{
"cells": [
{
"cell_type": "markdown",
"id": "5cbc8640",
"metadata": {},
"source": [
"## Comparison of: \n",
"(1) adaptive variable time steps \n",
"(2) fixed time steps \n",
"(3) exact solution \n",
"### for the elementary reaction `A <-> B`,\n",
"taken to equilibrium.\n",
"\n",
"This is a continuation of the experiments `react_2_a` (fixed time steps) and `react_2_b` (adaptive variable time steps)\n",
"\n",
"**Background**: please see experiments `react_2_a` and `react_2_b` "
]
},
{
"cell_type": "markdown",
"id": "44b03c7b-74d0-4776-8405-695ebd19d248",
"metadata": {},
"source": [
"### TAGS : \"numerical\", \"uniform compartment\""
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "060cf75d-57c8-4bb3-b6e0-39e0601b0443",
"metadata": {},
"outputs": [],
"source": [
"LAST_REVISED = \"Jan. 3, 2026\"\n",
"LIFE123_VERSION = \"1.0.0rc7\" # Library version this experiment is based on"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "bfc75f60-dd56-413b-a1e0-77e69953f0ed",
"metadata": {},
"outputs": [],
"source": [
"#import set_path # Using MyBinder? Uncomment this before running the next cell!"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "a29db1c7",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"#import sys\n",
"#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n",
"# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path \n",
"\n",
"from life123 import check_version, ChemData, UniformCompartment\n",
"\n",
"import numpy as np\n",
"import plotly.graph_objects as go\n",
"from life123 import ReactionKinetics, ReactionRegistry, PlotlyHelper"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "46794745-9412-473e-90f4-9cea7fe42bb5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"OK\n"
]
}
],
"source": [
"check_version(LIFE123_VERSION)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a7316c65-0489-404e-96ce-b045feff89bc",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "1bc60f3e-6552-43d4-aef2-a33d95811016",
"metadata": {},
"source": [
"## Common set up for the chemicals and the reaction (used by all the simulations)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "04be6f77-eb76-4c4c-a2f9-7c80ca9bd8f0",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"add_reaction(): detected reaction type `ReactionUnimolecular`\n",
"Number of reactions: 1\n",
"0: A <-> B Elementary Unimolecular reaction (kF = 3 / kR = 2 / K = 1.5)\n",
"Chemicals involved in the above reactions: ['A', 'B']\n"
]
}
],
"source": [
"# Set up the reactions and their chemicals (common for all the simulations below)\n",
"rxns = ReactionRegistry()\n",
"\n",
"rxns.add_reaction(reactants=\"A\", products=\"B\", kF=3., kR=2.) # ELementary reaction A <-> B\n",
"\n",
"rxns.describe_reactions()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b496f370-290f-4f3a-8ce4-3b0f3132e43c",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "23e12ad6-03b1-4856-bc39-92130e6f1b2f",
"metadata": {},
"source": [
"# PART 1 - VARIABLE TIME STEPS\n",
"We'll do this part first, because the number of steps taken is unpredictable; \n",
"we'll note that number, and in Part 2 we'll do exactly that same number of fixed steps"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "d3751799-542c-4d18-a4dd-36e42b63b138",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"2 species:\n",
" Species 0 (A). Conc: 10.0\n",
" Species 1 (B). Conc: 50.0\n",
"Chemicals involved in reactions: ['B', 'A']\n"
]
}
],
"source": [
"dynamics_variable = UniformCompartment(reactions=rxns, preset=\"mid\")\n",
"\n",
"# Initial concentrations of all the chemicals\n",
"dynamics_variable.set_conc({\"A\": 10., \"B\": 50.})\n",
"\n",
"dynamics_variable.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "9fd83080-a135-4f3d-bbf3-a1a9e815a915",
"metadata": {
"tags": []
},
"source": [
"### Run the reaction (VARIABLE adaptive time steps)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "cab9218d-0227-4d47-b128-0394c56f92c0",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"19 total variable step(s) taken in 0.042 sec\n",
"Number of step re-do's because of elective soft aborts: 2\n",
"Norm usage: {'norm_A': 17, 'norm_B': 15, 'norm_C': 15, 'norm_D': 15}\n",
"System Time is now: 1.2268\n"
]
}
],
"source": [
"dynamics_variable.single_compartment_react(initial_step=0.1, target_end_time=1.2,\n",
" variable_steps=True)\n",
"# Specifying variable_steps=True for emphasis; it's the default"
]
},
{
"cell_type": "markdown",
"id": "01dd1821-e725-48d7-b5fc-b76b3b95edd8",
"metadata": {},
"source": [
"#### The flag _variable_steps_ automatically adjusts up or down the time steps\n",
"In part 2, we'll remember that it took **19 steps**"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "08985297-d0a5-4351-aef2-354ce804cde6",
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics_variable.plot_history(colors=['darkturquoise', 'green'], show_intervals=True)"
]
},
{
"cell_type": "markdown",
"id": "017a76cd-9f36-4e8c-a98e-e32e659f45cf",
"metadata": {
"tags": []
},
"source": [
"#### Notice how the reaction proceeds in smaller steps in the early times, when [A] and [B] are changing much more rapidly\n",
"That resulted from passing the flag _variable_steps=True_ to `single_compartment_react()`"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d213e19d-4910-4f11-88c3-64b7d997e493",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "123ed7bd-cb03-4f5d-88b3-bfa5bc316274",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "10c710ac",
"metadata": {},
"source": [
"# PART 2 - FIXED TIME STEPS"
]
},
{
"cell_type": "markdown",
"id": "e0529a0c",
"metadata": {},
"source": [
"#### This is a re-do of the above simulation, but with a fixed time step\n",
"The fixed time step is chosen to attain the same total number of data points (i.e. 19) as obtained with the variable time steps of part 1"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "f9736433",
"metadata": {},
"outputs": [],
"source": [
"dynamics_fixed = UniformCompartment(reactions=rxns) # Re-use the chemicals and reactions of part 1"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "9fc3948d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"2 species:\n",
" Species 0 (A). Conc: 10.0\n",
" Species 1 (B). Conc: 50.0\n",
"Chemicals involved in reactions: ['B', 'A']\n"
]
}
],
"source": [
"# Initial concentrations of all the chemicals\n",
"dynamics_fixed.set_conc({\"A\": 10., \"B\": 50.})\n",
"\n",
"dynamics_fixed.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "6bb5d54d-e085-4467-856e-b7db5fe20d00",
"metadata": {},
"source": [
"### Run the reaction (FIXED time steps)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "635630b3-93a2-40c5-bb4b-b7e0b153a450",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"19 total fixed step(s) taken in 0.037 sec\n"
]
}
],
"source": [
"# Matching the total number of steps to the earlier, variable-step simulation\n",
"dynamics_fixed.single_compartment_react(n_steps=19, target_end_time=1.2,\n",
" variable_steps=False)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "7d2144b8-7331-441a-9122-918725791627",
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\n",
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" 45.578947 | \n",
" 1 | \n",
" 1st reaction step | \n",
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" | 2 | \n",
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" 42.554017 | \n",
" 2 | \n",
" | \n",
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\n",
" \n",
" | 3 | \n",
" 0.189474 | \n",
" 19.515673 | \n",
" 40.484327 | \n",
" 3 | \n",
" | \n",
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\n",
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" | 4 | \n",
" 0.252632 | \n",
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" | \n",
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" | \n",
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\n",
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" | 6 | \n",
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" 6 | \n",
" | \n",
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\n",
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" | 7 | \n",
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" 7 | \n",
" | \n",
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\n",
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" | 8 | \n",
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" | \n",
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" 16 | \n",
" | \n",
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" 17 | \n",
" | \n",
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\n",
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" 18 | \n",
" | \n",
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" 1.200000 | \n",
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" last reaction step | \n",
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" SYSTEM TIME A B step caption\n",
"0 0.000000 10.000000 50.000000 Set concentration\n",
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"2 0.126316 17.445983 42.554017 2 \n",
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"source": [
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics_fixed.plot_history(colors=['darkturquoise', 'green'], show_intervals=True)"
]
},
{
"cell_type": "markdown",
"id": "3396051b-ecff-4a08-8c71-7c96f7429da3",
"metadata": {},
"source": [
"Notice how grid points are being \"wasted\" on the tail part of the simulation, where little is happening - grid points that would be best used in the early part, as was done by the variable-step simulation of Part 1"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8f453c61-296d-4627-8d4f-85c531eb4abc",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "73229033-14a0-41cd-84fb-5d688efc2e9d",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "f2d90ba4-b243-4dc0-8c83-d6e73c9cd6eb",
"metadata": {},
"source": [
"# PART 3 - EXACT Solution (same fixed steps as in Part 2)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "e5d2e1fe-52df-4294-ba6f-5b865efc62bf",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"dynamics_exact = UniformCompartment(reactions=rxns, exact=True) \n",
"# Re-use the chemicals and reactions of part 1 . Note the `exact` flag"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "e5908f54-39b9-4c17-adcf-510e2b738d04",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"2 species:\n",
" Species 0 (A). Conc: 10.0\n",
" Species 1 (B). Conc: 50.0\n",
"Chemicals involved in reactions: ['B', 'A']\n"
]
}
],
"source": [
"# Initial concentrations of all the chemicals\n",
"dynamics_exact.set_conc({\"A\": 10., \"B\": 50.})\n",
"\n",
"dynamics_exact.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "7f861e7c-b81b-4f96-b52e-0874c2fc0e16",
"metadata": {},
"source": [
"### Run the reaction (same FIXED time steps as before, but now using the exact solver)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "2054d0e3-3e9e-445d-a77d-cea472fa13c4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"19 total fixed step(s) taken in 0.036 sec\n"
]
}
],
"source": [
"# Matching the total number of steps to those of Part 1 and Part 2\n",
"dynamics_exact.single_compartment_react(n_steps=19, target_end_time=1.2,\n",
" variable_steps=False)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "f98decf3-1ae7-4dfc-92f5-b848f75d3a66",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
" B | \n",
" step | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" 10.000000 | \n",
" 50.000000 | \n",
" | \n",
" Set concentration | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.063158 | \n",
" 13.791019 | \n",
" 46.208981 | \n",
" 1 | \n",
" 1st reaction step | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.126316 | \n",
" 16.555479 | \n",
" 43.444521 | \n",
" 2 | \n",
" | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.189474 | \n",
" 18.571359 | \n",
" 41.428641 | \n",
" 3 | \n",
" | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.252632 | \n",
" 20.041364 | \n",
" 39.958636 | \n",
" 4 | \n",
" | \n",
"
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\n",
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\n",
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\n",
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\n",
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\n",
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\n",
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\n",
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" 17 | \n",
" | \n",
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\n",
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" 18 | \n",
" | \n",
"
\n",
" \n",
" | 19 | \n",
" 1.200000 | \n",
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" 19 | \n",
" last reaction step | \n",
"
\n",
" \n",
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\n",
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"
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"text/plain": [
" SYSTEM TIME A B step caption\n",
"0 0.000000 10.000000 50.000000 Set concentration\n",
"1 0.063158 13.791019 46.208981 1 1st reaction step\n",
"2 0.126316 16.555479 43.444521 2 \n",
"3 0.189474 18.571359 41.428641 3 \n",
"4 0.252632 20.041364 39.958636 4 \n",
"5 0.315789 21.113312 38.886688 5 \n",
"6 0.378947 21.894989 38.105011 6 \n",
"7 0.442105 22.464999 37.535001 7 \n",
"8 0.505263 22.880657 37.119343 8 \n",
"9 0.568421 23.183761 36.816239 9 \n",
"10 0.631579 23.404788 36.595212 10 \n",
"11 0.694737 23.565964 36.434036 11 \n",
"12 0.757895 23.683495 36.316505 12 \n",
"13 0.821053 23.769200 36.230800 13 \n",
"14 0.884211 23.831698 36.168302 14 \n",
"15 0.947368 23.877272 36.122728 15 \n",
"16 1.010526 23.910505 36.089495 16 \n",
"17 1.073684 23.934739 36.065261 17 \n",
"18 1.136842 23.952411 36.047589 18 \n",
"19 1.200000 23.965297 36.034703 19 last reaction step"
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},
"execution_count": 18,
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"source": [
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Reaction `A <-> B` . Changes in concentrations with time (time steps shown in dashed lines)"
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics_exact.plot_history(colors=['darkturquoise', 'green'], show_intervals=True, title_prefix=\"EXACT solution\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "992a4700-9d42-4a46-8069-89becb69ad9c",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "d1d8c2c8-af8d-44d4-a6f2-ee7b5bc24ff4",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "766e8bba-3a15-461e-9bf6-9daf509197d5",
"metadata": {
"tags": []
},
"source": [
"# PART 4 - Comparing Variable Steps, Fixed Steps and Exact Solution \n",
"#### To avoid clutter, we'll just plot [A]"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "e9b8f945-b324-4d28-b2fd-b315df812de2",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "SYSTEM TIME=%{x}
A=%{y}",
"legendgroup": "",
"line": {
"color": "darkturquoise",
"dash": "solid",
"shape": "linear"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "",
"orientation": "v",
"showlegend": false,
"type": "scatter",
"x": [
0,
0.016000000000000004,
0.03200000000000001,
0.048000000000000015,
0.06720000000000002,
0.08640000000000003,
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ZEoDIzJIARMchkCXHwIXTIUvCQB2GQ5YcwhZOhSwJA3UcDllyDFwwHbIkCLNAKGSpADRmlgSgeQ6BLHkuQMn0yFJJgB67I0se4ZdMjSyVBOi5O7LkuQAl0iNLJeAJdEWWBCAysyQA0XEIZMkxcOF0yJIwUIfhkCWHsIVTIUvCQB2HQ5YcAxdMhywJwiwQClkqAI2ZJQFonkMgS54LUDI9slQSoMfuyJJH+CVTI0slAXrujix5LkCJ9MhSCXgCXZElAYjMLAlAdBwCWXIMXDgdsiQM1GE4ZMkhbOFUjbJ0cHZWTatZNam/Tul/5g4w5mvyT3+fPD7/2Nz388+lbU2bzGMLfZLn59pOqx79ndL/zH9zx8Ld1fQ32cfSFguPNTyf9O05HCftPBf/cOyFOPMPNj6fttTDmxuPvm9YOq7Dcea+M20Wx15clFndoPG8knxzIXX/+TjZ81401sPtmsZJ2+o4gwN9+t50M2omc14L4154rMV4stDnx7IwxoUc2XM9ctwpr7mcrZ83PI+oZabwrWqerfvhesznmeeZ1iQTbuH1dSSLw6+J9MwWvbYydT8iX5PXzqLzbvPaMlyzdU9fMeNZgItfRh1/mn3pizu2oUFrAsiSwKsDWRKA6DgEsuQYuHA6ZEkYqMNwdZSlac03lYhUAg6LhX6umXDoD/WJgOgPVYfFo0E2FiTFPD7Xbq7PnJiYr4nMJI8fFpO5x+dlJiMmpp25z3O2fypBh+PMxV347OzwtUMqCECgGAFkqRi3tBeyVI5f0htZEoDoOASy5Bi4cDpkSRiow3Ahy5KZKTk4M6P2z86oA/rffv3zAf3zAf01ecw8p/8sfzB5znw/91za1jy+zzyWPD7Xdq/+2s3HaG+vGtAn2K//yp5+7dezQebfgH5s8ePz7czjuk/yvGmbtNM/z8eZ63P4OcNvbn7JfJ37N/f94emChcf0N4efP9wu+3zSV4dr7J3Enn8wGyObr/H5dExpzORr0zEcHm/2+fS1sei85pMkj81b6aLxpINY4LD4nA+f69x3aezlo/3qwPi0mtavS/3hb+Fkm5/rPLvkXBbHyb6e585l/vkM0+b1OBxn4bwzvLN55njqcTZ5fhGzpvVanGdRXROebZ5fxLSh3eEXzKLXYMLSsu7ZsS967RiKjeeS4WmW4Q3096rd+ycXcg83vA6ydWn8/phVI+2e5rkOBJAlgZcIsiQA0XEIZMkxcOF0yJIwUIfhJGTJCM2CzMxLyZzAzEuNXmpknk/bLJKaednZN//8gaStG6lpFIu+VCgaxKJPf2hKZMFIQ0Ys+lKJSJ6fE4/kn163k4rJYglZLDFpzKSP7j9g4vT0Jt/PxcnKTDbmbPL8sBajZx81ojbvHHf4iiGVFAGuWZIi6T4O1yy5Z57NiCwJ8EeWBCA6DoEsOQYunA5ZEgZaUTgzU3NgZnpuhmZeamb1J/SDepZg6/ikmhOV5lKTzOZkZnlSqTHtzRKyKo4hLQQjWh6W6K9GbMzXJfrnEfO1r0+NZp4bnX8u+dprntN9ss/P91+qn+urYrAeYrLBgwfogimRJUGYjkMhS46BN6RDlgT4I0sCEB2HQJYcAxdOhywJA7UMd0gLzJbpKbVNC9D2qbmv6b/tU9nvp9R2/Zy5hqaKw0hNIia9GUHRP88JTvpVi09GeEx783wqOUnf5Oe5x7pJaqpgbmIiS1WRdRMXWXLDuYosyFIVVO1jIkv2rFq2RJYEIDoOgSw5Bi6cDlmSA7p5Xnp2arnZYuRHS8/OWf29kSL93C49k7PZfD89ra/VyX9Z/1Hzsy5L5sVleX+/lhx9nYsOZcQmmb3RP5vZm7mZmcVSk8hN32GpGdPxOPwQQJb8cJfKiixJkXQfB1lyzzybEVkS4I8sCUB0HAJZcgxcOB2y1BroHr10zYjN9pk5wUlmgeZng9Kfk6/63y79XB79MTM6K7WsrO7r1//61CrzffLz/L/571fp59fqf+ZamMZD4pol4ZcT4SwJIEuWoAJthiwFWhiLYSFLFpAqbIIsCcBFlgQgOg6BLDkGLpyuTrJktmnemsz4zC9/M9/Py04iQgs/zy19m8gx+2M2XzIzP4ns6K+rMtJjhCcVoVW9c3K0XM8AlT2QpbIE/fVHlvyxl8iMLElQ9BMDWfLDPc2KLAnwR5YEIDoOgSw5Bi6crhtk6Wk92/PjycmFa4DmZoCMCE2pHfr7rfNCZHZty3OY5WxGbNZp2Vmhl7St1sve1mjZSWaB+vv0933zs0N9yeyP6wNZck1cLh+yJMfSRyRkyQd1mZzIkgzHolGQpaLkMv2QJQGIjkMgS46BC6eLRZaM+Dw+Nal+qKXoh+br1IR6Qn99dOJQLiJGag7P8szNBCWzQPNL4tLvj+83G0qHfSBLYden3eiQpXhrZ0aOLMVbP2TJb+2QJQH+yJIARMchkCXHwIXThSRLZnvr72kJ+pGWoB9NTqgfaDH6sf75+/qruXFpq2OZnvX5qcHBZAbIzPqsmf9qxMfM/qRL4swyuW46kKV4q4ksxVs7ZCnu2iFLfuuHLAnwR5YEIDoOgSw5Bi6czrUsjevrgB7XAmRmiNKvZpbocXMdkZ49anWYnd1OGBhQJ+gZn+cODM597R/U3w8k1wrV8UCW4q06shRv7ZCluGuHLPmtH7IkwB9ZEoDoOASy5Bi4cLoqZMkoj5kRenxCS1GyZG5u+ZyRo2e0ELXaNc7sEGeWvz13XoSMHBkhOkHL0Xo9S8SxmACyFO8rAlmKt3bIUty1Q5b81g9ZEuCPLAlAdBwCWXIMXDhdUVkywvMTLUHpdUTJLFEiRRPqSf11usU4jfIct2h2yMwUmRmjweTx8nvECQMKOByyFHBxOgwNWYq3dshS3LVDlvzWD1kS4I8sCUB0HAJZcgxcOF0nWTI3WjUStGjpnP75x/rfoRZba5tttM1MUDIrNC9G6dK5Z+ufB/QMEkd5AshSeYa+IiBLvsjL5GWDBxmOPqIgSz6oH86JLAnwR5YEIDoOgSw5Bi6cLpWl7ZPT6qFDB9X/07vL/cfkoXlBmlQH9KYLrQ5zrVA6K/Q8LUFmuVyyhE5/Ndtuc1RLAFmqlm+V0ZGlKulWHxtZqp5xVRmQparI2sVFluw4tW2FLAlAdBwCWXIMXCjd9/VyuW9rOfqumlL/tG+f+r6+vqjZYaTnp7T8mBmh5w0Mqefoew0ZGXq+/md2oePwRwBZ8se+bGZkqSxBv/2RJb/8y2RHlsrQK98XWSrPUCFLAhAdh0CWHAMvmO4b4wfVtyYOqof014f17NEufbPWxuPEwSH18qER9YJkhmhuCd06LUccYRJAlsKsi82okCUbSuG2QZbCrU2nkSFLnQhV+zyyJMAXWRKA6DgEsuQYuEU6swX3Px8aV9/UcvSt8XH1yMS4mmzoN9bbq16mxei05UvVST0D6mf6h9SIfowjHgLIUjy1ahwpshRv7czIkaV464cs+a0dsiTAH1kSgOg4BLLkGHhDOnNF0b/pmaKHtRA9nMwajasn9OYLjYfZhvtnB0fUzw0Oq5OHh9UGvaTOXFXUaYMHv2dH9nYEkKV4Xx/IUry1Q5birh2y5Ld+yJIAf2RJAKLjEMiSW+D7ZmfUt/S1Rg8fOqS+qb9+R88gmceyh7lf0Ul6Sd3PaTk6edgI0pBa1dd8OR2y5LZ+ktmQJUmabmMhS255S2djZkmaqLt4yJI71s0yIUsC/JElAYiOQyBL1QI3W3Q/rKXom1qKvqX//bveqa5xf7rVWoRONnKkxehkLUgv1t8PWu5GhyxVW78qoyNLVdKtNjayVC3fqqMjS1UTri4+slQdW5vIyJINpQ5tkCUBiI5DIEtywCf0fYseMUvqzMyRWVan5WiLvv4oe5ilc2YJnZEjM2tk5MgssSt6IEtFyfnvhyz5r0HRESBLRcmF0Q9ZCqMORUaBLBWhJtcHWRJgiSwJQHQcAlkqDnyn3pHuIS1EczNHBxNRGm+40euo3nThpQNz1xnNXW80IrplN7JUvH6+eyJLvitQPD+yVJxdCD2RpRCqUGwMyFIxblK9kCUBksiSAETHIZClfMAfHD+gvnxwv3rg4AH1g6kj7210jFlSN6SlSO9UZ+Toxfr7Kg9kqUq61cZGlqrlW2V0ZKlKutXHRpaqZ1xVBmSpKrJ2cZElO05tWyFLAhAdh0CWOgP/By1HXzywL5Gkxvsb/YxZTmfEaP7f+r6+zgEFWyBLgjAdh0KWHAMXTIcsCcL0EApZ8gBdKCWyJASyYBhkqSC4bDdkSQCi4xDI0pHAD8zMKCNIXxrfr76iv5qf02ONnjk6Y2SJep3+9/PDo2rEciOGqsqKLFVFtvq4yFL1jKvKgCxVRdZNXGTJDecqsiBLVVC1j4ks2bNq2RJZEoDoOASyNAfczBjdOz+D9E96qV322qPn9g+oM0eXakFaqm8EO5zc3yiUA1kKpRL5x4Es5WcWSg9kKZRKFBsHslSMWwi9kCW/VUCWBPgjSwIQHYeosyyZnerumRekb2hBSvetMzL0Er287nVakM7QgvT8gUHHVbFPhyzZswqtJbIUWkXsx4Ms2bMKsSWyFGJV7MaELNlxqqoVsiRAFlkSgOg4RN1k6Ul936O/P7gvuQbp23onu9l53mbz7lfoZXVnzM8gub72qGjZkaWi5Pz3Q5b816DoCJClouTC6IcshVGHIqNAlopQk+uDLAmwRJYEIDoOUQdZMjeCvUfL0Rf1LNJ39fbe6bGkp1e9emROkE4fXqKW622+YzuQpdgqdni8yFK8tUOW4q2dGTmyFG/9kCW/tUOWBPgjSwIQHYfoVln6jr4p7Jwg7VOPT04uUF2tN2h47fwGDb+gZ5KGPG/QULbcyFJZgv76I0v+2JfNjCyVJei3P7Lkl3+Z7MhSGXrl+yJL5RkqZEkAouMQ3SJL05rbP+sbwxpBMv+e0dcjpcdz9AYNZnOGM0aXJFt8h7RBQ9lyI0tlCfrrjyz5Y182M7JUlqDf/siSX/5lsiNLZeiV74sslWeILAkwdB0iZlmamJ1VZuc6s0nDl7Ug7dA72qXHSfqGsGeaGSQtSC8YGHKN1Vk+ZMkZavFEyJI4UmcBkSVnqCtJhCxVgtVJUGTJCeaWSZAlAf7MLAlAdBwiRln6qpajv96/V31Z3wcpew+kV+pZI7ODndnm+xi93K4OB7IUb5WRpXhrhyzFWzszcmQp3vohS35rhywJ8EeWBCA6DhGLLO3Us0af37dH/cW+3erHekc7cwzr641era87MoL0Gj2LtKK3zzE9/+mQJf81KDoCZKkoOf/9kCX/NSgzAmSpDD2/fZElv/yRJQH+yJIARMchQpelb+ntvW/RgvRX+/cskHmpvgfSbyxboX55dFkiTHU+kKV4q48sxVs7ZCne2jGzFHftkCW/9UOWBPgjSwIQHYcIUZYO6muR/reWIzOL9Oj8Vt9m17pf0XL0Ni1JL9KyxDFHAFmK95WALMVbO2Qp3tohS3HXDlnyWz9kSYA/siQA0XGIkGTpB1MT6i/26lkkvdxuz+xMQsJce3TBsjH15iVjamVf/ZbZdXo5IEudCIX7PLIUbm06jQxZ6kQo7OdZhhd2fdqNDlnyWztkSYA/siQA0XEI37JkNvg2W33fsneX+pre+js9zGYNF+pZJHM9EorU+kWBLDn+hRFMhywJwnQcCllyDFw4HbIkDNRhOGTJIewmqZAlAf7IkgBExyF8ydKm6Wl9LdIudZueSdo8v+X3aG+veqNeaveby1eo5/UPOiYRZzpkKc66mVEjS/HWDlmKt3Zm5MhSvPVDlvzWDlnS/E87+11q247dC5W48cOXqVNPOWnh50s3fkrd+8DDyc8nbjhB3XHjxkVVQ5b8voiLZHcpS7N6gOa+SH+hZ5G+orf/Tu+KdMLAgLpw6Qp1ztLlallPb5HTqG0fZCne0iNL8dYOWYq3dshS3LVDlvzWr/ay9MRTm9XHPvNX6mNXvTOpxDp9bvIAACAASURBVG133aeuvu4W9dj9Ny38fMPNd6sH7vx48vM5F12lTn7JBnX5xecuVA5Z8vsiLpLdhSzt1jNHd+jrkG7ev1s9Pjm37bdRolfr7b5/Y+mYepX+Wu897YpUbq4PslScne+eyJLvChTPjywVZxdCT2aWQqhCsTEgS8W4SfWqvSw1gjTydOab363uufUadfyx646QIyNTWXky/ZElqZejuzhVytK/6J3szCzS3Qf2qnG9w505zL2QzlmyXP13fT3Scf31uHFsldVElqqkW21sZKlavlVGR5aqpFt9bGSpesZVZUCWqiJrFxdZauD04EOPqIuuuHZhZsks0Xv7BW9Q5511etKy8Xlkye6FFloraVkyUnSX2fZbX4v0r5OHFk73pweG9IYNY+qNWpTqfm8kydcAsiRJ020sZMktb8lsyJIkTfexkCX3zKUyIktSJIvFQZYauBk5ev1rXrGwzO5Fr7pQXXnJ+UfIUjrzZLpv3X34w3GxMtDLNYE+vR5ubHRQ7dg3USr1dr1hwyd2bVe3aknaMzO37bc5fk1fh2Qk6RUjo6Xi07k5gaOWDqq9BybU1GHkoIqEwOhQn+rR9w/bP272hDzymNV/eDDPc4RHoE+XZUz/7u3YW+59M7wzq8eIViwdUPsOTqmp6bkVDxzxEBgZ7FPmjxX7WrxvdjqTNWPcp7ETo3bPI0sZOkaUXnbS8xeuXzJP2cwsTfKJrcxr0E9f/WHMzC5NFazd7ukZ9dGtW9Untm1T5may5linl9e9deVR6qJVq9R6ltpVWtf+/l41rf+Hbz5Yc8RFoFf/D9+o0PRM89pN6t+tAfPXDI7wCOj3zQH9vsn/88Irjc2I+vXvlfm9433ThlZYbZL3Tf3Gaf6/V+QY0P/P5ChOAFmaZ9dMlMxTjRs6cM1S8RdbSD3LLMP7kz071af1v13zW3+frbf9/sXRJerX9FcONwRYhueGcxVZWIZXBVU3MVmG54ZzVVlYhlcV2erjsgyvesbtMiBLmo5ZanfhOWcs2uEuhdYoR+yG5/cFK5U9ryyZBUO37dutrtu9XZl7JZnjdL2b3ZUrVqufGuDeSFJ1sY2DLNmSCq8dshReTWxHhCzZkgqzHbIUZl1sRoUs2VCqrk3tZSndKrwR8WtPO3lhOR73WaruBegrsq0smQnvv9m/V310z/aF7b9fNjis/uioNepnh4Z9Db/2eZGleF8CyFK8tUOW4q2dGTmyFG/9kCW/tau9LEngZ+twCYpuY9jI0n36BrIf0jNJ39VbgZvjpweH1LvHVqlf0jNKHH4JIEt++ZfJjiyVoee3L7Lkl3/Z7MhSWYL++iNL/tibzMiSAH9kSQCi4xDtZOlbh8bVH+3cqr49MZ6M6jn9A+r3VqxSZ+lrktijy3GhWqRDlsKoQ5FRIEtFqIXRB1kKow5FR4EsFSXnvx+y5LcGyJIAf2RJAKLjEM1k6fuTE+rqXduUmVEyx9q+fnXp2Er1X5eOKW4j67hAHdIhS2HVI89okKU8tMJqiyyFVY+8o0GW8hILpz2y5LcWyJIAf2RJAKLjEFlZemJqUl2j75X0Nwf2KnON0lhvr7p4+VHqrcuOUiPc78VxZezSIUt2nEJshSyFWBW7MSFLdpxCbYUshVqZzuNCljozqrIFsiRAF1kSgOg4RHKPpZE+9Z4nnla3613uJnX+YS1Gb1m2Qv2WFqWx3j7HIyJdHgLIUh5aYbVFlsKqR57RIEt5aIXXFlkKrya2I0KWbElV0w5ZEuCKLAlAdBhit74/0vX7dqrP7d6V3FDWLLE7Ty+1+z295G61XnrHET4BZCn8GrUaIbIUb+2QpXhrZ0aOLMVbP2TJb+2QJQH+yJIARAchjBh9Vt9M9oa9O9XumZlks4Y3LFmm3qN3uDteb+LAEQ8BZCmeWjWOFFmKt3bIUry1Q5birh2y5Ld+yJIAf2RJAGLFIb6wf496v74uacu0ub2sUq8bXao+cOzRav3cruAckRFAliIrWGa4yFK8tUOW4q0dshR37ZAlv/VDlgT4I0sCECsK8cPJSfWeHZvV1w4dTDKYG8q+d8VqdeqSUbVy2ZDasmtue3COuAggS3HVKztaZCne2iFL8dYOWYq7dsiS3/ohSwL8kSUBiMIhJvSSu0/qJXef3rNDHdLf/4y+oey1q9apFw4MJZlsbkorPCTCCRJAlgRhOg6FLDkGLpgOWRKE6SEU1yx5gC6UElkSAlkwDLJUEFy2G7IkAFEwxDfGD6rL9GzSj/SW4Et6etUV+oayZpe77A1lkSVB4B5CIUseoAulRJaEQHoIgyx5gC6YElkShOk4FLLkGHhDOmRJgD+yJABRIMR2fT3SH+3cpu7U90syx2nDo+qjejbpmCY73CFLAsA9hkCWPMIvmRpZKgnQY3dkySN8gdTIkgBETyGQJU/g59MiSwL8kSUBiCVCmBvJ3rp3t/rg7u1ql94W3Gz//T59XdKv6p3uWh3IUgngAXRFlgIoQsEhIEsFwQXQDVkKoAglhoAslYDnuSuy5LcAyJIAf2RJAGLBEN+fnFC/u32T+s7E3LZ25y5drv6HFqUVHW4qiywVBB5IN2QpkEIUGAayVABaIF2QpUAKUXAYyFJBcAF0Q5b8FgFZEuCPLAlAzBliXG/a8FG9Ffhn9T2TzGbgz9b3SfrYynXq5cMjVpGQJStMwTZCloItTceBIUsdEQXbAFkKtjRWA0OWrDAF2QhZ8lsWZEmAP7IkADFHiPsP7leX79iintbXKPXrfhcvX6kuHVuphnqyWzi0D4gs5QAeYFNkKcCiWA4JWbIEFWAzZCnAouQYErKUA1ZgTZElvwVBlgT4I0sCEC1CbJqeVlfqXe7u0bJkjsbtwC1CLDRBlvLQCq8tshReTWxHhCzZkgqvHbIUXk3yjAhZykMrrLbIkt96IEsC/JElAYhtQszo5/50zy71Eb2Bw/7ZmZbbgecZBbKUh1Z4bZGl8GpiOyJkyZZUeO2QpfBqkmdEyFIeWmG1RZb81gNZEuCPLAlAbBHi0Ylxdalecvfd+Q0cfnFkibpm5dqm24HnGQWylIdWeG2RpfBqYjsiZMmWVHjtkKXwapJnRMhSHlphtUWW/NYDWRLgjywJQGwS4vo9O9XVu7Ylz5jtwP9Q31z2jUuWiyRDlkQweguCLHlDXzoxslQaobcAyJI39CKJkSURjF6CIEtesC8kRZYE+CNLAhAzIbbqjRt+Z/tm9X/GDySP/o7ewOGi5Ss6bgeeZxTIUh5a4bVFlsKrie2IkCVbUuG1Q5bCq0meESFLeWiF1RZZ8lsP77L0olddmJvAiRtOUHfcuDF3v6o6IEtyZL926IB6+9ZNaoe+uexz9Hbgf7bmaLVhYEguwXwkZEkcqdOAyJJT3KLJkCVRnE6DIUtOcYsnQ5bEkToLiCw5Q900URCy9Nj9N1lTuO2u+9Rd9zyILFkTi6OhuVfSB3duUzfq+ybN6u/P0cvt3n/UGjXS21vJCSBLlWB1FhRZcoZaPBGyJI7UWUBkyRnqShIhS5VgdRIUWXKCuWUSZEmAPzNL5SA+OTWp3rb1GfWvk4eSne6uXbVO/cro0nJBO/RGlirFW3lwZKlyxJUlQJYqQ1t5YGSpcsSVJkCWKsVbaXBkqVK8HYMjSx0RdW6ALHVm1KrF3x7Ypy7T1yeZLcFfrJfbfUYvu3uWXn5X9YEsVU242vjIUrV8q4yOLFVJt9rYyFK1fKuOjixVTbi6+MhSdWxtInuXJZtBht4GWcpfoYMzM+o9O7eqL+zfo3p097cvO0q956jVqj9/qEI9kKVC2ILphCwFU4rcA0GWciMLpgOyFEwpCg0EWSqELYhOyJLfMkQhS+kmEHmubXKJFVnKR/sxfc+kt217Rv1IL79b2dunblizXr1yaDRfkJKtkaWSAD13R5Y8F6BEemSpBDzPXZElzwUomR5ZKgnQY3dkySN8nTpYWTIbOVx93S0LdO659Rp1/LHr/NJqkR1Zsi/LZ/S9kz64e7uamJ3VgjSiPr16vVqj76Hk+kCWXBOXzYcsyfJ0GQ1ZcklbNheyJMvTdTRkyTVxuXzIkhzLIpGCk6VLN35K3fvAwwvncuOHL1OnnnJSkXNz1gdZ6ox6x/S0euf2TeoBfe8kc0XS5foGs+/Q908yS/B8HMiSD+pyOZElOZauIyFLronL5UOW5Fj6iIQs+aAukxNZkuFYNEowspS939KVl5yvzjvrdGUeQ5aKljacfubeSb+1bbMyN5t9Vn+/+syqo9WLh4a9DhBZ8oq/dHJkqTRCbwGQJW/oSydGlkoj9BoAWfKKv1RyZKkUvtKdg5ClVtckIUul6+s9wCf37FAf2rU9Gcfr9XbgH9Xbgi/T24P7PpAl3xUolx9ZKsfPZ29kySf9crmRpXL8fPdGlnxXoHh+ZKk4O4mewcjS6pVj6oE7P77onJAliRL7iTGur0m6VC+7u1tvDW6OD65cqy5YOuZnME2yIkvBlKLQQJClQtiC6IQsBVGGQoNAlgphC6YTshRMKXIPBFnKjUy0QxCyZM4ouwwvXXqHLInW2lmwTfr6pF/f+pR6VO96d5Te7e6zq49WrxgecZbfJhGyZEMp3DbIUri16TQyZKkToXCfR5bCrY3NyJAlG0phtkGW/NYlGFlKMbDBg98XRNnsDx8aV2/R24Jv09cnvUDfZPaWtceoYzzsdtfpPJClToTCfh5ZCrs+7UaHLMVbO2Qp3tqZkSNL8dYPWfJbu+BkKcWR3Tq82RI9v9gWZ2c3vDked+zbo67YsVlN6e9fN7JEfXrVejXS6//6pGavFWQppN+g/GNBlvIzC6UHshRKJfKPA1nKzyykHshSSNXINxZkKR8v6dbBylL2RLkprXTZZeNN63Abd25Rf753d7IV+KVjq9RlYytlkwhHQ5aEgToOhyw5Bi6YDlkShOk4FLLkGLhwOmRJGKjDcMiSQ9hNUnmXJSNCj91/kzUFM+N01z0Pqjtu3Gjdp+qGdZ5Z2jUzrd6ql919ffygGunp0TeZPTqZVQr9QJZCr1D78SFL8dYPWYq3dshSvLUzI0eW4q0fsuS3dsiSAP+6ytK/Tx5SF259Wj05NZVcl2SuTzLXKcVwIEsxVKn1GJGleOuHLMVbO2Qp3tohS3HXDlnyWz9kSYB/HWXpywf36xvNPqMO6i3CT9Y3mL1pzTHJznexHMhSLJVqPk5kKd76IUvx1g5Zird2yFLctUOW/NYvCFnKi+DEDSewDC8vNMH2f7x7u/rj3TvUrI5p7p30P/U9lPoF47sIhSy5oFxdDmSpOrZVR0aWqiZcXXxkqTq2LiKzDM8F5WpyIEvVcLWN6l2WbAcacrs6zSy9VS+7u0fPKpnjmqPWqv+2LJwbzeZ5jSBLeWiF1xZZCq8mtiNClmxJhdcOWQqvJnlGhCzloRVWW2TJbz2QJQH+dZCl/TMzyfVJ//fQwWS53Z/qjRxeHtiNZvOUElnKQyu8tshSeDWxHRGyZEsqvHbIUng1yTMiZCkPrbDaIkt+64EsCfDvdlnaqXe8O3fLU+rRiUNqnRalz687Tv2ngUEBcv5CIEv+2EtkRpYkKPqJgSz54S6RFVmSoOgvBrLkj33ZzMhSWYLl+iNL5fglvbtZljbrne7euPUn6vHJSXXCwID6/Nrjkp3vYj+QpbgriCzFWz9kKd7aIUvx1s6MHFmKt37Ikt/aIUsC/LtVlp6cmlRnb/6Jenp6Sp04OKRuX3tsVDvetSstsiTwwvcYAlnyCL9kamSpJECP3ZElj/AFUiNLAhA9hUCWPIGfT4ssCfDvRln6N30PpXO3PK22aVF65dBIsjX4aG+vAK0wQiBLYdSh6CiQpaLk/PdDlvzXoOgIkKWi5MLohyyFUYcio0CWilCT64MsCbDsNln6zsS4OnfzU2rf7Iz6L6NL1Z+sWq8GenoESIUTAlkKpxZFRoIsFaEWRh9kKYw6FBkFslSEWjh9kKVwapF3JMhSXmKy7ZElAZ7dJEtfO3RAXaBnlMb1zWbfrO+hdI2+h1J3adJcwZElgRe+xxDIkkf4JVMjSyUBeuyOLHmEL5AaWRKA6CkEsuQJ/HxaZEmAf7fI0hcP7FPv2PaMmtRM3jW2Ul0xtkqATpghkKUw62I7KmTJllR47ZCl8GpiOyJkyZZUmO2QpTDrYjMqZMmGUnVtkKUM23Muukqd/JIN6vKLz1149MGHHlEXXXHtERV47P6bFh7rBln6q/171KXbNyfnZGaTzKxSNx/IUtzVRZbirR+yFG/tkKV4a2dGjizFWz9kyW/tkCXN/9KNn1L3PvBwUokLzzmjqSxl5aixZLHL0p/v3aWu3LlVmQ3BP6GvT/rVJcv8viodZEeWHECuMAWyVCHcikMjSxUDrjA8slQhXAehkSUHkCtKgSxVBNYyLLKUAXXa2e9Sr3/NK2olSx/atV19cs8ONaw3cPizNUer04aXWL504m6GLMVdP2Qp3vohS/HWDlmKt3bMLMVdO2TJb/2QJUtZypapcZYp1pml9+zYrG7Zt0ct7+lV/2vdseqlg8N+X40OsyNLDmFXkApZqgCqo5DIkiPQFaRBliqA6jAkM0sOYQunQpaEgeYMhyx1kKVGnua6JnPccePGhad27ZvIid1/89/dskn9+e5dam1fv7r7uOPVhsFB/4NyOILe3h5l3nz2HjDbWXDERmDZ6IA6MD6lpmdmYxt67cc7NNiX7LA5PjHdlMWM3omzt8tuVdAtRe/RdVk22q/27Od9M8aaLh0ZUAcP8b4ZY+0GB/pUn77V5cFDzd83O53TiqX1+ozXiUfe55GlnLKUbviQnV06UPDFm7dYEu3NR8t3PP2UunnXLrWyr0/9w3NOUBuGhiRCRxVDu5Ia0m8+B1t8YIvqZGo42GH9gXticlrhSvEVf6CvR5kP3RNTM00HbwTYzGBwhEeA983wapJnRMODvfr3blbN8MaZB1sQbTu9b3Ya5OhQX6cmPN+GALIkIEsxLcO7TC+9u31+6d2d649TLxyonyiZkrMML+73RZbhxVs/luHFWzuW4cVbOzNyluHFWz+W4fmtHbLUQZbMTnmXvu1N6vhj1yUtzSYQLzvp+epjV71zoWcssvT7O7aom/ftTq5R+ry+RumkGl2j1Phrhiz5feMpmx1ZKkvQX39kyR/7spmRpbIE/fZHlvzyL5MdWSpDr3xfZEkzzG4dniJNl9l95Prb1U13fGmB9IkbTlh0vZJ5IgZZSkVpiRalv665KJmaIUvl3zx8RkCWfNIvlxtZKsfPZ29kySf98rmRpfIMfUVAlnyRn8uLLAnwD12WUlEa0dcJfH7dceplNZ5RSsuNLAm88D2GQJY8wi+ZGlkqCdBjd2TJI3yB1MiSAERPIZAlT+Dn0yJLAvxDlqVUlMx9lG5be6w6ZWhE4IzjD4EsxV1DZCne+iFL8dYOWYq3dmbkyFK89UOW/NYOWRLgH6ospaI0qEXpljXHqFOHRwXOtjtCIEtx1xFZird+yFK8tUOW4q0dshR37ZAlv/VDlgT4hyhLqSj16/O7SYvSq0eWCJxp94RAluKuJbIUb/2QpXhrhyzFWztkKe7aIUt+64csCfAPTZZSUTK76n9Oi9JrEaUjqowsCbzwPYZAljzCL5kaWSoJ0GN3ZMkjfIHULMMTgOgpBLLkCfx8WmRJgH9IsvT+XdvUn+zZmZzVjauPVq8fXSpwht0XAlmKu6bIUrz1Q5birR2yFG/tmFmKu3bIkt/6IUsC/EORJXMPJTOrZI7rVq1Tb1qyXODsujMEshR3XZGleOuHLMVbO2Qp3tohS3HXDlnyWz9kSYB/CLJ038H96sKtT6sZfT6Xj61Ul4ytEjiz7g2BLMVdW2Qp3vohS/HWDlmKt3bIUty1Q5b81g9ZEuDvW5YemRhXZ23+iRqfnVXnLR1TH125VuCsujsEshR3fZGleOuHLMVbO2Qp3tohS3HXDlnyWz9kSYC/T1n6ydSUOnPTE2rHzHSy493NekOHXoFz6vYQyFLcFUaW4q0fshRv7ZCleGuHLMVdO2TJb/2QJQH+vmRplxak129+Uj0+OaleOjikvrDuWcrcfJajMwFkqTOjkFsgSyFXp/3YkKV4a4csxVs7ZCnu2iFLfuuHLAnw9yFLE3rJ3Rv10rtv6yV4z+kfUF9c/yw11ms2C+ewIYAs2VAKtw2yFG5tOo0MWepEKNznkaVwa2MzMrYOt6EUZhtkyW9dkCUB/q5laVaP+Tf1Zg736E0d1vT1q7/XM0rH9pvbz3LYEkCWbEmF2Q5ZCrMuNqNClmwohdkGWQqzLrajQpZsSYXXDlnyWxNkSYC/a1m6euc2df3enWq0t1f97brj1AsGhgTOol4hkKW4640sxVs/ZCne2iFL8dbOjBxZird+yJLf2iFLAvxdytJf7t2t3r1zizLzSLeuPVadOjwqcAb1C4EsxV1zZCne+iFL8dYOWYq3dshS3LVDlvzWD1kS4O9KlrL3Urph9dHqV0aXCoy+niGQpbjrjizFWz9kKd7aIUvx1g5Zirt2yJLf+iFLAvxdyFL2XkrvXbFavWP5UQIjr28IZCnu2iNL8dYPWYq3dshSvLVDluKuHbLkt37IkgD/qmXJ3EvpDH0vpZ16q/Bf1zed/QA3nS1dNWSpNEKvAZAlr/hLJUeWSuHz2hlZ8oq/dHKuWSqN0FsAZMkb+iQxsiTAv0pZOjgzo96gtwj/7uQhdaa+6ezn9E1nOcoTQJbKM/QZAVnySb9cbmSpHD+fvZEln/TL50aWyjP0FQFZ8kV+Li+yJMC/Sll6i94i/Et6i/Dn9Q+qe/S9lJboHfA4yhNAlsoz9BkBWfJJv1xuZKkcP5+9kSWf9MvnRpbKM/QVAVnyRR5ZEiNflSx9YvcOdc3u7Wp5T6/60tHHq2frm89yyBBAlmQ4+oqCLPkiXz4vslSeoa8IyJIv8jJ5kSUZjj6iIEs+qB/OycySAP8qZOkf9WzSBXpWqUeP7za2CBeo0uIQyJI4UqcBkSWnuEWTIUuiOJ0GQ5ac4hZPhiyJI3UWEFlyhrppImRJgL+0LP1gakKd+cyTav/sjLpS73x3MTvfCVQJWRKH6DEgsuQRfsnUyFJJgB67I0se4QukRpYEIHoKgSx5Aj+fFlkS4C8pS3v0hg5m57sfT02qN+j7KF2v76fEIU+AmSV5pi4jIksuacvmQpZkebqMhiy5pC2fC1mSZ+oqIrLkinTzPMiSAH8pWZrRYzlvy1PqwfED6sTBIXX3umepoR6zEI9DmgCyJE3UbTxkyS1vyWzIkiRNt7GQJbe8pbMhS9JE3cVDltyxbpYJWRLgLyVLV+/cpq7fu1Ot6O1T/7j+eLWuv19gdIRoRgBZivt1gSzFWz9kKd7aIUvx1s6MHFmKt37Ikt/aIUsC/CVk6e79e9XF2zepPj2eL6w7Tp0yNCIwMkK0IoAsxf3aQJbirR+yFG/tkKV4a4csxV07ZMlv/ZAlAf5lZenRifHkxrOHZmfVB1euVRcsHRMYFSHaEUCW4n59IEvx1g9Zird2yFK8tUOW4q4dsuS3fsiSAP8ysrRrZlr90jNPqGemp9Q5S5arP161TmBEhOhEAFnqRCjs55GlsOvTbnTIUry1Q5birR2yFHftkCW/9UOWBPiXkaXf0PdSulffU+llg8Pqb9c/S2A0hLAhgCzZUAq3DbIUbm06jQxZ6kQo3OeRpXBrYzMyrlmyoRRmG2TJb12QJQH+RWXp5n271e/v2KJGe3vVfXpDh+P7BwRGQwgbAsiSDaVw2yBL4dam08iQpU6Ewn0eWQq3NjYjQ5ZsKIXZBlnyWxdkSYB/EVn64eSEeo2+n9K4vk7pOr307k16CR6HOwLIkjvWVWRClqqg6iYmsuSGcxVZkKUqqLqLiSy5Yy2dCVmSJpovHrKUj1fT1nllaUIL0pmbnlT/PnlI/bK+8exnuPGsQBXyhUCW8vEKrTWyFFpF7MeDLNmzCq0lshRaRfKNB1nKxyuk1siS32ogSwL888rSH+3cqj67d5c6pq9fffWYZ6ulPb0CoyBEHgLIUh5a4bVFlsKrie2IkCVbUuG1Q5bCq0meESFLeWiF1RZZ8lsPZEmAfx5Z+qfxA+rcLU8po0d/ozd0MBs7cLgngCy5Zy6ZEVmSpOk2FrLklrdkNmRJkqb7WMiSe+ZSGZElKZLF4iBLxbgt6mUrSzump9Vpz/xY7dDbhV8+tlJdMrZKIDshihBAlopQC6cPshROLfKOBFnKSyyc9shSOLUoMhJkqQi1MPogS37rgCwJ8LeVJTOjZGaWzGySmVVi8Z0A/IIhkKWC4ALphiwFUogCw0CWCkALpAuyFEghCg4DWSoILoBuyJLfIiBLAvxtZOlP9TVKf6ivVTLXJ5nrlMz1Shz+CCBL/thLZEaWJCj6iYEs+eEukRVZkqDoLway5I992czIUlmC5fojS+X4Jb07yZLZ9c7sfmd2wTM735kd8Dj8EkCW/PIvmx1ZKkvQX39kyR/7spmRpbIE/fZHlvzyL5MdWSpDr3xfZKk8w7ayZO6j9Bp9ndIPpybVeUvH1EdXrhXISIiyBJClsgT99keW/PIvkx1ZKkPPb19kyS//stmRpbIE/fVHlvyxN5mRJQH+7WaW3rtji7pp32713P4B9ZWjn62Ge3oEMhKiLAFkqSxBv/2RJb/8y2RHlsrQ89sXWfLLv2x2ZKksQX/9kSV/7JElIfatZOkfDu5Xv771aTWoBekevaHDCwaGhDISpiwBZKksQb/9kSW//MtkR5bK0PPbF1nyy79sdmSpLEF//ZElf+yRJSH2zWTJbBP+C3r53S69TfjGFavV25YfJZSNMBIEkCUJiv5iIEv+2JfNjCyVJeivP7Lkj71EZmRJgqKfGMiSH+5pVpbhCfBvJkvpNuG/MDyqbl97rEAWQkgSQJYkabqPhSy5Zy6VEVmSIuk+DrLkF0/EZQAAEghJREFUnrlkRmRJkqbbWMiSW96N2ZAlAf6NsnTjnp3qfbu2qZW9feoBfZ3Syr4+gSyEkCSALEnSdB8LWXLPXCojsiRF0n0cZMk9c8mMyJIkTbexkCW3vJGlCnhnZSm7TbiZUTIzSxzhEUCWwqtJnhEhS3lohdUWWQqrHnlGgyzloRVeW2QpvJrYjghZsiVVTTtmlgS4prKU3Sb8LctWqPcdtUYgOiGqIIAsVUHVXUxkyR1r6UzIkjRRd/GQJXesq8iELFVB1U1MZMkN51ZZkCUB/qksvXv7ZvWX+/cku96Z3e/MLngcYRJAlsKsi+2okCVbUuG1Q5bCq4ntiJAlW1JhtkOWwqyLzaiQJRtK1bVBlgTYGllKtwk391H6yvrj1XMHBgUiE6IqAshSVWTdxEWW3HCuIguyVAVVNzGRJTecq8qCLFVFtvq4yFL1jNtlQJYydM656Cp18ks2qMsvPncRs0s3fkrd+8DDyWMnbjhB3XHjxkXP/8uWverVzzyRbBP+wZVr1QVLx/xWlewdCSBLHREF3QBZCro8bQeHLMVbO2Qp3tqZkSNL8dYPWfJbO2RJ88/K0IXnnLFIlm676z51w813qwfu/HhSqUahmtWP/ed/+w/1jfGD6vSRJermNcf4rSjZrQggS1aYgm2ELAVbmo4DQ5Y6Igq2AbIUbGmsBoYsWWEKshGy5LcsyFKG/2lnv0u9/jWvWCRLjXLUKE8f2rxF/f7Tm9Tavn711aOPVyv0duEc4RNAlsKvUbsRIkvx1g9Zird2yFK8tWNmKe7aIUt+64csdZAlI1Bvv+AN6ryzTk9aPvjQI+qiK65Vj91/U/Jzz3f+Nfl659rj1MuHR/xWk+zWBJAla1RBNkSWgiyL1aCQJStMQTZCloIsi/WgmFmyRhVcQ2TJb0mQpQ6y9KJXXaiuvOT8I2TpnluvUccfuy6RpctWrlYb17BNuN+Xcr7svb09amSwT+0fn8rXkdZBEBgd7lfjE9NqZsYshOWIicDgQK/q0f8dmpxuOmxTU/P7yREegR69gdHosH7fPMj7ZnjV6Twi3jc7Mwq1xUB/b/K+eEj/f6/IsWx0oEg3+swTQJY6yFKnmaWv7N2nfr5/mBdUZATMZ7GRoX5kKbK6pcM1f2UbPzSlpnGl6Co4qP+nb+6qcGhyBlmKrHrmfXNUv2/u449MkVVubrijQ33J7900f2SKrn7mfdP8/o23eN/sdELLRvo7NeH5NgSQpQ6y1OmaJdM9vc8Sr7R4CLAML55aNRspy/DirR/L8OKtHcvw4q2dGTnL8OKtH8vw/NYOWeogS512w0OW/L6Ai2ZHloqSC6MfshRGHYqMAlkqQi2MPshSGHUoOgpkqSg5//2QJb81QJY0/+zW4Wk50g0czM+d7rPEzJLfF3GR7MhSEWrh9EGWwqlF3pEgS3mJhdMeWQqnFkVGgiwVoRZGH2TJbx2QJQH+yJIARMchkCXHwIXTIUvCQB2GQ5YcwhZOhSwJA3UcDllyDFwwHbIkCLNAKGSpALTGLsiSAETHIZAlx8CF0yFLwkAdhkOWHMIWToUsCQN1HA5ZcgxcMB2yJAizQChkqQA0ZEkAmucQyJLnApRMjyyVBOixO7LkEX7J1MhSSYCeuyNLngtQIj2yVAKeQFdkSQAiM0sCEB2HQJYcAxdOhywJA3UYDllyCFs4FbIkDNRxOGTJMXDBdMiSIMwCoZClAtCYWRKA5jkEsuS5ACXTI0slAXrsjix5hF8yNbJUEqDn7siS5wKUSI8slYAn0BVZEoBICAhAAAIQgAAEIAABCECg+wggS91XU84IAhCAAAQgAAEIQAACEBAggCwJQCQEBCAAAQhAAAIQgAAEINB9BJCl7qspZwQBCEAAAhCAAAQgAAEICBBAlgpCvHTjp9S9Dzyc9D5xwwnqjhs3FoxEt6oI3HbXferq625ZCP/Y/Te1TPXEU5vVmW9+96Ln27WvaszEnSPQWI8bP3yZOvWUk6zwnHb2u9T6NSv5nbSiVU2jIu+Ppm7bduxOBnTlJeer8846vZrBEbUtgTzvmybQR66/Xd10x5cWYub5XaUUbgmYWj38L9/jvdEt9lzZHnzoEXXRFdeqTp8/Gn9P+RyaC3PuxshSbmRKmRfpDTffrR648+NJ73Muukqd/JIN6vKLzy0QjS5VEEg/bN9z6zXq+GPXJf9Db/c/CVNTc6Qf0MyHvac3bed/KlUUxyKm+eD89gvekNTD9n8eJqzpZw5kyQJyRU2KvD++6FUXqgvPOYP30IpqYhu2yPum+YNU+sEu/QDX6YOe7XhoJ0Mg+8GaD9UyTKWjNP6BsNPvkPmMcunb3pR8vkn/3/f617yC91DpwszHQ5YKgG2Uo8YPBwVC0kWYQKMcNX4I6JSOmnYiVN3zzeQoK0+tMpvfy7POPFX95Jmt/PW0uvJ0jJz3/dH8rj69aZv62FXv7BibBtUSyPu+mbd9taMneicC/BGwEyH/zxf9g4OprTl4H62mhshSAa6NH9zy/OW7QDq6FCDQ7I3D/PXadolIp5moAkOiiyWBZqLaafY2+zy1swRdUbO874+mdpu27lhYgmeGlc4IVzREwrYgUOR907yvrl45lqy0QHzDfmkhS2HXx4yuqCx1+n9k+Gce9giRpQL1Mf9zyK6pT2WJ/8EXgFlRF/PGccz6VYv+ytJYt1ap01koW7Gq6BRqG9Z84Pq7r3x9YZmrAdGsnimgxg94yJLfl07e90cjV9nlI+k1MJ2Wofg9y+7MXuR9s1F2ed8M97WBLIVbm3RkRWSpSJ/wSYQ1QmSpQD3y/uW0QAq6lCRQ5C+kJmUqSlxgXrIAJbrnnVnKbgyQTZv+tbvEUOhagEDe98fG9nmXzBYYIl1aEMj7vtk4k5T+4RBhCvMlhiyFWZfsqPKKT9qeP9ZXW1tkqQDfvGvyC6SgS0kCRdbSI0oloQt1L3rNUpqemSWhQhQMk/f9sbE9slQQvEC3vO+bzZb+2M7gCwyXEDkJIEs5gXlonkeWECV3BUKWCrAusttTgTR0KUGg065OjX8B5S+iJWBX0LXTbnjtdk9DliooSI6Qnd4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"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# A streamlined version of the diagram seen in Part 1\n",
"fig_variable = dynamics_variable.plot_history(chemicals='A', colors='darkturquoise', title=\"VARIABLE time steps\", show=True) "
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "76070b5f-1bc1-42cf-bf7a-b06f6ec62e7b",
"metadata": {},
"outputs": [
{
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""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# A streamlined version of the diagram seen in Part 2\n",
"fig_fixed = dynamics_fixed.plot_history(chemicals='A', colors='blue', title=\"FIXED time steps\", show=True)"
]
},
{
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"execution_count": 22,
"id": "af104bd5-a726-4556-be26-3c580adb62c3",
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# A streamlined version of the diagram seen in Part 3\n",
"fig_exact = dynamics_exact.plot_history(chemicals='A', colors='red', title=\"EXACT solution (at fixed time steps)\", show=True)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "8c66fe16",
"metadata": {},
"outputs": [
{
"data": {
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"config": {
"plotlyServerURL": "https://plot.ly"
},
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A=%{y}",
"legendgroup": "",
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uSJBML9zsyFCqfz/0cyxZJj2eKKXzGWu1Tbr9yJQptgcBlQh4VpaMf2zjfSiY5zHIB/O54+9oUYku2R8Oqw/bVNrV7yujB93qojfet/VWcwykHbsfnubx53bus2S8T0uqGadM+mv8JkxnZTUu3cg+2X2W9HbMVfvsxMRqIm0qZYdl33ob8bazc8xuXeQbL3YTDVvTz6Fk91kys5b/m8fwC/c/3nBRq/t82flA1Au1WF1g2olVuhzj9U0/98xD2fT1jceuv1+teEjpZKthxNKOuTiN+f1g9f5OdJ8l/aLHeExWnyXm8zLV+yzZqYaXyqTxZPO4zMeV6D5Lyb5kMrKJJ0vJhtnpbVhJm1GuVZUl45cu5vPfeL6kcj5bvUfN51688zme8JjfH4nus2TnnLTzORRvHTvD7PRz3u7f70z6k+q28f52W32up9o21gcBPxDwrCz5AT6OIbsEkolxdnuDvYFA/hJwYs6V2/QSZZYy2Xcqw/Ay2Q+2BQEQAAEQcIYAZMkZjmjFAwQgSx4IErroewLmIYWqHjBkSdXIoF8gAAIgkF0CkKXs8sbeckgAspRD+Ng1CDQR0If82BmGlktoVkPH0p1wbzXMSfXjzyV77BsEQAAEVCIAWVIpGugLCIAACIAACIAACIAACICAMgQgS8qEAh0BARAAARAAARAAARAAARBQiQBkSaVooC8gAAIgAAIgAAIgAAIgAALKEIAsKRMKdAQEQAAEQAAEQAAEQAAEQEAlApAllaKBvoAACIAACIAACIAACIAACChDALKkTCjQERAAARAAARAAARAAARAAAZUIQJZUigb6AgIgAAIgAAIgAAIgAAIgoAwByJIyoUBHQAAEQAAEQAAEQAAEQAAEVCIAWVIpGugLCIAACIAACIAACIAACICAMgQgS8qEAh0BARAAARAAARAAARAAARBQiQBkSaVooC8gAAIgAAIgAAIgAAIgAALKEIAsKRMKdAQEQAAEQAAEQAAEQAAEQEAlApAllaKBvoAACIAACIAACIAACIAACChDALKkTCjQERAAARAAARAAARAAARAAAZUIQJZUigb6AgIgAAIgAAIgAAIgAAIgoAwByJIyoUBHQAAEQAAEQAAEQAAEQAAEVCIAWVIpGugLCIAACIAACIAACIAACICAMgQgS8qEAh0BARAAARAAARAAARAAARBQiQBkSaVooC8gAAIgAAIgAAIgAAIgAALKEIAsKRMKdAQEQAAEQAAEQAAEQAAEQEAlApAllaKBvoAACIAACIAACIAACIAACChDALKkTCjQERAAARAAARAAARAAARAAAZUIQJZUigb6AgIgAAIgAAIgAAIgAAIgoAwByJIyoUBHQAAEQAAEQAAEQAAEQAAEVCIAWVIpGugLCIAACIAACIAACIAACICAMgQgS8qEAh0BARAAARAAARAAARAAARBQiQBkSaVooC8gAAIgAAIgAAIgAAIgAALKEIAsKRMKdAQEQAAEQAAEQAAEQAAEQEAlApAllaKBvoAACIAACIAACIAACIAACChDALKkTCjQERAAARAAARAAARAAARAAAZUIQJZUigb6AgIgAAIgAAIgAAIgAAIgoAwByJIyoUBHQAAEQAAEQAAEQAAEQAAEVCIAWVIpGugLCIAACIAACIAACIAACICAMgQgS8qEAh0BARAAARAAARAAARAAARBQiQBkSaVooC8gAAIgAAIgAAIgAAIgAALKEIAsKRMKdAQEQAAEQAAEQAAEQAAEQEAlApAllaKBvoAACIAACIAACIAACIAACChDALKkTCjQERAAARAAARAAARAAARAAAZUIQJZUigb6AgIgAAIgAAIgAAIgAAIgoAwByJIyoUBHQAAEQAAEQAAEQAAEQAAEVCIAWVIpGugLCIAACIAACIAACIAACICAMgQgS8qEAh0BARAAARAAARAAARAAARBQiQBkSaVooC8gAAIgAAIgAAIgAAIgAALKEIAsKRMKdAQEQAAEQAAEQAAEQAAEQEAlApAllaKBvoAACIAACIAACIAACIAACChDALKkTCjQERAAARAAARAAARAAARAAAZUIQJZUigb6AgIgAAIgAAIgAAIgAAIgoAwByJIDoVi/rcaBVtCESgS6ti+mnTX1FK6PqNQt9MUBAr26lBLesw6AVKyJooIgtS8rpK0VdYr1DN1xgoC8b7GAAAiAQC4IQJYcoI4LLwcgKtYEZEmxgDjYHciSgzAVagqypFAwXOgKZMkFqGgSBEDAFgHIki1MiVeCLDkAUbEmIEuKBcTB7kCWHISpUFOQJYWC4UJXIEsuQEWTIAACtghAlmxhgiw5gMlTTUCWPBWulDoLWUoJl2dWhix5JlRpdRSylBY2bAQCIOAAAciSAxCRWXIAomJNQJYUC4iD3YEsOQhToaYgSwoFw4WuQJZcgIomQQAEbBGALNnChMySA5g81QRkyVPhSqmzkKWUcHlmZciSZ0KVVkchS2lhw0YgAAIOEIAsOQARmSUHICrWBGRJsYA42B3IkoMwFWoKsqRQMFzoCmTJBahoEgRAwBYByJItTMgsOYDJU01AljwVrpQ6C1lKCZdnVoYseSZUaXXU67K0aMnnNPa6+2jBM3dRn97d02KAjUAABHJDALLkAHdklhyAqFgTkCXFAuJgdyBLDsJUqCnIkkLBcKEr6crSQT8b06o3Y0acTNdeNlJ7fejwCXTYwP1oyuRxLvR6d5PpyJL0/earzqWzhh3f3NDESQ/R0s+/oYVzp7raXzQOAiCwmwBkyYGzAbLkAETFmoAsKRYQB7sDWXIQpkJNQZZiwQhHo9TAj3qKUmOUqF7+z6838P/lIf/XXpfXmtbd/bpsJ+s2rS/t8KOqlqiuIUq1/Is6eXAD4Yg8Yj/X889y/+56aZd/1vevtd+0n8ZArM3GgOyfX5dnfi3CD3ktoj+C/HPTIxri3/PPUXkc/sOUzrbV6zbRKaOuJ6MYSQPy+rnj78i6bDglSylBwMogAAKOEIAsOYARsuQARMWagCwpFhAHuwNZchCmQk15RZaqIxGqjsojuvuZX6vlx466KO1qiNAuto5KlpAqFpTKaCNV88/VLCGyXQ3xuiwdtQF+5kcdi0RYfi5kW/HxEj00NVm6Z/psmjXnVfri3VkJqYwYO5l69ejSnFnS/79+4zZavmKVtu3BA/rTnEcmaVmoreUV2msnDT2ieZtn571Ftz/wVIt9meXI/H99G2PnzBkvfV/6OnIsclwvv7G4hexJtun1hR81N2Uc6qfv95G7r9GGAeqL/H/IUQPjstH3c+no07Vjk0WyXEuWfUXCRnjoi7lPVtvKusli4ePTF4fmcQKQJQcCCFlyAKJiTUCWFAuIg92BLDkIU6Gm0pWlmhqiWn7U1AT4QVRdRbSlLkI7OVWiS0t1Y4Sq+BETlqgmLNX8qGuSljpdWoIRqg/xo0AenD0pilAjS4z24J+jxZx6ycbCx6KlbRqaHs0/886Nr8vv65vWbeTftVpffkdUQAEKRgNUwI9ONbuoXbiG2jfU8HM1tWuoprYNtVTSEKY2DXVUyo+SRv65kZ+bfo69VkfF/HpJYy0/y8/84NflUcQ/F/FzIbdTyO0U1tdSAf9cwD+H5Oe6aiLmnsqiy0iyOUJWsiSSpMuEnqGSfett6a/p66QrS2s3bGkeDmiUGl1irIbhmcXEPCzPfNx6u107d2gWLDsiqa9jlEJhIPuzI0siqsZthbMsRslKJZ5YFwRySQCy5AB9yJIDEBVrArKkWEAc7A5kyUGYLjdVy8O/RGA0keHrZXlU8887amNZmAoeB7YrLNkYlhjOvvBLVM7jxLQMTJPUSOaljiVGsi/hEAsMi0xDk7xEijkbU9r0KOFneRS6fVAsIDVBNjR+yLPhEawPUqiOH+Egi4I8AiwPwdijMUjFPGatOMLPLC2lFKSSpkcpy0xZMEilBQEqKiZq37idygJVVEZV1Ia1rixSyYdZRaWNVSwrlfyoZkmp0h5F9VVUyNJTGOZnlpKCuioqqK2iUE0VBfkRYHsMVldTYMd2l8EkaT5FWZLWjJkg+b95SJ68Fi+zZJzDJO2cduLgZrHR25asi8wnSkeWrI7WvB87siTrmLNEckxHDBqg9ddq+J8ue4lE0iqDlYosmbNfwmjGk/OzPvwxtyct9u4XApAlByIJWXIAomJNQJYUC4iD3YEsOQgzQVNbNhNVVASoYgfLzY7dP1fwzzv49R3b5Xf8OstQRbCBqooaqaaogWpZXuraNFB9Gc926ciPTvLg9Ib+c3v+mR3DtYV3J7ISEnERaeFnkZUCzsgUsbBoD5aWkqhICwtLk7iUiqywtLTh57ZBlpeCIJWFAtS+iJ8D/FwYpHZFvB3LTFERe1nNdpYWFhaWFZGagAgJi4k8B6sqW/w/UBWTFu13Tc8BNkft9crK3a8JUJeXaFlbipaVUbRNG36UUUSeS9vwAZVQlA8sWszP8nMxHyg/tP9rz00/8+8EQPN68jO3QYXyWpz12raldAs8CA7zkDd9WF2msqQLVLqypGdvjCEzCl0yWYo3D8qY/UkkS4mG4rkhS+ahii6fqmgeBBwjAFlyACVkyQGIijUBWVIsIA52B7JkD2Y9z/TXZEbEhoVH/1mTH04yiPDIzy1eFxGSrE6xLjoGyRHp6cj/156bJEieS1MbXiW9D4YDmshItkUyMEUsMpJxKQ2E+Gdukm2qNBBkcQlQWxaWtiwu8mhXGKAOLCzy6FgSpE5t5PexdUtZaDoFuaKAvoTDLQVFE5bdQqNlXAwSYyk0utjwekYBIoHr1hIKaRKjyQxLTUT/ufk1lh3+XUQTnt3S00J+9N8Z1pF2RIhytWQiS8Y+62Kji0ImmaVMZEn2K8P9jPN4Us0sQZZydTZiv/lGALLkQMQhSw5AVKwJyJJiAXGwO/koS+vXB2jTxgCVb2uSHz2rYxChnTt3Z3tEhGTIG09WaSk2WpbHID3N4tMkQR34d7JNCovMg2nPZc86UYg6s+x0LgjRHvzoyTLTOVRAnVlguvCjM0tN7LnAMrFkOWeJx/AF2eaCbHdBTm/JzzKcLLidH4bXA6Z1ZH2qq0vhKFJctaCgWVTiSksLYYllcTTJMQqOnuHhbI+W4RGhkYyOD5dUZUmyK1blwM1zg5yQJb1No/gkK/BglTVKVZYkzJkMw0snsyQZp48+WWGrwIOxvLlV9s2HpykOyacEIEsOBBay5ABExZqALCkWEAe74ydZWr+OJWhTTIQ28/PGpmf5v/7z1i0GeGU8J6c5q9MkOMZMj3G4m6zXLvUKa205S9OFsxua2PCQNJEb+Vlei4kPv8ayIGLUhaWoHa+faNGyOUaZ0cRnO0sPy8/OChafck2EQjt3UOGundS4dVtMhDZvyvisibbv0DILw8PBoiWlzUPQmjM0MjStSVZaCE3z601D1kRuOnXOuF/52EA6siQV4sz3KRIh6bFH5+aLfSdkSZ8DZNyXPl9KnxdkliezGOkykeweUOkWeDDOTzIXqLA6n+INwzMXkNDbMheQsJqzhGF4+fjO9ccxQ5YciCNkyQGIijUBWVIsIA52xwuyZJQgTYQ2s/xsaClEzRK0B0vNnpwF6WIxx0eEp3MDBfkR6Sp3vEl90SWna5PsGAWoM7/WVZMizgzxz71YjJItoVUrKcQiIzKjPW/bSkFOebXI/DRlgZwQnki37hTp0JEiHTtStGOn5p8jLC0RkSF+Xfu5aZ0IrxPln7V5NFiUIZCqLEnHreYEmau7OSFLsi/zvCgRJ5GDeLJkrLIn20u/5GazxkISumDpQcikdLhTsiR9MZYqF0mSPhvlyEq0kFlS5q2EjqRBALKUBjTzJpAlByAq1gRkSbGAONidXMlSA7uKSI+eBZJnPStk/JndoXWV5L3CMSGS5734ec8wBfty4eqe4ZTKUZc0zcvZnfnZnfER8ZEMkEiRzN2JDXkzzOFJEIPg+nUx8WHpCa1bS0Gu7g/2aSoAACAASURBVBDatDH2mvwsz5s2cUGCyrQi2Sw8nWIi0yw2BuEJdulCpT270vYCnqcD4UmLs8obpSNLKh8P+gYCIOAdApAlB2IFWXIAomJNQJYUC4iD3XFLltgN6LtVQX4EaPXqoJYJMktQ3MMo4SIHLEFF/cNUdgDfV4afo73qqLZbPVW2Z0FKsMgwtn0KC6mbzO9huekWLKCO2vA3nvvDwtNRm/cTm+8j5aXtLiI5WvZHf9azQSw9QU5rhTZu0H4vw+BSWRp770kiP417dKNI9x7U2KOnIxmedO+zlErfsW7uCECWcsceewaBfCcAWXLgDIAsOQBRsSYgS4oFxMHuZCJLa9cE6PvvA7Tqf/z8XZBWrYyJ0f++CZDcEyje0rNXlPbYv4GK9+GbbvavpyhniWq7hmlX+3raVhqm7aH4Q+T4rjzUncWnb0ERPwqpX9OjL5da7stzf1pUcEvCKcBzekIiO/oQOP1Zz/7I/9n6RIZIUmF2FhawSNc9qFGGu4kEyTOLUPP/u+9+XYbBubVAltwiq0a7kCU14oBegEA+EoAsORB1yJIDEBVrArKkWEAc7E4yWRIBkuyQZIlWrw6wCAVZjAL0LQuR1SLVlPv0jVLf/hHq/sMwle7PJac5S1TZMUzlLELr+B5C39eHaSeX1I63yEyfPTUJigmQCJHIUD/+WSRJhs/ZWaQQQsH331FozWoKrf6eClbzz/Is/+fXUxkGJ8PdWgmPZIN0ITKIEaWQsbJzHOmsA1lKh5p3toEseSdW6CkI+I0AZMmBiEKWHICoWBOQJcUC4mB3urYrpcUf12oyJGIkIqQPn5PMkVVChYugsQyxEO3TSJ0G1lHpvnUU4XlDNV3qaUtRHX3f2ECrG+qpLhr/nkFyHx9dhkSA+vHQOU2K+CGiZGd2UKBylyY9uvyE1q6mgu9WUWjtGu1ZMkcJFzY7EaDGnr0o0qVrTIZkKJyeDeKftaxQn74OEs9OU5Cl7HDO1V4gS7kij/2CAAhAlhw4ByBLDkBUrAnIkmIBSbE7co+glZoIxeYQaTIkGSMWow18z6GIRZJHRoj16xehPQc0UgcWoqK9WYh6hbUM0caCehaiMK1nk0pUTFuGxOnZoL4sQ/2bZKhvqJC6c5Yo2SJlskNrvm8hRAXyf84OySPZ/KBoaSk17tVXk52GvfpQY99+/Mz/5+dG/r8Ikl8XyJJfIxs7LsiSv+OLowMBlQlAlhyIDmTJAYiKNQFZUiwgcbqz/DMZHtckRCxGkiVatTJIPAXHcuGpNTRgf6KevRupJ88haji4mip6V9MuFqJ1gXr6jrND5RG+/1CCpafMH5L5QixA/VmI5Fn+vzf/nOyeQTKxqYCzQZIdkqFyBZoEcaZIl6EWN0Wy6ATfcLRhz71YhmLy08BSJD/HnvtqQ+TydYEs+TvykCV/xxdHBwIqE4AsORAdyJIDEBVrArKkWEC4OyJGn38WpC+WB+mTpUFaxg+rpWfPKPXfW+YQRakfzyPq24//z88VfWroi2Atfc1StHhXlSZG8RaRoP48VK4PV5LTh8zJXKIBhcVJwQS5Slzhiq8oxMPitOFyMm+oSYyCUjIvyaJlg0SGRIB0IerbX8sURXr1TrZ53v4esuTv0EOW/B1fHB0IqEwAsuRAdCBLDkBUrAnIUm4DImL02adB+vKLIH26LEhLP24tRv33idKgQRE6aGCE9t0vSnv1idAPDojNGfpfQ5iW1dXSZ+E67Xlp2LpU3Q9Zfo4oKaX9JDPEQ+b6ND3sHn3hJ0up8Mvl2qPgyy+o6NNlJEUWEi1SOts8PM4oR3b3jfVaEoAs+fuMgCz5O744OhBQmQBkyYHoQJYcgKhYE5Cl7AREiims+ComRvL4vEmQ6vi+q8alV28Wo0MjdAg/5HnQYRGSoguy7OBhcx+xEH3SJEafsBjJa+ZFCikcWlRCQzu1o30aQjSwqJiKbFaZ0zJD//2SCj//NCZHX69gOVpuCSnapg3VHzSQhYizQU1zhWJziDhT1H/v7IDNw71AlvwddMhSbuM7Yuxk6tWjC02ZPC63HcHeQSAHBCBLDkCHLDkAUbEmIEvOB0TE6L9fthSjr74MklmMpAbBIZwx0sRoUCMdeniE9LoEYa429zlL0VJNjmppGT++txhO15ELLRzCMnRocYkmSIfzs34/okSlw6XAgkhQ4RefN2eMCr9YToGdFa2BFBVRw34DqP4HB1L9AQdSwwEH8fNBnqwk53y0s98iZCn7zLO5R7/I0rPz3qLbH3iqFbpH7r6Gpv11Li1fsUr73cED+tOcRybR0OET6LCB+7WQlEVLPqex191Hsk2f3t3olFHXt2pP337ipIfo9YUftfj9mBEn07WXjYwbPr39Bc/cxe3H5kGqIEsH/WwM3XzVuXTWsOOzeephXyBAkCUHTgLIkgMQFWsCspRZQOp5OpA5Y2QlRu3aEf3wkJgY6VmjPfeKDaWTf1fycDoRIxlKJ3L0JYuSeaZRIa93oIgRS5HI0WH8vDcPq4u3aLK0lavOrVppEKKYHMk8IzKX/+Z7CMmwOREheTSIHB3Iz/typQgu9oBFDQKQJTXi4FYv/CZLX7w7yxKVyI0sxgyOSIKI0ZCjBmq/E4H64w0Xaf9fvW6TJkvG3xsblvbWb9ymiZe+yPayLJw71bIPVrLkVlxTaReylAotrOskgZzLkpz8qS76NyapbufW+pAlt8jmrl3Ikn32IkZ6xkiG0clwuv9+1TpjJDdvPfDg2DA6XYz22TdK+ki47Tx07uPaGlpaH5tn9CnLUYVFjW99OJ2eNUo2nE7uPVT4+WfNYtRmxRcUXc7ZoqqqVgcp9xzSpEhkSJOig6l+wAFEXJIbi9oEIEtqxyfT3uWzLEk2asaT8zW5MctUOrKkC9elo0+3zNKYr8tExF54ZaEWQpE4XaZOGnpEc9ZKfu7VoyvNmvOqtp45e2XOqMWTRdlWslh6hk3+Lxmua2+b0eI1vX39+PXzyyiNchzGPnbt3KGFIBqP0/y7TM9XbO8vAkrIUqI3jRm3vOHmLVjU4luSXIcEspTrCDi/f8iSNVOzGH36SUyMwuGW68sthQZwsQVNjHgonTz/4MBocyJGbt6qD6dbFq7RhtOtsbgbrAynG9SUMRrE2aMjOHMkr1kujY1U8O3XPIROL7gQG04XWre21erR9h20oXNapkjkSMTo4IEU7dDR+ZMJLWaFAGQpK5hztpN0Zem774jvr5b9bvfrJ/dta71fXRpSySzpArFxSzltLa8g47bpytI902fTR5+ssLyWssosGSVN/70uLEZ5MsqUPozP3J5VtksnZe6X8NqrVzcti2aVWTK+ZmYrvzN+uS4ZtdNOHKwNQRQhO2LQgObhiNInzMfK/vvEK3uELDkQKciSAxAVawKytDsgHy0J0ltvhOhf73LJbq5MZ7XsLZXpWIgG8pC6Q7n4wpFH7751qwyn+7Y+rA2j04bU8VC6r/hnnsLUYpFiCwfy8DnJGIkgJRtOV/jZJ1T0wWJqrkjHxReslvqBhzQPnRMp6vLjw2l9Gd9wCYuvCECWfBXOVgeTrizdeivR5MnZZzOJR73Jvs2L1ZwlyX7oF+pWw/D0NqxkwZxZ0dc1zlkyD8OTdZyQJV2G9D7E+7/5mHR5shJG6dfLbyy2HCJoPn5jxs3ISM8umdc3HrMKc7Cyf1Zij+kSgCylS86wHWTJAYiKNZHPslTNo9PeeTtEb7wWojdfD9H28pbB6b1nVJtnJBXp5HEoS1JZU2U6fc31jQ30SlUlvVtbTUs4c1QdZzjdIBEjLt99eHGpVoQh0VL0n39T0eJFVMyCVLT4fR5GV9li9YZ99qOGAT/QKtHVH/xDath/gFaAwbwkKvCg2GmI7qRAALKUAiwPrpquLM2aRfTEE9k/4PPO46FoY+LLUjqZJWlNhqepklkyy5EuKeZsl3lYnU7FWEDCSEoyQJJBk8U4PM5KfvRhf8bt9SIQieTKLJlGYc3+2YI9qk4g57KkOiA7/YMs2aHkrXXyTZbWrwvQKy+F6O03Yxkk49KhA9HPf9FIx5/YSMcMaaROna1jKeW736ypojf48V+ed2Rc2gaCmgwdxlJ0KA+nk5/jDqfjDaUqXdEHLEdL/kPF7/+Liv69qEV7kW7dKfyjH1Pd0T+m8NGDqX7QYbZPMMiSbVSeWhGy5KlwpdzZdGUp5R25vEE6w/CyPWfJ7jA8u7KUKFuWDLdx6JydzJKxvUSZJeN6yYYyJusjfu9/Ap6QJX0SXipzm7IZOshSNmlnZ19+lyVJ9Hz8YbA5e7Tiv4EWYPcfEKUTTmqkE3/eSEccFSEuCNdqkWzR25w5eovl6HV+mO9tNLSkDR1bUkZDS9vQ/gmq00nDAU5fFXO2qOg/71Mxi5Hcz4h4DpK+NPbrT3U/OobCg4/Rnhv32TftEwGylDY6pTeELCkdnow7l8+yJNdAxiyMCIRenCHZhX68ang99ugcd+63VZtWc5bsylK8UuTGCn36CSL7mXjJmc0ly43HahQnfX0rIRp8+EGWc5yM60q2S9+/eRhhxicrGvAdAWVlyTyuN166VoWIQJZUiIKzffCjLMmotbff4qF1PLzuLc4gGYfXFXL97aMHRzQ5OpmzSHr5bjNVGV73WnWllj1aXFdDct8jfenJZbSPK21Lx5eW0U85g1RqZVhNKwc3bqDiRQtjgsSPgm9W7C7ZzXOXpBJdHWeOwoOHUN0xPyGpUufUAllyiqRa7UCW1IqH073JB1kyDlfT5xzJBb65spzb91mS2BnvzxSvGp5dWZL2zNd08Ya9JVrP+Lt41fDMw/aM56GRo/n+U7h/k9PvWH+1p5wsmU/gePcOUCkMkCWVouFMX/wiS2vXBGjBK7G5Rx8sDpJUs9MXGU53/AmNdAIL0nHHN7aadyTriQpJUQZ9eN1XhuF1kmySQgwnsBzJ4yAeXhdvERmSoXTFMu+Is0ehNat3r8ql8+p/OIjqWIy0zNGPh5BUq3NrgSy5RTa37UKWcsvf7b37RZbc5oT2dxPAfZlwNjhFQBlZMta7N07Ogyw5FWq0kwoBr8qSDK/78IPdw+u++Tq94XVSmEEE6S1+3srZJH3pwNkiGV4n2SN5dLIq482d0CrVsRgVc0EGqVgX3LqluY0o37Oo/rAjNSnS5h0dNTir9zGCLKXyTvDOupAl78QqnZ5CltKhlt/bQJbyO/5OHr0SshRvTpL5rtVOHriTbSGz5CRNNdrykizt2sXD67i0t2SPZJjdju27GdodXrdBG14XK86wuK6a5D5I+iLzjY7nuUciR0eVlFKruxzV1VHRxx/G5htJ5oiLMgQquVNNi2SJtCF12oPnHR16OJF0LEcLZClH4F3eLWTJZcA5bh6ylOMAYPcgkMcElJElq7snQ5by+MzM8aGrLkurvw/Qq/rwuv8EyXg/1+bhdVyg4TgeZmcu6y1oRYXkRrAiR2+yJH1pGF5XwnOGBnP26AQWpJPalFGvEN9h1rCICEm2SC/IULTsYyIWJn2R+UUxOeIhdTysroFLeRO3qcoCWVIlEs72A7LkLE/VWoMsqRYR9AcE8oeAErIkuI3D8Iw3FMMwvPw5GVU6UtVkSQrDLWEpknsfyWPl/1rKx377R7XiDImq19Xw8DhteF0tD6+rqaYthuF1PVmITuCqdcdzgYYhLEqlJrkp/tc7VPzma1T83sJYpTrD0ti3X6xSXVNBhoZ991MplK36AllSOjxpdw6ylDY6T2wIWfJEmNBJEPAlAWVkSaeLAg++PM88d1AqyNLOnURvyfA6lqN3eHhdRewefdqSyvA6KestGaR/syjpw+ukOMNhfK8jfXidVXGG4oVvU8kr86l03gsULN/WvO+GAw+OzTc68kdUN+Snjlaqy8aJAlnKBuXs7wOylH3m2dwjZCmbtLEvEAABIwHlZEnvnLFEpNUQPZXCiDlLKkXDmb7kSpakvPffZxfQSy/GqtcZF/3msMceF7tBrNXwOll/LY/Jm121UyvxbRxepxdnOK6pep1VcQYRpNIX51Lp/H9QwDD5qfbkU6lm2K+p9qRTXK1U50z0ErcCWcoG5ezvA7KUfebZ3CNkKZu0sS8QAAFPyJKxk7gpLU7abBPItixJie+ZjxbQs08VUCULk74M+EFseJ3MPZL7ICVa5lbvotm7Kuh9vv+RvvygsFgr6308D7E7iu991Grh8X3F7/9Lyx6V/POl3VXrSkqo9tgTYoL081Mp2rZttkPg2v4gS66hzWnDkKWc4nd955Al1xFjByAAAnEI5DyzJCL0xbuzbAdIMk7zFiyKe+dp2w05uCIySw7CVKSpbMnSf/4dpMf+UkCvvLS7xlzPXlG64OIGOvWXjdS33+6qdFZoPuN7ID3LWaR/VO2iXdGYTO3B849GtW1PZ5V1oD35HkaWgsQ3hJUMkgyzC27bGlvFx4JkZABZUuRN5nA3IEsOA1WsOciSYgFBd0AgjwhAlhwINmTJAYiKNeGmLMmNYefPC9FfZhTS55/uLtTwox9H6MJLGujkXzQS384o7lIRaaS5LEciSV+EY1XoRLWktPeosvZ0bJu2rct7SwbpvXe14XX5KEiQJcXeYC50B7LkAlSFmoQsKRQMh7syYuxk6tWjC02ZPM7hltEcCDhDALLkAEfIkgMQFWvCDVnaXk705OMF9MRjBbRpU0ySiouJzhjeSJeNq6f9B8TPIslv3ucCDc9W7qQFNZXNhRokc3Q2Z5DO4kxSN1OJb4IgWZ5VyCwp9mZzqDuQJYdAKtqMH2Rp0ZLPaex199GCZ+6iPr27tyA9dPgEunT06XTWsOO11/ViV+aKwMb53HoDY0acTNdeNlL7r74P/Xfm7WU/W8srWo3oMRfXku2N7er7tRoJpLdpPnWs1rVioIIsqdAHRd966BYTUEKWUo3EwQP6YxheqtCwfkoEnJSlr1cE6NHphfSP50NUWxvrRvfuURp9foP26NwlftfkZrFzKiu0gg1rmm6mJAPrTuLskWSRhnI2qUURcREkLvPdnEHSq9jlyRA7O0GGLNmh5L11IEvei1kqPfaDLMnxykX5EYMGNMuNUXCMciFTFERW1m/c2iLjYpaW1es20Smjrqebrzq3WbT018xSJqIy7a9zNezDThnSvL78X2Rp/cZtzddWZqlJJkunnTi4xTHFi20iYUzlfHB6XciS00T91V7OZckPOJFZ8kMUWx5DprIU5VTQW28EaeYjhfTewt1j6gYdykPtxjbQL89o1Mp/Wy31vPFrXOpbBGkhP+tlHfoVFGoZJMkkdQ7tnuOkZZBEkGQOkhRpgCAlPCEhS/57v8oRQZb8GVf9qPwiS/dMn00ffbKixRe+8ppRinSpGX/hcC0TZZQoK2kxZ6XiyZLsR1/MfTDLkqwnwqZnppySJeM9NWUf0v4LryzUuqUPw5N1Thp6BL2+8CPtdamI/McbLtJYyGL+wtycbUs0D14YzJrzajMHkcy1G7a0eM3YvjFrZsy0WfVx4dypze0aj1P1is7+/uRw5uggS8zRnEI2p62N6WmrrBZkyZmTUaVW0pUlvterVvp75iMFzTeOlRoLp57eSBdy0YbDj4xf0e7r+jD9raqCXqjcReU8L0m7AOSbw54sc5HadqBj+GaxzVkkESQp863PQZIxfrLoGaQzhlPtyaf5qoqdU+cHZMkpkmq1A1lSKx5O9yZdWfouHKbvwjxRNMtLv6JC6ldU1GqvViIj1yAiA0OOGqitL9ccRx16gJb5MYuQWVqsMjXxZEnaemra77R9SDbKmHkyy5LsZ8aT80kXAKdkyaq/sm9ZjLJkvNYS8TAKh/xfz6SZ27OSPj0I+rq6TAmnOfPf0TJiVpkl42s6U/36UPpglio9u2bOHkqfMB8ry29Ah3eX97Ikb4Apjz7XfCKbPxDMHxhWKXTIksNnpQLNpSpL69cH6DEu/f03Lv2t3zxWhtedM7qBzr+onrq1HJ7efIRVkYhWyW4OZ5GWhpvG6PFv9ykoorPbtacRPNSu+X5IPAyvWZAkgwRBSutMgSylhU35jSBLyocoow6mK0u3bthEkzduymjf6Ww8qUd3urWn9Qe/8TpCLuBvunNms5TIvoxVgs1ZJ6s5S+bhdlaypGer5jwySTsc6YNxKJ7VnCWjoCSTJZkHZV7szlmykiXjsEKzMBr/b97WLETGPiUaAmiWJSuGxrgZhU32YcwYYkhfOu8YtbfJe1kyh8f8BjHLkVmeZHvIktoneTq9sytLH38YpEdnFNCCl0MyGk5bDjgwylXt6mn4mZz94QIOVssHtTVaNbuX+d5INTJmj5cSziL9orQtnc1ZpMElTfdEiidI3HDtcSdSDTJIKYcXspQyMk9sAFnyRJjS7mS6sjSrfDs9sa0p85723lPf8LwunWlM506WGxqvI6xkaMmyr5q/wNWvSXTxMEqLOduh78zqQt+YrZL1zLdhscrISN9efmOxJnLJZCmTOUt2ZMnYvsiSMYuzfMWqVpytimjISmYp1NczC465UIa+AxkeKFkisywZY6rzN2+T+lmELVQhAFkyRcL8rYT5Gw2rby0gS6qczs71I5EsSZ2Fl18MaUPtli2NzUeSUt9y81iZj3TMEOuhdlulWAML0myuaLeyYfewkAGFnEViQTqzrB11CPJcJBGkd9/ShtiVcgYpsGN77MAgSI4EGLLkCEblGoEsKRcSRzuUriw52gkHG5OLbblQP3f8HS2G4MlFu9XFv55psRr9cvsDT7WY12QlS+a5Qvqh6LJgJUvG6x1VZcksWqmEyHjMdjJLxrYTZZaM68UT2lT6iXVzTwCyZIqB8RsL+ZX5DWGVxt1SEbvXDRb/EOhYVkhVdQ1U37C7nPeOHVL6O0R/5ZvIblgfO9b2HYjOHtVIF1/aQHv1sT7+9zmLNLNiO73Cw+30RbJIv2I5GsUNHMVzkWQJcGGG0pmPaI/g5t3DRsKnnEq1w8+k8CmYg+TEGbZHh2LCe9YJkmq1URgKUFlpAe2ozP78FLVI+LM38r7106JfnC/9/JtWQ/DMWRHjEC8raTGLjlmWrIb6CUvjyBkrWTK+5pQsWclDJpmleKXI9eGGxnNGjkEWY3l2+b9kiqyO3yrbtPjjL7Q5TuZrQ+P/ZTt9//Hmj/npXM6HY4EsGaIsonTYwP1aTMSzk1mqb4g/aT8fTiI/HmNBKEiNkShFeYjcihVED04N0NNPB6imJna0++9PdPkVUTrvvCiVlVkTeLuykm7ZuJmWSNWHpuVgLsBwIQ/NGN2pE7XT7zy7ciWFHphCwccfI722ePSkn1Pk7FEUOeMMorZt/Yg4Z8dUWBBkCcZ7NmcBcGnHAf4CIhQMUEMjYusS4pw2K+9bPy26fBgrrBmHvRmP1XjB/f6Hy8mcSZJ15VpFFmPVOPm/FCSQcuFWN301Dh2zO2fJHANpX+Zc2Z2zJNsb9xWvGp55zlK8YXjSnnkelz5UztxX8/A445ws4+/iVcOT9nSRNWfqjHE0szQei5/O4Xw6FshSU7StREl+hTlL+fR22H2sMgxv3suNNP2hEC18J8jSxJkfLkX3059x6W+ej3TcCRHt/1bLO1zue+rOcvqwLlawQW4WO5ILNZzUpowOLSpp3qToww+o7Z8f0Mp9Exd6IK6cVP2bkVR55dXUsC/bGBZXCGAYnitYc94ohuHlPASudsBvw/BchYXGXSdgziy5vkPsIKcElJOleHeCFkqJaudnQlG/+Zt+B2xjW6iGlwlZ720rmaPn/15As2YW0n+/ivWfHYd+89sGbajd3vvsHpZnPrqFtVU0pWK3JPVkSRrfoTPfF6k9FepmxdZV8sp8TZJElmSJduxEVWMuosqLL6NI9x7eg+axHkOWPBYwm92FLNkE5dHVIEseDZxPuw1Z8mlg4xyWUrKUi3KLVmU4hZUxjYv7LPn/TbFxY4Ae57lITz/Jcx6a6inIHKQxF9bTKC7/3a5dfAaSSZrCmaSPmzJJvZok6SyjJLGFlf3tSWo7YxqFVq3UGmvs248qx46j6nPGULRNbN4SFvcJQJbcZ5yLPUCWckE9e/uELGWPNfYEAiDQkoBSsmS8W7SXAoVqeF6KVsu+fvoJl/5+uIBenh+SInTa8qMfR2giD//+2Un1Cec/vCWSVLGNloVjBT56N0mSDLnTM0nBrVuo7C/Tqezxv1CQCzjIUn/o4VR5xVVUc/qvYmX0sGSVAGQpq7iztjPIUtZQ52RHkKWcYMdOQQAEmABkyYHTALLkAMQsN8EOQzffWEQvzeNS3bzI/ZDOGN5Il42rp/0HRClR6fA3qyvpfs4kfdokSXsW8HC7dp1pZLsOVNB0HAXffk1tH3qA2jz3LFEdyxQPw6s96RRNksI/HpLlo8XujAQgS/48HyBL/oyrflSQJX/HF0cHAioTUEqWzHeUVhmcsW+QJa9EKtbP2c+E6LZbiqiCbzjOxelo3IR6Gn1+A3Xpuvs4rGTpdckk7dhGn9XHMkl7sSRd2b4z/ZbvkaRLUtGihdT24Qep5I1XeTISz2/iHVT/9mzaNW4iNe69j7dA+bS3kCV/Bhay5M+4Qpb8HVccHQh4gYBSshTvXgCqg4QsqR6hWP++/y5AE8cX0QeLY0Pf5Oax908L0557tS7aYJSlV5uG2y1vyiT1LSik8e07aZKk5aUaG6l03gssSVOp8NNlWtuRzl2o6oJLqOqiSynSdQ9vAMqTXkKW/BloyJI/4wpZ8ndccXQg4AUCSslSvDtM6yDdqoaXaaAgS5kSdHd7dhn684MFNPW+Qu02Rlx8jibdFqbfnsW/iLOILD2zpZzu3b6NvmySpH4sSZJJ+k3b9pokBfg+SmVPPkZlj/6ZQmvXaC019t+bKi+7kqrOOpeotNTdA0PraRGALKWFTfmNIEvKhyijDmIYXkb4sDEIgEAGBJSSpQyOI6ebQpZyij/hzqWAwzVXFtFXX8ZuwOZhGQAAIABJREFUiiTzkm7/U5g48WO5SI7pZZ6T9NCu7bS8qbpd/8KYJP2aCzeIJAU3buCqdg9pohTYyWP5eAkfcZQ2H6n2NL6JbLwbMKmLKa96BlnyZ7ghS/6Mq35UkCV/xxdHBwIqE1BOlmQo3tjr7mvBTO7wPOSogcpyhCypF5rqKqK77iikx7gcuNzvtWevKN03NUxDj+X/WCzy6stVu+gBLtywoj6srbG3QZJk4F7Bl8up3bQpPOTueS5pV69Vsqs9+dRY0YajB6sHAT2yJABZ8ueJAVnyZ1whS96L6+p1m+iUUdfTgmfuoj69u6d8APdMn00vv7GYFs6dmvK2djbQ+zdmxMlkdX9NO22Y1zHehmbksONo9ry30z7+ePuX29is37iN5jwyyVYX3eZoqxNZWklGphlv+eP0bpWSJf1kM77B9JP65qvOpbOGHe/08TvSHmTJEYyONbLwHc4mTSiiDesDWmXu8y5ooN/9vl67uazVIjeTvaV8K33bEJMkKdwwuUcP+mVxGYXrI1T81uta0YbihW9rv4/y8LrqEaOoUoo29OvvWL/RUHYIQJaywznbe4EsZZt4dvfnl8xSvHs7yoX7nj33oNsfeKrVRbYUv5LFeJGs3/8x3pfJxvtDyrZdO3fQ5CPRdAen5CFVWTLf4NXti/xUionpX+AnEz/jrW/sbpPqOyiZLGWbo53+Z/P+qUOHT6A/3nCRK8kVpWRJDvTS0ae3kiL5cJnx5HzXvmWwE/BE60CWMiXozPZyGyMpB/7i3Fg58P32j9LUh8N0yCDrbNL3DfV06/YtJFXuZNmb5yRN7NiFhrdpR11Lg1T3xFNUOu0BKvjqC+33UqihuWhDvHF8zhwKWnGRAGTJRbg5bBqylEP4Wdi132Qp3hxsEYWPPlnRLEZy/TNvwaJW2QS5MBa5Wb9xK02ZPK5FBORaqscenVtsI+2KjBm/dDZfXDsVxkxlyal+WLWTaiExO+KjH6/b8+pTlSU3OdptO5uyFO+9YrevidZTSpbi3ZRWP1ndPhHTBQpZSpecc9v9/dkQTeZy4Du2ExUVEV05sZ7GXdVAPJKu1VLN4/JkuN1fdu2gMJf3PrCwmO7u0o0OLSrR5iCVPfYotf/rDKING7RtG/bZjyovv5KqR54TuyETFk8TgCx5OnxxOw9Z8mdc9aPKF1mS49W/OD7myIMth7PJNdG0v86l8RcO16YtGK+N9MyVneslu7JkzEbpGSrpp3nahJ59McuS+YLZmDmS3y1fsar55NUzbOYvyI19MI400tte+vk3tLU8Noc4URZIhKNXj64tht/p/dU7YTxGcybOnMkzM5Btn5r2u+a4rV63WYuRcTvpg/RXH2ZozAIePKB/C8k18zH/Xu+zHY76ULXXF36kbSZ9lUyMPvXF3LaZS6IpMRLTWXP4lilNi8Ro7YYtLV4zti/nuB4vY0ZTj6feR3M8zcdpjrUcY7IsYDqflErJEjJL6YQwv7eRcuDXXlVE7y+KlQM/7IgITf1zmPbep3U5cHnl+aqd9KftW2lTpJE6BkN0PWeSzuES4IVrVlPb6Q9Sm2eeoEBVLNNUP/gY2nX5BG1eEoo2+Oc8gyz5J5bGI4Es+TOuGcvSd98RySPbS79+RPIwLXZkRr8Al4vZ004c3GpejVxcH3XoAVqWyHzdJL+TxZxtsjp8O7IkF6dHDBrQ3AdpX2/buL3xuFKRJemXuR/m0URG2dLb1i/c9Ytn/QI52fFbDdUS3rLoc+P1rJ3MZ7KTWTKvYz5+4xf+5mMzDzmU/ukxN/8u1cySeV9yXEZhkf+bxdAoovHiaz6XzAkNOf4589/RzhmrzJKdeOqybzxmq6zrXr26tRh2J23LlwhO1zlQSpYwZynbn+be3Z+UA5/x5wK6/x4uB15D1K4d0Y08L0luLmtVjO4zrmx3fflm7YayolVnsSDdyKLU7bNPqe20+6n05Re1+yVpRRu4ol3oxhuo4sBDtDlLWPxFALLkr3jqRwNZ8mdcM5alW28lmhyb85PVZRJPwpd9x5El8+vm+UKJ5u3IRax+MSnrGYfiJZMF437tylKvHl1ayZfV9Ih4GbFEmaVksmQ1pM94jFZtG4cxmjlLHyXzk6jwhLF9J2RJ+qBf9EsWzZj5MMuuUQisRDhRgYdk0mn+vbl94/+t4pts9JdVRsccH6t4GoXcvL5RxOzMZTN+keDk+10pWZIDQzU8J8Prz7a++DxAE64obi4HfvxJEbrn/jrq3qP18W5tbKA/7thGz3FGSTJLA3mo3T2d96BDyrdTx2snUMmCl2MblZRo90bSijb07UfGm9L6k2L+HhVkyZ+xhyz5M676UaU9DG/WLKInnsg+nPPOIxozJq4sJRomp18HSRbAmNWRxuQidsmyr5rlxTxfxmlZMg/F0iuOmb/ll77pWZERpx/bYvhgJrJkNQ3DmG1I1rZdWTIP79KP0ylZMvIxVuCzKrhhLMZhHr7ntCwZM5fmrJZxWJ3OMV6xNXNBEV2c4smPOS4672RyZRy+Z8yK6e3ljSxl/xMt8z1izlLmDO20UMMZpLv/VEh/faRASwLt0Y3oD3zPpF+e0frmsvU8F2kmz0l6oKKcKqMR6sxD7iSTJBmlto8+TO3vmMw3ld2lVbbbNfE6qjr/Yop26tzcDciSnYh4cx3IkjfjlqzXkKVkhLz9+7RlSbHDtjMML9GcJfNFvfki1k77+jZ2MktGfMYhcGvWb25VeCtev80CZ84QJMqIpJNZSlR23GoYntUcIjluGW7olCzpcimZJaMAxZt+osuVseiZE8PwjLJjlCOzzGVSWC2RzCYr/pEos2QlvuZhqnkxDE+xzzTb3YEs2UaV9opSDvy6q4to7ZrYzWVHjmqkSX8IU/v2rZt8k6vb3bpjC63ieyHJkDuZk3QDi1LXzz+jTldeSgVfxMYn1x13Im1/cAZFevRs1QhkKe1QKb8hZEn5EKXVQchSWtg8s1G+yJJ5WJ3VvBPzcCdzlsfJanhy8amXLDdf6Nqds2TVPznx9AIH5ov2VOcsGYcJJhuqZVXgwSxz0p/DBu6nyZJ5jpTVG8bOnKWb7pypHW+yOUvSvs7cLEdWcTX2JxlHq2F48TJL0q5VKfLBhx/Uaj6QHJMseqVFI08rwbMSosUff2E5x8m4rrQ18ZIzm4dQWolmXhR48MyntqmjkCX3IiflwCfdVERzn4+VA+/bL0pTpoXp6MGt5xKtZDm6cftmWlRbra17aBFXuevcnQ6qq6P2f7iFymbN5PrfEWrs1Zsq/nQf1Z56etyOQ5bci2muW4Ys5ToC7uwfsuQOV1Va9ZssmbnKnCVZZOiTeYieXDDKIkPyrLIm8eaBGKvMWVVRs5NZMg+vMmYm7FbD0y+89WOWIVfGanDGe0+lWw1PLzqRTJasSoebhxoKK6OAGRlYVYRLJEupVsMTRuYiCzo36Zcs8W5Km4xjqrKUqEqg8fxNtJ7xd/Gq4UlbxmF78c5b8z3KzDeh9X3pcD2AcjO2RIudUpi5+GCHLLlD/bk5XA7890W0vZyI7xNLYy9voGuur29VvVuG2d1XsY0e37mD6rkrXUMFdBNnks4sa09tXvg7dbjlBgpu2kgUClHlJZfTrhsnUbRNm4Sdhiy5E1MVWoUsqRAF5/sAWXKeqUot+kWWVGKar30R+Rx2ypBW9/TMVx4qHbdV9Ty7/cubm9LaBaLaepAlZyMiQ+2uHr+7HPhBA/nmsn+uowMObFkOXP43u7KC7uR5SVLIQXJPY9p1pGtZlDquWUOdxl1MRf9epHWu/pBDtSF3DQcNtNVZyJItTJ5cCbLkybAl7TRkKSkiT68AWfJ0+JTqvJ7tMFcgVKqTedqZdGVJv4eUnZL56aBVqhpevLKEmUw0SwdKqttAllIlZr0+j5CjR6cX0L13FVINj6Qr5eTP/3Em6ZLLGqSid4vlk3AdlwLfRMv5WZajikvpT1zl7gfRALWbei+1e+AenpRUR9H2HWjnzZO1Ag6p3CsJsuRMTFVsBbKkYlQy7xNkKXOGKrcAWVI5OugbCPibgCdkyap0pEphgSxlHg0pBz7xymKSZ1mOGRKh+3lu0p57tb657J1cCnzaTh6bx0u3piF3v+Ehd5JF6jThUgqtWqn9ruZXv9HmJkW67pFyByFLKSPzzAaQJc+EKqWOQpZSwuW5lSFLngsZOgwCviHgCVlKNmEv19GALKUfASkHfu+dhfSXGbFy4B07cUGH28L027NalwNfHq6lK7dtohX1YW2HY+TGsp26Uvtt26jDzddT6fOztdcb+/Sl7VOnU/gnP0u7Y5CltNEpvyFkSfkQpdVByFJa2DyzEWTJM6FCR0HAdwRyLktWN6G1omxVgUSVaECW0ovE+4uC2twkvRz4GcMb6Xa+b1LnLi3bk7p303he0hQu4iAFHHpxNmlq1x70Y77BbJsnH6MOt/2eAhU7iIqKaBffVHbXNTdQqyoQKXYRspQiMA+tDlnyULBS6CpkKQVYHlwVsuTBoKHLIOATAjmXJSPHeHOWVGcNWUotQjvYa6Qc+PNc7U6Wnr2idN/UMA09tnU5cLlX0uVbN9Bn9bG5SaM4m3RrR84mfbOCOo0fS4VLP9JeDx/1I9ohBRz23T+1zsRZG7LkCEYlG4EsKRmWjDsFWcoYodINQJaUDg86BwK+JqCULHmVNGTJfuTkfkm33lxE27aSVrThvAsa6He/r6c2ZS3bkJlKM7kU+J0VW6k2GqUeXPb7gS496KfsU+3uvI3aPvowUUMDRbp0pZ23/pGqzzrXfidsrAlZsgHJo6tAljwauCTdhiz5M676UUGW/B1fHB0IqEwAsuRAdCBLySHKULvrri6ihe/Eytrttz+XA384TIcMap1NWs9lwCWb9GFdrbbuyLbtaXKnPajrgleow43XUGjdWq2yXfXZo6nitj9RtEPH5B1IcQ3IUorAPLQ6ZMlDwUqhq5ClFGB5cFXIkgeDhi6DgE8IKCVL5rsAmxnjprTePOuWLQ3SqDOLqaIi1v9rrqunq69rsDyYv/F9kyZv30pyo1k9m/SzbeXUceIVVPz2G9o2MtROhtzJ0Du3FsiSW2Rz3y5kKfcxcKMHkCU3qKrTJmRJnVigJyCQbwSUkiW5++5pJw6mwYcfRDfdOZMWzp2qxUP1uy0jsxT/bbPovSCdf04xVVcR/ejHEbrrvjDtu1/rcuBbOJs0nivdvVfLN1ji5bdcCvwPHTpTj+nTqN09d1CgupqipaW06+rrqXL81UQFBa6+VyFLruLNaeOQpZzid23nkCXX0CrRMGRJiTCgEyCQlwSUkiW9wEOf3t3o3PF3NMuSVMwzypNqkYIsWUfkzdeCdNGYYuIaDXTmyEaawvdN4tFzrZYXq3bR77ZvoR2RRtqDK93d37kb/fyrr7QCDgUrvtLWr+My4Du4HLiUBc/GAlnKBuXc7AOylBvubu8VsuQ24dy2D1nKLX/sHQTymYCSsjTkqIEk4qQPu8NNab13ir44N0TjLi2iCE9JOv+iBrr9Tin63XLZznJ0NWeTXq/htBMvcmPZ24MFtNdtt1Cbp2cRcWGHSPceVPHHe6hm2K+zCgGylFXcWd0ZZCmruLO2M8hS1lDnZEeQpZxgx05BAASYgFKyJMPtjhg0gK69bKQ29E7/GTel9da5+syTIbr+miJxHbqRK92Nm9B6fpIMt7ti20baxnei1bNJp734D2p/600U3LpFK5VXdcEltPPm2yjatm3WAUCWso48azuELGUNdVZ3BFnKKu6s7wyylHXk2CEIgEATAaVkyRwVyS7py4Jn7qI+vbsrGTgMw9sdlgfuLaB77izUhtvJsDsZfmdeJvGQu5m7+GZLvAxv047uKt9Ofa66goqW/Ed7reGggbSdCzjUH3JozuINWcoZetd3DFlyHXFOdgBZygn2rO0UspQ11NgRCICAiYDSsuSVaEGWYpG6+YZCenxmgVZ7YfrMMP3itJaitIGLOFyyZQMtDddSWSBI09p2pN9Mf4jaPTSF7yob5gxSO9p54y1UdfFlsZsw5XCBLOUQvsu7hiy5DDhHzUOWcgQ+S7uFLGUJNHYDAiDQioBSsqQXeJA5S15a8l2WZF7S1VcW0XOzQ1RcTPT403U09NiW90+SYXeXbt2oFXHYr7CI5q34hgZcPZ5Cq7/XQl172hm0464p2hwlFRbIkgpRcKcPkCV3uOa6VchSriPg7v4hS+7yResgAALxCUCWHDg78lmWpNLdRecV0Zuvh0imFj09p46OPHq3KMlPUyrK6YGKbSQ/n19VSw/ecxe1nT9XI9/Ye0/aMeXPVHfciQ5EwrkmIEvOsVStJciSahFxpj+QJWc4qtoKZEnVyKBfIOB/AkrJkur3U4p3OuSrLNXUEJ13VjG9vyhInToTPTevlg44cPc9lKTa3cVbN9Di2hoq5WoPL730Mh13390U2LVTu09S5WVX0s7rbyYqKVHunQZZUi4kjnUIsuQYSqUagiwpFQ7HOwNZchwpGgQBELBJQClZWr1uU4v7K9k8hpyvlo+yVFlJNHJ4MS1bGqTu3aP0wkt11H/v3aK0jOclXbxlPW3ganeHVVTQO9dcTe2XfqTFKnzUj2jH/Q9Rww8OzHns4nUAsqRsaDLuGGQpY4RKNgBZUjIsjnUKsuQYSjQEAiCQIgGlZMlY/c7qOPT7LqV4jK6vnm+ytL2cbzI7rIS++jKgCdLf/1FHvXrvFqVHd+6gO3ZsIbmz0vlr19Ojl11MBevWUrRjJ6q45Q9UPfoC12OS6Q4gS5kSVHd7yJK6scmkZ5ClTOipvy1kSf0YoYcg4FcCysnSI3dfQ+YCD8/Oe4tmPDmfFs6dqmQc8kmWNm0k+vXpJbRqZUAbcidD72QIniyV0QiN5yIOcpNZLohHj3y1gs6/5AIKVFVSpGcv2vr8S9Qw4AAlY2juFGTJE2FKq5OQpbSwKb8RZEn5EGXUQchSRviwMQiAQAYEPCFLi5Z8TmOvu4+QWcog0g5sKoL0218V0/p1ATr0sAjNnlunFXWQ5av6OrqAy4KvbqinbqECev21N+iQG6/hCg6N2v2Stj07lyLd1LxPlhUayJIDJ4yiTUCWFA1Mht2CLGUIUPHNIUuKBwjdAwEfE/CELN0zfTa9/MZiZJZyeCLKkDsZeidD8I4ZEqEnnq2j0tJYh2ZXVtBNfKPZWi7icERRMf3z4Ydpj4cf1H5Xe9IpVP7YM0oWcUiEE7KUw5PN5V1DllwGnKPmIUs5Ap+l3UKWsgQauwEBEGhFIOeypGeNksXGanhesm2y9Xu/D8OTIg5SzEGKOsiNZh/+S5gKC2N0r962ieZUcXU7Xq4sLqW7Jk6gktcXaP+vHDeRdk66nSgQyFYoHNsPZMkxlMo1BFlSLiSOdAiy5AhGZRuBLCkbGnQMBHxPIOeyZCSMm9Kqd75JWfDRXB6cq3/TmSMbacq0sOY+FVwW/AIuC/4f/kWHYJAeCRTS8NFnUeGny4hCIdr+4AyqGTFKvQOy2SPIkk1QHlwNsuTBoNnoMmTJBiQPrwJZ8nDw0HUQ8DgBpWTJqyz9mll687UgXTSmmOTGs+df1EC33yn17Yi+53lJ52xeRyv5uSeL0bwdlXT4qDMptHYNRdt3oG1PzqbwkKFeDafWb8iSp8OXsPOQJX/GFrLkz7jqRwVZ8nd8cXQgoDIByJID0fGjLL04N0TjLi2iSIToxt/X07gJDRqppXz/pHM3r6cdnFn6YWExzf36W9p79Eit4l3jnnvRtudfpoZ993OAam6bgCzllr+be4csuUk3d21DlnLHPht7hixlgzL2AQIgYEVAOVkaOnwCbS2vsIwWquFl5yR+fGYB/f7G2KQkGXYnw+9kebFqF11VvonCXMjhhJI29Mzb71K3CZfGKt4dfiRt+9sLFOnSNTuddHkvkCWXAeewechSDuG7uGvIkotwFWgasqRAENAFEMhTAkrJ0oixk6lXjy40ZfI4T4XDT5mle+8qpCn3FFAB3yhp+sywVtBBlvsrttF9FVwKj5dL2nWg+x54gNr++QHt/7WnnUHljz5BVFTkqbgl6ixkyTehbHUgkCV/xhay5M+46kcFWfJ3fHF0IKAyAaVkCQUecneqcLKIrr+miJ55MkTFxUSPP11HQ4+NUD3/YgJnkySrFOTu3VPWni4ff3lzxbtd19xAu268JXcdd2nPkCWXwCrQLGRJgSC40AXIkgtQFWoSsqRQMNAVEMgzApAlBwLu9cySzEuS+UkyT0luMvv0nDo68uiINi/pfL7R7JK6GioLBOmJYCGdrle849rh2/88k2qGn+kAQfWagCypFxOnegRZcoqkWu1AltSKh9O9gSw5TRTtgQAI2CWglCzJMLxhpwyhs4Ydb7f/SqznZVmSSncXnVdEb74eok6diZ6bV0sHHBjVKt6dxRXv5LlVxbuOnWjb089R+Ec/VoK/G52ALLlBVY02IUtqxMHpXkCWnCaqVnuQJbXigd6AQD4RUEqW5Aa1N905kxbOnZqTGIisHTFoAF172cjm/ce7aa6x2IRXZamG7510Ht9DSe6l1L17lF54qY767x3VMkmSUZLM0oFc8W6+seJdv/60lSveNfKznxfIkn+jC1nyZ2whS/6Mq35UkCV/xxdHBwIqE1BKlmTOUqLFrWp4Eyc9RK8v/Ejb9ZgRJ1vKUqJ9e1GWKrjg4Kgzi2nZ0qAmSH//Rx316h3V5iZN2LaR5I5KsYp373DFu8u0ineSSZKMUpQzS35fIEv+jTBkyZ+xhSz5M66QJX/HFUcHAl4goJQs5RqYlC0/7cTBvpelrVuIfn16CX37TUAbcidD72QI3r1c7W4KV72T5eK2Hej+qbsr3sncJJmjRDxXKR8WyJJ/owxZ8mdsIUv+jCtkyd9xxdGBgBcIQJYMUUokS8ZgmrNMXsosrV8XoOG/LKY1qwN06GERmj23TivqMGHbJnq+aqd2mHdzxbvxesW7QIB23fB7kqp3+bRAlvwbbciSP2MLWfJnXCFL/o4rjg4EvEAAspRElsxBlHlNssx5ZFLzr3ZUhr0Qa1r5P6JTTy6ijRuJfvLTKM15vp5KS7nAw8b19MKunVTCYjSnqIROPWckhZYt1e6bVPX4U1R/+jBPHJ+TnWxbWkg14QYefcg11bH4ikDHtkXklfesr8C7fDChYIBKiwuoskYGEWPxGwF532IBARAAgVwQUE6WREaWr1ilsXjk7mtoyFEDSeYynTT0CNdvVmuVWTIHRS/4YMwuVdfFbtyq8rJ8OdEvfh6ibTzK7oxhUXriKa4XXhCl365ZTa9XVlIpi9KbXPFh8MgzKbB6NVHXrlQ790WKHHW0yoflWt9KCoNUz6LUGIEsuQY5Rw23KQ6RF96zOcLj2d2KLBUWBKg2zJ9tWHxHQN63WEAABEAgFwSUkiURpV49umhSJOLyxxsu0mTp2Xlv0Ywn57teJS9dWVJ9GN6HHwTpnBHFxE5EZ45spCnTwhSmKI3esp4W1VZTm2CQ3vh6JQ0+fxQFqiqpYZ/9aNsLXPFuz71ycU4qsU8Mw1MiDK50AsPwXMGa80YxDC/nIXC1A6iG5ypeNA4CIJCAgFKyJBmkBc/cRX16d28hS1bZHDeiaiVLUilv4iVnan2SRdY5bOB+LbJcKsvSwneCdP45xVRXR3T+RQ10+531VM13oT2HRekDLhHegUXpX+++Rz+8Znys4t2QobTtydkUbd/BDcSeaROy5JlQpdxRyFLKyDyxAWTJE2FKu5OQpbTRYUMQAIEMCSglSyIiT037XStZcjuzZCwdrvPUh9ndM302zZrzajPmgwf0bzFfSX6hqiz98+UQXXZRETU0EN34+3oaN6GBdkUj9NuNa+mz+jrqFAjSp48+SntNn6YdX/WIUbTjwRlEIQx3gCxl+Mmi8OaQJYWDk0HXIEsZwPPAppAlDwQJXQQBnxJQSpZETF5+Y7E23E4fhtendzc6ZdT1re5/pFI8VJSl52aHaOL42IRYGXYnw+8q+Cazv9m0jr5kUerd0Eif3fQ76vwGiyDPV9o56XaqHDdRJaw57QtkKaf4Xd05ZMlVvDlrHLKUM/RZ2TFkKSuYsRMQAAELAkrJkvRPH3Jn7OvNV51LZw07XtkAqiZLj88soJtvKKSCAqLpM8P0i9MaaTuL0vBNa+nr+jAduHMnLZkwnso+/YSopITK//o01f78F8ryzUXHIEu5oJ6dfUKWssM523uBLGWbeHb3B1nKLm/sDQRAYDcB5WTJi8FRSZZm/bWAbrq+kEq4JPhfn6ijnx0XoY08F+k3m9fQqvp6+tl339NrV15BRWvXUKRbd9r2txeoftBhXsTuap8hS67izWnjkKWc4ndt55Al19Aq0TBkSYkwoBMgkJcElJIlfe6Q+aav2Sodnu4ZoIosLf8sQD8/rkQ7jL89V0dDj43QOp6w9KtNa2hdYwONWLqU/sYZpaBUvBtwAG19/iWK9OyV7mH7ejvIkn/DC1nyZ2whS/6Mq35UkCV/xxdHBwIqE1BKlmSe0qWjT2815M7tAg+ZBkgFWaqpJjp2SAmtWR2gCy9poNvuqKfVDfWaKElm6boFC+iuW27SKt7VHXcilT/2DEXbts300H27PWTJt6ElyJI/YwtZ8mdcIUv+jiuODgS8QEApWZIMkn4jWiO8bJUOTzdgKsjS5ZcU0YtzQ3TQwCi9/FotrQ+wKG1eS1tYmB6b9iCNmfWYdnjVoy+gHfc+SMQlw7HEJwBZ8u/ZAVnyZ2whS/6MK2TJ33HF0YGAFwgoJUvILKV3ykjlu6vGFVFpG6J3FtVSUa96OoPnKG2pqqJXb7iOhi58V5OjitvvpqpLLk9vJ3m2FWTJvwGHLPkztpAlf8YVsuTvuOLoQMALBJSSJRlud/sDTzXfmFYArl63SSsdrnJFvFxmllb+L0AnHVtCMgzv4UfD9NNhYTp94xrauWUzvT0xrKeuAAAcN0lEQVT+Chr45RcUbdOGymc9qw2/w2KPAGTJHicvrgVZ8mLUkvcZspSckZfXwJwlL0cPfQcBbxNQSpYEpVXpcKuheSphz5UshcNEJ3NBhxX/DWj3Ubp9Wi3PUVpL9N8v6XUWpd4bNmgFHLbO/gc1HDRQJWTK9wWypHyI0u4gZCltdEpvCFlSOjwZdw6ylDFCNAACIJAmAeVkKc3jyOlmuZIlKREupcL77xOlV96uodGVa6ngwyX01mWXUJuaGqr/4SDaxqIkJcKxpEYAspQaLy+tDVnyUrTs9xWyZJ+VF9eELHkxaugzCPiDAGTJgTjmQpbeeiNIo88qpqIiYlGqpbs6r6WV335NH517NnWqqKDak0+l7Y/MomhZmQNHmH9NQJb8G3PIkj9jC1nyZ1z1o4Is+Tu+ODoQUJmAcrIkRR62lldYMjPff0kVsNmWpfXrA3TCT0qInYj+cGc9fTxsLS3cuI4+HH0O7bP6e6r59QgWpcdVwePJfkCWPBk2W52GLNnC5LmVIEueC1lKHYYspYQLK4MACDhIQClZGjF2MvXq0YWmTB7n4CG631Q2ZSkSITr95GJatjRIx58YoV5/XkOzt2+l9y6+kI7+7FMKH3k0bZ3/OlFhofsH7uM9QJb8G1zIkj9jC1nyZ1yRWfJ3XHF0IOAFAkrJUrz7LKkOMpuydNcdhfTg/QXUs1eUznhjHc2oK6dnb7qRRi74JzXssy9teW0hRTt2Uh2Z8v2DLCkforQ7CFlKG53SG0KWlA5Pxp1DZiljhGgABEAgTQKQpTTBGTfLliwt+U+Qhv+ymAIBogsXbqS/lG2mW2Y+SpMf/rMmSJvf/jc19unrwBGhCciSf88ByJI/YwtZ8mdckVnyd1xxdCDgBQJKyZIMwxt2yhA6a9jxXmDX3MdsyFL5NqLjf1pKmzcRnfLoVlpwxHo686036e/XXqMNuZOhdzIED4szBCBLznBUsRXIkopRybxPkKXMGarcAjJLKkcHfQMBfxNQSpbkHks33TmTFs6d6inq2ZClEcOLadG/grTvpdtp5SVrtPlJ7429mEJ1dVoxBynqgMU5ApAl51iq1hJkSbWIONMfyJIzHFVtBbKkamTQLxDwPwGlZEnmLCVa8rUa3vSHCuj2Wwup3XFVtOve/1G/9evoq1FnU0nFDtr1fzfSrht+7/8zNctHCFnKMvAs7g6ylEXYWdwVZCmLsHOwK8hSDqBjlyAAAhoBpWTJqzFxM7P0xecB+sWJJdSwVx2VPvcNFVbvpJVcIrzLd6uo9pfDqPzxv3kVm9L9hiwpHZ6MOgdZygifshtDlpQNjSMdgyw5ghGNgAAIpEFAOVmSoXhjr7uvxaE8cvc1NOSogWkcXnY2cUuWKiuJTvhpCa2paqSyeV9TuKiGPhl/BR245AOqH3QYbXnlLaLi4uwcZJ7tBbLk34BDlvwZW8iSP+OqHxVkyd/xxdGBgMoElJKlZ+e9Rbc/8BQteOYu6tO7u8Zt9bpNdMqo6+nmq85VtvCDW7J00XlFtOCtIJXM+YZq96ql1265mU56+SWt4t2WN96jSJeuKp9bnu4bZMnT4UvYeciSP2MLWfJnXCFL/o4rjg4EvEBAKVkaOnwCXTr69FZSJBI148n5yhZ+cEOWnn4iRNdfW0ShaauocfAuuveJWXTN1CkUbdeeNr+5iBr5nkpY3CMAWXKPba5bhizlOgLu7B+y5A5XVVpFZkmVSKAfIJB/BJSSpXg3pdWH5uVLgYcV/+V5SieUUO01a4l+XU7nv/M2PfZ/VxMFg7R17j8pfMxP8u9MzfIRQ5ayDDyLu4MsZRF2FncFWcoi7BzsCrKUA+jYJQiAgEZAKVlCZomotpbnKQ0toVWDtxJdvYF+/OWX9N6FYyjIJcJ3PDiDqs8ejVM3CwQgS1mAnKNdQJZyBN7l3UKWXAac4+YhSzkOAHYPAnlMQClZwpwlouuuLqJn1nBlh3u/p/4buET46HOpmO9IW3nFVbRz8h15fKpm99AhS9nlnc29QZaySTt7+4IsZY91LvYEWcoFdewTBEBAucySdCifq+EteCVEF93ZSDTrW2pft4u+O+9c6rRqJdWedAqVP/M85wEDOGuzRACylCXQOdgNZCkH0LOwS8hSFiDncBeQpRzCx65BIM8JKJVZ8mosnCjwsGZ1gI47M0TVj35NofZh+vKKy2n/Jf+hhoMG0uZX3yUqLfUqHk/2G7LkybDZ6jRkyRYmz60EWfJcyFLqMGQpJVxYGQRAwEECSsnSxEkP0esLPyJzIQcp/HDS0CNoyuRxDh66c01lKksNDUQ/H1ZI/73xW6K9wvTqH26jn//jBWrs1TtWIrx7D+c6i5ZsEYAs2cLkyZUgS54MW9JOQ5aSIvL0CpAlT4cPnQcBTxNQSpbytcDDHyYV0oxDvyc6rIruf+JJmjj1PoqWlWmi1LD/Dzx9gnm185Alr0Yueb8hS8kZeXENyJIXo2a/z5Al+6ywJgiAgLMElJKlfCwdvuhfQRqxsJzovC109sJF9MzVnD3juUnb/v4i1f3seGejjdZsE4As2UbluRUhS54Lma0OQ5ZsYfLsSpAlz4YOHQcBzxNQSpbyLbO0eRPRT66rp8o/fEdHLv+CFl9yIYVqa6jiT/dR1cWXef7k8vIBQJa8HL3EfYcs+TO2kCV/xlU/KsiSv+OLowMBlQkoJUv5VDo8GiU69bwgffq7b2jPXRtoxaiR1Ka8nKrOv5gq7pmq8jmTF32DLPk3zJAlf8YWsuTPuEKW/B1XHB0IeIGAUrIkwPKldPh9D4To/oO/o/a9ttJnY86jviu/1YbdyfA7Cga9cO74uo+QJf+GF7Lkz9hClvwZV8iSv+OKowMBLxBQTpa8AM3cx1Sr4S1bGqTTPthEoZO30Xtjx9LgpR9qhRykoIMUdsCSewKQpdzHwK0eQJbcIpvbdiFLueXv9t4xDM9twmgfBEAgHgHIkgPnRiqyVFFBNPi2aqqYsI4enzSJxrw0jyJdutLmdxZThEuFY1GDAGRJjTi40QvIkhtUc98mZCn3MXCzB5AlN+mibRAAgUQEIEsOnB+pyNKvJkZpyRX/o/+bPYvueeB+ivLNZre+9AbVDzrMgZ6gCacIQJacIqleO5Al9WLiRI8gS05QVLcNyJK6sUHPQMDvBCBLDkTYrizNeDxIfzhwJZ32zZs0f+IECvC+y59+jmp//gsHeoEmnCQAWXKSplptQZbUiodTvYEsOUVSzXYgS2rGBb0CgXwgAFlyIMp2ZGnFfwN0/Mcb6fAui+m9Cy+gkrpa2jnpdqocf7UDPUATThOALDlNVJ32IEvqxMLJnkCWnKSpXluQJfVigh6BQL4QgCw5EOlkslRTTXTUlF3U5qRPadlZI6jrju1UffZo2vHgDAf2jibcIABZcoOqGm1CltSIg9O9gCw5TVSt9iBLasUDvQGBfCIAWXIg2slk6dw7GuiDM76kD8ecTQesWknhY35CW+f+kygUcmDvaMINApAlN6iq0SZkSY04ON0LyJLTRNVqD7KkVjzQGxDIJwKQJQeinUiWnplPdGOvb2nBrWPpxP8spoZ99qUtby6iaLv2DuwZTbhFALLkFtnctwtZyn0M3OgBZMkNquq0CVlSJxboCQjkGwHIkgMRjydL368O0JCl62jm/P+j8+dzifCOnWjL2/+mxj59HdgrmnCTAGTJTbq5bRuylFv+bu0dsuQWWTXahSypEQf0AgTykQBkyYGoW8lSOEx05F8qaHTFvXTf/fdRtLiYts17lcJHHu3AHtGE2wQgS24Tzl37kKXcsXdzz5AlN+nmvm3IUu5jgB6AQL4SgCw5EHkrWbpgeh0VtnuKXrz6KgpGIlT++N+o9pfDHNgbmsgGAchSNijnZh+Qpdxwd3uvkCW3Cee2fchSbvlj7yCQzwQgSw5E3yxLc95ppFm7Xqf/XD6KSmtradd1N2kPLN4hAFnyTqxS7SlkKVVi3lgfsuSNOKXbS8hSuuSwHQiAQKYEIEuZEuTtjbK0bmOUfv3eR7Tk97+mHlu3atkkySph8RYByJK34pVKbyFLqdDyzrqQJe/EKp2eQpbSoYZtQAAEnCAAWXKAoi5LPNqOhsxaTQum/0IrEV7D85O28zwl4vlKWLxFALLkrXil0lvIUiq0vLMuZMk7sUqnp5CldKhhGxAAAScIQJYcoKjL0tinqujKOadrJcKr9+xDFe8upihXwMPiPQKQJe/FzG6PIUt2SXlrPciSt+KVam8hS6kSw/ogAAJOEYAsOUBSZOmFjxqo4JGL6LJ//J1qy9pRxdvvUyPfUwmLNwlAlrwZNzu9hizZoeS9dSBL3otZKj2GLKVCC+uCAAg4SQCyZKA5YuxkOmLQALr2spEtGE+c9BC9vvAj7bWDB/SnOY9MavH7JSuq6Nn7/khT/vInqi8opIoXXqbwMT9xMk5oK8sEIEtZBp7F3UGWsgg7i7uCLGURdg52BVnKAXTsEgRAQCMAWWIIRhkaM+LkFrL07Ly3aMaT82nh3KkaMCuhOuvqv9IzUy/RSoRvnv4YNZzZUrZwrnmPAGTJezGz22PIkl1S3loPsuSteKXaW8hSqsSwPgiAgFMEIEsGkkOHT6DTThzcQpbMcmSWpwn3LKQ7bzlZKxH+zf+3d3+hclR3HMCP/ypaREgjCYYKPhQpKv2DCKWBCIIYWiTYhyg2EuhDlFqMSBSqEFJEjCIqFTTgQ1BE0wexIkQUqSkBwdpSGlOQPgji/38ggq1otDnbnmUzmbu7Z+7ZvbMzn327d8+cOefz2z/z3TM7+6vt4du77yxVG/2soICwtIL4M961sDRj4BXqXlhaIfg57VZYmhO03RAgcJyAsDQhLMUAdd21V4SrN106aHnwlUNh2y33hsMv7R38/faaNWHdBx+Ef/z052H1H//gIdYRAWGpI4WsmYaw1M3aCkvdrGualbDU7fqaHYE2CwhLE8LS+ZdsDbdv33JcWNr/+O5wzro1R09kPCH889wfhO/+5c8hnHZam2ttbBkCp596cvjiqyPhyJFvMrbSdBEEzjj9lPDZ518uwlCNMUPgpBNPCKd+66Tw+X++ythK00URiM9bNwIECKyEgLA0ISxNWll64de7w092/DJ8c3SFya07AqefelL44suvw5GvhaXuVPV/MznjtJPDZ/92QN21ug7C0iknhs+/ONK1qZnP/5+3IAgQILASAsLShLA06TtLcfP0O0srUUD7nI2A0/Bm49qGXp2G14YqlB+D0/DKm7apR6fhtakaxkKgXwLC0oSwNM3V8ISl7j1phKXu1TTNSFjqZm2FpW7WdfR52+0Zmh0BAm0VEJaOVmb00uGpUOkCDvHvSb+zJCy19eHdfFzCUnO7tm8pLLW9Qs3GJyw1c1uUrawsLUqljJNA9wSEpQI1FZYKILasC2GpZQUpOBxhqSBmi7oSllpUjBkMRViaAaouCRCYSkBYmoppfCNhqQBiy7oQllpWkILDEZYKYraoK2GpRcWYwVCEpRmg6pIAgakEhKWpmISlAkwL1YWwtFDlyhqssJTFtTCNhaWFKVWjgQpLjdhsRIBAAQFhqQCilaUCiC3rQlhqWUEKDkdYKojZoq6EpRYVYwZDEZZmgKpLAgSmEhCWpmKyslSAaaG6EJYWqlxZgxWWsrgWprGwtDClajRQYakRm40IECggICwVQNQFAQIECBAgQIAAAQLdExCWuldTMyJAgAABAgQIECBAoICAsFQAURcECBAgQIAAAQIECHRPQFjqXk3NiAABAgQIECBAgACBAgLCUkPEm3Y+GJ4/8Opg6wvOOzfs27OzYU82WymBDVfeGD765NPB7rduvjzsuP6qJYcyWu9p2q/UnOw3hDfffj9svObWIcWeu28O6y++cCqa+JhYe9Yqz+eptObf6ImnXwx33P/YcMeHX9o7cRCjz93LNlwU7tt1w8RtNJi/QO576uZtu8Jrr7+R9ViY/6zskQCBLggISw2qGN+wH370mXDgqQcGW8cX7Yt+eN7Yg+0Gu7HJDAXiG3O8pQOn8y/ZGsYdVMcap0CcDsZzDsJnOBVdVwRi4Lnu2ivC1ZsuDQdfORS23XJvmOagOm4Xb8JSOx9S6Xm3//Hd4Zx1a8I9Dz0ZXv3762ODbXzexpsPs9pZ0zSq3PfU+Pr9znsfD+ta/bvdszU6AgQWTUBYalCxajiqvtA36NImcxaohqNqeJo0nNED8klt3T8/gbpwNE2t4nN608b14a13P5x4AD6/2djTqEA1HFXDU1UrPhZuu+uR4YdaNNsrkPuemtu+vTM3MgIEFkFAWGpQperBV86n1w12Z5PCAnUHWdN8Sj06jEkrUYWHrLspBeo+uJi08jt6f+7jYMphaVZAoO4DjXHPw1jLZ194eXiqbRzC7du3DFYc3dolkPuemt5z02mV6cMOtW1XXY2GQFcEhKUGlYxv0KNvuumFO50e0qBLm8xRoK5e6cAqnVo5bjhO+ZhjsTJ3VVfHeCB19trv1H5XpXoALixlgs+xeV0dq6/Fo8OpPk/T897ps3Ms2pS7avKeGrdZverMYRie5lTbKYejGQECBI4REJYaPCByPwVrsAubzFBgOStL8QDsb4f+5dSeGdZnOV3nriyNXuRjdL/xIGya4Lycsdo2TyB3Zamu/TSnZOaNSusSArnvqdWVpPghx959z0313cQS49UHAQL9EhCWGtTb+dIN0Fq2SZPvLAlKLStizXCafmcpdWVlqb01zv3OUl0thaV21jf3PbX6+u3sjnbW1agIdEVAWGpQydwr9zTYhU1mLDDpanjxzXj0cuKuqjXjghTsftzV8CadiiUsFSxE4a4mXQ2vurpQvWpluuy407UKF6ZAd5PeU6uvv9W/fZBVoAi6IEBgSQFhqeGDI/c3IRruxmYzFBj3O0ujYan6uz1pSE7VmmFxltH1uN9ZEpaWAduCTcf9zlLdqVip3mnovlfagiIuMYRx76l1H1aNvn57LW5vXY2MQBcEhKUuVNEcCBAgQIAAAQIECBAoLiAsFSfVIQECBAgQIECAAAECXRAQlrpQRXMgQIAAAQIECBAgQKC4gLBUnFSHBAgQIECAAAECBAh0QUBY6kIVzYEAAQIECBAgQIAAgeICwlJxUh0SIECAAAECBAgQINAFAWGpC1U0BwIECBAgQIAAAQIEigsIS8VJdUiAAAECBAgQIECAQBcEhKUuVNEcCBAgQIAAAQIECBAoLiAsFSfVIQECBAgQIECAAAECXRAQlrpQRXMgQIAAAQIECBAgQKC4gLBUnFSHBAgQIECAAAECBAh0QUBY6kIVzYEAAQIECBAgQIAAgeICwlJxUh0SIECAAAECBAgQINAFAWGpC1U0BwIECBAgQIAAAQIEigsIS8VJdUiAAAECBAgQIECAQBcEhKUuVNEcCBAgQIAAAQIECBAoLiAsFSfVIQECBAgQIECAAAECXRAQlrpQRXMgsAIC9zz0ZNi777nj9nz4pb3hiadfDHfc/1i4ffuWcPWmS49pc9POB8PzB14N+x/fHc5ZtyaM6+fgK4fCtlvuHTu7uI94i/uru6UxpDFdcN65Yd+encc0TWOouy81PP+SrWPHcdmGiwb3x7ml29bNl4cd118V3nz7/bDxmlsH/44+o7fROab70ljHzWcFSm6XBAgQIECgdwLCUu9KbsIEli+QAk/1wD/+/+IffX8QkFIAGW2TgsGeu28O6y++MEzTz+hoY/t33vv4uLCTwkV1PKPbjgaQFNTS/RuuvDF89MmnYVxYquurbn9pjqP7GA1L1QCZDEaD1DTzWX4V9UCAAAECBAhMEhCWJgm5nwCB4wTiKktaNRnHE0PIjy/8Xrhv1w2DZtW/p+0n7WO5YenhR58ZjCfe0phiMIn/X3vWqsH/q6tOdfMbF2bGhaVo9uwLL4cDTz0w6DaFqLgqFVekqitL48KfhyUBAgQIECAwewFhafbG9kCgcwLV0LPUBEdXkl7+6+FjgkJdeJoEVSIsPfb73w5OiUsrP5u37QqbNq4PT+8/OPOwFPe55Td3huuuvWK4+vbOex+Fs9euHpzSKCxNegS4nwABAgQIzFdAWJqvt70R6IRA3XdqlloFGT3NLJ1+lxBy+onbTApLdbij31mKK0hxVScGpLPXfif84mcbwm13PTL8X9x+litLMSzte+ZPw9AYV9bS/+rC0rj5dOKBZBIECBAgQKDlAsJSywtkeATaLpC+75PGWQ1E8f8xFMRTzdKpb3VzmqafSWFp0neWUlhKK17xO0pxVSl+xyoGqHmEpXhRi+gR9x0DWzSpfr/Ld5ba/qg3PgIECBDoi4Cw1JdKmyeBOQjEwBO/+1NdnZn2tL00xKX6KRWW4n5iOHrt9TeGp77NMyylcJSCpbA0hwenXRAgQIAAgQYCwlIDNJsQ6LNAvChBPJUsXhK7elsqcNSFpSb9lAxLcfXmrXc/HM5jnmEpzn3H7x4ehkphqc/PKHMnQIAAgTYLCEttro6xEWihQLqC2+pVZw6v6haHmU4dqzsNb6mwFC+0kNNPybA0bdCrK0HTq+FVL1me+haWWvhANyQCBAgQIHBUQFjyMCBAoJFA3Y+0LhUGxp2Gl9PPpLBUN5G6CzzUtSuxsjR6MYu4j+qP0uaGpXHzaVQ0GxEgQIAAAQJZAsJSFpfGBAgQIECAAAECBAj0RUBY6kulzZMAAQIECBAgQIAAgSwBYSmLS2MCBAgQIECAAAECBPoiICz1pdLmSYAAAQIECBAgQIBAloCwlMWlMQECBAgQIECAAAECfREQlvpSafMkQIAAAQIECBAgQCBLQFjK4tKYAAECBAgQIECAAIG+CAhLfam0eRIgQIAAAQIECBAgkCUgLGVxaUyAAAECBAgQIECAQF8EhKW+VNo8CRAgQIAAAQIECBDIEhCWsrg0JkCAAAECBAgQIECgLwLCUl8qbZ4ECBAgQIAAAQIECGQJCEtZXBoTIECAAAECBAgQINAXAWGpL5U2TwIECBAgQIAAAQIEsgSEpSwujQkQIECAAAECBAgQ6IuAsNSXSpsnAQIECBAgQIAAAQJZAsJSFpfGBAgQIECAAAECBAj0RUBY6kulzZMAAQIECBAgQIAAgSwBYSmLS2MCBAgQIECAAAECBPoiICz1pdLmSYAAAQIECBAgQIBAloCwlMWlMQECBAgQIECAAAECfREQlvpSafMkQIAAAQIECBAgQCBLQFjK4tKYAAECBAgQIECAAIG+CAhLfam0eRIgQIAAAQIECBAgkCUgLGVxaUyAAAECBAgQIECAQF8EhKW+VNo8CRAgQIAAAQIECBDIEhCWsrg0JkCAAAECBAgQIECgLwLCUl8qbZ4ECBAgQIAAAQIECGQJCEtZXBoTIECAAAECBAgQINAXAWGpL5U2TwIECBAgQIAAAQIEsgSEpSwujQkQIECAAAECBAgQ6IuAsNSXSpsnAQIECBAgQIAAAQJZAsJSFpfGBAgQIECAAAECBAj0RUBY6kulzZMAAQIECBAgQIAAgSwBYSmLS2MCBAgQIECAAAECBPoiICz1pdLmSYAAAQIECBAgQIBAloCwlMWlMQECBAgQIECAAAECfREQlvpSafMkQIAAAQIECBAgQCBLQFjK4tKYAAECBAgQIECAAIG+CPwXhJ0JWyobc4QAAAAASUVORK5CYII=",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"PlotlyHelper.combine_plots(fig_list=[fig_fixed, fig_variable, fig_exact],\n",
" xrange=[0, 0.8], y_label=\"concentration [A]\",\n",
" title=\"Variable time steps vs. Fixed vs. Exact soln, for [A] in reaction `A<->B`\",\n",
" legend_title=\"Simulation run\") \n",
"# All the 3 plots put together: show only the initial part (but it's all there; you can zoom out!)"
]
},
{
"cell_type": "markdown",
"id": "3d37253d-7510-4384-abd6-4bb5cc18ef95",
"metadata": {},
"source": [
"#### Not surprisingly, the adaptive variable time steps outperform the fixed ones (for the same total number of points in the time grid), in the early/middle part of the plot - i.e. at times when there's pronounced change. \n",
"All 3 curves essentially converge as the reaction approaches equilibrium."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d53d0255-2d5d-4d9b-8830-1f94b841f68c",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.9"
}
},
"nbformat": 4,
"nbformat_minor": 5
}