRffwLrPNpvO3I3yplp+nybyzN4l2ET0Ve5FdVU5juSdlJoH2CuwBLIjIUQiYVRV1wV2jVxY6gTElwLVNfWorY+mboQ94xKIRqMIhUK+JCRmXZCfhbLKWl/On5N2lkBOVhgitI/U1Ds7EK37kkBBXhaqjtSizsOXlqL8LF+y9fuk0y76NGCJ3tPnxsvZNYHXrk2rhnw9owgUczeKPpHTN67bt1h0sCdCoTDq6mpRXl4OIIpmBYXIikSAEJCdnROrqNm8uAVycnKwYf06jLriKrz79pvocfqZKCsvQ7t2HbDpy40YPmI0nnv6SVxy6WWoqCjHxx99iDFXjseO7d9iybtvY/w112L37l14a+HrmHDtJBzYvw9/f+VvuOHGKTG87y9bgnAkjL7nXRD7/ck/P4axV12D4uIWsd8/eH+pmB7OO79fQ/x+u+0bvP/eEowbP7FJTP/xd7/Fzbf8PDZv48+n69bE5nXJ0OFxj4WvNn2BT9etxeWjxyY9Xj5Z9REOHjqIiwZenLSt1kCw/Gbr1xg6bITlPvqGf1/wEr5/Tk+c0u3UlPrrO81+4o8YP+FaFBU1R3ZWGJFwSInok2FodxH6OLNrK9X+L7/0An7Yuy9O7tI1VROO9VM1t/zcLFTX1qEujVfmx/7wMCZNnoq8vDzH+Lhp+IXnn8aAiwajfYeTEEUIIXGi8+GPuKEvyMtGWWVNyrO3e15MeeAAdTS7VnpheUdFXwhHaoL/heJHH36Aqsoq9LvwIi+g98UcmgnRV12Heo9+ofjwrPsxY8YMX7AM2iQ9KfrS/XJ2M8GnOTpZTp8QfVcVv4H/i0xoEH2VFeWIRoH8ggJEIllC8yErOxvhcCT22oTs7Gx8uXE9ho4Yiw+WLkL3085AeXkZ2rRtjy2b+cqG0sMHcV6/QZaPNbulyRe+9jJOP/McdO7a3fKY8RrylQ22EcYMsJCLGo5GK6ze6QxX1VZVPN5p97yoek1+tMdCLu57jYVc5H3g9cc7+coGeZ+q6uFJ0SdekbB81YZGr0ZQtWCjHbPdPH0bK9U7x+fNw8K8mxGK5MZ2+ij6GlPeumUTxPv8Lhk+JqkbP12zChR9TTHJMEwKOUkD/fsg7dpKtT9FX6rkEvej6HOGq2qrFH2qiaZmj6IvNW4qe1H0ydOk6JNnlik90i76tJev79y9Ly7j9m1bN7wywWlHxJvPjVcPa3jMM9F7+rDgMmDLv3Cg35Oo7Nb0xeZOz5/2vUuAhVy86xsvzIyFXLzgBW/OQYXo8+bKOCsVBFjIRQXF4NrwuugT5INcvdPs/eNizb++c1JDUUi3oi/tok9baKKcPrdgpDTuh78Blt6FitMm4eCP/5iSCXYKJgGKvmD6VdWqKPpUkQyeHYq+4PlU5Yoo+lTSDJ4tij53fWr2ajd3Z3R8dNdEn1cA2J7HjveBF85HbYvTsWfUKtvmaCA4BCj6guNLJ1ZC0ecE1WDYpOgLhh+dWgVFn1Nkg2GXos9dP1L0ucvf0dFFIZfxzV7Goqr+qGvxPdTVR5nTZyAuk4/GnD7zcJVhaDfgmdOXmKCqfEM3RB9z+uweHenpr0L0sZCLfV8xp88+Q7sWmNMnT9Drok91IZf6vfWoL0//60sirSMIFTZ9LRBFX5yYTZTf58Z7+uQPLSD2yoYOa/HOrvaoL+yE2nA+RR9FHwoLi6Byp4+iL5Wj05k+FH3OcFVh9R9/ew59LxiItu06qDDnmg2KPtfQNxqYos99P1D0yfsg00Rf+T/LUb2mWh6UzR4FIwqQ07Ppq8yY02cCVl8185wzu+P5BW9h2i3jkZ+XA/GahH4/+j569+xh0yXOdxeib+yZNXj3s4OI5rZCTe4JFH0UfRR9Ng89VcLK5jRMu6uaG3f61HuHou84U+702Y8vij77DO1aoOiTJ5hpoq/qvSrUfJX6O03lCR/tkXd+HrK7ZTfpzp0+E6L6Qi7i41mPzcPMuyejZXER3Hg5e6pOF/0qPv8Xmr12GWpO6I3vLnvXjin2DRABlTt9AcLCpRwj4IboI3x/EFCx0+ePlXKWqRBgTl8q1DKnj9dFn/BE0Kt3PlQyH48/cFtM03jpx7VCLnrR16pFEWb+/nlM//mEGKB0v5zdrkPKDu1H4V9OBEJh7Jy4B9FInl2T7B8AAhR9AXCig0ug6HMQrs9NU/T53IEOT5+iz2HAPjdP0eeuA7nTZ8Lf+FJ08Uhnl07tYu+wSOfL2VWERmlFDfLm90H2vtXYO/TfqG53oQqztOFzAhR9Pnegw9On6HMYsI/NU/T52HlpmDpFXxog+3gIij53ncecPgv8xc7fLXc9gnWfbUY6X85uYWoJm4icvstHj8WyN+YhcmQfanLboLwuF9EokF9QgEgkC6K2T1Z2NsLhCIqaFyM7OxtfblyPoSPG4oOli9D9tDNQXl6GNm3bY8vmLzBoyEgsePFpXDhwKCorK7Bu9UpcOvJK6Ksq7t2zC0vfWYjRV12HQwf3Y+FrCzBu4k2xua5csQyRcBg/6P3j2O/zninB8FHjY2OLH7M8hZ3bt2HVh8tw2eimL5ifW/IoJtwwFdk5TRNWP9+wFrt37UD/gUPjcpIpQsLqneYYZRjajWlW70xMkDl9diPMuf7M6TvOljl99uOMOX32Gdq1wJw+eYJeF32qq3fKE8rcHq493hkU5JroW/rmP5FVsQ21keYoCxVT9OkcLCNYKPoo+gQBVcLKifOMqrm5sdPHVzY4ERHqbarY6aPos+8Xij77DO1aoOiTJ0jRJ88sU3q4Jvr0OX3dTvZveW1N9C1ZvAjZhzaiDtkozWpH0UfRx1c22DiLqhJWNqYQt6uquVH0qfcOd/q406cyqij6VNJMzRZFnzw3ij55ZpnSg6JPgadFTl9pZS3aLjgbkcNf4bvLlqHmhHMVWKYJPxNgTp+fvef83N0Qfc6viiOoIKBip0/FPGjDmwSY0+dNv3hlVl4XfYJTkKt3eiUOzObhmugTk/HT+/gSOVETfS2WTUGzTc/iUO8HUX7mz7zsd84tDQQo+tIA2cdDUPT52HkOT52iz2HAPjdP0edzBzo8fYo+hwH72Lyrok+8mkH/Una/ctREX7Mvn0aL925B1cmXY/9FL/h1OY7N+9CRgyivKUNFTcWx/5ajorY89u/ymnJUHPusuvYIauprUC/+V1+Humg96sX/xb9RF/t3Xb34b12sjfbvuvqj7WJtYp/Xo060Ef8W7aJ1EG2ix/4e+yxmW/z9qO3YZ/oxxWdau9jf9WMeHa+ytsIxZjRMAiRAAiRAAiRAAkEhcHvvu/HQsPuCshxfrcM10aev1mlG7OzTT/Hkiw2Nc23I6Xv3HYTqaxA6vAVl0SLUZxVmXPXO7aXb8M3hr7H18BZsPbg59t+vD21G1sEQTq3ujnmYl/Tg6Iu+aIEWeANvJG2rNeiJnuiCLvg7/m65j77hNbgGK7ESX+CLlPrrO92O2/EX/AWHcdi2Lb2BHugBsU4rDO0O3BmdMRiDMQdz7JpKuf+1uBbLsAybsTllG0519PLckq35LtyFR/EoqlCVrKkvP78JN8XOHd/iW1/OX+Wk7Z4XVc7Fr7YGYEBs6oux2K9L8P28L8AFyEMe3sJbvl8LF3CUwH/jvzFjxgzicIGAa6LPhbU6MmQj0RcKI3TwC5TVN0N9VgHyC4oC9cqGukhdTMRtO7wVWw5uwtZDW3BkeznCZcDz1c/F5asJlteyX0Oz7EIUxP5fgIKcIuRn5R/9PacAzbIKcMKBlsipzUFNFyASisT+HwqFERH/Dx/7NyKxf2uf1e06grr91Sg6+8TYqyrE38Pif8fahEPH/o0IssJZCIWA8DHb4rNN761Du26d0LpjO2E51k/8XYwZsyH+dmx80e/oZ+K/4v+h2FzyIvmx9f917uMYOXYiCguLWMjFxhGnqliKjSnE7apqbm483snqnU5EhHqbKh7vZPVO+35hIRf7DO1aYCEXeYJef7yTr2yQ96mqHq6JvkTVO8WLDV96dTHunTYJ+XlN3w2navEq7BhFH0q/RXkNUB/JQ35hC1+LvuU7lmLJN2+jaFU25uTOwY6qHU2QnYtz0REd8U/8Ey3yWuLk5qegS/HR/3cu7oouxV2RezAb323ZgUuGj0mKnK9sMEck89qLpJCTNOB7+hIDouizG2HO9Wf1zuNsKfrsxxlFn32Gdi1Q9MkTpOiTZ5YpPTwp+kSu36zH5mHm3ZPRsrjI877QcvrERAs2/AnFH05DRfef4OAFJZ6fu36CX+zfiKXfLooJvfe+fdc0V61T85NxcvOu6Ny8K7q26I6Ti7ugU/MuOKXFqSjMLvTVep2eLAu5OE3Y3/bd2OnzN7HMmb2Knb7MoZV5K2Uhl8zzucyKvS76xFpYvVPGo+raelL0LXh9CZav2uCLnT7hCr3oy977CU587XzUFZ2C3Vd8qs5TDlnaV7UXf9v4POZteAZf7P+s0SjntDkXP2x3Hn7csT96tD4DXYq7OTSLYJql6AumX1WtiqJPFcng2aHoC55PVa6Iok8lzeDZougLnk9VrSjtok/s4k258yHs3L0v7hrat22NkgfvgF9e2q4XfYjWo/3z7RCqLcOuq7ejPrelKl8ptfP21oUxofevr15psHvWCedgcJdL0afD+ejT4TzkZzVTOmamGaPoyzSPy62Xok+OVya1pujLJG/Lr5WiT55ZJvWg6Mskb8utNe2iT5teopw+uSW429qY01dXV4vKw98hFK1DfkExQrlFCAHIys6OFQUpal6M7OxsfLlxPYaOGIsPli5C99POQHl5Gdq0bY8tm7/AoCEjseDFp3HhwKGorKzAutUrcenIK6HPtdq7ZxeWvrMQo6+6DocO7sfC1xZg3MSbYjBWrlgWK2jyg94/jv0+75kSDB81HgewH39dPxdb1m1EWXVprCJZTjgXI04dgyvaXYXSTftw2eirmwCdW/IoJtwwFdk5TfMrP9+wFrt37UD/gUPjOkImH405feYYZRjaPSKY05eYIHP67EaYc/2Z03ecLXP67McZc/rsM7RrgTl98gS9LvpYyEXep6p6uCb6VC3AbTumoq/sAEK1VbHqjSjs4Lrom/Pkw1hU+A4Wf7cohkuUoW6eU4yzev0QV595PVrltcbO7duw6sNlFH02A4rVO20CPNZdlbBSM5vGVlTNzY2dPlbvdCIi1NtUsdNH0WffLxR99hnatUDRJ0+Qok+eWab0oOiz6WlT0VdRhlB1KQoiVYi26I4QQq7s9NV0BO5a/HNcuu8SzMVcHMRBDOg0GKObXYGuxd3Rq8/5Daun6DsHnbt2txkNfGWDbYAUfaoQmtqh6HMUrzLjFH3KUNoyRNFnC5+SzhR98hgp+uSZZUoPV0Vfohe0++Xl7CJQGuX0HYucti92Q6i2HHuHL0Ztix5pjafvKnbj3mW/xCtfzG8Y9+aeP8cN5/wUnYu6pHUumTwYc/oy2fvJ1+7GTl/yWbGFFwioEH1eWAfn4AwB5vQ5wzUoVr0u+gRnVu90J9pcFX0PlxwVJbdPGefO6hWNaib6ipffioKNf0bZ6T/D4R89qGik5GYWf/Mmpi68DoeOHIw1Hn3aONx13v+gY1Hn5J3ZQikBij6lOANnjKIvcC5VtiCKPmUoA2mIoi+QblW2KIo+ZSgDZ8g10ReUQi4iIsxEX86u93DCGxejPq8Ndo3fAsQy+5z9mbX8f/Doygdig/ygbW/85qI/4MwTvu/soLQelwBFH4MjEQGKPsZHPAIUfYyNRAQo+hgfiQhQ9DE+4hGg6LMZG+Y5feWIRoGi+j3Iih5BXVFXRPJbOFa9c9vur/G3V57Cb2tnxVZzW5tpuKjLxejV54LY71r1TlE5VPyY5Skwp485fdqhwOqdiU8KLORi86TpYHdW7zwOl4Vc7Acac/rsM7RrgTl98gS9LvpYvVPep6p6uCb6xALE451dOrXDmGH9Va0n7XYSib6CSCVyqveiPrcVwsUnOyL6Th3UE7/4x40YXDkQT+c8gz8NmYviXYWmr2yg6DMPj4WvvYzTz6Too+izdvqg6LPGyY1WFH0UfSrjjqJPJc3UbFH0yXOj6JNnlik9XBV94kXtzy94C9NuGY/8vKbvgPODExKJvmZ5EeSWfw2EIsCJ31cu+v7++vP438pfo7iuOa4NX4err52CDoUd476nj6KPos/KMcWdPu70WYkTL7ah6KPoUxmXFH0qaaZmi6JPnhtFnzyzTOnhmuhLVLlTwPd79U4tgNr87SxklW3Gvktew5EOA5XF1Z3v/AzPr58Tsycqc8644GguH3+8Q4A5fd7xhRdnwpw+L3rFG3NiTp83/ODVWTCnz6ue8ca8vC76BCVW73QnVlwTfe4s15lRzQq5aCMVrf5fFK2+HxWnXgSYv/kAACAASURBVI+D5z+mZAL3LPlPzFl71NZTw1/CJV2HK7FLI2oJUPSp5Rk0axR9QfOouvVQ9KljGURLFH1B9Kq6NVH0qWMZNEsUfQo8mkj0ZZVuRpuXz0J9Tgvsunrb0Uc9bfz8+r3peOKT3yErnI1nR7yC/p3U7R7amBa7mhCg6GNYJCJA0cf4iEeAoo+xkYgARR/jIxEBij7GRzwCroq+yqpqzJg1B/9atBzt27ZGyYN3oEPbE2J/69vrDF8UeEmU05dfUIBIJAtZhzcht/4w6lv0QMGJXZGdnY0vN67H0BFj8cHSReh+2hkoLy9Dm7btsWXzFxg0ZCQWvPg0Lhw4FJWVFVi3eiUuHXklHlv8W+z89GvMwRzMvXA+yjbsw+irrsOhg/ux8LUFGDfxppifV65YxkIuEsc8C7k0hsWcvsTBw0IuEgdXmpsyp+84cFbvtB98zOmzz9CuBeb0yRP0uuhj9U55n6rq4aro06p3XjqwL2Y9Pg8TxgxGt5M74KPVG/HSq4tx77RJni/wYkX0Raq+Q17VNiDvBOR36p2S6Cv4QWv88h9TMRiDcenocTgt+zQsfWchRR8Auzc3FH0UfTInVIo+GVrpbUvRR9GnMuIo+lTSTM0WRZ88N4o+eWaZ0sM10ad/ObvY3dOLPlHVc9Zj8zDz7sloWVzkaV9YEX2h+ho0O7wOkVAIud0uQVZOrtRO38pVy/Bf+6ajqKoQ1xXdgJ9e90vs3bOLou9YZFD0qT1EuNPHnT61EZU+axR9FH0qo42iTyXN1GxR9Mlzo+iTZ5YpPTwp+vy00ycCJVFOnxZIJ7w+EDl7lmP/wBdR1XmE5fiqra/BiJcGYO13n+DCzoPw/Mh/IoSQ5f5s6B4B5vS5x94PIzOnzw9ecmeOzOlzh7tfRmVOn1885c48vS76BBVW73QnNlwTfWK5C15fguWrNmD6zyfgD3NeiT3e2apFEW656xGMGzHAFzl9VkVfwWdPoHjF7ajseiUOXPi0ZW//8p2f4bn1c9CxqDPeHL8CzXOLLfdlQ3cJUPS5y9/ro1P0ed1D7s2Pos899n4YmaLPD15yb44Ufe6x9/rIroo+AUfs6l1/a+N3zM199C707tnD6+wa5mdlpy9ctQftXuyGaDgHu675FtFIftL1Lfh8Hv7jzUmxSp1vXPUeTm99VtI+bOAdAhR93vGFF2dC0edFr3hjThR93vCDV2dB0edVz3hjXhR93vCDF2fhuujzIhSZOVnK6QOQlZ2N3EOfoVXNFkRP6o/PdlQlrN751+efwO8OPoK8aC6ubXUDbrzmNuhzrZjTd9xLzOmTidjkbZnTl5gRC7kkjyG3WjCnT9150S0femlc5vS57w3m9Mn7wOuij9U75X2qqoerok9U79y1Z3+jKp3aaxyC9MoGkYEnRF/2ke9wQulHiDQ/CetKT4or+vpcdBH+9OT/4qW6lzCk43D0C/ePvbKBos887Cn6VJ0Ojtqh6KPoUxtR6bNG0UfRpzLaKPpU0kzNFkWfPDeKPnlmmdLDNdGnibsrRwxo8iinnwq5yOz0RUJRtPnu38gJVWM1zsfQEVeavqdvUd7byF8XxsfN1+C3/f6EL9ato+hLcERS9Kk9XVH0UfSpjaj0WaPoo+hTGW0UfSpppmaLok+eG0WfPLNM6eGa6NO/skG8m0//46dXNoh5W8np09bX8t1rkb/lbyg7exoO97q3SZxt3L8eg//aB1FE8erYxTi3XZ9MicXArZM5fYFzqdIFMadPKc5AGWNOX6DcqXwxzOlTjjRQBr0u+gRsVu90J+RcE31B2emTFX25O99B64XDUZ/bCruu+hoIZzV4Xgi94fP7Yc2ejzHhzEl48KI/uhMVHFUJAYo+JRgDa4SiL7Cutb0wij7bCANtgKIv0O61vTiKPtsIA2vANdEniIrHOKfPnI2SB++Attsndvmm3PkQpl53eaBe2aCPoDYvn42s0q+w/+JXUHXSkIaPnvl0NqYv/gVOzG+DpT9Zi6Kc5oENvExYGEVfJng59TVS9KXOLug9KfqC7mF766Pos8cv6L0p+oLu4dTX56roE9PWRN7O3fsaVuGnVzbI5PSFwxEUNS9Gs9INseqdV534Pv4dvQrdTzsDh8sO4uEND6BjzUm4+NJRqF5ZigsHDkVlZQXWrV7JnL4EMc6cvtRPAGY9mdOXmCerd6qNN5XWmNN3nKbd86JKv/jVFnP63Pccc/rkfeB10cfqnfI+VdXDddGnaiEq7Ihqol06tWuywyheIn/Pg3NiQwwf1LdRtdFURF9OBPhyw8eYkPcc/pUzFaecdR7e27IYr+x4CT/M7o37pvwJC158mqLPolPt3twsfO1lnH7mOejctbvFEeM3++vcxzFy7EQUFhZB5U7f1i2b8PmGtbhk+Bjbc0xmgKKPoi9ZjHj1c4o+ij6VsUnRp5JmarYo+uS5UfTJM8uUHhR9APSi7td3Tmok+sQjqA+VzMfjD9yGlsVFEMJQ/Nw+ZVzsv6mIvuzsbGza8Akm5MzBv2tHoWPvy1Gy4nfYUrcZP2k/CROv+ClFX79Blo9Bij7LqCw1pOij6LMUKB5sRNFH0acyLCn6VNJMzRZFnzw3ij55ZpnSw1XRJyp43nLXI1j32eYmvM8+/ZQGoZUuZ5jt9Bn/ZhSBYm4y1Tu1tYRqy9D2xe4I1xzGjM7X4H82/BWntvweFk/4JF3L5TgOE1C50+fwVGneBQLM6XMBuk+GZE6fTxzl0jSZ0+cSeJ8M63XRJzCyeqc7weSq6DPumrmD4PioRoFn9qJ4kYP4q5mzcd/0yQ3FZ1IRfWLUwrUPIrzqv9GlMoJ99XV4ctiLGHrKCLcxcHxFBCj6FIEMqBmKvoA6VsGyKPoUQAywCYq+ADtXwdIo+hRADKgJ10Rfovf0ucU6nujTv0DeTPQdqalHdW299LRDNWX4wxPtcHflEXyvqCM+umWLtA128C6B7EgIkUgYVdV13p0kZ+YaAfGlQHVNPWrro67NIcgDR6NRhEIhXy5RzLogPwtllbW+nD8n7SyBnKwwRGiLew/+kICRQEFeFqqO1KLOw5eWovzjryujB9NHgKJPxzqVnT6R03fF2HFY/M7bCIXCqKurRXl5OYAomhUUIisSAUJAdnYOIuEwmhe3QE5ODjasX4ehl4/A7Jf+iDVYh2vyO+BHg+/Bpi83YviI0Xju6SdxyaWXoaKiHB9/9CHGXDkeO7Z/iyXvvo3x11yL3bt34a2Fr2PCtZNwYP8+/P2Vv+GGG6fEVvP+siUIR8Loe94Fsd+f/PNjGHvVNSgubhH7/YP3l4rp4bzz+zWs/ttt3+D995Zg3PiJTaLvj7/7LW6+5eexeRt/Pl23JjavS4YOjxu1X236Ap+uW4vLR49NGtmfrPoIBw8dxEUDL07aVmsgWH6z9WsMHZbaLunfF7yE75/TE6d0O9XymPEazn7ijxg/4VoUFTVHdlYYkXBIieiTYWh3Efo4s2sr1f4vv/QCfti7L07u0jVVE471UzW3/NwsVNfWoS6NV+bH/vAwJk2eiry8PMf4uGn4heefxoCLBqN9h5MQRQghcaLz4Y+4oS/Iy0ZZZU3Ks7d7Xkx54AB1NLtWemF5R0VfCEdqgv+F4kcffoCqyir0u/AiL6D3xRyaCdFXXYd6j36h+PCs+zFjxgxfsAzaJF0TfQJkvGqZbkFOJacv1UIuX25cj7JTq7Fvww7sCa/HLZECFJ8zDl8cKsSgISNZyIWFXBodBqze6dZZoem4fGWDd3xhnAkLuRwnYrfAlXe9nL6ZsZBL+ljHG4mFXOR94PXHO/nKBnmfqurhqugTj0o+v+AtTLtlPPLzmu4iqVqkVTtmos+p6p3igvxs9Dn0r+2H77fLxqn7vkS74mysafkTir7DB3EeRR9F37l9cFKnLlYP37S1o+hLG2rpgSj6KPqkgyZBB4o+lTRTs0XRJ8+Nok+eWab0cE30JarcKeCns3qn/pUNYuz2bVuj5ME7Ggq1JHpPn2ifSiGX3638DR5cfm+sYue74z9A2/ndET6yH/sH/Q1VnYZlSvwFep0s5BJo99peHAu52EYYWAMs5BJY1ypZGAu5KMEYWCNeF30CPKt3uhN+rok+d5brzKiyoq+8pgy9nuqO0urDDRU7Cz99GM1X/hdqWp2D70Z+4MxEaTWtBCj60orbd4NR9PnOZWmbMEVf2lD7ciCKPl+6LW2TpuhLG2rfDUTRp8BlsqLv8U8exf++dzfOaH023rx6RWwGobpKtJ3/PYiKngcGPIOqzpcpmBlNuEmAos9N+t4fm6LP+z5ya4YUfW6R98e4FH3+8JNbs6Toc4u898d1XfSJnLnrb32gEam5j96F3j17eJ8egFQKufzjq5fQvaYbTuzdCdlfA91POwPl5WXoWL8R32z4AGNaLMHj+H/oP2g4KisrsG71Slw68krs3rkdK95fjJFXTMDePbuw9J2FGH3VdTh0cD8WvrYA4ybeFGO2csWyWKXQH/T+cez3ec+UYPio8ShqXhz73SxPYef2bVj14TJcNvrqJtznljyKCTdMRbZJ9c7PN6zF7l070H/g0Lj+kilC8umaVShlTl8TljIM7R44+jizayvV/qry5lIdP1E/VXNzQ/Q9M/v3uOram5GbG8zqnczpOx65LORi/+hnTp99hnYtMKdPnqDXRR8Lucj7VFUPV0WfsUiKWJQo7jLlzocw9brLMWZYf1XrdMyOrOirzKrAm9/8Gz3RE6NGT8SHy95tEH1t2rbDjqVPYFx4Nh6vvxsXjJhM0WfBc3Zvbha+9jJOP/McdO7a3cJoiZv8de7jGDl2IgoLi6Byp4+iz7ZrlBmg6FOGUrkhij6KPpVBRdGnkmZqtij65LlR9Mkzy5Qerom+yqpqzJg1B/oXn2vQhRh86dXFuHfaJE9U9UwUDLKib33pWnxV+iV6R/pg5OXX4IOli3Sirz22bvwIE/b9FCUVU9B/8GUozevKnb4kRyNFn9rTFXf6EvOk6FMbbyqtUfRR9KmMJ4o+lTRTs0XRJ8+Nok+eWab0cE30ieqd0++fjWlTxzdUydSgi92+WY/Nw8y7J6NlcZHnfWE1p6+0uhQ9/tw2tp5VN2xCu4IOpmsrXn4bCjaWoPrE87Bv6KuIRpp5ngEn2JSAyp0+8g0eATce7wwexWCuiDl9wfSrqlUxp08VyWDa8broE9RZvdOd2HNN9AVlp0+4zarom//Zs7ht0RRcespI/GXYvLgeD1cfxon/6ItI+deo7DoOBy6c6050cFRbBCj6bOELfGeKvsC7OOUFUvSljC4jOlL0ZYSbU14kRV/K6ALf0TXRJ8iK99/Nf3UxHn/gtoYdPb/l9MmIvmv+ORLvfvMWnhjyLEacekXC4Mo+8ClOeLUfQvVHcPC8P6DiezcGPhiDtkCKvqB5VO16KPrU8gySNYq+IHlT/Voo+tQzDZJFir4geVPtWlwVfWIpmVK9MxQJ4+M9H+Jw6DDGnnkNNn/+OYaOGNskp2/L5i8waMhILHjxaQw5LYTwx7/FB9XnYcj4/8C3VS1ZvdMk/pnTp/akwJy+xDyZ06c23lRaY07fcZp2z4sq/eJXW8zpc99zzOmT94HXRR+rd8r7VFUP10WfqoW4ZcdqIZcDNfvx9eHNKGxejH4nX4QvN65PKvouHDgUkVWz8PGWw7j6xCVY1+cfWP7RSr6yweBsuzc3rN7ZGChFH0WfW+dTu+NS9FH02Y0hfX+KPpU0U7NF0SfPjaJPnlmm9HBV9D1cMh+79uxvVKVTy/Xr2+uMQL2y4avDX+JwzSGcftL30aXVKZZFX1VFKTb+32P4SfYT+KrlaLxZO4yij6LP0fMTRR9Fn6MB5qBxij6KPpXhRdGnkmZqtij65LlR9Mkzy5Qerom+TCrksrNsO34491QUZhdi/eTtyApnS8VXpOwbnPjPHyFcfQiHz70XZd+fJtWfjd0hwJw+d7j7ZVTm9PnFU+mfJ3P60s/cTyMyp89P3kr/XL0u+gQRVu9Mf1yIEV0TfZn0yoY/ffwQ7n//HoztMQG/Gzw7JU/nbl+E1m+OQDSch31DXkV12/NTssNO6SNA0Zc+1n4ciaLPj15Lz5wp+tLD2a+jUPT51XPpmTdFX3o4+3EU10RfJu30XTyvLzbsXYtnR7yCgScPSTlOitY9jKJV/xXrv++Sf+FIh4tStsWOzhOg6HOesZ9HoOjzs/ecnTtFn7N8/W6dos/vHnR2/hR9zvL1s3XXRJ+AJip3Tp85GyUP3tHwgna/vbIhWSGX+lA9vjrwBcR/f9C+N4qat0B2drblnL7KygqsW70Sl468EiLXauXCpzEZ/4sd0ZPx9+z/D6Mm/gyHDu7HwtcWYNzEm2KxuHLFMkTCYfyg949jv897pgTDR41HUfPi2O9meQo7t2/Dqg+X4bLRVzeJ57klj2LCDVORnZPT5LPPN6zF7l070H/g0LjHwdYtmyDaXTJ8TNJj5dM1q1B6+CDO6zcoaVutAQu5WEZlqSFz+hJjYvVOS2HkSiPm9B3Hbve86IoDPTYoc/rcdwhz+uR94HXRx+qd8j5V1cNV0ScWoYm8nbv3Naxp7qN3oXfPHqrW6KidZKLvwJH92Fu5B8X5LdClZfeY8LIj+la8vxgTO65G6fpX8OqRkRg74hLsLuxD0fftNxgweFhKvmb1zsbYKPoo+lI6kDzQiaKPok9lGFL0qaSZmi2KPnluFH3yzDKlh+uiz++gk4m+rYc3o7q+Gl1adUNxXkslom/kFRNQteg/8dbntbi52Z/xTdefY8G27tzpo+hTcjhR9FH0KQkkF4xQ9FH0qQw7ij6VNFOzRdEnz42iT55ZpvSg6FPg6dKKGpRW1jaxtGbPxxg2/wKcmN8Gn9y4BSGEFIx23ETBxj+j+Yd3IlRfjZqWZ2P/4JdRV9BR6Rg0ljoB5vSlzi4TejKnLxO8nNoamdOXGrdM6cWcvkzxdGrr9LroE6ti9c7UfGu3F0WfXYIA4om+e9+7C3/+5Pe4/uwpuO/CRxSM1NRE9v41aPXWFYhU7EB9dnMcvHAuqjrGz69zZBI0akqAoo+BkYgARR/jIx4Bij7GRiICFH2Mj0QEKPoYH/EIUPQpiA0z0RdFFD2f7IK9ld/hlTFvoU+Ho0VVnPgJHzmAlm+PR+7upTHzZT2morTPTEQl3wfoxNwy2SZFXyZ7P/naKfqSM8rUFhR9mep5a+um6LPGKVNbUfRlqueTr5uiLzmjhC3i5fTV1tfhu9o9EE90ntqqB7KysxEOR5Tl9O3dswtL31mI0Vdd11C988YzdqBo7QN4p3ogokWdcPaQn6Km1Tms3pnExyzk0hgQc/oSBwyrd9o8aTrYnTl9x+Gyeqf9QGNOn32Gdi0wp0+eoNdFH6t3yvtUVQ+KPpsk44m+qtoqHKg/gOb5LdC2Wbu0iD7xyoa87f+HNf9+ApH6CvTPWYKKU67CE1t6Y/joCXxlQxxfU/RR9MmcBij6ZGilty1FH0Wfyoij6FNJMzVbFH3y3Cj65JllSg+KPpuejif6yqrLUIpSdCzujPysZmkTfWI5Hy97A/k738Kg8sdiq/tdxa24olcRcs4cj9rCrnxPn8HnFH0UfTKnAYo+GVrpbUvRR9GnMuIo+lTSTM0WRZ88N4o+eWaZ0oOiT4GnjTl96/euxSXz+qJlXiusu2mb8qqdVqecs/s9tHj/Z8g69HlDlyMdBqO8x2RUdR5h1QzbpUiAOX0pgsuQbszpyxBHp7BM5vSlAC2DujCnL4OcncJSvS76xJJYvTMFxyroQtGnAKJR9P1p1UO4/4N7cPUZ1+O3A4/utrn50+yrecj/Yg5ydy9rmEZdYWdUfG8yyk+bhPrclm5OL7BjU/QF1rVKFkbRpwRjII1Q9AXSrcoWRdGnDGUgDVH0BdKtShZF0acAo1H0Tfjn5Vj8zZsoufQ5XNZtjIIR1JjIKtuC/M/notlXz8de8SB+ouFcVHYdg4oeP0X1ib3VDEQrMQIUfQyERAQo+hgf8QhQ9DE2EhGg6GN8JCJA0cf4iEeAos9mbJjl9H13cDfqUY/WzdsgJzs39kr2dFTvFIVcxM/KFcsQCYfxg95HXxMx75kSDB81vlEhl8jhTRgQ+T/kb30l1mZrXRe8jVEY27sFqlv3QnW78xCNNIt9NrfkUUy4YSqyc3Ka0Pp8w1rs3rUD/QfGfzfg1i2bINpdMjy5AP50zSqUHj6I8/oNsuwZu1XqmNPXGDWrdyYOPeb0WT40096QOX3Hkds9L6bdeR4ckDl97juFOX3yPvC66GP1TnmfqupB0WeTpFH0VVSX41DpAYQQxgkt2iASyfKk6IsC6NXnfISP7EWzTc9j77rXseRAN1yfP7eBSE3rc3GkzXn4/SftMGHSf1D0WYiVv859HCPHTkRhYZHSnT4Z4WxhmgmbUPRR9NmNIbf6U/RR9KmMPYo+lTRTs0XRJ8+Nok+eWab0oOiz6Wmj6NtfsQ9HKiuRFc5Gy+atPS/6tOXv3L4NH7//f7jqrCrkbH8buTvfRaiuIvbxzPK7cUez3yInVI26wpNRW9Q1VgW0rrg71h5oiR2lWeh38ShEswtNacoIFu70mQekDEObIQ2KPoo+uzHkVn+KPoo+lbFH0aeSZmq2KPrkuVH0yTPLlB4UfQo8rc/pm/LGBLy26RXMuuhPuObMGxRYd89E7u6lyPl2EXJ3v4esw18iXLUn4WREQZjaom6oK+yK2qIuqCvuhjpNIBZ0dG8hLo3MnD6XwPtkWOb0+cRRLkyTOX0uQPfRkMzp85GzXJiq10WfQMLqnS4EBgCKPgXc9aLvzL+chINVB7Bk4mp0a3GaAuveMRGqq0TW4S2IlH2NrMObECndEvt/lvj/4S8TTrSmxRmoz23dpE00khfbIYxmFyCaVYD6rAJUdxgAhHOdW3gIiIYiACJAKHz03+Gj/xZ/i/0u/h0+9tmxdqJNw2eiXaxPCAhFEI3kN5kvRZ9zLgyCZYq+IHjRmTVQ9DnDNShWKfqC4kln1kHR5wzXIFil6FPgRU30bTn4FS547my0yGuJ9TdtV2DZXyYiZduQVf41Ioc3I3L4qBiMlG2O/Td8ZL+/FsPZkgAJkAAJkAAJkAAJKCVQes7dKBp8n1KbNGaNAEWfNU5xW+lz+g5VH8J3ZbtRHG6B/Eg+8gsKfJXTt+rDZbhs9NVN1qqqeufQwQMRqi1DqLYCoZoyhGvLEYr9vwyhmnKEa8uwemsFDpbX4qIuVQDqEYrWAfX1QPTYv1EX+zfq645+hnqs31+Abw7nY1jHb49+hjqE6o+1ix5vJ/octSPsiX8f7f+33b3Rs+ArnJq3HSEctR2zI9qK8Rr6He9zdPxjbY7lPgpwj5Tfjhvz/4Lm4cM2I6tx989re+CTmp4Ynz9PqV0zY9vqOuPNI4Mxqdkcx8eKN8Czldfi/OxlOCVrs2tz8OPcksH6Tfld+EWzR5EXEsdX8H6erLwJQ3LeQMfIt8FbnOSK1tT2xJbaLhiV93fJnmyuEXi3egBE0bMBOYsJxSUC71VfgMpoHgbnvuXSDDisagL3lv03ZsyYodos7VkgQNFnAVKiJnrRt7N8J8qPlKJ1Vmtkh3Io+o6BkylCwkIu5tEmw9BmSLOQSxKAfGWD3Qhzrj8LuRxny1c22I8zFnKxz9CuBRZykSfo9cc7+coGeZ+q6kHRZ5OkXvRtPrQJ9XX1aJPdFmGEKfoo+pCTHcHBsmqbUQZQ9NlGqMwARZ8ylMoNUfRR9KkMKoo+lTRTs0XRJ8+Nok+eWab0oOhT4GmR07ftwHcQRVxyI3nY9NO9CMeKgvAnkwmwkEsmez/52lnIJTmjTG3BQi6Z6nlr62YhF2ucMrWV10Wf8Aurd7oTnRR9CrgL0ffXdfPx0zcmol+ngZh3+WsKrNKE3wlQ9Pndg87On6LPWb5+tk7R52fvOT93ij7nGft5BIo+P3vP2blT9CngK0TfrQt/gTlrH8d/9vkv3NbnbgVWacLvBCj6/O5BZ+dP0ecsXz9bp+jzs/ecnztFn/OM/TwCRZ+fvefs3Cn6bPLVcvqe/edTqKyrQKfCk4HqekSjYE7fMbYy+Wgs5GIekDIMbYY0C7kkAcicPrsR5lx/5vQdZ8tCLvbjjDl99hnatcCcPnmCXhd9LOQi71NVPSj6bJIUom/IiOF47tW5iCKK7sWnoaqygqJPx1VGsFD0UfQJAqqElc3D27S7qrm5sdP3zOzf46prb0Zubp4TaFy3SdFH0acyCCn6VNJMzRZFnzw3ij55ZpnSg6LPpqeF6Dv5x92w8v3lyM3KQ6fCzqisKKfoo+iDysc7ZYSzzZDmTh93+uyGkGv9Kfoo+lQGH0WfSpqp2aLok+dG0SfPLFN6UPQp8PS0hdPx2+UP4Kc/uBX3nH+/Aos0EQQCKkVfEHhwDY0JuLHTRx/4gwBz+vzhJ7dmyZw+t8j7Y1yviz5BkdU73Yklij4F3M9/sh/e/3YZnhr+Ei7pOlyBRZoIAgGKviB40bk1UPQ5x9bvlin6/O5BZ+dP0ecsX79bp+jzuwedmz9Fn022tfW1yL8vH+K/n0/Zg8LsQpsW2T0oBCj6guJJZ9ZB0ecM1yBYpegLghedWwNFn3Nsg2CZoi8IXnRmDRR9NrmKnL55mIdLI8PQtUU31NXVMqfPwFQmH42FXMwDUoahzZBmTl8SgCzkYjfCnOvPnL7jbFm9036cMafPPkO7FpjTJ0/Q66KP1TvlfaqqB0WfBZILXl+Cex6cE2s5fFBf3DttEvLzcmK/a6JvTO4VaFfYgaLPhKeMYKHoo+gTBFQJKwuHt3QTVXNzY6eP1Tul3e1KBxU7fRR99l1H0WefoV0LFH3yBCn65JllSg+KviSe/mj1RjxUMh+PP3AbWhYX4eGS+bEet08Z10j0TSj4CYrzWlD0UfRh5NiJKCwsYvVOG2dRVcLKxhTireH5TQAAEihJREFUdlU1N4o+9d7hTt9xphR99uOLos8+Q7sWKPrkCVL0yTPLlB4UfUk8LURel07tMGZY/1hLowhs9ZtWOFB1ACuv/xLtC0/KlLjhOi0QYE6fBUgZ3MQN0ZfBuH21dBU7fb5aMCcrRYA5fVK4Mq6x10WfcAird7oTlhR9CbhXVlVjxqw56NvrjAbR99XWHfjVzNm4b/pkdDu5A0L3htCpeWcsv3ajOx7kqJ4lQNHnWdd4YmIUfZ5wgycnQdHnSbd4ZlIUfZ5xhScnQtHnSbd4YlIUfRZE35UjBqB3zx6xlmaib+L3J+LZ0c96wqGcBAmQAAmQAAmQAAmQAAmQAAnoCVD0WRB9iXb6RCGXwSMHY80HaxAKhVBXV4eysrKY1YKCAmRlZcX+nZOTg0gkghYtWsT+vWbNGkyYMAFvvPEGzj77bJSWluKkk07CZ599hrFjx6KkpASXX345ysvL8cEHH2DixInYtm0b3nzzTUyaNAk7d+7Eq6++iptvvhn79u3DCy+8gJ/97Gexsd55553YWP37H30k9Xe/+x2uu+662Nji591330U0GsWAAQMaVr9169ZYv+uvv74JkZkzZ+KOO+6Izdv488knn8TmNXLkyLgkP//8c4h248ePT3r0rVixAgcOHMDQoUOTttUaCJZbtmzBqFGjLPfRNxTsevXqhdNOOy2l/vpOjzzyCG688UY0b97cti29ARmGdgfWx5ldW6n2f/bZZ3H++efjlFNOSdWEY/28PLdki/7Nb36DX/ziF8jLy0vW1JefP/nkkxgyZAg6duzoy/mrnLTd86LKufjVltm10q9r8eu833vvPVRWVmLw4MF+XQLnbSAg7ptnzJhBLi4QoOhLAj1ZTp8I3stHj8WSd99BKBRmIRcTnqzeWW370JZhaHew3Tu3Y8X7izHyigl2TaXcX1WxlJQnkKCjqrm58Xgnq3c6ERHqbap4vJOFXOz7hYVc7DO0a4GFXOQJev3xTr6yQd6nqnpQ9CUhaaV6J0XfDvQfGH9nTkaw8JUN5gEpw9DuyYGiLzFBij67EeZcf1bvPM6Wos9+nFH02Wdo1wJFnzxBij55ZpnSg6LPgqcTvadPdC+tqEFpZa0FS2ySSQRYyCWTvC2/Vjd2+uRnyR5uEFCx0+fGvDlmegiwkEt6OPt1FK+LPsGV1TvdiS6KPgXcKfoUQAygCYq+ADpV4ZIo+hTCDJgpir6AOVTxcij6FAMNmDmKvoA5VOFyKPoUwKToUwAxgCYo+gLoVIVLouhTCDNgpij6AuZQxcuh6FMMNGDmKPoC5lCFy6HoswmThVzWYvcu5vRpYfTXuY9j5NiJKCwsgkrRx5w+mweqwu7M6VMIU7Ep5vQdB8qcPvvBxZw++wztWmBOnzxBr4s+FnKR96mqHhR9NklS9FH06UOIos/mAXWsuyphpWY2ja2ompsbO32s3ulERKi3qWKnj6LPvl8o+uwztGuBok+eIEWfPLNM6UHRZ9PTMdE35kosWfw2X9kQh6XMLhWrd5pDlGFoM6TB6p2JCVL02Y0w5/pzp487fSqji6JPJc3UbFH0yXOj6JNnlik9KPoyxdNcJwmQAAmQAAmQAAmQAAmQQEYSoOjLSLdz0SRAAiRAAiRAAiRAAiRAAplCgKIvUzzNdZIACZAACZAACZAACZAACWQkAYq+jHQ7F00CJEACJEACJEACJEACJJApBCj6UvT0gUOluOWuR7Dus80xC3MfvQu9e/ZI0Rq7+YXAR6s34vpbH4hN9+zTT8HjD9yGlsVFcaefqL3+M2Fg+KC+uHfaJOTn5fgFB+dpILDg9SW458E5sb9a8aeV9pVV1Zgx66hNxod/Q072mmGl/cMl8/HkC6/HoNx49TDcPmWcfwFl+MxVXluMscPYCFZwadeEfy1aHlvYr++chDHD+iddpLjefL1tF88TSUkFtwFFXwq+1Q64vr3OiB1oX23dgV/NnI37pk9Gt5M7pGCRXfxAwOhncQJdvmpD3BvxZO1F/04d2sS+LNBiql2bVjwh+yEYTOYobtoeKpnf8EWAuCEXP/FuxK2011/crYhIn6IL/LRlrxlW2ieLr8BDDdACk10rjEtN1F60FV8SafcnxlgKELaMXYr+2NcE/h1TxsXdeNB/ocAvADI2bGILp+hLwf/ihDvrsXmYeffk2C4PT6opQPRhF+O3ZMnEfirtE4lIHyLLqCmLC3GXTu0avnE1ijojDCvttTaiL2PDv+Eke81I1l7E1kuvLubOr39DotHMU7lW6Hds9NeiVi2KYk8h6UUAvyAISKAAECJv+v2zMW3q+IZNBqv+5U5fcOIg1ZVQ9KVAzuxmzupBl8Jw7OIRAkYfJ/uGzW57jyyb07BAwOyLn0RfClhpr4+fZLvKFqbIJi4SkL1mJGuvfyxYWxZTDFx0sM2h7V4rjNciLT5ETHTvelITkWBzuuzuIgGz64rV6wNFn4uO88jQFH0pOMLsW1aKvhRA+qyLcWfGiujT7/wkap9sV8hnqDJuupqIu3LEgIZHbKyIvnjt16zf1Cj3wupFPePA+2TBsteMZO3Ndomnz5yNkgfvYIqBT2JCP03V1xbt3CPGWLdxC/M9fRgT8aZsfApAtLN6faDoC1AgpLgUir4UwCX7FjYFk+ziAwKqv43VliziiTdsPgiABFO0snOn756s/T/eWNZQoEPfj3l9/owT2WtGsvZGkcAUA3/GhTZrldcW484e88X9HRvG2XOnL1j+TPdqKPpSIJ4s3yIFk+ziAwIq8y60gj8UfD5wvMUpWsnRS/TtfqLdXqvf5FqcKpulmYDsNSNZe+O5yGynOc1L5HA2CKi8tohp6GsOiN95/rDhHI91ZU6fxxzis+lQ9KXgMCuV1VIwyy4eJ5Cswpr4fMqdD2Hm9MmxR/yStecjnR53uOT0klXjFKJw1579DcU3krXXD8+bNklneKx5smuG9uj3uBEDYoWAkrU3nmt4LvGYwyWnk+xaIY7/+a8ubqgMnKh91ZEjsUIuxlhiZWhJp3i4eaLqncZzifE6wlc2eNixaZgaRV+KkK28QylF0+zmYQKJ3qVkvBETy0jUXv+OLW3J7du2Zl6Oh/2fbGqJ3rtnFH3aN/BW3utH0ZeMvPc/T3TNMLtRS3aN0Z9beN7wvv+TzTDRtcIo+pJdW7Rr0c7d+2LDskx/Mvr++jzRe/rMziXGdwKL1bLwk798rmq2FH2qSNIOCZAACZAACZAACZDA/9/e3YRqUUZxAH9W0ZdYFmaCFUlkgWVFJn2IFVLYFwhZ0SYMs1plomgRIRFXFK2VJZLlKjMIQrKVIUEgRWRF5kKzsMyErNAyWsUzNJd753690jzX8+rvXel755458ztzF3/mmRkCBAgEFBD6Ag5FSwQIECBAgAABAgQIEGhLQOhrS1IdAgQIECBAgAABAgQIBBQQ+gIORUsECBAgQIAAAQIECBBoS0Doa0tSHQIECBAgQIAAAQIECAQUEPoCDkVLBAgQIECAAAECBAgQaEtA6GtLUh0CBAgQIECAAAECBAgEFBD6Ag5FSwQIECBAgAABAgQIEGhLQOhrS1IdAgQIECBAgAABAgQIBBQQ+gIORUsECBAgQIAAAQIECBBoS0Doa0tSHQIECBAgQIAAAQIECAQUEPoCDkVLBAgQIECAAAECBAgQaEtA6GtLUh0CBAgQIECAAAECBAgEFBD6Ag5FSwQIECBAgAABAgQIEGhLQOhrS1IdAgQIECBAgAABAgQIBBQQ+gIORUsECBAgQIAAAQIECBBoS0Doa0tSHQIECBAgQIAAAQIECAQUEPoCDkVLBAgQIECAAAECBAgQaEtA6GtLUh0CBAicggLvbfs4vbBqY78jm3rV5em1lYvS3v0/pceeWZneenVZunHalH7brF2/JX26a0+13fljx6Th6hz5/WhauHRN+vmXX4cUfGnp/DRp4vhqf4N96h4+27Wn2uaeO2ekFUvmp7POPKN38+F+ljf67Y+j6allr6Svv/1uyD4ef2ROumzShH4mube5c2amfT8crI7jwnFje4+7LjTYz+p+hjueU/CUckgECBAgcBIEhL6TgG6XBAgQ6AaBZnCre87f33bTNVXQy2Fuy9Yd/UJODjjP92xILy9fkCZfOjF1UqevR6658/Pdg4a25T0b0vpVi6u6g33qIHXxRRf02+743/+kF1dvTB9s3zloIByq1pr1WwYEuLxt3k+zlzrY5fDaDMLZ4I23t6U6MOcgPFiNbjgv9EiAAAEC3Scg9HXfzHRMgACB4gL1Va95982qrmIN9anD1ITx49KzC+el+v8zbri6+r1O67QZ+nJQu+OW69KxP49XPdUh7d2tO9K5556djh37a0CgbCv05bB77+yb01e79/XuI4fB1es2p+unXpE++uSL3hAp9BU/je2AAAECBP4TEPqcCgQIECAwQKAZ5oYjqq9w9SxfkA4cPNzvyt+J1Kn38X+v9OXQt3jhvLTm9Xf6XW3MyzK/P3AoHTp8pGjoW/zkQ6nuob4amveb99/3qqjQ5w+PAAECBEZLQOgbLWn7IUCAQJcJNO8567s0sXko9fLF/H1zaeOJ1Mm/P1zo6+SevnpJ5pubP6zafODuW6srbT3PLUj5u9KhLy9r/fKbvdUS1UVPPJhWrN2Uljz9cPVdM/SNdDxddspolwABAgSCCgh9QQejLQIECEQR6Hs/XO6peb9c/q5exjl92pTeJZXN/jupM1Lo6+Sevjr05QfE5OWW+TPv/tur5aY5nI5G6Bt33pjqoTBjx5yTrpw8qTJp3v/oSl+UM1wfBAgQOPUFhL5Tf8aOkAABAq0JDLVcs3kv30g7HG7ZZxvLO+unhjYfIjNaoS8/aCYfx7pN7/c+UEboG+ms8HMCBAgQKCUg9JWSVZcAAQJdLJCv3OVXF8ycce2Ao8jBKX/qh6Tkfw8V+k60Tq7VZujL9xvu3f9jumvW9Krn0Qx9+di3bd+ZHp07u9q30NfFfxBaJ0CAQJcLCH1dPkDtEyBAoIRAvVzzkonj+z30pL4/r3nf3nChLy9z7LRO26GvaTOaoa+5b6GvxJmqJgECBAh0IiD0daJkGwIECJyGAoO9rHyw+/kyzXDLO0+kzkihb6QHn+RQOtS79XLtNkJf80XzfV/O3vf9hJ2EvpGO5zQ87RwyAQIECBQQEPoKoCpJgAABAgQIECBAgACBKAJCX5RJ6IMAAQIECBAgQIAAAQIFBIS+AqhKEiBAgAABAgQIECBAIIqA0BdlEvogQIAAAQIECBAgQIBAAQGhrwCqkgQIECBAgAABAgQIEIgiIPRFmYQ+CBAgQIAAAQIECBAgUEBA6CuAqiQBAgQIECBAgAABAgSiCAh9USahDwIECBAgQIAAAQIECBQQEPoKoCpJgAABAgQIECBAgACBKAJCX5RJ6IMAAQIECBAgQIAAAQIFBIS+AqhKEiBAgAABAgQIECBAIIqA0BdlEvogQIAAAQIECBAgQIBAAQGhrwCqkgQIECBAgAABAgQIEIgiIPRFmYQ+CBAgQIAAAQIECBAgUEBA6CuAqiQBAgQIECBAgAABAgSiCAh9USahDwIECBAgQIAAAQIECBQQEPoKoCpJgAABAgQIECBAgACBKAJCX5RJ6IMAAQIECBAgQIAAAQIFBIS+AqhKEiBAgAABAgQIECBAIIqA0BdlEvogQIAAAQIECBAgQIBAAQGhrwCqkgQIECBAgAABAgQIEIgiIPRFmYQ+CBAgQIAAAQIECBAgUEBA6CuAqiQBAgQIECBAgAABAgSiCAh9USahDwIECBAgQIAAAQIECBQQEPoKoCpJgAABAgQIECBAgACBKAJCX5RJ6IMAAQIECBAgQIAAAQIFBIS+AqhKEiBAgAABAgQIECBAIIqA0BdlEvogQIAAAQIECBAgQIBAAQGhrwCqkgQIECBAgAABAgQIEIgiIPRFmYQ+CBAgQIAAAQIECBAgUEBA6CuAqiQBAgQIECBAgAABAgSiCAh9USahDwIECBAgQIAAAQIECBQQEPoKoCpJgAABAgQIECBAgACBKAJCX5RJ6IMAAQIECBAgQIAAAQIFBIS+AqhKEiBAgAABAgQIECBAIIqA0BdlEvogQIAAAQIECBAgQIBAAQGhrwCqkgQIECBAgAABAgQIEIgiIPRFmYQ+CBAgQIAAAQIECBAgUEBA6CuAqiQBAgQIECBAgAABAgSiCPwLAlcBwANdsiQAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"WITH enzyme\")" ] }, { "cell_type": "code", "execution_count": 15, "id": "2cf77dd1-040e-4e3a-9867-678479a3dda6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 16\n" ] }, { "data": { "text/plain": [ "(0.0024674107137523833, 10.000000000000002)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(\"A\", \"B\", t_start=0, t_end=0.02)" ] }, { "cell_type": "code", "execution_count": 16, "id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A + E <-> B + E\n", "Final concentrations: [B] = 16.67 ; [E] = 30 ; [A] = 3.334 ; [E] = 30\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.99958\n", " Formula used: ([B][E]) / ([A][E])\n", "2. Ratio of forward/reverse reaction rates: 5.00000519021548\n", "Discrepancy between the two values: 0.008546 %\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": "markdown", "id": "97efd24d-c771-4354-a924-eb21bc3d070c", "metadata": {}, "source": [ "## Thanks to the (abundant) enzyme, the reaction reaches equilibrium roughtly around t=0.02, far sooner than the roughly t=3.5 without enzyme\n", "The concentrations of `A` and `B` now become equal (cross-over) at t=0.00246 , rather than t=0.740" ] }, { "cell_type": "code", "execution_count": 17, "id": "47c6d97b-a778-47c1-9cad-e75433a32f66", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABEcaption
00.00000020.0000000.00000030.0Initial state
10.00025018.5000001.50000030.0
20.00037517.8175002.18250030.0
30.00050017.1657122.83428830.0
40.00062516.5432553.45674530.0
50.00075015.9488094.05119130.0
60.00087515.3811124.61888830.0
70.00100014.8389625.16103830.0
80.00112514.3212095.67879130.0
90.00125013.8267556.17324530.0
100.00137513.3545516.64544930.0
110.00152512.8134057.18659530.0
120.00167512.3014817.69851930.0
130.00185511.7203458.27965530.0
140.00207111.0681718.93182930.0
150.00233010.3464179.65358330.0
160.0025899.69201210.30798830.0
170.0029008.98000311.01999730.0
180.0032748.22126411.77873630.0
190.0036477.56447612.43552430.0
200.0040956.88223313.11776730.0
210.0045436.30999713.69000330.0
220.0049915.83003014.16997030.0
230.0055285.34693914.65306130.0
240.0060664.95732215.04267830.0
250.0067114.58024815.41975230.0
260.0074854.23282115.76717930.0
270.0084133.93207316.06792730.0
280.0095283.69184316.30815730.0
290.0108653.51923016.48077030.0
300.0124703.41182416.58817630.0
310.0143963.35740316.64259730.0
320.0167073.33737516.66262530.0
330.0194803.33333716.66666330.0
340.0228083.33332916.66667130.0
350.0268023.33333116.66666930.0
360.0315943.33333016.66667030.0
370.0373453.33333116.66666930.0
380.0442453.33333016.66667030.0
390.0525263.33333216.66666830.0
400.0624633.33332716.66667330.0
410.0743883.33334116.66665930.0
420.0886973.33328516.66671530.0
430.1058693.33356816.66643230.0
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" ], "text/plain": [ " SYSTEM TIME A B E caption\n", "0 0.000000 20.000000 0.000000 30.0 Initial state\n", "1 0.000250 18.500000 1.500000 30.0 \n", "2 0.000375 17.817500 2.182500 30.0 \n", "3 0.000500 17.165712 2.834288 30.0 \n", "4 0.000625 16.543255 3.456745 30.0 \n", "5 0.000750 15.948809 4.051191 30.0 \n", "6 0.000875 15.381112 4.618888 30.0 \n", "7 0.001000 14.838962 5.161038 30.0 \n", "8 0.001125 14.321209 5.678791 30.0 \n", "9 0.001250 13.826755 6.173245 30.0 \n", "10 0.001375 13.354551 6.645449 30.0 \n", "11 0.001525 12.813405 7.186595 30.0 \n", "12 0.001675 12.301481 7.698519 30.0 \n", "13 0.001855 11.720345 8.279655 30.0 \n", "14 0.002071 11.068171 8.931829 30.0 \n", "15 0.002330 10.346417 9.653583 30.0 \n", "16 0.002589 9.692012 10.307988 30.0 \n", "17 0.002900 8.980003 11.019997 30.0 \n", "18 0.003274 8.221264 11.778736 30.0 \n", "19 0.003647 7.564476 12.435524 30.0 \n", "20 0.004095 6.882233 13.117767 30.0 \n", "21 0.004543 6.309997 13.690003 30.0 \n", "22 0.004991 5.830030 14.169970 30.0 \n", "23 0.005528 5.346939 14.653061 30.0 \n", "24 0.006066 4.957322 15.042678 30.0 \n", "25 0.006711 4.580248 15.419752 30.0 \n", "26 0.007485 4.232821 15.767179 30.0 \n", "27 0.008413 3.932073 16.067927 30.0 \n", "28 0.009528 3.691843 16.308157 30.0 \n", "29 0.010865 3.519230 16.480770 30.0 \n", "30 0.012470 3.411824 16.588176 30.0 \n", "31 0.014396 3.357403 16.642597 30.0 \n", "32 0.016707 3.337375 16.662625 30.0 \n", "33 0.019480 3.333337 16.666663 30.0 \n", "34 0.022808 3.333329 16.666671 30.0 \n", "35 0.026802 3.333331 16.666669 30.0 \n", "36 0.031594 3.333330 16.666670 30.0 \n", "37 0.037345 3.333331 16.666669 30.0 \n", "38 0.044245 3.333330 16.666670 30.0 \n", "39 0.052526 3.333332 16.666668 30.0 \n", "40 0.062463 3.333327 16.666673 30.0 \n", "41 0.074388 3.333341 16.666659 30.0 \n", "42 0.088697 3.333285 16.666715 30.0 \n", "43 0.105869 3.333568 16.666432 30.0 " ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": null, "id": "5e6c18d4", "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 }